Related papers: Delone sets and dynamical systems
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
The local theory for regular and multi-regular systems was developed in the assumption that these systems are Delone sets, or (r;R)-systems. The requirement for a set to be a (r;R)-system particularly implies that any two points in a Delone…
The paper presents mathematical models of quasicrystals with particular attention given to cut-and-project sets. We summarize the properties of higher-dimensional quasicrystal models and then focus on the one-dimensional ones. For the…
A new kind of aperiodic tiling is introduced. It is shown to underlie a structure obtained as a superposition of waves with incommensurate periods. Its connections to other other tilings and quasicrystals are discussed.
We construct examples of Delone sets of the plane (that is, discrete subsets that are uniformly separated and coarsely dense) that are repetitive (each patch of the set appears in every large-enough ball) though non-rectifiable (i.e. non…
An invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables is given in terms of modulus of continuity. The result is applied to certain H\'enon maps and…
Lecture-notes: introducing and discussing basics on axion electrodynamics with application in the calculation of the images generated by an electric (or a magnetic) charge located close to an interface ordinary insulator-topological…
A novel, protean, topological soliton has recently been shown to emerge in systems of repulsive particles in cylindrical geometries, whose statics is described by the number-theoretical objects of phyllotaxis. Here we present a minimal and…
Hysteresis can be defined from a dynamical systems perspective with respect to equilibrium points. Consequently, hysteresis naturally lends itself as a topic to illustrate and extend concepts in a dynamical systems course. A number of…
Two-dimensional dilational materials, for which the only easy mode of deformation is a dilation are reviewed and connections are drawn between models previously proposed in the literature. Some models which appear to be dilational…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…
We establish the existence of `time quasicrystals', tilings of the time axis with two unit cells of different duration. These aperiodic tilings can be constructed as slices through regular tilings of a space spanned by two orthogonal time…
In this talk I will review the present status and future perspectives of some popular extensions of the conventional three-neutrino oscillation scenario, from a purely phenomenological point of view. For concreteness I will focus only on…
We prove linearly repetitive Delone systems have finitely many Delone system factors up to conjugacy. This result is also applicable to linearly repetitive tiling systems.
This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.
We describe a method to analyze and decompose the dynamics of a control system on a Lie group subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the…
This lecture has the following sections: Systems and States; Brownian Motion; Segmental Relaxation and the Glass Transition; Dynamics of a Free Chain; Entanglement and Reptation. Appendices cover: Linear response theory, relaxation,…
A first principles approach to the nonlinear flow of dense suspensions is presented which captures shear thinning of colloidal fluids and dynamical yielding of colloidal glasses. The advection of density fluctuations plays a central role,…