QED2+1 radiation effects in a strong magnetic field

We develop the eigenfunction method for the Dirac operator in a background magnetic field in the (2+1)-dimensional quantum electrodynamics (QED₂₊₁). In the eigenfunction repressentation, we find the exact solutions and the Green's functions of the Dirac equation in a strong constant homogeneous magnetic field in 2+1 dimensions. In the one-loop QED₂₊₁ approximation, we derive the effective Lagrangian, the density of vacuum fermions induced by the field, and the electron mass operator in a homogeneous background magnetic field. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 3, pp. 412–423, December, 1999.     

On the motion of a solid in a magnetic field

The problem of the motion of a magnetic solid in a constant uniform magnetic field, taking gyromagnetic effects into account, is considered. The equations of motion are derived, the Hamiltonian structure is studied, and the cases of integrability indicated. Certain classes of stationary motions are studied and their stability examined.

The gyromagnetic effects arise because the electrons have magnetic and mechanical spin moments /1/. The rotation of the body causes it to become magnetized (the Barnett effect) and when a freely suspended body is magnetized, it begins to rotate (the Einsteinde Haas effect). It is found that gyromagnetic phenomena must be taken into account when analysing the motion of gyroscopic precision systems.     

Nonequilibrium state of a ferroelectric in a strong magnetic field

Vitebsk Branch of the Institute of Solid-State Physics and Semiconductors, Belorussian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 78, No. 1, pp. 147–153, January, 1989.     

Harmonic and anharmonic oscillations of a cylindrical plasma in the presence of a uniform axial magnetic field and a steady axial current

In the present note we have studied the harmonic and anharmonic oscillations of cylindrical plasma using Lagrangian formalism. In order to study the harmonic oscillations, the equations are linearized and the resulting equation for the displacement has been numerically solved. For situations present in thermonuclear reactors, the presence of axial magnetic field is found necessary to make the periods of oscillation to become comparable with the time required for the thermonuclear reactions to set in. A detailed analysis of the anharmonic oscillations reveals that the significant interaction is between the first and the second mode. The fundamental period of anharmonic oscillation is more than the corresponding period of harmonic oscillations by 9·2%. Graphs have been drawn for the amplitudes of relative variations in density and magnetic field and of the time-varying part of anharmonic oscillation.     

Quantum corrections to the conductivity of a two-dimensional disordered system in a strong magnetic field

A system of noninteracting electrons moving in a magnetic field and a field of randomly distributed impurities is considered. An exact expression is obtained for the sum of the series of maximally crossed diagrams; it is valid in an arbitrary magnetic field. It is shown that in the two-dimensional case the relative magnitude of the corrections to the conductivity due to this series reaches 60% in the center of the lower Landau sub-band.Physicotechnical Institute of the Urals Branch of the Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 3, pp. 486–495, March, 1993.     

Vacuum of the electroweak gauge theory in a strong magnetic field in A heat bath

Expressions are obtained for the thermodynamic potential of a gas of electrically charged vector bosons in a magnetic field and the effective potential of the Weinberg-salam theory in a strong magnetic field in a heat bath. In the single-loop approximation, an estimate is obtained for the value of the critical temperatureT _cr corresponding to the phase transition in the Weinberg-Salam theory in a magnetic field. It is shown that it is possible to determine correctly the total probability for production of aW ⁺W^– boson pair from the vacuum by an ultrastrong magnetic field in a heat bath, and an expression is obtained for this probability. It is argued that in the Weinberg-Salam theory the restoration of the spontaneously broken symmetry atT=0,B>B _cr ⁽¹⁾ is simultaneously accompanied by dynamical symmetry breaking of the theory.State University, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 3, pp. 446–456, March, 1995.     

Peristaltic motion of a Jeffrey fluid under the effect of a magnetic field in a tube

This study is concerned with the analysis of peristaltic motion of a Jeffrey fluid in a tube with sinusoidal wave travelling down its wall. The fluid is electrically conducting in the presence of a uniform magnetic field. Analytic solution is carried out for long wavelength and low Reynolds number considerations. The expressions for stream function, axial velocity and axial pressure gradient have been obtained. The results for pressure rise and frictional force per wavelength obtained in the analysis have been evaluated numerically and discussed briefly. The significance of the present model over the existing models has been pointed out by comparing the results with other theories. It is further noted that under the long wavelength approximation, the retardation time has no effect in the present analysis.     

Resonance effects in the field of a stationary electromagnetic wave and a constant magnetic field

We analyze the interaction of a charged relativistic particle with the electromagnetic field given by a superposition of a stationary wave and a constant magnetic field. The refraction coefficient of the medium is taken different from one. We investigate the problem in the low-signal approximation. To test the results, we used computer simulation of the original system with two scales of the variation rate of the variables taken into account.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 64–71, January, 2005.     

Global well-posedness and decay estimates of strong solutions to a two-phase model with magnetic field

In this paper, we consider the Cauchy problem for a two-phase model with magnetic field in three dimensions. The global existence and uniqueness of strong solution as well as the time decay estimates in $H^2({\mathbb{R}}^3)$ are obtained by introducing a new linearized system with respect to $(n^{\gamma }?{\stackrel{?}{n}}^{\gamma },n?\stackrel{?}{n},P?\stackrel{?}{P},u,H)$ for constants $\stackrel{?}{n}\ge 0$ and $\stackrel{?}{P}>0$, and doing some new a priori estimates in Sobolev Spaces to get the uniform upper bound of $(n?\stackrel{?}{n},n^{\gamma }?{\stackrel{?}{n}}^{\gamma })$ in $H^2({\mathbb{R}}^3)$ norm.     

On the motion of visco-elastic electrically conducting liquid in the presence of a magnetic field

Zusammenfassung Es wird die Strömung einer viskoelastischen, elektrisch leitenden Flüssigkeit untersucht auf Grund der elektromagnetischen Grundgleichung und der für solche Flüssigkeiten geltenden Bewegungsgleichungen. Im besonderen wird die Strömung zwischen parallelen Platten erörtert. Sie ist charakterisiert durch zwei dimensionslose Kennzahlen, die Hartmannsche Zahl und die Elastizitätszahl. Das elastische Verhalten bewirkt eine Verflachung des Geschwindigkeitsprofils und verändert auch den Druck und die Schubspannungen.

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Notations x ₁,x ₂,x ₃ space coordinates - B magnetic induction vector - E electric intensity - H magnetic field - D displacement vector - J current density vector - _e E electrostatic force - V×B current density due to the motion of the fluid - _e V convection current - _e excess charge density - electrical conductivity - magnetic permeability - dielectric constant - =1/ magnetic diffusivity - V=v ¹ i+v ² j+v ³ k velocity vector - v ₁= ₁/ kinematic viscosity - ₁ coefficient of viscosity - _c coefficient of cross-viscosity - v _c = _c / kinematic cross-viscosity - density of the fluid - relaxation time - S _j ⁱ stress-tensor - d _j ⁱ strain-tensor - x, y, z dimensionless coordinates - L spacing between the planes, taken as the characteristic length - U ₀ characteristic velocity - f non-dimensional velocity - H non-dimensionalx-component of the magnetic field.     

A numerical study of flows driven by a rotating magnetic field in a square container

The influence of the geometry on the magnetically driven flow is studied by means of numerical simulations. Low–frequency, low–induction and low–interaction conditions are assumed. The rotating magnetic field (RMF) gives rise to a time–independent magnetic body force, computed via the electrical potential equation and Ohm's law and a time–dependent part that is neglected due to the low interaction parameter. Flow results of the cylindrical and square container are compared with respect to the magnetic body force, time–averaged velocity fields, first flow instabilities and Reynolds stress tensors. The dependency of the maximal velocity magnitude and the intensity of the magnetic induction is identical in axisymmetric and non–axisymmetric containers and in good agreement with Davidson's theory. However, significant differences are recognized, for instance, in the distribution of the Reynolds stress tensors. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flow engendered by the time-varying motion of a porous plate in the presence of a magnetic field

The problem of flow of an electrically conducting viscous liquid due to the time-varying motion of an infinite porous plate has been studied. There is a uniform magnetic field imposed transversely to the plate and the magnetic lines of force are taken to be fixed relative to the fluid. Exact solutions for the velocity field and the skin-friction have been obtained and some particular cases have been discussed. The effect of suction parameter and magnetic field strength on the flow characteristics have been depicted through several graphs and tables.     

Resonant response of a strong electromagnetic wave beam to a gravitational wave in a static magnetic field

Concrete forms of resonant response (ER) for a strong electromagnetic (EM) wave beam (photon flux) propagating in a static magnetic field to a standing gravitational wave (gravitons) are given, and the corresponding perturbation solutions and resonant conditions are obtained. It is found that perturbed EM fields (PEMFs) contain three new components with frequencies Io,* w,l and ωP_g respectively. In the case of ω_e⋙ω_g, the PEMFs are manifested as the EM wave beams with frequency ω_e and a standing EM wave with ω_g. The former and the background EM wave beam (BE-MWB) have the same propagating direction, while in the case of ω_g⋙ω_e, all PEMFs are expressed as the standing EM waves with frequency ω_g. The resonant response occurs in two cases of ω_e = 1/2 ω_g andω_e, = ω_g only. Then not only the first order perturbed energy fluxes (PEFs) propagating in the same and opposite directions of the BEMWB can be generated, but also radial and tangential PEFs which are perpendicular to the above directions can be produced. This effect might provide a new way for the EM detection of the gravitational waves (GWs). Moreover, the possible schemes of displaying perturbed effects induced by the standing GW withh = 10^-33 - 10^-35 and λ_g = 0.1 m at the level of the single photon avalanche and in a typicla laboratory dimension are reviewed.     

Global well-posedness of strong solutions to a two-phase model with magnetic field for large oscillations in three dimensions

In this paper, we consider Cauchy problem for a two-phase model with magnetic field in three dimensions. Under some smallness assumptions on the initial data but possibly large oscillations, we obtain the global well-posedness of strong solution as well as its large-time behavior. Compared with Wen and the first author's work [28] where global well-posedness and large time behavior of strong solutions were obtained subject to smallness of initial data in $H^2$ norm, we only need the smallness of initial energy which allows large oscillations of the initial data.     

Numerical solution of the nonlinear problem of motion of a long rectangular plate in a variable magnetic field

The coupled problem of motion of a long rectangular plate in a variable magnetic field is analyzed in the framework of the geometrically nonlinear theory of thin shells. The proposed numerical procedure is applied to estimate the effect of external electromagnetic and mechanical fields on the stress- strain state of the plate.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 72, pp. 37–42, 1990.