Related papers: Analytical Treatment of Stabilization
We consider a class of nonlinear ordinary differential equations of the second order with parameters. We establish conditions for perturbations of the coefficients of the equation under which the zero solution is asymptotically stable.…
With the rise of network science old topics in ecology and economics are resurfacing. One such topic is structural stability (often referred to as qualitative stability or sign stability). A system is deemed structurally stable if the…
The qualitative behavior of charged particles in a vacuum is given by Earnshaw's Theorem which states that there is no steady configuration of charged particles in a vacuum which is asymptotically stable to perturbations. In a viscous…
We study the stability of static, spherically symmetric solutions of Rastall's theory in the presence of a scalar field with respect to spherically symmetric perturbations. It is shown that the stability analysis is inconsistent in the…
We study the non relativistic motions of a charged particle in the electromagnetic field generated by two parallel electrically neutral vertical wires carrying time depends currents. Under quantitative conditions on the currents we prove…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
We study the classical Antonov problem (of retrieving the statistical equilibrium properties of a self-gravitating gas of classical particles obeying Boltzmann statistics in space and confined in a spherical box) for a rotating system. It…
Magnetic excitations of single atoms on surfaces have been widely studied experimentally in the past decade. Lately, systems with unprecedented magnetic stability started to emerge. Here, we present a general theoretical investigation of…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
The so-called ``symplectic method'' is used for studying the linear stability of a self-gravitating collisionless stellar system, in which the particles are also submitted to an external potential. The system is steady and spherically…
Many experimental techniques aim at determining the Hamiltonian of a given system. The Hamiltonian describes the system's evolution in the absence of dissipation, and is often central to control or interpret an experiment. Here, we…
We examine here the classical dynamics of cold atoms in square optical lattices, i.e. lattices obtained with two orthogonal stationary plane waves. Contrary to much of the past studies in this domain, the potential is here time independent…
The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain…
The stabilization of steady state entanglement caused by action of a classical driving field in the system of two-level atoms with the dipole interaction accompanied by spontaneous emission is discussed. An exact solution shows that the…
A class of asymptotically autonomous systems on the plane with oscillatory coefficients is considered. It is assumed that the limiting system is Hamiltonian with a stable equilibrium. The effect of damped multiplicative stochastic…
Stability of self-similar solutions for gravitational collapse is an important problem to be investigated from the perspectives of their nature as an attractor, critical phenomena and instability of a naked singularity. In this paper we…
On the basis of the transfer matrix technique an analytical method to investigate the stationary states, for an electron in one-dimensional periodic structures in an external electrical field, displaying the symmetry of the problem is…
We use an averaging approach to prove bifurcation of asymptotically stable periodic solutions in a bi-linear oscillator whose one spring has nearly infinite stiffness. This leads to a singularly perturbed problem where the classical theory…
We give a new method to prove the existence, non-existence, multiplicity, orbital stability/instability of standing waves for NLS with partial confinement without the subcritical hypothesis, even in the reduction equation. Using this…
A theoretical approach for a non-perturbative dynamical description of two interacting atoms in an optical lattice potential is introduced. The approach builds upon the stationary eigenstates found by a procedure described in Grishkevich et…