Complex Systems: Nonlinearity and Structural Complexity in spatially extended and discrete systems

Resumen Esta Tesis doctoral aborda el estudio de sistemas de muchos elementos (sistemas discretos) interactuantes. La fenomenología presente en estos sistemas esta dada por la presencia de dos ingredientes fundamentales: (i) Complejidad dinámica: Las ecuaciones del movimiento que rigen la evolución de los constituyentes son no lineales de manera que raramente podremos encontrar soluciones analíticas. En el espacio de fases de estos sistemas pueden coexistir diferentes tipos de trayectorias dinámicas (multiestabilidad) y su topología puede variar enormemente dependiendo de dos parámetros usados en las ecuaciones. La conjunción de dinámica no lineal y sistemas de muchos grados de libertad (como los que aquí se estudian) da lugar a propiedades emergentes como la existencia de soluciones localizadas en el espacio, sincronización, caos espacio-temporal, formación de patrones, etc... (ii) Complejidad estructural: Se refiere a la existencia de un alto grado de aleatoriedad en el patrón de las interacciones entre los componentes. En la mayoría de los sistemas estudiados esta aleatoriedad se presenta de forma que la descripción de la influencia del entorno sobre un único elemento del sistema no puede describirse mediante una aproximación de campo medio. El estudio de estos dos ingredientes en sistemas extendidos se realizará de forma separada (Partes I y II de esta Tesis) y conjunta (Parte III). Si bien en los dos primeros casos la fenomenología introducida por cada fuente de complejidad viene siendo objeto de amplios estudios independientes a lo largo de los últimos años, la conjunción de ambas da lugar a un campo abierto y enormemente prometedor, donde la interdisciplinariedad concerniente a los campos de aplicación implica un amplio esfuerzo de diversas comunidades científicas. En particular, este es el caso del estudio de la dinámica en sistemas biológicos cuyo análisis es difícil de abordar con técnicas exclusivas de la Bioquímica, la Física Estadística o la Física Matemática. En definitiva, el objetivo marcado en esta Tesis es estudiar por separado dos fuentes de complejidad inherentes a muchos sistemas de interés para, finalmente, estar en disposición de atacar con nuevas perspectivas problemas relevantes para la Física de procesos celulares, la Neurociencia, Dinámica Evolutiva, etc..

Internal mode mechanism for collective energy transport in extended systems

We study directed energy transport in homogeneous nonlinear extended systems in the presence of homogeneous ac forces and dissipation. We show that the mechanism responsible for unidirectional motion of topological excitations is the coupling of their internal and translation degrees of freedom. Our results lead to a selection rule for the existence of such motion based on resonances that explains earlier symmetry analysis of this phenomenon. The direction of motion is found to depend both on the initial and the relative phases of the two harmonic drivings, even in the presence of noise.Comment: Final version, to appear in Physical Review Letter

Cooperative scale-free networks despite the presence of detector hubs

Recent results have shown that heterogeneous populations are better suited to support cooperation than homogeneous settings when the Prisoner’s Dilemma drives the evolutionary dynamics of the system. The same occurs when the network growth is coevolving together with the evolutionary dynamics, which also gives rise to highly cooperative scale-free networks. In the latter case, however, the organization of cooperation is radically different with respect to the case in which the underlying network is static. In this paper we study the structure of cooperation in static networks grown together with evolutionary dynamics and show that the general belief that hubs can only be occupied by cooperators does not hold. Moreover, these scale-free networks support high levels of cooperation despite having defector hubs. Our results have several important implications for the explanation of cooperative behavior in scale-free networks and highlight the importance that the formation of complex systems have on its function.YM is supported by MICINN (Spain) through the Ram´on y Cajal Programme. This work has been partially supported by MICINN through Grants FIS2006-12781- C02-01, FIS2008-01240 and MOSAICO, and by Comunidad de Madrid (Spain) through Grant SIMUMAT-CM.Publicad

Possible soliton motion in ac-driven damped nonlinear lattices

We study the possibility of kink motion induced by pure ac driving in damped nonlinear lattices, focusing on the Frenkel-Kontorova and Toda models. Numerical simulations of the Frenkel-Kontorova model show no evidence for steady kink motion. We point out that momentum-balance in addition to energy-balance arguments are needed to understand the translation of the collective excitation. Finally, our result is discussed in view of related theoretical predictions and numerical simulations.Support from a MEC/Fulbright grant, from DGICyT (Spain) under Project No. PB92-0248, and from the European Union Network ERBCHRXCT930413. Work at Zaragoza was supported by DGICyT (Spain) under Project No. PB92-0361, and by the European Union (NETWORK on Nonlinear Approaches to Coherent and Fluctuating Processes in Condensed Matter and Optical Physics). Work at Los Alamos was performed under the auspices of the U.S. Department of Energy.Publicad

Mode locking in discrete solition dynamics under ac forces

We present here analytical arguments and numerical evidence for the existence of net directional motion of highly discrete sine-Gordon kinks under ac forces of zero average. We have also characterized the depinning of the oscillating kink under those circumstances, and analyzed the instability mechanisms of the phase-locked running solutions. Possible experimental relevance of this phenomenon in circular arrays of Josephson junctions is discussed.Financial support from DGES (PB95-0797) and CICYT (MAT95-0325)Publicad

Co-evolutionnary network approach to cultural dynamics controlled by intolerance

Starting from Axelrod's model of cultural dissemination, we introduce a rewiring probability, enabling agents to cut the links with their unfriendly neighbors if their cultural similarity is below a tolerance parameter. For low values of tolerance, rewiring promotes the convergence to a frozen monocultural state. However, intermediate tolerance values prevent rewiring once the network is fragmented, resulting in a multicultural society even for values of initial cultural diversity in which the original Axelrod model reaches globalization

Los Pedregales (Lupiñén-Ortilla, Huesca): contribución al conocimiento del poblamiento altomedieval en la Hoya de Huesca

El conocimiento de la ocupación visigoda y paleoislámica en el valle del Ebro resulta un tanto difuso, más por falta de investigaciones y por la escasa visibilidad de los asentamientos, que por un efectivo despoblamiento. En este artículo presentamos los resultados de nuestras investigaciones en el yacimiento de Los Pedregales, en la provincia de Huesca, un conjunto complejo en el que se encuentran materiales de diversas cronologías (romanos, altomedievales, modernos…) junto con numerosas estructuras pétreas en un área completamente alterada por procesos erosivos. Una minuciosa prospección y la excavación de algunas estructuras en el marco de un estudio geoarqueológico, nos ha permitido explicar la ocupación principal del yacimiento como un campo de silos datado entre los siglos vi y ix, que aporta una nueva referencia para la comprensión de los paisajes rurales antiguos y las comunidades campesinas dispersas que los ocupan. En el artículo se describen e interpretan las estructuras, se estudian los materiales más relevantes, especialmente los cerámicos, y se contextualiza el yacimiento con relación al poblamiento y los procesos históricos que afectan a este territorio

Complex cooperative networks from evolutionary preferential attachment

In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes of a pre-existent network, we study network growth and formation by proposing an evolutionary preferential attachment model, its main feature being that the capacity of a node to attract new links depends on a dynamical variable governed in turn by the node interactions. As a specific example, we focus on the problem of the emergence of cooperation by analyzing the formation of a social network with interactions given by the Prisoner's Dilemma. The resulting networks show many features of real systems, such as scale-free degree distributions, cooperative behavior and hierarchical clustering. Interestingly, results such as the cooperators being located mostly on nodes of intermediate degree are very different from the observations of cooperative behavior on static networks. The evolutionary preferential attachment mechanism points to an evolutionary origin of scale-free networks and may help understand similar feedback problems in the dynamics of complex networks by appropriately choosing the game describing the interaction of nodes.Comment: 6 pages and 4 figures, APS format. Submitted for publicatio