Statistical properties of passive scalar in a random flow with a strong shear component

We study mixing of passive scalar by a chaotic velocity field with a relatively strong regular shear component. We show that the tail of partition distribution function (PDF) of coarse-grained passive scalar field differs qualitatively from the corresponding asymptotics in the case of isotropic flow statistics.     

Magnetic correlations in ferromagnets with quenched random fields

The critical dynamics of the relaxational model for ferromagnets in quenched random fields is studied within the framework of the -expansion (=6–d). The shape functionf _x () is obtained exactly atT _c ; it remains finite when the frequency vanishes. The static and dynamic properties of the model belowT _c are also considered. The equation of state and the static correlation function are related to those of the (d–2)-dimensional pure systems. The dynamic response functionG is obtained for zero momentum. The scaling form of the random correlation functionC ^(s) , which determines the spin-glass order parameter, is obtained. The coexistence curve singularities of ,G andC ^(s) when the number of spin componentsn2, are studied.     

Controlling multiparticle correlations with a strong laser field

The collective interaction via a surrounding thermalized electromagnetic reservoir of a two-level multiatom sample with an external applied strong coherent field is investigated. In a small sample following Dicke’s model, even at the exact resonances, very strong pumping leads to a complete transfer of the population into a particular dressed-state. This way very large Rabi frequencies are shown to modify and control the interatomic correlations in a system of spatially separated atoms of few wavelengths extend.     

Spatial correlations in the near field of random media

The conventional coherence theory suggests that the fields radiated by statistically homogeneous sources correlate over spatial regions of the order of the wavelength irrespective of the distance from the surface of the source. Contrary to these predictions, we show that the spatial correlations of optical fields in close proximity of highly scattering, randomly inhomogeneous media depend on this distance and, moreover, their extent can be significantly smaller than the wavelength. The contribution of evanescent fields is experimentally demonstrated and the coherence length in the near field is shown to relate to the coherence properties at the surface which are, in turn, determined by the structural characteristics of the random media.     

Magnetic properties of mixed Ising system with random field

A spin-1/2 and spin-3/2 mixed Ising system in a random field is studied by the use of effective-field theory with correlations. The phase diagrams and thermal behaviours of magnetizations are investigated numerically for the honeycomb lattice (z=3) and square lattice (z=4) respectively. The tricritical behaviours for both honeycomb and square lattices, as well as the reentrant behaviour for the square lattice are found.     

Magnetic field line random walk in non-axisymmetric turbulence

Including a random component of a magnetic field parallel to an ambient field introduces a mean perpendicular motion to the average field line. This effect is normally not discussed because one customarily chooses at the outset to ignore such a field component in discussing random walk and diffusion of field lines. A discussion of the basic effect is given, indicating that any random magnetic field with a non-zero helicity will lead to such a non-zero perpendicular mean motion. Several exact analytic illustrations are given of the effect as well as a simple numerical illustration.     

Wall shear rate distribution for flow in random sphere packings

The wall shear rate distribution P(gamma) is investigated for pressure-driven Stokes flow through random arrangements of spheres at packing fractions 0.1< or =varphi< or =0.64. For dense packings, P(gamma) is monotonic and approximately exponential. As varphi-->0.1, P(gamma) picks up additional structure which corresponds to the flow around isolated spheres, for which an exact result can be obtained. A simple expression for the mean wall shear rate is presented, based on a force-balance argument.     

Magnetic field-induced orientational phases of ferronematics in shear flow

We examine the effect of shear flow on the orientational phase transitions induced by a magnetic field in ferronematic liquid crystals. Continuum approach based on the generalized Leslie–Ericksen theory is used to describe the dynamics of ferronematic liquid crystals. We consider three orientations of the magnetic field in a plane of shear flow. Stationary solutions for the director and the magnetization are obtained as functions of the magnetic field strength for different values of material parameters. Our results show that shear flow can lead to the shift of the field thresholds or to a “smoothing” of the magnetic field-induced transitions in ferronematics. In the limiting case of pure nematic liquid crystals, we revealed threshold effects, which are unstipulated by the orientational elasticity of a liquid crystal, in contrast to the conventional Fréedericksz transition.     

The localization properties of a random steady flow on a lattice

We consider a random stationary vector field on a multidimensional lattice and investigate flow-connected subsets of the lattice invariant under the action of the associated flow. The subsets of primary interest are cycles, and vortices each of which is the set of orbits terminating in the same cycle. We prove that with probability 1 each vortex only involves a finite number of sites of the lattice. Under the assumption of independence of the vector field in different sites, we find that with probability 1 the vortices exhaust all possible maximal flowconnected invariant subsets of the lattice if and only if the probability of existence of a cycle is positive. Thus, if cycles exist, a particle under the action of the flow only moves within a bounded region, i.e., it is completely localized.     

Pairwise correlations in a three-partite quantum system from a prequantum random field

Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility to represent the averages of quantum observables (including correlations of observables on subsystems of a composite system) as averages with respect to fluctuations of classical random fields. In view of the PCSFT terminology, quantum states are classical random fields. The aim of our approach is to represent all quantum probabilistic quantities by means of classical random fields. We obtain the classical-random-field representation for pairwise correlations in three-partite quantum systems. The three-partite case (surprisingly) differs substantially from the bipartite case. As an important first step, we generalized the theory developed for pure quantum states of bipartite systems to the states given by density operators.     

Magnetic field rotation in the screw gallium flow

The magnetic field induced by the nonstationary screw flow of gallium in a toroidal channel has been investigated experimentally using a gallium prototype of the sodium apparatus developed in the frame of the experimental dynamo program at the Institute of Continuous Media Mechanics, Perm, Russia. The experimental set-up is a rapidly rotating toroidal channel subjected to abrupt braking. The screw flow is initiated by inertial forces pushing liquid gallium through diverters. The regular structure of the induced magnetic field is generated about 0.1 s after the stop of the channel and persists up to 1 s. The induced field is measured by sensors placed outside the channel. The inductive effects observed are attributed to the mean screw flow. The decay laws of the induced regular magnetic field and turbulent magnetic fluctuations are studied.Received: 27 August 2004, Published online: 5 November 2004PACS: 47.65. + a Magnetohydrodynamics and electrohydrodynamics - 07.55.Dd Generation of magnetic fields     

Noise correlations in shear flows

We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time correlations. We show that, in the presence of white noise, time correlations of transversal velocity components are exponential and that correlations of the longitudinal components are exponential with an algebraic prefactor. Cross correlations between transversal and downstream components are strongly asymmetric and provide a clear indication of non-normal amplification. We suggest experimental tests of our predictions. Received 26 February 2002 / Received in final form 11 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: bruno.eckhardt@physik.uni-marburg.de RID="b" ID="b"Also at: Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India     

Time correlations and persistence probability of a Brownian particle in a shear flow

This paper presents an adaptive lag synchronization based method for simultaneous identification of topology and parameters of uncertain general complex dynamical networks with and without time delays. Based on Lyapunov stability theorem and LaSalle??s invariance principle, an adaptive controller is designed to realize lag synchronization between drive and response systems, meanwhile, identification criteria of network topology and system parameters are obtained. Numerical simulations illustrate the effectiveness of the proposed method.     

磁场剪切对离子温度梯度模带状流产生的影响

对离子温度梯度模湍流非线性流体方程进行了解耦处理,得到包含磁场剪切效应的带状流与漂移波相互作用的非线性动力学方程.采用调制不稳定性的四波相互作用模型,研究了磁场剪切对带状流产生的影响.研究表明,在k_//值较小的范围内,当|k_//|增加时,带状流的增长率也呈增加的趋势. 关键词： 托卡马克等离子体 离子温度梯度模湍流 带状流 磁场剪切     

Nonlinear dielectric relaxation of polar molecules in a strong ac electric field: steady state response

The nonlinear dielectric relaxation ac stationary response of an assembly of rigid polar molecules acted on by strong superimposed external dc E0 and ac E1(t)=E(1) cos omegat electric fields is evaluated in the context of the noninertial rotational diffusion model. The calculation proceeds by expanding the relaxation functions f(n)(t) (the expectation value of the Legendre polynomials P(n)), which describe the nonlinear relaxation of the system, as a Fourier series in the time domain. Hence, an infinite hierarchy of recurrence equations for the Fourier components of f(n)(t) is obtained. The exact solution of this hierarchy can be obtained in terms of a matrix continued fraction, so allowing us to evaluate the ac nonlinear response. For a weak ac field our results are in complete agreement with previous solutions obtained by perturbation methods. Diagrams showing the behavior of the in-phase and out-of-phase components of the electric polarization are presented.     

Polarization correlations in two-dimensional random media

Abstract

Second-order polarization correlation functions, both theoretical and experimental, are presented for optical waves propagating through a highly random multiple-scattering two-dimensional (2D) medium. For normal incidence and scattering, a 2D medium is found to be fully described by two material parameters, one of which is complex. Simple formulae are developed for these parameters in terms of the anisotropy of the medium and the scattering mean free path. General theoretical expressions are given for polarized and unpolarized correlation functions and also for the intensity statistics of the scattered light for arbitrary input polarization states. Experimental data are presented for both types of correlation function and for the intensity statistics, and are found to be in reasonably good agreement with the theory.     

Density of states in the presence of a strong magnetic field and random impurities

A supersymmetric formalism is used to rederive a recent beautiful result of Wegner concerning the density of state of an electron gas in the presence of a strong magnetic field and impurities. The derivation is simple and applicable to any (local) distribution of scatterers. Explicit formulae are given in two dimensions. A Poisson distribution of scatterers leads to an interesting condensation phenomenon when the magnetic field is increased.     

Accretion in strong field gravity with eXTP

In this paper we describe the potential of the enhanced X-ray Timing and Polarimetry(eXTP) mission for studies related to accretion flows in the strong field gravity regime around both stellar-mass and supermassive black-holes. eXTP has the unique capability of using advanced "spectral-timing-polarimetry" techniques to analyze the rapid variations with three orthogonal diagnostics of the flow and its geometry, yielding unprecedented insight into the inner accreting regions, the effects of strong field gravity on the material within them and the powerful outflows which are driven by the accretion process.