Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Speed of reaction-diffusion fronts in spatially heterogeneous media

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic results have been compared with numerical results exhibiting a good agreement. Finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities

Aggregate shocks or vertical tax interdependence? Evidende from gasoline and cigarettes

[cat] Besley i Rosen -1998- van ser els primers autors en estimar empíricament la rellevància de les externalitats impositives verticals. Aquests autors varen fer-ho per al cas dels impostos sobre la benzina i el tabac, en concret, per al cas dels EEUU. Ara bé, no varen tenir en compte les diferències en el nivell de vida entre Estats: àrees amb un nivell elevat paguen menys en termes reals que àrees amb un nivell de vida baix, doncs l'impost unitari sobre la benzina o sobre el tabac no difereix d'acord amb l'Estat on l'impost s'aplica. En conseqüència, proposem que la competència impositiva vertical sigui estimada deflactant totes les variables monetàries utilitzant l'anomenat "House Price Index (HPI)", el qual està disponible al nivell dels Estats. Això genera una variable impositiva federal expressada en termes reals i que presenta variació entre Estats. Aquesta estratègia empírica ens permet diferenciar entre la interdependència vertical entre els tipus impositius federals i els estatals de shocks agregats al llarg del temps, utilitzant dades per als EEUU durant el període 1975 a 2006 per a benzina i tabac. Trobem una nivell significatiu de competència impositiva horitzontal, la qual és més elevada en el cas del tabac, però en cap cas reacció impositiva vertical. Els resultats són robustos al període analitzat.

Aggregate shocks or vertical tax interdependence? Evidende from gasoline and cigarettes

[cat] Besley i Rosen -1998- van ser els primers autors en estimar empíricament la rellevància de les externalitats impositives verticals. Aquests autors varen fer-ho per al cas dels impostos sobre la benzina i el tabac, en concret, per al cas dels EEUU. Ara bé, no varen tenir en compte les diferències en el nivell de vida entre Estats: àrees amb un nivell elevat paguen menys en termes reals que àrees amb un nivell de vida baix, doncs l'impost unitari sobre la benzina o sobre el tabac no difereix d'acord amb l'Estat on l'impost s'aplica. En conseqüència, proposem que la competència impositiva vertical sigui estimada deflactant totes les variables monetàries utilitzant l'anomenat "House Price Index (HPI)", el qual està disponible al nivell dels Estats. Això genera una variable impositiva federal expressada en termes reals i que presenta variació entre Estats. Aquesta estratègia empírica ens permet diferenciar entre la interdependència vertical entre els tipus impositius federals i els estatals de shocks agregats al llarg del temps, utilitzant dades per als EEUU durant el període 1975 a 2006 per a benzina i tabac. Trobem una nivell significatiu de competència impositiva horitzontal, la qual és més elevada en el cas del tabac, però en cap cas reacció impositiva vertical. Els resultats són robustos al període analitzat.

Classical horizontal inequity and reranking: an integrated approach

The last 20 years have seen a significant evolution in the literature on horizontal inequity (HI) and have generated two major and "rival" methodological strands, namely, classical HI and reranking. We propose in this paper a class of ethically flexible tools that integrate these two strands. This is achieved using a measure of inequality that merges the well-known Gini coefficient and Atkinson indices, and that allows a decomposition of the total redistributive effect of taxes and transfers in a vertical equity effect and a loss of redistribution due to either classical HI or reranking. An inequality-change approach and a money-metric cost-of-inequality approach are developed. The latter approach makes aggregate classical HI decomposable across groups. As in recent work, equals are identified through a nonparametric estimation of the joint density of gross and net incomes. An illustration using Canadian data from 1981 to 1994 shows a substantial, and increasing, robust erosion of redistribution attributable both to classical HI and to reranking, but does not reveal which of reranking or classical HI is more important since this requires a judgement that is fundamentally normative in nature.

Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher-Kolmogorov-Petrovskii-Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

Modelització de la producció de melanina a partir de polifenol oxidasa d'Agaricus bisporus

Les melanines són un grup heterogeni de polímers producte de reaccions enzimàtiques en els teixits vegetals que contenen compostos fenòlics o polifenòlics. Estudis recents han descobert algunes propietats benèfiques de les melanines sobre la salut, tals com antioxidants, antiinflamatòries, immunològiques i propietats anti-tumorals. Així, no només la seva eliminació ha de ser examinada, sinó que també podria considerar-se la seva addició a aliments funcionals de nova creació. D’aquesta manera, es requereix conèixer el mecanisme cinètic de la lanogènesi abans de la seva possible utilització industrial. S’ha desenvolupat un model cinètic per explicar la formació de melanina a partir de L-tirosina utilitzant polifenol oxidasa d’Agaricus bisporus i monitoritzant l'absorbància de la solució. Aquesta expressió permet descriure la formació de melanina en funció del temps de reacció i obtenir alguns paràmetres importants que defineixen el producte, com el coeficient d'extinció. L’absorbància comença a créixer després d'un període de latència en què es produeixen productes intermedis incolors. El coeficient d'extinció dels productes resultants no és un valor constant, perquè depèn de les condicions de cada experiment. La tirosinasa tingué un menor efecte catalitzador sobre la L-tirosina (primera reacció que catalitza), que sobre L-DOPA (segona reacció).

Ab initio absorption spectrum of NiO combining molecular dynamics with the embedded cluster approach in a discrete reaction field

We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the material model. By means ofcomplete active space self-consistent field second-order perturbation theory (CASPT2) calculations on embedded clusters extracted from the resulting trajectory, we describe localized spectroscopic phenomena on NiO with an efficient treatment of electron correlation. The inclusion of thermal motion into the theoretical description allowsus to study electronic transitions that, otherwise, would be dipole forbidden in the ideal structure and results in a natural reproduction of the band broadening. Moreover, we improved the embedded cluster model by incorporating self-consistently at the complete active space self-consistent field (CASSCF) level a discrete (or direct) reaction field (DRF) in the cluster surroundings. The DRF approach offers an efficient treatment ofelectric response effects of the crystalline embedding to the electronic transitions localized in the cluster. We offer accurate theoretical estimates of the absorption spectrum and the density of states around the Fermi level of NiO, and a comprehensive explanation of the source of the broadening and the relaxation of the charge transferstates due to the adaptation of the environment

Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

Dynamical features of reaction-diffusion fronts in fractals

The speed of front propagation in fractals is studied by using (i) the reduction of the reaction-transport equation into a Hamilton-Jacobi equation and (ii) the local-equilibrium approach. Different equations proposed for describing transport in fractal media, together with logistic reaction kinetics, are considered. Finally, we analyze the main features of wave fronts resulting from this dynamic process, i.e., why they are accelerated and what is the exact form of this acceleration

Effect of initial conditions on the speed of reaction-diffusion fronts

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed