Models of plastic depinning of driven disordered systems

Two classes of models of driven disordered systems that exhibit historydependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The second class allows for proliferation of topological defects due to the interplay of strong disorder and drive. In mean field theory both models exhibit a tricritical point as a function of disorder strength. At weak disorder depinning is continuous and the sliding state is unique. At strong disorder depinning is discontinuous and hysteretic.     

Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method

A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r） in the form of Coulomb potential. In the pseudospin（p-spin） symmetry setting Σ = Cps and Δ = V（r）, an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin–orbit coupling number κ. Special attention is devoted to the caseΣ = 0 for which p-spin symmetry is exact. The Laplace transform approach（LTA） is used in our calculations. Some numerical results are obtained and compared with those of other methods.     

Depinning dynamics of driven colloids with random pinning： a numerical study

Using Langevin simulations, we have investigated numerically the depinning dynamics of driven two-dimensional colloids subject to the randomly distributed point-like pinning centres. With increasing strength of pinning, we find a crossover from elastic to plastic depinnings, accompanied by an order to disorder transition of state and a substantial increase in the depinning force. In the elastic regime, no peaks are found in the differential curves of the velocity－force dependence (VFD) and the transverse motion is almost none. In addition, the scaling relationship between velocity and force is found to be valid above depinning. However, when one enters the plastic regime, a peak appears in the differential curves of VFD and transverse diffusion occurs above depinning. Furthermore, history dependence is found in the plastic regime.     

Collective diffusion of Brownian particles with square well and hydrodynamic interaction

The low wavenumber collective diffusion coefficient of a semi-dilute suspension of spherical Brownian particles interacting via square well potential and hydrodynamic pair interaction is considered. The first two nonvanishing terms of an expansion in powers of the wavenumber are calculated. Analytical expressions are found for extremely narrow wells and in the limit of large well diameters.     

Collective motion of active particles in environmental noise

We study the collective motion of active particles in environmental noise, where the environmental noise is caused by noise particles randomly diffusing in two-dimensional space. We show that active particles in a noisy environment can self organize into three typical phases: polar liquid, band, and disordered gas states. In our model, the transition between band and disordered gas states is discontinuous. Giant number fluctuation is observed in the polar liquid phase. We also compare our results with the Vicsek model and show that the interaction with noise particles can stabilize the band state to very low noise condition. This band structure could recruit most of the active particles in the system, which greatly enhances the coherence of the system. Our findings of complex collective behaviors in environmental noise help us to understand how individuals modify their self-organization by environmental factors, which may further contribute to improving the design of collective migration and navigation strategies.     

The role of the exchange and magnetic dipole interactions in the superconductors with helical magnetic ordering

The helical ordering of localized moments in the magnetic superconductors is considered by taking into account the exchange interaction of localized moments and electrons as well as their interaction via the magnetic field. We show that the structure of superconducting phase with helical magnetic order is determined mainly by the exchange interaction. The magnetic dipole interaction fixes only the direction of the helix wave vector so that it is transverse.     

Pair production and vacuum polarization of vector particles with electric dipole moments and anomalous magnetic moments

The matrix 8-component Dirac-like form of the P-odd equations for boson fields of spin 1 and 0 are obtained and the symmetry group of the equations is derived. We found exact solutions of the field equation for vector particles with arbitrary electric and magnetic moments in external constant and uniform electromagnetic fields. The differential probability of pair production of vector particles with electric dipole moments and anomalous magnetic moments by an external constant and uniform electromagnetic field has been found using exact solutions. We have calculated the imaginary and real parts of the electromagnetic field Lagrangian that takes into account the vacuum polarization of vector particles. Received: 14 April 2001 / Revised version: 13 July 2001 / Published online: 19 September 2001     

Analytic theory of wall configuration and depinning mechanism in magnetic nanostructure with perpendicular magnetic anisotropy

We present an analytic theory of the domain wall depinning in magnetic nanostructure with perpendicular magnetic anisotropy. The variational principle reveals that the wall is bent in the form of a circular arc which intersects the structure boundaries perpendicularly. The radius is inversely proportional to the magnetic field. With increasing the field the radius shrinks, followed by depinning from the constriction when the arc is not geometrically allowed. The depinning field is proportional to the sine of the constriction angle and the inverse of the constriction width. The validity of the theory is confirmed by comparison with the micromagnetic simulation.     

Influence of magnetic dipole and magnetoelastic interactions on the phase states of 2D non-Heisenberg ferromagnetic with complex exchange interactions

The phase states of the 2D non-Heisenberg ferromagnetic with anisotropic bilinear and biquadratic exchange interactions are investigated. The limiting cases of the system under consideration are the two-dimensional XY-model with biquadratic exchange interaction and the isotropic Heisenberg ferromagnetic. The account of the magnetic dipole interaction leads to the realization of spatially inhomogeneous quadrupolar phase. The stability regions of various phase transitions for different values of the material parameters are studied. The phase diagram is built. Besides, the temperature phase transitions are investigated. The influence of the magnetoelastic interaction on the formation of the long-range quadrupolar order is determined.     

Magnetophoresis and diffusion of colloidal particles in a thin layer of magnetic fluids

Experimental and theoretical studies were carried out to investigate the spatial distribution of colloidal particles in magnetic fluids formed under the influence of magnetophoresis and gradient diffusion in a strong magnetic field. Several theoretical models, describing the equilibrium concentration profiles for rigid chain-like and quasispherical aggregates, are discussed. The experiment was made for four samples of magnetic fluids, differing in the average diameter of magnetic particles and the width of the particle size distribution. The analysis of the experimental data shows that the aggregates essentially change the concentration profile, making it nonlinear even in small (2 mm) magnetic fluid samples. Good agreement between the experimental and theoretical curves is observed in the case when the aggregates contain on the average 40-50 particles. The average diameter of single particles, calculated from the concentration profile curves, coincides with the average diameter, found from the magnetogranulometric analysis.     

具有幂次相互作用的磁性粒子凝聚过程的数值研究

在扩散限制凝聚模型的基础上引入粒子的自旋自由度(包括自旋向上和向下),并假设粒子间存在幂次Ising磁相互作用,采用Monte Carlo方法研究了在不同相互作用力程情况下磁性粒子的分形生长规律.模拟结果表明,当粒子间以反铁磁方式耦合时,凝聚体中的粒子自旋交替凝聚.当粒子间以铁磁方式耦合时,凝聚体中粒子的自旋分布与相互作用力程有关:对于短程作用系统,凝聚体中存在大小不同的自旋畴块,即为铁磁生长;而对于长程相互作用系统,凝聚体中的自旋出现反常分布,即中心区域是近似反铁磁生长的结构,其外围后续生长的粒子却保持 关键词： 幂次相互作用 扩散限制凝聚模型 自旋     

Levitation, lift, and bidirectional motion of colloidal particles in an electrically driven nematic liquid crystal

We study electric-field-induced dynamics of colloids in a nematic cell, experimentally and by computer simulations. Solid particles in the nematic bulk create director distortions of dipolar type. Elastic repulsion from the walls keeps the particles in the middle of cell. The ac electric field reorients the dipoles and lifts them to top or bottom, depending on dipole orientation. Once near the walls, the colloids are carried along two antiparallel horizontal directions by nematic backflow. Computer simulations of the backflow agree with the experiment.     

Magnetic interactions in a classical system of charged particles with intrinsic magnetic moments

A classical, quasirelativistic Hamiltonian is found for a system of charged particles with intrinsic magnetic moments. It represents a generalization of the Darwin Hamiltonian and is the classical analog of the Breit Hamiltonian.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 73–76, November, 1973.     

Automatic detection of colloidal particles based on a shape regularized integrated active contour model

Manual segmentation of single colloidal particle in suspension encounters a bottleneck when a number of defocused particles simultaneously exist in an image. In this paper, we describe an image processing algorithm for extracting individual particle from digitized microscope images of colloidal suspensions. We propose a particle detection and location solution using a shape regularized integrated active contour model (ACM). Compared with existing methods where active contour models are not applied well to deal with multiple objects in complicated background, the proposed approach can automatically identify and locate multiple particles by combining characteristics of the particles such as shape, boundary and region. A regularization term is defined by prior information of specific shape, which is able to drive the shape of evolving curve toward the shape prior gradually. To locate the centers of the particles, the Hough transform is applied. Experimental results using polystyrene beads as sample particles reveal that the method has high efficiency and ability to deal with colloidal particles.     

Magnetic dipole and electric quadrupole responses of elliptic quantum dots in magnetic fields

The magnetic dipole (M1) and electric quadupole (E2) responses of two-dimensional quantum dots with an elliptic shape are theoretically investigated as a function of the dot deformation and applied static magnetic field. Neglecting the electron-electron interaction we obtain analytical results which indicate the existence of four characteristic modes, with different B-dispersion of their energies and associated strengths. Interaction effects are numerically studied within the time-dependent local-spin-density and Hartree approximations, assessing the validity of the non-interacting picture. Received 29 November 2001 Published online 6 June 2002     

Quasi-2D Monte Carlo simulations of a colloidal dispersion composed of magnetic plate-like particles with magnetic moment normal to the particle axis

We have investigated aggregation phenomena of a colloidal dispersion composed of magnetic plate-like particles by means of Monte Carlo simulations. Such plate-like particles have been modelled as disk-like particles with magnetic moment normal to the particle axis at the particle centre, with the section shape of a spherocylinder. The main objective of the present study is to clarify the influences of the magnetic field strength and magnetic interactions between particles on particle aggregation phenomena. We have concentrated our attention on a quasi-2D system from an application point of view such as the development of surface quality changing technology using such magnetic plate-like particles. A magnetic field is applied along the direction perpendicular to the plane of the monolayer. Internal structures of particle aggregates are discussed quantitatively in terms of radial distribution and orientational pair correlation functions. For the case of strong magnetic interactions between particles, particles form long column-like clusters with their magnetic moments alternating in direction between the neighbouring particles. These tendencies appear under circumstances of a weak applied magnetic field. However, as the magnetic field strength increases, particles incline towards the magnetic field direction, so that particles do not form such clusters.     

Brownian particles with long- and short-range interactions

We develop the kinetic theory of Brownian particles with long- and short-range interactions. Since the particles are in contact with a thermal bath fixing the temperature T, they are described by the canonical ensemble. We consider both overdamped and inertial models. In the overdamped limit, the evolution of the spatial density is governed by the generalized mean field Smoluchowski equation including a mean field potential due to long-range interactions and a generically nonlinear barotropic pressure due to short-range interactions. This equation describes various physical systems such as self-gravitating Brownian particles (Smoluchowski-Poisson system), bacterial populations experiencing chemotaxis (Keller-Segel model) and colloidal particles with capillary interactions. We also take into account the inertia of the particles and derive corresponding kinetic and hydrodynamic equations generalizing the usual Kramers, Jeans, Euler and Cattaneo equations. For each model, we provide the corresponding form of free energy and establish the H-theorem and the virial theorem. Finally, we show that the same hydrodynamic equations are obtained in the context of nonlinear mean field Fokker-Planck equations associated with generalized thermodynamics. However, in that case, the nonlinear pressure is due to the bias in the transition probabilities from one state to the other leading to non-Boltzmannian distributions while in the former case the distribution is Boltzmannian but the nonlinear pressure arises from the two-body correlation function induced by the short-range potential of interaction. As a whole, our paper develops connections between the topics of long-range interactions, short-range interactions, nonlinear mean field Fokker-Planck equations and generalized thermodynamics. It also justifies from a kinetic theory based on microscopic processes, the basic equations that were introduced phenomenologically to describe self-gravitating Brownian particles, chemotaxis and colloidal suspensions with attractive interactions.     

Magnetization relaxation of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics driven by DC/AC magnetic field

The response of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics subjected to alternating current(AC) or direct current(DC) bias magnetic field is evaluated by the reaction–diffusion equation for the probability distribution function of the molecular concentration in the spherical coordinate system. The magnetization function and the probability distribution function of the magnetic particles in the reaction system are derived by using the Legendre polynomials and Laplace transform. We discuss the characteristics of magnetization and probability distribution of the magnetic particles with different anisotropic parameters driven by a DC and AC magnetic fields, respectively. It is shown that both the magnetization and the probability distribution decrease with time increasing due to the reaction process. The uniformity of the probability distribution and the amplitude of the magnetization are both affected by the anisotropic parameters.Meanwhile, the difference between the case with linear reaction dynamics and the non-reaction case is discussed.