Related papers: Localization and Coherent Structures in Wave Dynam…
An approach to watermarking digital images using non-regular wavelets is advanced. Non-regular transforms spread the energy in the transform domain. The proposed method leads at the same time to increased image quality and increased…
The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
In this paper we study the dynamics of metamaterials composed of high-contrast subwavelength resonators and show the existence of localised modes in such a setting. A crucial assumption in this paper is time-modulated material parameters.…
In this second part we present a set of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
We propose a variational approach to the dynamics of the Bose-Hubbard model beyond the mean field approximation. To develop a numerical scheme, we use a discrete overcomplete set of Glauber coherent states and its connection to the…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
We derive exact expressions for effective elastodynamic properties of two-phase composites in the long-wavelength (quasistatic) regime via homogenized constitutive relations that are local in space. This is accomplished by extending the…
We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk.…
A general localization mechanism for waves in dissipative systems is identified that does not require the bistability of the basic state and the nonlinear plane-wave state. The mechanism explains the two-dimensional localized wave…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We introduce a self-supervised framework for learning predictive and structured representations of wireless channels by modeling the temporal evolution of channel state information (CSI) in a compact latent space. Our method casts the…
We consider space-charge dominated beam transport systems, where space-charge forces are the same order as external focusing forces and dynamics of the corresponding emittance growth. We consider the coherent modes of oscillations and…
In this work, we present a wireless localization method that operates on self-supervised and unlabeled channel estimates. Our self-supervising method learns general-purpose channel features robust to fading and system impairments. Learned…
We introduce a novel multi-resolution Localized Orthogonal Decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The method merges the concepts of LOD and operator-adapted wavelets…
The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly-used deep learning approaches suffer from a lack of interpretability of the trained models. Here we present an interpretable machine learning…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…