Related papers: Method of difference-differential equations for so…
Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is…
The paper is focused on the dynamic homogenization of lattice-like materials with lumped mass at the nodes to obtain energetically consistent models providing accurate descriptions of the acoustic behavior of the discrete system. The…
We apply the method of moments to the relativistic Boltzmann-Vlasov equation and derive the equations of motion for the irreducible moments of arbitrary tensor-rank of the invariant single-particle distribution function. We study two cases,…
The Boltzmann equation is a powerful theoretical tool for modeling the collective dynamics of quantum many-body systems subject to external perturbations. Analysis of the equation gives access to linear response properties including…
A low-dimensional model (LDM) for turbulent Rayleigh-Benard convection in a Cartesian cell with square domain, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The…
The convective Brinkman-Forchheimer (CBF) equations characterize the motion of incompressible fluid flows in a saturated porous medium. The small noise asymptotic for the two-time-scale stochastic convective Brinkman-Forchheimer (SCBF)…
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in $\mathbb{R}^d$. An important special case is the time-fractional diffusion equation, which has seen much…
The spectral function and dynamic structure factor of bosons interacting by contact repulsion and confined to one dimension exhibit power-law singularities along the dispersion curves of the collective modes. We find the corresponding…
We numerically study the momentum distribution of one-dimensional Bose and Fermi systems with long-range interaction $g/r^2$ for the ``special'' values $g= -\frac{1}{2}, 0, 4$, singled out by random matrix theory. The critical exponents are…
We analyze the two-body momentum correlation function for a uniform weakly interacting one-dimensional Bose gas. We show that the strong positive correlation between opposite momenta, expected in a Bose-Einstein condensate with a true…
The Bogoliubov - de Gennes equations are solved for the Coulomb Bose gas describing a fluid of charged bosons at finite temperature. The approach is applicable in the weak coupling regime and the extent of its quantitative usefulness is…
This paper concerns with numerical approximations of solutions of second order fully nonlinear partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, is introduced for second order fully nonlinear…
We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the $2$-Wasserstein gradient flow structure of the equations in order to obtain the nonlocal approximating PDEs…
The study of gapped quantum many-body systems in three spatial dimensions has uncovered the existence of quantum states hosting quasiparticles that are confined, not by energetics but by the structure of local operators, to move along lower…
We study a three-mode Hamiltonian modelling a heteronuclear molecular Bose--Einstein condensate. Two modes are associated with two distinguishable atomic constituents, which can combine to form a molecule represented by the third mode.…
In this work, we investigate a class of quasilinear wave equations of Westervelt type with, in general, nonlocal-in-time dissipation. They arise as models of nonlinear sound propagation through complex media with anomalous diffusion of…
Admissible point transformations between Burgers equations with linear damping and time-dependent coefficients are described and used in order to exhaustively classify Lie symmetries of these equations. Optimal systems of one- and…
A new Bateman-Hillion solution to the Dirac equation for a relativistic Gaussian electron beam taking explicit account of the $4$-position of the beam waist is presented. This solution has a pure Gaussian form in the paraxial limit but…
We apply Quantum Monte Carlo technique to analyze the non equlibrium state of a trapped 1d Bose gas just after the quenching of the confining potential. As a matter of fact we solve the time dependent Schroedinger equation for the system of…
We address the problem of calculating the correlation functions of one-dimensional two-component gases with strong repulsive contact interactions. The model considered in this paper describes particles with fractional statistics and in…