Balance equation and the quasitemperature of channeled particles in equilibrium

Using the methods of nonequilibrium statistical thermodynamics, we obtain the equation for the transverse energy and momentum balance for fast atomic particles moving in the planar channeling regime. Based on the solution of this equation, we obtain an expression for the transverse quasitemperature in the quasiequilibrium in terms of the basic parameters of the theory. We show that the equilibrium quasitemperature of channeled particles is established because of particle diffusion in the space of transverse energies (subsystem “heating”), the dissipative process (“cooling”), and the anharmonic effects of particle oscillations between the channel walls (the redistribution of energies over the oscillatory degrees of freedom is the internal thermalization of the subsystem). According to the estimates for particles with an energy of the order of 1 MeV, the quasitemperature values are in the characteristic temperature range for a low-temperature plasma.     

Discrete dipole approximation simulations on GPUs using OpenCL—Application on cloud ice particles

The global distribution and climatology of ice clouds are among the main uncertainties in climate modeling and prediction. In order to retrieve ice cloud properties from remote sensing measurements, the scattering properties of all cloud ice particle types must be known. The discrete dipole approximation (DDA) simulates scattering of radiation by arbitrarily shaped particles and is thus suitable for cloud ice crystals. The DDA models the particle as a collection of equal dipoles on a lattice, and is computationally much more expensive than approximations restricted to more regularly shaped particles. On a single computer the calculation for an ice particle of a specific size, for a given scattering plane at one specific wavelength can take several days. We have ported the core routines of the scattering suite “ADDA” to the open computing language (OpenCL), a framework for programming parallel devices like PC graphics cards (graphics processing units, GPUs) or multi-core CPUs. In a typical case we can achieve a speed-up on a GPU as compared to a CPU by a factor of 5 in double precision and a factor of 15 in single precision. Spreading the work load over multiple GPUs will allow calculating the scattering properties even of large cloud ice particles.     

Existence of an infinite particle limit of stochastic ranking process

We study a stochastic particle system which models the time evolution of the ranking of books by online bookstores (e.g., Amazon.co.jp). In this system, particles are lined in a queue. Each particle jumps at random jump times to the top of the queue, and otherwise stays in the queue, being pushed toward the tail every time another particle jumps to the top. In an infinite particle limit, the random motion of each particle between its jumps converges to a deterministic trajectory. (This trajectory is actually observed in the ranking data on web sites.) We prove that the (random) empirical distribution of this particle system converges to a deterministic space–time-dependent distribution. A core of the proof is the law of large numbers for dependent random variables.     

The Green formula in the theory of potential scattering and corrections to the eikonal scattering amplitude

A method based on the Green formula is developed for calculating the scattering amplitude of fast charged particles in an external field. The scattering amplitude is representable as an integral over an arbitrary closed surface enveloping the domain of influence of the external field on the particle. Corrections to the eikonal scattering amplitude are simply derived without using the specific form of the potential. The resulting formulas can be used to investigate the interaction between particles and fields of complex configuration. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. No. 2, pp. 280–288, May, 1998.     

Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation

We study the time evolution of a quantum particle in a Gaussian random environment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to a solution of a linear Boltzmann equation globally in time. The Boltzmann collision kernel is given by the Born approximation of the quantum differential scattering cross section. © 2000 John Wiley & Sons, Inc.     

Scattering measurements in nuclear emulsions and their application to measuring the charge of primary cosmic ray nuclei

Small local dislocations in processed emulsions give rise to spurious scattering whose effect on tracks is indistinguishable from the multiple scattering produced by coulomb interaction. Because of this effect the atomic number of fast primary cosmic ray nuclei will be underestimated in more than 50% of the cases in experiments where multiple scattering of tracks and ionization measurements are employed for charge determination. The spurious scattering was investigated by measuring the track contours of 100 very long tracks due to energetic primary particles; the effect was present in comparable strength in all plates and all types of emulsions which have been investigated. It is too small to affect measurements on medium energy particle tracks (protons with energy below 600 MeV and heavy nuclei with energy below 300 MeV/ nucleon). It dominates, however, other sources or error and noise for tracks of energetic particles although it does not preclude occasional observations of very low scattering values. New methods for measuring various forms of noise have also been developed in the course of this work and the noise level for scattering measurements has been reduced below previously accepted values. Spurious scattering is presumably largely responsible for the discrepancies which appear when one compares the primary charge and energy spectra derived from experiments involving scattering measurements with the corresponding spectra derived from numerous other experiments which employ different techniques. If the experiments based on scattering measurements are omitted, the remaining evidence strongly favours a spectrum in which the energy per nucleon is nearly independent of atomic number for all primaries. It also favours a charge distribution which has a pronounced minimum for charges 3≤ Z≤ 5 and, therefore, yields a fairly low upper limit for the amount of interstellar matter traversed by primary cosmic ray nuclei.     

Using the Evolution Operator Method to Describe a Particle in a Homogeneous Alternating Field

Using the evolution operator method, we construct coherent states of a nonrelativistic free particle with a variable mass M(t) and a nonrelativistic particle with a variable mass M(t) in a homogeneous alternating field. Under certain physical conditions, they can be regarded as semiclassical states of particles. We discuss the properties (in particular, the completeness relation, the minimization of the uncertainty relations, and the time evolution of the corresponding probability density) of the found coherent states in detail. We also construct exact wave functions of the oscillator type and of the plane-wave type for the considered systems and compute the quantum Wigner distribution functions for the wave functions of coherent and oscillator states. We establish the unitary equivalence of the problems of a free particle and a particle in a homogeneous alternating field.     

Numerical Investigation of Particulate Flow over a Backward‐Facing Step

Flow separation and recirculation caused by a sudden expansion in the channel geometry in the form of a backwardfacing step (BFS) appear in numerous practical applications. Additionally, BFS flow has been used as a generic test case to study fundamental flow properties, such as separation or re‐attachment. In the present work, BFS flow laden with dispersed particles is investigated by numerical simulations using a spectral element method [1]. The motion of the dispersed particles is computed by Lagrangian particle tracking. In a first step, only the influence of the flow on the particles is accounted for, while possible effects of the particle motion on the flow are neglected. Spatial distribution of the particles is investigated, and effects of different wall‐particle interaction models on the computational results are examined.     

Chaotic mixing and fractals in a geophysical jet current

We model Lagrangian lateral mixing and transport of passive scalars in meandering oceanic jet currents by two-dimensional advection equations with a kinematic streamfunction with a time-dependent amplitude of a meander imposed. The advection in such a model is known to be chaotic in a wide range of the meander’s characteristics. We study chaotic transport in a stochastic layer and show that it is anomalous. The geometry of mixing is examined and shown to be fractal-like. The scattering characteristics (trapping time of advected particles and the number of their rotations around elliptical points) are found to have a hierarchical fractal structure as functions of initial particle’s positions. A correspondence between the evolution of material lines in the flow and elements of the fractal is established.     

Ostwald ripening: The screening length revisited

We are interested in the coarsening of a spatial distribution of two phases, driven by the reduction of interfacial energy and limited by diffusion, as described by the Mullins–Sekerka model. We address the regime where one phase covers only a small fraction of the total volume and consists of many disconnected components (“particles”). In this situation, the energetically more advantageous large particles grow at the expense of the small ones, a phenomenon called Ostwald ripening. Lifshitz, Slyozov and Wagner formally derived an evolution for the distribution of particle radii. We extend their derivation by taking into account that only particles within a certain distance, the screening length, communicate. Our arguments are rigorous and are based on a homogenization within a gradient flow structure. Received December 27, 1999 / Accepted June 2, 2000 / Published online November 9, 2000     

Convergence to a stationary state and diffusion for a charged particle in a standing medium

Summary We study a one-dimensional semi-infinite system of identical particles, driven by a constant force acting only on the first particle. Particles interact through elastic collisions. At time zero all particles are at rest, and the interparticle distances are i.i.d. r.v.'s, the support of the distribution being in (d, ), d>0. We show that if d is large enough the dynamics has a strong cluster property, and prove, for large times, convergence to a limiting distribution for the system as seen from the first particle, as well as existence of drift velocity and invariance principle for the motion of the first particle.Partially supported by C.N.R.-C.N.Pq. agreementPartially supported by M.P.I. research funds     

Ostwald ripening in two dimensions—the rigorous derivation of the equations from the Mullins-Sekerka dynamics

We consider a dilute mixture of a finite number of particles and we are interested in the coarsening of the spatial distribution in two space dimensions under Mullins-Sekerka dynamics. Under the appropriate scaling hypotheses we associate radii and centers to each particle and derive equations for the whole evolution.     

Non-extinction of a Fleming-Viot particle model

We consider a branching particle model in which particles move inside a Euclidean domain according to the following rules. The particles move as independent Brownian motions until one of them hits the boundary. This particle is killed but another randomly chosen particle branches into two particles, to keep the population size constant. We prove that the particle population does not approach the boundary simultaneously in a finite time in some Lipschitz domains. This is used to prove a limit theorem for the empirical distribution of the particle family.     

The asymptotic characteristics of the solutions of the diffusion equation with a non-linear sink: A renormalization group approach

A non-linear generalization of the diffusion equation, which describes the mass or heat transfer accompanied with chemical reactions, is used to consider the spreading of an initially localized distribution. The use of a renormalization group method enabled the nature of the solution to be analysed for long times and two characteristics of its asymptotic behaviour to be distinguished. When the dimension of the space is greater than a certain critical value, a state of asymptotic freedom is attained for which the role of non-linearity is small and the evolution of the density distribution is governed by diffusion processes. When the dimension is less than the critical value, the non-linear term remains substantial for long periods of time and a state of incomplete self-similarity of the evolution of the density distribution is established. The exponent of the exponential dependence of the radius of the diffusion spot on time is calculated for this case. The relation between the renormalization group method and perturbation theory and difficulties in substantiating the method when applied to a given problem are discussed.     

Debye–Waller Factor in Neutron Scattering by Ferromagnetic Metals

We obtain an expression for the neutron scattering cross section in the case of an arbitrary interaction of the neutron with the crystal. We give a concise, simple derivation of the Debye–Waller factor as a function of the scattering vector and the temperature. For ferromagnetic metals above the Curie temperature, we estimate the Debye–Waller factor in the range of scattering vectors characteristic of polarized magnetic neutron scattering experiments. In the example of iron, we compare the results of harmonic and anharmonic approximations.     

Analysis of double surface plasmon resonance by the discrete source method

The discrete source method is modified in order to mathematically simulate and study the scattering properties of nonspherical particles located on the surface of a conducting film deposited on a glass prism. Both differential and integral scattering properties of metal nanoparticles are examined. It is shown that the scattering cross section behind the film can be increased by 10⁷ times by deforming the particle and shifting it with respect to the film. It is also shown that the scattered intensity distribution in the prism is localized in two directions, forming sharp narrow fingers with the intensity exceeding the incident wave amplitude by 15–30 times.     

Tunneling cosmological state and the origin of Higgs inflation in the standard model

For the tunneling cosmological state, we propose a path integral formulation admitting a consistent renormalization and renormalization-group improvement in particle physics applications of quantum cosmology with heavy massive quantum fields. We apply this formulation to the inflationary cosmology driven by the standard-model Higgs boson playing the role of an inflaton with a strong nonminimal coupling to gravity. A complete cosmological scenario is thus obtained, embracing the formation of initial conditions for the inflationary background in the form of a sharp probability peak in the distribution of the inflaton field and the ongoing generation of the cosmic microwave background spectrum on this background. We also discuss the status of the no-boundary and tunneling states in a cosmology driven by massless fields conformally coupled to gravity.     

Numerical analysis of convergent perturbation expansions in quantum theory

We present the results of a numerical analysis of the convergence of the new perturbation expansion recently proposed by Belokurov, Solovyev, and Shavgulidze. Two particular examples are considered: the anharmonic oscillator in quantum mechanics and the renormalization group β-function in field theory. It is shown that in the first case, the series converges to an exact value in a wide range of expansion parameters. This range can be enlarged with the help of the Padé approximation. In field theory, the results have a stronger dependence on the regularization parameter. We discuss an algorithm for choosing this parameter that produces stable results. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 2, pp. 291–297, February, 1997.     

Multi-temperature Hydrodynamic Limit from Kinetic Theory in a Mixture of Rarefied Gases

Starting from the Boltzmann kinetic equations for a mixture of gas molecules whose internal structure is described by a discrete set of internal energy levels, hydrodynamic equations at Euler level are deduced by a consistent hydrodynamic limit in the presence of a two-scale collision process. The fast process driving evolution is constituted by mechanical encounters between particles of the same species, whereas inter-species scattering proceeds at the macroscopic scale. The resulting multi-temperature and multi-velocity fluid-dynamic equations are briefly commented on, and some results in closed analytical form are given for special simplified situations like Maxwellian collision kernels, or mono-atomic hard sphere gases.