Relaxation dynamics of an unlike spin pair system

Redfield master equation was applied to study the dynamics of an ensemble of interacting pair of unlike spins at room temperature. This spin quantum system is a workbench quantum model to analyze the relaxation dynamics of a heteronuclear two-level spin system interacting by a pure dipole-dipole coupling. Expressions for the density matrix elements and their relaxation rate constants of each coherence order were computed. In addition, the solutions were evaluated considering three initial quantum states, and the theoretical predictions, such as multi-exponential evolutions and enhancement, are behaviors that the solutions preserve and agree with previous studies performed for magnetization time evolutions. Moreover, the solutions computed to predict the dynamics of the longitudinal magnetization avoid the disagreement reported by I. Solomon

On the stability of Mindlin-Timoshenko plates

We consider a Mindlin-Timoshenko model with frictional dissipations acting on the equations for the rotation angles. We prove that this system is not exponentially stable independent of any relations between the constants of the system, which is different from the analogous' one-dimensional case. Moreover, we show that the solution decays polynomially to zero, with rates that can be improved depending on the regularity of the initial data

On the stability of damped Timoshenko systems - Cattaneo versus Fourier law

We consider vibrating systems of hyperbolic Timoshenko type that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. While proving exponential stability under the Fourier law of heat conduction, it turns out that the coupling via the Cattaneo law does not yield an exponentially stable system. This seems to be the first example that a removal of the paradox of infinite propagation speed inherent in Fourier's law by changing to the Cattaneo law distroys the exponential stability property. Actually, for systems with history, the Fourier law keeps the exponential stability known for the pure Timoshenko system without heat conduction, but introducing the Cattaneo coupling even destroys this property

Regularity analysis for an abstract thermoelastic system with inertial term

In this paper, we provide a complete regularity analysis for the following abstract thermoelastic system with inertial term ρutt+lAγu tt+σAu-mAαθ =0, cθt+mAαu t+kAβθ =0, u(0)=u0,ut(0)=v0, θ(0)=θ0, where A is a self-adjoint, positive definite operator on a complex Hilbert space H and (α,β,γ)∈E=[0,β+12 ]×[0,1]×[0,1]. It is regarded as the second part of Fernández Sare et al. [J. Diff. Eqs. 267 (2019) 7085–7134]. where the asymptotic stability of this model was investigated. We are able to decompose the region E into three parts where the associated semigroups are analytic, of Gevrey classes of specific order, and non-smoothing, respectively. Moreover, by a detailed spectral analysis, we will show that the orders of Gevrey class are sharp, under proper conditions. We also show that the orders of polynomial stability obtained in Fernández Sare et al. [J. Diff. Eqs. 267 (2019) 7085–7134] are optimal

Stability of Abstract Thermoelastic Systems with Inertial Terms

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Stability for a transmission problem in thermoelasticity with second sound

We consider a semilinear transmission problem for a coupling of an elastic and a thermoelastic material. The heat conduction is modeled by Cattaneo's law removing the physical paradox of infinite propagation speed of signals. The damped, totally hyperbolic system is shown to be exponentially stable