In this work, we introduce discontinuous Galerkin and enriched Galerkin formulations for the spatial discretization of phase-field fracture propagation. The nonlinear coupled system is formulated in terms of the Euler-Lagrange equations, which are subject to a crack irreversibility condition. The resulting variational inequality is solved in a quasi-monolithic way in which the irreversibility c...

The aim of this paper is to analyze the concepts of time-reversal invariance and irreversibility in the so-called ’time-asymmetric quantum mechanics’. We begin with pointing out the difference between these two concepts. On this basis, we show that irreversibility is not as tightly linked to the semigroup evolution laws of the theory -which lead to its non time-reversal invarianceas usually sug...

Three independent literatures have contributed to the understanding of irreversibility in economics. The first focuses on the future opportunities forgone by investments with irreversible consequences. The second considers irreversibility (and hysteresis) in the context of the dynamics of systems characterized by multiple equilibria. The third, with roots in complex systems theory, focuses on e...

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Irreversibility is an important issue for many quantum processes. Loschmidt echoes, originally introduced as a way to gauge sensitivity to perturbations in quantum mechanics, have turned out to be a useful tool for its investigation. Following the philosophy supporting this idea, and using quantum trajectories as defined in the causal interpretation of quantum mechanics due to Bohm, we introduc...

© 2006 American Institute of Physics, S-0031-9228-0608-210-X The origin of irreversible behavior is a persistent theme in physics. Since the fundamental microscopic laws, including both Newton’s laws and quantum mechanics, are reversible (except for the weak interactions), the fact that most macroscopic systems behave irreversibly has long been recognized as an important issue. The problem of u...

The intermetallic compound SmMn2Ge2, displaying multiple magnetic phase transitions, is being investigated in detail for its magnetization behavior near the 145 K first order ferromagnetic to antiferromagnetic transition occuring on cooling, in particular for thermomagnetic history effects in the magnetization data. The most unusual finding is that the thermomagnetic irreversibility, [= M (T)-M...