Showing papers in "Physical Review E in 2005"
TL;DR: It is shown here that a modification of the standard S-parameter retrieval procedure yields physically reasonable values for the retrieved electromagnetic parameters, even when there is significant inhomogeneity within the unit cell of the structure.
Abstract: We discuss the validity of standard retrieval methods that assign bulk electromagnetic properties, such as the electric permittivity « and the magnetic permeability m, from calculations of the scattering sSd parameters for finite-thickness samples. S-parameter retrieval methods have recently become the principal means of characterizing artificially structured metamaterials, which, by nature, are inherently inhomogeneous. While the unit cell of a metamaterial can be made considerably smaller than the free space wavelength, there remains a significant variation of the phase across the unit cell at operational frequencies in nearly all metamaterial structures reported to date. In this respect, metamaterials do not rigorously satisfy an effective medium limit and are closer conceptually to photonic crystals. Nevertheless, we show here that a modification of the standard S-parameter retrieval procedure yields physically reasonable values for the retrieved electromagnetic parameters, even when there is significant inhomogeneity within the unit cell of the structure. We thus distinguish a metamaterial regime, as opposed to the effective medium or photonic crystal regimes, in which a refractive index can be rigorously established but where the wave impedance can only be approximately defined. We present numerical simulations on typical metamaterial structures to illustrate the modified retrieval algorithm and the impact on the retrieved material parameters. We find that no changes to the standard retrieval procedures are necessary when the inhomogeneous unit cell is symmetric along the propagation axis; however, when the unit cell does not possess this symmetry, a modified procedure—in which a periodic structure is assumed—is required to obtain meaningful electromagnetic material parameters. DOI: 10.1103/PhysRevE.71.036617
2,565 citations
TL;DR: The MSE method is applied to the analysis of coding and noncoding DNA sequences and it is found that the latter have higher multiscale entropy, consistent with the emerging view that so-called "junk DNA" sequences contain important biological information.
Abstract: Traditional approaches to measuring the complexity of biological signals fail to account for the multiple time scales inherent in such time series. These algorithms have yielded contradictory findings when applied to real-world datasets obtained in health and disease states. We describe in detail the basis and implementation of the multiscale entropy (MSE) method. We extend and elaborate previous findings showing its applicability to the fluctuations of the human heartbeat under physiologic and pathologic conditions. The method consistently indicates a loss of complexity with aging, with an erratic cardiac arrhythmia (atrial fibrillation), and with a life-threatening syndrome (congestive heart failure). Further, these different conditions have distinct MSE curve profiles, suggesting diagnostic uses. The results support a general "complexity-loss" theory of aging and disease. We also apply the method to the analysis of coding and noncoding DNA sequences and find that the latter have higher multiscale entropy, consistent with the emerging view that so-called "junk DNA" sequences contain important biological information.
2,101 citations
TL;DR: Here it is seen how a proper design of these lossless metamaterial covers near their plasma resonance may induce a dramatic drop in the scattering cross section, making these objects nearly "invisible" or "transparent" to an outside observer--a phenomenon with obvious applications for low-observability and noninvasive probe design.
Abstract: The possibility of using plasmonic and metamaterial covers to drastically reduce the total scattering cross section of spherical and cylindrical objects is discussed. While it is intuitively expected that increasing the physical size of an object may lead to an increase in its overall scattering cross section, here we see how a proper design of these lossless metamaterial covers near their plasma resonance may induce a dramatic drop in the scattering cross section, making these objects nearly "invisible" or "transparent" to an outside observer--a phenomenon with obvious applications for low-observability and noninvasive probe design. Physical insights into this phenomenon and some numerical results are provided.
1,557 citations
TL;DR: The method outperforms the optimal modularity found by the existing algorithms in the literature and is feasible to be used for the accurate identification of community structure in large complex networks.
Abstract: We propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity The method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure We present the results of the algorithm for computer-simulated and real networks and compare them with other approaches The efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks
1,534 citations
TL;DR: In this article, a universal back-projection algorithm for three-dimensional photoacoustic computed tomography is presented for three types of imaging geometries: planar, spherical, and cylindrical surfaces.
Abstract: We report results of a reconstruction algorithm for three-dimensional photoacoustic computed tomography. A universal back-projection formula is presented for three types of imaging geometries: planar, spherical, and cylindrical surfaces. A solid-angle weighting factor is introduced in the back-projection formula to compensate for the variations of detection views. A method for implementing this algorithm is described. Numerical simulation is used to demonstrate the performance of the algorithm.
1,114 citations
TL;DR: A new centrality measure that characterizes the participation of each node in all subgraphs in a network, C(S)(i), which is better able to discriminate the nodes of a network than alternate measures such as degree, closeness, betweenness, and eigenvector centralities.
Abstract: We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network motifs. We show that the subgraph centrality [C(S)(i)] can be obtained mathematically from the spectra of the adjacency matrix of the network. This measure is better able to discriminate the nodes of a network than alternate measures such as degree, closeness, betweenness, and eigenvector centralities. We study eight real-world networks for which C(S)(i) displays useful and desirable properties, such as clear ranking of nodes and scale-free characteristics. Compared with the number of links per node, the ranking introduced by C(S)(i) (for the nodes in the protein interaction network of S. cereviciae) is more highly correlated with the lethality of individual proteins removed from the proteome.
1,102 citations
TL;DR: From those dilatancy and friction laws, the constitutive law for dense granular flows is deduced, with a plastic Coulomb term and a viscous Bagnold term, for the limit of rigid grains.
Abstract: We study the plane shear flow of a dense assembly of dissipative disks using discrete simulation and prescribing the pressure and the shear rate. Those shear states are steady and uniform, and become intermittent in the quasistatic regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called the inertial number I , which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic critical state of soil mechanics, while large values of I correspond to the fully collisional regime of kinetic theory. When I increases in the intermediate dense flow regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. The mechanical characteristics of the grains (restitution, friction, and elasticity) have a small influence in the dense flow regime. Finally, we show that the evolution of the relative velocity fluctuations and of the contact force anisotropy as a function of I provides a simple explanation of the friction law.
966 citations
TL;DR: This paper applies motif scores and clustering coefficient to financial and metabolic networks and finds that inclusion of weights may considerably modify the conclusions obtained from the study of unweighted characteristics.
Abstract: The local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network. The clustering coefficient, reflecting the local configuration of triangles, can be seen as a special case of this approach. In this paper we generalize this method for weighted networks. We introduce subgraph ``intensity'' as the geometric mean of its link weights and ``coherence'' as the ratio of the geometric to the corresponding arithmetic mean. Using these measures, motif scores and clustering coefficient can be generalized to weighted networks. To demonstrate these concepts, we apply them to financial and metabolic networks and find that inclusion of weights may considerably modify the conclusions obtained from the study of unweighted characteristics.
957 citations
TL;DR: This work defines both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time, and uses this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer.
Abstract: Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time. This algorithm runs in time O(k2d) for general graphs when d is the mean degree and k is the number of vertices to be explored. For graphs where exploring a new vertex is time consuming, the running time is linear, O(k). We show that on computer-generated graphs the average behavior of this technique approximates that of algorithms that require global knowledge. As an application, we use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer.
813 citations
TL;DR: This work proposes and analyzes a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices.
Abstract: Uncorrelated random scale-free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two- and three-vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k , respectively.
682 citations
TL;DR: It is shown that the observed dependence of the deposit dimensions on the experimental parameters can indeed be attributed to the finite dimensions of the solute particles.
Abstract: A model accounting for the finite spatial dimensions of the deposit patterns in evaporating sessile drops of a colloidal solution on a plane substrate is proposed. The model is based on the assumption that the solute particles occupy finite volume and hence these dimensions are of steric origin. Within this model, the geometrical characteristics of the deposition patterns are found as functions of the initial concentration of the solute, the initial geometry of the drop, and the time elapsed from the beginning of the drying process. The model is solved analytically for small initial concentrations of the solute and numerically for arbitrary initial concentrations of the solute. The agreement between our theoretical results and the experimental data is demonstrated, and it is shown that the observed dependence of the deposit dimensions on the experimental parameters can indeed be attributed to the finite dimensions of the solute particles. These results are universal and do not depend on any free or fitting parameters; they are important for understanding evaporative deposition and may be useful for creating controlled deposition patterns.
TL;DR: It is shown that a nanopore can be used to distinguish the lengths of DNA fragments present in a mixture and paved the way for quantitative analytical techniques with solid-state nanopores.
Abstract: We report double-strand DNA translocation experiments using silicon oxide nanopores with a diameter of about 10 nm . By monitoring the conductance of a voltage-biased pore, we detect molecules with a length ranging from 6557 to 48 500 base pairs. We find that the molecules can pass the pore both in a straight linear fashion and in a folded state. Experiments on circular DNA further support this picture. We sort the molecular events according to their folding state and estimate the folding position. As a proof-of-principle experiment, we show that a nanopore can be used to distinguish the lengths of DNA fragments present in a mixture. These experiments pave the way for quantitative analytical techniques with solid-state nanopores.
TL;DR: This analysis reveals a striking relation between this process and the condition for the linear stability of the synchronized states and shows that, for a given degree distribution, the maximum synchronizability is achieved when the network of coupling is weighted and directed and the overall cost involved in the couplings is minimum.
Abstract: Many complex networks display strong heterogeneity in the degree (connectivity) distribution. Heterogeneity in the degree distribution often reduces the average distance between nodes but, paradoxically, may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength. Here we offer a solution to this apparent paradox. Our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states. We show that, for a given degree distribution, the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum. This enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size. Numerical verification of the main results is provided for representative classes of small-world and scale-free networks.
TL;DR: The entire range of observed spherulite morphologies can be reproduced by this generalized phase field model of polycrystalline growth, which describes and explores three physically prevalent sources of disorder that lead to this kind of growth.
Abstract: Many structural materials (metal alloys, polymers, minerals, etc.) are formed by quenching liquids into crystalline solids. This highly nonequilibrium process often leads to polycrystalline growth patterns that are broadly termed "spherulites" because of their large-scale average spherical shape. Despite the prevalence and practical importance of spherulite formation, only rather qualitative concepts of this phenomenon exist. It is established that phase field methods naturally account for diffusional instabilities that are responsible for dendritic single-crystal growth. However, a generalization of this model is required to describe spherulitic growth patterns, and in the present paper we propose a minimal model of this fundamental crystal growth process. Our calculations indicate that the diversity of spherulitic growth morphologies arises from a competition between the ordering effect of discrete local crystallographic symmetries and the randomization of the local crystallographic orientation that accompanies crystal grain nucleation at the growth front [growth front nucleation (GFN)]. This randomization in the orientation accounts for the isotropy of spherulitic growth at large length scales and long times. In practice, many mechanisms can give rise to GFN, and the present work describes and explores three physically prevalent sources of disorder that lead to this kind of growth. While previous phase field modeling elucidated two of these mechanisms--disorder created by particulate impurities or other static disorder or by the dynamic heterogeneities that spontaneously form in supercooled liquids (even pure ones)--the present paper considers an additional mechanism, crystalline branching induced by a misorientation-dependent grain boundary energy, which can significantly affect spherulite morphology. We find the entire range of observed spherulite morphologies can be reproduced by this generalized phase field model of polycrystalline growth.
TL;DR: Using Monte Carlo simulations and the generalized mean-field approximations, the phase boundaries (critical points) are determined separating the two phases on the plane of the temperature (noise) and temptation to choose defection.
Abstract: The effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary prisoner's dilemma game with players located on the sites of different two-dimensional lattices. This system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive. Using Monte Carlo simulations and the generalized mean-field approximations we have determined the phase boundaries (critical points) separating the two phases on the plane of the temperature (noise) and temptation to choose defection. In the zero temperature limit the cooperation can be sustained only for those connectivity structures where three-site clique percolation occurs.
TL;DR: It is found that there is a critical rate of information generation, below which the network traffic is free but above which traffic congestion occurs, and this model may be practically useful for designing communication protocols.
Abstract: Free traffic flow on a complex network is key to its normal and efficient functioning. Recent works indicate that many realistic networks possess connecting topologies with a scale-free feature: the probability distribution of the number of links at nodes, or the degree distribution, contains a power-law component. A natural question is then how the topology influences the dynamics of traffic flow on a complex network. Here we present two models to address this question, taking into account the network topology, the information-generating rate, and the information-processing capacity of individual nodes. For each model, we study four kinds of networks: scale-free, random, and regular networks and Cayley trees. In the first model, the capacity of packet delivery of each node is proportional to its number of links, while in the second model, it is proportional to the number of shortest paths passing through the node. We find, in both models, that there is a critical rate of information generation, below which the network traffic is free but above which traffic congestion occurs. Theoretical estimates are given for the critical point. For the first model, scale-free networks and random networks are found to be more tolerant to congestion. For the second model, the congestion condition is independent of network size and topology, suggesting that this model may be practically useful for designing communication protocols.
TL;DR: The model describes both the unpairing and unstacking parts of the spectroscopically determined experimental melting curves and explains the observed temperature dependence of the effective thermodynamic parameters used in models of the nearest neighbor type.
Abstract: We propose a statistical mechanics model for the melting transition of DNA. Base pairing and stacking are treated as separate degrees of freedom, and the interplay between pairing and stacking is described by a set of local rules which mimic the geometrical constraints in the real molecule. This microscopic mechanism intrinsically accounts for the cooperativity related to the free energy penalty of bubble nucleation. The model describes both the unpairing and unstacking parts of the spectroscopically determined experimental melting curves. Furthermore, the model explains the observed temperature dependence of the effective thermodynamic parameters used in models of the nearest neighbor type. We compute the partition function for the model through the transfer matrix formalism, which we also generalize to include nonlocal chain entropy terms.
TL;DR: A general method to find the critical components of an infrastructure network, i.e., the nodes and the links fundamental to the perfect functioning of the network, can be used as an improvement analysis to better shape a planned expansion of thenetwork.
Abstract: Infrastructure systems are a key ingredient of modern society. We discuss a general method to find the critical components of an infrastructure network, i.e., the nodes and the links fundamental to the perfect functioning of the network. Such nodes, and not the most connected ones, are the targets to protect from terrorist attacks. The method, used as an improvement analysis, can also help to better shape a planned expansion of the network.
TL;DR: The model shows the expected elastic behavior on large length scales, and its physical properties can be widely tuned via a single parameter, at least within 3-30 k(B) T.
Abstract: We present a model for the efficient simulation of generic bilayer membranes. Individual lipids are represented by one head bead and two tail beads. By means of simple pair potentials these robustly self-assemble to a fluid bilayer state over a wide range of parameters, without the need for an explicit solvent. The model shows the expected elastic behavior on large length scales, and its physical properties (e.g., fluidity or bending stiffness) can be widely tuned via a single parameter. In particular, bending rigidities in the experimentally relevant range are obtained, at least within $3\char21{}30{k}_{\mathrm{B}}T$. The model is naturally suited to study many physical topics, including self-assembly, fusion, bilayer melting, lipid mixtures, rafts, and protein-bilayer interactions.
TL;DR: Public transport systems in 22 Polish cities have been analyzed and a transition between dissortative small networks and assortative large networks N approximately > or = 500 is observed.
Abstract: Public transport systems in 22 Polish cities have been analyzed. The sizes of these networks range from N = 152 to 2881. Depending on the assumed definition of network topology, the degree distribution can follow a power law or can be described by an exponential function. Distributions of path lengths in all considered networks are given by asymmetric, unimodal functions. Clustering, assortativity, and betweenness are studied. All considered networks exhibit small-world behavior and are hierarchically organized. A transition between dissortative small networks N approximately or = 500 is observed.
TL;DR: The gradient index metamaterial proposed may be suited for terahertz applications, where the magnetic resonant response of SRRs has recently been demonstrated and may prove an advantageous alternative approach to the development of gradient index lenses and similar optics.
Abstract: Metamaterials—artificially structured materials with tailored electromagnetic response—can be designed to have properties difficult or impossible to achieve with traditional materials fabrication methods. Here we present a structured metamaterial, based on conducting split ring resonators sSRRsd, which has an effective index of refraction with a constant spatial gradient. We experimentally confirm the gradient by measuring the deflection of a microwave beam by a planar slab of the composite metamaterial over a range of microwave frequencies. The gradient index metamaterial may prove an advantageous alternative approach to the development of gradient index lenses and similar optics, especially at higher frequencies. In particular, the gradient index metamaterial we propose may be suited for terahertz applications, where the magnetic resonant response of SRRs has recently been demonstrated.
TL;DR: A procedure to quantify the occurrence of force chains is built on a proposed definition having two parts: first, the chain is a quasilinear arrangement of three or more particles, and second, along the chain, stress concentration within each grain is characterized by the vector delineating the most compressive principal stress.
Abstract: It has been observed that the majority of particles in a granular material carries less than the average load and that the number of particles carrying larger than the average load decreases exponentially with increasing contact force. The particles carrying above average load appear to form a strong network of forces while the majority of particles belong to a weak network. The strong network of forces appear to have a spatial characteristic whereby the stronger forces are carried though chainlike particle groups referred to as force chains. There is a strong case for a connection between force chains of the discrete medium and the trajectory of the most compressive principal stress in its continuous idealization. While such properties seem obvious from descriptive analysis of physical and numerical experiments in granular media, progress in quantification of the force chain statistics requires an objective description of what constitutes a force chain. A procedure to quantify the occurrence of force chains is built on a proposed definition having two parts: first, the chain is a quasilinear arrangement of three or more particles, and second, along the chain, stress concentration within each grain is characterized by the vector delineating the most compressive principal stress. The procedure is incorporated into an algorithm that can be applied to large particle assemblies to compile force chain statistics. The procedure is demonstrated on a discrete element simulation of a rigid punch into a half space. It was found that only approximately half of the particles within the group of so-called strong network particles are part of force chains. Throughout deformation, the average length of force chains varied slightly but the number of force chains decreased as the punch advanced. The force chain lengths follow an exponential distribution. The procedure provides a tool for objective analysis of force chains, although future work is required to incorporate branching of force chains into the analysis.
TL;DR: A contact model of a blunted pyramidal tip indenting an elastic half-space is developed and the suitability of pyramides tips for probing mechanical properties of soft gels and living cells is assessed.
Abstract: Atomic force microscopy (AFM) allows the acquisition of high-resolution images and the measurement of mechanical properties of living cells under physiological conditions. AFM cantilevers with blunted pyramidal tips are commonly used to obtain images of living cells. Measurement of mechanical properties with these tips requires a contact model that takes into account their blunted geometry. The aim of this work was to develop a contact model of a blunted pyramidal tip and to assess the suitability of pyramidal tips for probing mechanical properties of soft gels and living cells. We developed a contact model of a blunted pyramidal tip indenting an elastic half-space. We measured Young's modulus (E) and the complex shear modulus (G*= G' +i G" ) of agarose gels and A549 alveolar epithelial cells with pyramidal tips and compared them with those obtained with spherical tips. The gels exhibited an elastic behavior with almost coincident loading and unloading force curves and negligible values of G". E fell sharply with indentation up to approximately 300 nm , showing a linear regime for deeper indentations. A similar indentation dependence of E with twofold lower values at the linear regime was obtained with the spherical tip fitted with Hertz's model. The dependence of E on indentation in cells paralleled that found in gels. Cells exhibited viscoelastic behavior with G"/G' approximately 1/4 . Pyramidal tips commonly used for AFM imaging are suitable for probing mechanical properties of soft gels and living cells.
TL;DR: The requirement of stability despite the destabilizing effect of pressure yields a lower bound on the number of extra contact per particle deltaz:deltaz> or =p1/2, which generalizes the Maxwell criterion for rigidity when pressure is present.
Abstract: Glasses have a large excess of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature is a necessary consequence of the weak connectivity of the solid, and that the frequency of modes in excess is very sensitive to the pressure. We analyze, in particular, two systems whose density $D(\ensuremath{\omega})$ of vibrational modes of angular frequency $\ensuremath{\omega}$ display scaling behaviors with the packing fraction: (i) simulations of jammed packings of particles interacting through finite-range, purely repulsive potentials, comprised of weakly compressed spheres at zero temperature and (ii) a system with the same network of contacts, but where the force between any particles in contact (and therefore the total pressure) is set to zero. We account in the two cases for the observed (a) convergence of $D(\ensuremath{\omega})$ toward a nonzero constant as $\ensuremath{\omega}\ensuremath{\rightarrow}0$, (b) appearance of a low-frequency cutoff ${\ensuremath{\omega}}^{*}$, and (c) power-law increase of ${\ensuremath{\omega}}^{*}$ with compression. Differences between these two systems occur at a lower frequency. The density of states of the modified system displays an abrupt plateau that appears at ${\ensuremath{\omega}}^{*}$, below which we expect the system to behave as a normal, continuous, elastic body. In the unmodified system, the pressure lowers the frequency of the modes in excess. The requirement of stability despite the destabilizing effect of pressure yields a lower bound on the number of extra contact per particle $\ensuremath{\delta}z:\ensuremath{\delta}z\ensuremath{\geqslant}{p}^{1∕2}$, which generalizes the Maxwell criterion for rigidity when pressure is present. This scaling behavior is observed in the simulations. We finally discuss how the cooling procedure can affect the microscopic structure and the density of normal modes.
TL;DR: It has been demonstrated that the electric field in the streamer head is hardly affected by the pressure decrease, while the electron concentration decreases with pressure by an order of magnitude.
Abstract: The results are given of an experimental investigation of a cathode-directed streamer discharge in synthetic air in the pressure range from 760 to 300 torr and their comparison with the results of direct numerical simulation in a 2D hydrodynamic approximation. The pattern of discharge branching upon variation of pressure is investigated experimentally. The results are given of comparison of the predicted and measured values of anode current, streamer propagation velocity, and channel diameter. It has been demonstrated that the electric field in the streamer head is hardly affected by the pressure decrease, while the electron concentration decreases with pressure by an order of magnitude. At the same time, production of chemical species in a cathode-directed streamer discharge varies at a rate of at least the second power of inverse pressure.
TL;DR: A method of community detection that is computationally inexpensive and possesses physical significance to a member of a social network is proposed and is local in the sense that a community can be detected within a network without requiring knowledge of the entire network.
Abstract: We propose a method of community detection that is computationally inexpensive and possesses physical significance to a member of a social network. This method is unlike many divisive and agglomerative techniques and is local in the sense that a community can be detected within a network without requiring knowledge of the entire network. A global application of this method is also introduced. Several artificial and real-world networks, including the famous Zachary karate club, are analyzed.
TL;DR: This study is the largest and the most accurate empirical analysis of disordered packings at the grain-scale to date, mapping over 380,000 sphere coordinates with precision within 0.1% of the sphere diameters.
Abstract: The three-dimensional structure of large packings of monosized spheres with volume fractions ranging between 0.58 and 0.64 has been studied with x-ray computed tomography. We search for signatures of organization, classifying local arrangements and exploring the effects of local geometrical constrains on the global packing. This study is the largest and the most accurate empirical analysis of disordered packings at the grain-scale to date, mapping over 380,000 sphere coordinates with precision within 0.1% of the sphere diameters. We discuss topological and geometrical methods to characterize and classify these systems emphasizing the implications that local geometry can have on the mechanisms of formation of these amorphous structures. Some of the main results are (1) the observation that the average number of contacts increases with the volume fraction; (2) the discovery that these systems have a very compact contact network; (3) the finding that disordered packing can be locally more efficient than crystalline packings; (4) the observation that the peaks of the radial distribution function follow power law divergences; (5) the discovery that geometrical frustration plays no role in the formation of such amorphous packings.
TL;DR: It is shown how the network adaptation dynamics favors the emergence of cooperators with the highest payoff, and these "leaders" are shown to sustain the global cooperative steady state.
Abstract: Cooperative behavior among a group of agents is studied assuming adaptive interactions. Each agent plays a Prisoner's Dilemma game with its local neighbors, collects an aggregate payoff, and imitates the strategy of its best neighbor. Agents may punish or reward their neighbors by removing or sustaining the interactions, according to their satisfaction level and strategy played. An agent may dismiss an interaction, and the corresponding neighbor is replaced by another randomly chosen agent, introducing diversity and evolution to the network structure. We perform an extensive numerical and analytical study, extending results in M. G. Zimmermann, V. M. Eguiluz, and M. San Miguel, Phys. Rev. E 69, 065102(R) (2004). We show that the system typically reaches either a full-defective state or a highly cooperative steady state. The latter equilibrium solution is composed mostly by cooperative agents, with a minor population of defectors that exploit the cooperators. It is shown how the network adaptation dynamics favors the emergence of cooperators with the highest payoff. These "leaders" are shown to sustain the global cooperative steady state. Also we find that the average payoff of defectors is larger than the average payoff of cooperators. Whenever "leaders" are perturbed (e.g., by addition of noise), an unstable situation arises and global cascades with oscillations between the nearly full defection network and the fully cooperative outcome are observed.
TL;DR: A three-dimensional network model is presented to simulate two- and three-phase capillary dominated processes at the pore level based on the physics of multiphase flow observed in micromodel experiments.
Abstract: We present a three-dimensional network model to simulate two- and three-phase capillary dominated processes at the pore level. The displacement mechanisms incorporated in the model are based on the physics of multiphase flow observed in micromodel experiments. All the important features of immiscible fluid flow at the pore scale, such as wetting layers, spreading layers of the intermediate-wet phase, hysteresis, and wettability alteration are implemented in the model. Wettability alteration allows any values for the advancing and receding oil-water, gas-water, and gas-oil contact angles to be assigned. Multiple phases can be present in each pore or throat (element), in wetting and spreading layers, as well as occupying the center of the pore space. In all, some 30 different generic fluid configurations for two- and three-phase flow are analyzed. Double displacement and layer formation are implemented as well as direct two-phase displacement and layer collapse events. Every element has a circular, square, or triangular cross section. A random network that represents the pore space in Berea sandstone is used in this study. The model computes relative permeabilities, saturation paths, and capillary pressures for any displacement sequence. A methodology to track a given three-phase saturation path is presented that enables us to compare predicted and measured relative permeabilities on a point-by-point basis. A robust displacement-based clustering algorithm is also presented.
TL;DR: A three-dimensional simulator is developed to show the capability of the model to describe phase transitions, complex microstructure formation, and grain growth in polycrystalline textures.
Abstract: A general formulation of phase-field models for nonisothermal solidification in multicomponent and multiphase alloy systems is derived from an entropy functional in a thermodynamically consistent way. General expressions for the free energy densities, for multicomponent diffusion coefficients, and for both weak and faceted types of surface energy and kinetic anisotropy are possible. A three-dimensional simulator is developed to show the capability of the model to describe phase transitions, complex microstructure formation, and grain growth in polycrystalline textures.