Jordi Ripoll

University of Girona

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Francesc Pozo

Universitat Politècnica de Catalunya

Núria Parés Marine

Universitat Politècnica de Catalunya

Teresa Sancho Vinuesa

Universitat Oberta de Catalunya

ÀC

Àngel Calsina

Universitat Autònoma de Barcelona

Joan Saldaña

University of Girona

Eusebi Calle

University of Girona

C. Olivé

Hospital Sant Joan de Déu Barcelona

Remei Calm

University of Girona

Ramon Masià

Catalan Society of Family and Community Medicine

Dimitri Breda

University of Udine

Cooperative Institutions

University of Girona

Universitat Politècnica de Catalunya

Universitat Autònoma de Barcelona

Universitat de Barcelona

Kansas State University

University of Trento

Istituto Superiore di Sanità

Catalan Institute for Water Research

Fondazione Bruno Kessler

Centre de Recerca Matemàtica

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Spread of epidemic-like failures in telecommunication networks

Physica A Statistical Mechanics and its Applications (2014)

Jordi Ripoll M. Manzano Eusebi Calle

Adjacency matrix

Epidemic model

Stochastic matrix

Basic reproduction number

10.1016/j.physa.2014.05.052

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A multiple failure propagation model in GMPLS-based networks

IEEE Network (2010)

Eusebi Calle Jordi Ripoll Juan Segovia Pere Vilà Marc Manzano

In this article, a new model to simulate different failure propagation scenarios in GMPLS-based networks is proposed. Several types of failures and malfunctions may spread along the network following different patterns (hardware failures, natural disasters, accidents, configuration errors, viruses, software bugs, etc.). The current literature presents several models for the spreading of failures in general networks. In communication networks, a failure affects not only nodes but also the connections passing through those nodes. The model in this article takes into account GMPLS node failures, affecting both data and control planes. The model is tested by simulation using different types of network topologies. In addition, a new method for the classification of network robustness is also introduced.

Robustness

Cascading failure

10.1109/mnet.2010.5634438

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Límites de funciones y continuidad

Fundació per a la Universitat Oberta de Catalunya eBooks (2021)

Francesc Pozo Jordi Ripoll Núria Parés Marine

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Evolution of age-dependent sex-reversal under adaptive dynamics

Journal of Mathematical Biology (2009)

Àngel Calsina Jordi Ripoll

Trait

10.1007/s00285-009-0261-z

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Mathematical modelling of fibre coating

arXiv (Cornell University) (2021)

María Aguareles Francesc Font T.G. Myers Jordi Ripoll

In this report we formulate and analyse a mathematical model describing the evolution of a thin liquid film coating a wire via an extrusion process. We consider the Navier-Stokes equations for a 2D incompressible Newtonian fluid coupled to the standard equation relating the fluid surface tension with the curvature. Taking the lubrication theory approximation and assuming steady state, the problem is reduced to a single third-order differential equation for the thin film height. An approximate analytical solution for the final film height is derived and compared with a numerical solution obtained by means of a shooting scheme. Good agreement between the two solutions is obtained, resulting in a relative error of around 5\%. The approximate solution reveals that the key control parameters for the process are the initial film height, the fluid surface tension and viscosity, the wire velocity and the angle of exit at the extruder.

Lubrication theory

Stream function

10.48550/arxiv.2101.02598

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Integración: El problema del área

Fundació per a la Universitat Oberta de Catalunya eBooks (2021)

Francesc Pozo Jordi Ripoll Núria Parés Marine

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Mathematical Modelling of Fibre Coating

RSME Springer series (2023)

María Aguareles Francesc Font T.G. Myers Jordi Ripoll

Lubrication theory

Stream function

10.1007/978-3-031-32130-6_4

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Hopf bifurcation in a structured population model for the sexual phase of monogonont rotifers

Journal of Mathematical Biology (2002)

Àngel Calsina Jordi Ripoll

Limit cycle

10.1007/s002850200147

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Models matemàtics en dinàmica de poblacions

Butlletí de la Societat Catalana de Matemàtiques (2018)

Carles Barril Basil Sı́lvia Cuadrado Jordi Ripoll

catalaLa dinamica de poblacions, com el seu nom indica, estudia l’evolucio de la mida i la composicio de les poblacions. En aquest article presentem un recull dels principals models matematics que descriuen la dinamica de poblacions biologiques. Primerament, farem una introduccio historica a la materia tot descrivint diferents problemes en ecologia, demografia i epidemiologia, aixi com les eines i tecniques matematiques emprades. Seguidament, descriurem una nova formulacio en termes d’equacions amb retard que estableix un marc general rigoros per a la modelitzacio matematica de la dinamica de poblacions. EnglishPopulation dynamics studies the evolution of size and composition of populations. In this article we present a compilation of the main mathematical models describing the dynamics of biological populations. We start with a historical introduction to the subject showing different problems in ecology, demography and epidemiology, as well as the tools and mathematical techniques used. Then we describe a new formulation in terms of delay equations that establishes a thorough general framework for the mathematical modeling of population dynamics.

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Evolution of Sex-Ratio in Structured Population Dynamics

TDX (Tesis Doctorals en Xarxa) (2005)

Jordi Ripoll

In this Thesis we address the study of some non-linear evolution equations (e.g. pde's) modelling the dynamics of sexually-reproducing structured populations, with special emphasis on biological evolution driven by natural selection. The latter is incorporated into the models through the adaptive dynamics, which is a way of describing how the hereditary characteristics of the population evolve. The sex-ratio, defined as the proportion between females and males, is analyzed from the evolutionary point of view. The memoir is divided into two parts plus a brief introduction to age-structured population dynamics (Chapter 1). The first part (Chapter 2) is devoted to a model for the dynamics of a sequential hermaphrodite species, i.e. a population where every individual functions early in life as one sex (specfically as a female) and then switches to the other sex for the rest of its life, and the sex-reversal occurs at a specific age which is considered as a non-negative random variable. This phenomenon happens in a variety of animals including fish species like the sea bream (Sparus aurata), the anemone fish, the parrot fish and the blue-headed wrasse (Thalassoma bifasciatum). First of all we introduce the basic hypotheses and the parameters of the model: the probability law of the age at sex-reversal, the non-linear (due to the sexual reproduction) birth function giving the influx of newborns, and the density-dependent per capita mortality rate. The complete system (which displays the birth, transition and death processes) for the age-densities of females and males, is formulated and derived in the form of non-linear integral equations as well as the smooth version in the form of nonlocal non-linear first-order hyperbolic partial differential equations (partial integro-differential equations) with boundary, at age zero, and initial conditions. We take the former approach because of the lack of regularity in general, and in the latter, the derivative of the probability law appears in the transition term from female to male. In Section 2.3 we show the existence and uniqueness of global solutions which are non-negative and biologically meaningful for the present model. We introduce additional hypotheses, namely, suitable Lipschitz conditions on the birth function and the mortality rate. In Section 2.4 we show that the system can be reduced to the intrinsic sex-ratio subspace where the dynamics is given by a single non-linear integral equation for the age-density of individuals of both sexes. An explicit form of the birth function, in terms of the fertility rates, is derived for latter numerical purposes. It corresponds to a Holling type II functional response, and it is based on the fact that females arrange its time in looking for mates and handling the production of new offspring. The expected searching time is proportional to 1-(number of males), whereas the expected handling time is a constant. Section 2.5 studies the asymptotic behaviour of the solutions as time tends to infinity. We have determined a sufficient condition for having bounded trajectories and the possibility of non-trivial dynamics. On the other hand we have seen that the extinction equilibrium is always locally asymptotically stable, displaying the Allee effect, which is a common feature of sexually reproducing populations. In Section 2.6 we address the stationary problem, i.e. we look for solutions independent of time in L1 +. The non-trivial steady states are determined according to a scalar non-linear equation for the total population at equilibrium as an independent variable. We end the section by illustrating two cases. The first one is the (non-linear) case of neglecting the competition for the resources, obtaining that there is at most a non-trivial steady state which is always unstable. An explicit expression of this equilibrium is given, and the instability is obtained by means of a linearization procedure. The second case, which is rather general, includes some sort of competition and we have found two non-trivial equilibria for each value of the expected age at sex-reversal in a bounded open interval. Both cases are depicted in a bifurcation diagram, for two choices of the probability law (Heaviside/exponential). The theory of accretive operators, i.e. those such that its resolvent operator is a non-expansive map, is needed in order to study the local stability of equilibria for the general case. A proof of the principle of linearized stability for the reduced system is given in Appendix A, and it is based on a principle for non-linear evolution equations governed by accretive operators, where the stability is determined by the accretiveness of an associated linear operator. In Section 2.7 we rewrite the reduced system as an evolution equation and introduce additional hypotheses, mainly, suitable conditions on the regularity of the birth function and the mortality rate. Finally we get a sufficient condition for the local stability without computing the spectrum of the linear part. Considering phenotypic evolution in the context of diploid population models, in Section 2.8 we study the evolutionary dynamics of the age at sex-reversal. The function-valued trait considered is the probability law. We assume a resident population at stable equilibrium and consider a small invading/mutant population make up of heterozygotes, and homozygotes (negligible). We have used convex analysis in order to show that an unbeatable strategy or evolutionarily stable strategy (ESS) is a Heaviside step function: all individuals of the population change sex at the same age. More precisely, the computation of such an (infinite dimensional) strategy is based on linear/affine optimization on compact convex sets. Our result is a generalization of the one obtained by Charnov. Finally, Section 2.9 is devoted to the adaptive value of the sex-ratio of the population at equilibrium, which is in general different from one. However, if the fertilities are age independent then the sex-ratio equals to one. In addition, assuming also an age independent mortality we have that the transition from female to male takes place at 69,3% of the life expectancy of the population. The second part (Chapter 3) is devoted to a model for the sexual phase of a haplodiploid species (monogonont rotifers) which exhibits the so-called cyclic parthenogenesis (both forms of reproduction: non-sexual and sexual). Monogonont rotifers are small micro-invertebrate animals who inhabit aquatic media with seasonal variations. The original system, which was introduced by Aparici, Carmona and Serra from the department of ecology at the Universitat de Valencia, is formulated in the form of nonlocal non-linear first order hyperbolic partial differential equations. The state variables are the age-densities of virgin mictic females (male-producing), mated mictic females (resting egg-producing), and haploid males, whereas the time-independent parameters of the model are the per capita mortality rates, the male-female encounter rate, the recruitment rate of mictic females, the fertility of male-producing mictic females, the age at maturity for females, and the threshold age of fertilization (which is less than or equal to the maturation age). The transition from virgin to mated is given in terms of the characteristic function of the fertilization period and the total population of haploid males. The equation for mated females turns out to be uncoupled from the others, so we focus on the other ones. Scaling the units in age, time and population we have reduced the number of parameters to only four: the new mortality rates, the new threshold age of fertilization, and the new encounter rate. As a result, we obtain the reduced and nondimensionalized system. Section 3.3 addresses the stationary problem, i.e. we look for time-independent solutions in W 1;1. We have found that there is a unique continuous steady state which can be written in terms of the total male population at equilibrium. The latter is obtained as the unique solution of a scalar non-linear equation. Section 3.4 studies the local stability of the equilibrium by means of a linearization procedure. On the one hand, we analyze the characteristic equation obtaining complex solutions that cross the imaginary axis, and on the other hand we prove a principle of linearized stability which is based on a semilinear formulation in L1, and the fact that the essential growth bound is negative (as usual in this kind of equations). The linear stability analysis reveals that the equilibrium is stable for values of the parameters in a large region containing the empirical ones. However, it can be unstable for values not too far. In Section 3.5 we apply a Hopf bifurcation theorem in an infinite dimensional setting. We check that there is a pair of conjugate eigenvalues on the imaginary axis which cross with positive speed. Rewriting the system as a non-linear evolution equation and computing both the adjoint and the resolvent operators (the latter solving a linear ode with piecewise constant coeffcients), we can determine if the bifurcation is subcritical or supercritical. As a result, we have shown the appearance of a stable limit cycle (isolated periodic orbit). Section 3.6 is devoted to the numerical solution of the problem. We have designed an explicit numerical scheme based on both analytical and numerical integration along the characteristic curves. Several numerical experiments are presented. The numerical simulations confirm and extend the analytical results obtained.

Dynamics

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