Existence results for non-smooth second order differential inclusions, Convergence result for a numerical scheme and applications for modelling inelastic collisions

We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal normal cone to a time-dependent set. Moreover we extend a numerical scheme, introduced in [8] and proved a convergence result. We propose applications in modelling inelastic collisions between rigid particles too.Comment: 22 pages, 1 figur

The Sustainable Globalization Index: historical divergence and future convergence to sustainable globalization

In this Kühne Impact Series we provide a historical perspective on globalizationʼs contribution to climate change, and the historical role of trade in bringing us closer to (or further away from) a sustainable world. We introduce the Sustainable Globalization Index (SGI) that tracks the worldʼs progress towards a Sustainable Globalization scenario. The SGI reveals that globalization has historically diverged from a sustainable pattern of trade until the Great Recession, but is now on a converging trend. The comparison in the recent period suggests that the (green) future of trade and logistics involves more trade from and to the economic North, more intraregional trade, and a shift of trade flows in favor of energy and raw materials and away from agricultural goods

The distributional effects of carbon pricing: a global view of common but differentiated responsibilities

In this Kühne Impact Series, we focus on the distributional effects of climate action. We simulate the distributional effects of a global carbon tax – the optimal economic policy tool in the fight against climate change – with or without international redistribution schemes. Our main result is that the economic costs of climate action are disproportionately borne by poor countries, but that realistic cross-country transfers could remedy this inequality. For example, annual North-South transfers of an average $200 per person would suffice to equalize the economic costs of climate action

Numerical simulation of rigid particles in Stokes flow: lubrication correction for any (regular) shape of particles

We address the problem of numerical simulation of suspensions of rigid particles in a Stokes flow. We focus on the inclusion of the singular short range interaction effects (lubrication effects) in the simulations when the particles come close one to another. The problem is solved without introducing new hypothesis nor model. As in [Lefebvre-Lepot, Merlet, Nguyen, JFM, 2015], the key idea is to decompose the velocity and pressure flows in a sum of a singular and a regular part. In this article, the singular part is computed using an explicit asymptotic expansion of the solution when the distance goes to zero. This expansion is similar to the asymptotic expansion proposed in [Hillairet, Kelai, Asymptotic Analysis, 2015] but is more appropriate for numerical simulations of suspensions. It can be computed for any shape of particles. Using [Hillairet, Kelai, Asymptotic Analysis, 2015] as an intermediate result, we prove that the remaining part is regular in the sense that it is bounded independently of the distance. As a consequence, only a small number of degrees of freedom are necessary to obtain accurate results. The method is tested in dimension 2 for clusters of two or three aligned particles with general rigid velocities. We show that, as expected, the convergence is independent on the distance

Micro-Macro Modelling of an Array of Spheres Interacting Through Lubrication Forces

We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relies on an elongational viscosity, which is proportional to the reciprocal of the local fluid fraction. We then establish the convergence in a weak sense of solutions to the discrete problem towards the solution to the partial differential equation which we identified as the macroscopic constitutive equation

Le cœur équivoque dans l’Avis aus roys : un « miroir des princes » du XIVe siècle

From the 13t century onwards, the heart was the subject of a great deal of attention in the medical, literary, religious and political fields. Various theories about the royal heart were expounded and disseminated, particularly through literature dedicated to rulers. The author of L’Avis aus roys – an anonymous and little-studied mid-14th-century “mirror for princes”, which is heavily indebted to Giles of Rome’s De Regimine Principum – grants an important place to the princely heart in his text, endowing it with multiple meanings. The royal organ is seen, in turn, as the origin of life, spirituality, the soul, the virtues, the passions, and even reason itself. Preserved at the Pierpont Morgan Library, manuscript M. 456 is the only one out of the five known examples of this text to have an iconographic programme representing the princely heart, an organ which rarely featured in either religious or secular art of the 13th and 14th centuries. Representing the royal heart in all its various facets, the artists working on this manuscript treat this perishable organ as having an unprecedented mystical and eternal dimension.À partir du XIIIe siècle, le cœur est l’objet des plus vives attentions dans les sphères médicale, littéraire, religieuse et politique. Des théories sur l’organe royal vont notamment se propager à travers la littérature spécialement destinée aux gouvernants. L’auteur de l’Avis aus roys – un « miroir des princes » anonyme et méconnu du milieu du XIVe siècle fortement inspiré du De regimine principum de Gilles de Rome -accorde au cœur princier une place de choix dans son discours, lui conférant une image pour le moins équivoque. L’organe y fait successivement figure de siège de la vie, de la spiritualité, de l’âme, des vertus, des passions et de la raison. Des cinq témoins recensés à ce jour, seul le manuscrit M. 456 conservé à la Pierpont Morgan Library dispose d’un programme iconographique mettant en scène le cœur du prince, habituellement peu représenté aux XIIIe et XIVe siècles dans l’art religieux et profane. En plus d’entretenir l’ambiguïté, les artistes ont su donner à cet organe princier pourtant putrescible une dimension mystique et perpétuelle inédite

Le cœur équivoque dans l’Avis aus roys : un « miroir des princes » du XIVe siècle

From the 13t century onwards, the heart was the subject of a great deal of attention in the medical, literary, religious and political fields. Various theories about the royal heart were expounded and disseminated, particularly through literature dedicated to rulers. The author of L’Avis aus roys – an anonymous and little-studied mid-14th-century “mirror for princes”, which is heavily indebted to Giles of Rome’s De Regimine Principum – grants an important place to the princely heart in his text, endowing it with multiple meanings. The royal organ is seen, in turn, as the origin of life, spirituality, the soul, the virtues, the passions, and even reason itself. Preserved at the Pierpont Morgan Library, manuscript M. 456 is the only one out of the five known examples of this text to have an iconographic programme representing the princely heart, an organ which rarely featured in either religious or secular art of the 13th and 14th centuries. Representing the royal heart in all its various facets, the artists working on this manuscript treat this perishable organ as having an unprecedented mystical and eternal dimension.À partir du XIIIe siècle, le cœur est l’objet des plus vives attentions dans les sphères médicale, littéraire, religieuse et politique. Des théories sur l’organe royal vont notamment se propager à travers la littérature spécialement destinée aux gouvernants. L’auteur de l’Avis aus roys – un « miroir des princes » anonyme et méconnu du milieu du XIVe siècle fortement inspiré du De regimine principum de Gilles de Rome -accorde au cœur princier une place de choix dans son discours, lui conférant une image pour le moins équivoque. L’organe y fait successivement figure de siège de la vie, de la spiritualité, de l’âme, des vertus, des passions et de la raison. Des cinq témoins recensés à ce jour, seul le manuscrit M. 456 conservé à la Pierpont Morgan Library dispose d’un programme iconographique mettant en scène le cœur du prince, habituellement peu représenté aux XIIIe et XIVe siècles dans l’art religieux et profane. En plus d’entretenir l’ambiguïté, les artistes ont su donner à cet organe princier pourtant putrescible une dimension mystique et perpétuelle inédite

Trade, innovation and optimal patent protection

This paper provides a first comprehensive quantitative analysis of optimal patent policy in the global economy. We introduce a new framework, which combines trade and growth theory into a tractable tool for quantitative research. Our application delivers three main results. First, the potential gains from international cooperation over patent policies are large. Second, only a small share of these gains has been realized so far. And third, the WTO’s TRIPS agreement has been counterproductive, slightly reducing welfare in the Global South and for the world. Overall, there is substantial scope for policy reform

Fibre persistence on static textiles under outdoor conditions

The persistence of fibres under outdoor conditions is seldom investigated. This research aimed to study simultaneously the influence of several factors (and their cross-interactions) on the persistence of fibres on static textile surfaces. In order to achieve this aim, a design of experiments was successfully implemented under laboratory conditions. Four factors were considered: time, inclination of the recipient textile, wind speed, and rainfall. The model obtained by this supervised method was compared with the results collected under actual outdoor conditions near a weather station. The resulting model appears to be reliable as long as the values of the factors are kept within the range used in the study. The results of the laboratory tests showed that wind speed and rainfall significantly influence the persistence of fibres while time and inclination of the recipient textile have been found to be nonsignificant. In general, the observed persistence was high: between 90.4 and 100 %. This might be attributed to the recipient textile surface possessing abundant protruding fibres which “traps” the transferred fibres. Outdoor experiments usually suffer from a higher variability and result in a higher fibre loss. In outdoor conditions, wind and rainfall have shown an extensive influence on the fibre persistence. Finally, the trend of fibre persistence on static textiles in outdoor conditions is generally linear with time, but extreme meteorological condition will induce exponential losses