Related papers: Interacting particle models and the Pieri-type for…
We study model transition for representations occurring in the local theta correspondence between split even special orthogonal groups and symplectic groups, over a non-archimedean local field of characteristic zero.
This paper gives an overview of the particle transport theory essentials, the basics of particle-material interaction simulation, physical quantities needed to simulate particle transport and interactions in materials, Monte Carlo…
This paper presents a proposal of a rather new type of effective interatomic interaction for molecular dynamics and similar applications. The model consists of atoms with prescribed geometric arrangement of active orbitals, represented by…
In symmetric Macdonald polynomial theory the Pieri formula gives the branching coefficients for the product of the rth elementary symmetric function and the Macdonald polynomial. In this paper we give the nonsymmetric analogues for the…
We establish a general perturbative method to prove entropic Ricci curvature bounds for interacting stochastic particle systems. We apply this method to obtain curvature bounds in several examples, namely: Glauber dynamics for a class of…
An important open problem in materials science is whether a direct connection exists between single-particle elastic properties and the macroscopic bulk behavior. Here we address this question by focusing on the archetype of soft colloids:…
We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative $U(1)$ gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we…
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…
The action of parity inversion, time inversion and charge conjugation operations on several differential equations for a classical point charged particle are described. Moreover, we consider the notion of {\it symmetrized acceleration}…
A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite patch of the wedgeshaped, which meets the interface at a right angle and is loaded with tangential and normal forces is considered. By using methods of the theory…
Diagonal or chevron patterns are known to spontaneously emerge at the intersection of two perpendicular flows of self-propelled particles, e.g. pedestrians. The instability responsible for this pattern formation has been studied in previous…
Bianchi -I, -III, and FRW type models minimally coupled to a massive spatially homogeneous scalar field (i.e. a particle) are studied in the framework of semiclassical quantum gravity. In a first step we discuss the solutions of the…
We develop a new model of a spinning particle in Brans-Dicke spacetime using a metric-compatible connection with torsion. The particle's spin vector is shown to be Fermi-parallel (by the Levi-Civita connection) along its worldline (an…
We apply the "systematic" $1^{st}$ order cosmological perturbation theory method to re-derive the formulation of an inflationary model generated by variation of constants, then to study the case where it is non-minimally coupled to gravity…
We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…
In this paper a possibility of the accelerated expansion of the large scale universe with a varying polytropic fluid of a certain type is presented. About a special role of non-gravitational interactions between dark energy and dark matter,…
I show how the symmetry-breaking of a recently proposed embedding of the standard model of particle physics in $E_8$ can be explained in terms of the representation theory of the binary tetrahedral group. This finite group provides a link…
We prove a color-position symmetry for a class of ASEP-like interacting particle systems with discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our systems allows to apply the result to colored (or…
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…
In this thesis, we develop multiscale models for particle simulations in population dynamics. These models are characterised by prescribing particle motion on two spatial scales: microscopic and macroscopic. At the microscopic level, each…