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.

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

Chemoconvection patterns in the Methylene-blue-glucose system: Weakly nonlinear analysis

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments.

Equivalent representation form of oscillators with elastic and damping nonlinear terms

In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others

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.

Firm Size and Short-Term Dynamics in Aggregate Entry and Exit

Much of the research on industry dynamics focuses on the interdependence between the sectorial rates of entry and exit. This paper argues that the size of firms and the reaction-adjustment period are important conditions missed in this literature. I illustrate the effects of this omission using data from the Spanish manufacturing industries between 1994 and 2001. Estimates from systems of equations models provide evidence of a conical revolving door phenomenon and of partial adjustments in the replacement-displacement of large firms. KEYWORDS: aggregation, industry dynamics, panel data, symmetry, simultaneity. JEL CLASSIFICATION: C33, C52, L60, L11

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Internship report: improving asymmetric term extraction from bilingual text

Estudi elaborat a partir d’una estada a Xerox Research Centre Europe a Grenoble, França,entre juny i desembre del 2006. El projecte tradueïx termes tècnics anglesos a noruec. És asimètric perquè no tenim recursos lingüístics per a la llengua noruega, però solament per a l'anglès. S’ha desenvolupat i posat en pràctica mètodes que comprovaven contigüitat ("local reordering" i permutació selectiva) per a millorar el funcionament d’una eina anterior. Contigüitat és quan una paraula es traduïx en paraules múltiples, aquestes paraules han de ser adjacents en l'oració. A més, s’ha construït una taula de les operacions de recerca per als termes tècnics i s’ha integrat aquesta taula en un programa de demostració.

A nonlinear threshold model for the dependence of extremes of stationary sequences

One of the main implications of the efficient market hypothesis (EMH) is that expected future returns on financial assets are not predictable if investors are risk neutral. In this paper we argue that financial time series offer more information than that this hypothesis seems to supply. In particular we postulate that runs of very large returns can be predictable for small time periods. In order to prove this we propose a TAR(3,1)-GARCH(1,1) model that is able to describe two different types of extreme events: a first type generated by large uncertainty regimes where runs of extremes are not predictable and a second type where extremes come from isolated dread/joy events. This model is new in the literature in nonlinear processes. Its novelty resides on two features of the model that make it different from previous TAR methodologies. The regimes are motivated by the occurrence of extreme values and the threshold variable is defined by the shock affecting the process in the preceding period. In this way this model is able to uncover dependence and clustering of extremes in high as well as in low volatility periods. This model is tested with data from General Motors stocks prices corresponding to two crises that had a substantial impact in financial markets worldwide; the Black Monday of October 1987 and September 11th, 2001. By analyzing the periods around these crises we find evidence of statistical significance of our model and thereby of predictability of extremes for September 11th but not for Black Monday. These findings support the hypotheses of a big negative event producing runs of negative returns in the first case, and of the burst of a worldwide stock market bubble in the second example. JEL classification: C12; C15; C22; C51 Keywords and Phrases: asymmetries, crises, extreme values, hypothesis testing, leverage effect, nonlinearities, threshold models

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

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.

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.

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

Prediction of the economic cost of individual long-term care in the Spanish population

Pensions together with savings and investments during active life are key elements of retirement planning. Motivation for personal choices about the standard of living, bequest and the replacement ratio of pension with respect to last salary income must be considered. This research contributes to the financial planning by helping to quantify long-term care economic needs. We estimate life expectancy from retirement age onwards. The economic cost of care per unit of service is linked to the expected time of needed care and the intensity of required services. The expected individual cost of long-term care from an onset of dependence is estimated separately for men and women. Assumptions on the mortality of the dependent people compared to the general population are introduced. Parameters defining eligibility for various forms of coverage by the universal public social care of the welfare system are addressed. The impact of the intensity of social services on individual predictions is assessed, and a partial coverage by standard private insurance products is also explored. Data were collected by the Spanish Institute of Statistics in two surveys conducted on the general Spanish population in 1999 and in 2008. Official mortality records and life table trends were used to create realistic scenarios for longevity. We find empirical evidence that the public long-term care system in Spain effectively mitigates the risk of incurring huge lifetime costs. We also find that the most vulnerable categories are citizens with moderate disabilities that do not qualify to obtain public social care support. In the Spanish case, the trends between 1999 and 2008 need to be further explored.

Longer-term impacts of mentoring, educational services, and incentives to learn: evidence from a randomized trial in the United States

This paper is the first to use a randomized trial in the US to analyze the short- and long-term educational and employment impacts of an afterschool program that offered disadvantaged high-school youth: mentoring, educational services, and financial rewards with the objective to improve high-school graduation and postsecondary schooling enrollment. The short-term hefty beneficial average impacts quickly faded away. Heterogeneity matters. While encouraging results are found for younger youth, and when the program is implemented in relatively small communities of 9th graders; detrimental longlived outcomes are found for males, and when case managers are partially compensated by incentive payments and students receive more regular reminders of incentives.