相关论文: Stability Rates for Patchy Vector Fields

The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. For chaotic systems, there are two distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach…

Gravitational vector degrees of freedom typically arise in many examples of modified gravity models. We start to systematically explore their role in these scenarios, studying the effects of coupling gravitational vector and scalar degrees…

The goal of this paper is to theoretically investigate the origin of the standing wave-like perturbation observed on the vortex rings falling through another liquid. We simplified the Navier-Stokes equation based on observational evidence…

We consider discrete-time switching systems composed of a finite family of affine sub-dynamics. First, we recall existing results and present further analysis on the stability problem, the existence and characterization of compact…

We are interested in studying the sensitivity of diffusion processes or their approximations by Markov Chains with respect to a perturbation of the coefficients.

The study of circular orbits in spacetime is of astrophysical importance. The identification and classification of circular orbits in both static and stationary spacetimes remains an active area of interest. Even in the simplest static…

In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the minimizer, we prove that for any harmonic function $q$…

We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we…

We study the dynamics of a timelike vector field which violates Lorentz invariance when the background spacetime is in an accelerating phase in the early universe. It is shown that a timelike vector field is difficult to realize an…

To understand the empirical success of approximate MAP inference, recent work (Lang et al., 2018) has shown that some popular approximation algorithms perform very well when the input instance is stable. The simplest stability condition…

The vector field problem is an important and classical problem in differential topology. In this survey we shall consider the vector field problem focusing mainly on the class of compact homogeneous spaces.

We investigate the global stability of a differentially rotating fluid shell threaded by vertical and azimuthal magnetic fields to linear, axisymmetric perturbations. This system, which models a thick accretion disk in the vicinity of its…

The stationary distribution of passive tracers chaotically advected by a two-dimensional large-scale flow is investigated. The tracer field is force by resetting the value of the tracer in certain localised regions. This problem is…

Modified theories of gravity usually present new degrees of freedom, as well as higher order derivatives, wrong signs in certain terms and complicated couplings already present in the Lagrangian from the beginning or originated by the field…

The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…

We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby…

Models with vector fields acquiring a non-vanishing vacuum expectation value along one spatial direction have been proposed to sustain a prolonged stage of anisotropic accelerated expansion. Such models have been used for realizations of…

This paper deals with the impulsive formation control of spacecraft in the presence of constraints on the position vector and time. Determining a set of path constraints can increase the safety and reliability in an impulsive relative…

The Hartree-Fock equation admits homogeneous states that model infinitely many particles at equilibrium. We prove their asymptotic stability in large dimensions, under assumptions on the linearised operator. Perturbations are moreover…

In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…