A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Influence of configurational atomic order on the relative stability of bcc and close-packed structures in Cu-based alloys

We present a study of the influence of atomic order on the relative stability of the bcc and the 18R martensitic structures in a Cu2.96Al0.92Be0.12 crystal. Calorimetric measurements have shown that disorder increases the stability of the 18R phase, contrary to what happens in Cu-Zn-Al alloys for which it is the bcc phase that is stabilized by disordering the system. This different behavior has been explained in terms of a model recently reported. We have also proved that the entropy change at the martensitic transition is independent of the state of atomic order of the crystal, as predicted theoretically. Our results suggest that differences in the vibrational spectrum of the crystal due to different states of atomic order must be equal in the bcc and in the close-packed phases.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

The Patterson-Sullivan embedding and minimal volume entropy for outer space

"Vegeu el resum a l'inici del document del fitxer adjunt."

Absolute and relative deprivation and the measurement of poverty

This paper develops the link between poverty and inequality by focussing on a class of poverty indices (some of them well-known) which aggregate normative concerns for absolute and relative deprivation. The indices are distinguished by a parameter that captures the ethical sensitivity of poverty measurement to ``exclusion'' or ``relative-deprivation'' aversion. We also show how the indices can be readily used to predict the impact of growth on poverty. An illustration using LIS data finds that he United States show more relative deprivation than Denmark and Belgium whatever the percentiles considered, but that overall deprivation comparisons of the four countries considered will generally necessarily depend on the intensity of the ethical concern for relative deprivation. The impact of growth on poverty is also seen to depend on the presence of and on the attention granted to concerns over relative deprivation. }

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

A relative double commutant theorem for hereditary sub-C*-algebras

We prove a double commutant theorem for hereditary subalgebras of a large class of C*-algebras, partially resolving a problem posed by Pedersen[8]. Double commutant theorems originated with von Neumann, whose seminal result evolved into an entire field now called von Neumann algebra theory. Voiculescu proved a C*-algebraic double commutant theorem for separable subalgebras of the Calkin algebra. We prove a similar result for hereditary subalgebras which holds for arbitrary corona C*-algebras. (It is not clear how generally Voiculescu's double commutant theorem holds.)

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

Relative clauses in Iraqi Arabic and the status of resumptive pronouns

Not much has been said about the grammar of Iraqi Arabic. This research is an attempt to shed light on the nature of IA relative clauses. The research focuses on the behavior of the resumptive strategy as opposed to the gap strategy. We consider islandhood, Weak and Strong CrossOver, reconstruction and scope binding, in order to further understand the behavior of resumption. The final conclusion reached is that in Iraqi Arabic the resumptive strategy is actually related to the gap strategy in several respects; and in those where it differs we propose that gaps (traces) are replaced by trace+pronoun complex

Extremal principle of entropy production in the climate system

Paltridge found reasonable values for the most significant climatic variables through maximizing the material transport part of entropy production by using a simple box model. Here, we analyse Paltridge's box model to obtain the energy and the entropy balance equations separately. Derived expressions for global entropy production, which is a function of the radiation field, and even its material transport component, are shown to be different from those used by Paltridge. Plausible climatic states are found at extrema of these parameters. Feasible results are also obtained by minimizing the radiation part of entropy production, in agreement with one of Planck's results, Finally, globally averaged values of the entropy flux of radiation and material entropy production are obtained for two dynamical extreme cases: an earth with uniform temperature, and an earth in radiative equilibrium at each latitudinal point

Greenhouse gases and climatic states of minimum entropy production

The hypothesis of minimum entropy production is applied to a simple one-dimensional energy balance model and is analysed for different values of the radiative forcing due to greenhouse gases. The extremum principle is used to determine the planetary “conductivity” and to avoid the “diffusive” approximation, which is commonly assumed in this type of model. For present conditions the result at minimum radiative entropy production is similar to that obtained by applying the classical model. Other climatic scenarios show visible differences, with better behaviour for the extremal case

Relative price riddles in international business cycle theory: Are transport costs the explanation?

We study relative price behavior in an international business cyclemodel with specialization in production, in which a goods marketfriction is introduced through transport costs. The transporttechnology allows for flexible transport costs. We analyze whetherthis extension can account for the striking differences betweentheory and data as far as the moments of terms of trade and realexchange rates are concerned. We find that transport costs increaseboth the volatility of the terms of trade and the volatility of thereal exchange rate. However, unless the transport technology isspecified by a Leontief technology, transport costs do not resolvethe quantitative discrepancies between theory and data. Asurprising result is that transport costs may actually lower thepersistence of the real exchange rate, a finding that is in contrastto much of the emphasis of the empirical literature.

The importance of relative performance feedback information: Evidence from a natural experiment using high school students

We study the effect of providing relative performance feedback information onperformance, when individuals are rewarded according to their absolute performance. Anatural experiment that took place in a high school offers an unusual opportunity to testthis effect in a real-effort setting. For one year only, students received information thatallowed them to know whether they were performing above (below) the class average aswell as the distance from this average. We exploit a rich panel data set and find that theprovision of this information led to an increase of 5% in students grades. Moreover, theeffect was significant for the whole distribution. However, once the information wasremoved, the effect disappeared. To rule out the concern that the effect may beartificially driven by teachers within the school, we verify our results using nationallevel exams (externally graded) for the same students, and the effect remains.

The provision of relative performance feedback information: An experimental analysis of performance and happiness

This paper studies the effect of providing relative performance feedback information onindividual performance and on individual affective response, when agents are rewardedaccording to their absolute performance. In a laboratory set-up, agents perform a realeffort task and when receiving feedback, they are asked to rate their happiness, arousaland feeling of dominance. Control subjects learn only their absolute performance, whilethe treated subjects additionally learn the average performance in the session.Performance is 17 percent higher when relative performance feedback is provided.Furthermore, although feedback increases the performance independent of the content(i.e., performing above or below the average), the content is determinant for theaffective response. When subjects are treated, the inequality in the happiness and thefeeling of dominance between those subjects performing above and below the averageincreases by 8 and 6 percentage points, respectively.

Relative payoffs and happiness: An experimental study

Some current utility models presume that people are concerned with their relative standing in a reference group. If this is true, do certain types care more about this than others? Using simple binary decisions and self-reported happiness, we investigate both the prevalence of ``difference aversion'' and whether happiness levels influence the taste for social comparisons. Our decision tasks distinguish between a person s desire to achieving the social optimum, equality or advantageous relative standing. Most people appear to disregard relative payoffs, instead typically making choices resulting in higher social payoffs. While we do not find a strong general correlation between happiness and concern for relative payoffs, we do observe that a willingness to lower another person s payoff below one s own (competitive preferences) seems correlated with unhappiness.