Existence of Dyons in the Coupled Georgi�CGlashow�CSkyrme Model

We prove the existence of a continuous family of finite-energy particle-like solutions in the coupled Georgi–Glashow–Skyrme model carrying both electric and magnetic charges, known as dyons. Due to the presence of electricity and the Minkowski spacetime signature, we need to solve a variational problem with an indefinite action functional. Our results show that, while the magnetic charge is uniquely determined by the topological monopole number, the electric charge of a solution can be arbitrarily prescribed in an open interval.     

Existence of dyons in minimally gauged Skyrme model via constrained minimization

We prove the existence of electrically and magnetically charged particle-like static solutions, known as dyons, in the minimally gauged Skyrme model developed by Brihaye, Hartmann, and Tchrakian. The solutions are spherically symmetric, depend on two continuous parameters, and carry unit monopole and magnetic charges but continuous Skyrme charge and non-quantized electric charge induced from the ?t Hooft electromagnetism. The problem amounts to obtaining a finite-energy critical point of an indefinite action functional, arising from the presence of electricity and the Minkowski spacetime signature. The difficulty with the absence of the Higgs field is overcome by achieving suitable strong convergence and obtaining uniform decay estimates at singular boundary points so that the negative sector of the action functional becomes tractable.     

Neutral Fermion with a Magnetic Moment in External Electromagnetic Fields

The interaction between a massive neutral fermion with a static (spin) magnetic dipole moment and an external electromagnetic field is described by the Dirac–Pauli equation. Exact solutions of this equation are obtained along with the corresponding energy spectrum for an axially symmetric external magnetic field and for some centrally symmetric electric fields. It is shown that the spin–orbital interaction of a neutral fermion with a magnetic moment determines both the characteristic properties of the quantum states and the fermion energy spectrum. It is found that (1) the discrete energy spectrum of a neutral fermion depends on the projection of the fermion spin on a certain quantization axis, (2) the ground energy level of a fermion in these electric fields as well as the energy levels of all bound states with a fixed value of the quantum number characterizing the projection of the fermion spin in the electric field E = er is degenerate and the degeneration order is countably infinite, and (3) the energy spectra of neutral fermions and antifermions with spin magnetic moments are symmetric in centrally symmetric fields. Bound states of a neutral fermion with a magnetic moment in an external electric field do exist even if the Dirac–Pauli equation does not explicitly contain the term with the fermion mass. In addition, in centrally symmetric electric fields, there exist a countably infinite set of pairs of isolated charge-conjugate zero-energy solutions of the Dirac–Pauli equation.     

Eddy-current braking of a translating solid bar by a magnetic dipole

The paper addresses the problem of a conducting rectangular bar of square cross-section which is moving with constant velocity in the field of an arbitrarily oriented magnetic dipole. The braking Lorentz force on the bar is obtained by FEM and compared with the analytical solution for a moving infinite plate in the field of a magnetic dipole [2]. The computation of the induced currents requires solution of a Laplace equation with mixed boundary conditions for the electric potential inside the moving bar. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

规范场中Skyrme模型单位拓扑电荷的双荷子（英文）

Dyons are an important family of topological solitons carrying both electric and magnetic charges and the presence of a nontrivial temporal component of the gauge field essential for the existence of electricity often makes the analysis of the underlying nonlinear equations rather challenging since the governing action functional assumes an indefinite form. In this work, developing a constrained variational technique, We establish an existence theorem for the dyon solitons in a Skyrme model coupled with SO(3)-gauge fields, formulated by Brihaye, Kleihaus, and Tchrakian. These solutions carry unit monopole and Skyrme charges.     

Scattering of a neutral fermion with anomalous magnetic moment by a charged straight thin thread

We consider the scattering of a massive neutral fermion with an anomalous magnetic moment in the electric field of a homogeneously charged straight thin thread from the standpoint of the quantum mechanical problem of constructing a self-adjoint Hamiltonian for the nonrelativistic Dirac-Pauli equation. Using the solutions obtained for the self-adjoint Hamiltonian, we investigate the scattering of the neutral fermion in the electric field of a thread oriented perpendicular to the plane of fermion motion (the Aharonov-Casher effect). We find expressions for the scattering amplitude and cross section of neutral fermions in the electric field of the thread. We show that the scattering amplitude and cross section depend both on the direct interaction between the fermion anomalous magnetic moment and the electric field and on the polarization of the fermionic beam in the initial state.     

Solution of the problem of charge motion in crossed electric and magnetic fields

Using the method of first integrals, we find an exact solution for the relativistic motion of a charge in orthogonal and uniform electric and magnetic fields with respect to laboratory time and for any value of the dimensionless governing parameter equal to the ratio of the magnetic field strength to the electric field strength.     

Neutral Fermion Having Electric and Magnetic Moments in an External Electromagnetic Field

We show that in 2+1 dimensions, the Dirac equation for a neutral fermion possessing electric and magnetic dipole moments in an external electromagnetic field reduces to the Dirac equation for a charged fermion in a external field characterized by a certain 3-pseudo-vector potential. The effective charge of the neutral fermion is determined by its dipole moments. The effects of coupling electric and magnetic moments of the neutral fermion to the external electromagnetic field seem to be inseparable in physical experiments of any type. We find an exact solution of the Dirac equation for a massive neutral fermion with electric and magnetic dipole moments in a external plane-wave electromagnetic field. We derive expressions for the fermionic vacuum current induced by neutral fermions in the presence of external electromagnetic fields.     

Reducibility of pointlike problems

We show that the pointlike and the idempotent pointlike problems are reducible with respect to natural signatures in the following cases: the pseudovariety of all finite semigroups in which the order of every subgroup is a product of elements of a fixed set \(\pi \) of primes; the pseudovariety of all finite semigroups in which every regular \(\mathcal J\)-class is the product of a rectangular band by a group from a fixed pseudovariety of groups that is reducible for the pointlike problem, respectively graph reducible. Allowing only trivial groups, we obtain \(\omega \)-reducibility of the pointlike and idempotent pointlike problems, respectively for the pseudovarieties of all finite aperiodic semigroups (\(\mathsf{A}\)) and of all finite semigroups in which all regular elements are idempotents (\(\mathsf{DA}\)).     

Hamilton operator and the semiclassical limit for scalar particles in an electromagnetic field

We successively apply the generalized Case-Foldy-Feshbach-Villars (CFFV) and the Foldy-Wouthuysen (FW) transformation to derive the Hamiltonian for relativistic scalar particles in an electromagnetic field. In contrast to the original transformation, the generalized CFFV transformation contains an arbitrary parameter and can be performed for massless particles, which allows solving the problem of massless particles in an electromagnetic field. We show that the form of the Hamiltonian in the FW representation is independent of the arbitrarily chosen parameter. Compared with the classical Hamiltonian for point particles, this Hamiltonian contains quantum terms characterizing the quadrupole coupling of moving particles to the electric field and the electric and mixed polarizabilities. We obtain the quantum mechanical and semiclassical equations of motion of massive and massless particles in an electromagnetic field. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 398–411, September, 2008.     

An interface crack moving between magnetoelectroelastic and functionally graded elastic layers

A constant crack moving along the interface of magnetoelectroelastic and functionally graded elastic layers under anti-plane shear and in-plane electric and magnetic loading is investigated by the integral transform method. Fourier transforms are applied to reduce the mixed boundary value problem of the crack to dual integral equations, which are expressed in terms of Fredholm integral equations of the second kind. The singular stress, electric displacement and magnetic induction near the crack tip are obtained asymptotically and the corresponding field intensity factors are defined. Numerical results show that the stress intensity factors are influenced by the crack moving velocity, the material properties, the functionally graded parameter and the geometric size ratios. The propagation of the moving crack may bring about crack kinking, depending on the crack moving velocity and the material properties across the interface.     

Inverse scattering for the magnetic Schrödinger operator

We show that fixed energy scattering measurements for the magnetic Schrödinger operator uniquely determine the magnetic field and electric potential in dimensions n?3. The magnetic potential, its first derivatives, and the electric potential are assumed to be exponentially decaying. This improves an earlier result of Eskin and Ralston (1995) [5] which considered potentials with many derivatives. The proof is close to arguments in inverse boundary problems, and is based on constructing complex geometrical optics solutions to the Schrödinger equation via a pseudodifferential conjugation argument.     

Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space

We consider the first mixed problem for the Vlasov–Poisson equations with an external magnetic field in a half-space. This problem describes the evolution of the density distributions of ions and electrons in a high temperature plasma with a fixed potential of electric field on a boundary. For arbitrary potential of electric field and sufficiently large induction of external magnetic field, it is shown that the characteristics of the Vlasov equations do not reach the boundary of the halfspace. It is proved the existence and uniqueness of classical solution with the supports of charged-particle density distributions at some distance from the boundary, if initial density distributions are sufficiently small.     

Quantized planary dynamics in orthogonal magneto-electrostatic fields

At the first quantization level, we deal with the planary dynamics of a charged scalar evolving in static orthogonal magnetic and electric fields. Working in a relativistic approach, we get the quantum eigenstates and the energy spectrum exhibiting a non-linear dependence on the exterior fields and the particle momentum parameter. Analyzing the generalized Landau-type energy levels, we point out a shift of the Larmor pulsation, due to the electrostatic field and derive a critical induction-energy spectrum. The same has been done for strong magnetic fields and a compulsory relation between the particle momentum and the electric field intensity has been obtained. For quasi-on-shell particles, moving in either strong or weak magnetic field, we derive the completely possible momentum spectrum. It turns out that, in extremely faint electrostatic fields, it yields the same momentum quantization.     

Influence of moving magnetic field on three dimensional Couette flow

A three dimensional steady fully developed MHD Couette flow of a viscous incompressible electrically conducting fluid is analysed. The lower stationary porous plate is subjected to a periodic injection velocity and the upper porous plate in uniform motion to a constant suction velocity. A magnetic field of uniform strength applied normal to the planes of the plates is fixed with the moving plate. Neglecting the induced magnetic field, an approximate solution for the flow field is obtained and discussed with the help of graphs.     

Influence of moving magnetic field on three dimensional Couette flow

A three dimensional steady fully developed MHD Couette flow of a viscous incompressible electrically conducting fluid is analysed. The lower stationary porous plate is subjected to a periodic injection velocity and the upper porous plate in uniform motion to a constant suction velocity. A magnetic field of uniform strength applied normal to the planes of the plates is fixed with the moving plate. Neglecting the induced magnetic field, an approximate solution for the flow field is obtained and discussed with the help of graphs.     

Asymptotics of the Spectrum and Eigenharmonics of a Discrete String Containing a Bead of Vanishing Mass

A discrete string with fixed endpoints containing a finite number of pointlike masses (beads) is considered. The behavior of the eigenfrequences and eigenharmonics of the string is studied as one of the masses tends to zero. Bibliography: 1 title.     

Electromagnetic force on the wall of cylindrical waveguide

When transverse electric (TE) wave or transverse magnetic (TM) wave propagates inside a cylindrical waveguide, the electromagnetic force on the wall is investigated. The characteristics of surface charge, current, electric force, magnetic force and electromagnetic force are studied. The results show that the electric force is tension and magnetic force is press. The surface density of electromagnetic force on the wall can be calculated by the difference between magnetic and electric energy density there. For TE wave, the electromagnetic force distribution on the walls may be either tension or pressure in general. However, the electromagnetic force is always pressure for TM wave.     

Electromagnetic interaction of moving conductors with magnets: kinematic solutions for infinitely long square and cylindrical geometries

The electromagnetic drag force on a point dipole near a moving conductor caused by the induced electric currents is investigated by numerical and analytical computations. Our focus is on prototypical configurations for Lorentz force velocimetry, i.e. velocity measurement from the electromagnetic drag force on the dipole. We examine the particular cases of conducting infinite bars of square or round cross-section, which are moving with constant velocity in the field of arbitrary oriented magnetic dipole. In addition, we study the laminar liquid-metal flow in a square duct. The motion of the conductor is prescribed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)