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Standard spectral codes for full sphere dynamics utilize a combination of spherical harmonics and a suitableradial basis to represent fluid variables. These basis functions have a rotational invariance not present ingeophysical flows.…
The main purpose of this paper is to present a general method for the controllability of the stability of a system of fractional-order differential equations around its equilibrium states. This method is applied to analyze and control the…
Stability criteria are given for linear periodic Hamiltonian systems with impulse effect. A Lyapunov type inequality and a disconjugacy criterion are also established. The results improve the ones in the literature for such systems.
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
In this work we construct reliable a posteriori estimates for some discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together…
The dynamics of the oscillator system is investigated. The conditions under which this dynamics becomes unstable are determined. In particular, it is shown that plasma in constant magnetic field becomes unstable if its density exceeds a…
This manuscript introduces a passivity-based integral control approach for fully-actuated mechanical systems. The novelty of our methodology is that we exploit the gyroscopic forces of the mechanical systems to exponentially stabilize the…
In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal…
In this paper, we investigate a system composed of two degenerate wave equations which are connected at one point. By introducing some inequalities on the weighted spaces and employing the frequency domain method, we prove that the system…
We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits…
We discovered an oscillatory instability in a system of inelastically colliding hard spheres, driven by two opposite "thermal" walls at zero gravity. The instability, predicted by a linear stability analysis of the equations of granular…
Filamentary molecular clouds are omnipresent in the cold interstellar medium. Observational evidences show that the non-isothermal equations of state describe the filaments properties better than the isothermal one. In this paper we use the…
We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability…
We study spherical and disk clusters in a near-Keplerian potential of galactic centers or massive black holes. In such a potential orbit precession is commonly retrograde, i.e. direction of the orbit precession is opposite to the orbital…
In a recent article (Forterre, PRL, 2001), we have reported a new instability observed in rapid granular flows down inclined planes that leads to the spontaneous formation of longitudinal vortices. From the experimental observations, we…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We study the modes and stability of non - isothermal coronal loop models with different intensity values of the equilibrium magnetic field. We use an energy principle obtained via non - equilibrium thermodynamic arguments. The principle is…