Related papers: Gap distributions and homogeneous dynamics
Using the theory of $L^p$-graphons (Borgs et al, 2014), we derive and rigorously justify the continuum limit for systems of differential equations on sparse random graphs. Specifically, we show that the solutions of the initial value…
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
The $S$-gap shifts have a dynamically and combinatorially rich structure. Dynamical properties of the $S$-gap shift can be related to the properties of the set $S$. This interplay is particularly interesting when $S$ is not syndetic such as…
Let $G$ be a noncompact semisimple Lie group, $\Gamma$ be an irreducible cocompact lattice in $G$, and $P<G$ be a minimal parabolic subgroup. We consider the dynamics of $P$ acting on $G/\Gamma$ by left translation. For any infinite subset…
Interest in the dynamical arrest leading to a fluid --> solid transition in thermal and athermal systems has led to questions about the nature of these transitions. These jamming transitions may be dependent on the influence of extended…
By means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case.
We consider isometric actions of lattices in semisimple algebraic groups on (possibly non-compact) homogeneous spaces with (possibly infinite) invariant Radon measure. We assume that the action has a dense orbit, and demonstrate two novel…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
In this paper the phenomenon of dynamic heterogeneity in supercooled liquid systems is considered in terms of the recently proposed gauge theory of glass transition. The physical interpretation of the dynamic scaling is considered. It is…
Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
The behavior of many complex systems, from nanostructured materials to animal colonies, is governed by local transitions that, while involving a restricted number of interacting units, may generate collective cascade phenomena. Tracking…
We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy…
In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the…
The statistics of gap ratios between consecutive energy levels is a widely used tool, in particular in the context of many-body physics, to distinguish between chaotic and integrable systems, described respectively by Gaussian ensembles of…
Granular segregation is ubiquitous in industrial, geological or daily-life context, but there is still no unifying theoretical approach. In this review, we examine two examples of granular segregation -- shallow rapid flows and rotating…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
We study the dynamics of one--dimensional discrete models of one--component active medium built up of spatially inhomogeneous chains of diffusively coupled piecewise linear maps. The nonhomogeneities (``defects'') are treated in terms of…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
The main purpose of this paper is calculation of differential invariants which arise from prolonged actions of two Lie groups SL(2) and SL(3) on the $n$th jet space of $R^2$. It is necessary to calculate $n$th prolonged infenitesimal…