2,342 research outputs found
A constrained optimization problem in quantum statistical physics
In this paper, we consider the problem of minimizing quantum free energies
under the constraint that the density of particles is fixed at each point of
Rd, for any d 1. We are more particularly interested in the
characterization of the minimizer, which is a self-adjoint nonnegative trace
class operator, and will show that it is solution to a nonlinear
self-consistent problem. This question of deriving quantum statistical
equilibria is at the heart of the quantum hydrody-namical models introduced by
Degond and Ringhofer. An original feature of the problem is the local nature of
constraint, i.e. it depends on position, while more classical models consider
the total number of particles in the system to be fixed. This raises
difficulties in the derivation of the Euler-Lagrange equations and in the
characterization of the minimizer, which are tackled in part by a careful
parametrization of the feasible set
Small volume expansions for elliptic equations
This paper analyzes the influence of general, small volume, inclusions on the
trace at the domain's boundary of the solution to elliptic equations of the
form \nabla \cdot D^\eps \nabla u^\eps=0 or (-\Delta + q^\eps) u^\eps=0
with prescribed Neumann conditions. The theory is well-known when the
constitutive parameters in the elliptic equation assume the values of different
and smooth functions in the background and inside the inclusions. We generalize
the results to the case of arbitrary, and thus possibly rapid, fluctuations of
the parameters inside the inclusion and obtain expansions of the trace of the
solution at the domain's boundary up to an order \eps^{2d}, where is
dimension and \eps is the diameter of the inclusion. We construct inclusions
whose leading influence is of order at most \eps^{d+1} rather than the
expected \eps^d. We also compare the expansions for the diffusion and
Helmholtz equation and their relationship via the classical Liouville change of
variables.Comment: 42 page
Strategic Port Graph Rewriting: An Interactive Modelling and Analysis Framework
We present strategic portgraph rewriting as a basis for the implementation of
visual modelling and analysis tools. The goal is to facilitate the
specification, analysis and simulation of complex systems, using port graphs. A
system is represented by an initial graph and a collection of graph rewriting
rules, together with a user-defined strategy to control the application of
rules. The strategy language includes constructs to deal with graph traversal
and management of rewriting positions in the graph. We give a small-step
operational semantics for the language, and describe its implementation in the
graph transformation and visualisation tool PORGY.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767
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