Related papers: Statistical Design of Chaotic Waveforms with Enhan…
A sensor was developed to quantitatively measure perturbations which change the volume of a wave chaotic cavity while leaving its shape intact. The sensors work in the time domain by using either scattering fidelity of the transmitted…
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
We propose an information-theoretic statistical model to describe the universal features of those chaotic scattering processes characterized by a prompt and an equilibrated component. The model, introduced in the past in nuclear physics,…
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for…
We propose a model to describe the statistical properties of wave scattering through a classically chaotic cavity in the presence of surface absorption. Experimentally, surface absorption could be realized by attaching an "absorbing patch"…
Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal…
Intensities of LEED and PED are analyzed from a statistical point of view. The probability distribution is compared with a Porter-Thomas law, characteristic of a chaotic quantum system. The agreement obtained is understood in terms of…
Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
Scattering properties of a material are changed when the material is injected with small acoustically soft particles. It is shown that its new scattering behavior can be understood as a solution of a potential scattering problem with the…
Spiral waves are investigated in chemical systems whose underlying spatially-homogeneous dynamics is governed by a deterministic chaotic attractor. We show how the local periodic behavior in the vicinity of a spiral defect is transformed to…
In this work, we present a theoretical study of the statistical properties of wave scattering in a disordered ballistic waveguide of length L; we have called this system the "building block". The building block is interesting as a physical…
Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident…
This paper is concerned with the reconstruction of the shape of an acoustic obstacle. Based on the use of the tapered waves with very narrow widths illuminating the obstacle, the boundary of the obstacle is reconstructed by a direct imaging…
The spatiotemporal chaos in the system described by a one-dimensional nonlinear drift-wave equation is controlled by directly adding a periodic force with appropriately chosen frequencies. By dividing the solution of the system into a…
We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach…
Design and cryptanalysis of chaotic encryption schemes are major concerns to provide secured information systems. Pursuing our previous research works, some well-defined discrete chaotic iterations that satisfy the reputed Devaney's…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…