The structure and dynamics of a harmonically confined three dimensional finite dust cluster are investigated via both Langevin Dynamics (LD) and frictionless Molecular Dynamics (fMD) simulation. The static structure of the system is analyzed through...
We study the recombination process of three atoms scattering into an atom and diatomic molecule in heteronuclear mixtures of ultracold atomic gases with large and positive interspecies scattering length at finite temperature. We calculate the tempera...
Given a finite point set $P \subset \mathbb{R}^d$, a $k$-ary semi-algebraic relation $E$ on $P$ is the set of $k$-tuples of points in $P$, which is determined by a finite number of polynomial equations and inequalities in $kd$ real variables. The des...
Linearized polynomials over finite fields have been much studied over the last several decades. Recently there has been a renewed interest in linearized polynomials because of new connections to coding theory and finite geometry. We consider the pr...
We investigate finite-size effects on diffusion in confined fluids using molecular dynamics simulations and hydrodynamic calculations. Specifically, we consider a Lennard-Jones fluid in slit pores without slip at the interface and show that the use o...
In this paper, we study properties of the Diophantine exponents $w_n$ and $w_n^{*}$ for Laurent series over a finite field. We prove that for an integer $n\geq 1$ and a rational number $w>2n-1$, there exist a strictly increasing sequence of positive...
This paper has two parts. First, we recall and detail the definition of the Grothendieck topos of a connectivity space, that is the topos of sheaves on such a space. In the second part, we prove that every finite connectivity space is Morita-equivale...
Let for a prime $p$, $\mathfrak{X}$ (respectively $\mathfrak{Y}$) be the class of all $p$-biprimitively finite (respectively periodic $p$-conjugatively biprimitively finite) groups and $G\in \mathfrak{X}$ (respectively $G\in \mathfrak{Y}$), $V$ be a...
We show that all finite lattices, including non-distributive lattices, arise as stable matching lattices under standard assumptions on choice functions. In the process, we introduce new tools to reason on general lattices for optimization purposes: t...
An infinite family of finite axisymmetric charged dust disks is presented. The disks are obtained by solving the Einstein-Maxwell equations for conformastatic spacetimes by assuming a functional dependency between the time-like component of the ele...
We present a new method of establishing the finite-dimensionality of limit dynamics (in terms of bi-Lipschitz Mane projectors) for semilinear parabolic systems with cross diffusion terms and illustrate it on the model example of 3D complex Ginzburg-L...
We study the global attractors of abstract semilinear parabolic equations and their projections to finite-dimensional planes. It is well-known that the attractor can be embedded into the finite-dimensional inertial manifold if the so-called spectral...
We analyse and clarify the finite-size scaling of the weakly-coupled hierarchical $n$-component $|\varphi|^4$ model for all integers $n \ge 1$ in all dimensions $d\ge 4$, for both free and periodic boundary conditions. For $d>4$, we prove that for a...
In this paper, we are interested in the numerical analysis of blow up for the Chipot-Weissler equation with Dirichlet boundary conditions in bounded domain. To approximate the blow up solution, we construct a finite difference scheme and we prove tha...
In this paper we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attracting or repulsive forces given by a certain inter molecular potential. We limit ourselves...
We investigate finite amplitude stability of spatially inhomogeneous steady state of an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls kept at spatially non-uniform temperature. For a wide class of incompre...
We explicitly construct a finite set of separating invariants for the basic $\Ga$-actions. These are the finite dimensional indecomposable rational linear representations of the additive group $\Ga$ of a field of characteristic zero, and their invari...
A two-dimensional, transient, multi-scale modeling approach is presented for predicting the magnitude and rate of percolation segregation for binary mixtures of granular material in a rotating drum and conical hopper. The model utilizes finite elemen...
Consider a finite irreducible Markov chain with invariant probability $π$. Define its inverse communication speed as the expectation to go from x to y, when x, y are sampled independently according to $π$. In the discrete time setting and when $π$...
We prove that homotopy invariants of finite degree distinguish homotopy classes of maps of a connected compact CW-complex to a nilpotent connected CW-complex with finitely generated homotopy groups....