Ultrafast manipulation of magnetic anisotropy in a uniaxial intermetallic heterostructure TbCo2/FeCo

We study experimentally and theoretically the dynamics of spin relaxation motion excited by a femtosecond pulse in the TbCo2/FeCo multilayer structures with different ratios of TbCo2 to FeCo thicknesses rd = dTbCo2 / dFeCo. The main attribute of the structure is in-plane magnetic anisotropy artificially induced during sputtering under DC magnetic field. The optical pump-probe method revealed strongly damped high-frequency oscillations of the dynamical Kerr rotation angle, followed by its slow relaxation to the initial state. Modeling experimental results using the Landau-Lifshitz-Gilbert (LLG) equation showed that the observed entire dynamics is due to destruction and restoration of magnetic anisotropy rather than to demagnetization. For the pumping fluence of 7 mJ/cm2, the maximal photo-induced disruption of the anisotropy field is about 14% for the sample with rd = 1 and decreases when rd increases. The anisotropy relaxation is a three-stage process: the ultrafast one occurs within several picoseconds, and the slow one occurs on a nanosecond time scale. The Gilbert damping in the multilayers is found one order of magnitude higher than that in the constituent monolayers.

Passing through resonance of the unbalanced rotor with self-balancing device

The slow dynamics of unbalanced rotors with a passive self-balancing system are investigated considering the interaction of the mechanical system with a limited power engine. The slow dynamics equations are obtained using the averaging technique for partially strongly damped systems. Stationary system configurations, different types of nonstationary solutions while passing through resonance, and areas of stability and attraction are investigated.

Blow-up for a viscoelastic von Karman equation with strong damping and variable exponent source terms

In this article, we deal with a strongly damped von Karman equation with variable exponent source and memory effects. We investigate blow-up results of solutions with three levels of initial energy such as non-positive initial energy, certain positive initial energy, and high initial energy. Furthermore, we estimate not only the upper bound but also the lower bound of the blow-up time.

Upper semicontinuity of pullback attractors for a nonautonomous damped wave equation

In this paper, we study the local uniformly upper semicontinuity of pullback attractors for a strongly damped wave equation. In particular, under some proper assumptions, we prove that the pullback attractor $\{A_{\varepsilon }(t)\}_{t\in \mathbb{R}}$ { A ε ( t ) } t ∈ R of Eq. (1.1) with $\varepsilon \in [0,1]$ ε ∈ [ 0 , 1 ] satisfies $\lim_{\varepsilon \to \varepsilon _{0}}\sup_{t\in [a,b]} \operatorname{dist}_{H_{0}^{1}\times L^{2}}(A_{\varepsilon }(t),A_{ \varepsilon _{0}}(t))=0$ lim ε → ε 0 sup t ∈ [ a , b ] dist H 0 1 × L 2 ( A ε ( t ) , A ε 0 ( t ) ) = 0 for any $[a,b]\subset \mathbb{R}$ [ a , b ] ⊂ R and $\varepsilon _{0}\in [0,1]$ ε 0 ∈ [ 0 , 1 ] .

Correction to: Viscosity Measurement by the “Oscillating Drop Method”: The Case of Strongly Damped Oscillations

A correction to this paper has been published: https://doi.org/10.1007/s10765-021-02870-5

A generalized finite element method for the strongly damped wave equation with rapidly varying data

We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition, and is designed to handle independent variations in both the damping and the wave propagation speed respectively. The method does so by automatically correcting for the damping in the transient phase and for the propagation speed in the steady state phase. Convergence of optimal order is proven, independent of the derivatives of the coefficients. We present numerical examples that confirm the theoretical findings.

On the inverse problem for nonlinear strongly damped wave equations with discrete random noise

In this paper, we consider the existence of a solution u(x, t) for the inverse backward problem for the nonlinear strongly damped wave equation with statistics discrete data. The problem is severely ill-posed in the sense of Hadamard, i.e., the solution does not depend continuously on the data. In order to regularize the unstable solution, we use the trigonometric method in non-parametric regression associated with the truncated expansion method. We investigate the convergence rate under some a priori assumptions on an exact solution in both L 2 and H q (q > 0) norms. Moreover, a numerical example is given to illustrate our results.