On the Asymptotic Behavior of an Ornstein-Uhlenbeck Process with Random Forcing

We study the asymptotic behavior of an inertial tracer particle in a random force field. We show that there exists a probability measure, under which the process describing the velocity and environment seen from the vantage point of the moving particle is stationary and ergodic. This measure is equivalent to the underlying probability for the Eulerian flow. As a consequence of the above we obtain the law of large numbers for the trajectory of the tracer. Moreover, we prove also some decorrelation properties of the velocity of the particle, which lead to the existence of a non-degenerate asymptotic covariance tensor. The research of both authors was supported by the Polish Committee for Scientific Research (KBN) grant No. 2PO3A03123.     

Mixing Properties for Mechanical Motion¶of a Charged Particle in a Random Medium

We study a one-dimensional semi-infinite system of particles driven by a constant positive force F which acts only on the leftmost particle of mass M, called the heavy particle (the h.p.), and all other particles are mechanically identical and have the same mass m < M. Particles interact through elastic collisions. At initial time all neutral particles are at rest, and the initial measure is such that the interparticle distances ξ _i are i.i.d. r.v. Under conditions on the distribution of ξ which imply that the minimal velocity obtained by each neutral particle after the first interaction with the h.p. is bigger than the drift of an associated Markovian dynamics (in which each neutral particle is annihilated after the first collision) we prove that the dynamics has a strong cluster property, and as a consequence, we prove existence of the discrete time limit distribution for the system as seen from the first particle, a ψ-mixing property, a drift velocity, as well as the central limit theorem for the tracer particle. Received: 22 March 2000 / Accepted: 8 December 2000     

Analyses of radiation force and torque on a spherical particle near a substrate illuminated by a focused Laguerre-Gaussian beam

We present the analyses of radiation force and torque on a spherical particle illuminated by Laguerre-Gaussian beam. Since Laguerre-Gaussian beam has angular momentum, the particle can be rotated by illumination of Laguerre-Gaussian beam. Radiation forces and torques for a silver sphere and a silicon sphere near the silver substrate are analyzed. We found that the maximum torque on silicon sphere is about five times higher than the maximum torque on silver sphere and fine control of the focused spot is required to push the particle to the substrate.     

Microscopic Shape of Shocks in a Domain Growth Model

Considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities, e.g., the inviscid Burgers equation for the simple exclusion process. The physical solutions of these partial differential equations develop discontinuities, called shocks. The microscopic structure of these shocks is of much interest and far from being well understood. We introduce a domain growth model in which we find a stationary (in time) product measure for the model, as seen from a defect tracer or second class particle, traveling with the shock. We also show that under some natural assumptions valid for a wider class of domain growth models, no other model has stationary product measure as seen from the moving defect tracer.     

Colloids in cholesterics: size-dependent defects and non-stokesian microrheology

We simulate a colloidal particle (radius R) in a cholesteric liquid crystal (pitch p) with tangential order parameter alignment at the particle surface. The local defect structure evolves from a dipolar pair of surface defects (boojums) at small R/p to a pair of twisted disclination lines wrapping around the particle at larger values. On dragging the colloid with small velocity v through the medium along the cholesteric helix axis (an active microrheology measurement), we find a hydrodynamic drag force that scales linearly with v but superlinearly with R-in striking violation of Stokes' law, as generally used to interpret such measurements.     

Particle pairing using genetic algorithms for PIV

This paper presents a new particle pairing algorithm using “Genetic Algorithms” for DPIV (Digital Particle Image Velocimetry), which are searching algorithms for obtaining an optimal solution based on the mechanism of evolution. The particle pairing between two tracer images with a constant time interval is needed to obtain a velocity vector field. Since the algorithm adopts a fitness function which totally evaluates the similarity between respective small particle patterns in the two tracer images over the field, it promises to give a more correct velocity vector distribution than the conventional PTV (Particle Tracking Velocimetry) which identifies each particle based on its local information. In addition, a particle pattern matching for the similarity is performed after correcting fluid rotation. It therefore is robust against a high particle density and an increase in the time interval. The algorithm is applied to the PIV standard images distributed through the Internet (http://www.vsj.or.jp/piv). It gives a correct velocity vector distribution as a result even if a pair of the successive images has a large time interval.     

带电粒子在电磁场中动态受力平衡条件

导体的电平衡条件为E =0 ,这是静电学中一个重要结论 ,但它显然不是相对论协变的 .由于洛伦兹力公式F =q(E +v×B)为相对论协变式 ,故带电粒子 (包括导体中的自由电子 )在电磁场中动态受力平衡条件即应为E +v×B =0 .这个条件是相对论协变的 ,即它在任何惯性系中均成立 .     

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density ${\to \infty}$ ). Our estimates allow us to interchange the thermodynamic with the mean-field limit.     

Self-adaptive behavior of nunchakus-like tracer induced by active Brownian particles

We design a nunchakus-like tracer and investigate its self-adaptive behavior in an active Brownian particle (ABP) bath via systematically tuning the self-propelled capability and density of ABPs. Specifically, the nunchakus-like tracer will have a stable wedge-like shape in the ABP bath when the self-propelled force is high enough. We analyze the angle between the two arms of the tracer and the velocity of the joint point of the tracer. The angle exhibits a non-monotonic phenomenon as a function of active force. However, it increases with density of ABPs increasing monotonically. A simple linear relationship between the velocity and the self-propelled force is found under the highly active force. In other words, the joint points of the tracer diffuse and the super-diffusive behavior can make the relation between the self-propelled force and the density of ABPs persist longer. In addition, we find that the tracer can flip at high density of ABPs. Our results also suggest the new self-adaptive model research of the transport properties in a non-equilibrium medium.     

On the theory of slowing down gracefully

We discuss the transport of a tracer particle through the Bose?CEinstein condensate of a Bose gas. The particle interacts with the atoms in the Bose gas through two-body interactions. In the limiting regime where the particle is very heavy and the Bose gas is very dense, but very weakly interacting (??mean-field limit??), the dynamics of this system corresponds to classical Hamiltonian dynamics. We show that, in this limit, the particle is decelerated by emission of gapless modes into the condensate (Cerenkov radiation). For an ideal gas, the particle eventually comes to rest. In an interacting Bose gas, the particle is decelerated until its speed equals the propagation speed of the Goldstone modes of the condensate. This is a model of ??Hamiltonian friction??. It is also of interest in connection with the phenomenon of ??decoherence?? in quantum mechanics. This note is based on work we have carried out in collaboration with D Egli, I M Sigal and A Soffer.     

Influence of a uniform driving force on tracer diffusion in a one-dimensional hard-core lattice gas

The influence of a uniform driving force on tracer diffusion is investigated for a one-dimensional lattice gas where particles jump stochastically to unoccupied neighboring sites. A new, simple calculation is presented for the diffusion coefficient of a tracer particle with respect to its average drift, obtained recently by rigorous methods by De Masi and Ferrari. A theoretical expression describing the tracer particle mean square displacement approximately for all times is derived and found to be in excellent agreement with the results of Monte Carlo simulations.     

Friction in a Model of Hamiltonian Dynamics

We study the motion of a heavy tracer particle weakly coupled to a dense ideal Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations describing a process of emission of Cerenkov radiation of sound waves into the Bose-Einstein condensate along the particle’s trajectory. The emission of Cerenkov radiation results in a friction force with memory acting on the tracer particle and causing it to decelerate until it comes to rest.

“A moving body will come to rest as soon as the force pushing it no longer acts on it in the manner necessary for its propulsion.”—— Aristotle     

Einstein Relation for a Tagged Particle in Simple Exclusion Processes

 It is known that the rescaled position of a tagged particle in symmetric simple exclusion processes converges to a diffusion. If now the tracer particle is driven by a small force, then it picks up a velocity. The Einstein relation states that in the limit, this velocity is proportional to the small force, and the constant of proportionality can be computed from the diffusion matrix of the tracer particle with no driving force. Such a relation is believed to be generally valid. In this article we establish its validity for all symmetric simple exclusion processes in dimension and we prove a density property for certain invariant states of the driven system. Received: 2 September 2001 / Accepted: 28 March 2002 Published online: 31 July 2002     

Anomalous transport in heterogeneous media

The diffusion dynamics of particles in heterogeneous media is studied using particle-based simulation techniques. A special focus is placed on systems where the transport of particles at long times exhibits anomalies such as subdiffusive or superdiffusive behavior. First, a two-dimensional model system is considered containing gas particles (tracers) that diffuse through a random arrangement of pinned, disk-shaped particles. This system is similar to a classical Lorentz gas. However, different from the original Lorentz model, soft instead of hard interactions are considered and we also discuss the case where the tracer particles interact with each other. We show that the modification from hard to soft interactions strongly affects anomalous-diffusive transport at high obstacle densities. Second, non-linear active micro-rheology in a glass-forming binary Yukawa mixture is investigated, pulling single particles through a deeply supercooled state by applying a constant force. Here, we observe superdiffusion in force direction and analyze its origin. Finally, we consider the Brownian dynamics of a particle which is pulled through a two-dimensional random force field. We discuss the similarities of this model with the Lorentz gas as well as active micro-rheology in glass-forming systems.     

Experimental realization of a model glass former in 2D

We have studied binary two-dimensional (2D) mixtures of superparamagnetic colloidal particles interacting through magnetic dipole moments, which were induced by an external magnetic field B. By tuning B the effective system temperature could be widely adjusted. Time-dependent particle coordinates measured by video-microscopy provide radial pair-distribution functions, mean-square displacements as well as evidence for heterogeneous dynamics. Characteristic features of 3D glass formers are observed experimentally in 2D for the first time.     

Dilatonic Entropic Force

We show in detail that the entropic force of the static spherically symmetric spacetimes with unusual asymptotics can be calculated through the Verlinde’s arguments. We introduce three different holographic screen candidates, which are first employed thoroughly by Myung and Kim [Phys. Rev. D 81, 105012 (2010)] for Schwarzschild black hole solutions, in order to identify the entropic force arising between a charged dilaton black hole and a test particle. The significance of the dilaton parameter on the entropic force is highlighted, and shown graphically.     

Starting to move through a granular medium

We explore the process of initiating motion through a granular medium by measuring the force required to push a flat circular plate upward from underneath the medium. In contrast with previous measurements of the drag and penetration forces, which were conducted during steady state motion, the initiation force has a robust dependence on the diameter of the grains in the medium. We attribute this dependence to the requirement for local dilation of the grains around the circumference of the plate, as evidenced by an observed linear dependence of the initiation force on the plate diameter.     

4D traction force microscopy reveals asymmetric cortical forces in migrating Dictyostelium cells

We present a 4D (x; y; z; t) force map of Dictyostelium cells crawling on a soft gel substrate. Vertical forces are of the same order as the tangential ones. The cells pull the substratum upward along the cell, medium, or substratum contact line and push it downward under the cell except for the pseudopods. We demonstrate quantitatively that the variations in the asymmetry in cortical forces correlates with the variations of the direction and speed of cell displacement.     

Driven Tracer Particle in One Dimensional Symmetric Simple Exclusion

Consider an infinite system of particles evolving in a one dimensional lattice according to symmetric random walks with hard core interaction. We investigate the behavior of a tagged particle under the action of an external constant driving force. We prove that the diffusively rescaled position of the test particle εX(ε^-2 t), t > 0, converges in probability, as ε→ 0, to a deterministic function v(t). The function v(⋅) depends on the initial distribution of the random environment through a non-linear parabolic equation. This law of large numbers for the position of the tracer particle is deduced from the hydrodynamical limit of an inhomogeneous one dimensional symmetric zero range process with an asymmetry at the origin. An Einstein relation is satisfied asymptotically when the external force is small. Received: 5 December 1996 / Accepted: 30 June 1997     

On the Existence of Invariant Measure for Lagrangian Velocity in Compressible Environments

We study transport of a passive tracer particle in a time dependent turbulent flow in the medium with positive molecular diffusivity. We show that there exists then a probability measure equivalent to the underlying physical probability, corresponding to the Eulerian velocity field, under which the particle Lagrangian velocity observations are stationary. As an application we derive the existence of the Stokes drift and the effective diffusivity—the characteristics of the long time behavior of the particle motion.