# Showing papers in "Physical Review E in 2003"

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TL;DR: This work proposes a number of measures of assortative mixing appropriate to the various mixing types, and applies them to a variety of real-world networks, showing that assortsative mixing is a pervasive phenomenon found in many networks.

Abstract: We study assortative mixing in networks, the tendency for vertices in networks to be connected to other vertices that are like (or unlike) them in some way. We consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age. As a special example of the latter we consider mixing according to vertex degree, i.e., according to the number of connections vertices have to other vertices: do gregarious people tend to associate with other gregarious people? We propose a number of measures of assortative mixing appropriate to the various mixing types, and apply them to a variety of real-world networks, showing that assortative mixing is a pervasive phenomenon found in many networks. We also propose several models of assortatively mixed networks, both analytic ones based on generating function methods, and numerical ones based on Monte Carlo graph generation techniques. We use these models to probe the properties of networks as their level of assortativity is varied. In the particular case of mixing by degree, we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices.

2,588 citations

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TL;DR: In this article, the authors show that many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering, implying that small groups of nodes organize in a hierarchical manner into increasingly large groups, while maintaining a scale free topology.

Abstract: Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering We show that these two features are the consequence of a hierarchical organization, implying that small groups of nodes organize in a hierarchical manner into increasingly large groups, while maintaining a scale-free topology In hierarchical networks, the degree of clustering characterizing the different groups follows a strict scaling law, which can be used to identify the presence of a hierarchical organization in real networks We find that several real networks, such as the Worldwideweb, actor network, the Internet at the domain level, and the semantic web obey this scaling law, indicating that hierarchy is a fundamental characteristic of many complex systems

1,894 citations

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TL;DR: It is demonstrated that group structure in networks can also account for degree correlations and that the predicted level of assortative mixing compares well with that observed in real-world networks.

Abstract: We argue that social networks differ from most other types of networks, including technological and biological networks, in two important ways. First, they have nontrivial clustering or network transitivity and second, they show positive correlations, also called assortative mixing, between the degrees of adjacent vertices. Social networks are often divided into groups or communities, and it has recently been suggested that this division could account for the observed clustering. We demonstrate that group structure in networks can also account for degree correlations. We show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real-world networks.

1,302 citations

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TL;DR: The results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam, and suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition.

Abstract: We have studied how two- and three-dimensional systems made up of particles interacting with finite range, repulsive potentials jam (ie, develop a yield stress in a disordered state) at zero temperature and zero applied stress At low packing fractions phi, the system is not jammed and each particle can move without impediment from its neighbors For each configuration, there is a unique jamming threshold phi(c) at which particles can no longer avoid each other, and the bulk and shear moduli simultaneously become nonzero The distribution of phi(c) values becomes narrower as the system size increases, so that essentially all configurations jam at the same packing fraction in the thermodynamic limit This packing fraction corresponds to the previously measured value for random close packing In fact, our results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam The jamming threshold, point J, occurring at zero temperature and applied stress and at the random-close-packing density, has properties reminiscent of an ordinary critical point As point J is approached from higher packing fractions, power-law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure, shear modulus, and excess number of overlapping neighbors Moreover, near point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J However, point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential Finally, as point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes Indeed, at point J, the density of states is a constant all the way down to zero frequency All of these results suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition

1,266 citations

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TL;DR: The results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar, suggesting that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.

Abstract: We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.

1,250 citations

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TL;DR: The time dependence of the recently introduced minimum spanning tree description of correlations between stocks, called the "asset tree", has been studied in order to reflect the financial market taxonomy and the basic structure of the tree topology is very robust with respect to time.

Abstract: The time dependence of the recently introduced minimum spanning tree description of correlations between stocks, called the ‘‘asset tree’’ has been studied in order to reflect the financial market taxonomy. The nodes of the tree are identified with stocks and the distance between them is a unique function of the corresponding element of the correlation matrix. By using the concept of a central vertex, chosen as the most strongly connected node of the tree, an important characteristic is defined by the mean occupation layer. During crashes, due to the strong global correlation in the market, the tree shrinks topologically, and this is shown by a low value of the mean occupation layer . The tree seems to have a scale-free structure where the scaling exponent of the degree distribution is different for ‘‘business as usual’’ and ‘‘crash’’ periods. The basic structure of the tree topology is very robust with respect to time. We also point out that the diversification aspect of portfolio optimization results in the fact that the assets of the classic Markowitz portfolio are always located on the outer leaves of the tree. Technical aspects such as the window size dependence of the investigated quantities are also discussed.

641 citations

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TL;DR: It is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules and that the local models offer an explanation for other properties like the clustering hierarchy and degree correlations recently observed in complex networks.

Abstract: The linear preferential attachment hypothesis has been shown to be quite successful in explaining the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a general principle based on local rules. In this work it is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules. It is also shown that the local models offer an explanation for other properties like the clustering hierarchy and degree correlations recently observed in complex networks. These conclusions are based on both analytical and numerical results for different local rules, including some models already proposed in the literature.

596 citations

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TL;DR: This network displays the typical properties of complex networks, namely, scale-free degree distribution, the small-world property, a high clustering coefficient, and, in addition, degree-degree correlation between different vertices.

Abstract: Economy, and consequently trade, is a fundamental part of human social organization which, until now, has not been studied within the network modeling framework. Here we present the first, to the best of our knowledge, empirical characterization of the world trade web, that is, the network built upon the trade relationships between different countries in the world. This network displays the typical properties of complex networks, namely, scale-free degree distribution, the small-world property, a high clustering coefficient, and, in addition, degree-degree correlation between different vertices. All these properties make the world trade web a complex network, which is far from being well described through a classical random network description.

515 citations

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TL;DR: Rigorous analysis of the existing data shows that the Indian railway network displays small-world properties and several other quantities associated with this network are defined and estimated.

Abstract: Structural properties of the Indian railway network is studied in the light of recent investigations of the scaling properties of different complex networks. Stations are considered as "nodes" and an arbitrary pair of stations is said to be connected by a "link" when at least one train stops at both stations. Rigorous analysis of the existing data shows that the Indian railway network displays small-world properties. We define and estimate several other quantities associated with this network.

507 citations

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TL;DR: A semiclassical Dicke model is derived that exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos, and it is demonstrated that the system undergoes a transition from quasi-integrability to quantum chaotic.

Abstract: We investigate the quantum-chaotic properties of the Dicke Hamiltonian; a quantum-optical model that describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. This model exhibits a zero-temperature quantum phase transition in the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite N, and by analyzing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase transition. Our considerations of the wave function indicate that this is connected with a delocalization of the system and the emergence of macroscopic coherence. We also derive a semiclassical Dicke model that exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.

505 citations

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TL;DR: The purpose of this paper is to characterize certain fundamental aspects of local density fluctuations associated with general point patterns in any space dimension d, and to study the variance in the number of points contained within a regularly shaped window of arbitrary size to further illuminate the understanding of hyperuniform systems.

Abstract: Questions concerning the properties and quantification of density fluctuations in point patterns continue to provide many theoretical challenges. The purpose of this paper is to characterize certain fundamental aspects of local density fluctuations associated with general point patterns in any space dimension $d.$ Our specific objectives are to study the variance in the number of points contained within a regularly shaped window $\ensuremath{\Omega}$ of arbitrary size, and to further illuminate our understanding of hyperuniform systems, i.e., point patterns that do not possess infinite-wavelength fluctuations. For large windows, hyperuniform systems are characterized by a local variance that grows only as the surface area (rather than the volume) of the window. We derive two formulations for the number variance: (i) an ensemble-average formulation, which is valid for statistically homogeneous systems, and (ii) a volume-average formulation, applicable to a single realization of a general point pattern in the large-system limit. The ensemble-average formulation (which includes both real-space and Fourier representations) enables us to show that a homogeneous point pattern in a hyperuniform state is at a ``critical point'' of a type with appropriate scaling laws and critical exponents, but one in which the direct correlation function (rather than the pair correlation function) is long ranged. We also prove that the non-negativity of the local number variance does not add a new realizability condition on the pair correlation. The volume-average formulation is superior for certain computational purposes, including optimization studies in which it is desired to find the particular point pattern with an extremal or targeted value of the variance. We prove that the simple periodic linear array yields the global minimum value of the average variance among all infinite one-dimensional hyperuniform patterns. We also evaluate the variance for common infinite periodic lattices as well as certain nonperiodic point patterns in one, two, and three dimensions for spherical windows, enabling us to rank-order the spatial patterns. Our results suggest that the local variance may serve as a useful order metric for general point patterns. Contrary to the conjecture that the lattices associated with the densest packing of congruent spheres have the smallest variance regardless of the space dimension, we show that for $d=3,$ the body-centered cubic lattice has a smaller variance than the face-centered cubic lattice. Finally, for certain hyperuniform disordered point patterns, we evaluate the direct correlation function, structure factor, and associated critical exponents exactly.

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TL;DR: A general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations is presented, to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy.

Abstract: We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder.

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TL;DR: The results indicate that increased clustering leads to a decrease in the size of the giant component of the network, and clustering causes epidemics to saturate sooner, meaning that they infect a near-maximal fraction of thenetwork for quite low transmission rates.

Abstract: We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the giant component of the network. We also study susceptible/infective/recovered type epidemic processes within the model and find that clustering decreases the size of epidemics, but also decreases the epidemic threshold, making it easier for diseases to spread. In addition, clustering causes epidemics to saturate sooner, meaning that they infect a near-maximal fraction of the network for quite low transmission rates.

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TL;DR: A recently introduced cellular automaton model for pedestrian dynamics is extended by a friction parameter mu, which controls the probability that the movement of all particles involved in a conflict is denied at one time step.

Abstract: We investigate the role of conflicts in pedestrian traffic, i.e., situations where two or more people try to enter the same space. Therefore a recently introduced cellular automaton model for pedestrian dynamics is extended by a friction parameter mu. This parameter controls the probability that the movement of all particles involved in a conflict is denied at one time step. It is shown that these conflicts are not an undesirable artifact of the parallel update scheme, but are important for a correct description of the dynamics. The friction parameter mu can be interpreted as a kind of an internal local pressure between the pedestrians which becomes important in regions of high density, occurring, e.g., in panic situations. We present simulations of the evacuation of a large room with one door. It is found that friction has not only quantitative effects, but can also lead to qualitative changes, e.g., of the dependence of the evacuation time on the system parameters. We also observe similarities to the flow of granular materials, e.g., arching effects.

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TL;DR: A fluid particle model that is both a thermodynamically consistent version of smoothed particle hydrodynamics (SPH) and a version of dissipative particle dynamics (DPD), capturing the best of both methods is presented.

Abstract: We present a fluid particle model that is both a thermodynamically consistent version of smoothed particle hydrodynamics (SPH) and a version of dissipative particle dynamics (DPD), capturing the best of both methods. The model is a discrete version of Navier-Stokes equations, like SPH, and includes thermal fluctuations, like DPD. This model solves some problems with the physical interpretation of the original DPD model.

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TL;DR: A numerical study of the electromagnetic response of the metamaterial elements that are used to construct materials with negative refractive index finds that the resonant behavior of the effective magnetic permeability is accompanied by an antiresonant behavior by an array of split ring resonators.

Abstract: We present a numerical study of the electromagnetic response of the metamaterial elements that are used to construct materials with negative refractive index. For an array of split ring resonators (SRR) we find that the resonant behavior of the effective magnetic permeability is accompanied by an antiresonant behavior of the effective permittivity. In addition, the imaginary parts of the effective permittivity and permeability are opposite in sign. We also observe an identical resonant versus antiresonant frequency dependence of the effective materials parameters for a periodic array of thin metallic wires with cuts placed periodically along the length of the wire, with roles of the permittivity and permeability reversed from the SRR case. We show in a simple manner that the finite unit cell size is responsible for the antiresonant behavior.

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TL;DR: A simulation technique for creating dense random packings of hard particles is introduced, particularly suited to handle particles of different shapes, and Comparisons between the equilibrium phase diagram for hard spherocylinders and the densest possible amorphous packings have interesting implications on the crystallization of sphero cylinders as a function of aspect ratio.

Abstract: We introduce a simulation technique for creating dense random packings of hard particles. The technique is particularly suited to handle particles of different shapes. Dense amorphous packings of spheres have been formed, which are consistent with the existing work on random sphere packings. Packings of spherocylinders have also been simulated out to the large aspect ratio of alpha=160.0. Our method packs randomly oriented spherocylinders to densities that reproduce experimental results on anisotropic powders and colloids very well. Interestingly, the highest packing density of phi=0.70 is achieved for very short spherocylinders rather than spheres. This suggests that slightly changing the shapes of the particles forming a hard sphere glass could cause it to melt. Comparisons between the equilibrium phase diagram for hard spherocylinders and the densest possible amorphous packings have interesting implications on the crystallization of spherocylinders as a function of aspect ratio.

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TL;DR: This work has examined software collaboration graphs contained within several open-source software systems, and found them to reveal scale-free, small-world networks similar to those identified in other technological, sociological, and biological systems.

Abstract: Software systems emerge from mere keystrokes to form intricate functional networks connecting many collaborating modules, objects, classes, methods, and subroutines. Building on recent advances in the study of complex networks, I have examined software collaboration graphs contained within several open-source software systems, and have found them to reveal scale-free, small-world networks similar to those identified in other technological, sociological, and biological systems. I present several measures of these network topologies, and discuss their relationship to software engineering practices. I also present a simple model of software system evolution based on refactoring processes which captures some of the salient features of the observed systems. Some implications of object-oriented design for questions about network robustness, evolvability, degeneracy, and organization are discussed in the wake of these findings.

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TL;DR: It is shown analytically that for noisy expression data the proposed approach leads to better classification due to the implementation of the threshold, and argues that the method is in fact a generalization of singular value decomposition, which corresponds to the special case where no threshold is applied.

Abstract: We present an approach for the analysis of genome-wide expression data. Our method is designed to overcome the limitations of traditional techniques, when applied to large-scale data. Rather than alloting each gene to a single cluster, we assign both genes and conditions to context-dependent and potentially overlapping transcription modules. We provide a rigorous definition of a transcription module as the object to be retrieved from the expression data. An efficient algorithm, which searches for the modules encoded in the data by iteratively refining sets of genes and conditions until they match this definition, is established. Each iteration involves a linear map, induced by the normalized expression matrix, followed by the application of a threshold function. We argue that our method is in fact a generalization of singular value decomposition, which corresponds to the special case where no threshold is applied. We show analytically that for noisy expression data our approach leads to better classification due to the implementation of the threshold. This result is confirmed by numerical analyses based on in silico expression data. We discuss briefly results obtained by applying our algorithm to expression data from the yeast Saccharomyces cerevisiae.

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TL;DR: It is shown that the HTLBE scheme is far superior to the existing thermal LBE schemes in terms of numerical stability, flexibility, and possible generalization for complex fluids.

Abstract: The focus of the present work is to provide an analysis for the acoustic and thermal properties of the energy-conserving lattice Boltzmann models, and a solution to the numerical defects and instability associated with these models in two and three dimensions. We discover that a spurious algebraic coupling between the shear and energy modes of the linearized evolution operator is a defect universal to the energy-conserving Boltzmann models in two and three dimensions. This spurious mode coupling is highly anisotropic and may occur at small values of wave number k along certain directions, and it is a direct consequence of the following key features of the lattice Boltzmann equation: (1) its simple spatial-temporal dynamics, (2) the linearity of the relaxation modeling for collision operator, and (3) the energy-conservation constraint. To eliminate the spurious mode coupling, we propose a hybrid thermal lattice Boltzmann equation (HTLBE) in which the mass and momentum conservation equations are solved by using the multiple-relaxation-time model due to d'Humieres, whereas the diffusion-advection equation for the temperature is solved separately by using finite-difference technique (or other means). Through the Chapman-Enskog analysis we show that the hydrodynamic equations derived from the proposed HTLBE model include the equivalent effect of gamma=C(P)/C(V) in both the speed and attenuation of sound. Appropriate coupling between the energy and velocity field is introduced to attain correct acoustics in the model. The numerical stability of the HTLBE scheme is analyzed by solving the dispersion equation of the linearized collision operator. We find that the numerical stability of the lattice Boltzmann scheme improves drastically once the spurious mode coupling is removed. It is shown that the HTLBE scheme is far superior to the existing thermal LBE schemes in terms of numerical stability, flexibility, and possible generalization for complex fluids. We also present the simulation results of the convective flow in a rectangular cavity with different temperatures on two opposite vertical walls and under the influence of gravity. Our numerical results agree well with the pseudospectral result.

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TL;DR: The empirical tree obtained from a large group of stocks traded at the New York Stock Exchange during a 12-year trading period is found to have features of a complex network that cannot be reproduced by a random market model and by the widespread one-factor model.

Abstract: We compare the topological properties of the minimal spanning tree obtained from a large group of stocks traded at the New York Stock Exchange during a 12-year trading period with the one obtained from surrogated data simulated by using simple market models. We find that the empirical tree has features of a complex network that cannot be reproduced, even as a first approximation, by a random market model and by the widespread one-factor model.

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TL;DR: The general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure and an extension is presented, to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.

Abstract: We study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure. We also present an extension of the class, to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.

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TL;DR: A statistical ensemble method is used to study the behavior of sloppy model parameter fluctuations by various spectral decompositions and it is found that model entropy is as important to the problem of model choice as model energy is to parameter choice.

Abstract: Models of biochemical regulation in prokaryotes and eukaryotes, typically consisting of a set of first-order nonlinear ordinary differential equations, have become increasingly popular of late. These systems have large numbers of poorly known parameters, simplified dynamics, and uncertain connectivity: three key features of a class of problems we call sloppy models, which are shared by many other high-dimensional multiparameter nonlinear models. We use a statistical ensemble method to study the behavior of these models, in order to extract as much useful predictive information as possible from a sloppy model, given the available data used to constrain it. We discuss numerical challenges that emerge in using the ensemble method for a large system. We characterize features of sloppy model parameter fluctuations by various spectral decompositions and find indeed that five parameters can be used to fit an elephant. We also find that model entropy is as important to the problem of model choice as model energy is to parameter choice.

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TL;DR: D dissipative particle dynamics is discussed as a thermostat to molecular dynamics, and some of its virtues are highlighted, including universal applicability irrespective of the interatomic potential.

Abstract: We discuss dissipative particle dynamics as a thermostat to molecular dynamics, and highlight some of its virtues: (i) universal applicability irrespective of the interatomic potential; (ii) correct and unscreened reproduction of hydrodynamic correlations; (iii) stabilization of the numerical integration of the equations of motion; and (iv) the avoidance of a profile bias in boundary-driven nonequilibrium simulations of shear flow. Numerical results on a repulsive Lennard-Jones fluid illustrate our arguments.

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TL;DR: It is shown that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals.

Abstract: We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one-parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl-von Karman number gamma=YR(2)/kappa, where Y is the two-dimensional Young's modulus of the protein shell, kappa is its bending rigidity, and R is the mean virus radius. The shape can be parametrized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large gamma, 10(3)

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TL;DR: An optical bi-stable switch includes a photonic crystal cavity structure, which is used to characterize a bi-stable switch so that optimal control is provided over input and output of the switch as mentioned in this paper.

Abstract: An optical bi-stable switch includes a photonic crystal cavity structure using its photonic crystal properties to characterize a bi-stable switch so that optimal control is provided over input and output of the switch. A plurality of waveguide structures are included, at least one of the waveguide structures providing the input to the switch and at least one providing the output to the switch.

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TL;DR: Numerical experiments showed that the simplified thermal model can keep the same order of accuracy as the thermal energy distribution model, but it requires much less computational effort.

Abstract: Considering the fact that the compression work done by the pressure and the viscous heat dissipation can be neglected for the incompressible flow, and its relationship with the gradient term in the evolution equation for the temperature in the thermal energy distribution model, a simplified thermal energy distribution model is proposed. This thermal model does not have any gradient term and is much easier to be implemented. This model is validated by the numerical simulation of the natural convection in a square cavity at a wide range of Rayleigh numbers. Numerical experiments showed that the simplified thermal model can keep the same order of accuracy as the thermal energy distribution model, but it requires much less computational effort.

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Harvard University

^{1}, Dalhousie University^{2}, University of Toronto^{3}, University of Barcelona^{4}TL;DR: These findings define an unanticipated integrative framework for studying protein interactions within the complex microenvironment of the cell body, and appear to set limits on what can be predicted about integrated mechanical behavior of the matrix based solely on cytoskeletal constituents considered in isolation.

Abstract: In dealing with systems as complex as the cytoskeleton, we need organizing principles or, short of that, an empirical framework into which these systems fit. We report here unexpected invariants of cytoskeletal behavior that comprise such an empirical framework. We measured elastic and frictional moduli of a variety of cell types over a wide range of time scales and using a variety of biological interventions. In all instances elastic stresses dominated at frequencies below 300 Hz, increased only weakly with frequency, and followed a power law; no characteristic time scale was evident. Frictional stresses paralleled the elastic behavior at frequencies below 10 Hz but approached a Newtonian viscous behavior at higher frequencies. Surprisingly, all data could be collapsed onto master curves, the existence of which implies that elastic and frictional stresses share a common underlying mechanism. Taken together, these findings define an unanticipated integrative framework for studying protein interactions within the complex microenvironment of the cell body, and appear to set limits on what can be predicted about integrated mechanical behavior of the matrix based solely on cytoskeletal constituents considered in isolation. Moreover, these observations are consistent with the hypothesis that the cytoskeleton of the living cell behaves as a soft glassy material, wherein cytoskeletal proteins modulate cell mechanical properties mainly by changing an effective temperature of the cytoskeletal matrix. If so, then the effective temperature becomes an easily quantified determinant of the ability of the cytoskeleton to deform, flow, and reorganize.

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TL;DR: The well studied totally asymmetric exclusion process, in which particles typically cover a single lattice site, is expanded to include cases with extended objects, and an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase.

Abstract: The process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent, covering more than one lattice site. We expand the well studied totally asymmetric exclusion process, in which particles typically cover a single lattice site, to include cases with extended objects. Exact solutions can be determined for a uniform closed system. We analyze the uniform open system through two approaches. First, a continuum limit produces a modified diffusion equation for particle density profiles. Second, an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase. Finally, we briefly consider approximate approaches to a nonuniform open system with quenched disorder in the particle hopping rates and compare these approaches with Monte Carlo simulations.