Generalized Kirchhoff approximation for Helmholtz equation

We give integral formulas to approximate solutions of Dirichlet and Neumann problems for Helmholtz equation at high frequencies. These approximations are valid in the complementary of a union of convex compact obstacles. The first step of the iterative procedure is the classical Kirchhoff approximation. Convergence is proved by comparison with the geometrical optics asymptotics. The method is shown to be numerically stable.Comment: 15 page

Rwandan economic involvement in the conflict in the Democratic Republic of Congo

According to the International Rescue Committee, as many as 3.3 million people have lost their lives, either in direct fighting or from the outbreak of diseases as a result of the war. Despite the formation of a two-year national transition government, composed of representatives of the former Kinshasa regime, the pro-government Mayi Mayi-militias, rebel movements, the unarmed political opposition and civil society, the prospects for durable peace remain bleak. While intensified ethnic strife between Hema and Lendu militias in the resource-rich Ituri province has triggered a massive flow of refugees and the creation of a multilateral intervention force in June 2003, the Kivu provinces have witnessed renewed fighting between rebel forces of the Rwandan-backed RCD-Goma rebel movement and Mayi-Mayi militiamen. Even the south-eastern Katanga province has shown signs of evolving instability: on 8 August 2003, the international relief non-governmental organisation GOAL reported that six different armed groups were occupying the town of Manono, following the ejection of the local RCD-Goma administrator by the 8th Brigade, a mysterious group of 150 men claiming to be members of the former Kinshasa government’s army. Unfortunately, the spiral of violence in Congo’s border regions is not the only source of concern to diplomats involved in overseeing the peace process. The dubious track record of some of the key members of the national transition government does not inspire much confidence in the preparatory work for the country’s first democratic elections since independence. Whereas a Belgian court has sentenced vicepresident Jean-Pierre Bemba to one year’s imprisonment for human trafficking, his colleague Abdoulaye Yerodia Ndombasi has also faced a Belgian judicial inquiry for his inflammatory statements concerning the DRC’s Tutsi population in August 1998. Finally, one of the biggest impediments to the Congolese peace process may be the issue of resource trafficking. According to the UN expert panel investigating the illegal exploitation of natural resources and other forms of wealth of the DRC, members of the Rwandan and Ugandan regime have developed mechanisms to continue the looting of diamonds, gold, coltan and timber after the official withdrawal of their troops from Congolese territory, as agreed in the Pretoria and Luanda peace accords. Previous reports by the Panel contained a detailed account of the multiple ways in which a selected group of Rwandan and Ugandan military officers, politicians and businessmen have taken advantage of the military presence of the Rwandan Patriotic Front and the Ugandan People’s Defence Forces to secure their stake in the Congolese mining business.

An efficient way to assemble finite element matrices in vector languages

Efficient Matlab codes in 2D and 3D have been proposed recently to assemble finite element matrices. In this paper we present simple, compact and efficient vectorized algorithms, which are variants of these codes, in arbitrary dimension, without the use of any lower level language. They can be easily implemented in many vector languages (e.g. Matlab, Octave, Python, Scilab, R, Julia, C++ with STL,...). The principle of these techniques is general, we present it for the assembly of several finite element matrices in arbitrary dimension, in the P1 finite element case. We also provide an extension of the algorithms to the case of a system of PDE's. Then we give an extension to piecewise polynomials of higher order. We compare numerically the performance of these algorithms in Matlab, Octave and Python, with that in FreeFEM++ and in a compiled language such as C. Examples show that, unlike what is commonly believed, the performance is not radically worse than that of C : in the best/worst cases, selected vector languages are respectively 2.3/3.5 and 2.9/4.1 times slower than C in the scalar and vector cases. We also present numerical results which illustrate the computational costs of these algorithms compared to standard algorithms and to other recent ones

A probabilistic algorithm approximating solutions of a singular PDE of porous media type

The object of this paper is a one-dimensional generalized porous media equation (PDE) with possibly discontinuous coefficient $\beta$, which is well-posed as an evolution problem in $L^1(\mathbb{R})$. In some recent papers of Blanchard et alia and Barbu et alia, the solution was represented by the solution of a non-linear stochastic differential equation in law if the initial condition is a bounded integrable function. We first extend this result, at least when $\beta$ is continuous and the initial condition is only integrable with some supplementary technical assumption. The main purpose of the article consists in introducing and implementing a stochastic particle algorithm to approach the solution to (PDE) which also fits in the case when $\beta$ is possibly irregular, to predict some long-time behavior of the solution and in comparing with some recent numerical deterministic techniques

Mining in comparative perspective : trends, transformations and theories

This article offers a brief introduction to a special issue based on a selection of papers originally presented at an international mining conference in Ghent (Belgium) in December 2017. The aim of the conference was to promote a comparative and multidisciplinary approach to a selective number of political, economic and sociocultural aspects of mining in the Global South. The five papers included in the special issue have been grouped around three main themes: (1) mining elites, (2) the antagonism between artisanal and small-scale mining (ASM) and large-scale mining (LSM), and (3) mining in a globalizing world