Time-independent Decay Research Articles

Spatial Behavior in Linear Theory of Thermoviscoelasticity with Voids

In the present article we study the spatial behavior of the solutions to the initial boundary value problem associated with the linear theory of thermoviscoelastic materials with voids. We prove a set of properties for an appropriate time-weighted surface power function, which allows us to obtain an idea of the domain of influence in linear thermoviscoelasticity with voids. Some spatial estimates of the Saint–Venant type, for bounded bodies, and Phragmén–Lindelöf type, for unbounded bodies, are obtained. Such estimates are characterized by time-dependent as well as time-independent decay and growth rates.

Asymptotic analysis of homogeneous isotropic decaying turbulence with unknown initial conditions

In decaying grid turbulence there is a transition from the initial state immediately behind the grid to the state of fully developed turbulence downstream, which is believed to be self-similar. This state is characterized by a power law decay of the turbulent kinetic energy with a time-independent decay exponent n. The value of this exponent, however, depends on the initial distribution of the velocity, about which we have only general information at the very best. For homogeneous isotropic decaying turbulence, the evolution of the two-point velocity correlation is described by the von Kármán–Howarth equation. In the non-dimensionalized form of this equation a decay exponent dependent term occurs, whose coefficient will be called δ. We exploit the fact that δ vanishes for n→2, which is shown to correspond to the limit d→∞, where d denotes the dimensionality of space to formulate a singular perturbation problem. It is shown that a distinguished limit exists for d→∞ and δ→0. We obtain in the limit of infinitely large Reynolds numbers an outer layer of limited, but a priori unknown extension, as well as an inner layer of the thickness of the order , where the Kolmogorov scaling is valid. To leading order, we obtain an algebraic balance in the outer layer between the two-point correlation and the third-order structure function. In the inner layer the analysis yields the emergence of higher order terms to the classical K41 scaling. All leading order solutions are shown to be subject to a band of uncertainty of the order , which is argued to be due to intrinsically unknown initial conditions.

Some results on the spatial behaviour for elastic mixtures

This article studies the spatial behaviour of solutions for some classes of homogeneous and isotropic simple elastic mixtures, for which the internal energy density is not always a positive definite quadratic form. By introducing some appropriate measures, we obtain the domain of influence theorem and the spatial decay estimates with time-independent decay rate inside the domain of influence.

Some results in the dynamics of porous elastic mixtures

The present work describes a method for studying the spatial and temporal behaviour of the dynamic processes in porous elastic mixtures taking into account memory effects for the intrinsic equilibrated body forces. The method is based on a set of properties for an appropriate time-weighted surface power function associated with the process at issue. We get the domain of influence and the spatial decay estimates with time-independent decay rate inside the domain of influence. We establish the spatial decay estimates with time-independent decay rate for the interior of the domain of influence. Using the Cesáro means associated with the kinetic and strain energies, we establish the asymptotic partition of the total energy.

On the Spatial and Temporal Behavior in Dynamics of Porous Elastic Mixtures

In this paper, we study the spatial and temporal behavior of dynamic processes in porous elastic mixtures. For the spatial behavior, we use the time-weighted surface power function method in order to obtain a more precise determination of the domain of influence and establish spatial-decay estimates of the Saint-Venant type with respect to time-independent decay rate for the inside of the domain of influence. For the asymptotic temporal behavior, we use the Cesaro means associated with the kinetic and strain energies and establish the asymptotic equipartition of the total energy. A uniqueness theorem is proved for finite and infinite bodies, and we note that it is free of any kind of a priori assumptions on the solutions at infinity.

On the spatial behaviour in dynamics of elastic mixtures

This paper studies the spatial behaviour of the dynamic processes in elastic mixtures. With this aim we use the time-weighted surface power function method associated with the linear processes. Consequently, we obtain a precise determination of the domain of influence and the spatial decay estimates with time-independent decay rate inside of the domain of influence. A uniqueness theorem is proved for finite and infinite bodies and we note that it is free of any kind of a priori assumptions on the solutions at infinity.

Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua

The present paper describes a method for studying the spatial behaviour of the thermodynamic processes. The method is based on a set of properties for an appropriate time-weighted surface power function associated with the process in question. It allows to obtain a more precisely idea of domain of influence in linear elastodynamics and viscoelastodynamics and, furthermore, to get spatial decay estimates with time-independent decay rate inside of the domain of influence. It also allows to obtain a good description for the spatial behaviour of the thermoelastic processes by means of spatial estimates characterized by independent as well as time-dependent decay and growth rates.

A test of RRKM theory against numerical simulation for classical chain molecules. I. Method and preliminary results

A systematic investigation of the internal part of the unimolecular reaction dynamics of one-dimensional chain molecules has been undertaken to examine the validity of RRKM theory. The basic aims, means and scope of this program of research are reported here together with results for uniform chains. Classical mechanics is used and the atoms in the chain interact by Morse pair potentials acting between neighbouring particles. The simulation method described here consists of a very efficient Monte Carlo sampling of microcanonical initial states coupled with a predictor-corrector molecular dynamics algorithm. Time-dependent and best fitting time-independent decay rate coefficients can be extracted from the set of lifetimes to dissociation observed in the simulation. These are then compared to the corresponding rate coefficients predicted by the usual form of RRKM theory where anharmonic contributions ot the density of states are neglected or to a more rigorous implementation where the anharmonic contributions are accounted for. Calculations for uniform chains reported here establish a pattern of deviations from RRKM prediction which will be explored and explained in greater detail in this program of research.