Modelization of surface diffusion of a molecular dimer

A simple model for a dimer molecular diffusion on a crystalline surface, as a function of temperature, is presented. The dimer is formed by two particles coupled by a quadratic potential. The dimer diffusion is modeled by an overdamped Langevin equation in the presence of a two-dimensional periodic potential. Numerical simulation¿s results exhibit some dynamical properties observed, for example, in Si2 diffusion on a silicon [100] surface. They can be used to predict the value of the effective friction parameter. Comparison between our model and experimental measurements is presented.

Front and domain growth in the presence of gravity

Front and domain growth of a binary mixture in the presence of a gravitational field is studied. The interplay of bulk- and surface-diffusion mechanisms is analyzed. An equation for the evolution of interfaces is derived from a time-dependent Ginzburg-Landau equation with a concentration-dependent diffusion coefficient. Scaling arguments on this equation give the exponents of a power-law growth. Numerical integrations of the Ginzburg-Landau equation corroborate the theoretical analysis.

Diffusion on a solid surface: anomalous is normal

We present a numerical study of classical particles diffusing on a solid surface. The particles motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic or a random two-dimensional potential. The model leads to a rich variety of different transport regimes, some of which correspond to anomalous diffusion such as has recently been observed in experiments and Monte Carlo simulations. We show that this anomalous behavior is controlled by the friction coefficient and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics.

Cationic Diffusion in La2/3Ca1/3MnO3 Thin Films Grown on LaAlO3 (001) Substrates.

Microstructural features of La2/3Ca1/3MnO3 layers of various thicknesses grown on top of 001 LaAlO3 substrates are studied by using transmission electron microscopy and electron energy loss spectroscopy. Films are of high microstructural quality but exhibit some structural relaxation and mosaicity both when increasing thickness or after annealing processes. The existence of a cationic segregation process of La atoms toward free surface has been detected, as well as a Mn oxidation state variation through layer thickness. La diffusion would lead to a Mn valence change and, in turn, to reduced magnetization.

Atomic diffusion induced by stress relaxation in InGaAs/GaAs epitaxial layers

The origin of the microscopic inhomogeneities in InxGa12xAs layers grown on GaAs by molecular beam epitaxy is analyzed through the optical absorption spectra near the band gap. It is seen that, for relaxed thick layers of about 2.8 mm, composition inhomogeneities are responsible for the band edge smoothing into the whole compositional range (0.05,x,0.8). On the other hand, in thin enough layers strain inhomogeneities are dominant. This evolution in line with layer thickness is due to the atomic diffusion at the surface during growth, induced by the strain inhomogeneities that arise from stress relaxation. In consequence, the strain variations present in the layer are converted into composition variations during growth. This process is energetically favorable as it diminishes elastic energy. An additional support to this hypothesis is given by a clear proportionality between the magnitude of the composition variations and the mean strain.

Morphological changes in convection-diffusion-limited deposition

The effect of hydrodynamic flow upon diffusion-limited deposition on a line is investigated using a Monte Carlo model. The growth process is governed by the convection and diffusion field. The convective diffusion field is simulated by the biased-random walker resulting from a superimposed drift that represents the convective flow. The development of distinct morphologies is found with varying direction and strength of drift. By introducing a horizontal drift parallel to the deposition plate, the diffusion-limited deposit changes into a single needle inclined to the plate. The width of the needle decreases with increasing strength of drift. The angle between the needle and the plate is about 45° at high flow rate. In the presence of an inclined drift to the plate, the convection-diffusion-limited deposit leads to the formation of a characteristic columnar morphology. In the limiting case where the convection dominates, the deposition process is equivalent to ballistic deposition onto an inclined surface.

Atomic diffusion induced by stress relaxation in InGaAs/GaAs epitaxial layers

The origin of the microscopic inhomogeneities in InxGa1-xAs layers grown on GaAs by molecular beam epitaxy is analyzed through the optical absorption spectra near the band gap. It is seen that, for relaxed thick layers of about 2.8μm, composition inhomogeneities are responsible for the band edge smoothing into the whole compositional range (0.05diffusion at the surface during growth, induced by the strain inhomogeneities that arise from stress relaxation. In consequence, the strain variations present in the layer are converted into composition variations during growth. This process is energetically favorable as it diminishes elastic energy. An additional support to this hypothesis is given by a clear proportionality between the magnitude of the composition variations and the mean strain

Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

A topological proof that surface relators are test words

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A proof that all Seifert 3-manifold groups and all virtual surface groups are conjugacy separable

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished infinite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

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.

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.

Addressing Sea Surface Salinity retrieval at different spatial resolution. Feasibility study using OCCAM data within SEPS simulator and L2 processor tools

Projecte de recerca elaborat a partir d’una estada a la National Oceanography Centre of Southampton (NOCS), Gran Bretanya, entre maig i juliol del 2006. La possibilitat d’obtenir una estimació precissa de la salinitat marina (SSS) és important per a investigar i predir l’extensió del fenòmen del canvi climàtic. La missió Soil Moisture and Ocean Salinity (SMOS) va ser seleccionada per l’Agència Espacial Europea (ESA) per a obtenir mapes de salinitat de la superfície marina a escala global i amb un temps de revisita petit. Abans del llençament de SMOS es preveu l’anàlisi de la variabilitat horitzontal de la SSS i del potencial de les dades recuperades a partir de mesures de SMOS per a reproduir comportaments oceanogràfics coneguts. L’objectiu de tot plegat és emplenar el buit existent entre les fonts de dades d’entrada/auxiliars fiables i les eines desenvolupades per a simular i processar les dades adquirides segons la configuració de SMOS. El SMOS End-to-end Performance Simulator (SEPS) és un simulador adhoc desenvolupat per la Universitat Politècnica de Catalunya (UPC) per a generar dades segons la configuració de SMOS. Es va utilitzar dades d’entrada a SEPS procedents del projecte Ocean Circulation and Climate Advanced Modeling (OCCAM), utilitzat al NOCS, a diferents resolucions espacials. Modificant SEPS per a poder fer servir com a entrada les dades OCCAM es van obtenir dades de temperatura de brillantor simulades durant un mes amb diferents observacions ascendents que cobrien la zona seleccionada. Les tasques realitzades durant l’estada a NOCS tenien la finalitat de proporcionar una tècnica fiable per a realitzar la calibració externa i per tant cancel•lar el bias, una metodologia per a promitjar temporalment les diferents adquisicions durant les observacions ascendents, i determinar la millor configuració de la funció de cost abans d’explotar i investigar les posibiltats de les dades SEPS/OCCAM per a derivar la SSS recuperada amb patrons d’alta resolució.

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

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What is the Jacobian of a Riemann surface with boundary?

We define the Jacobian of a Riemann surface with analytically parametrized boundary components. These Jacobians belong to a moduli space of "open abelian varieties" which satisfies gluing axioms similar to those of Riemann surfaces, and therefore allows a notion of "conformal field theory" to be defined on this space. We further prove that chiral conformal field theories corresponding to even lattices factor through this moduli space of open abelian varieties.