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1

Non-monotonic Relaxation in a HarmonicWell

King M. R., Jepps O. G.

Computational Methods in Science and Technology

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2017

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Vol. 23, No. 3

199--209

EN

The dissipation function of Evans and Searles has its origins in describing entropy production, yet it has a straightforward dynamical interpretation as well. The ability to consider either dynamical or thermodynamical contexts deepens our understanding of the dissipation function as a concept, and of numerical results involving the dissipation function. One recent, important application of the dissipation function is in relaxation to equilibrium. Here we look at relaxation in a system of interacting molecules that are confined within a harmonic potential, undergoing Hamiltonian dynamics. We note some similarities, but also important differences, to previous studies. The dissipation function sheds light on the periodic return of our system towards its initial state.We find that intermolecular interactions play a much more significant role in the relaxation toward a non-uniform spatial distribution (induced by a conservative background field) than they do toward a uniform distribution, which is reflected in the strongly non-monotonic relaxation we observe. We also find that the maximum dissipation does not occur in the long-time limit, as one might expect of a relaxation process, but shortly after relaxation begins, beyond which a significant net overall decrease in the dissipation function is observed.

2

Physical Ergodicity and Exact Response Relations for Low-dimensional Maps

Rondoni L., Dematteis G.

Computational Methods in Science and Technology

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2016

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Vol. 22, No. 2

71--85

EN

Recently, novel ergodic notions have been introduced in order to find physically relevant formulations and derivations of fluctuation relations. These notions have been subsequently used in the development of a general theory of response, for time continuous deterministic dynamics. The key ingredient of this theory is the Dissipation Function , that in nonequilibrium systems of physical interest can be identified with the energy dissipation rate, and that is used to determine exactly the evolution of ensembles in phase space. This constitutes an advance compared to the standard solution of the (generalized) Liouville Equation, that is based on the physically elusive phase space variation rate. The response theory arising in this framework focuses on observables, rather than on details of the dynamics and of the stationary probability distributions on phase space. In particular, this theory does not rest on metric transitivity, which amounts to standard ergodicity. It rests on the properties of the initial equilibrium, in which a system is found before being perturbed away from that state. This theory is exact, not restricted to linear response, and it applies to all dynamical systems. Moreover, it yields necessary and sufficient conditions for relaxation of ensembles (as in usual response theory), as well as for relaxation of single systems. We extend the continuous time theory to time discrete systems, we illustrate our results with simple maps and we compare them with other recent theories.

3

Dissipation function and yield condition for modelling plasticity of incompressible metals

Szwed A.

Logistyka

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2009

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nr 6

CD-CD

EN

Dissipation function for use in modeling of plastic properties of incompressible metals is proposed in this paper. The dissipation function is dependent on the two invariants of plastic strain rate tensor and material parameters. Constant dissipation surface have three axes of symmetry in the deviatoric plane and the shape of deviatoric cross-section can change from the equilateral triangle to circle. The dissipation function is used for deriving the constitutive relation and the yield condition for perfectly plastic material. All equations describing the model are given in closed analytical form. Deviatoric cross-sections of the failure surface can change from the equilateral triangle to circle. Material parameters are calibrated using typical strength tests.

PL

W artykule zaproponowano szczegółową postać funkcji dyssypacji przeznaczoną do modelowania plastyczności nieściśliwych metali. Funkcja zależy od dwóch niezmienników dewiatora prędkości odkształcenia plastycznego i parametrów materiałowych. Przekrój dewiatorowy powierzchni stałej dyssypacji ma trzy osie symetrii i jego kształt może zmieniać się od trójkąta równobocznego do koła. Funkcję dyssypacji stosuje się do wyznaczenia relacji konstytutywnej materiału idealnie plastycznego oraz warunku plastyczności. Przekroje dewiatorowe powierzchni plastyczności mogą zmieniać się od trójkątnego do kołowego. Parametry materiałowe są wyznaczane z typowych testów wytrzymałościowych.