Phase transitions in a system of unstable particles

A study is reported of phase separation in a system of particles created at a constant rate and having a finite lifetime. It is shown that (1) phase separation is possible if the particle lifetime exceeds a certain critical value, (2) the particle-density difference between the phases depends on particle lifetime, and (3) the correlation function in the two-phase region oscillates (with damping) as a function of spatial coordinates, which implies correlation between the phase locations. Fiz. Tverd. Tela (St. Petersburg) 40, 741–745 (April 1998)     

Locating the minimum: Approach to equilibrium in a disordered, symmetric zero range process

We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site k hops to its nearest neighbor with a quenched rate w(k). These rates are chosen randomly from the probability distribution f(w) ∼ (w − c) ⁿ , where c is the lower cutoff. For n>0, this model is known to exhibit a phase transition in the steady state from a low density phase with a finite number of particles at each site to a high density aggregate phase in which the site with the lowest hopping rate supports an infinite number of particles. In the latter case, it is interesting to ask how the system locates the site with globally minimum rate. We use an argument based on the local equilibrium, supported by Monte Carlo simulations, to describe the approach to the steady state. We find that at large enough time, regions with a smooth density profile are described by a diffusion equation with site-dependent rates, while the isolated points where the mass distribution is singular act as the boundaries of these regions. Our argument implies that the relaxation time scales with the system size L as L ^z with z = 2 + 1/(n + 1) for n>1 and suggests a different behavior for n<1.     

Modelling of particle paths passing through an ultrasonic standing wave

Within an ultrasonic standing wave particles experience acoustic radiation forces causing agglomeration at the nodal planes of the wave. The technique can be used to agglomerate, suspend, or manipulate particles within a flow. To control agglomeration rate it is important to balance forces on the particles and, in the case where a fluid/particle mix flows across the applied acoustic field, it is also necessary to optimise fluid flow rate. To investigate the acoustic and fluid forces in such a system a particle model has been developed, extending an earlier model used to characterise the 1-dimensional field in a layered resonator. In order to simulate fluid drag forces, CFD software has been used to determine the velocity profile of the fluid/particle mix passing through the acoustic device. The profile is then incorporated into a MATLAB model. Based on particle force components, a numerical approach has been used to determine particle paths. Using particle coordinates, both particle concentration across the fluid channel and concentration through multiple outlets are calculated. Such an approach has been used to analyse the operation of a microfluidic flow-through separator, which uses a half wavelength standing wave across the main channel of the device. This causes particles to converge near the axial plane of the channel, delivering high and low particle concentrated flow through two outlets, respectively. By extending the model to analyse particle separation over a frequency range, it is possible to identify the resonant frequencies of the device and associated separation performance. This approach will also be used to improve the geometric design of the microengineered fluid channels, where the particle model can determine the limiting fluid flow rate for separation to occur, the value of which is then applied to a CFD model of the device geometry.     

Effect of particles on the flow structure and dispersion of solid impurities in a two-phase axisymmetric jet

The Euler approach is used for studying the structure of a flow and the propagation of a disperse impurity in a submerged two-phase jet for small values of the mass concentration of particles (M _L1 = 0 to 0.5) upon a variation of the size and material of particles in a wide range. The effect of particles on the propagation of a two-phase jet, gas turbulence, and solid phase dispersion is analyzed. The addition of particles decreases the jet opening angle, increases the jet range, suppresses turbulence, and deteriorates turbulent mixing with the surrounding submerged space. It is shown that at the first stage, particle accumulation effects (pinching) in the axial region of the jet appear upon an increase in the particle size and the density of the particle material. Then, upon an increase in the inertia of particles, pinching changes to intense scattering of the disperse phase in the initial cross sections of the jet. The results are compared with the results of measurements for mono- and polydisperse two-phase jet flows.     

Particle in cell simulation of relativistic Buneman instability in a current-carrying plasma

Abstract

Non-linear evolution of the relativistic Buneman instability in a current-carrying plasma is investigated by a particle in cell simulation. These simulations show that as the time progresses, some electrons are trapped in phase space holes and thus counter-streaming and plateau can be formed. Moreover, the electron and ion density profiles indicate a periodic pattern of the density steepening. This density distribution is similar to the generation of the grating-like patterns which strongly depends on the initial electron velocity and saturation time. It is also shown that the electric field profile has the sawtooth form; charged particles can be accelerated by this field. Finally, it is found that increasing the electron velocity increases the saturation time and consequently the growth rate decreases which is in good agreement with the result obtained by the fluid model.     

A Particle-Picture Approach to Anomalies in Chiral Gauge Theories

The system of a chiral fermion field coupled to a background gauge field is considered. By taking what we call the particle picture and carefully defining the S-matrix in the Heisenberg picture, we investigate anomalous phenomena in this system. It is shown by explicit calculations that the gauge-field configuration with nonvanishing topological-charge causes anomalous production of particles that is directly responsible for the chiral U(1) anomaly. Unlike the chiral U(1) anomaly, the gauge anomaly, that is, gauge non-invariance of the S-matrix is a problem that arises in the phase of the S-matrix. It is shown that this phase is related to the freedom existing in the quantization method, and that a suitably chosen phase which of course is consistent with the equation of motion can remove the gauge anomaly. Finally, a modified form of path-integral quantization for this system is proposed.     

Colour conductivity of hard spheres

We present an analytic solution for the d-dimensional (d > 1) hard-sphere free flight trajectories in a thermostatted colour field. The solution shows that particles can only reach a finite distance in the direction perpendicular to the field in the absence of collisions. Using a numerical algorithm we designed to simulate many-body hard-sphere systems with curved trajectories, we study the onset of the instability leading to phase separation in the two-dimensional case for a range of field strengths and three densities. For the two fluid densities we find that phase separation occurs for sufficiently strong fields regardless of the initial configuration, and that the phase-separated state eventually becomes a collisionless, non-ergodic steady state. For solid densities the phase-separated configuration is stable and conducting, but is not an attractor for other charge distributions because of the impossibility of particle rearrangement.     

Influence of hydrodynamic interactions on lane formation in oppositely charged driven colloids

The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are considered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic interactions strongly disfavor laning. In the steady state of lanes, a macroscopic phase separation of lanes is observed. This is in marked contrast to the simple Brownian case where a finite size of lanes was obtained in the steady state. For strong Coulomb interactions between the colloidal particles a lateral square lattice of oppositely driven lanes is stable similar to the simple Brownian dynamics. In an electric field, on the other hand, the behavior is found in qualitative and quantitative accordance with the case of neglected hydrodynamics.     

Asymptotic and Numerical Analyses for Mechanical Models of Heat Baths

A mechanical model of a particle immersed in a heat bath is studied, in which a distinguished particle interacts via linear springs with a collection of n particles with variable masses and random initial conditions; the jth particle oscillates with frequency j ^p , where p is a parameter. For p>1/2 the sequence of random processes that describe the trajectory of the distinguished particle tends almost surely, as n, to the solution of an integro-differential equation with a random driving term; the mean convergence rate is 1/n ^p–1/2. We further investigate whether the motion of the distinguished particle can be well approximated by an integration scheme—the symplectic Euler scheme—when the product of time step h and highest frequency n ^p is of order 1, that is, when high frequencies are underresolved. For 1/2<p<1 the numerical solution is found to converge to the exact solution at a reduced rate of |log h| h ^2–1/p . These results shed light on existing numerical data.     

A Counter Example to Cercignani’s Conjecture for the <Emphasis Type="Italic">d</Emphasis> Dimensional Kac Model

Kac’s d dimensional model gives a linear, many particle, binary collision model from which, under suitable conditions, the celebrated Boltzmann equation, in its spatially homogeneous form, arise as a mean field limit. The ergodicity of the evolution equation leads to questions about the relaxation rate, in hope that such a rate would pass on the Boltzmann equation as the number of particles goes to infinity. This program, starting with Kac and his one dimensional ‘Spectral Gap Conjecture’ at 1956, finally reached its conclusion in the Maxwellian case in a series of papers by authors such as Janvresse, Maslen, Carlen, Carvalho, Loss and Geronimo, but the hope to get a limiting relaxation rate for the Boltzmann equation with this linear method was already shown to be unrealistic (although the problem is still important and interesting due to its connection with the linearized Boltzmann operator). A less linear approach, via a many particle version of Cercignani’s conjecture, is the grounds for this paper. In our paper, we extend recent results by the author from the one dimensional Kac model to the d dimensional one, showing that the entropy-entropy production ratio, Γ _N , still yields a very strong dependency in the number of particles of the problem when we consider the general case.     

On the relation between conduction and diffusion in a random walk along self-similar clusters

The relation between diffusion and conduction in the random walk of a particle by means of Lévy hops is investigated. It is shown that on account of the unusual character of Lévy hops, the mobility of a particle is a nonlinear function of the electric field for arbitrarily weak fields. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 518–520 (10 April 1998)     

Criteria for the capture of large bottom particles by eddies in a dam break flow

The bottom layer of a dam break flow is experimentally studied. It is shown that the thickness of the viscous layer exceeds the diameter of a bottom particle (d _p < 1.2 cm). Small particles d _p < 0.05 cm are captured by single satellite eddies that occur under main eddies periodically formed in the viscous layer. Two satellite eddies approach each other and merge into one eddy capable of capturing a large particle if the flow velocity is higher than the critical value U _dip. The particle is captured for large U _cr > U _dip which provides particle rotation without slipping.     

Drift in a random walk along self-similar clusters

This paper is a study of the relationship between diffusion and conductivity when the random walks of particles occur via Lévy hops. It shows that because of the unusual nature of Lévy hops the particle mobility is a nonlinear function of the electric field in arbitrarily weak fields. The crossover to ordinary diffusion by introduction of a finite displacement in each step is also discussed. Zh. éksp. Teor. Fiz. 115, 1016–1023 (March 1999)     

The Motion of a Nonferromagnetic Particle in a Periodic Magnetic Field

The motion of a spherical nonferromagnetic particle in an axially symmetric periodic permanent magnetic field is considered. It is shown that in this field configuration the focusing of fast particles and the mass separation of a particle beam are realizable.     

Primordial pairing and binding of superheavy charged particles in the early universe

Primordial superheavy particles, considered as the source of Ultra High Energy Cosmic Rays (UHECR) and produced in local processes in the early Universe, should bear some strictly or approximately conserved charge to be sufficiently stable to survive to the present time. Charge conservation dictates that they be produced in pairs, and the estimated separation of particle and antiparticle in such a pair is shown to be in some cases much smaller than the average separation determined by the averaged number density of considered particles. If the new U(1) charge is the source of a long-range field similar to the electromagnetic field, the particle and antiparticle, possessing that charge, can form a primordial bound system with an annihilation timescale, which can satisfy the conditions assumed for this type of UHECR source. These conditions severely constrain the possible properties of the considered particles.     

On the derivation of the generalized Langevin equation for interacting Brownian particles

The main result of this paper is a derivation of a generalized nonlinear Langevin equation (GLE) forn interacting particles in a bath. A consequence of the derivation is that the exact form of the (generalized) fluctuation-dissipation theorem is obtained. We discuss also the relation between the memory kernel of the GLE and some corresponding correlation functions which can be easily obtained in a molecular dynamics computer experiment. In the same spirit it is shown that the approach applies to a Brownian particle subjected to a stationary external field. The technique presented in a previous paper to simulate generalized Brownian dynamics can be easily extended to the present case. Our derivation intends to clarify the uses and (possibly) abuses of the Langevin equation in Brownian dynamics studies.     

Features of the resonant interaction of moving neutral atoms and clusters with superlattice surface

Features of the interaction of moving neutral atoms, molecules, and clusters with a superlattice field (for example, the system of linear magnetic and electric domains) are considered. It is shown that the character of the particle motion depends on the ratio of the frequency ω₂₁ of the internal electromagnetic resonance to the bounce frequency Ω _s determined by the superlattice period, the velocity of the particle motion, and the possible moments of the particle in the ground d ₁₁ and excited d ₂₂ states. The conditions for regimes of attraction and repulsion of particles by the superlattice are considered. The preconditions for formation of a one-dimensional potential well located far from the superlattice and for stable channeling of neutral and charged particles in this well are also considered. Depending on the ratio of ω₂₁ to Ω _s , particle sorting and beam separation occur during interaction of the multicomponent beam consisting of different particles with the superlattice field.     

The wave properties of matter and the zeropoint radiation field

The origin of the wave properties of matter is discussed from the point of view of stochastic electrodynamics. A nonrelativistic model of a charged particle with an effective structure embedded in the random zeropoint radiation field reveals that the field induces a high-frequency vibration on the particle; internal consistency of the theory fixes the frequency of this jittering at mc²/. The particle is therefore assumed to interact intensely with stationary zeropoint waves of this frequency as seen from its proper frame of reference; such waves, identified here as de Broglie's phase waves, give rise to a modulated wave in the laboratory frame, with de Broglie's wavelength and phase velocity equal to the particle velocity. The time-independent equation that describes this modulated wave is shown to be the stationary Schrödinger equation (or the Klein-Gordon equation in the relativistic version). In a heuristic analysis appled to simple periodic cases, the quantization rules are recovered from the assumption that for a particle in a stationary state there must correspond a stationary modulation. Along an independent and complementary line of reasoning, an equation for the probability amplitude in configuration space for a particle under a general potential V(x) is constructed, and it is shown that under conditions derived from stochastic electrodynamics it reduces to Schrödinger's equation. This equation reflects therefore the dual nature of the quantum particles, by describing simultaneously the corresponding modulated waveand the ensemble of particles.     

Investigation of the Flow Field in the Upper Part of a Cyclone with Laser and Phase Doppler Anemometry

The cyclone is a well known apparatus for separating particles out of a gas stream. With the modern laser diagnostic technologies of laser and phase Doppler anemometry (LDA and PDA), there is the potential to measure the flow and particle field inside the cyclone. The gas phase only measurements used micron‐sized oil seeding droplets, whereas the solid phase, chosen for the PDA particle size measurements, was limestone powder. To assess the possibility of measuring milled limestone particles with PDA, the measured size distribution was compared with those obtained by laser diffraction. The measurements inside the cyclone showed that the flow field in the upper part of the cyclone was different to that commonly thought. Therefore, the vertical height of the cyclone's vortex finder could be shortened without deterioration of the separation efficiency. The particles found in the hold‐up of the cyclone air flow were considerably larger than the average particle size in the feed pipe.