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The properties that characterize the stationary Hall effect in a Hall bar are derived from the Langevin equations describing the Brownian motion of an ensemble of interacting moving charges in a constant externally applied electromagnetic field. It is demonstrated that a non-uniform current density (a) superimposes on the injected one, (b) is confined in a boundary layer located near the edges over the Debye–Fermi length scale, (c) results from coupling between diffusion and conduction, and (d) arises because of charge accumulation at the edges. The theory can easily be transposed to describe the Hall effect in metals, semi-conductors, and plasmas and agrees with standard and previously published results. [ABSTRACT FROM AUTHOR]

Analytical formulas for the electric birefringence response of interacting polar and anisotropically polarizable molecules due to a uniform alternating electric field are derived using Berne's forced rotational diffusion model [B. J. Berne, J. Chem. Phys. 62, 1154 (1975)] in the nonlinear version described by Warchol and Vaughan [J. Chem. Phys. 71, 502 (1979)]. It is found for noninteracting molecules that the signal consists of a frequency-dependent DC component superimposed on an oscillatory part with a frequency twice that of the AC driving field. However, unlike noninteracting molecules, the AC part strongly deviates from its dilute counterpart. This suggests a possible way of motivating new experimental studies of intermolecular interactions involving electro-optical methods and complementary nonlinear dielectric relaxation experiments. [ABSTRACT FROM AUTHOR]

Long range dipole-dipole interactions in the thermal fluctuations of the magnetization of an assembly of single-domain ferromagnetic particles are considered, ignoring orientational correlations between the particles, so that the evolution of the magnetization orientations may be described by a nonlinear Fokker-Planck equation (FPE) reducing to the usual linear one in the limit of infinite dilution [W. F. Brown Jr., Phys. Rev. 130, 1677 (1963)]. The thermally activated relaxation time scale of the assembly is estimated, leading to a simple and transparent modification of the axially symmetric asymptotes for the superparamagnetic relaxation time. [ABSTRACT FROM AUTHOR]

The magnetization spectrum and reversal time of uniaxial single-domain ferromagnetic particles driven by an ac magnetic field of arbitrary strength applied along the easy axis are evaluated by solving the infinite hierarchy of recurrence equations for the Fourier components of the relaxation functions governing the frequency dependence of the magnetization. A simple analytic equation for the reversal time is also obtained via the mean first passage time method exhibiting pronounced nonlinear effects such as a rapid decrease in the reversal time as the strength of the ac field increases. For weak ac fields, the results agree with perturbation theory. [ABSTRACT FROM AUTHOR]

The statistical mechanics of arbitrary holonomic scleronomous systems subjected to arbitrary external forces is described by specializing the Lagrange and Hamilton equations of motion to those of the Brownian motion on a manifold. In this context, the Klein-Kramers and Smoluchowski equations are derived in covariant form, and it is demonstrated that these equations have equilibrium solutions corresponding to the Gibbs distribution, in agreement with standard thermodynamics. At last, the Langevin dynamics corresponding to the Smoluchowski limit is found to exactly correspond to the Brownian motion on a smooth manifold. These results find significant applications in the study of several statistical properties of constrained molecular assemblies (e.g. polymers) of interest in chemistry, physics and biology. [ABSTRACT FROM AUTHOR]

The individual motion of a colloidal particle is described by an overdamped Langevin equation. When rotational degrees of freedom are relevant, these are described by a corresponding Langevin process. Our purpose is to show that the microscopic local density of colloids, in terms of a space and rotation state, also evolves according to a Langevin equation. The latter can then be used as the starting point of a variety of approaches, ranging from dynamical density functional theory to mode-coupling approximations. [ABSTRACT FROM AUTHOR]

Abstract: The nonlinear ac stationary response of the magnetization of noninteracting uniaxial single-domain ferromagnetic particles acted on by superimposed dc and ac magnetic fields applied along the anisotropy axis is evaluated from the Fokker–Planck equation, expressed as an infinite hierarchy of recurrence equations for Fourier components of the relaxation functions governing longitudinal relaxation of the magnetization. The exact solution of this hierarchy comprises a matrix continued fraction, allowing one to evaluate the ac nonlinear response and reversal time of the magnetization. For weak ac fields, the results agree with perturbation theory. It is shown that the dc bias field changes substantially the magnetization dynamics leading to new nonlinear effects. In particular, it is demonstrated that for a nonzero bias field as the magnitude of the ac field increases the reversal time first increases and having attained its maximum at some critical value of the ac field, decreases exponentially. [Copyright &y& Elsevier]

Abstract: The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel’nikov and Meshkov [V.I. Mel’nikov, S.V. Meshkov, J. Chem. Phys. 85 (1986) 1018] is applied to the inertial rotational Brownian motion of a fixed axis rotator in a potential , where is the angle specifying the orientation of the rotator and and are constants. It is shown that in the neighbourhood of (flat barrier), the Mel’nikov–Meshkov method must suitably be adapted so that the effect of a nonparabolic barrier top can be correctly accounted for in the calculation of the relaxation time. The results obtained are compared with numerical calculations of the longest relaxation time (inverse smallest nonvanishing eigenvalue) using a matrix continued fraction algorithm and reasonable agreement is obtained for and all values of the dissipation parameter. [Copyright &y& Elsevier]

Abstract: The classical approximation of the quantum model dealing with the IR spectra of weak hydrogen bond involving indirect damping [B. Boulil, O. Henri-Rousseau, P. Blaise, Chem. Phys. 126 (1988) 263] is obtained. It transforms, via a crude approximation concerning the interpretation of stochastic averages, into the classical Robertson–Yarwood (RY) model [G. Robertson, J. Yarwood, Chem. Phys. 32 (1978) 267]. [Copyright &y& Elsevier]

The nonlinear stationary ac response of the magnetization of assemblies consisting of (i) noninteracting uniaxial superparamagnetic nanoparticles with aligned easy axes and (ii) randomly oriented nanoparticles subjected to superimposed ac and dc bias magnetic fields of arbitrary strength and orientation is calculated by averaging Gilbert's equation augmented by a random field. The magnetization dynamics of uniaxial particles driven by a strong ac field applied at an angle to the easy axis of the particle (so that the axial symmetry is broken) alters drastically leading to new nonlinear effects due to coupling of the thermally activated magnetization reversal mode with the precessional modes via the driving ac field. In particular, the high frequency response reveals significant nonlinear effects in the precessional motion with significant consequences for the dynamic hysteresis and ultra-fast switching of the magnetization following an ultrafast change in the applied field. [ABSTRACT FROM AUTHOR]

External dc bias-field effects on the nonlinear dielectric relaxation and dynamic Kerr effect of a system of permanent dipoles in a uniaxial mean-field potential are studied via the rotational Brownian motion model postulated in terms of the infinite hierarchy of differential-recurrence equations for the statistical moments fn(t) = 〈Pn〉(t) (the expectation value of the Legendre polynomials Pn). By solving these equations, the nonlinear dielectric and Kerr-effect ac stationary responses are evaluated for arbitrary dc field strength via perturbation theory in the ac field. Simple analytic equations based on the large separation of the time scales of the fast intrawell and slow overbarrier (interwell) relaxation processes are also derived. [ABSTRACT FROM AUTHOR]