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New formulas are given for the grand partition function of paraboson systems of order p with n orbitals and parafermion systems of order p with m orbitals. These formulas allow the computation of statistical and thermodynamic functions for such systems. We analyze and discuss the average number of particles on an orbital, and the average number of particles in the system. For some special cases (identical orbital energies, or equidistant orbital energies) we can simplify the grand partition functions and describe thermodynamic properties in more detail. Some specific properties are also illustrated in plots of thermodynamic functions.

The software described in the article provides a method for determining the particle size distribution of the solid pulp phase, first implemented in world practice. The program for numerical analysis and representation of the simulation results of changes in the particle size distribution of the pulp solid phase under the controlling influence of high-energy ultrasound radiation pressure is developed. The particle distribution function according to the useful component disclosure degree is built.

Single particle distribution function of plasma particles has been derived from the first member of the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy utilising the pair correlation function evaluated in [Bose, Phys. Plasmas 26, 064501 (2019)] from the second member of the BBGKY hierarchy. This distribution function may be employed to probe the thermodynamic properties of the weakly inhomogeneous plasma systems.

We analyze the problem of the beam-plasma instability via the analytical treatment of the so-called Dyson equation. We first compared the prediction of the model constructed by fixing the electric field amplitude with respect to a N-body Hamiltonian numerical simulation. Then, we demonstrate that the shortcomings of such an analytical formulation must be essentially identified with the breaking-down of the self-consistent evolution of the field and the particle distribution function., Comment: 7 pages, 6 figures

Bernstein-Kruskal-Greene (or BGK) modes are ubiquitous nonlinear solutions for the 1D electrostatic Vlasov equation, with the particle distribution function $f$ given as a function of the particle energy. Here, we consider other solutions $f = f[\epsilon]$ where the particle energy is equal to the second-order velocity space Taylor expansion of the function $\epsilon(x,v,t)$ near the wave-particle resonance. This formalism allows us to analytically examine the time evolution of plasma waves with time-varying complex frequency $\omega(t) + i \gamma(t)$ in the linear and nonlinear phases. Using a Laplace-like decomposition of the electric potential, we give allowed solutions for the time-varying complex frequencies. Then, we show that $f$ can be represented analytically via a family of basis decompositions in such a system. Using a Gaussian decomposition, we give approximate solutions for contours of constant $f$ for a single stationary frequency mode, and derive the evolution equation for the nonlinear growth of a frequency sweeping mode. For this family of modes, highly nonlinear orbits are found with the effective width in velocity of the island roughly a factor of $\sqrt{2}$ larger than the width of a BGK island., Comment: 12 pages, 3 figures

This paper reports on a one-step simulation study of the generation and propagation of thermoacoustic waves in a two-dimensional enclosure using a finite-difference lattice-Boltzmann-type method (FDLBM) with a single relaxation time and one equilibrium particle distribution function (EPDF), and a direct aeroacoustic simulation (DAS) technique that solves the primitive Navier–Stokes (N–S) equations. Conventional expansion of the EPDF is not adopted; instead, it is expanded in terms of the particle velocity alone, and the expansion coefficients are determined by requiring the FDLBM to fully recover the N–S equations. The expansion coefficients are found to depend on the flow and thermal properties and their nonlinear interactions. Thus formulated, physical boundary conditions can be specified for the FDLBM. This EPDF has been validated against simple aeroacoustic problems and good agreement with DAS results is obtained. In this paper, the EPDF is further validated against three thermoacoustic cases: 1) a sudden increase of temperature on the left vertical wall of the enclosure; 2) a sudden increase of temperature on the left vertical wall coupled by a sudden decrease of temperature on the right vertical wall in the enclosure; 3) a gradually heated up left vertical wall of the enclosure. Comparisons with DAS simulations show that FDLBM and DAS give essentially identical results; hence, the validity and extent of the EPDF is ascertained for the calculation of these thermoacoustic waves. The FDLBM results are also compared with known theoretical and numerical results. These known solutions are found to be less accurate compared to the FDLBM results. The discrepancy could be attributed to the partially linearized equations solved in the theoretical analysis, and the inadequacy of the numerical scheme to replicate the nonlinear effects accurately in the generation and propagation of thermoacoustic waves.

Reconnection outflows have been under intense recent scrutiny, from in situ observations and from simulations. These regions are host to a variety of instabilities and intense energy exchanges, often even superior to the main reconnection site. We report here a number of results drawn from an investigation of simulations. First, the outflows are observed to become unstable to drift instabilities. Second, these instabilities lead to the formation of secondary reconnection sites. Third, the secondary processes are responsible for large energy exchanges and particle energization. Finally, the particle distribution function are modified to become non-Maxwellian and include multiple interpenetrating populations.

Using the linearized version of the time dependent Gross-Pitaevskii equation we calculate the dynamic response of a Bose-Einstein condensed gas to periodic density and particle perturbations. The zero temperature limit of the fluctuation-dissipation theorem is used to evaluate the corresponding quantum fluctuations induced by the elementary excitations in the ground state. In uniform conditions the predictions of Bogoliubov theory, including the infrared divergency of the particle distribution function and the quantum depletion of the condensate, are exactly reproduced by Gross-Pitaevskii theory. Results are also given for the crossed particle-density response function and the extension of the formalism to non uniform systems is discussed. The generalization of the Gross-Pitaevskii equation to include beyond mean field effects is finally considered and an explicit result for the chemical potential is found, in agreement with the prediction of Lee-Huang-Yang theory., Comment: 6 pages. To appear in the Journal of the Experimental and Theoretical Physics (JETP) dedicated to the 85th anniversary of L.P. Pitaevskiy

A model of Forbush-decrease in a magnetic cloud is presented. We calculate moments of the particle distribution function depending on time. The calculated results of cosmic ray intensity generally agree with the observed ones in events registered by ground based detectors. It is found that the magnetic flux rope is of great importance in dynamics of Forbush decrease.

Asymptotic formulas have been derived for distribution functions in cylindrical slits with finite cross-section radii. The problem has been solved based on the asymptotic principle of interbody interactions within the framework of dispersion forces. Symmetric and asymmetric slits between two identical cylinders and between a cylinder and a planar infinite solid surface have been considered. Calculations have been performed for a symmetric slit with a width equal to two cylinder radii.

Article history: We prove the existence of the global weak entropy solution to the Doi-Saintillan-Shelley model for active and passive rod-like particle suspensions, which couples a Fokker-Planck equation with the incompressible Navier-Stokes or Stokes equation, under the no-flux boundary conditions, L 2 (Ω; L 1 (S d−1 )) initial data, and finite initial entropy for the particle distribution function in two and three dimensions. Furthermore, for the model with the Stokes equation, we obtain the global L 2 (Ω × S d−1 ) weak solution in two and three dimensions and the uniqueness in two dimension.