Related papers: Causality and Passivity in Elastodynamics
This paper revisits the physical meaning of linear, time-domain constitutive models with complex parameters that have been presented in the literature and concludes that such models are not physically realizable. While complex-parameter…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
We present an asymptotic framework that rigorously generates nonlinear constitutive relations between stress and linearized strain for elastic bodies. Each of these relations arises as the leading order relationship satisfied by a…
The main purpose of this work is to address the question of the utility of "effective constitutive relations" for problems in dynamics. This is done in the context of longitudinal shear waves in an elastic medium that is periodically…
Results of the idealized mode-coupling theory for the structural relaxation in suspensions of hard-sphere colloidal particles are presented and discussed with regard to recent light scattering experiments. The structural relaxation becomes…
Willis dynamic homogenization theory revealed that the effective linear momentum of elastic composites is coupled to their effective strain. % This result, which is partially due to asymmetry at the subwavelength scale, implies that…
Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…
We study the static and dynamic structure of thermally fluctuating elastic thin sheets by investigating the overdamped dynamic F\"oppl-von K\'arm\'an equation, in which the F\"oppl-von K\'arm\'an equation from elasticity theory is driven by…
For monodomain nematic elastomers, we construct generalised elastic-nematic constitutive models combining purely elastic and neoclassical-type strain-energy densities. Inspired by recent developments in stochastic elasticity, we extend…
In this paper, we examine the shifted passivity property of port-Hamiltonian systems. Shifted passivity accounts for the fact that in many applications the desired steady-state values of the input and output variables are nonzero, and thus…
Electronic devices exhibit changes in electrical resistance over time at varying rates, depending on the configuration of certain components. Since measuring overall electrical resistance requires partial disassembly, only a limited number…
We consider a class of parametrically forced Hamiltonian systems with one-and-a-half degrees of freedom and study the stability of the dynamics when the frequency of the forcing is relatively high or low. We show that, provided the…
In the current density functional theory of linear and nonlinear time-dependent phenomena, the treatment of exchange and correlation beyond the level of the adiabatic local density approximation is shown to lead to the appearance of…
I present a theory of electron dynamics in semiconductors with slowly varying composition. I show that the frequency-dependent conductivity, required for the description of transport and optical properties, can be obtained from a knowledge…
We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…
The recent progress of non-Hermitian physics and the notion of exceptional point (EP) degeneracies in elastodynamics has led to the development of novel metamaterials for the control of elastic wave propagation, hypersensitive sensors, and…
We study the three-dimensional structural stability of shock waves for the equations of elastodynamics governing isentropic flows of compressible inviscid elastic materials. By nonlinear structural stability of a shock wave we mean the…
A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…
Event Structures (ESs) address the representation of direct relationships between individual events, usually capturing the notions of causality and conflict. Up to now, such relationships have been static, i.e., they cannot change during a…
The manipulation of mechanical waves is a long-standing challenge for scientists and engineers, as numerous devices require their control. The current forefront of research in the control of classical waves has emerged from a seemingly…