From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

Reaction-diffusion lattice gas: Theory and computer results

We report on the study of nonequilibrium ordering in the reaction-diffusion lattice gas. It is a kinetic model that relaxes towards steady states under the simultaneous competition of a thermally activated creation-annihilation $(reaction$) process at temperature T, and a diffusion process driven by a heat bath at temperature T?T. The phase diagram as one varies T and T, the system dimension d, the relative priori probabilities for the two processes, and their dynamical rates is investigated. We compare mean-field theory, new Monte Carlo data, and known exact results for some limiting cases. In particular, no evidence of Landau critical behavior is found numerically when d=2 for Metropolis rates but Onsager critical points and a variety of first-order phase transitions.

Plasma-enhanced chemical vapor deposition of boron nitride thin films from B2H6-H2-NH3 and B2H6-N2 gas mixtures

Highly transparent and stoichiometric boron nitride (BN) films were deposited on both electrodes (anode and cathode) of a radio-frequency parallel-plate plasma reactor by the glow discharge decomposition of two gas mixtures: B2H6-H2-NH3 and B2H6-N2. The chemical, optical, and structural properties of the films, as well as their stability under long exposition to humid atmosphere, were analyzed by x-ray photoelectron, infrared, and Raman spectroscopies; scanning and transmission electron microscopies; and optical transmittance spectrophotometry. It was found that the BN films grown on the anode using the B2H6-H2-NH3 mixture were smooth, dense, adhered well to substrates, and had a textured hexagonal structure with the basal planes perpendicular to the film surface. These films were chemically stable to moisture, even after an exposition period of two years. In contrast, the films grown on the anode from the B2H6-N2 mixture showed tensile stress failure and were very unstable in the presence of moisture. However, the films grown on the cathode from B2H6-H2-NH3 gases suffered from compressive stress failure on exposure to air; whereas with B2H6-N2 gases, adherent and stable cathodic BN films were obtained with the same crystallographic texture as anodic films prepared from the B2H6-H2-NH3 mixture. These results are discussed in terms of the origin of film stress, the effects of ion bombardment on the growing films, and the surface chemical effects of hydrogen atoms present in the gas discharge.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Composition of Greenhouse Gas Emissions in Spain: an Input-Output Analysis

Extending the traditional input-output model to account for the environmental impacts of production processes reveals the channels by which environmental burdens are transmitted throughout the economy. In particular, the environmental input-output approach is a useful technique for quantifying the changes in the levels of greenhouse emissions caused by changes in the final demand for production activities. The inputoutput model can also be used to determine the changes in the relative composition of greenhouse gas emissions due to exogenous inflows. In this paper we describe a method for evaluating how the exogenous changes in sectorial demand, such as changes in private consumption, public consumption, investment and exports, affect the relative contribution of the six major greenhouse gases regulated by the Kyoto Protocol to total greenhouse emissions. The empirical application is for Spain, and the economic and environmental data are for the year 2000. Our results show that there are significant differences in the effects of different sectors on the composition of greenhouse emissions. Therefore, the final impact on the relative contribution of pollutants will basically depend on the activity that receives the exogenous shock in final demand, because there are considerable differences in the way, and the extent to which, individual activities affect the relative composition of greenhouse gas emissions. Keywords: Greenhouse emissions, composition of emissions, sectorial demand, exogenous shock.

Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Trade of permits for greenhouse gas emissions; bilateral trade need not be the answer

The Kyoto Protocol sets national quotas on CO2 emissions and allows international trade of these quotas. We argue that this trade is characterized by asymmetric, identity-dependent externalities, and show that bilateral trade may not be sufficient for an efficient allocation of emissions. We derive conditions under which bilateral trade does improve the allocation of permits. The conditions are strong. In this sense, we argue that, for emissions permits, market design matters.

Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions

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

Estudi de la reductibilitat de catalitzadors basats en cobalt i el seu comportament en la reacció de desplaçament de gas d'aigua de CO

Projecte de recerca elaborat a partir d’una estada a la universitat d'Udine, Itàlia, entre setembre i desembre del 2006.S'han caracteritzat mitjançant la reducció a temperatura programada i tests catalítics catalitzadors en pols basats en cobalt i supostats en òxid de zinc i monòlits ceràmics funcionaliltzats també amb cobalt i òxid de zinc. L'addició de promotors (manganès, crom i ferro ) als catalitzadors en pols, preparats per impregnació i precipitació, no afecta significativament ni la temperatura a la qual té lloc la reducció ni al percentatge global de reducció. En els cicles de reducció-oxidació sí que s'observen diferències entre el primer perfil de reducció i els següents, especialment en el cas de la mostra que té ferro com a promotor, on les diferències s'accentuen en cicles successius (fins al quart). S'ha evaluat l'activitat d'aquests catalitzadors en la reacció de desplaçament de gas d'aigua, obtenint uns resultats satisfactoris. Finalment s'han realitzat reduccions a temperatura programada i tests catalítics en la reacció de desplaçament de gas d'aigua amb monòlits funcionalitzats amb cobalt i òxid de zinc (en cap d'ells s'ha introduït promotors). El nivell de conversió assolit és menor que en el cas de catalitzadors en pols, fet que s'associa a la geometria d'aquests sistemes catalítics, però la relació CH4/CO2 és més favorable que en els catalitzadors en pols, el que els converteix en sistemes molt selectius.

Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

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

The Global Diffusion of Regulatory Agencies: Channels of Transfer and Stages of Diffusion

The autonomous regulatory agency has recently become the ‘appropriate model’ of governance across countries and sectors. The dynamics of this process is captured in our data set, which covers the creation of agencies in 48 countries and 16 sectors since the 1920s. Adopting a diffusion approach to explain this broad process of institutional change, we explore the role of countries and sectors as sources of institutional transfer at different stages of the diffusion process. We demonstrate how the restructuring of national bureaucracies unfolds via four different channels of institutional transfer. Our results challenge theoretical approaches that overemphasize the national dimension in global diffusion and are insensitive to the stages of the diffusion process. Further advance in study of diffusion depends, we assert, on the ability to apply both cross-sectoral and cross-national analysis to the same research design and to incorporate channels of transfer with different causal mechanisms for different stages of the diffusion process.

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.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

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.

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.