Incompressible immiscible multiphase flows in porous media: a variational approach

We describe the competitive motion of (N + 1) incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of non-negative measures with prescribed mass endowed with some tensorial Wasserstein distance. We show the convergence of the approximation obtained by a minimization schem\`e a la [R. Jordan, D. Kinder-lehrer \& F. Otto, SIAM J. Math. Anal, 29(1):1--17, 1998]. This allow to obtain a new existence result for a physically well-established system of PDEs consisting in the Darcy-Muskat law for each phase, N capillary pressure relations, and a constraint on the volume occupied by the fluid. Our study does not require the introduction of any global or complementary pressure

Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically $O(N^{2d+1})$ where $d$ is the dimension of the velocity space. In this paper, following the ideas introduced in [27,28], we derive fast summation techniques for the evaluation of discrete-velocity schemes which permits to reduce the computational cost from $O(N^{2d+1})$ to $O(\bar{N}^d N^d\log_2 N)$, $\bar{N} << N$, with almost no loss of accuracy.Comment: v2: 22 pages, improvement of the presentation and more details given in some proofs. arXiv admin note: text overlap with arXiv:1106.1020 by other author

The gradient flow structure for incompressible immiscible two-phase flows in porous media

We show that the widely used model governing the motion of two incompressible immiscible fluids in a possibly heterogeneous porous medium has a formal gradient flow structure. More precisely, the fluid composition is governed by the gradient flow of some non-smooth energy. Starting from this energy together with a dissipation potential, we recover the celebrated Darcy-Muskat law and the capillary pressure law governing the flow thanks to the principle of least action. Our interpretation does not require the introduction of any algebraic transformation like, e.g., the global pressure or the Kirchhoff transform, and can be transposed to the case of more phases

Memoization for Unary Logic Programming: Characterizing PTIME

We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms. More precisely, we study the restriction of this framework to terms (and logic programs, rewriting rules) using only unary symbols. We prove it is complete for polynomial time computation, using an encoding of pushdown automata. We then introduce an algebraic counterpart of the memoization technique in order to show its PTIME soundness. We finally relate our approach and complexity results to complexity of logic programming. As an application of our techniques, we show a PTIME-completeness result for a class of logic programming queries which use only unary function symbols.Comment: Soumis {\`a} LICS 201

Textos sobre violencia: de lo impuro. (Contaminaciones, equívocos, temblores)

This article interrogates a certain philosophical scene – one which constitutes itself through the position of what Jacques Derrida calls “the ethical instance of violence.” In the course of the essay, I analyze this quasi-juridical scene through readings of Aristotle, Walter Benjamin, and Giorgio Agamben among others. The scene, built on texts on texts on violence, demands a logic of purity; it is wary of contaminations and equivocations. And yet it thrives on them. In analyzing the implications of text, writing, and trace for the philosophical discourse on violence, I follow Derrida “just to see” what could make the scene tremble.Este artículo interroga cierta escena filosófica –una que se constituye a través de la posición de lo que Jacques Derrida llama “la instancia ética de la violencia”. En el curso del ensayo, analizo esta escena cuasi-jurídica a través de las lecturas de Aristóteles, Walter Benjamin y Giorgio Agamben, entre otros. La escena, construida sobre textos sobre textos sobre violencia, exige una lógica de la pureza; es recelosa de conta-minaciones y equívocos. Y sin embargo, se alimenta de ellos. Analizando las implicaciones del texto, la escritura y la huella para el discurso filosófico sobre la violencia, sigo a Derrida “solo para ver” que puede hacer temblar esta escena

Characterizing co-NL by a group action

International audienceIn a recent paper, Girard proposes to use his recent construction of a geometry of interaction in the hyperfinite factor in an innovative way to characterize complexity classes. We begin by giving a detailed explanation of both the choices and the motivations of Girard's definitions. We then provide a complete proof that the complexity class co-NL can be characterized using this new approach. We introduce as a technical tool the non-deterministic pointer machine, a concrete model to computes algorithms