Related papers: Transverse Rigidity is Prestress Stability

In this paper we show the relation between robust transitivity and robust ergodicity for conservative diffeomorphisms. In dimension 2 robustly transitive systems are robustly ergodic. For the three dimensional case, we define it almost…

In [Gallego and Aolita, Physical Review X 5, 041008 (2015)], the authors proposed a definition for the relative entropy of steering and showed that the resulting quantity is a convex steering monotone. Here we advocate for a different…

We introduce a new geometric invariant called the obtuse constant of spaces with curvature bounded below. We first find relations between this invariant and the normalized volume. We also discuss the case of maximal obtuse constant equal to…

In this letter, a new notion of stability is introduced, which is called triangular stability. A system is called triangularly stable if the norm of its state vector is bounded by a decreasing linear function of time such that its…

This paper studies switching stabilization problems for continuous-time switched linear systems. We consider four types of switching stabilizability defined under different assumptions on the switching control input. The most general…

In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem,…

Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction…

We construct a subset of the space of stability conditions for any projective threefold with an ample polarization that satisfies a certain Bogomolov-Gieseker inequality to refine the result in arXiv:1410.1585. Then, we demonstrate that the…

New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…

The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid's bus angles to retain synchronism after the occurrence of a major fault. In this paper a…

A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.

A recently proposed theory of modified gravity with an explicit ``anomalous'' coupling of the Ricci curvature to matter is discussed, and an inequality is derived which expresses a necessary and sufficient condition to avoid the notorius…

In modern power systems, the operating point, at which the demand and supply are balanced, may take different values due to changes in loads and renewable generation levels. Understanding the dynamics of stressed power systems with a range…

We summarize recent progress on one- and multi-dimensional stability of viscous shock wave solutions of compressible Navier--Stokes equations and related symmetrizable hyperbolic--parabolic systems, with an emphasis on the large-amplitude…

Rigid origami is examined from the perspective of rigidity theory. First and second order rigidity are defined from local differential analysis of the consistency constraint; while the static rigidity and prestress stability are defined…

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…

We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…

This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from…

In the Vlasov-Poisson equation, every configuration which is homogeneous in space provides a stationary solution. Penrose gave in 1960 a criterion for such a configuration to be linearly unstable. While this criterion makes sense in a…

In this letter, by regarding finite-time stability as an inverse problem, we reveal the essence of finite-time stability and fixed-time stability. Some necessary and sufficient conditions are given. As application, we give a new approach…