Related papers: General Mapping between Complex Spatial and Tempor…
We consider the propagation of both fully coherent and partially coherent complex scalar fields, through linear shift-invariant imaging systems. The state of such imaging systems is characterized by a countable infinity of aberration…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…
We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the…
This study introduces the Bragg Frequency Convertor, a spatial-temporal-periodic grating that extends the concept of conventional Bragg gratings into the dynamic domain to achieve pure parametric frequency conversion. By time-modulating…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the…
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…
The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by $\gamma$ one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime $(M,g_{ab})$. First, it is…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…
This paper uses an alternative approach to study the monochromatic plane wave propagation within dielectric and conductor linear media of plane-parallel-faces. This approach introduces the time-averaged Poynting vector modulus as field…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
Energy conversion in a physical system requires time-translation invariance breaking according to Noether's theorem. Closely associated with this symmetry-conservation relation, the frequencies of electromagnetic waves are found to be…
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide…
We introduce the concept of coherent temporal imaging and its combination with the anamorphic stretch transform. The new system can measure both temporal profile of fast waveforms as well as their spectrum in real time and at…
Using a dynamical model relevant to cold-atom experiments, we show that long-lasting exponential spreading of wave packets in momentum space is possible. Numerical results are explained via a pseudo-classical map, both qualitatively and…
We study the regularity results of holomorphic correspondences. As an application, we combine it with certain recently developed methods to obtain the extension theorem for proper holomorphic mappings between domains with real analytic…
A new construction of decomposition smoothness spaces of homogeneous type is considered. The smoothness spaces are based on structured and flexible decompositions of the frequency space $\mathbb{R}^d\backslash\{0\}$. We construct simple…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…