Understanding Complex Systems Symposium

Abstracts, Audio Recordings, Slides

Congestion control in communication and computer networks involves the problem of regulating the source rates (in a decentralized and distributed fashion), so that the available bandwidths on different links are used most efficiently. We study the congestion control problem within a fairly general mathematical framework that utilizes noncooperative game theory, where behaviors of independent users (players) on a large scale network are captured in a nonlinear continuous time (CT) model. We prove the existence and uniqueness of a Nash equilibrium point under mild convexity assumptions on the cost function associated with users, and establish its global stability. However, analytical counterpart of the stability result is difficult to obtain in the discrete-time (DT) version of the model, which is of practical importance. Therefore, the local stability and robustness to parameter variations of the DT model at a single bottleneck link is investigated using randomized algorithms. We make use of Monte Carlo as well as Quasi-Monte Carlo techniques to provide a probabilistic estimate of the local stability of the network.

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Materials are often processed by and used in nonequilibrium conditions. Examples range from materials undergoing wear or corrosion, to materials exposed to energetic particles in nuclear reactors, to powder materials synthesized by ball milling, and to thin films processed by ion beams. In such cases, the response of the material is controlled by several kinetic processes, which are often competing. An remarkable point in these driven systems is their tendency to spontaneously self-organize and develop patterns at the nanometer scale. We will review several experimental observations and discuss how analytical modeling and computer simulations shed light on this phenomenon. We will indicate the potential applications toward the synthesis of nanostructured materials with optimized mechanical, electrical, or magnetic properties.

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An outstanding question in social insect biology is how the behavioral decisions of hundreds or thousands of individual workers yields adaptive behavior patterns at the level of the colony. Division of labor is one type of behavior that is a notable feature of colonies and that is believed to be largely responsible for the tremendous ecological success of these insects. I have been studying the properties of a"response threshold" model to understand how individual decisions give rise to the colony behavior. This type of model postulates that division of labor results from individual variation among workers in their responsiveness to specific stimuli associated with each task. The response threshold mechanism tends to keep stimulus levels at or near a steady state that is determined by the distribution of response thresholds among workers and by the level of "need" for a task. The model shows that changing the threshold distribution changes the stimulus in the steady state, and may also lead to qualitatively different responses by the colony to perturbations in the stimulus. These responses correspond to different strategies that colonies might use in managing stimulus levels of tasks that present different types of challenges to the colony. The behavioral organization of the colony must unite within a single work force the different strategies required for the full array of tasks.

Many applications have been found for fractal models in material science including the study of surface morphology, fractures, chemical reactivity, phase transitions, and aggregation. Over the past two decades many methods have been developed to estimate fractal dimensions for experimental data. Unfortunately, not all estimators are created equal. Numerical issues plague the accurate estimation of fractal dimensions and complicate the interpretation of fractal analysis. This study compares the performance of four algorithms for estimating fractal dimension on different classes of fractal objects to see if a synergy of knowledge regarding estimator limitations can progress the ability to interpret fractal analysis with greater confidence.

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In recent decades, several distinct classes of organic electronic materials-including conducting polymers, molecular crystals, and charge transfer solids-have been synthesized and widely studied for their novel elecrtrical conductivity and optical response properties. These materials are often characterized by low effective electronic dimensionality and the interplay of both electron-phonon (e-ph) and electron-electron (e-e) interactions. These characteristics lead to a wealth of exotic low-temperature phases-including spin density wave (SDW), charge density wave (CDW), spin-Peierls (SP), and superconducting states-as well as spatially inhomogeneous "charge-ordered" states. I will present an introductory overview of this interesting class of "complex materials" and will mention a few of the outstanding current challenges for experiment and theory in this area.

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[1] D. R. Nelson and N. M. Shnerb, Phys. Rev. E 58, 1383 (1998).

Your biggest mistake in a movie theater, is to unwrap a candy minutes after the movie has just started. The unwrapping make that obnoxious noise. A candy is wrapped in a piece of an elastic sheet. When you crumple a sheet of regular paper you hear that same noise. When you look at the result of your crumpling you find out that the sheet of paper is made of almost cylindrical ridges that terminates by conical regions that are sharp enough that they hurt your fingers when you keep on crumpling. We will address the geometry and the mechanics of this pattern using simple arguments.

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Granular materials exhibit a wide spectrum of behavior ranging from gaseous to liquid to solid. Remarkably, all of these phases of granular matter respond to external stimuli in a manner strikingly different from ordinary fluids and solids. Spatial inhomogeneities are thought to play a crucial role in determining the macroscopic properties of these systems. In static granular piles, the inhomogeneous stress distribution is strikingly demonstrated by the appearance of force chains. Experiments have also shown that the force distribution at the walls is exponential at large forces and exhibits a plateau at small forces A recent proposal for a unified picture of jamming in thermal and non-thermal systems is that jamming is signaled by a scarcity of small forces leading to the appearance of a dip or plateau in the force distribution.. It is tempting to speculate that changes in the force distribution are related to the growth of spatially extended structures which evolve in to the force chains in the jammed, static system. I will discuss results of simulations of a simple model of granular systems and show that the dissipative nature of the system leads to the formation of large-scale structures as the flow gets arrested. I will also discuss the effects of these structures on the distribution of forces and collision times.

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This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

Crackling noise arises when a system responds to changing external conditions through discrete, impulsive events spanning a broad range of scales. Examples that have been studied range from magnets to earthquakes. The fact that models and real systems with crackling noise can share the same behavior on many scales is called universality. We illustrate the dependence of these universal features on history, disorder, and field sweep rate using our model of crackling noise in magnets. We observe a reflection of critical behavior of the saturation hysteresis loops in the demagnetization curves and the inner subloops. Recent experimental tests in magnets will be discussed. Some of these ideas are relevant also to the study of earthquake statistics.

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This presentation introduces a new paradigm for the distributed coordination of complex systems. The intent is to reformulate and expand existing technologies in mechanics, controls and planning in order to provide a unified perspective for their collaborative implementation. The proposed approach will emphasize the coordinated interaction among the subsystems over the design and function of any single subsystem. Solitary tasks, such as the optimization of a particular planning problem, will be set aside as we search for team-oriented tasks that can be addressed among ensembles of interacting subsystems.

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Bacteria make use of a remarkable array of signaling circuits in order to sense and respond to their environment. Despite an enormous amount of information regarding the underlying components (e.g. the proteins, DNA, RNA, etc.), the basic organizing principals for these circuits remain poorly understood. We have been studying a particularly simple and well-characterized example of signal transduction in which cells modulate the permeability of their outer walls in response to changes in osmotic pressure. We have constructed fluorescent reporter strains for this circuit, which provide sensitive measures of signaling activity within single cells. Using these strains we have tested mathematical models of this system and explored the implications of open-loop continuous control in a biological circuit.

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The brain is a complex system whose organization seems to be governed to a significant extent by the following rule: "Assume that tomorrow will be much like today or those days that have preceded today, and prepare accordingly." Thus the organization of the brain reflects its past experience. At the most evident level this is seen in the capacities of learning and memory. At a less evident level, the brain can exhibit the equivalent of a callous--a change in functional organization brought about by wear. These are seen in support systems for the brain's neurons, including the vasculature and the glial supportive tissue of astrocytes and myelin. Some of these callouses soften and disappear rapidly with discontinuation of the form of use that brought them into being. Others, like the synapses that we believe encode memory, endure for long periods if not indefinitely once they are established. Enduring non-synaptic changes arising from experience include the myelination that enhances the rate of conduction by axons, suggesting that it has informational value for brain organization in the long term, a form of functional memory. Of interest is that different aspects of experience regulate changes in different aspects of brain. Some changes reflect little more than the envelope of activity, while others, such as the brain's synaptic organization, appear to reflect specific demands for learning.

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In heterogenous materials, the component materials interact to produce the observable spectral signature of the material based on the properties and proportions of those components. We are conducting on-going research to model this relationship in order to determine the properties of the components, which are normally expensive to measure directly, based on observed hyperspectral data(the spectrum divided into hundreds of wavelength ranges), which has the potential to be significantly cheaper to collect as the technology matures. Our experiments focus on the agriculture domain, where hard to measure soil and crop properties influence the observable reflectance values captured through remote-sensing techniques. Methods to determine most informative wavelength for different material properties and a framework to find the optimal modelling technique for a property will be discussed.

Traditional data mining systems and methods assume that data resides on disks or in main memory, and a data mining process can scan the data sets multiple times to uncover interesting patterns. However, real-time production systems and other dynamic environments often generate tremendous (potentially infinite) volumes of stream data in fast speed---the volume of data is too huge to be stored on disks or even if it were stored on disks, it could be too expensive be fetched and scanned multiple times. Moreover, many applications may require real time mining of unusual patterns in data streams, including finding unusual network or telecommunication traffic, real-time pattern mining in video surveillance, detecting suspicious on-line transactions or terrorist activities, and so on. Recently there have been substantial growing research interests in developing methods for querying and mining stream data. In this talk, I will first present an overview of recent developments on stream data querying and mining and outline what are the major challenging research problems for mining dynamics of data streams in multi-dimensional space. In particular, I will be addressing the following issues in detail: (1) multi-dimensional on-line analysis methods for discovering unusual patterns in stream data; (2) mining time-sensitive frequent patterns in stream data; (3) mining clusters and outliers in stream data; and (4) single-pass classification methods for stream data mining.

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Can one predict the future evolution of a physical process which is described or modeled by a computationally irreducible mathematical algorithm? Complex physical systems that are computationally irreducible might seem to be inherently unpredictable. Here we show that because in practice one only seeks coarse-grained information, complex physical systems can be predictable and even computationally reducible at some level of description. Using nearest neighbor, one-dimensional cellular automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's classification. At least one of the CA that can be coarse-grained by this construction is known to be a universal Turing machine, which can therefore emulate any CA. The resulting coarse-grained CA which we construct are capable of emulating the large-scale behavior of the original systems without accounting for small-scale details.

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Recently, Nuzzo, Frenkel, and co-workers at UIUC have produced bimetallic nanoassemblies on carbon composed of Ru-Pt via metallorganic chemistry that intringuingly exhibit bulk metallic cuboctahedral structural properties. Such properties have been fully experimental characterized by EXAFS, XANES, RBS, ... As structure and bonding (e.g. adsorption sites) dictate usefulness as catalysis and fuel cells, it is important to understand structure and its origin. Direct density-functional calculations are used to reveal the nature and origin of the structure, with a goal to control and design properties.

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The single greatest risk factor for the development of cancer is advancing age. Multicellular eukaryotic organisms have evolved to exchange, in a sense, the limitless replication capacity of unicellular organisms for a distribution of the physiologic workload into specialized cells and organs. This transition to multicellular life was accomplished through the function of what are now called tumor suppressor genes. As cells and tissues age, a myriad of malfunctions arise that can ultimately lead to loss of control of cell replication, such that individual cells again emerge as cancer, with apparently limitless replication capacity. Tumor suppressor genes exist to prevent the emergence of cancers in higher life forms, but evidence is mounting that these same anticancer genes contribute to the phenomenon of ageing. Developmentally regulated genes that are normally expressed only during embryogenesis are upregulated when cells lose tumor suppressor gene function, and individual cells disengage from normal tissue homeostatic mechanisms to result in death of the host. The interaction of advancing age and the onset of cancer will be discussed.

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The field of quantum information promises incredible gains in solving certain problems in the areas of computation and communication. One of the underlying reasons for the immense computing power is that the processing takes place in the vastness of the Hilbert space inhabited by the multiparticle quantum states. We have been experimentally exploring part of this space, using a controllable source of correlated photons. In particular, we have been able to produce very precisely a wide range of possible states, some of which had never been observed before, or even presumed to exist! I will discuss our latest attempts to access even the most remote corner of Hilbert space.

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Multicomponent (binary, ternary and quaternary) phase diagrams are used to guide the design of complex microstructures in oxide ceramics. Duplex, triplex and quadruplex phases are in intimate contact are developed from homogeneous precursor powders produced by a new organic-inorganic steric entrapment method developed in our laboratory. The microstructures produced appear to follow paths to the lowest energy, stable equilibrium state. Simultaneous crystallization and densification of multiphase, multicomponent systems occur during an atomic ?traffic jam? leading to mutual retardation of grain growth, homogeneous microstructures and possibly superior mechanical properties. The systems under study include alumina (Al₂O₃ ) - zirconia (ZrO₂), alumina - YAG (Y3 Al₅O₁₂), alumina - YAG - spinel (Mg Al₅O₄), alumina - zirconia - ceria (CeO₂) - strontia (SrO₂). Such materials may be beneficial as strong and tough ceramic drill bits. Other homogeneous solid solutions include lanthanum doped strontium gallium magnesium oxide (La_0.8Sr_0.2Ga_0.75Mg_0.25O_0.255) or ?LSGM?, and SrFeCo_0.5Ox solid oxide fuel cell materials (SOFC?s).

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Soft matter systems, including polymer solutions, polyelectrolytes and colloidal suspensions, exhibit a variety of complex behavior, arising from the collective properties of the constituents. While experiments continue to uncover such phenomena, both theory and computer simulation have difficulty keeping up, as these phenomena typically involve various length and time scales. In simulations, such problems can sometimes be overcome with a system-specific approach, but there exist very few general solutions. We present a new cluster Monte Carlo method that applies to large classes of complex fluids and mitigates several of the dynamical problems that plague the numerical study of these systems. Illustrative examples are shown for a binary mixture of colloidal particles with a large size difference.

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Swarm theories of self-propelled biological agents have become of interest to theoretical physicists. But well-defined swarming experiments using real biological agents have been problematic up to now due to size limitations or lack of precise knowledge of the agent-agent or agent-medium interactions. We present the results of lab experiments with the zooplankton Daphnia - intermediate in size (but probably not complexity) between bacteria and birds or fish, for example. Our experiments show the entire range of behaviors from single agent to collective motions of a swarm, and can be observed to perform a fascinating bio-hydrodynamic vortex under certain conditions.

*Supported by Office of Naval Research

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My project is testing a collaborative filtering algorithm for visual displays - users set their preferences for a number of different art categories (cezanne, midevil, etc), and the system tries to find categories that will satisfy everyone more-or-less equally; current phase is trying to break down pictures so that the preferences for categories are useful. Eventually this will be directed at patterns in scientific data.

Cooper pairs are thought to exist in two quite distinct ground states: 1) localized in a Mott insulator or 2) condensed in a superconductor. However, recent experiments on 2D films exhibiting a nominal insulator-superconductor transition indicate that there may be a third possibility: a metal with a finite resistivity at zero temperature. I will review the standard theoretical framework used to understand the insulator-superconductor transition, the recent experimental results and I will show quite generally how Cooper pairs lacking phase coherence can form a metal in the presence of disorder rather than an insulating phase.
The metallic state is rather weird, however. The phase degrees of freedom are glassy. At the heart of the metallic state is the dissipation inherent in the glassy state.
Cooper pairs moving in such a glassy environment fail to localize because no true ground state exists.

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Crazes are intriguing structures that give glassy polymers much of their resistance to fracture. Polymers (~0.5 nm diameter) are bundled into an intricate network of ~10 nm diameter polymers that extends ~10micrometers on either side of ~mm cracks. Phenomena on all of these length scales must be included to determine the macroscopic fracture energy. We do this by combining molecular dynamics simulations of craze growth, deformation, and failure at the submicron scale with a continuum fracture mechanics calculation for the onset of crack propagation. Our results are in quantitative agreement with dimensionless ratios that describe experimental polymers and their variation with temperature, polymer length and polymer rigidity. They also help to reveal why and how crazes form. Analysis of local geometry and stresses provide new insight into the real-space nature of the entanglements that control melt dynamics. Crazes are also shown to share many features with jammed systems such as granular media and foams, but are unique in jamming under a tensile load. This allows explanations for the exponential stress distribution in jammed systems to be tested.

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Dislocations and their interactions with other microstructural features, such as impurity atoms, precipitates, dispersoids, dislocations, and grain boundaries are known to determine the mechanical properties of metallic systems. However, no clear methodology exists to transfer this information into a constitutive model that can predict the response of a material. The ideal model should incorporate the behavior at different length and time scales within one grand multi-scale scheme. Such a scheme is, however, impractical and lower length scale models are used to provide fundamental information to serve as the foundation for the development of the next higher length scale. In this talk, I will present an example illustrating how large-scale molecular dynamics simulations and in-situ straining in the transmission electron microscope have been combined to gain a better understanding of the basic interactions between glissile dislocations and obstacle fields, and how this information has been used to develop a model to predict the macroscopic response of a material.

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Unconventional tools for nanofabrication provide new opportunities for building and studying the behavior of organic optoelectronic systems. This talk begins by describing two such methods ?Esoft contact lamination and nanotransfer printing -- and some of their unusual capabilities. It then focuses on their use for building organic test structures and devices to probe transport on three important length scales: those that are comparable to (i) the typical grain size (~300 nm) in thin film organic semiconductors, (ii) the thickness (~100 nm) of thin layers of electroluminescent polymers and (iii) the size (~1 nm) of the molecules themselves. In the first case, we study the behavior of transistors with printed channel lengths that range from several microns to ~100 nm. In the second, we examine the current-voltage characteristics and quantum efficiencies of polymer light emitting diodes (PLEDs) that use laminated electrodes. For the third, we construct organic transistors whose laminated contacts are chemically modified with organic self-assembled monolayers of linear aliphatic molecules with lengths of 1-2 nm. In all cases, detailed knowledge concerning the contact resistance between the metal electrodes and the organic is paramount. We describe systematic measurements of the resistance of contacts formed in various ways, and use the information to interpret the behavior of the systems described above. The results provide some guidelines for the design of organic transistors and PLEDs for applications in displays and other areas.

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Adsorption of molecules, whether intentionally or unavoidably adsorbed, can cause significant changes in the electronic properties of carbon nanotubes. The extreme sensitivity of carbon nanotubes to oxygen is currently a debated issue that has important implications on our understanding of (and therefore on the exploitation of) unique electrical conductivity of carbon nanotubes. Low-intensity UV-induced desorption of oxygen is examined here by a combination of electron transport and optical measurements. Possible sites of oxygen photodesorption and its implications on the observed electronic properties of nanotubes are discussed.

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We study the motion of a particle on a vibrated string of length L. We assume there is a friction force between the particle and the string. The string is sinusoidally forced at both ends. We find that the particle has attractors located at x=L/2 + nπ/k, where k = wavenumber of the waves on the string, and |n|=0,1,2....

The proper description of stress response in noncohesive granular materials is a surprisingly complex problem. A salient feature of stress patterns in these materials, observed in numerous experiments and computer simulations, is the emergence of filamentary structures called force chains. I will describe recent theoretical work on the connection between force chain networks and macroscopic stresses in two-dimensional systems. I also will present a few relevant experimental results from the Behringer lab at Duke.

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We study prediction of noise-free chaotic dynamics when the initial condition of the system is not well specified. Conventional trajectory methods are accurate only in the short term regime described by the Lyapunov Exponent. We find the probability density describing chaotic dynamics develops sharp peaks which exponentially diverge from images of the initial condition. Markov Models are used to describe the devolopment and trajectories of these peaks, extending prediction into the medium term regime.

"Nematic" flocks are collections of moving organisms, in which, crudely speaking, half of the creatures are moving in one direction, and half in the opposite direction, with, as a result, zero mean velocity for the flock. Such phases have been observed in, e.g, melanocytes, the critters that carry human skin pigment. Surprisingly, even though such flocks have no net motion, the theory I'll present predicts that their behavior is very different from that of conventional equilibrium nematic liquid crystals, despite the fact that they have the same symmetry). In particular, they exhibit huge number fluctuations, scaling like the mean number N of creatures, rather than sqrt (N) as in equilibrium materials.

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Smectics A and C are both phases of long, rod-like molecules arranged in regular stacks of 2-dimensional liquid layers. In smectics A, these layers are perpendicular to the long axes of the molecules, while in smectics C they are tipped relative to this axis. In this talk, I'll describe recent work which shows that when the transition between these two occurs in an anisotropic random medium (e.g., strained aerogel), it exhibits the paradoxical property that the low temperature, ostensibly more ordered SmC phase is actually LESS translationally ordered than the high temperature SmA phase. Equally bizarre is the behavior at the critical point separating the two phases: although it is described by a model ALMOST identical to that for the SmA PHASE in an ISOTROPIC random medium, it's elastic properties are QUALITATIVELY and quantitatively completely different.

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The "box-counting" dimension (also called capacity dimension) of a geometric object is one of the most widely used notions of a fractal dimension. Box-counting dimension has many desirable properties, is generally considered a good approximation to hard-to-compute Hausdorff dimension, and is (arguably) particularly useful for scale-invariant geometric objects embedded in spaces of low topological dimensionality. We argue, however, that if the standard definition of the box-counting dimension is applied, this dimension fails to be well-defined even for some very simple geometric objects, when these objects are viewed as resulting from scale-invariant limiting processes. Hence we propose a seemingly slight yet important modification of the definition of the box-counting dimension, so that this particular fractal dimension can capture well the intuitive dimensionality of both fractals and non-fractals that are obtainable via recursive application of scale-invariant transformations. We also suggest, given the recursive procedure for constructing a geometric object, how to choose the sequence of box sizes in order to compute the object's box-counting dimension.

Keywords: fractals, fractal dimension, box-counting dimension, scale invariance

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Disclinations play a crucial role in two dimensional crystals and in many liquid crystalline phases. In this talk I will present a detailed theoretical analysis of the energetics of disclinations and dislocations in different geometries, phases and external conditions. It will be shown that the understanding and control of disclinations is crucial for constructing spherical cages that may be used to encapsulate materials or living cells. An explicit experimental example is presented for colloidal cages (Colloidosomes).

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The studies of non-linearity of the Einstein field equations near the threshold of black hole formation by gravitational collapse reveal very rich phenomena, which are quite similar to critical phenomena in Statistical Mechanics and Quantum Field Theory. In particular, in 1993 it was first found numerically that the mass of the black holes takes a scaling form, M_BH ~ (p -p^*)^γ , where p parameterizes a family of initial data in such a way that when p > p^* black holes are formed, and when p = p^* no black holes are formed. It was shown that the exponent γis universal to all the families of initial data studied, and was numerically determined as γ ~ 0.37 . The critical solution with p = p^* is also universal. Universality of the critical solution and exponent, as well as the power-law scaling of the black hole mass all have given rise to the name Critical Phenomena in Gravitational Collapse. The studies were soon generalized to other matter fields, and now become a very active and well-estabelished sub-area in General Relativity.

In this talk, I shall give a brief review on the topic and pay particular attention on the mathematical structure of the problems.

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Aging and noise are used to elucidate the types of frozen order formed in the relaxor regime, a disordered state with mesoscale ferroelectric nanodomains, suspected of forming overall spinglass-like order. We find that in several of the most common cubic relaxors, aging deep in the relaxor regime shows several features characteristic of spinglasses, including multiple independent susceptibility 'holes' formed at different aging temperatures. This effect requires complex cooperative glassy freezing of many local units. However, the field scale required to disrupt the aging is anomalously high compared to spinglasses, if a nanodomain is the unit corresponding to a spin. Barkhausen noise results imply cooperative moment changes involving several nanodomains near Tg, but much smaller steps below Tg. This result suggests that kinetic barriers increase at Tg without increasing coupling among nanodomains. Together, these results suggest that in prototypical relaxors the glassy state is not formed by nanodomains, although it affects their dynamics, but rather by smaller units. We tentatively propose that the canted components of the local polarizations (found in scattering experiments) are analogous to the x-y spins in a reentrant spinglass. The first tested prediction of this new picture is that spinglass-like aging effects would be absent in a uniaxial 'relaxor' , and this prediction is confirmed.

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We will discuss effects of temperature on spectral and pulse measurements in disordered magnets. Of primary interest are the relationships between time scales of the equilibration and the driven relaxation to local minima seen in the zero temperature case and the subsequent manifestations in primary and higher order spectra. We will show how the zero temperature far from equilibrium critical dynamics are obscured upon increasing temperature and provide criteria for critical time and temperature scales above which thermal fluctuations dominate behavior observed with spectral probes and render useless (or at least questionable) the use of 'pulses' for analysis. We will also give numerical results obtained using the random field Ising model using Glauber checkerboard update in the low temperature driven regime.

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Micro- and nanostructured materials with their extraordinary and sometimes counter-intuitive optical properties are bound to have a profound influence on the way we manipulate and use light. I will review some of the exciting new developments in the field of microphotonics, including our own work on colloidal self-assembly and multibeam holography which are used to create photonic crystals.

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We analytically model a simple system to show that electric shortcuts may be supressed by superimposing a heat flow on the same system. We discuss two phases for this system, a smooth phase and a dentritic phase. Given constant current and constant heatflow boundary conditions we solve for the heat flow required to keep the system in the smooth phase. (maybe a numerical simulation for a larger system is given)

Global climate change is occurring largely as a result of human activities. This change is recognized as one of the world?s most important environmental issues, with the potential to greatly affect natural resources, ecological systems, human health, infrastructure and the economy. Because of the regional nature of many of these impacts, accurate approaches are needed to apply global climate modeling results to assessing climate change impacts at smaller scales such as Illinois and the Great Lakes region. New assessments, such as ?Confronting Climate Change in the Great Lakes Region? (Kling, Hayhoe, Wuebbles, et al., 2003), utilize more sophisticated models to assess indicators of the range of impacts that can be expected to occur in the region over the next century. Nonetheless, much needs to be done to enhance the capabilities for downscaling the results of global climate models to the local microclimate scale required for accurate regional impacts analyses. This talk will discuss our existing analyses of regional climate, and future directions for improving climate predictions through dynamical and statistical downscaling approaches utilizing regional climate models and statistical correlations between historical observed and modeled climate patterns over the region.

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Halogens are widely used to modify surfaces during the drying etching of semiconductors. For Si(100), etching is due to the desorption of silicon dihalide. Very recently, we showed that surfaces can also deteriorate at much lower temperatures than those needed for etching. With variable temperature STM, we have followed the surface dynamics of Cl-Si(100) at elevated temperature with atomic precision. These results demonstrate the dynamics of roughening. Studies of the evolution and equilibrium morphologies achieved with initial Cl coverages 0f 0.1 ~ 0.99 ML show that it takes longer for a higher coverage surface to reach dynamic equilibrium. Monte Carlo modeling indicates the main driving force for surface roughening could be adsorbate-adsorbate interactions, but contributions from other interactions cannot be ruled out.

We study the diffraction patterns of a one-dimensional Fibonacci chain from quasiperiodic pulse trains. We find a single prominent peak when the dynamics of the incident wave matches the arrangement of the scatterers, that is, when the pulse train and the scatterers are in resonance. The maximum diffraction angle and the resonant pulse train determine the positions of the scatterers. These results may provide a methodology for the quality control of Fibonacci multilayers, and may have further impact when extended to higher dimensions.

Thermodynamics and ordering in complex alloys can be predicted from first principles using a cluster expansion approach to combine electronic-structure and lattice Monte Carlo methods. A methodology for the optimal truncation of a cluster expansion basis set is presented and exemplified in Ni-V and Al-Ag alloys.

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