Related papers: Dynamical instability criterion for circular (vort…
This paper concerns the instability and stability of the trivial steady states of the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a slab domain in dimension two. The main results show that the stability…
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…
Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…
The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results precisely…
Systems of interacting networks of strings such as cosmic strings or quantum vortices can be approximated in a certain regime as an anisotropic fluid with an equation of state depending on a conserved flux. The equations for ideal…
We present for the first time solutions in the gauged $U(1)\times U(1)$ model of Witten describing vortons -- spinning flux loops stabilized against contraction by the centrifugal force. Vortons were heuristically described many years ago,…
We establish the nonlinear orbital stability of circular vortex filaments governed by the Localized Induction Equation (LIE) under non-symmetric perturbations, within the framework of [Tani-Nishiyama, 1997]. This result extends the first…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
The Rossby wave instability, associated with density bumps in differentially rotating discs, may arise in several different astrophysical contexts, such as galactic or protoplanetary discs. While the linear phase of the instability has been…
We have performed a linear pulsational stability survey of 6 series of long period variable models with M=1.0 Msun, L=3000 - 8000Lsun, and (X,Z)= (0.700,0.020),(0.735,0.005). The dynamic and thermodynamic couplings between convection and…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
Earlier attempts to calculate the nonlinear dynamical evolution of Witten type superconducting vacuum vortex defects relied on the use of approximate conducting string models that were too simple to take proper account of the effect of…
In this paper, we propose to draw attention to the stability criterion of the superconductor current state. We use for this purpose the rough systems mathematical apparatus allowing us to relate the desired criterion with the dielectric…
Causality and stability are fundamental requirements for the differential equations describing predictable relativistic many-body systems. In this work, we investigate the stability and causality criteria in linear mode analysis. We discuss…
The Standard Model is the low-energy limit of a microscopic theory which includes extra dimensions and new symmetries. A part of my thesis consisted in constructing a new class of models with two extra dimensions. We showed that these…
Nonlinear evolution of a continuous spectrum of unstable waves near the first bifurcation point in circular Couette flow has been investigated. The disturbance is represented by a Fourier integral over all possible axial wavenumbers, and an…
This work is a theoretical investigation of the stability of the non-linear behavior of an oscillating tip-cantilever system used in dynamic force microscopy. Stability criterions are derived that may help to a better understanding of the…
It is known that in a hydrodynamic Taylor-Couette system uniform rotation or a rotation law with positive shear ('super-rotation') are linearly stable. It is also known that a conducting fluid under the presence of a sufficiently strong…
The robust instability of an unstable plant subject to stable perturbations is of significant importance and arises in the study of sustained oscillatory phenomena in nonlinear systems. This paper analyzes the robust instability of linear…
We revisit the somewhat classical problem of the linear stability of a rigidly rotating liquid column in this communication. Although literature pertaining to this problem dates back to 1959, the relation between inviscid and viscous…