Dynamic behavior of non-uniform granular gases system with the fractal characteristic in one dimension

A one-dimensional dynamic model of polydisperse granular mixture with a power-law size distribution is presented, in which the particles are subject to inelastic mutual collisions and driven by Gaussian white noise. The particle size distribution of the mixture has the fractal characteristic, and a fractal dimension D as a measurement of the inhomogeneity of the particle size distribution is introduced. We define the global granular temperature and the kinetic pressure of the mixture, and obtain their expressions. By molecular dynamics simulations, we have mainly investigated how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the steady-state dynamic properties of the system, focusing on the global granular temperature, kinetic pressure, velocity distribution and distribution of interparticle spacing. Some novel results are found that, with the increase of the fractal dimension D, the global granular temperature and the kinetic pressure decrease, the velocity distribution deviates more obviously from the Gaussian one and the particles cluster more pronouncedly at the same value of the restitution coefficient e (0<e<1). On the other hand, as the restitution coefficient e decreases, the dynamic behavior has the similar evolution as above at the fixed fractal dimension D. The dynamic behavior changing with e and D is, respectively, presented.     

X-ray absorption intensity at high-energy region

We theoretically discuss X-ray absorption intensity in high-energy region far from the deepest core threshold to explain the morphology-dependent mass attenuation coefficient of some carbon systems, carbon nanotubes (CNTs), highly oriented pyrolytic graphite (HOPG) and fullerenes (C₆₀). The present theoretical approach is based on the many-body X-ray absorption theory including the intrinsic losses (shake-up losses). In the high-energy region the absorption coefficient has correction term dependent on the solid state effects given in terms of the polarization part of the screened Coulomb interaction W_p. We also discuss the tail of the valence band X-ray absorption intensity. In the carbon systems C 2s contribution has some influence on the attenuation coefficient even in the high energy region at 20 keV.     

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.     

Separation of S-wave pseudoscalar and pseudovector amplitudes in π−P↑ → π+π−n reaction on polarized target

A new analysis of S-wave production amplitudes for the reaction π^?p↑ → π⁺π^?n on a transversely polarized target is performed. It is based on the results obtained by the CERN-Cracow-Munich collaboration in the ππ energy range from 600 MeV to 1600 MeV at 17.2 GeV/c π^? momentum. Energy-independent separation of the S-wave pseudoscalar amplitude (π exchange) from the pseudovector amplitude (a ₁ exchange) is carried out using assumptions much weaker than those in all previous analyses. We show that, especially around 1000 MeV and around 1500 MeV, the a₁ exchange amplitude cannot be neglected. The scalarisoscalar ππ phase shifts are calculated using fairly weak assumptions. Below the KK? threshold we find two solutions for the π — π phase shifts, for which the phases increase slower with the effective π — π mass than the P-wave phases. Both solutions are consistent with a broad f ₀(500) but only one is similar to the well-known “down” solution. We find also the third solution (with a somewhat puzzling behavior of inelasticity) which exhibits a narrow f ₀(750) claimed by Svec. All the solutions undergo a rapid change at the KK? threshold. Above 1420 MeV the phase shifts increase with energy faster than those obtained without the polarized-target data. This phase behavior as well as an increase of the modulus of the a₁-exchange amplitude can be due to the presence of the f ₀(1500).     

A generalized treatment of the chemical diffusion coefficient in binary oxides as a function of the oxygen activity

The dependence of the chemical diffusion coefficient and of the self-diffusion coefficient of the metal on the oxide composition (a₀) in a binary oxide which is predominantly an electronic semiconductor and contains defects only in the cation sublattice has been examined theoretically. For the case where there is only one type dominant lattice defect following an ideal solution behavior the chemical diffusion coefficient is independent of a₀ When more than one type of defect is present instead, the chemical diffusion coefficient depends on a₀. Furthermore, it is shown that values of the chemical diffusion coefficient obtained by thermogravimetric analysis may differ from those obtained using changes in electrical conductivity. Results are compared with available experimental data for NiO and CoO at 1000°C and reasonable agreement is found.     

A variational derivation of the velocity distribution functions for nonequilibrium,multispecies, weakly interacting,spherically symmetric many-body systems

The most probable velocity distribution function of each component,f _a , of a nonequilibrium multispecies spherically symmetric system of particles (stellar plasma atmospheres and winds, stellar systems, pellet-fusion systems) is analytically derived forthe case in which each component is described by the first six moments of f _a . This is achieved by the aid of a variational approach based on the requirement that the BoltzmannH function for the system be a minimum, subject to the constraints provided by the sets of six macroscopic parameters describing the nonequilibrium state. The use of the so-obtained velocity distribution functions for the closure of the moment equations as well as for the calculation of their collisional terms (via the Fokker-Planck equation) is discussed. The limitations on the maximum deviations from the equilibrium state which are consistent with the assumptions used are also indicated.     

Dynamical properties of colloidal systems: III. Collective and self-diffusion of interacting charged particles

The formalism, developed in two earlier papers, for the dynamics of interacting Brownian particles is applied to a system of charged spherical particles in solution. Memory-type transport equations are derived for the propagators of collective and self-diffusion. The memory function for collective diffusion can be related, in the hydrodynamic limit, to the viscosity of the “fluid” of Brownian particles. The memory functions are calculated for a Debye-Hückel system, from an experimentally determined static structure factor S(k), and for an overdamped one-component plasma (OCP). In the two latter cases satisfactory agreement is found with dynamical light scattering results on solutions of polystyrene spheres; in particular, the deviation of the dynamical structure factor from a simple exponential decay can be related to memory effects. With regard to self-diffusion the velocity autocorrelation function, the mean square displacement of one particle and from it the self-diffusion coefficient D_s are calculated. Using S(k) for an actual system, $\text{D}{}_{\mathrm{s}}\text{≈}\text{1}\text{3}\text{D}{}_0$ is obtained, where D₀ is the free diffusion constant. The calculations on the basis of the overdamped OCP-model show that the dynamical properties of the experimentally investigated systems of charged polystyrene spheres can be described by this model for a wide range of scattering angles.     

Radiative transfer in the lyman α spectral line with self-consistent electron velocity distribution

Radiative transfer in the Ly α spectral line in a stationary, plane-parallel plasma of constant temperature and electron density is studied using model H-atoms with only two bound levels and a continuum. For this purpose, the equation of radiative transfer is solved simultaneously with the steady-state equations of the atomic levels and the kinetic equation of the electrons. The numerical results indicate that, in hydrogen plasmas with temperatures T ? 12,000°K and electron densities n_e ? 10¹⁶cm^?3, the high-energy tail of the electron velocity distribution deviates from a Maxwell distribution, even in cases of rather large optical thicknesses and that therefore the deviations from local thermodynamic equilibrium are increased compared with estimates based on the assumption of a Maxwellian electron velocity distribution. This qualitative conclusion should hold in spite of some deficiencies of the model which are discussed.     

The angular distributions of secondaries in proton-nucleus interactions at 200 and 300 GeV

The angular distributions of shower particles from proton-nucleus collisions at 200 and 300 GeV are investigated and correlated to the nuclear parameters (heavy prong emission), the inelasticity coefficient and the angle of the leading track. A partition is made into two components, the LP component associated with a single collision and the RC component corresponding to the excess from repeated collisions at the same proton and the nucleons inside the nucleus. Results from earlier investigations on the multiplicity distributions are confirmed. The LP component exhibits an excess of about 30% as compared to the shower particle emission in proton-proton collisions at the same energy. We find that the excess particles are slow moving in the equal velocity system, i.e., the frame in which the proton and the nucleus have equal but oppositely directed velocities. The opening angle of the cone inside which the proton-nucleus distributions are similar to the proton-proton distributions at the same energy is small (? 0.5°) and is energy dependent. We also find indications of A dependence and a noticeable correlation to the inelasticity coefficient and to the angle of the leading track.     

An investigation of the internal temperature dependence of Pd-Pt cluster beam deposition: A molecular dynamics study

We investigated the internal temperature dependence of the Pd_1−aPt_a cluster beam deposition in the present study via the molecular dynamics simulations of soft-landing. By analysis of the velocity distribution and diffusion coefficient of the bimetallic cluster, Pd atoms with better mobility improved the diffusibility of Pt atoms. The radial composition distribution showed that a Pt-core/Pd-shell structure of the cluster formed at high internal temperatures through migrations of the Pd atoms from inner to surface shells. In the soft-landing process, the diffusing and epitaxial behaviors of the deposited clusters mainly depended on the internal temperature because the incident energy of the cluster was very small. By depositing clusters at high internal temperatures, we obtained a thin film of good epitaxial growth as the energetic cluster impact. Furthermore, nonepitaxial configurations such as scattered nonepitaxial atoms, misoriented particles, and grain boundaries of (1 1 1) planes were produced in the growth of the cluster-assembled film. As the size of the incident cluster increased, the internal temperature of the cluster needed for better interfacial diffusion and contact epitaxy on the substrate also rose.     

Hamiltonian and Brownian systems with long-range interactions: V. Stochastic kinetic equations and theory of fluctuations

We developed a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic Smoluchowski equation governing the evolution of the fluctuating density field of Brownian particles, we determine the expression of the correlation function of the density fluctuations around a spatially homogeneous equilibrium distribution. In the stable regime, we find that the temporal correlation function of the Fourier components of density fluctuations decays exponentially rapidly, with the same rate as the one characterizing the damping of a perturbation governed by the deterministic mean field Smoluchowski equation (without noise). On the other hand, the amplitude of the spatial correlation function in Fourier space diverges at the critical point T=T_c (or at the instability threshold k=k_m) implying that the mean field approximation breaks down close to the critical point, and that the phase transition from the homogeneous phase to the inhomogeneous phase occurs sooner. By contrast, the correlations of the velocity fluctuations remain finite at the critical point (or at the instability threshold). We give explicit examples for the Brownian Mean Field (BMF) model and for Brownian particles interacting via the gravitational potential and via the attractive Yukawa potential. We also introduce a stochastic model of chemotaxis for bacterial populations generalizing the deterministic mean field Keller-Segel model by taking into account fluctuations and memory effects.     

Laser impulse coupling at 130 fs

We measured the momentum coupling coefficient C_m and laser-generated ion drift velocity and temperature in the femtosecond (fs) region, over a laser intensity range from ablation threshold to about one hundred times threshold. Targets were several pure metals and three organic compounds. The organic compounds were exothermic polymers specifically developed for the micro-laser plasma thruster, and two of these used “tuned absorbers” rather than carbon particles for laser absorption. The metals ranged from Li to W in atomic weight. We measured time of flight (TOF) profiles for ions. Specific impulse reached record values for this type of measurement and ablation efficiency was near 100%. These measurements extend the laser pulsewidth three orders of magnitude downward in pulsewidth relative to previous reports. Over this range, we found C_m to be essentially constant. Ion velocity ranged from 60 to 180 km/s.     

Steady State Properties of One-Dimensional Non-uniform Granular Gases Subjected to Gaussian White Noise Driving

We present a model of non-uniform granular gases in one-dimensional case, whose granularity distribution has the fractal characteristic. We have studied the nonequilibrium properties of the system by means of Monte Carlo method. When the typical relaxation time T of the Brownian process is greater than the mean collision time To, the energy evolution of the system exponentially decays, with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state in which the velocity distribution strongly deviates from the Gaussian one. Three other aspects have also been studied for the steady state： the visualized change of the particle density, the entropy of the system and the correlations in the velocity of particles. And the results of simulations indicate that the system has strong spatial clustering; Furthermore, the influence of the inelasticity and inhomogeneity on dynamic behaviors have also been extensively investigated, especially the dependence of the entropy and the correlations in the velocity of particles on the restitute coefficient e and the fractal dimension D.     

Velocity distributions of granular gases with drag and with long-range interactions

We study velocity statistics of electrostatically driven granular gases. For two different experiments, (i) nonmagnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(upsilon) approximately exp(-/upsilon/). This behavior is consistent with the kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gases are sensitive to the fluid environment and to the form of the particle interaction.     

On the velocity distribution of excited Fe-atoms by sputtering of iron

From the velocity distribution of excited sputtered particles detailed information on the excitation process can be obtained. In the present paper the first direct measurement of velocity distribution of excited atoms sputtered from a metal target is presented. The irradiation of the Fe-target was performed with 10keV Ar⁺-ions. The sputtered atoms were detected using pulsed laser induced fluorescence (LIF). The sputtered Fe atoms in the metastable statea ⁵ F ₅ at 0.86 eV shows a much broader distribution, than found for the ground-state atoms, but no energy threshold, implied in the statistical excitation models, was found.     

An asymptotic approximation of the Fokker–Planck model of evolution of superthermal ultrarelativistic particles in the presence of interaction scaling

The evolution of a superthermal relict plasma component is studied using a nonequilibrium model of the Universe [1] and a kinetic equation of the Fokker–Planck type [2]. Given is the evidence of two maxima in the distribution of superthermal particles. The first maximum can further evolve into an equilibrium distribution, whereas the second one can result in a high-energy tail of superthermal relict particles. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 87–91, February, 2009.     

Investigation on the electric properties in molten quaternary systems by MD simulation

For the pyrochemical reprocessing of spent metallic fuels in molten salt, it is of importance to estimate the enrichment degree of Cs. The molecular dynamics simulation has been carried out on molten quaternary systems (Li, Na, K, Cs)Cl at 625K and (Li, Na, K, Cs)F at 727K for the various compositions in order to investigate the electric properties, i.e., the electric conductivity, self-diffusion coefficient, self-exchange velocity and the relative differences in the internal cation mobilities of Cs in molten LiCl-NaCl-KCl eutectic mixtures and in the FLINAK melts. These results allow us to conclude that the electric conductivities, self-diffusion coefficients and self-exchange velocities of Li⁺, Na⁺, K⁺ and Cs⁺ with reference to Cl⁻ and F⁻ have almost similar tendencies for each composition. We found it possible to enrich at up to χ_Cs = 0.38 in molten LiCl-NaCl-KCl eutectic as well as LiCl-KCl system and up to χ_Cs = 0.42 in the FLINAK melts as well as in molten FLINA system. In addition, the sequence of the simulated electric conductivity in molten quaternary alkali chloride and fluoride systems was in a fair agreement with that of the current simulated self-exchange velocities and self-diffusion coefficients.     

Experimental determination of the electron-avalanche and the electron-ion recombination coefficient

The electron-ion recombination coefficient γ and the avalanche coefficient δ = (α ? a) · v_d, where α and a are the ionizat ion and attachment coefficients respectively and v_d the drift velocity of the electrons, have been experimentally determined in a self-sustained CO₂-laser system (1:1:3 mixture) as a function of the E/N value. For low voltages we found the expected decrease of the recombination coefficient for increasing E/N values. However, it appears that for larger voltage the recombination coefficient increases sharply for increasing E/N values. The measurements of δ show a much smaller value than expected from theoretical calculations. This must be explained by a lower value of the electron-energy distribution function for higher energies, which may be consistent with our measured high recombination probability for electrons having high energy.     

Stationary states and energy cascades in inelastic gases

We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transferred from large velocity scales to small velocity scales. These steady states exist for arbitrary collision rules and arbitrary dimension. Their signature is a stationary velocity distribution f(v) with an algebraic high-energy tail, f(v) approximately v(-sigma). The exponent sigma is obtained analytically and it varies continuously with the spatial dimension, the homogeneity index characterizing the collision rate, and the restitution coefficient. We observe these stationary states in numerical simulations in which energy is injected into the system by infrequently boosting particles to high velocities. We propose that these states may be realized experimentally in driven granular systems.