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We carry out a general study of the stability of astrophysical flows that appear steady in a uniformly rotating frame. Such a flow might correspond to a stellar pulsation mode or an accretion disk with a free global distortion giving it…
This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons given by a suitably projected Dirac operator and with Coulomb interactions. In addition there is an arbitrary…
While active matter physics has traditionally focused on particles with overdamped dynamics, recent years have seen an increase of experimental and theoretical work on active systems with inertia. This also leads to an increased need for…
We investigate the stability of scalar perturbations around a magnetized stationary compact object in General Relativity. The considered object is one of the simplest exact solutions of Einstein electrovacuum equations corresponding to a…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a…
In the works by the author it has been shown that the conservation laws for material media (the conservation laws for energy, linear momentum, angular momentum, and mass, that establish a balance between the variation of a physical quantity…
Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a…
This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order…
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…
The paper presents methods of eigenvalue localisation of regular matrix polynomials, in particular, stability of matrix polynomials is investigated. For this aim a stronger notion of hyperstability is introduced and widely discussed. Matrix…
We study the problem of the instability of inhomogeneous radiation universes in quadratic lagrangian theories of gravity written as a system of evolution equations with constraints. We construct formal series expansions and show that the…
Shocks in granular media, such as vertically oscillated beds, have been shown to develop instabilities. Similar jet formation has been observed in explosively dispersed granular media. Our previous work addressed this instability by…
The equations of motion of compact binary systems have been derived in the post-Newtonian (PN) approximation of general relativity. The current level of accuracy is 3.5PN order. The conservative part of the equations of motion (neglecting…
We present a general approach to the analysis of gauge stability of 3+1 formulations of General Relativity (GR). Evolution of coordinate perturbations and the corresponding perturbations of lapse and shift can be described by a system of…
A number of low-mass millisecond pulsar (MSP) binaries in their rotation-powered state exhibit double-peaked X-ray orbital modulation centered at inferior pulsar conjunction. This state, which has been known to persist for years, has…