Collision of a structurally composite particle with a barrier

We suggest a simple model of a structurally composite particle with internal degrees of freedom and study the simplest kinematical and dynamical properties of such a particle. The collision of a structurally composite particle with one internal degree of freedom with a barrier is analyzed in detail. We show that both total cooling and “heating” of the internal degree of freedom can be observed during the reflection of such a particle. We calculate such basic parameters of the collision as its duration, the number of collisions in the interaction time, and the velocities of the envelope and the internal particle after the collision. Properties characteristic of chaotic scattering are shown to appear when a structurally composite particle collides with a barrier.     

Spontaneous photon emission from a non-relativistic free charged particle in collapse models: A case study

We study the photon emission rate of a non-relativistic charged particle interacting with an external classical noise through its position. Both the particle and the electromagnetic field are quantized. Under only the dipole approximation, the equations of motion can be solved exactly for a free particle, or a particle bounded by an harmonic potential. The physical quantity we will be interested in is the spectrum of the radiation emitted by the particle, due to the interaction with the noise. We will highlight several properties of the spectrum and clarify some issues appearing in the literature, regarding the exact mathematical formula of a spectrum for a free particle.     

Diffusion and mobility in a stirred dense granular material

We describe a probe of diffusivity (D) and mobility (B) for a dense 2D granular system. We introduce random motion by stirring, and characterize D by particle tracking. To measure B we measure the force needed to push a particle through the medium at fixed velocity, v, using three sizes of tracer particle. We find simple Brownian diffusion, but B depends strongly on v because the force needed to push a tracer through a sample is nearly independent of v. Data for D/B depend on the tracer particle size.     

Depinning by fracture in a glassy background

We force a single particle through a two-dimensional simulated glass of smaller particles. We find that the particle velocity obeys a robust power law that persists to drive wells above threshold. As the single driven particle moves, it induces cooperative distortions in the surrounding medium. We show theoretically that a fracture model for these distortions produces power-law behavior and discuss implications for experimental probes of soft matter systems.     

Penetration depth anisotropy in d-density wave scenario

We discuss thermalization of a test particle schematized as a harmonic oscillator and coupled to a Boltzmann heat bath of finite size and with a finite bandwidth for the frequencies of its particles. We find that complete thermalization only occurs when the test particle frequency is within a certain range of the bath particle frequencies, and for a certain range of mass ratios between the test particle and the bath particles. These results have implications for the study of classical and quantum behaviour of high-frequency nanomechanical resonators.     

Brownian ratchets driven by asymmetric nucleation of hydrolysis waves

We propose a stochastic process wherein molecular transport is mediated by asymmetric nucleation of domains on a one-dimensional substrate, in contrast with molecular motors that hydrolyze nucleotide triphosphates and undergo conformational change. We show that asymmetric nucleation of hydrolysis waves on a track can also result in directed motion of an attached particle. Asymmetrically cooperative kinetics between hydrolyzed and unhydrolyzed states on each lattice site generate moving domain walls that push a particle sitting on the track. We use a novel fluctuating-frame, finite-segment mean field theory to accurately compute steady-state velocities of the driven particle and to discover parameter regimes yielding maximal domain wall flux, leading to optimal particle drift.     

Gaussian Quantum Fluctuations in Interacting Many Particle Systems

We consider a many particle quantum system, in which each particle interacts only with its nearest neighbours. Provided that the energy per particle has an upper bound, we show, that the energy distribution of almost every product state becomes a Gaussian normal distribution in the limit of infinite number of particles. We indicate some possible applications.     

Optical Tomograms and Husimi Q-Function for a Particle Moving in the Dirac Delta Potential

We study the problem of a quantum particle moving in the Dirac delta potential with instant changes in the well depth using the formalism of the tomographic-probability representation of quantum mechanics. We calculate the Husimi function for a particle moving in the Dirac delta potential and study the relation of the Husimi function to the state tomogram. We check numerically the tomographic entropic uncertainty relation for the bound state of the particle moving in the Dirac delta potential.     

Particle production, back reaction and singularity avoidance

We consider particle production in Robertson-Walker spacetime as particle-antiparticle rotation. We thereby obtain a scale factor that guarantees particle production. We then study quantum field effects in spatially flat homogeneous and isotropic spacetime with energy density of created particles and one loop quantum correction as back reaction. In the numerical solution initial values are determined from particle production simulated scale factor and obtain the evolution of the universe both at early and late times having a bounce.     

On mechanical motion damping of a magnetically trapped diamagnetic particle

We discuss eddy-current-induced limitations of the attenuation of mechanical motion of a diamagnetic particle trapped by an inhomogeneous magnetic field in the Earth's gravitational potential. We show that the mechanical frequency of the particle oscillation is independent on the particle properties and is proportional to the free fall acceleration constant, similarly to the classical mechanical pendulum. The frequency can be used to measure the gravity field. The eddy-current induced attenuation constant does not depend on the mass of the particle and reduces with the particle volume. The quality factor of the mechanical motion can be as high as 10⁹ and is comparable with the attenuation due to interaction of the particle with incompletely evacuated air. A possibility of usage of the particle as a quantum mechanical system is discussed.     

Topological Aharonov-Bohm Effect of Neutral Scalar Particle on Noncommutative Space

We study the interactions between a neutral scalar particle and electromagnetic fields on noncommutative space. Because of the noncommutativity of space, neutral particle can couple to electromagnetic fields at the tree level, and the interaction strength is represented by a new coupling constant. We find that on noncommtuative space the topological Aharonov-Bohm effect is nontrivial even for neutral scalar particle.     

Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon

We study the asymptotic statistical behavior of the 2-dimensional periodic Lorentz gas with an infinite horizon. We consider a particle moving freely in the plane with elastic reflections from a periodic set of fixed convex scatterers. We assume that the initial position of the particle in the phase space is random with uniform distribution with respect to the Liouville measure of the periodic problem. We are interested in the asymptotic statistical behavior of the particle displacement in the plane as the timet goes to infinity. We assume that the particle horizon is infinite, which means that the length of free motion of the particle is unbounded. Then we show that under some natural assumptions on the free motion vector autocorrelation function, the limit distribution of the particle displacement in the plane is Gaussian, but the normalization factor is (t logt)^1/2 and nott ^1/2 as in the classical case. We find the covariance matrix of the limit distribution.     

Local melting and drag for a particle driven through a colloidal crystal

We numerically investigate a colloidal particle driven through a colloidal crystal as a function of temperature. When the charge of the driven particle is larger or comparable to that of the colloids comprising the crystal, a local melting can occur, characterized by defect generation in the lattice surrounding the driven particle. The generation of the defects is accompanied by an increase in the drag force on the driven particle, as well as large noise fluctuations. We discuss the similarities of these results to the peak effect phenomena observed for vortices in superconductors.     

Improved particle filters for multi-target tracking

We present a novel approach for improving particle filters for multi-target tracking. The suggested approach is based on drift homotopy for stochastic differential equations. Drift homotopy is used to design a Markov Chain Monte Carlo step which is appended to the particle filter and aims to bring the particle filter samples closer to the observations while at the same time respecting the target dynamics. We have used the proposed approach on the problem of multi-target tracking with a nonlinear observation model. The numerical results show that the suggested approach can improve significantly the performance of a particle filter.     

Most likely ensemble with a given average energy prepared by a single slit

We discuss an ensemble of particle selected by a single slit within the statistical model of quantization reported earlier. We look for the most probable distribution of the position of the particle with a given average energy by applying Jaynes’s maximum entropy principle. We first show that the most likely ensemble with the lowest possible average energy is given by the quantum mechanical ground state of a particle trapped inside the slit. We further show that in general it takes a larger energy to collect the beam of particles into a target position with a higher precision.     

A particle across a medium: How decoherence relates to the index of refraction

We deduce from a microscopic point of view the equation that describes how the state of a particle crossing a medium decoheres. We find out that the part of the density matrix that evolves preserving coherence, is fully described with the index of refraction. Its imaginary part has the origin in the Lindblad operators, which are the responsible of decoherence. We apply our results to the example of a particle crossing a gas: we find a master equation of the Lindblad type, and compute explicitly the Lindblad operators in terms of the interaction potential between the particle and a target of the medium. Two limit situations are treated: when the particle is much heavier than the targets of the medium and vice versa.     

On aggregate structures in a rod-like haematite particle suspension by means of Brownian dynamics simulations

We have investigated aggregation phenomena in a suspension composed of rod-like haematite particles by means of Brownian dynamics simulations. The magnetic moment of the haematite particles lies normal to the particle axis direction and therefore the present Brownian dynamics method takes into account the spin rotational Brownian motion about the particle axis. We have investigated the influence of the magnetic particle–field and particle–particle interactions, the shear rate and the volumetric fraction of particles on the particle aggregation phenomena. Snapshots of aggregate structures are used for a qualitative discussion and the cluster size distribution, radial distribution function and the orientational correlation functions of the direction of particle axis and magnetic moment are the focus for a quantitative discussion. The significant formation of raft-like clusters is found to occur at a magnetic particle–particle interaction strength much larger than that required for a magnetic spherical particle suspension. This is because the rotational Brownian motion has a significant influence on the formation of clusters in a suspension of rod-like particles with a large aspect ratio. An applied magnetic field enhances the formation of raft-like clusters. A shear flow does not have a significant influence on the internal structure of the clusters, but influences the cluster size distribution of the raft-like clusters.     

Nonlinear dynamics of charged particles in an oblique electromagnetic wave

We study dynamics of a charged particle under action of an electromagnetic wave that propagates obliquely to a background uniform magnetic field. The dynamics is described by a slow-fast Hamiltonian system. We show that long-term dynamics is dominated by phenomena of capture of particle into resonance with the wave and escape from this resonance, as well as of scattering on resonance. We find that the variation of the particle?s kinetic energy on the time interval between capture and escape is bounded and accumulated in the motion along the background field. We discuss possible applications of the obtained results.     

Dynamics of a single particle in a horizontally shaken box

We study the dynamics of a particle in a horizontally and periodically shaken box as a function of the box parameters and the coefficient of restitution. For certain parameter values, the particle becomes regularly chattered at one of the walls, thereby loosing all its kinetic energy relative to that wall. The number of container oscillations between two chattering events depends in a fractal manner on the parameters of the system. In contrast to a vertically vibrated particle, for which chattering is claimed to be the generic fate, the horizontally shaken particle can become trapped on a periodic orbit and follow the period-doubling route to chaos when the coefficient of restitution is changed. We also discuss the case of a completely elastic particle, and the influence of friction between the particle and the bottom of the container. Received: 19 September 1997 / Received in final form: 9 December 1997 / Accepted: 17 December 1997     

Nodal patterns of floaters in surface waves

We argue theoretically and demonstrate experimentally that in a standing wave floating particles drift towards the nodes or anti-nodes depending on their hydrophilic or hydrophobic properties. We explain this effect as the breakdown of Archimedes' law by a surface tension, which creates a difference between the masses of the floater and displaced liquid, making the particle effectively inertial. We describe analytically the motion of a small floating particle in a small-amplitude wave and show that the drift appears as a second order effect in wave amplitude. We confirm experimentally that indeed the clustering rate is proportional to the square of the wave amplitude. In the case of surface random waves we show experimentally that the inertial effects significantly change the statistics of floater distribution on a liquid surface. The analysis of particle concentration moments and probability distribution functions shows that particle concentrate on a multi-fractal set with caustics.