Related papers: Approximations of symbolic substitution systems in…
In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms.…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and…
Quasicrystals are solid structures with symmetry forbidden by crystallographic rules. Because of this some structural characteristics of quasicrystals, for instance, radial distribution function, can look similar to the ones of amorphous…
In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of…
Despite considerable progress during the last decades in devising a semiclassical theory for classically chaotic quantum systems a quantitative semiclassical understanding of their dynamics at late times (beyond the so-called Heisenberg…
We study random perturbations of quasi-periodic uniformly discrete sets in the $d$-dimensional euclidean space. By means of Diffraction Theory, we find conditions under which a quasi-periodic set $X$ can be almost surely recovered from its…
Quasi-crystals are aperiodic structures that present crystallographic properties which are not compatible with that of a single unit cell. Their revolutionary discovery in a metallic alloy, less than three decades ago, has required a full…
The concept of near resonances for harmonic approximations of semiclassical Schr\"odinger operators is introduced and explored. Combined with a natural extension of the Birkhoff-Gustavson normal form, we obtain formulas for approaching the…
In this paper we extend previous results on convergent perturbative solutions of the Schroedinger equation of a class of periodically time-dependent two-level systems. The situation treated here is particularly suited for the investigation…
A function is called quasiperiodic if its fundamental frequencies are linearly independent over the rationals. With appropriate parameters, the sliding window point clouds of such functions can be shown to be dense in tori with dimension…
The various magnetic orders observed in approximant crystals of Tsai-type quasicrystal are important for deepening our understanding of mysterious magnetism in quasicrystals. Using an icosahedral cluster model with inter-cluster…
We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…
A continuous infinite system of point particles interacting via two-body strong superstable potential is considered in the framework of classical statistical mechanics. We define some kind of approximation of main quantities, which describe…
The determination of the spectrum of a Schr\"odinger operator is a fundamental problem in mathematical quantum mechanics. We discuss a series of results showing that Schr\"odinger operators can exhibit spectra that are remarkably thin in…
We study a chain of identical glassy systems in a constrained equilibrium where each bond of the chain is forced to remain at a preassigned distance to the previous one. We apply this description to Mean Field Glassy systems in the limit of…
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…
In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov Chain. [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi…
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 provide bounds on the error between dynamics of an infinite dimensional bilinear Schr\"odinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used on the finite dimensional approximations…