Related papers: Stability of three-and four-charge systems
In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an…
The conditions of multi-phase equilibrium are solved for generic polydisperse systems. The case of multiple polydispersity is treated, where several properties (e.g. size, charge, shape) simultaneously vary from one particle to another. By…
The existence of a ground state of the Nelson Hamiltonian with a perturbation is considered. The self-adjointness of the Hamiltonian and the existence of a ground state are proven for arbitrary values of coupling constants.
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of…
The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric…
We investigate the incremental stability properties of It\^o stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
Transformations accompanying shape-instability govern the morphological configuration and distribution of the phases in a microstructure. Owing to the influence of the microstructure on the properties of a material, the stability of…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…
We derive formulae for the time variation of the gravitational ``constant'' and of the fine structure ``constant'' in various models with extra dimensions and analyze their consistency with the observational data.
This work continues and substantially extends our recent work on switching diffusions with the switching processes that depend on the past states and that take values in a countable state space. That is, the discrete components of the…
This article explores the stability of stratified Couette flow in the viscous $3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal…
Voltage instability is a major threat in power system operation. The growing presence of constant power loads significantly aggravates this issue, hence motivating the development of new analysis methods for both existence and stability of…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…
In this paper, we investigate the stabilization of a linear Bresse system with one singular local frictional damping acting in the longitudinal displacement, under fully Dirichlet boundary conditions. First, we prove the strong stability of…
A quantum Monte Carlo simulation of a system of hard rods in one dimension is presented and discussed. The calculation is exact since the analytical form of the wavefunction is known, and is in excellent agreement with predictions obtained…
The stability of the linear chain structure of three $\alpha$ clusters for $^{12}$C against the bending and fission is investigated in the cranking covariant density functional theory, in which the equation of motion is solved on a 3D…