Related papers: In search of Robbins stability
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation,…
This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE) and a finite-dimensional linear time…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
We investigate the behavior of some thin sets of integers defined through random trigonometric polynomial when one replaces Gaussian or Rademacher variables by p-stable ones, with 1 < p < 2. We show that in one case this behavior is…
By imaging single-shot realizations of an organic polariton quantum fluid, we observe the long-sought dynamical instability of non-equilibrium condensates. Without any free parameters, we find an excellent agreement between the experimental…
We study surface modes of the condensate in the presence of a rotating thermal cloud in an axisymmetric trap. By considering collisions that transfer atoms between the condensate and noncondensate, we find that modes which rotate in the…
We consider transition to strong turbulence in an infinite fluid stirred by a gaussian random force. The transition is {\bf defined} as a first appearance of anomalous scaling of normalized moments of velocity derivatives (dissipation…
The mathematical physics of mechanical systems in thermal equilibrium is a well studied, and relatively easy, subject, because the Gibbs distribution is in general an adequate guess for the equilibrium state. On the other hand, the…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.
The Bogoliubov equations are solved for a three-dimensional Bose-Einstein condensate containing a doubly quantized vortex, trapped in a harmonic potential. Complex frequencies, signifying dynamical instability, are found for certain ranges…
The nonlinear stability domain of Lagrange's celebrated 1772 solution of a three-body problem is obtained numerically as a function of the masses of the bodies and the common eccentricity of their Keplerian orbits. This domain shows that…
We prove that any stable method for resolving the Gibbs phenomenon - that is, recovering high-order accuracy from the first $m$ Fourier coefficients of an analytic and nonperiodic function - can converge at best root-exponentially fast in…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
We consider a linear runs and tumbles equation in dimension d $\ge$ 1 for which we establish the existence of a unique positive and normalized steady state as well as its asymptotic stability, improving similar results obtained by Calvez et…
We theoretically examine the vortex states of a gas of trapped quasi-two-dimensional ultracold bosons subject to a density-dependent gauge potential, realizing an effective nonlinear rotation of the atomic condensate, which we also show is…
We investigate the gradual emergence of the disorder-related phenomena in intermediate regimes between a deterministic periodic Bragg grating and a fully random grating and highlight two critical properties of partially disordered Bragg…
Although the critical Reynolds number for linear instability of the laminar flow in a straight pipe is infinite, we show that it is finite for a divergent pipe, and approaches infinity as the inverse of the divergence angle. The velocity…
In this paper we show that a normal total number-of-particle fluctuation can be obtained consistently from the static thermodynamic relation and dynamic compressibility sum rule. In models using the broken U(1) gauge symmetry, in order to…