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We investigate the asymptotic behaviour of a reduced {\alpha}{\Omega}-dynamo model of magnetic field generation in spiral galaxies where fluctuation in the {\alpha}-effect results in a system with state-dependent stochastic perturbations.…
For the statistics of global observables in disordered systems, we discuss the matching between typical fluctuations and large deviations. We focus on the statistics of the ground state energy $E_0$ in two types of disordered models : (i)…
We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the the angular frequency $\omega$ and ratio of the Lam\'e…
We study the diffusion of a tracer particle driven out-of-equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
The flow in a Hele-Shaw cell with a time-increasing gap poses a unique shrinking interface problem. When the upper plate of the cell is lifted perpendicularly at a prescribed speed, the exterior less viscous fluid penetrates the interior…
The growth of the density fluctuations is considered to be an important cosmological test. In the standard model, for a matter dominated universe, the growth of the density perturbations evolves with redshift z like (1/{1+z))^s with s=1.…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
Several analysis methods for nonstationary fluctuations are described and applied to the edge localized mode (ELM) instabilities of limiter H-mode plasmas. The microwave scattering diagnostic observes poloidal $k_{\theta}$ values of 3.3…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…
A set of coupled complex Ginzburg-landau type amplitude equations which operates near a Hopf-Turing instability boundary is analytically investigated to show localized oscillatory patterns. The spatial structure of those patterns are the…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
The Nikolaevskiy equation has been proposed as a model for seismic waves, electroconvection and weak turbulence; we show that it can also be used to model transverse instabilities of fronts. This equation possesses a large-scale "Goldstone"…
The energy dependence of the spectral fluctuations in the interacting boson model (IBM) and its connections to the mean-field structures have been analyzed through adopting two statistical measures, the nearest neighbor level spacing…
Amplitude expansions are used to determine steady states of a semi-infinite solid subject to the Grinfeld instability in systems with a fixed (wave)length. We present two methods to obtain high-order weakly nonlinear results. Using the…
We consider an overdamped particle with a general physical mechanism that creates noisy active movement (e.g., a run-and-tumble particle or active Brownian particle etc.), that is confined by an external potential. Focusing on the limit in…
We study one-dimensional fluctuating interfaces of length $L$ where the interface stochastically resets to a fixed initial profile at a constant rate $r$. For finite $r$ in the limit $L \to \infty$, the system settles into a nonequilibrium…
This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. These one-dimensional stochastic differential equations exhibit a quadratic drift function and a…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…