Equation of solvated ion oscillations in solution under an external periodic electric field

An equation describing ion oscillations with respect to solvent molecules is derived as a result of the consideration of the interaction of an external electric field with free and bound charges in the volume of a salt solution in a polar dielectric liquid. An analysis of the equation shows that the ion motion represents a drift toward one of the electrodes forming the field in the electroinsulated solution volume if amplitudes and durations of sinusoidal field half-periods are different.     

The method of calculating forced oscillations in nonlinear discrete-time systems under periodic external actions

We consider a method for calculating forced oscillations in nonlinear discrete-time systems under periodic external actions. The method is based on representing the stationary oscillations in the form of an invariant set of nonlinear discrete point mappings and allows one to calculate the nonlinear-system response in the steady-state regime. The examples of using this method for calculating forced oscillations in the first- and second-order nonlinear recursive systems under the harmonic-signal action on such systems are presented.     

Dynamics of the intermediate state and domain walls in an external oscillating magnetic field

We study the dynamics of 90-degree domain walls in the intermediate state of antiferromagnets, the state being realized in a first-order spin-flop transition in an external magnetic field. We show that an additional oscillating external magnetic field leads to a drift in the domain walls and find the dependence of the drift velocity on the amplitude, frequency, and polarization of the oscillating field. Finally, we discuss the possibility of the domain structure drifting as a whole. Zh. éksp. Teor. Fiz. 112, 1374–1385 (October 1997)     

Dynamic oscillations of coupled domain walls

In domain wall (DW) excitation experiments, nonlinearity (NL) intrinsic to the DW dynamics is often hard to distinguish from perturbation due to the confining potential or DW distortion. Here we numerically investigate the dynamic oscillations of magnetostatically coupled DWs: a system well understood in the quasistatic limit. NL is observed, even for a harmonic potential, due to the intrinsic DW motion. This behavior is principally dependent on terms normally associated with the DW canonical momentum and is in contrast with a NL restoring potential. This NL is not observable in quasistatic measurements, relatively insensitive to the confining potential, and may be tuned by the nanowire parameters. The shown NLs are present in any DW restoring potential and must be accounted for when probing DW potential landscapes.     

Superalgebras for three interacting particles in an external magnetic field

In this paper we discuss interacting particles in an external magnetic field. By comparing the Schr?dinger equation of three interacting particles with the associated Laguerre differential equation, we obtain the energy spectrum which corresponds to indices n_i and m_i. Finally by using the so called factorization method we obtain the raising and lowering operators. These operators are supersymmetric structures related to the Hamiltonian partner. Also these operators lead to the realization of Heisenberg Lie superalgebras with two, four and six supercharges.     

Directed motion of domain walls in biaxial ferromagnets under the influence of periodic external magnetic fields

Directed motion of domain walls (DWs) in a classical biaxial ferromagnet placed under the influence of periodic unbiased external magnetic fields is investigated. Using the symmetry approach developed in this article the necessary conditions for the directed DW motion are found. This motion turns out to be possible if the magnetic field is applied along the easiest axis. The symmetry approach prohibits the directed DW motion if the magnetic field is applied along any of the hard axes. With the help of the soliton perturbation theory and numerical simulations, the average DW velocity as a function of different system parameters such as damping constant, amplitude, and frequency of the external field, is computed.     

The retarded energy shift and pair polarizabilities of interacting atoms in an external field

The interaction energy of two atoms in the presence of an external electrostatic field is evaluated up to sixth order with the help of covariant field-theoretical perturbation theory. The divergent Feynman diagrams entering the calculation are resummed according to a systematic procedure that has been developed in a previous paper. The pair polarizability and first hyperpolarizability that give the response of the interacting atoms to the external field are subsequently obtained from the energy shift by virtue of a Hellmann-Feynman theorem. The retardation effects showing up in the pair polarizability are discussed in detail.     

The dynamics of domain walls in an easy-plane magnet in the field of an acoustic wave

The drift of a 180° domain wall is studied in an easy-plane weak two-sublattice ferromagnet subject to an elastic-stress field generated by an acoustic wave. The dependences of the drift velocity on the amplitude and polarization of the acoustic wave are found. The conditions of the drift of a stripe domain structure are determined.     

Furry representation for fermions interacting with an external gauge field

We have obtained a Furry representation for the fermion sector (spin 1/2) of any gauge theory based on a semisimple compact group with an external field breaking down the stability of the vacuum. We have found expressions for the generating functionals of the matrix elements of the processes and averages, and have determined all the required types of propagators.Tomsk Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 83–89, April, 1995.     

Chaotic dynamics of interacting domain walls in uniaxial ferromagnetic films

The nonlinear dynamics of a periodic system of interacting domain walls in a thin ferromagnetic uniaxial film with transverse anisotropy is examined. The interaction between the domain walls takes place through the magnetostatic demagnifying fields of the domains. The equations of motion derived for such a system of walls are solved numerically by a 4–5th-order Runge-Kutta scheme, while the uniformity of the distributions of the phase trajectory, the form of the Poincaré cross section, and the spectral density of the vibrations serve as indicators of the type of oscillations. All the known types of oscillations are observed in a computer simulation of this nonlinear system: periodic, quasiperiodic, and chaotic. The computational results have a universal character for uniaxial, highly-anisotropic ferromagnetic films having a strip domain structure, since the results can be easily scaled for materials with different magnetic characteristics. Fiz. Tverd. Tela (St. Petersburg) 39, 2036–2039 (November 1997)     

Nonlinear oscillations of an uncharged conducting drop in an external uniform electrostatic field

The problem of nonlinear oscillations of the finite amplitude of an uncharged drop of an ideal incompressible conducting liquid in an external uniform electrostatic field is solved for the first time by analytical asymptotic methods. The problem is solved in an approximation quadratic in amplitude of the initial deformation of the equilibrium shape of the drop and in eccentricity of its equilibrium spheroidal deformation. Compared with the case of nonlinear oscillations of charged drops in the absence of the field, the curvature of the vertices of uncharged drops nonlinearly oscillating in the field is noticeably higher, whereas the number of resonant situations (in the sense of internal resonant interaction of modes) is much smaller.     

The effect of an external field on an interface,entropic repulsion

We consider the effects of an external potential -h∑f(S _x ) withh>0,f increasing, on the equilibrium state of a system with a Hamiltonian of the form $$H^0 (S) = \sum\limits_{\left\langle {xy} \right\rangle } {\Phi (S_x - S_y )} ,S_x \in R,x \in Z^d ,d \geqslant 3$$ Φ even and convex, e.g.,Φ(t)=1/2t ² andf(t)=signt. This can be thought of as a model of the interactions between a random interface S _x and a “soft” wall. We show that the random surface is (entropically) repelled to infinity for allh>0, i.e., with probability one,S _x ≥K, for anyK ε R.     

Application of nonlinear dynamic system approach to oscillations of mercury arc in external magnetic field

Oscillations of an arc burning in mercury vapours and exposed to an external axial magnetic field were recorded. The fast Fourier transform, phase portrait construction and attractor dimension calculations show that the experimental results present a nonlinear dynamic system with a rich scenario of various metastable states and transitions between them. The system develops spontaneously with time mainly through a formation of new subharmonic frequencies. Among the different transition types especially the chaotic transitions may result in relatively long intervals of chaotic behaviour which are interesting from the point of view of the nonlinear system studies.     

Painleve property of anharmonic systems with an external periodic field

The Painlevé property of anharmonic systems with an external periodic field is investigated. This property tell us that the only movable singularities exhibited by the solutions are poles. The Painlevé property can serve to distinguish between integrable and nonintegrable systems.     

The external field effect on transient radiation of an ultrarelativistic particle

An external field determining the law of particle motion was shown to change the intensity of transient radiation in the ultrarelativistic case. The angular and frequency distribution of transient radiation in an external field was obtained. The possibility of determining the energy of an ultrarelativistic particle from the measured azimuthal asymmetry of particle transient radiation in an external field was discussed.     

Brownian motion in periodic potentials; nonlinear response to an external force

The Brownian motion of particles in a periodic potential in response to a constant external force is investigated. By expanding the distribution function into Hermite-functions and into a Fourier-series, the Fokker-Planck-equation is transformed into a set of coupled equations for the expansion coefficients. These equations are solved by a continued fraction method for matrices. This continued fraction for the matrices converges for large, intermediate and even for very small damping constants. The mobility, the kinetic and potential energy for various damping constants and external forces are given for a cos-potential. The current-voltagecharacteristic of the Josephson tunneling junction is also shown.     

Effect of a pulsed magnetic field on the nonlinear dynamics of vortexlike domain walls in magnetic films

The Landau-Lifshitz equation is numerically solved to study the nonlinear dynamic behavior of domain walls with the 2D vortexlike magnetization distribution in magnetically uniaxial films that have in-plane anisotropy and are exposed to a pulsed magnetic field. It is shown that a pulsed magnetic field H _p may induce transitions between various steady wall motions that differ in magnetization distribution. Solitary rectangular pulses, as well as a regular train of rectangular pulses, may be used to control the period of nonlinear dynamic transformations of the wall internal structure and the related period of variation of the wall velocity.