Simulación de fluidos inmiscibles con el Particle Finite Element Method (PFEM)

Proyecto de investigación realizado a partir de una estancia en el Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC), Argentina, entre febrero y abril del 2007. La simulación numérica de problemas de mezclas mediante el Particle Finite Element Method (PFEM) es el marco de estudio de una futura tesis doctoral. Éste es un método desarrollado conjuntamente por el CIMEC y el Centre Internacional de Mètodos Numèrics en l'Enginyeria (CIMNE-UPC), basado en la resolución de las ecuaciones de Navier-Stokes en formulación Lagrangiana. El mallador ha sido implementado y desarrollado por Dr. Nestor Calvo, investigador del CIMEC. El desarrollo del módulo de cálculo corresponde al trabajo de tesis de la beneficiaria. La correcta interacción entre ambas partes es fundamental para obtener resultados válidos. En esta memoria se explican los principales aspectos del mallador que fueron modificados (criterios de refinamiento geométrico) y los cambios introducidos en el módulo de cálculo (librería PETSc, algoritmo predictor-corrector) durante la estancia en el CIMEC. Por último, se muestran los resultados obtenidos en un problema de dos fluidos inmiscibles con transferencia de calor.

Finite Horizon Learning

Incorporating adaptive learning into macroeconomics requires assumptions about how agents incorporate their forecasts into their decision-making. We develop a theory of bounded rationality that we call finite-horizon learning. This approach generalizes the two existing benchmarks in the literature: Eulerequation learning, which assumes that consumption decisions are made to satisfy the one-step-ahead perceived Euler equation; and infinite-horizon learning, in which consumption today is determined optimally from an infinite-horizon optimization problem with given beliefs. In our approach, agents hold a finite forecasting/planning horizon. We find for the Ramsey model that the unique rational expectations equilibrium is E-stable at all horizons. However, transitional dynamics can differ significantly depending upon the horizon.

Why do UK banks securitize?

The eight years from 2000 to 2008 saw a rapid growth in the use of securitization by UK banks. We aim to identify the reasons that contributed to this rapid growth. The time period (2000 to 2010) covered by our study is noteworthy as it covers the pre- financial crisis credit-boom, the peak of the fi nancial crisis and its aftermath. In the wake of the financial crisis, many governments, regulators and political commentators have pointed an accusing finger at the securitization market - even in the absence of a detailed statistical and economic analysis. We contribute to the extant literature by performing such an analysis on UK banks, focussing principally on whether it is the need for liquidity (i.e. the funding of their balance sheets), or the desire to engage in regulatory capital arbitrage or the need for credit risk transfer that has led to UK banks securitizing their assets. We show that securitization has been signi ficantly driven by liquidity reasons. In addition, we observe a positive link between securitization and banks credit risk. We interpret these latter findings as evidence that UK banks which engaged in securitization did so, in part, to transfer credit risk and that, in comparison to UK banks which did not use securitization, they had more credit risk to transfer in the sense that they originated lower quality loans and held lower quality assets. We show that banks which issued more asset-backed securities before the financial crisis suffered more defaults after the financial crisis.

Central banks and house prices in the run-up to the crisis

The financial crisis and the role played within it by fluctuations in house prices has reopened the debate about whether monetary policy should respond to asset prices. This paper investigates how the central banks of the euro area, the UK and the US considered, understood and responded to the trends in house prices in the six or seven years preceding the crisis, and how they have analysed those developments since the crisis. It suggests that these central banks, particularly the Anglo-Saxon ones, might have been able to take some useful action if they had devoted more intellectual resources to analysing the possible misalignments of house prices and been willing to act on them.

Prevalence of Trypanosoma cruzi infection in blood banks of seven departments of Bolivia

Trypanosoma cruzi infection was studied in 1,298 sera samples of blood banks from 7 capital departments of Bolivia, using the immunofluorescence test (IFI) and Enzyme Linked Immunosorbent Assay (Elisa). The percentages of positivity in these 7 departments have an average of 28% and are distributed as follows: Sta. Cruz 51%, Tarija 45%, Cochabamba 28%, Sucre 39%, La Paz 4.9%, Oruro 6% and Potosi 24%. The prevalence is related with the altitude levels of the different departments. However in Potosi (3,945 m) we found a 24% of prevalence, probably due to the proximity of endemic valleys to the city. The authors suggest a strict control in blood donors since there exists a great risk of infection

Use of terrestrial laser scanning for the characterization of retrogressive landslides in sensitive clay and rotational landslides in river banks

Depuis plus de 10 ans les modèles numériques d'altitude (MNA) produits par technologie de « light detection and ranging » (« LIDAR ») ont fourni de nouveaux outils très utiles pour des études géomorphologiques, particulièrement dans le cas des glissements de terrain. Le balayage laser terrestre (« TLS ») permet une utilisation très souple. Le TLS peut être employé pour la surveillance ou dans des situations d'urgence qui nécessitent une acquisition rapide d'un MNA afin d'évaluer l'aléa. Au travers de trois exemples, nous démontrons l'utilité du TLS pour la quantification de volumes de glissements de terrain, la création de profils et l'analyse de séries temporelles. Ces études de cas sont des glissements de terrain situés dans les argiles sensibles de l'est du Canada (Québec, Canada) ou de petits glissements rotationnels dans les berges d'une rivière (Suisse).

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.

Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models.

The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.

On finite unions and finite products with the D-property

We show that the product of a subparacompact C-scattered space and a Lindelöf D-space is D. In addition, we show that every regular locally D-space which is the union of a finite collection of subparacompact spaces and metacompact spaces has the D-property. Also, we extend this result from the class of locally D-spaces to the wider class of D-scattered spaces. All the results are shown in a direct way.

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

Random mating with a finite number of matings.

Random mating is the null model central to population genetics. One assumption behind random mating is that individuals mate an infinite number of times. This is obviously unrealistic. Here we show that when each female mates a finite number of times, the effective size of the population is substantially decreased.