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The spatiotemporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatiotemporal patterns arising from the cyclic competition between three species in two dimensions. Inspired by recent experiments, we consider a generic metapopulation model comprising "rock-paper-scissors" interactions via dominance removal and replacement, reproduction, mutations, pair exchange, and hopping of individuals. By combining analytical and numerical methods, we obtain the model's phase diagram near its Hopf bifurcation and quantitatively characterize the properties of the spiraling patterns arising in each phase. The phases characterizing the cyclic competition away from the Hopf bifurcation (at low mutation rate) are also investigated. Our analytical approach relies on the careful analysis of the properties of the complex Ginzburg-Landau equation derived through a controlled (perturbative) multiscale expansion around the model's Hopf bifurcation. Our results allow us to clarify when spatial "rock-paper-scissors" competition leads to stable spiral waves and under which circumstances they are influenced by nonlinear mobility. [ABSTRACT FROM AUTHOR]

We investigate the population dynamics in generalized rock-paper-scissors models with an arbitrary number of species Ν. We show that spiral patterns with Ν arms may develop both for odd and even N, in particular in models where a bidirectional prédation interaction of equal strength between all species is modified to include one -cyclic predator-prey rule. While the former case gives rise to an interface network with Y-type junctions obeying the scaling law L ∝ t1/2, where L is the characteristic length of the network and t is the time, the latter can lead to a population network with N-armed spiral patterns, having a roughly constant characteristic length scale. We explicitly demonstrate the connection between interface junctions and spiral patterns in these models and compute the corresponding scaling laws. This work significantly extends the results of previous studies of population dynamics and could have profound implications for the understanding of biological complexity in systems with a large number of species. [ABSTRACT FROM AUTHOR]

We introduce a family of rock-paper-scissors-type models with ZN symmetry (N is the number of species), and we show that it has a very rich structure with many completely different phases. We study realizations that lead to the formation of domains, where individuals of one or more species coexist, separated by interfaces whose (average) dynamics is curvature driven. This type of behavior, which might be relevant for the development of biological complexity, leads to an interface network evolution and pattern formation similar to the ones of several other nonlinear systems in condensed matter and cosmology. [ABSTRACT FROM AUTHOR]

We study the static and dynamic properties of networks of crumpled creases formed in hand crushed sheets of paper. The fractal dimensionalities of crumpling networks in the unfolded (flat) and folded configurations are determined. Some other noteworthy features of crumpling networks are established. The physical implications of these findings are discussed. Specifically, we state that self-avoiding interactions introduce a characteristic length scale of sheet crumpling. A framework to model the crumpling phenomena is suggested. Mechanics of sheet crushing under external confinement is developed. The effect of compaction geometry on the crushing mechanics is revealed. [ABSTRACT FROM AUTHOR]

The two-dimensional optimal velocity model has potential applications to pedestrian dynamics and the collective motion of animals. In this paper, we extend the linear stability analysis presented in a previous paper [A Nakayama et al., Phys. Rev. E. 77, 016105 (2008)] and investigate the effects of particle configuration on the stability of several wave modes of collective oscillations of moving particles. We find that, when a particle moves without interacting with particles that are positioned in a diagonally forward or backward direction, the stable region of the particle flow is completely removed by the elliptically polarized mode. [ABSTRACT FROM AUTHOR]

Can one hear the shape of a graph? This is a modification of the famous question of Mark Kac "Can one hear the shape of a drum?" which can be asked in the case of scattering systems such as quantum graphs and microwave networks. It addresses an important mathematical problem whether scattering properties of such systems are uniquely connected to their shapes? Recent experimental results based on a characteristics of graphs such as the cumulative phase of the determinant of the scattering matrices indicate a negative answer to this question [O. Hul, M. Lawniczak, S. Bauch, A. Sawicki, M. Kus, and L. Sirko, Phys. Rev. Lett. 109, 040402 (2012)]. In this paper we consider important local characteristics of graphs such as structures of resonances and poles of the determinant of the scattering matrices. Using these characteristics we study experimentally and theoretically properties of graphs and directly confirm that the pair of graphs considered in the cited paper is isoscattering. The experimental results are compared to the theoretical ones for a broad frequency range from 0.01 to 3 GHz. In the numerical calculations of the resonances of the graphs absorption present in the experimental networks is taken into account. [ABSTRACT FROM AUTHOR]

In two recent papers [Phys. Rev. E 85, 025302(R) (2012) and Phys. Rev. E 85, 056314 (2012)], the authors proposed fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. While in general providing a certain advancement of continuum mechanics modeling of fractal media to fluid flows, some results and statements to previous works need clarification. We first show that the nonlocal character those authors alleged in our paper [Proc. R. Soc. A 465,2521 (2009)] actually does not exist; instead, all those works are in the same general representation of derivative operators differing by specific forms of the line coefficient C|. Next, the claimed generalization of the volumetric coefficient c3 is, in fact, equivalent to previously proposed product measures when considering together the separate decomposition of C3 on each coordinate. Furthermore, the modified Jacobian proposed in the two commented papers does not relate the volume element between the current and initial configurations, which henceforth leads to a correction of the Reynolds' transport theorem. Finally, we point out that the asymmetry of the Cauchy stress tensor resulting from the conservation of the angular momentum must not be ignored; this aspect motivates a more complete formulation of fractal continuum models within a micropolar framework. [ABSTRACT FROM AUTHOR]

Crumpling and folding of paper are at first sight very different ways of confining thin sheets in a small volume: the former one is random and stochastic whereas the latest one is regular and deterministic. Nevertheless, certain similarities exist. Crumpling is surprisingly inefficient: a typical crumpled paper ball in a waste-bin consists of as much as 80% air. Similarly, if one folds a sheet of paper repeatedly in two, the necessary force becomes so large that it is impossible to fold it more than six or seven times. Here we show that the stiffness that builds up in the two processes is of the same nature, and therefore simple folding models allow us to capture also the main features of crumpling. An original geometrical approach shows that crumpling is hierarchical, just as the repeated folding. For both processes the number of layers increases with the degree of compaction. We find that for both processes the crumpling force increases as a power law with the number of folded layers, and that the dimensionality of the compaction process (crumpling or folding) controls the exponent of the scaling law between the force and the compaction ratio. [ABSTRACT FROM AUTHOR]

Many complex networks from the World Wide Web to biological networks grow taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document such as personal page, thematic website, news, blog, search engine, social network, etc., or the classification of a gene in a functional module. Moreover the feature of a node can be a continuous variable such as the position of a node in the embedding space. In order to account for these properties, in this paper we provide a generalization of growing network models with preferential attachment that includes the effect of heterogeneous features of the nodes. The main effect of heterogeneity is the emergence of an "effective fitness" for each class of nodes, determining the rate at which nodes acquire new links. The degree distribution exhibits a multiscaling behavior analogous to the the fitness model. This property is robust with respect to variations in the model, as long as links are assigned through effective preferential attachment. Beyond the degree distribution, in this paper we give a full characterization of the other relevant properties of the model. We evaluate the clustering coefficient and show that it disappears for large network size, a property shared with the Barabási-Albert model. Negative degree correlations are also present in this class of models, along with nontrivial mixing patterns among features. We therefore conclude that both small clustering coefficients and disassortative mixing are outcomes of the preferential attachment mechanism in general growing networks. [ABSTRACT FROM AUTHOR]

Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We theoretically study the queuing model of an agent trying to execute a task of interest, the priority of which may vary with time due to the agent's "state of mind." However, its execution is disrupted by other tasks of random priorities. By considering the priority of the task of interest either decreasing or increasing algebraically in time, we analytically obtain and numerically confirm the bimodal and unimodal waiting time distributions with power-law decaying tails, respectively. These results are also compared to the updating time distribution of papers in arXiv.org and the processing time distribution of papers in Physical Review journals. Our analysis helps to understand human task execution in a more realistic scenario. [ABSTRACT FROM AUTHOR]

Weight distribution greatly impacts the epidemic spreading taking place on top of networks. This paper presents a study of a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation results show that the more homogeneous weight distribution leads to higher epidemic prevalence, which, unfortunately, could not be captured by the traditional mean-field approximation. This paper gives an edge-based mean-field solution for general weight distribution, which can quantitatively reproduce the simulation results. This method could be applied to characterize the nonequilibrium steady states of dynamical processes on weighted networks. [ABSTRACT FROM AUTHOR]

The propagation of the primary pulse through an uncompressed granular chain subject to external on-site perturbation is studied. An analytical procedure predicting the evolution of the primary pulse is devised for the general form of the on-site perturbation applied on the chain. The validity of the analytical model is confirmed with several specific granular setups, such as chains mounted on the nonlinear elastic foundation, chains perturbed by the dissipative forces, as well as randomly perturbed chains. An additional interesting finding made in the present paper corresponds to the chains subject to a special type of perturbation, including the terms leading to dissipation and those acting as an energy source. In the paper, it is shown that an application of such a perturbation may lead to the formation of stable stationary primary pulses propagating with constant amplitudes and acting as attractors for the initially unperturbed Nesterenko solitary waves. Interestingly enough, the developed analytical procedure provides an extremely close estimation for the amplitudes of these stationary primary pulses as well as predicts zones of their stability. In conclusion, we would like to stress that the developed analytical model has demonstrated spectacular agreement with the results of the direct numerical simulations, and this is for various configurations considered in the current paper. [ABSTRACT FROM AUTHOR]

Spiral waves subjected to an external periodic force exhibit very rich spatiotemporal dynamics including resonance attractors. In previous research, the modulation was mainly described as additional induced flow in the system, and a theory has been developed based on reducing the spiral wave dynamics to a low-dimensional map. In this paper, another perspective for study of the resonance attractors is suggested. The periodic modulation of excitability is directly described by the time dependence of the parameters. This approach gives us nice results that are well consistent with the experiments. Additionally, when we force the spiral with a frequency larger than its intrinsic frequency, another branch of spiral meandering with qualitatively different properties is observed. Full resonances are also clearly indicated. Furthermore, a kinetic model for spiral movement suggested in our previous paper is applied to this case. The theoretical results are in good quantitative agreement with numerical simulations. The model could be widely used in different excitable systems. [ABSTRACT FROM AUTHOR]

Many biological systems possess hierarchical and fractal-like interfaces and joint structures that bear and transmit loads, absorb energy, and accommodate growth, respiration, and/or locomotion. In this paper, an elastic deterministic fractal composite mechanical model was formulated to quantitatively investigate the role of structural hierarchy on the stiffness, strength, and failure of suture joints. From this model, it was revealed that the number of hierarchies (N) can be used to tailor and to amplify mechanical properties nonlinearly and with high sensitivity over a wide range of values (orders of magnitude) for a given volume and weight. Additionally, increasing hierarchy was found to result in mechanical interlocking of higher-order teeth, which creates additional load resistance capability, thereby preventing catastrophic failure in major teeth and providing flaw tolerance. Hence, this paper shows that the diversity of hierarchical and fractal-like interfaces and joints found in nature have definitive functional consequences and is an effective geometric-structural strategy to achieve different properties with limited material options in nature when other structural geometries and parameters are biologically challenging or inaccessible. This paper also indicates the use of hierarchy as a design strategy to increase design space and provides predictive capabilities to guide the mechanical design of synthetic flaw-tolerant bioinspired interfaces and joints. [ABSTRACT FROM AUTHOR]

It has been alleged in several papers that the so-called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since the telegraph equation describes phenomena with finite propagation speed, while the velocity of the motion of particles in the DCTRWs is infinite. In this paper we investigate the accuracy of the approximations to the DCTRWs provided by the telegraph equation. We show that the diffusion equation, being the correct limit of the DCTRWs, gives better approximations in L2 norm to the DCTRWs than the telegraph equation. We conclude, therefore, that first, the DCTRWs do not provide any correct microscopic interpretation of the one-dimensional telegraph equation, and second, the kinetic (exact) model of the telegraph equation is different from the model based on the DCTRWs. [ABSTRACT FROM AUTHOR]

This is the first part of a two-part study on the generation of droplets at a microfluidic T-junction operating in the transition regime where confinement of the droplet creates a large squeezing pressure that influences droplet formation. In this regime, the operation of the T-junction depends on the geometry of the intersection (height-to-width ratio, inlet width ratio), capillary number, flow ratio, and viscosity ratio of the two phases. Here in paper I we presented our experimental observations through the analysis of high-speed videos of the droplet formation process. Various parameters are tracked during the formation cycle such as the shape of the droplet (penetration depth and neck), interdroplet spacing, production rate, and flow of both phases across several T-junction designs and flow conditions. Generally, the formation process is defined by a two-stage model consisting of an initial filling stage followed by a necking stage. However, video evidence suggests the inclusion of a third stage, which we term the lag stage, at the beginning of the formation process that accounts for the retraction of the interface back into the injection channel after detachment. Based on the observations made in this paper, a model is developed to describe the formation process in paper II, which can be used to understand the design and operation of T-junction generators in the transition regime. [ABSTRACT FROM AUTHOR]

For two-phase flow in porous media, the natural medium heterogeneity necessarily gives rise to capillary nonequilibrium effects. The relaxation to the equilibrium is a slow process which should be introduced in macroscopic flow models. Many nonequilibrium models are based on a phenomenological approach. At the same time there exists a rigorous mathematical way to develop the nonequilibrium equations. Its formalism, developed by Bourgeat and Panfilov [Computational Geosciences 2, 191 (1998)], is based on the homogenization of the microscale flow equations over medium heterogeneities. In contrast with the mentioned paper, in which the case of a sufficiently fast relaxation was analyzed, we consider the case of long relaxation, which leads to the appearance of long-term memory on the macroscale. Due to coupling between the nonlinearity and nonlocality in time, the macroscopic model remains, however, incompletely homogenized, in the general case. At the same time, frequently only the relationship for the nonequilibrium capillary pressure is of interest for applications. In the present paper, we obtain such an exact relationship in two different independent forms for the case of long-term memory. This relationship is more general than that obtained by Bourgeat and Panfilov. In addition, we prove the comparison theorem which determines the upper and lower bounds for the macroscopic model. These bounds represent linear flow models, which are completely homogenized. The results obtained are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

Dissipation of mechanical energy underlies the sensitivity of many nanomechanical devices, with environmental effects often having a significant effect. One case of practical relevance is the interaction of elastic beam resonators with fluid, which is known to dramatically increase energy dissipation. Recently, we investigated energy dissipation in a different class of elastic beam resonator that embeds a microfluidic channel in its interior. In this paper, we examine the effect of the beam material Poisson ratio on these devices and discover that it can strongly affect energy dissipation-this is in direct contrast to conventional cantilever beams immersed in fluid. Increasing the Poisson ratio in these microfluidic devices is found to decrease energy dissipation, with the incompressible material limit providing minimum energy dissipation. Our paper establishes that, in this limit, placement of the fluid channel away from the beam neutral axis has negligible effect on energy dissipation in many cases of practical interest. The physical implications of these findings are discussed, and a detailed comparison with available experimental results is provided. [ABSTRACT FROM AUTHOR]

In this paper a simple model is proposed for computation of rate coefficients related to vibration-translation transitions based on the forced harmonic oscillator theory. This model, which is developed by considering a quadrature method, provides rate coefficients that are in very good agreement with those found in the literature for the high temperature regime (≳ 10 000 K). This model is implemented to study a one-dimensional nonequilibrium inviscid N2 flow behind a plane shock by considering a state-to-state approach. While the effects of ionization and chemical reactions are neglected in our study, our results show that multiquantum transitions have a great influence on the relaxation of the macroscopic parameters of the gas flow behind the shock, especially on vibrational distributions of high levels. All vibrational states are influenced by multiquantum processes, but the effective number of transitions decreases inversely according to the vibrational quantum number. For the initial conditions considered in this study, excited electronic states are found to be weakly populated and can be neglected in modeling. Moreover, the computing time is considerably reduced with the model described in this paper compared to others found in the literature. [ABSTRACT FROM AUTHOR]

Liquids are condensed matter in which atoms are strongly correlated in position and momentum. The atomic pair density function (PDF) is used often in describing such correlation. However, elucidation of many properties requires higher degrees of correlation than the pair correlation. For instance, viscosity depends upon the stress correlations in space and time. In this paper, we examine the cross correlation between the stress correlation at the atomic level and the PDF for two-dimensional liquids. We introduce the concept of the stress-resolved pair distribution function (SRPDF) that uses the sign of atomic-level stress as a selection rule to include particles from density correlations. The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. We further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method of solving the viscous hydrodynamics order by order in a derivative expansion. In such a method, the zero-order solution is just one of the ideal hydrodynamics. All the other higher order corrections satisfy the same first-order partial differential equations but with different inhomogeneous terms. We take the Bjorken flow as an example to test the validity of our method and present how to deal with the problems about the initial condition and perturbation evolution in our formalism. [ABSTRACT FROM AUTHOR]

The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using a Eulerian type mathematical model for compressible multicomponent flow problems. The model, which accounts forpressure nonequilibrium and applies different equations of state for individual flow components, shows excellent capabilities for the resolution of interfaces separating compressible fluids as well as for capturing the baroclinic source of vorticity generation. The developed finite volume Godunov type computational approach is equipped with an approximate Riemann solver for calculating fluxes and handles numerically diffused zones at flow component interfaces. The computations are performed for various initial conditions and are compared with available experimental data. The initial conditions promoting a shock-bubble interaction process include weak to high planar shock waves with a Mach number ranging from 1.2 to 3 and isolated cylindrical bubble inhomogeneities of helium, argon, nitrogen, krypton, and sulphur hexafluoride. The numerical results reveal the characteristic features of the evolving flow topology. The impulsively generated flow perturbations are dominated by the reflection and refraction of the shock, the compression, and acceleration as well as the vorticity generation within the medium. The study is further extended to investigate the influence of the ratio of the heat capacities on the interface deformation. [ABSTRACT FROM AUTHOR]

The low-frequency cutoff paradox occurring in 1/f processes has been revisited in a recent Letter [M. Niemann, H. Kantz, and E. Barkai, Phys. Rev. Lett. 110, 140603 (2013)]. A model of independent pulses exhibiting an integrable 1/fβ power spectrum with β > 1 explains this paradox. In this paper we explore a complementary possibility based on the use of multiplicative models to generate integrable 1/fβ processes. Three distinct types of models are considered. One of the most used methods of generating 1/f processes based on correlated pulses is among these models. Consequently we find that, contrary to what is generally thought, the low-frequency cutoff is not necessary to avoid the postulated divergence in a wide variety of processes. [ABSTRACT FROM AUTHOR]

The Gaussian chain model is the classical description of a polymeric chain, which provides analytical results regarding end-to-end distance, the distribution of segments around the mass center of a chain, coarse-grained interactions between two chains and effective interactions in binary mixtures. This hierarchy of results can be calculated thanks to the a stability of the Gaussian distribution. In this paper we show that it is possible to generalize the model of Gaussian chain to the entire class of a-stable distributions, obtaining the analogous hierarchy of results expressed by the analytical closed-form formulas in the Fourier space. This allows us to establish the α-stable chain model. We begin with reviewing the applications of Levy flights in the context of polymer sciences, which include: chains described by the heavy-tailed distributions of persistence length; polymers adsorbed to the surface; and the chains driven by a noise with power-law spatial correlations. Further, we derive the distribution of segments around the mass center of the α-stable chain and construct the coarse-grained interaction potential between two chains. These results are employed to discuss the model of binary mixture consisting of the α-stable chains. In what follows, we establish the spinodal decomposition condition generalized to the mixtures of the α-stable polymers. This condition is further applied to compare the on-surface phase separation of adsorbed polymers (which are known to be described with heavy-tailed statistics) with the phase separation condition in the bulk. Finally, we predict the four different scenarios of simultaneous mixing and demixing in the two- and three-dimensional systems. [ABSTRACT FROM AUTHOR]

The generation of directed movement of cellular components frequently requires the rectification of Brownian motion. Molecular motor enzymes that use ATP to walk on filamentous tracks are typically involved in cell transport, however, a track-altering motor can arise when an enzyme interacts with and alters its track. In Caulobacter crescentus and other bacteria, an active DNA partitioning (Par) apparatus is employed to segregate replicated chromosome regions to specific locations in dividing cells. The Par apparatus is composed of two proteins: ParA, an ATPase that can form polymeric structures on the nucleoid, and ParB, a protein that can bind and destabilize ParA structures. It has been proposed that the ParB-mediated alteration of ParA structures could be responsible for generating the directed movement of DNA during bacterial division. How precisely these actions are coordinated and translated into directed movement is not clear. In this paper we consider the C. crescentus segregation apparatus as an example of a track altering motor that operates using a so-called burnt-bridge mechanism. We develop and analyze mathematical models that examine how diffusion and ATP-hydrolysis-mediated monomer removal (or cleaving) can be combined to generate directed movement. Using a mean first passage approach, we analytically calculate the effective ParA track-cleaving velocities, effective diffusion coefficient, and other higher moments for the movement a ParB protein cluster that breaks monomers away at random locations on a single ParA track. Our model results indicate that cleaving velocities and effective diffusion constants are sensitive to ParB-induced ATP hydrolysis rates. Our analytical results are in excellent agreement with stochastic simulation results. [ABSTRACT FROM AUTHOR]

Based on an energy variational approach, we propose a sharp interface model for simulating solid-state dewetting of thin films with (weakly) anisotropic surface energies. The morphology evolution of thin films is governed by surface diffusion and contact line migration. For the contact line migration, we introduce a relaxation kinetics with a finite contact line mobility by energy gradient flow method. We implement the mathematical model in an explicit finite-difference scheme with cubic spline interpolation for evolving marker points. Following validation of the mathematical and numerical approaches, we simulate the evolution of thin-film islands, semi-infinite films, and films with holes as a function of film dimensions, isotropic Young angle 0,, anisotropy strength and crystal symmetry, and film crystal orientation relative to the substrate normal. We find that in addition to classical wetting (where holes in a film heal) and dewetting (where holes in a film grow), we observe cases where a hole through the film heals but leaves a finite-size hole/bubble between the continuous film and substrate or where the hole heals leaving a continuous film that is not bonded to the substrate. Surface energy anisotropy (i) increases the instability that leads to island breakup into multiple islands, (ii) enhances hole healing, and (iii) leads tofinite island size even under some conditions where the isotropic Young angle 6, suggests that the film wets the substrate. The numerical results presented in the paper capture many of the complexities associated with solid-state dewetting experiments. [ABSTRACT FROM AUTHOR]

In this paper, we examine the conditions under which the nonlinear transport theory is inescapable, when a correlated quantum dot is symmetrically coupled to two leads submitted to temperature and voltage biases. By detailed numerical comparisons between nonlinear and linear currents, we show that the claimed nonlinear behavior in a temperature gradient for the electric current is not so genuine, and the linear theory made at the operating temperature T = (TH + TC)/2 is unexpectedly robust. This is demonstrated for the single impurity Anderson model, in different regimes: resonant tunneling, Coulomb blockade, and Kondo regimes. [ABSTRACT FROM AUTHOR]

Internal friction (IF) describes the ability of materials to damp out mechanical oscillations. It is a crucial engineering parameter and also conveys unique microscopic information about structural defects, transport phenomena, and phase transformations in solids. While IF predominately results from lattice defects in crystalline materials, the origin of IF remains unclear in disordered materials, like metallic glasses. In this paper, we study the atomic rearrangements that govern IF in a model metallic glass, via numerical simulations of dynamical mechanical spectroscopy together with structural analysis. We identify cooperative and avalanchelike thermaldriven excitations as an underlying mechanism and demonstrate a linearlike relation between the concentrations of these excitations and the values of IF. Structurally, these excitations can be hindered, and thus suppress IF, by slow atoms that usually associate with full icosahedral symmetry. Our results also provide practical guides in tuning IF in metallic glasses from atomistic perspectives. [ABSTRACT FROM AUTHOR]

In this paper we study the susceptible-infected-susceptible epidemic dynamics, considering a specialized setting where popular places (termed passive entities) are visited by agents (termed active entities). We consider two types of spreading dynamics: direct spreading, where the active entities infect each other while visiting the passive entities, and indirect spreading, where the passive entities act as carriers and the infection is spread via them. We investigate in particular the effect of selection strategy, i.e., the way passive entities are chosen, in the spread of epidemics. We introduce a mathematical framework to study the effect of an arbitrary selection strategy and derive formulas for prevalence, extinction probabilities, and epidemic thresholds for both indirect and direct spreading. We also obtain a very simple relationship between the extinction probability and the prevalence. We pay special attention to preferential selection and derive exact formulas. The analysis reveals that an increase in the diversity in the selection process lowers the epidemic thresholds. Comparing the direct and indirect spreading, we identify regions in the parameter space where the prevalence of the indirect spreading is higher than the direct one. [ABSTRACT FROM AUTHOR]

Most of the investigations to date on tight-binding, quantum percolation models focused on the quantum percolation threshold, i.e., the analog to the Anderson transition. It appears to occur if roughly 30% of the hopping terms are actually present. Thus, models in the delocalized regime may still be substantially disordered, hence analyzing their transport properties is a nontrivial task which we pursue in the paper at hand. Using a method based on quantum typicality to numerically perform linear response theory we find that conductivity and mean free paths are in good accord with results from very simple heuristic considerations. Furthermore we find that depending on the percentage of actually present hopping terms, the transport properties may or may not be described by a Drude model. An investigation of the Einstein relation is also presented. [ABSTRACT FROM AUTHOR]

Defects in the rutile TiO2 structures have been extensively studied, but the intrinsic defects of the oxygen-deficient TinO2n-1phases have not been given the same amount of consideration. Those structures, known as Magnéli phases, are characterized by the presence of ordered planes of oxygen vacancies, also known as shear planes, and it has been shown that they form conducting channels inside TiO-based memristor devices. Memristors are excellent candidates for a new generation of memory devices in the electronics industry. In this paper we present density-functional-theory-based electronic structure calculations for TinO2n-1Magnéli structures using PBESol+U (0 ⩽ U ⩽ 5 eV) and Heyd-Scuseria-Emzerhof functionals, showing that intrinsic defects present in these structures are responsible for the appearance of states inside the band gap, which can act as intrinsic dopants for the enhanced conductivity of TiO2 memristive devices. [ABSTRACT FROM AUTHOR]

The time-dependent numerical renormalization group method (TDNRG) [Anders et al, Phys. Rev. Lett. 95, 196801 (2005)] was recently generalized to multiple quenches and arbitrary finite temperatures [Nghiem et al, Phys. Rev. B 89, 075118 (2014)] by using the full density matrix approach [Weichselbaum et al., Phys. Rev. Lett. 99, 076402 (2007)]. The formalism rests solely on the numerical renormalization group (NRG) approximation. In this paper, we numerically implement this formalism to study the response of a quantum impurity system to a general pulse and to periodic driving, in which a smooth pulse or a periodic train of pulses is approximated by a sufficient number of quenches. We show how the NRG approximation affects the trace of the projected density matrices and the continuity of the time evolution of a local observable. We also investigate the long-time limit of a local observable upon switching from a given initial state to a given final state as a function of both the pulse shape and the switch-on time, finding that this limit is improved for smoother pulse shapes and longer switch-on times. This lends support to our earlier suggestion that the long-time limit of observables, following a quench between a given initial state and a given final state, can be improved by replacing a sudden large and instantaneous quench by a sequence of smaller ones acting over a finite time interval: longer switch-on times and smoother pulses, i.e., increased adiabaticity, favor relaxation of the system to its correct thermodynamic long-time limit. For the case of periodic driving, we compare the TDNRG results to the exact analytic ones for the noninteracting resonant level model, finding better agreement at short to intermediate time scales in the case of smoother driving fields. Finally, we demonstrate the validity of the multiple-quench TDNRG formalism for arbitrary temperatures by studying the time evolution of the occupation number in the interacting Anderson impurity model in response to a periodic switching of the local level from the mixed valence to the Kondo regime at low, intermediate, and high temperatures. [ABSTRACT FROM AUTHOR]

Distinguishing different topologically ordered phases and characterizing phase transitions between them is a difficult task due to the absence of local order parameters. In this paper, we use a combination of analytical and numerical approaches to distinguish two such phases and characterize a phase transition between them. The "toric code" and "double semion" models are simple lattice models exhibiting Z2 topological order. Although both models express the same topological ground state degeneracies and entanglement entropies, they are distinct phases of matter because their emergent quasiparticles obey different statistics. For a ID model, we tune a phase transition between these two phases and obtain an exact solution to the entire phase diagram, finding a second-order Ising × lsing transition. We then use exact diagonalization to study the 2D case and find indications of a first-order transition. We show that the quasiparticle statistics provides a robust indicator of the distinct topological orders throughout the whole phase diagram. [ABSTRACT FROM AUTHOR]

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 1012). [ABSTRACT FROM AUTHOR]

Traffic congestion in isolated complex networks has been investigated extensively over the last decade. Coupled network models have recently been developed to facilitate further understanding of real complex systems. Analysis of traffic congestion in coupled complex networks, however, is still relatively unexplored. In this paper, we try to explore the effect of interconnections on traffic congestion in interconnected Barabási-Albert scale-free networks. We find that assortative coupling can alleviate traffic congestion more readily than disassortative and random coupling when the node processing capacity is allocated based on node usage probability. Furthermore, the optimal coupling probability can be found for assortative coupling. However, three types of coupling preferences achieve similar traffic performance if all nodes share the same processing capacity. We analyze interconnected Internet autonomous-system-level graphs of South Korea and Japan and obtain similar results. Some practical suggestions are presented to optimize such real-world interconnected networks accordingly. [ABSTRACT FROM AUTHOR]

Understanding how stimuli and synaptic connectivity influence the statistics of spike patterns in neural networks is a central question in computational neuroscience. The maximum-entropy approach has been successfully used to characterize the statistical response of simultaneously recorded spiking neurons responding to stimuli. However, in spite of good performance in terms of prediction, the fitting parameters do not explain the underlying mechanistic causes of the observed correlations. On the other hand, mathematical models of spiking neurons (neuromimetic models) provide a probabilistic mapping between the stimulus, network architecture, and spike patterns in terms of conditional probabilities. In this paper we build an exact analytical mapping between neuromimetic and maximum-entropy models. [ABSTRACT FROM AUTHOR]

The generation and conduction of action potentials (APs) represents a fundamental means of communication in the nervous system and is a metabolically expensive process. In this paper, we investigate the energy efficiency of neural systems in transferring pulse signals with APs. By analytically solving a bistable neuron model that mimics the AP generation with a particle crossing the barrier of a double well, we find the optimal number of ion channels that maximizes the energy efficiency of a neuron. We also investigate the energy efficiency of a neuron population in which the input pulse signals are represented with synchronized spikes and read out with a downstream coincidence detector neuron. We find an optimal number of neurons in neuron population, as well as the number of ion channels in each neuron that maximizes the energy efficiency. The energy efficiency also depends on the characters of the input signals, e.g., the pulse strength and the interpulse intervals. These results are confirmed by computer simulation of the stochastic Hodgkin-Huxley model with a detailed description of the ion channel random gating. We argue that the tradeoff between signal transmission reliability and energy cost may influence the size of the neural systems when energy use is constrained. [ABSTRACT FROM AUTHOR]

We study random transitions between two metastable states that appear below a critical temperature in a one-dimensional self-gravitating Brownian gas with a modified Poisson equation experiencing a second order phase transition from a homogeneous phase to an inhomogeneous phase [P. H. Chavanis and L. Delfini, Phys. Rev. E 81, 051103 (2010)]. We numerically solve the N-body Langevin equations and the stochastic Smoluchowski-Poisson system, which takes fluctuations (finite N effects) into account. The system switches back and forth between the two metastable states (bistability) and the particles accumulate successively at the center or at the boundary of the domain. We explicitly show that these random transitions exhibit the phenomenology of the ordinary Kramers problem for a Brownian particle in a double-well potential. The distribution of the residence time is Poissonian and the average lifetime of a metastable state is given by the Arrhenius law; i.e., it is proportional to the exponential of the barrier of free energy ΔF divided by the energy of thermal excitation kBT. Since the free energy is proportional to the number of particles N for a system with long-range interactions, the lifetime of metastable states scales as eN and is considerable for N≫1. As a result, in many applications, metastable states of systems with long-range interactions can be considered as stable states. However, for moderate values of N, or close to a critical point, the lifetime of the metastable states is reduced since the barrier of free energy decreases. In that case, the fluctuations become important and the mean field approximation is no more valid. This is the situation considered in this paper. By an appropriate change of notations, our results also apply to bacterial populations experiencing chemotaxis in biology. Their dynamics can be described by a stochastic Keller-Segel model that takes fluctuations into account and goes beyond the usual mean field approximation. [ABSTRACT FROM AUTHOR]

Strain-induced crystallization is a unique crystallization process taking place solely in polymers subjected to large deformations. It plays a major role for reinforcement and improvement of mechanical properties of polymers with a high regularity of the molecular structure. In this paper, we develop a micromechanical model for the strain-induced crystallization in filled rubbers. Accordingly, the strain-induced crystallization is considered as a process triggered by fully stretched and continued by semistretched polymer chains. The model extends the previously proposed network evolution model [Dargazany and Itskov, Int. J. Solids Struct. 46, 2967 (2009)] and can thus, in addition to the stress upturn and evolution of crystallinity, take into account several inelastic features of filled rubbers, such as the Mullins effect, permanent set, and induced anisotropy. Finally, the accuracy of the model is verified against different set of experimental data both with respect to the stress-stain and crystallization-strain relations. The model exhibits good agreement with the experimental results, which, besides its relative simplicity, makes it a good option for finite-element implementations. [ABSTRACT FROM AUTHOR]

The Berry curvature and its descendant, the Berry phase, play an important role in quantum mechanics. They can be used to understand the Aharonov-Bohm effect, define topological Chern numbers, and generally to investigate the geometric properties of a quantum ground state manifold. While Berry curvature has been well studied in the regimes of few-body physics and noninteracting particles, its use in the regime of strong interactions is hindered by the lack of numerical methods to solve for it. In this paper I fill this gap by implementing a quantum Monte Carlo method to solve for the Berry curvature, based on interpreting Berry curvature as a leading correction to imaginary time ramps. I demonstrate my algorithm using the transverse-field Ising model in one and two dimensions, the latter of which is nonintegrable. Despite the fact that the Berry curvature gives information about the phase of the wave function, I show that the algorithm has no sign or phase problem for standard sign-problem-free Hamiltonians. My algorithm scales similarly to conventional methods as a function of system size and energy gap, and therefore should prove a valuable tool in investigating the quantum geometry of many-body systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider a radial displacement of a viscous fluid by another one of much lower viscosity through a three-dimensional uniform porous medium. It is well known that when a less viscous fluid is pumped at a constant injection rate, very complex interfacial patterns are formed. The control and eventual suppression of these instabilities are relevant to a large number of areas in science and technology. Here, we use a variational approach to search for an analytical form of an optimal flow rate so that the interface between two almost neutrally buoyant fluids grows, but the emergence of interfacial disturbances is minimized. We find a closed analytical solution for the ideal flow rate which surprisingly does not depend on either the properties of the fluids or the permeability of the porous medium. [ABSTRACT FROM AUTHOR]

In this paper, we present the effects of memory decay on a bootstrap percolation model applied to random directed graphs (quorum percolation). The addition of decay was motivated by its natural occurrence in physical systems previously described by percolation theory, such as cultured neuronal networks, where decay originates from ionic leakage through the membrane of neurons and/or synaptic depression. Surprisingly, this feature alone appears to change the critical behavior of the percolation transition, where discontinuities are replaced by steep but finite slopes. Using different numerical approaches, we show evidence for this qualitative change even for very small decay values. In experiments where the steepest slopes can not be resolved and still appear as discontinuities, decay produces nonetheless a quantitative difference on the location of the apparent critical point. We discuss how this shift impacts network connectivity previously estimated without considering decay. In addition to this particular example, we believe that other percolation models are worth reinvestigating, taking into account similar sorts of memory decay. [ABSTRACT FROM AUTHOR]

In this paper we consider a model of accelerated dynamics with the rules modified from those of the recently proposed [Dong et al., Phys. Rev. Lett. 109, 130602 (2012)] accelerated exclusion process (AEP) such that particle-vacancy symmetry is restored to facilitate a mapping to a solid-on-solid growth model in 1 + I dimensions. In addition to kicking a particle ahead of the moving particle, as in the AEP, in our model another particle from behind is drawn, provided it is within the "distance of interaction" denoted by lmM. We call our model the doubly accelerated exclusion process (DAEP). We observe accelerated transport and interface growth and widening of the cluster size distribution for cluster sizes above lmax, when compared with the ordinary totally asymmetric exclusion process (TASEP). We also characterize the difference between the TASEP, AEP, and DAEP by computing a "staggered" order parameter, which reveals the local order in the steady state. This order in part explains the behavior of the particle current as a function of density. The differences of the steady states are also reflected by the behavior of the temporal and spatial correlation functions in the interface picture. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann method has been shown to be successful for microscale gas flows, and it has attracted significant research interest. In this paper, the recently proposed filter-matrix lattice Boltzmann (FMLB) model is first applied to study the microchannel gas flows, in which a Bosanquet-type effective viscosity is used to capture the flow behaviors in the transition regime. A kinetic boundary condition, the combined bounce-back and specular-reflection scheme with the second-order slip scheme, is also designed for the FMLB model. By analyzing a unidirectional flow, the slip velocity and the discrete effects related to the boundary condition are derived within the FMLB model, and a revised scheme is presented to overcome such effects, which have also been validated through numerical simulations. To gain an accurate simulation in a wide range of Knudsen numbers, covering the slip and the entire transition flow regimes, a set of slip coefficients with an introduced fitting function is adopted in the revised second-order slip boundary condition. The periodic and pressure-driven microchannel flows have been investigated by the present model in this study. The numerical results, including the velocity profile and the mass flow rate, as well as the nonlinear pressure distribution along the channel, agree fairly well with the solutions of the linearized Boltzmann equation, the direct simulation Monte Carlo results, the experimental data, and the previous results of the multiple effective relaxation lattice Boltzmann model. Also, the present results of the velocity profile and the mass flow rate show that the present model with the fitting function can yield improved predictions for the microchannel gas flow with higher Knudsen numbers in the transition flow regime. [ABSTRACT FROM AUTHOR]

In this paper, we aim to address an important issue about the pseudopotential lattice Boltzmann (LB) model, which has attracted much attention as a mesoscopic model for simulating interfacial dynamics of complex fluids, but suffers from the problem that the surface tension cannot be tuned independently of the density ratio. In the literature, a multirange potential was devised to adjust the surface tension [Sbragaglia et al., Phys. Rev. E 75, 026702 (2007)]. However, it was recently found that the density ratio of the system will be changed when the multirange potential is employed to adjust the surface tension. An alternative approach is therefore proposed in the present work. The basic strategy is to add a source term to the LB equation so as to tune the surface tension of the pseudopotential LB model. The proposed approach can guarantee that the adjustment of the surface tension does not affect the mechanical stability condition of the pseudopotential LB model, and thus provides a separate control of the surface tension and the density ratio. Meanwhile, it still retains the mesoscopic feature and the computational simplicity of the pseudopotential LB model. Numerical simulations are carried out for stationary droplets, capillary waves, and droplet splashing on a thin liquid film. The numerical results demonstrate that the proposed approach is capable of achieving a tunable surface tension over a very wide range and can keep the density ratio unchanged when adjusting the surface tension. [ABSTRACT FROM AUTHOR]

This paper introduces a spatiotemporal resonator model and an inference method for detection and estimation of nearly periodic temporal phenomena in spatiotemporal data. The model is derived as a spatial extension of a stochastic harmonic resonator model, which can be formulated in terms of a stochastic differential equation. The spatial structure is included by introducing linear operators, which affect both the oscillations and damping, and by choosing the appropriate spatial covariance structure of the driving time-white noise process. With the choice of the linear operators as partial differential operators, the resonator model becomes a stochastic partial differential equation, which is compatible with infinite-dimensional Kalman filtering. The resulting infinite-dimensional Kalman filtering problem allows for a computationally efficient solution as the computational cost scales linearly with measurements in the temporal dimension. This framework is applied to weather prediction and to physiological noise elimination in functional magnetic resonance imaging brain data. [ABSTRACT FROM AUTHOR]

The formation of a gel in a disperse coagulating system, wherein binary coagulation governs the temporal changes of the particle mass spectrum is studied for the coagulation kernel proportional to K(g,l)=gl with g,l being the numbers of monomers in the coalescing pair of particles. This model is known to reveal the sol-gel transition, i.e., the formation of one giant cluster with the mass comparable to the total mass of the whole system. This paper reports on some exact results that are valid for arbitrary initial particle mass spectra. The particle spectrum is shown to be expressed through a contour integral of the exponentiated initial generating function of the particle mass spectrum. The exact formula for the gel mass is derived for the scenario of passive gelation. Two scenarios of gelation, where the gel is either active or passive, are considered. [ABSTRACT FROM AUTHOR]

In the present paper, the possibility of invoking stochastic resonance (SR, periodic and aperiodic) by regulating the operating value of an appropriate parameter is explored. The operating values of these parameters are defined as the set point of the system throughout the present paper. Brusselator, a mathematical model [I. Prigogine and R. Lefever, J. Chem. Phys. 48, 1695 (1968)] of nonlinear chemical reactions, is used for this purpose. We consider the effect of intrinsic noise in the Brusselator due to the Markovian nature of the chemical reactions. The stochastic time evolution is studied using the Gillespie algorithm [D. T. Gillespie, J. Comput. Phys. 22, 403 (1976)], which is an exact stochastic simulation algorithm. We analyze the dependence of the resonance point on both the strength of the intrinsic noise as well as the distance from the bifurcation point. Subsequently, the phenomena of SR is explored using both periodic and aperiodic stimulus. It was found that, for a given system size, in both cases, SR is achieved by variation of the set point. Set-point variation can be achieved by regulating either the source concentration or the rate constants. Resonance is observed in both cases. However, this resonance occurs at different values of the set point, even with a fixed system size. This is clearly seen in the set-point versus system-size plane, where the resonance line has different slopes for the two scenarios. Our semianalytic treatment points to the fact that for a given system size intrinsic noise is affected differently for different methods involving the variation of the set point. This is explained by writing the corresponding chemical Langevin equation and comparing the various intrinsic noise sources. [ABSTRACT FROM AUTHOR]

While historically many quantum-mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a great deal of interest has arisen in quantum effects in nuclear dynamics as well. Due to the computational difficulty of solving the Schrödinger equation in full, these effects are often treated with approximate methods. In this paper, we present an algorithm to tackle these problems using an extension to the many-interacting-worlds approach to quantum mechanics. This technique uses a kernel function to rebuild the probability density, and therefore, in contrast with the approximation presented in the original paper, it can be naturally extended to n-dimensional systems. This opens up the possibility of performing quantum ground-state searches with steepest-descent methods, and it could potentially lead to real-time quantum molecular-dynamics simulations. The behavior of the algorithm is studied in different potentials and numbers of dimensions and compared both to the original approach and to exact Schrödinger equation solutions whenever possible. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann method (LBM) is an effective tool for simulating the contact-line motion due to the nature of its microscopic dynamics. In contact-line motion, contact-angle hysteresis is an inherent phenomenon, but it is neglected in most existing color-gradient based LBMs. In this paper, a color-gradient based multiphase LBM is developed to simulate the contact-line motion, particularly with the hysteresis of contact angle involved. In this model, the perturbation operator based on the continuum surface force concept is introduced to model the interfacial tension, and the recoloring operator proposed by Latva-Kokko and Rothman is used to produce phase segregation and resolve the lattice pinning problem. At the solid surface, the color-conserving wetting boundary condition [Hollis et al., IMA J. Appl. Math. 76, 726 (2011)] is applied to improve the accuracy of simulations and suppress spurious currents at the contact line. In particular, we present a numerical algorithm to allow for the effect of the contact-angle hysteresis, in which an iterative procedure is used to determine the dynamic contact angle. Numerical simulations are conducted to verify the developed model, including the droplet partial wetting process and droplet dynamical behavior in a simple shear flow. The obtained results are compared with theoretical solutions and experimental data, indicating that the model is able to predict the equilibrium droplet shape as well as the dynamic process of partial wetting and thus permits accurate prediction of contact-line motion with the consideration of contact-angle hysteresis. [ABSTRACT FROM AUTHOR]