5,903 research outputs found
A Local Entropy Minimum Principle for Deriving Entropy Preserving Schemes
International audienceThe present work deals with the establishment of stability conditions of finite volume methods to approximate weak solutions of the general Euler equations to simulate compressible flows. In oder to ensure discrete entropy inequalities, we derive a new technique based on a local minimum principle to be satisfied by the specific entropy. Sufficient conditions are exhibited to satisfy the required local minimum entropy principle. Arguing these conditions, a class of entropy preserving schemes is thus derived
An entropy preserving relaxation scheme for ten-moments equations with source terms
International audienceThe present paper concerns the derivation of finite volume methods to approximate weak solutions of Ten-Moments equations with source terms. These equations model compressible anisotropic flows. A relaxation-type scheme is proposed to approximate such flows. Both robustness and stability conditions of the suggested finite volume methods are established. To prove discrete entropy inequalities, we derive a new strategy based on local minimum entropy principle and never use some approximate PDE's auxiliary model as usually recommended. Moreover, numerical simulations in 1D and in 2D illustrate our approach
Entropy estimates for a class of schemes for the euler equations
In this paper, we derive entropy estimates for a class of schemes for the
Euler equations which present the following features: they are based on the
internal energy equation (eventually with a positive corrective term at the
righ-hand-side so as to ensure consistency) and the possible upwinding is
performed with respect to the material velocity only. The implicit-in-time
first-order upwind scheme satisfies a local entropy inequality. A
generalization of the convection term is then introduced, which allows to limit
the scheme diffusion while ensuring a weaker property: the entropy inequality
is satisfied up to a remainder term which is shown to tend to zero with the
space and time steps, if the discrete solution is controlled in L and
BV norms. The explicit upwind variant also satisfies such a weaker property, at
the price of an estimate for the velocity which could be derived from the
introduction of a new stabilization term in the momentum balance. Still for the
explicit scheme, with the above-mentioned generalization of the convection
operator, the same result only holds if the ratio of the time to the space step
tends to zero
Boltzmann's H-theorem, its limitations, and the birth of (fully) statistical mechanics
A comparison is made of the traditional Loschmidt (reversibility) and Zermelo
(recurrence) objections to Boltzmann's H-theorem, and its simplified variant in
the Ehrenfests' 1912 wind-tree model. The little-cited 1896 (pre-recurrence)
objection of Zermelo (similar to an 1889 argument due to Poincare) is also
analysed. Significant differences between the objections are highlighted, and
several old and modern misconceptions concerning both them and the H-theorem
are clarified. We give particular emphasis to the radical nature of Poincare's
and Zermelo's attack, and the importance of the shift in Boltzmann's thinking
in response to the objections as a whole.Comment: 40 page
Teleportation and entanglement distillation in the presence of correlation among bipartite mixed states
The teleportation channel associated with an arbitrary bipartite state
denotes the map that represents the change suffered by a teleported state when
the bipartite state is used instead of the ideal maximally entangled state for
teleportation. This work presents and proves an explicit expression of the
teleportation channel for the teleportation using Weyl's projective unitary
representation of the space of 2n-tuples of numbers from Z/dZ for integers d>1,
n>0, which has been known for n=1. This formula allows any correlation among
the n bipartite mixed states, and an application shows the existence of
reliable schemes for distillation of entanglement from a sequence of mixed
states with correlation.Comment: 12 pages, 1 figur
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