Related papers: Stability Rates for Patchy Vector Fields
The Rayleigh--Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method the sharp fluid interface is replaced by a thin, yet finite, transition layer…
Accurately following a geometric desired path in a two-dimensional space is a fundamental task for many engineering systems, in particular mobile robots. When the desired path is occluded by obstacles, it is necessary and crucial to…
Let us give a two dimensional family of real vector fields. We suppose that there exists a stationary point where the linearized vector field has successively a stable focus, an unstable focus and an unstable node. When the parameter moves…
The identification of singular points or topological defects in discretized vector fields occurs in diverse areas ranging from the polarization of the cosmic microwave background to liquid crystals to fingerprint recognition and bio-medical…
Path equations of different orbiting objects in the presence of very strong gravitational fields are essential to examine the impact of its gravitational effect on the stability of each system. Implementing an analogous method, used to…
Predictive safety filters enable the integration of potentially unsafe learning-based control approaches and humans into safety-critical systems. In addition to simple constraint satisfaction, many control problems involve additional…
Most studies on path-vector routing stability have been conducted empirically by means of ad-hoc analysis of BGP data traces. None of them consider prior specification of an analytic method including the use of stability measurement metrics…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…
We construct a series of vortex patch solutions in a doubly-periodic rectangular domain (flat torus), which is accomplished by studying the contour dynamic equation for patch boundaries. We will illustrate our key idea by discussing the…
We study semi-stable ideal lattices coming from real quadratic number fields. Specifically, we demonstrate infinite families of semi-stable and unstable ideal lattices of trace type, establishing explicit conditions on the canonical basis…
We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
Various extensions of standard inflationary models have been proposed recently by adding vector fields. Because they are generally motivated by large-scale anomalies, and the possibility of statistical anisotropy of primordial fluctuations,…
Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the…
We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated random velocity field. We carry on an expansion in powers of the inverse square…
Complex vector light fields have become a topic of late due to their exotic features, such as their non--homogeneous transverse polarisation distributions and the non-separable coupling between their spatial and polarisation degrees of…
We study the behaviour of heavy inertial particles in the flow field of two like-signed vortices. In a frame co-rotating with the two vortices, we find that stable fixed points exist for these heavy inertial particles; these stable…
The stability of persistence diagrams is among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bottleneck distance between diagrams and the $\infty$-norm of…