Biomagnetic phenomena

A treatment of the magnetic resonance is given for a particle with spin \textonehalf{} in a constant field ${H}_{0}$ and under the action of an arbitrary alternating field with circular frequency $\ensuremath{\omega}$ perpendicular to ${H}_{0}$. A method of finding a solution, valid at any time, is given which converges the better the smaller the deviations from a rotating field or the larger ${H}_{0}$. It is shown that in the lowest order correction the shape of the resonance curve is unchanged but that it is shifted by a percentage amount $\frac{{{H}_{1}}^{2}}{16 {{H}_{0}}^{2}}$ where ${H}_{1}$ is the effective amplitude of the oscillating field. This also involves a correction in the values of the magnetic moments thus obtained towards smaller values which however in all practical cases is negligibly small.

@article{doi101103physrev57522,
    author = "Bloch, F. and Siegert, A. J. F.",
    title = "Magnetic Resonance for Nonrotating Fields",
    year = "1940",
    journal = "Physical Review",
    abstract = "A treatment of the magnetic resonance is given for a particle with spin \textonehalf{} in a constant field ${H}\_{0}$ and under the action of an arbitrary alternating field with circular frequency $\ensuremath{\omega}$ perpendicular to ${H}\_{0}$. A method of finding a solution, valid at any time, is given which converges the better the smaller the deviations from a rotating field or the larger ${H}\_{0}$. It is shown that in the lowest order correction the shape of the resonance curve is unchanged but that it is shifted by a percentage amount $\frac{{{H}\_{1}}^{2}}{16 {{H}\_{0}}^{2}}$ where ${H}\_{1}$ is the effective amplitude of the oscillating field. This also involves a correction in the values of the magnetic moments thus obtained towards smaller values which however in all practical cases is negligibly small.",
    url = "https://doi.org/10.1103/physrev.57.522",
    doi = "10.1103/physrev.57.522",
    openalex = "W2081961796"
}

If one supposes that a particle with a single magnetic pole can exist and that it interacts with charged particles, the laws of quantum mechanics lead to the requirement that the electric charges shall be quantized---all charges must be integral multiples of a unit charge $e$ connected with the pole strength $g$ by the formula $eg=\frac{1}{2}\ensuremath{\hbar}c$. Since electric charges are known to be quantized and no reason for this has yet been proposed apart from the existence of magnetic poles, we have here a reason for taking magnetic poles seriously. The fact that they have not yet been observed may be ascribed to the large value of the quantum of pole.In 1931 I gave a primitive theory which described the motion of a pole in the field of a charged particle whose motion is given, or the motion of a charged particle in the field of a pole whose motion is given. The present paper sets up a general theory of charged particles and poles in interaction through the medium of the electromagnetic field. The idea which makes this generalization possible consists in supposing each pole to be at the end of an observable string, which is the line along which the electromagnetic potentials are singular, and introducing dynamical coordinates and momenta to describe the motion of the strings. The whole theory then comes out by the application of standard methods. There are unsolved difficulties, concerned with the interaction of a point charge or a point pole with the field it produces itself, such as occur in all dynamical theories of fields and particles in interaction.

@article{doi101103physrev74817,
    author = "Dirac, P. A. M.",
    title = "The Theory of Magnetic Poles",
    year = "1948",
    journal = "Physical Review",
    abstract = "If one supposes that a particle with a single magnetic pole can exist and that it interacts with charged particles, the laws of quantum mechanics lead to the requirement that the electric charges shall be quantized---all charges must be integral multiples of a unit charge $e$ connected with the pole strength $g$ by the formula $eg=\frac{1}{2}\ensuremath{\hbar}c$. Since electric charges are known to be quantized and no reason for this has yet been proposed apart from the existence of magnetic poles, we have here a reason for taking magnetic poles seriously. The fact that they have not yet been observed may be ascribed to the large value of the quantum of pole.In 1931 I gave a primitive theory which described the motion of a pole in the field of a charged particle whose motion is given, or the motion of a charged particle in the field of a pole whose motion is given. The present paper sets up a general theory of charged particles and poles in interaction through the medium of the electromagnetic field. The idea which makes this generalization possible consists in supposing each pole to be at the end of an observable string, which is the line along which the electromagnetic potentials are singular, and introducing dynamical coordinates and momenta to describe the motion of the strings. The whole theory then comes out by the application of standard methods. There are unsolved difficulties, concerned with the interaction of a point charge or a point pole with the field it produces itself, such as occur in all dynamical theories of fields and particles in interaction.",
    url = "https://doi.org/10.1103/physrev.74.817",
    doi = "10.1103/physrev.74.817",
    openalex = "W2040807242"
}

In order to gain additional information about the origin of preferred orientation of recrystallized grains, the influence of a magnetic field on recrystallization of iron-cobalt alloys is being studied. Preliminary results indicate a change of the texture which can be qualitatively accounted for by considering the magnetostrictive properties of the alloy and their influence on the stability of the recrystallization centers.

@article{doi10106311698523,
    author = "Smoluchowski, R. and Turner, Ronald W.",
    title = "Influence of Magnetic Field on Recrystallization",
    year = "1949",
    journal = "Journal of Applied Physics",
    abstract = "In order to gain additional information about the origin of preferred orientation of recrystallized grains, the influence of a magnetic field on recrystallization of iron-cobalt alloys is being studied. Preliminary results indicate a change of the texture which can be qualitatively accounted for by considering the magnetostrictive properties of the alloy and their influence on the stability of the recrystallization centers.",
    url = "https://doi.org/10.1063/1.1698523",
    doi = "10.1063/1.1698523",
    openalex = "W2043899868"
}

The motion of a charged particle in a constant magnetic field is treated in both relativistic and non-relativistic quantum theory. Operators representing the center of the orbit, which obey the commutation law for conjugate variables, are introduced and their connections with energy, angular momentum, and magnetic moment studied. Energy eigenfunctions in an operator form are obtained by factorization. Previously derived eigenfunctions in coordinate space are obtained and are shown to be eigenfunctions for the operators for the center of the orbit as well as for the energy. Corresponding relativistic eigenfunctions are derived by a simple device which enables one to construct solutions of the Dirac equation from solutions of the Schr\"odinger equation.

@article{doi101103physrev76828,
    author = "Johnson, M. H. and Lippmann, B. A.",
    title = "Motion in a Constant Magnetic Field",
    year = "1949",
    journal = "Physical Review",
    abstract = {The motion of a charged particle in a constant magnetic field is treated in both relativistic and non-relativistic quantum theory. Operators representing the center of the orbit, which obey the commutation law for conjugate variables, are introduced and their connections with energy, angular momentum, and magnetic moment studied. Energy eigenfunctions in an operator form are obtained by factorization. Previously derived eigenfunctions in coordinate space are obtained and are shown to be eigenfunctions for the operators for the center of the orbit as well as for the energy. Corresponding relativistic eigenfunctions are derived by a simple device which enables one to construct solutions of the Dirac equation from solutions of the Schr\"odinger equation.},
    url = "https://doi.org/10.1103/physrev.76.828",
    doi = "10.1103/physrev.76.828",
    openalex = "W1991387770"
}

The electric discharges of Gymnarchus niloticus and of representative species of seven genera of the Mormyridae have been examined in their natural habitat in Africa and in the laboratory. Comparable investigations of the South American Gymnotidae have shown the existence of two discharge types in both these unrelated fish families. The first type of electric discharge consists of very regular sequences of continuously emitted, monophasic pulses, varying from species to species in frequency, and within narrower limits from individual to individual. Fish emitting this first type of pulses include Gymnarchus, Hypopomus and Eigenmannia. The frequency range for these fish lies between 60 and 400 discharges/sec. The frequency does not alter with the state of excitation of the fish. The duration of individual pulses is relatively long, i.e. 2–10 msec. The second type of discharge is less regular in frequency, the pulse duration much shorter and the pulse shape more complex. The individual discharge from the whole electric organ lasts about 0.2 msec, in Petrocephalus. This type of discharge is found in all the examined species of the Mormyridae and in such forms as Gymnotus carapo and Staetogenes elegans. The basic discharge rate of a resting mormyrid is somewhat variable and not strictly rhythmical. It usually lies between 1 and 6 pulses/sec. Stimuli which excite the mormyrids cause an increase in the discharge frequency. The recorded maximum is about 130 pulses/sec. Suitable stimuli can inhibit the discharges of the Mormyridae for prolonged periods. In Gymnotus carapo and Staetogenes elegans the basic discharge rate is higher and of regular rhythmicity. Depending on temperature the frequencies lie between 30 and 87 pulses/sec. When these fish are excited the frequencies are increased up to 200 pulses/sec, for a short time. The shape of the electric field, which is set up with each pulse around the fish, has been examined. A theory has been proposed which suggests that these fish, by means of their electric pulses, can locate objects if their electrical conductivity differs from that of water. These fish have shown themselves extremely sensitive to influences affecting the electric field. This has been studied by applying artificial electric stimuli, by studying the effects of conductors and non-conductors introduced into the field, and the reactions towards magnetic fields and electrostatic charges. Conditioned reflex experiments with Gymnarchus niloticus and Gymnotus carapo have shown that these fish can detect the presence of a stationary magnet, and that they can discriminate between conductors and non-conductors. The prey of these fish does not appear to be affected by the discharges. Inter alia, the electric pulses have a social significance. This locating mechanism may be considered as an adaptation to life in turbid water. Gymnotidae and Mormyridae (taken to include Gymnarchus) show striking features of convergent evolution. Unusual locomotory adaptations such as swimming by means of the dorsal fin (Gymnarchus), the anal fin (Gymnotidae) and ‘Gemminger‘s bones’ (Mormyridae) may be considered as a means which tends to make the axis of symmetry of the fish and of its electric field coincide during active movements. A new theory for the evolution of electric organs has been suggested. A major prerequisite appears to be a receptor sensitive to electrical stimulation. It is suggested that special sensory and nervous differentiations of the lateralis system (‘mormyromasts’, valvulae cerebelli) are concerned with the perception and integration of electric stimuli. Muscular action potentials have been recorded in the water at some distance from non-electric fish. The easiest explanation for the evolution of strong electric organs would appear to start from such muscular action potentials, and proceed via weak electric organs used for orientation, to the powerful offensive and defensive electric organs."

@article{lissmann1958on,
    author = "Lissmann, H. W.",
    title = "On the Function and Evolution of Electric Organs in Fish",
    year = "1958",
    journal = "Journal of Experimental Biology",
    abstract = {The electric discharges of Gymnarchus niloticus and of representative species of seven genera of the Mormyridae have been examined in their natural habitat in Africa and in the laboratory. Comparable investigations of the South American Gymnotidae have shown the existence of two discharge types in both these unrelated fish families. The first type of electric discharge consists of very regular sequences of continuously emitted, monophasic pulses, varying from species to species in frequency, and within narrower limits from individual to individual. Fish emitting this first type of pulses include Gymnarchus, Hypopomus and Eigenmannia. The frequency range for these fish lies between 60 and 400 discharges/sec. The frequency does not alter with the state of excitation of the fish. The duration of individual pulses is relatively long, i.e. 2–10 msec. The second type of discharge is less regular in frequency, the pulse duration much shorter and the pulse shape more complex. The individual discharge from the whole electric organ lasts about 0.2 msec, in Petrocephalus. This type of discharge is found in all the examined species of the Mormyridae and in such forms as Gymnotus carapo and Staetogenes elegans. The basic discharge rate of a resting mormyrid is somewhat variable and not strictly rhythmical. It usually lies between 1 and 6 pulses/sec. Stimuli which excite the mormyrids cause an increase in the discharge frequency. The recorded maximum is about 130 pulses/sec. Suitable stimuli can inhibit the discharges of the Mormyridae for prolonged periods. In Gymnotus carapo and Staetogenes elegans the basic discharge rate is higher and of regular rhythmicity. Depending on temperature the frequencies lie between 30 and 87 pulses/sec. When these fish are excited the frequencies are increased up to 200 pulses/sec, for a short time. The shape of the electric field, which is set up with each pulse around the fish, has been examined. A theory has been proposed which suggests that these fish, by means of their electric pulses, can locate objects if their electrical conductivity differs from that of water. These fish have shown themselves extremely sensitive to influences affecting the electric field. This has been studied by applying artificial electric stimuli, by studying the effects of conductors and non-conductors introduced into the field, and the reactions towards magnetic fields and electrostatic charges. Conditioned reflex experiments with Gymnarchus niloticus and Gymnotus carapo have shown that these fish can detect the presence of a stationary magnet, and that they can discriminate between conductors and non-conductors. The prey of these fish does not appear to be affected by the discharges. Inter alia, the electric pulses have a social significance. This locating mechanism may be considered as an adaptation to life in turbid water. Gymnotidae and Mormyridae (taken to include Gymnarchus) show striking features of convergent evolution. Unusual locomotory adaptations such as swimming by means of the dorsal fin (Gymnarchus), the anal fin (Gymnotidae) and ‘Gemminger‘s bones’ (Mormyridae) may be considered as a means which tends to make the axis of symmetry of the fish and of its electric field coincide during active movements. A new theory for the evolution of electric organs has been suggested. A major prerequisite appears to be a receptor sensitive to electrical stimulation. It is suggested that special sensory and nervous differentiations of the lateralis system (‘mormyromasts’, valvulae cerebelli) are concerned with the perception and integration of electric stimuli. Muscular action potentials have been recorded in the water at some distance from non-electric fish. The easiest explanation for the evolution of strong electric organs would appear to start from such muscular action potentials, and proceed via weak electric organs used for orientation, to the powerful offensive and defensive electric organs."},
    url = "https://doi.org/10.1242/jeb.35.1.156",
    doi = "10.1242/jeb.35.1.156",
    number = "1",
    openalex = "W2287496592",
    pages = "156-191",
    volume = "35",
    references = "doi101002cne910110302, doi101017cbo9780511693281002, doi101038167201a0, doi10108000222931108692993, doi101098rspb19380041, doi101113jphysiol1952sp004695, doi101113jphysiol1953sp004849, doi1023071416035, doi1023072485224, doi105962bhltitle53990"
}

A quantum field theory of magnetic and electric charge is constructed. It is verified to be relativistically invariant in consequence of the charge quantization condition $\frac{\mathrm{eg}}{\ensuremath{\hbar}c}=n$, an integer. This is more restrictive than Dirac's condition, which would also allow half-integral values.

@article{doi101103physrev1441087,
    author = "Schwinger, Julian",
    title = "Magnetic Charge and Quantum Field Theory",
    year = "1966",
    journal = "Physical Review",
    abstract = "A quantum field theory of magnetic and electric charge is constructed. It is verified to be relativistically invariant in consequence of the charge quantization condition $\frac{\mathrm{eg}}{\ensuremath{\hbar}c}=n$, an integer. This is more restrictive than Dirac's condition, which would also allow half-integral values.",
    url = "https://doi.org/10.1103/physrev.144.1087",
    doi = "10.1103/physrev.144.1087",
    openalex = "W2083667531"
}

We present a local Lagrangian density, depending on a pair of four-potentials $A$ and $B$, and charged fields ${\ensuremath{\psi}}_{n}$ with electric and magnetic charges ${e}_{n}$ and ${g}_{n}$. The resulting local Lagrangian field equations are equivalent to Maxwell's and Dirac's equations. The Lagrangian depends on a fixed four-vector, so manifest isotropy is lost and is regained only for quantized values of (${e}_{n}{g}_{m}\ensuremath{-}{g}_{n}{e}_{m}$). This condition results from the requirement that the representation of the Poincar\'e Lie algebra which results from Poincar\'e invariance, integrate to a representation of the finite Poincar\'e group. The finite Lorentz transformation laws of $A$, $B$, and ${\ensuremath{\psi}}_{n}$ are presented here for the first time. The familiar apparatus of Lagrangian field theory is applied to yield directly the canonical commutation relations, the energy-momentum tensor, and Feynman's rules.

@article{doi101103physrevd3880,
    author = "Zwanziger, Daniel",
    title = "Local-Lagrangian Quantum Field Theory of Electric and Magnetic Charges",
    year = "1971",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields",
    abstract = "We present a local Lagrangian density, depending on a pair of four-potentials $A$ and $B$, and charged fields ${\ensuremath{\psi}}\_{n}$ with electric and magnetic charges ${e}\_{n}$ and ${g}\_{n}$. The resulting local Lagrangian field equations are equivalent to Maxwell's and Dirac's equations. The Lagrangian depends on a fixed four-vector, so manifest isotropy is lost and is regained only for quantized values of (${e}\_{n}{g}\_{m}\ensuremath{-}{g}\_{n}{e}\_{m}$). This condition results from the requirement that the representation of the Poincar\'e Lie algebra which results from Poincar\'e invariance, integrate to a representation of the finite Poincar\'e group. The finite Lorentz transformation laws of $A$, $B$, and ${\ensuremath{\psi}}\_{n}$ are presented here for the first time. The familiar apparatus of Lagrangian field theory is applied to yield directly the canonical commutation relations, the energy-momentum tensor, and Feynman's rules.",
    url = "https://doi.org/10.1103/physrevd.3.880",
    doi = "10.1103/physrevd.3.880",
    openalex = "W2089863876"
}

@article{mccleave1971weak,
    author = "McCleave, James D. and Rommel, Sentiel A. and Cathcart, Carole L.",
    title = "WEAK ELECTRIC AND MAGNETIC FIELDS IN FISH ORIENTATION*",
    year = "1971",
    journal = "Annals of the New York Academy of Sciences",
    url = "https://doi.org/10.1111/j.1749-6632.1971.tb13103.x",
    doi = "10.1111/j.1749-6632.1971.tb13103.x",
    number = "1",
    openalex = "W2080889788",
    pages = "270-281",
    volume = "188",
    references = "doi101007bf00343146, doi101038199088a0, doi1010382121232b0, doi101093icesjms182187, doi101139f68101, doi101242jeb352451, doi101242jeb372417, doi101242jeb391119, lissmann1958on, openalexw612836844"
}

@article{doi101007bf00620494,
    author = "Akoev, G. N. and Ilyinsky, O. B. and Zadan, P. M.",
    title = "Responses of electroreceptors (ampullae of lorenzini) of Skates to electric and magnetic fields",
    year = "1976",
    journal = "Journal of Comparative Physiology A",
    url = "https://doi.org/10.1007/bf00620494",
    doi = "10.1007/bf00620494",
    openalex = "W2027592599",
    references = "mccleave1971weak"
}

@techreport{adey1977brain1,
    author = "Adey, W. R. and Bawin, S. M",
    title = "Brain interactions with weak electric and magnetic fields",
    year = "1977",
    howpublished = "Neurosciences Research Program Bulletin, v. 15; 129 pp",
    note = "talkorigins\_source = {true}; raw\_reference = {Adey, W. R., and Bawin, S. M., 1977, Brain interactions with weak electric and magnetic fields: Neurosciences Research Program Bulletin, v. 15; 129 pp.}"
}

@article{comay1983interactions,
    author = "Comay, E.",
    title = "Interactions of static electric and magnetic fields",
    year = "1983",
    journal = "Lettere al Nuovo Cimento",
    url = "https://doi.org/10.1007/bf02783636",
    doi = "10.1007/bf02783636",
    number = "12",
    openalex = "W2081505391",
    pages = "421-422",
    volume = "38",
    references = "doi10106313067575"
}

@article{doi1010160003491683900672,
    author = "Guillou, J. C. Le and Zinn‐Justin, Jean",
    title = "The hydrogen atom in strong magnetic fields: Summation of the weak field series expansion",
    year = "1983",
    journal = "Annals of Physics",
    url = "https://doi.org/10.1016/0003-4916(83)90067-2",
    doi = "10.1016/0003-4916(83)90067-2",
    openalex = "W2750146709",
    references = "doi1010160022369760902432"
}

Classical trajectories of an atomic electron in a magnetic field are calculated for various values of the field strength $B$. Qualitative properties of these trajectories are examined. With use of a scaling law, it is shown that the equations of motion can be written in a form such that they depend upon only one parameter, which may be regarded as a reduced angular momentum (proportional to ${L}_{z}{B}^{\frac{1}{3}}$). For small values of this parameter there is an "elliptical regime" in which the trajectory may be regarded as a Kepler ellipse with orbital parameters that evolve slowly in time. For large values of the parameter there is a "helical regime" in which the electron circles rapidly around a magnetic field line and bounces slowly back and forth along the field. Between these two regimes there is an irregular regime, with "chaotic" orbits and a "transition regime" in which the trajectories can be described in oblate spheroidal coordinates. Bound states persist even at energies above the escape energy, provided that the angular momentum (or field strength) is sufficiently large. With use of action-variable quantization, some formulas for semiclassical energy eigenvalues are given for regimes where the trajectories are regular.

@article{doi101103physreva301208,
    author = "Delos, J. B. and Knudson, S. K. and Noid, D. W.",
    title = "Trajectories of an atomic electron in a magnetic field",
    year = "1984",
    journal = "Physical review. A, General physics",
    abstract = {Classical trajectories of an atomic electron in a magnetic field are calculated for various values of the field strength $B$. Qualitative properties of these trajectories are examined. With use of a scaling law, it is shown that the equations of motion can be written in a form such that they depend upon only one parameter, which may be regarded as a reduced angular momentum (proportional to ${L}\_{z}{B}^{\frac{1}{3}}$). For small values of this parameter there is an "elliptical regime" in which the trajectory may be regarded as a Kepler ellipse with orbital parameters that evolve slowly in time. For large values of the parameter there is a "helical regime" in which the electron circles rapidly around a magnetic field line and bounces slowly back and forth along the field. Between these two regimes there is an irregular regime, with "chaotic" orbits and a "transition regime" in which the trajectories can be described in oblate spheroidal coordinates. Bound states persist even at energies above the escape energy, provided that the angular momentum (or field strength) is sufficiently large. With use of action-variable quantization, some formulas for semiclassical energy eigenvalues are given for regimes where the trajectories are regular.},
    url = "https://doi.org/10.1103/physreva.30.1208",
    doi = "10.1103/physreva.30.1208",
    openalex = "W1989739296",
    references = "doi1010160022369760902432"
}

In this paper basic mathematical and physical concepts of the biomagnetic inverse problem are reviewed with some new approaches. The forward problem is discussed for both homogeneous and inhomogeneous media. Geselowitz' formulae and a surface integral equation are presented to handle a piecewise homogeneous conductor. The special cases of a spherically symmetric conductor and a horizontally layered medium are discussed in detail. The non-uniqueness of the solution of the magnetic inverse problem is discussed and the difficulty caused by the contribution of the electric potential to the magnetic field outside the conductor is studied. As practical methods of solving the inverse problem, a weighted least-squares search with confidence limits and the method of minimum norm estimate are discussed.

@article{doi10108800319155321004,
    author = "Sarvas, Jukka",
    title = "Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem",
    year = "1987",
    journal = "Physics in Medicine and Biology",
    abstract = "In this paper basic mathematical and physical concepts of the biomagnetic inverse problem are reviewed with some new approaches. The forward problem is discussed for both homogeneous and inhomogeneous media. Geselowitz' formulae and a surface integral equation are presented to handle a piecewise homogeneous conductor. The special cases of a spherically symmetric conductor and a horizontally layered medium are discussed in detail. The non-uniqueness of the solution of the magnetic inverse problem is discussed and the difficulty caused by the contribution of the electric potential to the magnetic field outside the conductor is studied. As practical methods of solving the inverse problem, a weighted least-squares search with confidence limits and the method of minimum norm estimate are discussed.",
    url = "https://doi.org/10.1088/0031-9155/32/1/004",
    doi = "10.1088/0031-9155/32/1/004",
    openalex = "W1987333243"
}

This is the first of two papers that develop the theory of oscillatory spectra. When an atom is placed in a magnetic field, and the absorption spectrum into states close to the ionization threshold is measured at finite resolution, so that individual energy levels are not resolved, it is found that the absorption as a function of energy is a superposition of sinusoidal oscillations. These papers present a quantitative theory of this phenomenon. In this first paper, we describe the physical ideas underlying the theory in the simplest possible way, and we present our first calculations based upon the theory. In the second paper, the theory is developed in full detail, proofs of all of the assertions are given, and we describe the algorithm that was used to make the calculations.

@article{doi101103physreva381896,
    author = "Du, M. L. and Delos, J. B.",
    title = "Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. I. Physical picture and calculations",
    year = "1988",
    journal = "Physical review. A, General physics",
    abstract = "This is the first of two papers that develop the theory of oscillatory spectra. When an atom is placed in a magnetic field, and the absorption spectrum into states close to the ionization threshold is measured at finite resolution, so that individual energy levels are not resolved, it is found that the absorption as a function of energy is a superposition of sinusoidal oscillations. These papers present a quantitative theory of this phenomenon. In this first paper, we describe the physical ideas underlying the theory in the simplest possible way, and we present our first calculations based upon the theory. In the second paper, the theory is developed in full detail, proofs of all of the assertions are given, and we describe the algorithm that was used to make the calculations.",
    url = "https://doi.org/10.1103/physreva.38.1896",
    doi = "10.1103/physreva.38.1896",
    openalex = "W2056680027",
    references = "doi101103physrev85259"
}

@article{doi101007bf02753831,
    author = "Tejedor, M. and Rubio, H.",
    title = "Comment on «interactions of static electric and magnetic fields»",
    year = "1989",
    journal = "˜Il œNuovo cimento della Società italiana di fisica. B/˜Il œNuovo cimento B",
    url = "https://doi.org/10.1007/bf02753831",
    doi = "10.1007/bf02753831",
    openalex = "W2033932573",
    references = "comay1983interactions"
}

The recent works carried out by the authors' research group on magnetic field-induced martensitic transformations are reviewed, which are concerned with various kinds of ferrous alloys, such as Fe-Ni poly- and mono-crystals, invar and non-invar Fe-Ni-C polycrystals, discordered and ordered Fe-Pt polycrystals, ausaged Fe-Ni-Co-Ti polycrystals and paramagnetic Fe-Mn-C polycrystals. The works clarified influences of composition, the existence of grain boundaries, crystal orientation, invar characteristic, thermoelastic nature and austenitic magnetism on the magnetic field-induced martensitic trnasformations. In the work on the ausaged Fe-Ni-Co-Ti alloy, the appearance of ''magnetoelastic martensitic transformation'' was newly found. By taking into account the influences of composiiton, grain boundaries, crystal orientation, invar characteristic, thermoelastic nature and austenite magnetism, a new and exact equation was proposed to generally expalin the shift of Ms temperature as a function of critical magnetic field to induce martensitic transformations in those alloys, which consisted of three terms of the Zeeman energy, high field susceptibility energy and forced volume magnetostriction energy. The new and exact equation was experimentally verified to hold in all the alloys studied.

@article{doi102355isijinternational2997,
    author = "Shimizu, Ken‐ichi and Kakeshita, Tomoyuki",
    title = "Effect of magnetic fields on martensitic transformations in ferrous alloys and steels.",
    year = "1989",
    journal = "ISIJ International",
    abstract = "The recent works carried out by the authors' research group on magnetic field-induced martensitic transformations are reviewed, which are concerned with various kinds of ferrous alloys, such as Fe-Ni poly- and mono-crystals, invar and non-invar Fe-Ni-C polycrystals, discordered and ordered Fe-Pt polycrystals, ausaged Fe-Ni-Co-Ti polycrystals and paramagnetic Fe-Mn-C polycrystals. The works clarified influences of composition, the existence of grain boundaries, crystal orientation, invar characteristic, thermoelastic nature and austenitic magnetism on the magnetic field-induced martensitic trnasformations. In the work on the ausaged Fe-Ni-Co-Ti alloy, the appearance of ''magnetoelastic martensitic transformation'' was newly found. By taking into account the influences of composiiton, grain boundaries, crystal orientation, invar characteristic, thermoelastic nature and austenite magnetism, a new and exact equation was proposed to generally expalin the shift of Ms temperature as a function of critical magnetic field to induce martensitic transformations in those alloys, which consisted of three terms of the Zeeman energy, high field susceptibility energy and forced volume magnetostriction energy. The new and exact equation was experimentally verified to hold in all the alloys studied.",
    url = "https://doi.org/10.2355/isijinternational.29.97",
    doi = "10.2355/isijinternational.29.97",
    openalex = "W2015717667"
}

@incollection{aronov1991magnetooptical,
    author = "ARONOV, A.G. and PIKUS, G.E.",
    title = "Magneto-Optical Phenomena in Electric and Magnetic Fields",
    year = "1991",
    booktitle = "Modern Problems in Condensed Matter Sciences",
    url = "https://doi.org/10.1016/b978-0-444-88535-7.50017-0",
    doi = "10.1016/b978-0-444-88535-7.50017-0",
    openalex = "W2497459303",
    pages = "513-578",
    references = "doi1010160003491658900320, doi1010160003491660900610, doi1010160022369760902432, doi101049sqj19660063, doi101103physrev1021030, doi101103physrev1081384, doi101103physrev11490, doi101103physrev85259, doi101103physrev96266, openalexw2064573497"
}

Results concerning the rigorous justification of the effective Hamiltonians for band electrons in the presence of weak homogeneous electric and magnetic fields are reviewed. In the electric-field case the existence, in the sense of spectral concentration, of the Stark-Wannier resonances is proved. In the magnetic-field case, the existence of exponentially localized magnetic Wannier functions is established. As a consequence the Peierls-Onsager effective Hamiltonian is obtained.

@article{doi101103revmodphys6391,
    author = "Nenciu, G.",
    title = "Dynamics of band electrons in electric and magnetic fields: rigorous justification of the effective Hamiltonians",
    year = "1991",
    journal = "Reviews of Modern Physics",
    abstract = "Results concerning the rigorous justification of the effective Hamiltonians for band electrons in the presence of weak homogeneous electric and magnetic fields are reviewed. In the electric-field case the existence, in the sense of spectral concentration, of the Stark-Wannier resonances is proved. In the magnetic-field case, the existence of exponentially localized magnetic Wannier functions is established. As a consequence the Peierls-Onsager effective Hamiltonian is obtained.",
    url = "https://doi.org/10.1103/revmodphys.63.91",
    doi = "10.1103/revmodphys.63.91",
    openalex = "W2017745389",
    references = "doi1010160003491660900610"
}

The inconsistency met in calculating the interaction energy of a magnetic monopole with an electrical current can be avoided considering the interaction between the Dirac's string of the monopole and the current. The interaction energy does not vanish and leads to the correct Lorentz force on the monopole.

@article{doi10120902955075158003,
    author = "Getino, J. and Rojo, O. and Rubio, H.",
    title = "Interaction between Electric Currents and Magnetic Monopoles",
    year = "1991",
    journal = "Europhysics Letters (EPL)",
    abstract = "The inconsistency met in calculating the interaction energy of a magnetic monopole with an electrical current can be avoided considering the interaction between the Dirac's string of the monopole and the current. The interaction energy does not vanish and leads to the correct Lorentz force on the monopole.",
    url = "https://doi.org/10.1209/0295-5075/15/8/003",
    doi = "10.1209/0295-5075/15/8/003",
    openalex = "W2094500872",
    references = "comay1983interactions, doi1010160304885384902749, doi1010160370269386904454, doi1010160370269387900815, doi101098rspa19310130, doi101103physrev1501104, doi101103physrev74817, doi101103physrevd123845, doi101111j174966321986tb12424x"
}

Magnetoencephalography (MEG) is a noninvasive technique for investigating neuronal activity in the living human brain. The time resolution of the method is better than 1 ms and the spatial discrimination is, under favorable circumstances, 2-3 mm for sources in the cerebral cortex. In MEG studies, the weak 10 fT-1 pT magnetic fields produced by electric currents flowing in neurons are measured with multichannel SQUID (superconducting quantum interference device) gradiometers. The sites in the cerebral cortex that are activated by a stimulus can be found from the detected magnetic-field distribution, provided that appropriate assumptions about the source render the solution of the inverse problem unique. Many interesting properties of the working human brain can be studied, including spontaneous activity and signal processing following external stimuli. For clinical purposes, determination of the locations of epileptic foci is of interest. The authors begin with a general introduction and a short discussion of the neural basis of MEG. The mathematical theory of the method is then explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices. Finally, several MEG experiments performed in the authors' laboratory are described, covering studies of evoked responses and of spontaneous activity in both healthy and diseased brains. Many MEG studies by other groups are discussed briefly as well.

@article{doi101103revmodphys65413,
    author = "Hämäläinen, Matti and Hari, Riitta and Ilmoniemi, Risto J. and Knuutila, Jukka and Lounasmaa, O. V.",
    title = "Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain",
    year = "1993",
    journal = "Reviews of Modern Physics",
    abstract = "Magnetoencephalography (MEG) is a noninvasive technique for investigating neuronal activity in the living human brain. The time resolution of the method is better than 1 ms and the spatial discrimination is, under favorable circumstances, 2-3 mm for sources in the cerebral cortex. In MEG studies, the weak 10 fT-1 pT magnetic fields produced by electric currents flowing in neurons are measured with multichannel SQUID (superconducting quantum interference device) gradiometers. The sites in the cerebral cortex that are activated by a stimulus can be found from the detected magnetic-field distribution, provided that appropriate assumptions about the source render the solution of the inverse problem unique. Many interesting properties of the working human brain can be studied, including spontaneous activity and signal processing following external stimuli. For clinical purposes, determination of the locations of epileptic foci is of interest. The authors begin with a general introduction and a short discussion of the neural basis of MEG. The mathematical theory of the method is then explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices. Finally, several MEG experiments performed in the authors' laboratory are described, covering studies of evoked responses and of spontaneous activity in both healthy and diseased brains. Many MEG studies by other groups are discussed briefly as well.",
    url = "https://doi.org/10.1103/revmodphys.65.413",
    doi = "10.1103/revmodphys.65.413",
    openalex = "W2084333685"
}

The effect of magnetic fields on the athermal martensitic transformation in an Fe-31.4Ni-0.5Mn alloy (mass%), whose Ms temperature is about 195 K, and on the isothermal one in an Fe-24.9Ni-3.9Mn alloy (mass%), whose nose temperature is about 153 K, have been examined in order to clarify the difference between the athermal and isothermal kinetics of martensitic transformations by measuring magnetic field susceptibility and magnetization, and by observing optical microstructure, applying pulsed ultra high magnetic fields up to 31 MA/m. As a result, the following characteristics were found: The austenitic state in the former alloy was ferromagnetic, whereas that in the latter alloy was micromagnetic and/or spin glass. Even in the latter alloy, martensitic transformation was induced instantaneously under pulsed magnetic fields higher than a critical one over a wide temperature range, as in the former alloy. This result suggests that the originally isothermal kinetics of martensitic transformation is changed to the athermal one under high magnetic fields. Optical microscopy showed that respective isothermal martensite plates of the Fe–24.9Ni–3.9Mn alloy under no magnetic field grew gradually during isothermal holding. Moreover, morphology of the magnetic field-induced martensites of both the alloys was almost the same as that of thermally-induced ones, irrespective of the formation temperature. A thermodynamic calculation for the critical magnetic field vs. temperature relation was done for both the alloys by using an equation previously proposed, and the calculated relations were all in good agreement with the experimental ones in the wide temperature range examined.

@article{doi102320matertrans198934415,
    author = "Kakeshita, Tomoyuki and Kuroiwa, Koichi and Shimizu, Ken‐ichi and Ikeda, T. and Yamagishi, A. and Date, M.",
    title = "Effect of Magnetic Fields on Athermal and Isothermal Martensitic Transformations in Fe\–Ni\–Mn Alloys",
    year = "1993",
    journal = "Materials Transactions JIM",
    abstract = "The effect of magnetic fields on the athermal martensitic transformation in an Fe-31.4Ni-0.5Mn alloy (mass\%), whose Ms temperature is about 195 K, and on the isothermal one in an Fe-24.9Ni-3.9Mn alloy (mass\%), whose nose temperature is about 153 K, have been examined in order to clarify the difference between the athermal and isothermal kinetics of martensitic transformations by measuring magnetic field susceptibility and magnetization, and by observing optical microstructure, applying pulsed ultra high magnetic fields up to 31 MA/m. As a result, the following characteristics were found: The austenitic state in the former alloy was ferromagnetic, whereas that in the latter alloy was micromagnetic and/or spin glass. Even in the latter alloy, martensitic transformation was induced instantaneously under pulsed magnetic fields higher than a critical one over a wide temperature range, as in the former alloy. This result suggests that the originally isothermal kinetics of martensitic transformation is changed to the athermal one under high magnetic fields. Optical microscopy showed that respective isothermal martensite plates of the Fe–24.9Ni–3.9Mn alloy under no magnetic field grew gradually during isothermal holding. Moreover, morphology of the magnetic field-induced martensites of both the alloys was almost the same as that of thermally-induced ones, irrespective of the formation temperature. A thermodynamic calculation for the critical magnetic field vs. temperature relation was done for both the alloys by using an equation previously proposed, and the calculated relations were all in good agreement with the experimental ones in the wide temperature range examined.",
    url = "https://doi.org/10.2320/matertrans1989.34.415",
    doi = "10.2320/matertrans1989.34.415",
    openalex = "W4241311704",
    references = "doi102320matertrans198934423"
}

Strains of nearly 0.2% have been induced along [001] in unstressed crystals of Ni2MnGa with magnetic fields of 8 kOe applied at 265 K. These stains are associated with the superelastic motion of twin boundaries in the martensitic phase that is stable below about 274 K.

@article{doi1010631117637,
    author = "Ullakko, K. and Huang, Junjie and Kantner, C. and O’Handley, R. C. and Kokorin, V. V.",
    title = "Large magnetic-field-induced strains in Ni2MnGa single crystals",
    year = "1996",
    journal = "Applied Physics Letters",
    abstract = "Strains of nearly 0.2\% have been induced along [001] in unstressed crystals of Ni2MnGa with magnetic fields of 8 kOe applied at 265 K. These stains are associated with the superelastic motion of twin boundaries in the martensitic phase that is stable below about 274 K.",
    url = "https://doi.org/10.1063/1.117637",
    doi = "10.1063/1.117637",
    openalex = "W2044740984"
}

Effects of high magnetic field and tensile stress on martensitic transformation behavior and microstructure at 4.2 K have been studied in Fe-31Ni-0.4C and Fe-27Ni-0.8C (wt%) shape memory alloys. In order to make clear the difference of the effects of high magnetic field and tensile stress on the amount of martensite, two types of experiments were conducted, that is, the magentic field of 10 T was applied first and then the tensile stress of 220 MPa was applied in constant magnetic field in one type of experiment and the tensile stress of 220 MPa was applied first and then the magnetic field of 10 T was applied under constant tensile stress in the other type if experiment. The amount of martensite formed in these two experiments were compared. It was found that the critical magnetic field to induce martensitic transformation is between 7.5 T and 10 T. In the case of Fe–27Ni–0.8C, martensitic transformation is stress-induced at lower level of stress in magnetic field than in the case no magnetic field is applied. The amount of martensite formed by increasing the magnetic field under constant stress is larger than that formed by increasing the stress in the constant magnetic field, which shows that the effect of tensile stress on the number density of martensite is larger than that of magnetic field in this experimental condition.

@article{doi102320matertrans1989371044,
    author = "Ohtsuka, Hideyuki and Nagai, Kotobu and Kajiwara, Setsuo and Kitaguchi, Hitoshi and Uehara, Mitsuru",
    title = "Effects of High Magnetic Field and Tensile Stress on Martensitic Transformation Behavior and Microstructure at 4.2 K in Fe\–Ni\–C Alloys",
    year = "1996",
    journal = "Materials Transactions JIM",
    abstract = "Effects of high magnetic field and tensile stress on martensitic transformation behavior and microstructure at 4.2 K have been studied in Fe-31Ni-0.4C and Fe-27Ni-0.8C (wt\%) shape memory alloys. In order to make clear the difference of the effects of high magnetic field and tensile stress on the amount of martensite, two types of experiments were conducted, that is, the magentic field of 10 T was applied first and then the tensile stress of 220 MPa was applied in constant magnetic field in one type of experiment and the tensile stress of 220 MPa was applied first and then the magnetic field of 10 T was applied under constant tensile stress in the other type if experiment. The amount of martensite formed in these two experiments were compared. It was found that the critical magnetic field to induce martensitic transformation is between 7.5 T and 10 T. In the case of Fe–27Ni–0.8C, martensitic transformation is stress-induced at lower level of stress in magnetic field than in the case no magnetic field is applied. The amount of martensite formed by increasing the magnetic field under constant stress is larger than that formed by increasing the stress in the constant magnetic field, which shows that the effect of tensile stress on the number density of martensite is larger than that of magnetic field in this experimental condition.",
    url = "https://doi.org/10.2320/matertrans1989.37.1044",
    doi = "10.2320/matertrans1989.37.1044",
    openalex = "W2059985519"
}

@article{doi101016s0921509300007772,
    author = "Conrad, H.",
    title = "Influence of an electric or magnetic field on the liquid–solid transformation in materials and on the microstructure of the solid",
    year = "2000",
    journal = "Materials Science and Engineering A",
    url = "https://doi.org/10.1016/s0921-5093(00)00777-2",
    doi = "10.1016/s0921-5093(00)00777-2",
    openalex = "W2050602188"
}

@article{doi101016s0921509300007784,
    author = "Koch, C.C.",
    title = "Experimental evidence for magnetic or electric field effects on phase transformations",
    year = "2000",
    journal = "Materials Science and Engineering A",
    url = "https://doi.org/10.1016/s0921-5093(00)00778-4",
    doi = "10.1016/s0921-5093(00)00778-4",
    openalex = "W1973945936",
    references = "doi101007bf00240796, doi1010160167577x90901278, doi1010160956716x9500267y, doi101023a1018513411517"
}

A room temperature extensional strain of 5.1% was observed in martensitic Ni/sub 48/Mn/sub 31/Ga/sub 21/ alloy in the magnetic field of 480 kA/m. The magnitude of field-induced strain decreases with increasing external compressive stress applied in the direction of expansion. The compressive stress of about 3 MPa prevents the development of the substantial field-induced strain. Magnetization curves obtained by VSM exhibit an abrupt magnetization change and a transient hysteresis in the first quadrant. Large reversible field-induced strain and the abrupt magnetization change are due to the rearrangement or redistribution of martensitic twin variants by the applied magnetic field. It was confirmed by optical observation of movement and nucleation of martensitic twin boundaries.

@article{doi10110920908764,
    author = "Heczko, Oleg and Sozinov, A. and Ullakko, K.",
    title = "Giant field-induced reversible strain in magnetic shape memory NiMnGa alloy",
    year = "2000",
    journal = "IEEE Transactions on Magnetics",
    abstract = "A room temperature extensional strain of 5.1\% was observed in martensitic Ni/sub 48/Mn/sub 31/Ga/sub 21/ alloy in the magnetic field of 480 kA/m. The magnitude of field-induced strain decreases with increasing external compressive stress applied in the direction of expansion. The compressive stress of about 3 MPa prevents the development of the substantial field-induced strain. Magnetization curves obtained by VSM exhibit an abrupt magnetization change and a transient hysteresis in the first quadrant. Large reversible field-induced strain and the abrupt magnetization change are due to the rearrangement or redistribution of martensitic twin variants by the applied magnetic field. It was confirmed by optical observation of movement and nucleation of martensitic twin boundaries.",
    url = "https://doi.org/10.1109/20.908764",
    doi = "10.1109/20.908764",
    openalex = "W2143250053",
    references = "doi101016s1359646296004836"
}

We report results obtained from polarization measurements on PbMg1/3Nb2/3O3 single crystal under static electric field, in both field cooling and field switching after zero field cooling processes. In the field cooling process, two kinds of regime are observed depending on the field strength, i.e., above and below threshold value Et≈1.7 kV/cm. From the low field regime results we have extracted both linear and nonlinear susceptibilities, which exhibit an anomaly close to the freezing temperature. In the field switching after zero field cooling experiments, a local polarization corresponding to the appearance of polar nuclei develops up to a critical value where the nuclei collapse into macroscopic ferroelectric macrodomains.

@article{doi10106311408597,
    author = "Dkhil, Brahim and Kiat, J. M.",
    title = "Electric-field-induced polarization in the ergodic and nonergodic states of PbMg1/3Nb2/3O3 relaxor",
    year = "2001",
    journal = "Journal of Applied Physics",
    abstract = "We report results obtained from polarization measurements on PbMg1/3Nb2/3O3 single crystal under static electric field, in both field cooling and field switching after zero field cooling processes. In the field cooling process, two kinds of regime are observed depending on the field strength, i.e., above and below threshold value Et≈1.7 kV/cm. From the low field regime results we have extracted both linear and nonlinear susceptibilities, which exhibit an anomaly close to the freezing temperature. In the field switching after zero field cooling experiments, a local polarization corresponding to the appearance of polar nuclei develops up to a critical value where the nuclei collapse into macroscopic ferroelectric macrodomains.",
    url = "https://doi.org/10.1063/1.1408597",
    doi = "10.1063/1.1408597",
    openalex = "W1483644259",
    references = "doi102320matertrans198934423"
}

The properties of matter are drastically modified by strong magnetic fields, $B\ensuremath{\gg}{m}_{e}^{2}{e}^{3}c/{\ensuremath{\Elzxh}}^{3}=2.35\ifmmode\times\else\texttimes\fi{}{10}^{9}\mathrm{G}$ $(1\mathrm{G}{=10}^{\ensuremath{-}4}\mathrm{T}),$ as are typically found on the surfaces of neutron stars. In such strong magnetic fields, the Coulomb force on an electron acts as a small perturbation compared to the magnetic force. The strong-field condition can also be mimicked in laboratory semiconductors. Because of the strong magnetic confinement of electrons perpendicular to the field, atoms attain a much greater binding energy compared to the zero-field case, and various other bound states become possible, including molecular chains and three-dimensional condensed matter. This article reviews the electronic structure of atoms, molecules, and bulk matter, as well as the thermodynamic properties of dense plasma, in strong magnetic fields, ${10}^{9}\mathrm{G}\ensuremath{\ll}B\ensuremath{\lesssim}{10}^{16}\mathrm{G}.$ The focus is on the basic physical pictures and approximate scaling relations, although various theoretical approaches and numerical results are also discussed. For a neutron star surface composed of light elements such as hydrogen or helium, the outermost layer constitutes a nondegenerate, partially ionized Coulomb plasma if $B\ensuremath{\lesssim}{10}^{15}$ G (at temperature $T\ensuremath{\gtrsim}{10}^{6}$ K), and may be in the form of a condensed liquid if the magnetic field is stronger (and T $\ensuremath{\gtrsim}{10}^{6}\mathrm{K}).$ For an iron surface, the outermost layer of the neutron star can be in a gaseous or a condensed phase, depending on the cohesive property of the iron condensate.

@article{doi101103revmodphys73629,
    author = "Lai, Dong",
    title = "Matter in strong magnetic fields",
    year = "2001",
    journal = "Reviews of Modern Physics",
    abstract = "The properties of matter are drastically modified by strong magnetic fields, $B\ensuremath{\gg}{m}\_{e}^{2}{e}^{3}c/{\ensuremath{\Elzxh}}^{3}=2.35\ifmmode\times\else\texttimes\fi{}{10}^{9}\mathrm{G}$ $(1\mathrm{G}{=10}^{\ensuremath{-}4}\mathrm{T}),$ as are typically found on the surfaces of neutron stars. In such strong magnetic fields, the Coulomb force on an electron acts as a small perturbation compared to the magnetic force. The strong-field condition can also be mimicked in laboratory semiconductors. Because of the strong magnetic confinement of electrons perpendicular to the field, atoms attain a much greater binding energy compared to the zero-field case, and various other bound states become possible, including molecular chains and three-dimensional condensed matter. This article reviews the electronic structure of atoms, molecules, and bulk matter, as well as the thermodynamic properties of dense plasma, in strong magnetic fields, ${10}^{9}\mathrm{G}\ensuremath{\ll}B\ensuremath{\lesssim}{10}^{16}\mathrm{G}.$ The focus is on the basic physical pictures and approximate scaling relations, although various theoretical approaches and numerical results are also discussed. For a neutron star surface composed of light elements such as hydrogen or helium, the outermost layer constitutes a nondegenerate, partially ionized Coulomb plasma if $B\ensuremath{\lesssim}{10}^{15}$ G (at temperature $T\ensuremath{\gtrsim}{10}^{6}$ K), and may be in the form of a condensed liquid if the magnetic field is stronger (and T $\ensuremath{\gtrsim}{10}^{6}\mathrm{K}).$ For an iron surface, the outermost layer of the neutron star can be in a gaseous or a condensed phase, depending on the cohesive property of the iron condensate.",
    url = "https://doi.org/10.1103/revmodphys.73.629",
    doi = "10.1103/revmodphys.73.629",
    openalex = "W2062322544",
    references = "doi1010160022369760902432, doi101103physrev85259"
}

Giant magnetic-field-induced strain of about 9.5% was observed at ambient temperature in a magnetic field of less than 1 T in NiMnGa orthorhombic seven-layered martensitic phase. The strain proved to be caused by magnetic-field-controlled twin boundary motion. According to an analysis of x-ray diffraction data, the crystal structure of this phase is nearly orthorhombic, having lattice parameters a=0.619 nm, b=0.580 nm, and c=0.553 nm (in cubic parent phase coordinates) at ambient temperature. Seven-layer shuffling-type modulation along the (110)[11̄0]p system was recorded. The results of mechanical tests and magnetic anisotropy property measurements are also reported.

@article{doi10106311458075,
    author = "Sozinov, A. and Likhachev, A. A. and Lanska, N. and Ullakko, K.",
    title = "Giant magnetic-field-induced strain in NiMnGa seven-layered martensitic phase",
    year = "2002",
    journal = "Applied Physics Letters",
    abstract = "Giant magnetic-field-induced strain of about 9.5\% was observed at ambient temperature in a magnetic field of less than 1 T in NiMnGa orthorhombic seven-layered martensitic phase. The strain proved to be caused by magnetic-field-controlled twin boundary motion. According to an analysis of x-ray diffraction data, the crystal structure of this phase is nearly orthorhombic, having lattice parameters a=0.619 nm, b=0.580 nm, and c=0.553 nm (in cubic parent phase coordinates) at ambient temperature. Seven-layer shuffling-type modulation along the (110)[11̄0]p system was recorded. The results of mechanical tests and magnetic anisotropy property measurements are also reported.",
    url = "https://doi.org/10.1063/1.1458075",
    doi = "10.1063/1.1458075",
    openalex = "W1982067377",
    references = "doi101016s1359646296004836"
}

We describe monocrystalline graphitic films, which are a few atoms thick but are nonetheless stable under ambient conditions, metallic, and of remarkably high quality. The films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands, and they exhibit a strong ambipolar electric field effect such that electrons and holes in concentrations up to 10(13) per square centimeter and with room-temperature mobilities of approximately 10,000 square centimeters per volt-second can be induced by applying gate voltage.

@article{doi101126science1102896,
    author = "Novoselov, Kostya S. and Geǐm, A. K. and Морозов, С. В. and Jiang, Da and Zhang, Y. and Dubonos, S. V. and Grigorieva, I. V. and Firsov, А. А.",
    title = "Electric Field Effect in Atomically Thin Carbon Films",
    year = "2004",
    journal = "Science",
    abstract = "We describe monocrystalline graphitic films, which are a few atoms thick but are nonetheless stable under ambient conditions, metallic, and of remarkably high quality. The films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands, and they exhibit a strong ambipolar electric field effect such that electrons and holes in concentrations up to 10(13) per square centimeter and with room-temperature mobilities of approximately 10,000 square centimeters per volt-second can be induced by applying gate voltage.",
    url = "https://doi.org/10.1126/science.1102896",
    doi = "10.1126/science.1102896",
    openalex = "W2058122340",
    references = "doi1010160008622381900336, doi1010160039602892901837, doi101016s0009261401010661, doi101023a1010907928709, doi10103841284, doi10108000018730110113644, doi10108010408430208500497, doi101126science1060928, doi101126science2875453622, doi101147rd4510011"
}

Abstract The application of an external dc electric field during the solution heat treatment (SHT) of AA6111 Al alloy increased the as-quenched resistivity ρ and hardness Hv. The increases represented reductions in SHT of 10–20 K required for a constant ρ or Hv. Analysis of the results gave that the field reduced both the enthalpy and entropy of solution. The resulting reduction in Gibbs free energy gave increases of 0.03–0.04 at.% in solubility of Mg2Si (or Al–Mg–Si–(Cu)-vacancy complexes) at 400–600°C, amounting to a factor of 33 % increase in solubility at 400°C and 6% at 600°C.

@article{doi103139146017965,
    author = "Conrad, H. and Jung, Kang",
    title = "Effects of an external electric field applied during the solution heat treatment of the Al–Mg–Si–Cu alloy AA6111",
    year = "2004",
    journal = "Zeitschrift für Metallkunde",
    abstract = "Abstract The application of an external dc electric field during the solution heat treatment (SHT) of AA6111 Al alloy increased the as-quenched resistivity ρ and hardness Hv. The increases represented reductions in SHT of 10–20 K required for a constant ρ or Hv. Analysis of the results gave that the field reduced both the enthalpy and entropy of solution. The resulting reduction in Gibbs free energy gave increases of 0.03–0.04 at.\% in solubility of Mg2Si (or Al–Mg–Si–(Cu)-vacancy complexes) at 400–600°C, amounting to a factor of 33 \% increase in solubility at 400°C and 6\% at 600°C.",
    url = "https://doi.org/10.3139/146.017965",
    doi = "10.3139/146.017965",
    openalex = "W1976841708"
}

@article{conrad2005enhanced,
    author = "Conrad, Hans",
    title = "Enhanced Phenomena in Metals with Electric and Magnetic Fields: I Electric Fields",
    year = "2005",
    journal = "MATERIALS TRANSACTIONS",
    url = "https://doi.org/10.2320/matertrans.46.1083",
    doi = "10.2320/matertrans.46.1083",
    number = "6",
    openalex = "W2040243948",
    pages = "1083-1087",
    volume = "46",
    references = "doi101007bf00240796, doi1010160036974889902524, doi1010160036974889905140, doi1010160167577x90901278, doi1010160921509390902622, doi1010160956716x9500267y, doi101016s0921509301009686, doi101023a1018513411517, doi101023bjmsc00000448866679895, doi1010631106191"
}

@article{enomoto2005enhanced,
    author = "Enomoto, Masato",
    title = "Enhanced Phenomena in Metals with Electric and Magnetic Fields: II Magnetic Fields",
    year = "2005",
    journal = "MATERIALS TRANSACTIONS",
    url = "https://doi.org/10.2320/matertrans.46.1088",
    doi = "10.2320/matertrans.46.1088",
    number = "6",
    openalex = "W1988847232",
    pages = "1088-1092",
    volume = "46",
    references = "doi1010160001616056900335, doi101016jactamat200403044, doi101016s0167577x99002633, doi101016s135964540300106x, doi101016s1359646200003948, doi101016s1359646296004836, doi10106311729261, doi10108009500839008203733, doi101557jmr19980059, doi102320matertrans198934423"
}

A magnetic field has a remarkable influence on solid/solid phase transformations and it can be used to control the structure and function of materials during phase transformations. The effects of magnetic fields on diffusional solid/solid phase transformations, mainly from austenite to ferrite, in Fe-based alloys are reviewed. The effects of magnetic fields on the transformation temperature and phase diagram are explained thermodynamically, and the transformation behavior and transformed structures in magnetic fields are discussed.

@article{doi1010881468699691013004,
    author = "Ohtsuka, Hideyuki",
    title = "Structural control of Fe-based alloys through diffusional solid/solid phase transformations in a high magnetic field",
    year = "2008",
    journal = "Science and Technology of Advanced Materials",
    abstract = "A magnetic field has a remarkable influence on solid/solid phase transformations and it can be used to control the structure and function of materials during phase transformations. The effects of magnetic fields on diffusional solid/solid phase transformations, mainly from austenite to ferrite, in Fe-based alloys are reviewed. The effects of magnetic fields on the transformation temperature and phase diagram are explained thermodynamically, and the transformation behavior and transformed structures in magnetic fields are discussed.",
    url = "https://doi.org/10.1088/1468-6996/9/1/013004",
    doi = "10.1088/1468-6996/9/1/013004",
    openalex = "W2044885472",
    references = "enomoto2005enhanced"
}

A modest dc electric field markedly reduced the tensile flow stress at high temperatures in three polycrystalline oxides, i.e. MgO, Al2O3 and yttria-stabilized tetragonal ZrO2 (Y-TZP). The reduction in flow stress ΔσE in Y-TZP consisted of three components: (i) ΔσT due to Joule heating, (ii) a rapid, reversible component obtained in on-off and electric field step tests and (iii) the cumulative effect of the field on microstructure. Only ΔσT and occurred in MgO and Al2O3. It is concluded that results from a reduction in the electrochemical potential for the formation of vacancies corresponding to the diffusion of the rate-controlling ion in the space-charge at the grain boundary. The calculated magnitude of the space-charge zone width and its temperature and solute composition dependence are in accord with theory and experiment; is attributed mainly to the retardation of grain growth by the field. The retardation could be due to one or more of the following effects of the field on the space-charge zone: (i) an increase in the segregated solute ions, (ii) a decrease in grain boundary energy and (iii) a decrease in solute ion mobility.

@article{doi10108014786430903304137,
    author = "Conrad, H. and Yang, Di",
    title = "Influence of an applied dc electric field on the plastic deformation kinetics of oxide ceramics",
    year = "2010",
    journal = "The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics",
    abstract = "A modest dc electric field markedly reduced the tensile flow stress at high temperatures in three polycrystalline oxides, i.e. MgO, Al2O3 and yttria-stabilized tetragonal ZrO2 (Y-TZP). The reduction in flow stress ΔσE in Y-TZP consisted of three components: (i) ΔσT due to Joule heating, (ii) a rapid, reversible component obtained in on-off and electric field step tests and (iii) the cumulative effect of the field on microstructure. Only ΔσT and occurred in MgO and Al2O3. It is concluded that results from a reduction in the electrochemical potential for the formation of vacancies corresponding to the diffusion of the rate-controlling ion in the space-charge at the grain boundary. The calculated magnitude of the space-charge zone width and its temperature and solute composition dependence are in accord with theory and experiment; is attributed mainly to the retardation of grain growth by the field. The retardation could be due to one or more of the following effects of the field on the space-charge zone: (i) an increase in the segregated solute ions, (ii) a decrease in grain boundary energy and (iii) a decrease in solute ion mobility.",
    url = "https://doi.org/10.1080/14786430903304137",
    doi = "10.1080/14786430903304137",
    openalex = "W2066038111",
    references = "conrad2005enhanced, doi101007bf01105274, doi1010160001616062900925, doi101016jactamat200704051, doi101016jactamat200707029, doi101016s1359645498001712, doi1010631332035, doi101111j115129161974tb11350x, doi101111j115129161990tb06449x, doi101111j115129161998tb02695x, enomoto2005enhanced, openalexw1480130188"
}

Microwaves and spark plasma sintering (SPS) enhance sinterability. Simple electrical fields, applied by means of a pair of electrodes to bare specimens, have been shown to accelerate the rate of superplastic deformation, reduce the time and temperature for sintering, and to retard the rate of grain growth. By inference, the influence of electrical and electromagnetic fields on grain boundary energetics and kinetics is unmistakable. Often, in ceramics, grain boundaries are themselves endowed with space charge that can couple with externally applied fields. The frequency dependence of this coupling ranging from zero frequency to microwave frequencies is discussed. The classical approach for modeling grain growth, creep, and sintering, considers chemical diffusion (self‐diffusion) under a thermodynamic driving force, underpinned by a physical mechanism that visualizes the flow of mass transport in a way that reproduces the phenomenological observations. In all instances, the final analytical result can be separated into a product of three functions: one of the grain size, the second related to the thermodynamic driving force, and the third to the kinetics of mass transport. The influence of an electrical field on each of these functions is addressed.The fundamental mechanisms of these electrical interactions are discussed in the following ways: (i) dielectric loss and Joule heating in the crystal and at the grain boundary, (ii) the coupling between mechanical stress and the electrochemical potential of charged species, (iii) the interaction between applied electrical fields and the intrinsic fields that exist within the space charge layers, (iv) and the possibility of nucleating defect avalanches under electrical fields. We limit ourselves to ceramics that have at least some degree of ionic character. In these experiments the electrical fields range from several volts to several hundred volts per centimeter, and the power dissipation from Joule heating is of the order of several watts per cubic centimeter of the specimen. Metals, where very high current densities are obtained at relatively low applied electric fields, leading to phenomenon such as electromigration, are not considered.

@article{doi101111j15512916201104652x,
    author = "Raj, Rishi and Cologna, Marco and Francis, John S. C.",
    title = "Influence of Externally Imposed and Internally Generated Electrical Fields on Grain Growth, Diffusional Creep, Sintering and Related Phenomena in Ceramics",
    year = "2011",
    journal = "Journal of the American Ceramic Society",
    abstract = "Microwaves and spark plasma sintering (SPS) enhance sinterability. Simple electrical fields, applied by means of a pair of electrodes to bare specimens, have been shown to accelerate the rate of superplastic deformation, reduce the time and temperature for sintering, and to retard the rate of grain growth. By inference, the influence of electrical and electromagnetic fields on grain boundary energetics and kinetics is unmistakable. Often, in ceramics, grain boundaries are themselves endowed with space charge that can couple with externally applied fields. The frequency dependence of this coupling ranging from zero frequency to microwave frequencies is discussed. The classical approach for modeling grain growth, creep, and sintering, considers chemical diffusion (self‐diffusion) under a thermodynamic driving force, underpinned by a physical mechanism that visualizes the flow of mass transport in a way that reproduces the phenomenological observations. In all instances, the final analytical result can be separated into a product of three functions: one of the grain size, the second related to the thermodynamic driving force, and the third to the kinetics of mass transport. The influence of an electrical field on each of these functions is addressed.The fundamental mechanisms of these electrical interactions are discussed in the following ways: (i) dielectric loss and Joule heating in the crystal and at the grain boundary, (ii) the coupling between mechanical stress and the electrochemical potential of charged species, (iii) the interaction between applied electrical fields and the intrinsic fields that exist within the space charge layers, (iv) and the possibility of nucleating defect avalanches under electrical fields. We limit ourselves to ceramics that have at least some degree of ionic character. In these experiments the electrical fields range from several volts to several hundred volts per centimeter, and the power dissipation from Joule heating is of the order of several watts per cubic centimeter of the specimen. Metals, where very high current densities are obtained at relatively low applied electric fields, leading to phenomenon such as electromigration, are not considered.",
    url = "https://doi.org/10.1111/j.1551-2916.2011.04652.x",
    doi = "10.1111/j.1551-2916.2011.04652.x",
    openalex = "W2157660514",
    references = "doi10108014786430903304137"
}

We study the effect of a static homogeneous external magnetic field on charmonium and bottomonium states. In an external magnetic field, quarkonium states do not have a conserved center-of-mass momentum. Instead there is a new conserved quantity called the pseudomomentum which takes into account the Lorentz force on the particles in the system. When written in terms of the pseudomomentum, the internal and center-of-mass motions do not decouple and, as a result, the properties of quarkonia depend on the states' center-of-mass momentum. We analyze the behavior of heavy particle-antiparticle pairs subject to an external magnetic field assuming a three-dimensional harmonic potential and Cornell potential plus spin-spin interaction. In the case of the Cornell potential, we also take into account the mixing of the ${\ensuremath{\eta}}_{c}$ and $J/\ensuremath{\psi}$ states and ${\ensuremath{\eta}}_{b}$ and $\ensuremath{\Upsilon}$ states due to the background magnetic field. We then numerically calculate the dependence of the masses and mixing fractions on the magnitude of the background magnetic field and center-of-mass momentum of the state.

@article{doi101103physrevd88105017,
    author = "Alford, Jeremy and Strickland, Michael",
    title = "Charmonia and bottomonia in a magnetic field",
    year = "2013",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology",
    abstract = "We study the effect of a static homogeneous external magnetic field on charmonium and bottomonium states. In an external magnetic field, quarkonium states do not have a conserved center-of-mass momentum. Instead there is a new conserved quantity called the pseudomomentum which takes into account the Lorentz force on the particles in the system. When written in terms of the pseudomomentum, the internal and center-of-mass motions do not decouple and, as a result, the properties of quarkonia depend on the states' center-of-mass momentum. We analyze the behavior of heavy particle-antiparticle pairs subject to an external magnetic field assuming a three-dimensional harmonic potential and Cornell potential plus spin-spin interaction. In the case of the Cornell potential, we also take into account the mixing of the ${\ensuremath{\eta}}\_{c}$ and $J/\ensuremath{\psi}$ states and ${\ensuremath{\eta}}\_{b}$ and $\ensuremath{\Upsilon}$ states due to the background magnetic field. We then numerically calculate the dependence of the masses and mixing fractions on the magnitude of the background magnetic field and center-of-mass momentum of the state.",
    url = "https://doi.org/10.1103/physrevd.88.105017",
    doi = "10.1103/physrevd.88.105017",
    openalex = "W2019973914",
    references = "doi101103physrev85259"
}

In the review, contemporary data on the influence of natural and artificial magnetic fields on fish behavior are considered. In this regard, elasmobranchs and teleosts appear to be studied most exhaustively. Elasmobranchs and some teleosts are able to perceive magnetic fields via electroreceptors. A number of teleosts can sense magnetic fields via sensory cells containing crystals of biogenic magnetite. Laboratory experiments and field observations indicate the influence of magnetic fields on fish locomotor activity and spatial distribution. The geomagnetic field can be used by fish for navigation. Besides, artificial magnetic fields and natural fluctuations of the geomagnetic field can affect fish embryos leading to alterations in their development. It is suggested that, afterwards, these alterations can have an effect on fish behavior.

@article{doi101134s2079086414030049,
    author = "Крылов, В. В. and Izyumov, Yu. G. and Извеков, Е. И. and Nepomnyashchikh, V. A.",
    title = "Magnetic fields and fish behavior",
    year = "2014",
    journal = "Biology Bulletin Reviews",
    abstract = "In the review, contemporary data on the influence of natural and artificial magnetic fields on fish behavior are considered. In this regard, elasmobranchs and teleosts appear to be studied most exhaustively. Elasmobranchs and some teleosts are able to perceive magnetic fields via electroreceptors. A number of teleosts can sense magnetic fields via sensory cells containing crystals of biogenic magnetite. Laboratory experiments and field observations indicate the influence of magnetic fields on fish locomotor activity and spatial distribution. The geomagnetic field can be used by fish for navigation. Besides, artificial magnetic fields and natural fluctuations of the geomagnetic field can affect fish embryos leading to alterations in their development. It is suggested that, afterwards, these alterations can have an effect on fish behavior.",
    url = "https://doi.org/10.1134/s2079086414030049",
    doi = "10.1134/s2079086414030049",
    openalex = "W2016498927",
    references = "mccleave1971weak"
}

@incollection{heller2014electric,
    author = "Heller, Leon and Volegov, Petr",
    title = "Electric and Magnetic Fields of the Brain",
    year = "2014",
    booktitle = "Magnetoencephalography",
    url = "https://doi.org/10.1007/978-3-642-33045-2\_3",
    doi = "10.1007/978-3-642-33045-2\_3",
    openalex = "W141074880",
    pages = "73-105",
    references = "doi101007978146120919516, doi10108800319155321004, doi101090qam10666, doi101093comjnl74308, doi101103revmodphys65413, doi10110979962275, doi1011370111030, doi1023072005193, doi1023072226151, openalexw2986444355"
}

@incollection{teisseyre2014mutual,
    author = "Teisseyre, Roman and Teisseyre-Jeleńska, Maria",
    title = "Mutual Interactions: Electric/Magnetic Fields and Strains",
    year = "2014",
    booktitle = "GeoPlanet: Earth and Planetary Sciences",
    url = "https://doi.org/10.1007/978-3-642-31860-3\_9",
    doi = "10.1007/978-3-642-31860-3\_9",
    openalex = "W21283838",
    pages = "133-147",
    references = "doi1010079783642164491, doi1010160040195184900593, doi101016004019518490060x, doi1010160040195191904622, doi101016004019519390055o, doi101016s0074614209601194, doi101103physreve66011902, doi101512iumj1956555033, openalexw1531504342, openalexw595429427"
}

@article{doi101016jmattod201803026,
    author = "Guillon, Olivier and Elsässer, Christian and Gutfleisch, Oliver and Janek, Jürgen and Korte‐Kerzel, Sandra and Raabe, Dierk and Volkert, Cynthia A.",
    title = "Manipulation of matter by electric and magnetic fields: Toward novel synthesis and processing routes of inorganic materials",
    year = "2018",
    journal = "Materials Today",
    url = "https://doi.org/10.1016/j.mattod.2018.03.026",
    doi = "10.1016/j.mattod.2018.03.026",
    openalex = "W2795654769",
    references = "doi101016s1359646200003948"
}

Abstract We investigated the interaction energy of a Gilbertian magnetic charge with each of the “point” magnetic field sources. Finally we extrapolated a Dirac string can only be defined if there is at most one Dirac monopole in the medium. If there is only one Dirac monopole/string in the universe, the probability of detecting it is essential zero, such that Dirac’s monopole would remain just a “theorist’s particle”.

@article{doi102478jee20190034,
    author = "Zor, Ömer",
    title = "On interactions of static magnetic fields",
    year = "2019",
    journal = "Journal of Electrical Engineering",
    abstract = "Abstract We investigated the interaction energy of a Gilbertian magnetic charge with each of the “point” magnetic field sources. Finally we extrapolated a Dirac string can only be defined if there is at most one Dirac monopole in the medium. If there is only one Dirac monopole/string in the universe, the probability of detecting it is essential zero, such that Dirac’s monopole would remain just a “theorist’s particle”.",
    url = "https://doi.org/10.2478/jee-2019-0034",
    doi = "10.2478/jee-2019-0034",
    openalex = "W2963762394",
    references = "comay1983interactions, doi10100797814684292201, doi1010160370269386904454, doi1010160370269387900815, doi101098rspa19310130, doi101103physrev1441087, doi101103physrev74817, doi101103physrevd123845, doi101103physrevd3880, doi10120902955075158003, openalexw2549722719"
}

@incollection{heller2019electric,
    author = "Heller, Leon and Volegov, Petr",
    title = "Electric and Magnetic Fields of the Brain",
    year = "2019",
    booktitle = "Magnetoencephalography",
    url = "https://doi.org/10.1007/978-3-319-62657-4\_3-1",
    doi = "10.1007/978-3-319-62657-4\_3-1",
    openalex = "W4234132848",
    pages = "1-33",
    references = "doi101002andp18531650603, doi10108800319155321004, doi101090qam10666, doi101093comjnl74308, doi101103revmodphys65413, doi1011091016463, doi10110979962275, doi1011370111030, doi1023072005193, doi1023072332454"
}

Magnetography with superconducting quantum interference device (SQUID) sensor arrays is a well-established technique for measuring subtle magnetic fields generated by physiological phenomena in the human body. Unfortunately, the SQUID-based systems have some limitations related to the need to cool them down with liquid helium. The room-temperature alternatives for SQUIDs are optically pumped magnetometers (OPM) operating in spin exchange relaxation-free (SERF) regime, which require a very low ambient magnetic field. The most common two-layer magnetically shielded rooms (MSR) with residual magnetic field of 50 nT may not be sufficiently magnetically attenuated and additional compensation of external magnetic field is required. A cost-efficient compensation system based on square Helmholtz coils was designed and successfully used for preliminary measurements with commercially available zero-field OPM. The presented setup can reduce the static ambient magnetic field inside a magnetically shielded room, which improves the usability of OPMs by providing a proper environment for them to operate, independent of initial conditions in MSR.

@article{doi103390s20164563,
    author = "Jodko-Władzińska, Anna and Wildner, Krzysztof and Pałko, Tadeusz and Władziński, Michał",
    title = "Compensation System for Biomagnetic Measurements with Optically Pumped Magnetometers inside a Magnetically Shielded Room.",
    year = "2020",
    journal = "Sensors (Basel, Switzerland)",
    abstract = "Magnetography with superconducting quantum interference device (SQUID) sensor arrays is a well-established technique for measuring subtle magnetic fields generated by physiological phenomena in the human body. Unfortunately, the SQUID-based systems have some limitations related to the need to cool them down with liquid helium. The room-temperature alternatives for SQUIDs are optically pumped magnetometers (OPM) operating in spin exchange relaxation-free (SERF) regime, which require a very low ambient magnetic field. The most common two-layer magnetically shielded rooms (MSR) with residual magnetic field of 50 nT may not be sufficiently magnetically attenuated and additional compensation of external magnetic field is required. A cost-efficient compensation system based on square Helmholtz coils was designed and successfully used for preliminary measurements with commercially available zero-field OPM. The presented setup can reduce the static ambient magnetic field inside a magnetically shielded room, which improves the usability of OPMs by providing a proper environment for them to operate, independent of initial conditions in MSR.",
    url = "https://pmc.ncbi.nlm.nih.gov/articles/PMC7471992/",
    doi = "10.3390/s20164563",
    pmcid = "PMC7471992",
    pmid = "32823964"
}

Abstract A new thermal analysis technique is described that allows measurements to be performed on bulk samples at extreme heating and cooling rates and in high magnetic fields. High heating rates, up to 1000 °C min −1, are achieved through electromagnetic induction heating of a custom-built apparatus fitted with commercial thermal analysis heads and sensor. Rapid cooling rates, up to 100 °C min −1, are enabled by gas quenching and the small thermal mass of the induction furnace. The custom apparatus is designed to fit inside a superconducting magnet capable of fields up to 9 Tesla. This study demonstrates that the instrument is capable of collecting accurate thermal analysis data in high magnetic fields and rapidly acquiring data for dynamic processes. While the full potential of the technique is still unrealized, currently, it can provide insight into phenomena at time scales relevant to heat treatment in many industrial processes and into little understood effects of high magnetic field processing.

@article{doi101007s1097302111010y,
    author = "Kesler, Michael S. and McGuire, Michael A. and Conner, Benjamin S. and Rios, Orlando and Murphy, Bart and Carter, William G. and Henderson, Hunter B. and Ludtka, Gerard M. and Kisner, R.A.",
    title = "A rapid heating and high magnetic field thermal analysis technique",
    year = "2021",
    journal = "Journal of Thermal Analysis and Calorimetry",
    abstract = "Abstract A new thermal analysis technique is described that allows measurements to be performed on bulk samples at extreme heating and cooling rates and in high magnetic fields. High heating rates, up to 1000 °C min −1, are achieved through electromagnetic induction heating of a custom-built apparatus fitted with commercial thermal analysis heads and sensor. Rapid cooling rates, up to 100 °C min −1, are enabled by gas quenching and the small thermal mass of the induction furnace. The custom apparatus is designed to fit inside a superconducting magnet capable of fields up to 9 Tesla. This study demonstrates that the instrument is capable of collecting accurate thermal analysis data in high magnetic fields and rapidly acquiring data for dynamic processes. While the full potential of the technique is still unrealized, currently, it can provide insight into phenomena at time scales relevant to heat treatment in many industrial processes and into little understood effects of high magnetic field processing.",
    url = "https://doi.org/10.1007/s10973-021-11010-y",
    doi = "10.1007/s10973-021-11010-y",
    openalex = "W3197616387",
    references = "enomoto2005enhanced"
}

The high uniform magnetic field combined with pre-deformation and vacuum heat treatment processing is designed for improving the diffusion bonding properties of the 1420 Al-Li alloy. Serial magneto-thermal coupling treatment experiments of 1420 Al-Li alloy and the pure aluminium diffusion couple, together with the gallium interlayer, is carried out in a superconducting high magnetic field device. Various parameter combinations are used to produce different samples on which interface organization and connection performance are studied. Electron microscopic analysis reveals various interface topographies and fracture morphologies after shear strength tests. Influence of diffusion bonding temperature on element diffusion under a high uniform magnetic field is investigated. The diffusion activation energy of Mg element in pure aluminum under a 12 T magnetic field is calculated in this paper. It is found that the bonding quality and bonding performance of the interface are improved greatly after heat treatment with a strong magnetic field, and the bonding temperature is an important factor affecting the interface bonding and bonding strength. The diffusion coefficient of the Mg element in the 1420 Al-Li alloy to L2 pure aluminum increases with the increase of diffusion bonding temperature. Reducing the activation energy of elemental diffusion is beneficial to atomic diffusion.

@article{doi103390cryst12111508,
    author = "Zhang, Huang and Niu, Tao and Li, Yaoming and Yuan, Meini",
    title = "Influence of High Magnetic Field-Thermal Coupling Processing on Diffusion Bonding Properties and Element Diffusion of 1420 Al-Li Alloy",
    year = "2022",
    journal = "Crystals",
    abstract = "The high uniform magnetic field combined with pre-deformation and vacuum heat treatment processing is designed for improving the diffusion bonding properties of the 1420 Al-Li alloy. Serial magneto-thermal coupling treatment experiments of 1420 Al-Li alloy and the pure aluminium diffusion couple, together with the gallium interlayer, is carried out in a superconducting high magnetic field device. Various parameter combinations are used to produce different samples on which interface organization and connection performance are studied. Electron microscopic analysis reveals various interface topographies and fracture morphologies after shear strength tests. Influence of diffusion bonding temperature on element diffusion under a high uniform magnetic field is investigated. The diffusion activation energy of Mg element in pure aluminum under a 12 T magnetic field is calculated in this paper. It is found that the bonding quality and bonding performance of the interface are improved greatly after heat treatment with a strong magnetic field, and the bonding temperature is an important factor affecting the interface bonding and bonding strength. The diffusion coefficient of the Mg element in the 1420 Al-Li alloy to L2 pure aluminum increases with the increase of diffusion bonding temperature. Reducing the activation energy of elemental diffusion is beneficial to atomic diffusion.",
    url = "https://doi.org/10.3390/cryst12111508",
    doi = "10.3390/cryst12111508",
    openalex = "W4307372662",
    references = "doi1010801040843620222080177"
}

Gastric motility is coordinated by bioelectric slow waves (SWs) and dysrhythmic SW activity has been linked with motility disorders. Magnetogastrography (MGG) is the non-invasive measurement of the biomagnetic fields generated by SWs. Dysrhythmia identification using MGG is currently challenging because source models are not well developed and the impact of anatomical variation is not well understood. A novel method for the quantitative spatial co-registration of serosal SW potentials, MGG, and geometric models of anatomical structures was developed and performed on two anesthetized pigs to verify feasibility. Electrode arrays were localized using electromagnetic transmitting coils. Coil localization error for the volume where the stomach is normally located under the sensor array was assessed in a benchtop experiment, and mean error was 4.2±2.3mm and 3.6±3.3° for a coil orientation parallel to the sensor array and 6.2±5.7mm and 4.5±7.0° for a perpendicular coil orientation. Stomach geometries were reconstructed by fitting a generic stomach to up to 19 localization coils, and SW activation maps were mapped onto the reconstructed geometries using the registered positions of 128 electrodes. Normal proximal-to-distal and ectopic SW propagation patterns were recorded from the serosa and compared against the simultaneous MGG measurements. Correlations between the center-of-gravity of normalized MGG and the mean position of SW activity on the serosa were 0.36 and 0.85 for the ectopic and normal propagation patterns along the proximal-distal stomach axis, respectively. This study presents the first feasible method for the spatial co-registration of MGG, serosal SW measurements, and subject-specific anatomy. This is a significant advancement because these data enable the development and validation of novel non-invasive gastric source characterization methods.

@article{doi101016jcompbiomed2023107384,
    author = "Drake, Chad E and Cheng, Leo K and Muszynski, Nicole D and Somarajan, Suseela and Paskaranandavadivel, Niranchan and Angeli-Gordon, Timothy R and Du, Peng and Bradshaw, Leonard A and Avci, Recep",
    title = "Electroanatomical mapping of the stomach with simultaneous biomagnetic measurements.",
    year = "2023",
    journal = "Computers in biology and medicine",
    abstract = "Gastric motility is coordinated by bioelectric slow waves (SWs) and dysrhythmic SW activity has been linked with motility disorders. Magnetogastrography (MGG) is the non-invasive measurement of the biomagnetic fields generated by SWs. Dysrhythmia identification using MGG is currently challenging because source models are not well developed and the impact of anatomical variation is not well understood. A novel method for the quantitative spatial co-registration of serosal SW potentials, MGG, and geometric models of anatomical structures was developed and performed on two anesthetized pigs to verify feasibility. Electrode arrays were localized using electromagnetic transmitting coils. Coil localization error for the volume where the stomach is normally located under the sensor array was assessed in a benchtop experiment, and mean error was 4.2±2.3mm and 3.6±3.3° for a coil orientation parallel to the sensor array and 6.2±5.7mm and 4.5±7.0° for a perpendicular coil orientation. Stomach geometries were reconstructed by fitting a generic stomach to up to 19 localization coils, and SW activation maps were mapped onto the reconstructed geometries using the registered positions of 128 electrodes. Normal proximal-to-distal and ectopic SW propagation patterns were recorded from the serosa and compared against the simultaneous MGG measurements. Correlations between the center-of-gravity of normalized MGG and the mean position of SW activity on the serosa were 0.36 and 0.85 for the ectopic and normal propagation patterns along the proximal-distal stomach axis, respectively. This study presents the first feasible method for the spatial co-registration of MGG, serosal SW measurements, and subject-specific anatomy. This is a significant advancement because these data enable the development and validation of novel non-invasive gastric source characterization methods.",
    url = "https://pubmed.ncbi.nlm.nih.gov/37633085/",
    doi = "10.1016/j.compbiomed.2023.107384",
    pmid = "37633085"
}

@article{doi101016jmatchar2023112906,
    author = "Kang, Kaijiao and Jiang, Shunde and Li, Dayong and Shi, Dequan",
    title = "Effect of electric pulse and rotating magnetic field on solidification microstructure and properties of Al-Zn-Mg-Cu alloy",
    year = "2023",
    journal = "Materials Characterization",
    url = "https://doi.org/10.1016/j.matchar.2023.112906",
    doi = "10.1016/j.matchar.2023.112906",
    openalex = "W4362721860",
    references = "doi101016s1359646200003948"
}

Abstract An external electric or magnetic field can transfer high-intensity energy directly to the electronic scale of materials, and change the spin, energy level arrangement and trajectory of electrons. These changes produce tremendous and profound impacts on the microstructure and mechanical properties of metal materials, which may be impossible with traditional technologies. This paper reviews the effects of electric or magnetic field on the microstructures of solid metals including phase transformation, precipitation, recrystallization, dislocations and so on. Based on the existing research results, the mechanisms of these effects have been discussed. Additionally, some typical applications of electric and magnetic treatments on solid metals have been described and the challenges in this field have also been discussed.

@article{doi101186s1003302300961y,
    author = "Song, Yanli and Wu, Wenlin and Yu, Yongqing and Hua, Lin",
    title = "Effects of Electric and Magnetic Treatments on Microstructures of Solid Metals: A Review",
    year = "2023",
    journal = "Chinese Journal of Mechanical Engineering",
    abstract = "Abstract An external electric or magnetic field can transfer high-intensity energy directly to the electronic scale of materials, and change the spin, energy level arrangement and trajectory of electrons. These changes produce tremendous and profound impacts on the microstructure and mechanical properties of metal materials, which may be impossible with traditional technologies. This paper reviews the effects of electric or magnetic field on the microstructures of solid metals including phase transformation, precipitation, recrystallization, dislocations and so on. Based on the existing research results, the mechanisms of these effects have been discussed. Additionally, some typical applications of electric and magnetic treatments on solid metals have been described and the challenges in this field have also been discussed.",
    url = "https://doi.org/10.1186/s10033-023-00961-y",
    doi = "10.1186/s10033-023-00961-y",
    openalex = "W4388976366",
    references = "doi1010160001616056900335, doi1010160036974889902524, doi101016s1359646200003948"
}

In this paper, the impact of low-density DC electric field treatment (LDCT) on the microstructure and mechanical properties of cast TC4 titanium alloy (CTC4) was investigated. The findings indicate that the driving force for the current provided by LDCT enhances the texture of CTC4. When the current density is sufficiently high, the induced recrystallization effect weakens the texture, leading to an isotropic state. The polygonization of grain boundaries in the LDCT state CTC4 has been identified, along with the emergence of a secondary α phase due to recrystallization. Additionally, this study highlights the phenomenon of preferential nucleation and growth occurring at the grain boundaries. LDCT induces a grain refinement effect in the CTC4 material, whereby the average grain size of the LDCT3 sample decreases from 31.05 μm in the untreated sample to 28.93 μm. The observed reduction in dislocation density in the LDCT states is believed to result from the diffusion of impurity atoms and vacancies. The observation of dislocation plugging at the inner grain boundary of the LDCT3 sample suggests that the electron wind promotes dislocation slip toward the grain boundary. Furthermore, the simultaneous enhancement of strength and toughness in the LDCT state of the CTC4 alloy has been achieved. The LDCT3 sample demonstrates superior performance, exhibiting noteworthy increases of 7.7%, 22.0%, and 10.9% in tensile strength, elongation, and fracture energy, respectively, compared to the untreated sample. The significant role of non-thermal effects in LDCT and the mechanism of atomic diffusion induced by this effect are discussed. The origins of dislocation motion and phase transition are elucidated from the perspective of atomic diffusion.

@article{doi101016jjmrt202411238,
    author = "Li, Guirong and Zhang, J.J. and Liu, C.X. and Wang, H.M. and Zhang, Ji and Nan, Hai and Zhao, Bowen and Guo, Shuangfeng and Luo, Yong and Liu, Y.",
    title = "Microstructure and property alterations and toughening mechanism of cast TC4 alloy by solid state treatment with low-density DC electric field",
    year = "2024",
    journal = "Journal of Materials Research and Technology",
    abstract = "In this paper, the impact of low-density DC electric field treatment (LDCT) on the microstructure and mechanical properties of cast TC4 titanium alloy (CTC4) was investigated. The findings indicate that the driving force for the current provided by LDCT enhances the texture of CTC4. When the current density is sufficiently high, the induced recrystallization effect weakens the texture, leading to an isotropic state. The polygonization of grain boundaries in the LDCT state CTC4 has been identified, along with the emergence of a secondary α phase due to recrystallization. Additionally, this study highlights the phenomenon of preferential nucleation and growth occurring at the grain boundaries. LDCT induces a grain refinement effect in the CTC4 material, whereby the average grain size of the LDCT3 sample decreases from 31.05 μm in the untreated sample to 28.93 μm. The observed reduction in dislocation density in the LDCT states is believed to result from the diffusion of impurity atoms and vacancies. The observation of dislocation plugging at the inner grain boundary of the LDCT3 sample suggests that the electron wind promotes dislocation slip toward the grain boundary. Furthermore, the simultaneous enhancement of strength and toughness in the LDCT state of the CTC4 alloy has been achieved. The LDCT3 sample demonstrates superior performance, exhibiting noteworthy increases of 7.7\%, 22.0\%, and 10.9\% in tensile strength, elongation, and fracture energy, respectively, compared to the untreated sample. The significant role of non-thermal effects in LDCT and the mechanism of atomic diffusion induced by this effect are discussed. The origins of dislocation motion and phase transition are elucidated from the perspective of atomic diffusion.",
    url = "https://doi.org/10.1016/j.jmrt.2024.11.238",
    doi = "10.1016/j.jmrt.2024.11.238",
    openalex = "W4404801177",
    references = "doi1010801040843620222080177"
}

Biomagnetic monitoring has rapidly emerged as a valuable tool in urban atmospheric pollution (UAP) assessment due to its high spatial resolution, complementing traditional monitoring systems. This review systematically elucidates the principles of plant dust retention and the factors influencing it, while also reviewing the advancements in global research on UAP monitoring through the magnetic properties of various plant species. We provide a comprehensive analysis of the current applications of biomagnetic monitoring in UAP and identify critical challenges, including species-specific monitoring discrepancies, complex pollution sources, and non-standardized sample preparation methods. Additionally, we propose future research directions to address these challenges and enhance the efficacy of biomagnetic monitoring in UAP.

@article{doi101016jscitotenv2025178518,
    author = "Chen-Ming, Gu and Bo, Wang and Xiao-Han, Sun",
    title = "Biomagnetic monitoring of urban atmospheric pollution: A review of magnetic signatures from different types of plants.",
    year = "2025",
    journal = "The Science of the total environment",
    abstract = "Biomagnetic monitoring has rapidly emerged as a valuable tool in urban atmospheric pollution (UAP) assessment due to its high spatial resolution, complementing traditional monitoring systems. This review systematically elucidates the principles of plant dust retention and the factors influencing it, while also reviewing the advancements in global research on UAP monitoring through the magnetic properties of various plant species. We provide a comprehensive analysis of the current applications of biomagnetic monitoring in UAP and identify critical challenges, including species-specific monitoring discrepancies, complex pollution sources, and non-standardized sample preparation methods. Additionally, we propose future research directions to address these challenges and enhance the efficacy of biomagnetic monitoring in UAP.",
    url = "https://pubmed.ncbi.nlm.nih.gov/39824111/",
    doi = "10.1016/j.scitotenv.2025.178518",
    pmid = "39824111"
}

Light alloys have irreplaceable advantages such as high specific strength and low density. They are indispensable structural materials in aerospace, military, and marine engineering. It is an enduring research hotspot to prepare high-strength and high-toughness light alloys to play a more significant role in advanced engineering applications. As a new method to improve the mechanical properties of light alloys, the magnetic field-assisted process can produce magnetoplastic effects. Therefore, in this paper, research progress on the magnetoplastic effects of light alloys assisted by magnetic fields was reviewed, and the effects of magnetic fields on dislocations, grain refinement, precipitation kinetics, phase transformation, and mechanical properties of light alloys were elucidated. Magnetic field treatment transforms radical pairs from the ground state to the excited state, which reduces the resistance between dislocations and obstacles, facilitating dislocation depinning. Moreover, magnetic field can promote grain refinement and phase transformation, increase precipitation kinetics, and synergistically improve strength and elongation. Finally, the prospects of magnetic field-assisted processes of light alloys were discussed.

@article{doi101016s1003632625668981,
    author = "CHE, Bo and HUANG, Liang and XIE, Bing-xin and ZHOU, Wei",
    title = "Research progress on magnetoplastic effects of light alloys assisted by magnetic field",
    year = "2025",
    journal = "Transactions of Nonferrous Metals Society of China",
    abstract = "Light alloys have irreplaceable advantages such as high specific strength and low density. They are indispensable structural materials in aerospace, military, and marine engineering. It is an enduring research hotspot to prepare high-strength and high-toughness light alloys to play a more significant role in advanced engineering applications. As a new method to improve the mechanical properties of light alloys, the magnetic field-assisted process can produce magnetoplastic effects. Therefore, in this paper, research progress on the magnetoplastic effects of light alloys assisted by magnetic fields was reviewed, and the effects of magnetic fields on dislocations, grain refinement, precipitation kinetics, phase transformation, and mechanical properties of light alloys were elucidated. Magnetic field treatment transforms radical pairs from the ground state to the excited state, which reduces the resistance between dislocations and obstacles, facilitating dislocation depinning. Moreover, magnetic field can promote grain refinement and phase transformation, increase precipitation kinetics, and synergistically improve strength and elongation. Finally, the prospects of magnetic field-assisted processes of light alloys were discussed.",
    url = "https://doi.org/10.1016/s1003-6326(25)66898-1",
    doi = "10.1016/s1003-6326(25)66898-1",
    openalex = "W7116107051",
    references = "doi1010801040843620222080177"
}

Mobile electric field sensors are indispensable across various domains. Optically levitated nano-resonators have demonstrated unique advantages in electric field sensing, yet their integration remains challenging. By integrating the optical path, circuit, and vacuum systems, we have successfully developed a mobile electric field device based on optically levitated nano-resonators with dimensions under 1,200 mm × 549 mm × 524 mm. The optical probe employs microcrystalline glass with housing dimensions of 60 mm × 70 mm × 200 mm to ensure miniaturization. Simultaneously, to reduce the measurement impact of external electric fields, simulations were also conducted on the structural components inside the chamber. Experimental results demonstrate that the sensor achieves a thermal noise equivalent electric field detection sensitivity of 800 μV/cm/Hz 1/2 with optimal sensitivity observed at 129.6 kHz within the low-frequency band. This device provides a new approach to developing mobile electric field sensors operating at frequencies below megahertz and paves a practical path for engineering and practical application of levitated optomechanics in vacuum.

@article{doi1034133adi0090,
    author = "Shi, Yun‐Jie and Chen, Zhiming and Zhang, Yizhou and Wang, Yuehao and He, Peitong and Zhu, Xunmin and Zheng, Yi and Wang, Yingying and Guo, Leilei and Wu, Bin and Fu, Zhenhai and Gao, Xiaowen and Hu, Huizhu",
    title = "A Mobile Electric Field Sensor Device Based on Optically Levitated Nano-resonators",
    year = "2025",
    journal = "Advanced Devices \& Instrumentation",
    abstract = "Mobile electric field sensors are indispensable across various domains. Optically levitated nano-resonators have demonstrated unique advantages in electric field sensing, yet their integration remains challenging. By integrating the optical path, circuit, and vacuum systems, we have successfully developed a mobile electric field device based on optically levitated nano-resonators with dimensions under 1,200 mm × 549 mm × 524 mm. The optical probe employs microcrystalline glass with housing dimensions of 60 mm × 70 mm × 200 mm to ensure miniaturization. Simultaneously, to reduce the measurement impact of external electric fields, simulations were also conducted on the structural components inside the chamber. Experimental results demonstrate that the sensor achieves a thermal noise equivalent electric field detection sensitivity of 800 μV/cm/Hz 1/2 with optimal sensitivity observed at 129.6 kHz within the low-frequency band. This device provides a new approach to developing mobile electric field sensors operating at frequencies below megahertz and paves a practical path for engineering and practical application of levitated optomechanics in vacuum.",
    url = "https://doi.org/10.34133/adi.0090",
    doi = "10.34133/adi.0090",
    openalex = "W4408403216",
    references = "doi1010801040843620222080177"
}

@incollection{marshallNoneparticle,
    author = "Marshall, Jeffrey S. and Li, Shuiqing",
    title = "Particle Interactions with Electric and Magnetic Fields",
    year = "None",
    booktitle = "Adhesive Particle Flows",
    url = "https://doi.org/10.1017/cbo9781139424547.009",
    doi = "10.1017/cbo9781139424547.009",
    openalex = "W2498258698",
    pages = "223-255",
    references = "doi101002anie200701812, doi101002anie200905281, doi1010160021999187901409, doi1010160376042167900036, doi101017cbo9780511574498, doi101021ac971063b, doi101038324446a0, doi101038366442a0, doi101163156855203763593958, doi102307jctv131bv375"
}