Related papers: Planar dynamical systems with pure Lebesgue diffra…
Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
Glasses behave as solids due to their long relaxation time; however the origin of this slow response remains a puzzle. Growing dynamic length scales due to cooperative motion of particles are believed to be central to the understanding of…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
The spectral density for vector vibrations in the f.c.c. lattice with force-constant disorder is analysed within the coherent potential approximation. The phase diagram showing the weak- and strong-scattering regimes is presented and…
Positional disorder has been introduced into the atomic structure of certain crystalline lattices, and the orientationally-averaged structure factor S(k) and pair-correlation function g(r) of these disordered lattices have been studied.…
The vibrational anomalies of glasses, in particular the boson peak, are addressed from the standpoint of heterogeneous elasticity, namely the spatial fluctuations of elastic constants caused by the structural disorder of the amorphous…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
We investigate, theoretically and experimentally,the properties of diffraction spectra of Fibonacci lattices with arbitrary spacings. We show that, by means of a suitable composition rule, a Fibonacci sequence can be mapped into another one…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…
We present a novel approach to learn the formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a statistical dynamical model of the system which…
If an invertible linear dynamical systems is Li-York chaotic or other chaotic, what's about it's inverse dynamics? what's about it's adjoint dynamics? With this unresolved but basic problems, this paper will give a criterion for Lebesgue…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We consider viscous two-dimensional steady flows of incompressible fluids past doubly periodic arrays of solid obstacles. In a class of such flows, the autocorrelations for the Lagrangian observables decay in accordance with the power law,…
Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a…
The diffraction spectrum of the dart-rhombus random tiling of the plane is derived in rigorous terms. Using the theory of dimer models, it is shown that it consists of Bragg peaks and an absolutely continuous diffuse background, but no…
We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…
The presence of dynamical heterogeneities, i.e. nanometer-scale regions containing molecules rearranging cooperatively at very different rates compared to the bulk, is increasingly being recognized as crucial in our understanding of the…