Nonlinear wave propagation in disordered media

We briefly review the state-of-the-art of research on nonlinear wave propagation in disordered media. The paper is intended to provide the non-specialist reader with a flavor of this active field of physics. Firstly, a general introduction to the subject is made. We describe the basic models and the ways to study disorder in connection with them. Secondly, analytical and numerical techniques suitable for this purpose are outlined. We summarize their features and comment on their respective advantages, drawbacks and applicability conditions. Thirdly, the Nonlinear Klein-Gordon and Schrbdinger equations are chosen as specific examples. We collect a number of results that are representative of the phenomena arising from the competition between nonlinearity and disorder. The review is concluded with some remarks on open questions, main current trends and possible further developments.This work has been supported in part by the C.I.C. y T. (Spain) under project MAT90-0S44. A S. was also supported by fellowships from the Universidad Complutense and the Ministerio de Educacion y Ciencia.Publicad

Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics

Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.Comment: Review, 48 pages, 26 figure

Time Scales in Evolutionary Dynamics

Evolutionary game theory has traditionally assumed that all individuals in a population interact with each other between reproduction events. We show that eliminating this restriction by explicitly considering the time scales of interaction and selection leads to dramatic changes in the outcome of evolution. Examples include the selection of the inefficient strategy in the Harmony and Stag-Hunt games, and the disappearance of the coexistence state in the Snowdrift game. Our results hold for any population size and in the presence of a background of fitness.Comment: Final version with minor changes, accepted for publication in Physical Review Letter

On the discrete Peyrard-Bishop model of DNA: stationary solutions and stability

As a first step in the search of an analytical study of mechanical denaturation of DNA in terms of the sequence, we study stable, stationary solutions in the discrete, finite and homogeneous Peyrard-Bishop DNA model. We find and classify all the stationary solutions of the model, as well as analytic approximations of them, both in the continuum and in the discrete limits. Our results explain the structure of the solutions reported by Theodorakopoulos {\em et al.} [Phys. Rev. Lett. {\bf 93}, 258101 (2004)] and provide a way to proceed to the analysis of the generalized version of the model incorporating the genetic information.Comment: 15 pages, 12 figure

Patrimonio bibliográfico fuera de las bibliotecas: los fondos judiciales del Archivo Histórico Provincial de Córdoba

Often the printing shops resorted to the printing of small documents, which allowed them to remain active. Despite being abundant, many of these have not been preserved. The minor forms that we find in the archives present a double nature: bibliographic and archival. In the latter case, the forms must have a producer entity, functional origins, date, place of production and a substantive content. They must also respond to archival paradigms: the origin principle, the life cycle of documents and the continuity of documents. We collect the printed documents from the Rute Local Justice fund. These forms are produced for the most part by the Chancery of Granada, and addressed to the Judges and Justice of Rute. They are signed between 1778 and 1833. They are also short, from 1 to 8 pages, and the folio format predominates. They do not cater to literary tastes but to the development of the functions of an institution. Normally they do not have title proper, nor data of impression

Nonlinear excitatios in DNA: aperiodic models versus actual genome sequences

We study the effects of the genetic sequence on the propagation of nonlinear excitations in simple models of DNA in which we incorporate actual data from the human genome. We show that kink propagation requires forces over a certain threshold, a phenomenon already found for aperiodic sequences [F. Domínguez-Adame et al., Phys. Rev. E 52, 2183 (1995)]. For forces below threshold, the final stop positions are highly dependent on the specific sequence. Contrary to the conjecture advanced by Domínguez-Adame and co-workers, we find no evidence supporting the dependence of the kink dynamics on the information content of the genetic sequences considered. We discuss possible reasons for that result as well as its practical consequences. Physically, the results of our model are consistent with the stick-slip dynamics of the unzipping process observed in experiments. We also show that the effective potential, a collective coordinate formalism introduced by Salerno and Kivshar [Phys. Lett. A 193, 263 (1994)], is a useful tool to identify key regions in DNA that control the dynamical behavior of large segments. As a side result, we extend the previous studies on aperiodic sequences by analyzing the effect of the initial position of the kink, leading to further insight on the phenomenology observed in such systems.This work has been supported by the Ministerio de Ciencia y Tecnología of Spain through Grant No. BFM2003-07749-C05-01. S.C. is supported by the Consejería de Educación de la Comunidad Autónoma de Madrid and the Fondo Social Europeo.Publicad

Dynamics of a Ø4 kink in the presence of strong potential fluctuations, dissipation, and boundaries

We have carried out a number of simulations to study the dynamical behavior of kinks in the ifJ4 model in the presence of strong fluctuations of its double-well potential. Our work widens the computational and analytical knowledge of this system in four directions. First, we describe in detail a numerical procedure that can be easily generalized to other stochastic, soliton-bearing equations. We demonstrate that it exhibits consistency features never found in previous research on nonlinear stochastic partial differential equations. Second, we fix the range of validity of theoretical approaches based on secular perturbative expansions. We show how this range depends on a combination of noise strength and duration. Third, we numerically study the model beyond the applicability of analytical methods. We compute the main characteristics of kink dynamics in this regime and discuss their stability under this random perturbation. Finally, we introduce dissipation and boundaries in the dynamically disordered model. We establish that the essential consequence of friction action is to soften the noise effects, while boundaries give rise to a critical velocity below which kinks cannot enter the noisy zone.We are thankful for partial financial support from the Direccion General de Investigacion Cientifica y Tecnica (DGICyT) through Project No. TIC 73/89. A.S. was supported by the program ((Formacion de Personal Investigador" of the Ministerio de Educación y Ciencia of Spain.Publicad

Turnout Intention and Social Networks

How can networking affect the turnout in an election? We present a simple model to explain turnout as a result of a dynamic process of formation of the intention to vote within Erdös-Renyi random networks. Citizens have fixed preferences for one of two parties and are embedded in a given social network. They decide whether or not to vote on the basis of the attitude of their immediate contacts. They may simply follow the behavior of the majority (followers) or make an adaptive local calculus of voting (Downsian behavior). So they either have the intention of voting when the majority of their neighbors are willing to vote too, or they vote when they perceive in their social neighborhood that elections are "close". We study the long run average turnout, interpreted as the actual turnout observed in an election. Depending on the combination of values of the two key parameters, the average connectivity and the probability of behaving as a follower or in a Downsian fashion, the system exhibits monostability (zero turnout), bistability (zero turnout and either moderate or high turnout) or tristability (zero, moderate and high turnout). This means, in particular, that for a wide range of values of both parameters, we obtain realistic turnout rates, i.e. between 50% and 90%.turnout, social networks, adaptative behavior