Related papers: In search of Robbins stability
Within the framework of the algebra of canonical commutation relations in Euclidean space, a long range order between particles in bounded regions is established in states with a sufficiently large particle number. It occurs whenever…
In this paper, we associate to every $p$-adic representation $V$ a $p$-adic differential equation $\mathbf{D}^{\dagger}_{\mathrm{rig}}(V)$, that is to say a module with a connection over the Robba ring. We do this via the theory of…
Let $(x_n)_{n=1}^\infty$ be a sequence of integers. We study the number variance of dilations $(\alpha x_n)_{n=1}^\infty$ modulo 1 in intervals of length $S$, and establish pseudorandom (Poissonian) behavior for Lebesgue-almost all $\alpha$…
We study the equilibrium fluctuations of an interacting particle system evolving on the discrete ring with $N\in\mathbb N$ points, denoted by $\mathbb T_N$, and with three species of particles that we name $A,B$ and $C$, but such that at…
We study four dimensional non-abelian gauge theories with classical moduli. Introducing a chemical potential for a flavor charge causes moduli to become unstable and start condensing. We show that the moduli condensation in the presence of…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
We consider the three dimensional gravitational Vlasov Poisson system which describes the mechanical state of a stellar system subject to its own gravity. A well-known conjecture in astrophysics is that the steady state solutions which are…
Here we present an experimental observation of the self-organization effect of the polystyrene particles formed by acoustically-induced interaction forces. Two types of stable configurations are observed experimentally: one is mechanically…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
For each integer $n\geq2$ we describe the space of stability conditions on the derived category of the $n$-dimensional Ginzburg algebra associated to the $A_2$ quiver. The form of our results points to a close relationship between these…
We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schr\"{o}dinger and Korteweg-de Vries equations under random perturbations of…
We have found a way to analyze Edwards' density of states for static granular packings in the special case of round, rigid, frictionless grains assuming constant coordination number. It obtains the most entropic density of single grain…
The study of structures involving vortices in one component and bright solitary waves in another has a time-honored history in two-component atomic Bose-Einstein condensates. In the present work, we revisit this topic extending…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of…
A tempered version of the discrete Linnik distribution is introduced in order to obtain integer-valued distribution families connected to stable laws. The proposal constitutes a generalization of the well-known Poisson-Tweedie law, which is…
Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit…
We investigate dynamics near Turing patterns in reaction-diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a "normal form" coordinate system near such Turing patterns…
The multidimensional ($n$-D) systems described by Roesser model are presented in this paper. These $n$-D systems consist of discrete systems and continuous fractional order systems with fractional order $\nu$, $0<\nu<1$. The stability and…
Given a set $A\subseteq\mathbb{N}$, we consider the relationship between stability of the structure $(\mathbb{Z},+,0,A)$ and sparsity of the set $A$. We first show that a strong enough sparsity assumption on $A$ yields stability of…