Regularity of the minimiser of one-dimensional interaction energies

We consider both the minimisation of a class of nonlocal interaction energies over non-negative measures with unit mass and a class of singular integral equations of the first kind of Fredholm type. Our setting covers applications to dislocation pile-ups, contact problems, fracture mechanics and random matrix theory. Our main result shows that both the minimisation problems and the related singular integral equations have the same unique solution, which provides new regularity results on the minimiser of the energy and new positivity results on the solutions to singular integral equations.Comment: 46 page

Upscaling of dislocation walls in finite domains

We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our microscopic model to be a one dimensional particle system, in which the interactions between the particles (dislocation walls) are singular and non-local. As a first step towards treating realistic geometries, we focus on finite-size effects rather than considering an infinite domain as typically discussed in the literature. We derive effective equations for the dislocation density by means of \Gamma-convergence on the space of probability measures. Our analysis yields a classification of macroscopic models, in which the size of the domain plays a key role

Die Transformation in den baltischen Staaten: baltische Wirtschaft und russische Diaspora

'Seit der Unabhängigkeit der baltischen Staaten 1991 steht die Frage der russischen Diaspora im Mittelpunkt der Aufmerksamkeit. Die Gründe dafür reichen von den Moskauer Versuchen, sich über die Russischsprachigen in die baltische Politik einzuschalten, über den Umfang der Minderheiten in Estland und Lettland bis zur moralischen und praktischen Abwägung zwischen baltischer Nationalstaatsbildung und Grundrechten der Einwanderer. Aus der baltisch-nationalen Innensicht ist die Konfrontation zwischen Titularnationen und Russischsprachigen ein ethnisch-zivilisatorischer Gegensatz a la Huntington. Die westlichen Stellungnahmen beschränken sich meist auf normative Politikberatung zur Minderheitengesetzgebung und deren Implementierung oder auf postmoderne Betrachtungen zur apodiktischen Identitätskrise der Diasporarussen oder Umfragen zu deren Integrationsfortschritten und Selbsteinschätzungen. Gemeinsames Defizit dieser Ansätze ist die Vernachlässigung der von der forcierten sowjetischen Modernisierungs- und Migrationspolitik verursachten Schnittstellen von national-kultureller Ethnizität und sozioökonomischer Prosperität. Die postkommunistische Transformation hat diese Asymmetrien zwischen Ethnizität und sozioökonomischer Prosperität (oft unter umgekehrten Vorzeichen) noch verstärkt. Zu einer Identifikation und Analyse dieser Schnittstellen gehören zwei Aspekte: eine Bestandsaufnahme des Politikbereiches, in dem die Diaspora disproportional vertreten ist, und eine Erörterung des für diese Schnittstelle relevanten Politikfeldes, in dem nationale und wirtschaftliche Motive um den Vorrang streiten. Kernpunkt ist der Teufelskreis aus vorhandenen Asymmetrien, Transformationspolitik und einer ethnopolitischen Deutung. Nach diesen beiden Aspekten lassen sich - zusätzlich zur eigentlichen Minderheitenpolitik - drei größere Politikbereiche als ethnopolitisch relevant identifizieren: Wirtschaftspolitik, Regionalpolitik und Sozialpolitik.' (Textauszug)'Since the Baltic states achieved independence in 1991, the question of the Russians in Diaspora has been at the focal point of attention. The reasons for this range from Moscow's attempts to intervene in the politics of the Baltic states through their Russian-speaking minorities, via the sheer size of these minorities in Estonia and Latvia, to ongoing moral and practical considerations as to how to achieve a balance between the formation of national states in the Baltic region and the basic rights of the non-nationals. From the Baltic national viewpoint, the confrontation between the titular nation and the Russian-speakers is a classical ethno-civilisational clash a la Huntington. Western commentaries restrict themselves mainly to normative political counselling on legislation concerning the minorities and its implementation or to post-modern observations on the apodictic identity crisis of the Russians in Diaspora, or to surveys on the progress they have made in integration and on their self-assessment. A deficit common to all these approaches is that they fall to take due account of the intersections between national-cultural ethnicity and socio-economic prosperity that have been created by the Soviet policies of high-pace modernisation and migration. Post-communist transformation has even aggravated these asymmetries between ethnicity and socio-economic prosperity (often with the signs reversed). Any attempt to identify and analyse these points of intersection must take into account two aspects: an examination of the status quo in the area of politics in which the Diaspora is disproportionately represented, and a discussion of the field of politics that is of relevance to this intersection and in which national and economic motives vie for superiority. The crucial point is the vicious circle of existing asymmetries, transformation policy, and ethno-political interpretation. In the light of these two aspects, three major areas of politics - above and beyond policy towards the minorities in the stricter sense - can be identified as being of ethno-political relevance: economic policy, regional policy, and social policy.' (extract

Stabilizing Fluid-Fluid Displacements in Porous Media Through Wettability Alteration

We study experimentally how wettability impacts fluid-fluid-displacement patterns in granular media. We inject a low-viscosity fluid (air) into a thin bed of glass beads initially saturated with a more-viscous fluid (a water-glycerol mixture). Chemical treatment of glass surfaces allows us to control the wetting properties of the medium and modify the contact angle θ from 5° (drainage) to 120° (imbibition). We demonstrate that wettability exerts a powerful influence on the invasion morphology of unfavorable mobility displacements: increasing θ stabilizes fluid invasion into the granular pack at all capillary numbers. In particular, we report the striking observation of a stable radial displacement at low capillary numbers, whose origin lies on the cooperative nature of fluid invasion at the pore scale.Eni S.p.A. (Firm)ARCO Chair in Energy Studie

Inhaled Nitric Oxide Therapy for Pulmonary Disorders of the Term and Preterm Infant

The 21st century began with the FDA approval of inhaled nitric oxide therapy for the treatment of neonatal hypoxic respiratory failure associated with pulmonary hypertension in recognition of the two randomized clinical trials demostrating a significant reduction in the need for extracorporeal support in the term and near-term infant. Inhaled nitric oxide is one of only a few therapeutic agents approved for use through clinical investigations primarily in the neonate. This article provides an overview of the pertinent biology and chemistry of nitric oxide, discusses potential toxicities, and reviews the results of pertinent clinical investigations and large randomized clinical trials including neurodevelopmental follow-up in term and preterm neonates. The clinical investigations conducted by the Eunice Kennedy Shriver NICHD Neonatal Research Network will be discussed and placed in context with other pertinent clinical investigations exploring the efficacy of inhaled nitric oxide therapy in neonatal hypoxic respiratory failure