Patterns and Collective Behavior in Granular Media: Theoretical Concepts

Granular materials are ubiquitous in our daily lives. While they have been a subject of intensive engineering research for centuries, in the last decade granular matter attracted significant attention of physicists. Yet despite a major efforts by many groups, the theoretical description of granular systems remains largely a plethora of different, often contradicting concepts and approaches. Authors give an overview of various theoretical models emerged in the physics of granular matter, with the focus on the onset of collective behavior and pattern formation. Their aim is two-fold: to identify general principles common for granular systems and other complex non-equilibrium systems, and to elucidate important distinctions between collective behavior in granular and continuum pattern-forming systems.Comment: Submitted to Reviews of Modern Physics. Full text with figures (2Mb pdf) avaliable at http://mti.msd.anl.gov/AransonTsimringReview/aranson_tsimring.pdf Community responce is appreciated. Comments/suggestions send to [email protected]

25 Years of Self-Organized Criticality: Solar and Astrophysics

Shortly after the seminal paper {\sl "Self-Organized Criticality: An explanation of 1/f noise"} by Bak, Tang, and Wiesenfeld (1987), the idea has been applied to solar physics, in {\sl "Avalanches and the Distribution of Solar Flares"} by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme.Comment: 139 pages, 28 figures, Review based on ISSI workshops "Self-Organized Criticality and Turbulence" (2012, 2013, Bern, Switzerland

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

Statistical mechanics and dynamics of surfaces and membranes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1990.Vita.Includes bibliographical references (leaves 243-248).by Terence Tai-Li Hwa.Ph.D

Approaches to scaling phenomena in space and laboratory plasma

Many laboratory and space plasma phenomena exhibit scaling, i.e., no characteristic spatial and/or temporal scale can be identified in their dynamics. This lack of a characteristic scale makes the dynamics of these systems extremely complex and intractable to analytical approaches. Their statistical features, however, appear to be simple and exhibit a degree of universality. We will explore two approaches to scaling in plasma systems, one based on avalanching sandpile model and the second one based on turbulence. The avalanching model developed here exhibits a wide range of dynamic behavior and incorporates other established models as limiting cases. A single control parameter that specifies the length scale over which the redistribution rule operates compared to the finite system size, allows us to explore different regimes of the model's dynamics close to and away from the existing fixed points. An advanced Virtual Reality visualization technique was employed to gain a better qualitative understanding of the sandpile behavior in the parameter space. This sandpile model was used to simulate features found in the fusion plasma in both low and high confinement modes. Because of the simplicity of this model, it was possible to formally characterize and explain the mechanisms underlying steep gradients formation and appearance of internal transport barriers, and to identify links to tokamak plasma behavior. The solar wind is a supersonic, super-Alfvenic flow of compressible and inhomogeneous plasma from the Sun. The solar wind provides a natural laboratory for observations of MHD turbulence over extended temporal scales. In this case a generic and model independent method of differencing and rescaling was applied to identify self-similarity in the Probability Density Functions (PDF) of fluctuations in solar wind bulk plasma parameters as seen by the WIND spacecraft. The single curve, which we found to describe the fluctuations PDF of some quantities, is non-Gaussian. We model this PDF with two approaches-Fokker-Planck, for which we derived the transport coefficients and associated Langevin equation, and the Castaing distribution that arises from a model for the intermittent turbulent cascade. The technique was also used to quantify the statistical properties of fluctuations in the coupled solar wind-magnetosphere system. These quantitative and model-independent results place important constraints on models for the coupled solar wind-magnetosphere system

Universality classes in nonequilibrium lattice systems

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs included. Scheduled for publication in Reviews of Modern Physics in April 200

Universality classes in nonequilibrium lattice systems

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs included. Scheduled for publication in Reviews of Modern Physics in April 200

Generic scale invariance in continuum models of two-dimensional surfaces

Mención Internacional en el título de doctorThe study of interfacial phenomena has always constituted an integral part of condensed matter physics and materials science. Indeed, most properties of real materials depend crucially on the presence of imperfections, such as bulk vacancies, dislocations, surface roughness, etc. which derive from the non-equilibrium conditions under which the material has formed [1, 2]. In the last century, the increasing interest in systems with considerable surface to volume ratio, such as for instance devices at the nanoscale, has attracted scientists from different fields, from physics to chemistry, biology, or engineering [3]. This is due to the great amount of technological applications of such systems to a wide variety of situations. Moreover, the improvement of production and characterization techniques for the growth of surfaces at micro and nano-scale, such as Molecular Beam Epitaxy, or for surface etching, such as Ion Beam Sputtering , have unveiled unexpected interesting physical properties of the grown interfaces. From a technological point of view, the ability to control and predict the effect induced by disorder and the mechanisms of self-organization that ensue during the growth dynamics is of great interest [4]. For instance, the possibility to control the surface roughness could improve electric conductivity or the mechanical contact of certain devices, whereas the ability to control the formation of a pattern could change, for instance, the optical properties of the material. ------------------------------------------------------------------Esta tesis se centra en fenómenos de invariancia de escala genérica en modelos de crecimiento de superficies. Concretamente, hemos considerado sistemas fuera de equilibrio que presentaran desorden a grandes escalas espaciales y temporales (rugosidad cinética), y que estuvieran descritos por ecuaciones continuas. El objetivo de la tesis ha sido utilizar métodos propios de la mecánica estadística para estudiar la interacción de este tipo de sistemas con otros dos fenómenos: la aparición de inestabilidades morfológicas que dan lugar a la formación de patrones, y la presencia de anisotropía. En cuanto al primer problema, hemos considerado un ejemplo paradigmático de ecuación que presente invariancia de escala genérica e inestabilidades morfológicas, la ecuación de Kuramoto-Siashinsky. Hasta la fecha, el comportamiento asintótico de este modelo no se había entendido completamente. De hecho, existe una controversia acerca de cual sea la clase de universalidad a la que este modelo pertenece en dos dimensiones. Utilizando simulaciones numéricas de gran escala, hemos comprobado que esta ecuación en dos dimensiones pertenece a la clase de universalidad de Kardar-Parisi-Zhang. Sucesivamente, nos hemos centrado en modelos que presenten invariancia de escala genérica, cuyos exponentes críticos sean distintos cuando se miden en direcciones distintas del sustrato. Cuando eso ocurre, decimos que el sistema presenta anisotropía fuerte. A pesar de la presencia generalizada de anisotropía en sistemas naturales, hasta el momento se había dedicado relativamente poca atención a este fenómeno. Eso se debe probablemente al hecho de que los modelos mas estudiados en este ´ambito no presentan anisotropía fuerte, aunque la forma de la ecuación sea en algunos casos completamente anisótropa. Después de introducir un marco teórico para el estudio de modelos fuertemente anisótropos, hemos comprobado nuestra hipótesis a través de simulaciones numéricas de distintas ecuaciones que presentaran anisotropía fuerte. Sucesivamente, hemos llevado a cabo un estudio numérico y analítico de otros modelos, con el objetivo de encontrar condiciones para la aparición de anisotropía fuerte. Encontramos que este fenómeno ocurre en presencia de una dinámica conservada, siempre que la ecuación tenga una forma bastante especifica. Finalmente, hemos presentado evidencias experimentales de la aparición de anisotropía fuerte, a través de un análisis de datos de experimentos de erosión iónica en distintas condiciones experimentales.......Programa Oficial de Doctorado en Ingeniería MatemáticaPresidente: Mario Castro Ponce.- Secretario: Javier Manuel Muñoz García.- Vocal: Gnnar Pruessne