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The aim of this work is to investigate the application of partial moment approximations to kinetic chemotaxis equations in one and two spatial dimensions. Starting with a kinetic equation for the cell densities we apply a…
A canonical approach to Cherenkov radiation in the presence of a magnetodielectric medium is presented in classical, nonrelativistic and relativistic quantum regimes. The equations of motion for the canonical variables are solved explicitly…
A general discussion is made concerning the ways in which one can get signatures about a possible liquid-gas phase transition in nuclear matter. Microcanonical temperature, heat capacity and second order derivative of the entropy versus…
We provide a rigorous justification of the semiclassical quasi-neutral and the quantum many-body limits to the isothermal Euler equations. We consider the nonlinear Schr\"{o}dinger-Poisson-Boltzmann system under a quasi-neutral scaling and…
We consider a sharp interface formulation for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling. The flow is characterized by a cluster of surfaces evolving such that the total surface energy plus a weighted sum…
This work concerns the numerical approximation with a finite volume method of inviscid, nonequilibrium, high-temperature flows in multiple space dimensions. It is devoted to the analysis of the numerical scheme for the approximation of the…
The neon isotopic chain displays a rich phenomenology, ranging from clustering in the ground-state of the self-conjugate doubly open-shell stable $^{20}$Ne isotope to the physics of the island of inversion around the neutron-rich $^{30}$Ne…
Using charged hard spheres model as an example, the dense one-component plasma is considered. For this model the Enskog-Landau kinetic equation is obtained and its normal solution is found using the Chapman-Enskog method. Transport…
A novel refinement of the conventional treatment of Kadanoff--Baym equations is suggested. Besides the Boltzmann equation another differential equation is used for calculating the evolution of the non-equilibrium two-point function.…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in…
We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time points. The algorithm is obtained through a delicate…
Quantum Max Cut (QMC), also known as the quantum anti-ferromagnetic Heisenberg model, is a QMA-complete problem relevant to quantum many-body physics and computer science. Semidefinite programming relaxations have been fruitful in designing…
Ab initio approaches to the nuclear many-body problem have seen their reach considerably extended over the past decade. However, collective excitations have been scarcely addressed so far due to the prohibitive cost of solving the…
Analyses of multifragmentation in terms of the Fisher droplet model (FDM) and the associated construction of a nuclear phase diagram bring forth the problem of the actual existence of the nuclear vapor phase and the meaning of its…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
Nucleation in systems with a metastable liquid-gas critical point is the prototypical example of a two-step nucleation process, in which the appearance of the critical nucleus is preceded by the formation of a liquid-like density…
Spectral method related to Lame equation with finite-gap potential is used to study the optical cascading equations. These equations are known not to be integrable by inverse scattering method. Due to "partial integrability" two-gap…
The Hamiltonian structure for the supersymmetric $N=2$ Novikov equation is presented. The bosonic sector give us two-component generalization of the cubic peakon equation. The double extended: two-component and two-peakon Novikov equation…
The existence of entire solutions to quasilinear elliptic systems exhibiting both singular and convective reaction terms is discussed. An auxiliary problem, obtained by `freezing' the convection terms and `shifting' the singular ones, is…