on the occasion of his 50th birthday Abstract In their 1993 paper 16], Schimansky-Geier and Herzel discovered numerically that the Kramers oscillator (which is identical with the Duung oscillator forced by additive white noise) has a positive top Lyapunov exponent in the low damping regime. In this paper, we study the Kramers oscillator from the point of view of random dynamical systems, to whi...

Deployment of distributed renewable energy resources is increasing rapidly, which is leading to growing concerns over the impact of distributed power electronics energy converters on grid stability. In general, power electronic coupled systems do not provide frequency or voltage support through feedback compensation. This is leading to changes in utility interconnection requirements for distrib...

We examine surface modes at the nematic-isotropic interface in polymer-liquid-crystal mixtures using the dynamical Landau-de Gennes model for the orientational (non-conserved) order parameter coupled with Cahn-Hilliard equation for concentration (conserved order parameter) and with hydrodynamic degrees of freedom. The generalized dispersion relation is obtained and analyzed in particular cases....

A scheme is presented that is based on the alloy analogy model and allows one to account for thermal lattice vibrations as well as spin fluctuations when calculating response quantities in solids. Various models to deal with spin fluctuations are discussed concerning their impact on the resulting temperature-dependent magnetic moment, longitudinal conductivity, and Gilbert damping parameter. It...

The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [7] concerning existence and uniqueness of renormalized solutions of continuity equations with unbounded damping coe cient. Second, we show how the ideas in [7] can be used to provide an alternative proof of the result in [6, 9, 12], where the usual requirement of bo...

Wave control in the solid state has opened new avenues in modern information technology. Surface-acoustic-wave-based devices are found as mass market products in 100 millions of cellular phones. Spin waves (magnons) would offer a boost in today's data handling and security implementations, i.e., image processing and speech recognition. However, nanomagnonic devices realized so far suffer from t...

The calibration of model parameters is a crucial subproblem for realistic model-based sound synthesis. This paper describes the revision of the calibration process of a classical guitar model, and extends the parameter extraction procedure to capture information about performance characteristics, such as the damping regimes, repeated plucks, vibrato characteristics, different pluck styles and d...

We design a perfectly matched layer for the advection-diffusion equation. We show that the reflection coefficient is exponentially small with respect to the damping parameter and the width of the PML and this independently of the advection and of the viscosity. Numerical tests assess the efficiency of the approach.

Energy shaping and passivity-based control designs have proven to be effective in solving control problems for underactuated mechanical systems. In recent works, Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) has been successfully applied to open loop conservative models, i.e. with no physical damping (e.g., friction) present. In a number of cases, in particular when I...

Carbon nanotube field-effect transistors (CNTFETs) have been studied in recent years as a potential alternative to CMOS devices, because of the capability of ballistic transport. In order to account for the ballistic transport we solved the coupled Poisson and Schrödinger equations for the analysis these devices. Conventionally the coupled Schrödinger-Poisson equation is solved iteratively, by ...