Papers by Víctor Fairén Le Lay
Xv Congreso De Ecuaciones Diferenciales Y Aplicaciones V Congreso De Matematica Aplicada Vigo 23 26 Septiembre 1997 Vol 1 1998 Isbn 84 8158 096 1 Pags 291 296, 1998
Physics Letters A, 1999
A generalization of the reduction technique for ODEs recently introduced by Gao and Liu is given.... more A generalization of the reduction technique for ODEs recently introduced by Gao and Liu is given. It is shown that the use of algebraic methods allows the extension of the procedure to much more general flows, as well as the derivation of simple criteria for the identification of reducible systems.
Computers in Physics, 1998
The aim of this work is to supply the necessary tools for an optimal choice of initial values of ... more The aim of this work is to supply the necessary tools for an optimal choice of initial values of the Taylor-integrator parameters, step size, and order. The optimization in the first step is fundamental to the future evolution of both the global error and the complexity of the algorithm. The local error in the Taylor approximation is controlled by two methods for obtaining an accurate analytic expression for the local error as a function of step size and order.
Physical Review E, 2004
Anomalous reaction rates have been found in the hydrogen desorption of H-terminated surfaces in s... more Anomalous reaction rates have been found in the hydrogen desorption of H-terminated surfaces in semiconductor epitaxy, with a reaction order shifting from two to one, or even taking fractional values. We analyze the issue in terms of a cooperative full desorption (CFD) reaction A+A--k3-->S+S , coupled to an adsorption reaction S--k1-->A and an alternative desorption route A--k2-->S . Steady state properties of the three-step reactive scheme are analyzed in a one-dimensional lattice in the absence of diffusion. Microscopic Monte Carlo simulations show anomalous spatial distributions of reactants in the stationary state: depending on the reaction rate constants of the overall scheme, either a local "aggregation" or a local "dispersion" of A -particles is observed. The CFD reaction itself is well described by a fractional order kinetics that takes into account these anomalies and that depends on the kinetic rate constants of the overall adsorption-desorption reaction mechanism. The problem is addressed with an analytical approach for the active neighborhood of a reactant, which provides a closed expression of the reaction order as a function of the kinetic parameters. This approach is in excellent agreement with numerical simulations. Spatial correlations, as well as fluctuation correlations, are also formalized in terms of the kinetic constants. We discuss the results in the context of the hydrogen evolution reaction on silicon surfaces.
Mathematical Biosciences, 1999
The power-law formalism has been succesfully used as a modeling tool in many applications. The re... more The power-law formalism has been succesfully used as a modeling tool in many applications. The resulting models, either as Generalized Mass Action or as S-systems models, allow one to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. The power-law formalism was ®rst derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The especial characteristics of this approximation produce an extremely useful systemic representation that allows a complete system characterization. Furthermore, their parameters have a precise interpretation as local sensitivities of each of the individual processes and as rate-constants. This facilitates a qualitative discussion and a quantitative estimation of their possible values in relation to the kinetic properties. Following this interpretation, parameter estimation is also possible by relating the systemic behavior to the underlying processes. Without leaving the general formalism, in this paper we suggest deriving the power-law representation in an alternative way that uses least-squares minimization. The resulting power-law mimics the target rate-law in a
Mathematical Biosciences, 2000
The power-law formalism was initially derived as a Taylor series approximation in logarithmic spa... more The power-law formalism was initially derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The resulting models, either as generalized mass action (GMA) or as S-systems models, allow to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. This approach has been succesfully used as a modeling tool in many applications from cell metabolism to population dynamics. Without leaving the general formalism, we recently proposed to derive the power-law representation in an alternative way that uses least-squares (LS) minimization instead of the traditional derivation based on Taylor series [B. Hern andez-Bermejo, V. Fair en, A. Sorribas, Math. Biosci. 161 (1999) 83±94]. It was shown that the resulting LS power-law mimics the target rate-law in a wider range of concentration values than the classical power-law, and that the prediction of the steady-state using the LS power-law is closer to the actual steady-state of the target system. However, many implications of this alternative approach remained to be established. We explore some of them in the present work. Firstly, we extend the de®nition of the LS power-law within a given operating interval in such a way that no preferred operating point is selected. Besides providing an alternative to the classical Taylor powerlaw, that can be considered a particular case when the operating interval is reduced to a single point, the LS power-law so de®ned is consistent with the results that can be obtained by ®tting experimental data points. Secondly, we show that the LS approach leads to a system description, either as an S-system or a GMA model, in which the systemic properties (such as the steady-state prediction or the log-gains) appear averaged over the corresponding interval when compared with the properties that can be computed from Taylorderived models in dierent operating points within the considered operating range. Finally, we also show that the LS description leads to a global, accurate description of the system when it is submitted to external forcing.
Journal of Physics A: Mathematical and General, 1998
It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpl... more It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpler structural form, but it is well known that this goal may imply an increase in the dimension of the system. This is what happens if in this new representation the vector field has a lower degree of nonlinearity or a smaller number of nonlinear contributions. Until now both issues have been treated separately, rather unsystematically and, in some cases, at the expense of an excessive increase in the number of dimensions. We unify here the treatment of both issues in a common algebraic framework. This allows us to proceed algorithmically in terms of simple matrix operations.
Journal of Mathematical Physics, 1981
ABSTRACT A method based on the equivalence between finite-dimensional nonlinear and infinite-dime... more ABSTRACT A method based on the equivalence between finite-dimensional nonlinear and infinite-dimensional linear systems of ordinary differential equations is presented in order to calculate the time-dependent solutions of nonlinear physico-chemical systems. The solution is cast in the form of power series whose general term is known analytically.
Journal of Mathematical Analysis and Applications, 2001
We present a method for determining the local stability of equilibrium points of conservative gen... more We present a method for determining the local stability of equilibrium points of conservative generalizations of the Lotka-Volterra equations. These generalizations incorporate both an arbitrary number of species-including odd-dimensional systemsand nonlinearities of arbitrarily high order in the interspecific interaction terms. The method combines a reformulation of the equations in terms of a Poisson structure and the construction of their Lyapunov functionals via the energy-Casimir method. These Lyapunov functionals are a generalization of those traditionally known for Lotka-Volterra systems. Examples are given.
Journal of Electroanalytical Chemistry, 2002
Abstract This paper is aimed at investigating the possibility of predicting interface roughness b... more Abstract This paper is aimed at investigating the possibility of predicting interface roughness behavior from reaction kinetic parameters of a simple open-circuit potential corrosion mechanism. A cellular automaton algorithm simulates the evolution of a dissolving metallic front according to specific rules that govern transitions between the different states associated with surface reactants. A first mathematical model presents a rigorous mesoscopic treatment incorporating kinetic parameters and purely morphologic descriptors and yields an analytical expression accounting for the interplay between reaction kinetics and morphology. Comparing the mean cell-lifetimes of active species taking part in the model does this. A new morphological descriptor built on reaction kinetic parameters is introduced and shown to represent the interface roughness very well. Finally, a simplified version of the model, which resorts to the exclusive use of measurable electrochemical quantities, is proposed. Results are promising, showing the approach to be an interesting tool for the understanding and even forecasting of the complex interaction between reaction kinetic parameters and morphological features of metal ∣ electrolyte interfaces.
Journal of Electroanalytical Chemistry, 2004
A metal corrosion mechanism involves several steps with their associated intermediate reactants a... more A metal corrosion mechanism involves several steps with their associated intermediate reactants and rates. The mechanism determines the time evolution of a metal atom through a sequence of states, beginning as soon as it is exposed to the electrolyte and ending ...
Journal of Electroanalytical Chemistry, 2003
Electrochemical reactions are usually described by balance equations derived upon the assumption ... more Electrochemical reactions are usually described by balance equations derived upon the assumption that whatever the interface particularities, reactants are perfectly mixed and every particle is able to interact with any other one (mean-field approximation, MFA). This paper investigates the limits of validity of this kind of approach in the case of electrochemical systems involving a single reactant, bimolecular desorption under conditions of hindered surface mobility of adsorbates. This is achieved by means of cellular automaton (CA) simulations of a multi-step electrochemical reaction on a bi-dimensional homogeneous lattice. Results show that local correlations between adsorbates lead to departures from the MFA predictions concerning the bimolecular desorption step rate. The desorption reaction seems to be better described by fractional order kinetics, which take into account non-homogeneous distribution of adsorbates over the surface. The dependence of this fractional reaction order on the kinetic parameters of the overall reaction, as well as the circumstances leading to a recovery of the standard second-order rate law, are fully discussed.
International Journal of Innovation and Sustainable Development, 2012
Science has made a great leap forward in the last 20 years in supporting the claim of the anthrop... more Science has made a great leap forward in the last 20 years in supporting the claim of the anthropogenic origin of climate change. The community of scientists working on disciplines related to climate is virtually unanimous on the point. According to polls, respondents in some Western countries are showing a growing scepticism, if not plain confusion. This article aims at describing and analysing the intricate factors which are at the root of the lack of confidence in science and the disconnection between science and the public perception of the problem. We certainly find difficulties in understanding the complex epistemological issues involved in the creation of science. But we also meet with biased presentations of the issues by opponents to climate change and journalist alike. The resulting confusion can only be understood when we invoke the inadequacy of the still-in-force hierarchical means of communication in a progressively more horizontal society.
Ecological Complexity, 2006
... Julien Esteban 1, Victor Fairén * Departamento de Fısica Matemática y Fluidos, UNED, Apdo. 60... more ... Julien Esteban 1, Victor Fairén * Departamento de Fısica Matemática y Fluidos, UNED, Apdo. 60141, 28080 Madrid, Spain 1. Introduction One of the most conspicuous patterns in arid or semi-arid environments is a two-phase mosaic (Aguiar and Sala, 1999) characterized by ...
International Journal of Bifurcation and Chaos, 2002
The estimation of the domain of stability of fixed points of nonlinear differential systems const... more The estimation of the domain of stability of fixed points of nonlinear differential systems constitutes a practical problem of much interest in engineering. The procedures based on Lyapunov's second method configures an alternative worth consideration. It has the appeal of reducing calculation complexity and is time-saving with respect to the direct, computer crunching approach which requires a systematic numerical integration of the evolution equations from a gridlike pattern of initial conditions. However, it is not devoid of problems inasmuch as the Lyapunov function itself is problem-dependent and relies too much on presumptions. Additionally, the evaluation of its corresponding domain is produced in terms of a nonlinear programming problem with inequality constraints the resolution of which may sometimes require a large investment in computer time. These problems are in part avoided by restricting to quadratic Lyapunov functions, with the possible obvious consequence of lim...
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Papers by Víctor Fairén Le Lay