Related papers: On a connection between nonstationary and periodic…
We propose a wavelet based method for the characterization of the scaling behavior of non-stationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes.…
Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
We prove the height functions for a class of non-integrable and non-stationary particle systems converge to the KPZ equation, thereby making progress on the universality of the KPZ equation. The models herein are ASEP [4] with a mesoscopic…
Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
A theory for kinetic arrest in isotropic systems of repulsive, radially-interacting particles is presented that predicts exponents for the scaling of various macroscopic quantities near the rigidity transition that are in agreement with…
The linear stability of a rotating, stratified, inviscid horizontal plane Couette flow in a channel is studied in the limit of strong rotation and stratification. An energy argument is used to show that unstable perturbations must have…
We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…
We study standing periodic waves modeled by the nonlinear Schrodinger equation with the intensity-dependent dispersion coefficient. Spatial periodic profiles are smooth if the frequency of the standing waves is below the limiting frequency,…
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
In linear disordered systems Anderson localization makes any wave packet stay localized for all times. Its fate in nonlinear disordered systems is under intense theoretical debate and experimental study. We resolve this dispute showing that…
Extending investigations of Antman & Malek-Madani, Schecter & Shearer, Slemrod, Barker & Lewicka & Zumbrun, and others, we investigate phase-transitional elasticity models of strain-gradient effect. We prove the existence of non-constant…
Non-reciprocal interactions between scalar fields that represent the concentrations of two active species are known to break the parity and time-reversal (PT) symmetries of the equilibrium state, as manifested in the emergence of travelling…
We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic…
Rotating waves (RW) bifurcating from the axisymmetric basic magnetized spherical Couette (MSC) flow are computed by means of Newton-Krylov continuation techniques for periodic orbits. In addition, their stability is analysed in the…
We consider several different bidirectional Whitham equations that have recently appeared in the literature. Each of these models combine the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow…
In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…