On the Homogenization of Geological Fissured Systems With Curved non-periodic Cracks

We analyze the steady fluid flow in a porous medium containing a network of thin fissures i.e. width $\mathcal{O}(\epsilon)$, where all the cracks are generated by the rigid translation of a continuous piecewise $C^{1}$ functions in a fixed direction. The phenomenon is modeled in mixed variational formulation, using the stationary Darcy's law and setting coefficients of low resistance $\mathcal{O}(\epsilon)$ on the network. The singularities are removed performing asymptotic analysis as $\epsilon \rightarrow 0$ which yields an analogous system hosting only tangential flow in the fissures. Finally the fissures are collapsed into two dimensional manifolds.Comment: 24 pages, 4 figure

The Interaction Between PDE and Graphs in Multiscale Modeling

In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open map in $\mathbb{R}^{2}$ or $\mathbb{R}^{3}$. The behavior of the quantities is modeled as flowing in the map constructed and thus it is subject to be described by partial differential equations. We follow this approach using the Darcy Porous Media, saturated fluid flow model in mixed variational formulation.Comment: 14 pages, 4 figure

The asymptotic analysis of a Darcy-Stokes system coupled through a curved interface

The asymptotic analysis of a Darcy-Stokes system modeling the fluid exchange between a narrow channel (Stokes) and a porous medium (Darcy) coupled through a $C^{2}$ curved interface, is presented. The channel is a cylindrical domain between the interface ($\Gamma$) and a parallel translation of it ($\Gamma + \epsilon \, \boldsymbol{\widehat{e}}_{N}$). The introduction of a change variable to fix the domain's geometry and the introduction of two systems of coordinates: the Cartesian and a local one (consistent with the geometry of the surface), permit to find a Darcy-Brinkman lower dimensional coupled system as the limiting form, when the width of the channel tends to zero ($\epsilon \rightarrow 0$).Comment: 27 pages, 4 figure

Application and Assessment of Divide-and-Conquer-based Heuristic Algorithms for some Integer Optimization Problems

In this paper three heuristic algorithms using the Divide-and-Conquer paradigm are developed and assessed for three integer optimizations problems: Multidimensional Knapsack Problem (d-KP), Bin Packing Problem (BPP) and Travelling Salesman Problem (TSP). For each case, the algorithm is introduced, together with the design of numerical experiments, in order to empirically establish its performance from both points of view: its computational time and its numerical accuracy.Comment: 16 pages, 6 figures, 8 table