Tensor-based multiscale method for diffusion problems in quasi-periodic heterogeneous media

This paper proposes to address the issue of complexity reduction for the numerical simulation of multiscale media in a quasi-periodic setting. We consider a stationary elliptic diffusion equation defined on a domain $D$ such that $\overline{D}$ is the union of cells $\{\overline{D_i}\}_{i\in I}$ and we introduce a two-scale representation by identifying any function $v(x)$ defined on $D$ with a bi-variate function $v(i,y)$, where $i \in I$ relates to the index of the cell containing the point $x$ and $y \in Y$ relates to a local coordinate in a reference cell $Y$. We introduce a weak formulation of the problem in a broken Sobolev space $V(D)$ using a discontinuous Galerkin framework. The problem is then interpreted as a tensor-structured equation by identifying $V(D)$ with a tensor product space $\mathbb{R}^I \otimes V(Y)$ of functions defined over the product set $I\times Y$. Tensor numerical methods are then used in order to exploit approximability properties of quasi-periodic solutions by low-rank tensors.Comment: Changed the choice of test spaces V(D) and X (with regard to regularity) and the argumentation thereof. Corrected proof of proposition 3. Corrected wrong multiplicative factor in proposition 4 and its proof (was 2 instead of 1). Added remark 6 at the end of section 2. Extended remark 7. Added references. Some minor improvements (typos, typesetting

Regional security cooperation in Central Asia: the influence of Uzbekistan’s leader change on the Rogun Dam project

In Central Asia, the past three decades have been characterised by a lack of cooperation in security matters, despite the strong incentives for states to cooperate to solve their common security issues. One of the main sources of tension is the Rogun Dam project pushed forward by Tajikistan and historically met with strong opposition from Uzbekistan. Yet, the recent power change following the assession of Mirziyoyev to the presidency has led to a political U-turn in the Uzbek foreign policy towards the dam project which cannot be explain by rational system-level theories. This thesis aims to question the supremacy of the rationalist approach and system-level theories in explaining interstate cooperation and addresses its limitation in providing comprehensive explanations in the case of Central Asia. Rather, this research seeks to provide a complementary individual-focused approach to the study of states’ relations that focuses on the influence of leadership perceptions in shaping foreign policy decisions towards security cooperation. The chosen method of analysis is the conduct of a content analysis on speeches and statements made by key actors of the two respective administrations. The thesis concludes by stating the key findings that have been established from the analysis, and are presented in two categories: cooperation-adverse and cooperation-prone perceptions. The findings confirm the existence of diverging perceptions between the two leaderships and shed light on their relation with the respective foreign policy carried by the each leadership, therefore demonstrating the value of an individual-level analysis

Le garde-meuble : album de l'exposition de l'industrie, 1844

Copia digital. España : Ministerio de Cultura y Deporte. Subdirección General de Coordinación Bibliotecaria, 201

D6.3 Report on stochastic optimisation for simple problems

This report addresses the general matter of optimisation under uncertainties, following a previous report on stochastic sensitivities (deliverable 6.2). It describes several theoretical methods, as well their application into implementable algorithms. The specific case of the conditional value at risk chosen as risk measure, with its challenges, is prominently discussed. In particular, the issue of smoothness – or lack thereof – is addressed through several possible approaches. The whole report is written in the context of high-performance computing, with concern for parallelisation and cost-efficiency.&nbsp

Influence of the gun barrel straightness on projectile exit conditions

Gun accuracy is influenced by several parameters during the internal ballistics phase. Accuracy is defined by the bias and dispersion of impact points on the target. The aim of this study is to determine the influence of gun barrel straightness on projectile exit conditions, in order to understand how to improve weapon accuracy. A numerical firing analysis was carried out with LS-Dyna software. The model validity is proven by its ability to accurately predict the measured circumferential strains caused by the forcing effect of the projectile, and by the consistency of the contact forces at the projectile-tube interface. To validate the firing simulation, circumferential strains of the tube were measured and compared to LS-Dyna results. Subsequently, the barrel geometry was modified to add a straightness defect to the initial curvature due to gravity. Lastly, a post-treatment was performed to determine the angular and transverse velocities of the projectile during internal ballistics phase. This analysis shown the influence of specific shapes on ammunition balloting and velocity