Related papers: Aperiodic order via dynamical systems: Diffraction…
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
This article deals with pure point diffraction and its connection to various notions of almost periodicity. We explain why the Fibonacci chain does not fit into the classical class of Bohr almost periodicity and how it fits into the classes…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which,…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
In this paper, we propose and analyze a third-order dynamical system for solving a generalized inverse mixed variational inequality problem in a Hilbert space H. We establish the existence and uniqueness of the trajectories generated by the…
The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of…
We study the empirical process arising from a multi-dimensional diffusion process with periodic drift and diffusivity. The smoothing properties of the generator of the diffusion are exploited to prove the Donsker property for certain…
An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for…
We examine the diffraction properties of lattice dynamical systems of algebraic origin. It is well-known that diverse dynamical properties occur within this class. These include different orders of mixing (or higher-order correlations), the…
A general input-output modelling technique for aperiodic-sampling linear systems has been developed. The procedure describes the dynamics of the system and includes the sequence of sampling periods among the variables to be handled. Some…
When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order "guiding system", placing the time dependence at higher orders. Recent research focused on…
We will construct ``higher-dimensional" versions of the Wiener-Wintner dynamical system that was originally studied by I. Assani in 2003. We will show that on these systems we can provide very simple proofs of the a.e. convergence of the…
A simple method for presenting a dynamic transition between Fresnel and Fraunhofer diffraction zones is considered. Experiments are conducted on different apertures and diffraction patterns are photographed at various distances between the…
We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…
In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the…
The article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models viz. Fractional continuously variable order mass-spring damper systems. Here, we use the…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
Very short pulses of x-ray free-electron lasers opened the way to obtain diffraction signal from single particles beyond the radiation dose limit. For 3D structure reconstruction many patterns are recorded in the object's unknown…