Related papers: Spectral BBGKY: a scalable scheme for nonlinear Bo…
We apply the spectral-Lagrangian method of Gamba and Tharkabhushanam for solving the homogeneous Boltzmann equation to compute the low probability tails of the velocity distribution function, $f$, of a particle species. This method is based…
The time-dependent density-matrix theory (TDDM) where the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for reduced density matrices is truncated by approximating a three-body density matrix with one-body and two-body density matrices is…
In this work, we study the Cauchy problem for the spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. We prove that this Cauchy problem enjoys Gelfand-Shilov regularizing effect, that means the smoothing…
The class of higher-dimensional scenarios, based on a brane-localised Higgs boson coupled to bulk fermions, can address both the flavour puzzle and gauge hierarchy problem. A key question arises due to the possibility of fermion profile…
We consider semigroups of operators for hierarchies of evolution equations of large particle systems, namely, of the dual BBGKY hierarchy for marginal observables and the BBGKY hierarchy for marginal distribution functions. We establish…
This article explores the exceptional integrability property of a family of higher-order Benjamin-Bona-Mahony (BBM)-type nonlinear dispersive equations. Here, we highlight its deep relationship with a generalized infinite hierarchy of the…
A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single…
We develop an analytical approach to the spectral form factor and out-of-time ordered correlators in zero-dimensional Brownian models of quantum chaos. The approach expresses these spectral correlations as part of a closed hierarchy of…
A general framework for constructing discrete Boltzmann model for non-equilibrium flows based on the Shakhov model is presented. The Hermite polynomial expansion and a set of discrete velocity with isotropy are adopted to solve the kinetic…
We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift $-\mu$ and killed upon reaching $0$. More precisely, the particles branch at rate…
In this paper, we present a new class of conservative semi-Lagrangian schemes for kinetic equations. They are based on the conservative reconstruction technique introduced in [S. Y. Cho, et al., Conservative semi-Lagrangian schemes for…
We present a hybrid Boltzmann-BGK model for inert mixtures, where each kind of binary interaction may be described by a classical Boltzmann integral or by a suitable relaxation-type operator. We allow also the possibility of changing the…
In this paper, we propose a general framework to design asymptotic preserving schemes for the Boltzmann kinetic kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source)…
We propose a global geometric framework which allows one to encode a natural non-perturbative generalisation of usual Batalin-Vilkovisky (BV-)theory. Namely, we construct a concrete model of derived differential geometry, whose geometric…
The kinetic Boltzmann equation models gas dynamics over a wide range of spatial and temporal scales. Simplified versions of the full Boltzmann collision operator, such as the classical Bhatnagar-Gross-Krook and the closely related…
We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the riveting properties of the single-species fast spectral method (Gamba et al. SIAM J. Sci. Comput., 39 pp. B658--B674…
Time-resolved spectroscopy is a powerful tool for probing electron dynamics in molecules and solids, revealing transient phenomena on sub-femtosecond timescales. The interpretation of experimental results is often enhanced by parallel…
The mathematical analysis of diffuse-interface models for multiphase flows has attracted significant attention due to their ability to capture complex interfacial dynamics, including curvature effects, within a unified, energetically…
Stochastic differential equations and the associated partial differential equations are the cornerstone formalism in stochastic control problems. The universality of bilinear stochastic systems can be found in autonomous systems, non-linear…
This work is aimed to develop a new class of methods for the BGK model of the Boltzmann equation. This technique allows to get high order of accuracy both in space and time, theoretically without CFL stability limitation. It's based on a…