Showing papers in "Physical Review E in 2010"
TL;DR: It is shown that targeted transport processes without global topology knowledge are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure.
Abstract: We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as noninteracting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure.
1,002 citations
TL;DR: It is shown that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum, implying that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts.
Abstract: Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations. First, we revisit and clarify the resolution limit phenomenon for modularity maximization. Second, we show that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum. Third, we derive the limiting behavior of the maximum modularity Q(max) for one model of infinitely modular networks, showing that it depends strongly both on the size of the network and on the number of modules it contains. Finally, using three real-world metabolic networks as examples, we show that the degenerate solutions can fundamentally disagree on many, but not all, partition properties such as the composition of the largest modules and the distribution of module sizes. These results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts. They also explain why many heuristics are often successful at finding high-scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network. We conclude by discussing avenues for mitigating some of these behaviors, such as combining information from many degenerate solutions or using generative models.
982 citations
TL;DR: In this paper, the capability of mean square displacement (MSD) analysis to extract reliable values of the diffusion coefficient D of a single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty was examined.
Abstract: We examine the capability of mean square displacement (MSD) analysis to extract reliable values of the diffusion coefficient D of a single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least-squares fit of the MSD curve can provide the best estimate of D provided an optimal number of MSD points are used for the fit. We discuss the practical implications of these results for data analysis in single-particle tracking experiments.
560 citations
TL;DR: The Darboux transformation technique is modified to show how to construct the hierarchy of rational solutions of the Hirota equation, a modified nonlinear Schrödinger equation that takes into account higher-order dispersion and time-delay corrections to the cubic nonlinearity.
Abstract: The Hirota equation is a modified nonlinear Schrodinger equation (NLSE) that takes into account higher-order dispersion and time-delay corrections to the cubic nonlinearity In describing wave propagation in the ocean and optical fibers, it can be viewed as an approximation which is more accurate than the NLSE We have modified the Darboux transformation technique to show how to construct the hierarchy of rational solutions of the Hirota equation We present explicit forms for the two lower-order solutions Each one is a regular (nonsingular) rational solution with a single maximum that can describe a rogue wave in this model Numerical simulations reveal the appearance of these solutions in a chaotic field generated from a perturbed continuous wave solution
392 citations
TL;DR: The backward MFDMA algorithm is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed, and it is found that the backward M FDMA algorithm also outperforms the multifractional detrended fluctuation analysis.
Abstract: The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter $\ensuremath{\theta}$ determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward $(\ensuremath{\theta}=0)$, centered $(\ensuremath{\theta}=0.5)$, and forward $(\ensuremath{\theta}=1)$ detrending windows. We find that the estimated multifractal scaling exponent $\ensuremath{\tau}(q)$ and the singularity spectrum $f(\ensuremath{\alpha})$ are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis. The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.
374 citations
TL;DR: A formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints and furthermore driven by external time-dependent forces is proposed, leading to a splitting of the second law leading to three second-law-like relations.
Abstract: We propose a formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second law occurs in this description leading to three second-law-like relations. The general results are illustrated on specific solvable models. The present paper uses a master equation based approach.
340 citations
TL;DR: In this article, level statistics and the structure of the eigenvectors of one-dimensional gapless bosonic and fermionic systems across the transition from integrability to quantum chaos are studied.
Abstract: By means of full exact diagonalization, we study level statistics and the structure of the eigenvectors of one-dimensional gapless bosonic and fermionic systems across the transition from integrability to quantum chaos. These systems are integrable in the presence of only nearest-neighbor terms, whereas the addition of next-nearest-neighbor hopping and interaction may lead to the onset of chaos. We show that the strength of the next-nearest-neighbor terms required to observe clear signatures of nonintegrability is inversely proportional to the system size. Interestingly, the transition to chaos is also seen to depend on particle statistics, with bosons responding first to the integrability breaking terms. In addition, we discuss the use of delocalization measures as main indicators for the crossover from integrability to chaos and the consequent viability of quantum thermalization in isolated systems.
322 citations
TL;DR: A generalized version of the susceptible-infected-recovered model of epidemic disease that allows for arbitrary distributions of transmission and recovery times is studied and it is shown that the calculation gives a rigorous bound on the size of disease outbreaks.
Abstract: In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for transmission and recovery. Time intervals for real diseases, however, have distributions that in most cases are far from exponential, which leads to disagreements, both qualitative and quantitative, with the models. In this paper, we study a generalized version of the susceptible-infected-recovered model of epidemic disease that allows for arbitrary distributions of transmission and recovery times. Standard differential equation approaches cannot be used for this generalized model, but we show that the problem can be reformulated as a time-dependent message passing calculation on the appropriate contact network. The calculation is exact on trees (i.e., loopless networks) or locally treelike networks (such as random graphs) in the large system size limit. On non-tree-like networks we show that the calculation gives a rigorous bound on the size of disease outbreaks. We demonstrate the method with applications to two specific models and the results compare favorably with numerical simulations.
321 citations
TL;DR: A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians and shows good agreement with empirical data obtained in controlled experiments.
Abstract: A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians We discuss the phenomena of oscillations and overlapping which occur for certain choices of the forces The main intention of this work is the quantitative description of pedestrian movement in several geometries Measurements of the fundamental diagram in narrow and wide corridors are performed The results of the proposed model show good agreement with empirical data obtained in controlled experiments
320 citations
TL;DR: In this article, a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) valid in the limit of thin double layers is presented.
Abstract: The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by supercapacitors, water desalination and purification by capacitive deionization, and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) valid in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory for the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) in the "supercapacitor regime" of small voltages and/or early times, the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore, and (ii) in the "desalination regime" of large voltages and long times, the porous electrode slowly absorbs counterions, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration.
306 citations
TL;DR: This work defines as temporal small world a time-varying graph in which the links are highly clustered in time, yet the nodes are at small average temporal distances, and explores the small-world behavior in synthetic time- varying networks of mobile agents and in real social and biological time-Varying systems.
Abstract: Connections in complex networks are inherently fluctuating over time and exhibit more dimensionality than analysis based on standard static graph measures can capture. Here, we introduce the concepts of temporal paths and distance in time-varying graphs. We define as temporal small world a time-varying graph in which the links are highly clustered in time, yet the nodes are at small average temporal distances. We explore the small-world behavior in synthetic time-varying networks of mobile agents and in real social and biological time-varying systems.
TL;DR: It is found that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated.
Abstract: Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a "resonant" frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate.
TL;DR: It is found that increasing the probability of adopting the strategy from the fittest player within reach, i.e., setting w positive, promotes the evolution of cooperation, and the introduction of w effectively alters the interaction network and thus also the impact of uncertainty by strategy adoptions on the Evolution of cooperation.
Abstract: Strategy changes are an essential part of evolutionary games. Here, we introduce a simple rule that, depending on the value of a single parameter $w$, influences the selection of players that are considered as potential sources of the new strategy. For positive $w$ players with high payoffs will be considered more likely, while for negative $w$ the opposite holds. Setting $w$ equal to zero returns the frequently adopted random selection of the opponent. We find that increasing the probability of adopting the strategy from the fittest player within reach, i.e., setting $w$ positive, promotes the evolution of cooperation. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process and for different interaction networks. Since the evolution to widespread defection is tightly associated with cooperators having a lower fitness than defectors, the fact that positive values of $w$ facilitate cooperation is quite surprising. We show that the results can be explained by means of a negative feedback effect that increases the vulnerability of defectors although initially increasing their survivability. Moreover, we demonstrate that the introduction of $w$ effectively alters the interaction network and thus also the impact of uncertainty by strategy adoptions on the evolution of cooperation.
TL;DR: This study establishes a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables based on the generalized variances of residual errors and motivates reformulations of "causal density" and "Granger autonomy."
Abstract: Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables but may occur among groups or "ensembles" of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer additional justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy." Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.
TL;DR: The horizontal visibility algorithm is used to characterize and distinguish between correlated stochastic, uncorrelated and chaotic processes, and it is shown that in every case the series maps into a graph with exponential degree distribution P(k)∼exp(-λk), where the value of λ characterizes the specific process.
Abstract: Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In the last years, some methods mapping time series to network representations have been proposed. The purpose is to investigate on the properties of the series through graph theoretical tools recently developed in the core of the celebrated complex network theory. Among some other methods, the so-called visibility algorithm has received much attention, since it has been shown that series correlations are captured by the algorithm and translated in the associated graph, opening the possibility of building fruitful connections between time series analysis, nonlinear dynamics, and graph theory. Here we use the horizontal visibility algorithm to characterize and distinguish between correlated stochastic, uncorrelated and chaotic processes. We show that in every case the series maps into a graph with exponential degree distribution P(k)∼exp(-λk), where the value of λ characterizes the specific process. The frontier between chaotic and correlated stochastic processes, λ=ln(3/2) , can be calculated exactly, and some other analytical developments confirm the results provided by extensive numerical simulations and (short) experimental time series.
TL;DR: The displacement correlation function is defined and it is found that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.
Abstract: Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.
TL;DR: A unifying mathematical theory of nonequilibrium thermodynamics of stochastic systems in terms of master equations is presented, and two kinds of irreversibility, and the meaning of the arrow of time, emerge.
Abstract: A unifying mathematical theory of nonequilibrium thermodynamics of stochastic systems in terms of master equations is presented. As generalizations of isothermal entropy and free energy, two functions of state play central roles: the Gibbs entropy $S$ and the relative entropy $F$, which are related via the stationary distribution of the stochastic dynamics. $S$ satisfies the fundamental entropy balance equation $dS/dt={e}_{p}\ensuremath{-}{h}_{d}/T$ with entropy production rate ${e}_{p}\ensuremath{\ge}0$ and heat dissipation rate ${h}_{d}$, while $dF/dt=\ensuremath{-}{f}_{d}\ensuremath{\le}0$. For closed systems that satisfy detailed balance: $T{e}_{p}(t)={f}_{d}(t)$. For open systems, one has $T{e}_{p}(t)={f}_{d}(t)+{Q}_{hk}(t)$, where the housekeeping heat, ${Q}_{hk}\ensuremath{\ge}0$, was first introduced in the phenomenological nonequilibrium steady-state thermodynamics put forward by Oono and Paniconi. ${Q}_{hk}$ represents the irreversible work done by the surrounding to the system that is kept away from reaching equilibrium. Hence, entropy production ${e}_{p}$ consists of free energy dissipation associated with spontaneous relaxation (i.e., self-organization), ${f}_{d}$, and active energy pumping that sustains the open system ${Q}_{hk}$. The amount of excess heat involved in the relaxation ${Q}_{ex}={h}_{d}\ensuremath{-}{Q}_{hk}={f}_{d}\ensuremath{-}T(dS/dt)$. Two kinds of irreversibility, and the meaning of the arrow of time, emerge. Quasistationary processes, adiabaticity, and maximum principle for entropy are also generalized to nonequilibrium settings.
TL;DR: In this article, the authors study the topological properties of commodity-specific trade relations among world countries over the 1992-2003 period, comparing them with those of the aggregate-trade network, known in the literature as the international trade network (ITN).
Abstract: We study the topological properties of the multinetwork of commodity-specific trade relations among world countries over the 1992-2003 period, comparing them with those of the aggregate-trade network, known in the literature as the international-trade network (ITN). We show that link-weight distributions of commodity-specific networks are extremely heterogeneous and (quasi) log normality of aggregate link-weight distribution is generated as a sheer outcome of aggregation. Commodity-specific networks also display average connectivity, clustering, and centrality levels very different from their aggregate counterpart. We also find that ITN complete connectivity is mainly achieved through the presence of many weak links that keep commodity-specific networks together and that the correlation structure existing between topological statistics within each single network is fairly robust and mimics that of the aggregate network. Finally, we employ cross-commodity correlations between link weights to build hierarchies of commodities. Our results suggest that on the top of a relatively time-invariant "intrinsic" taxonomy (based on inherent between-commodity similarities), the roles played by different commodities in the ITN have become more and more dissimilar, possibly as the result of an increased trade specialization. Our approach is general and can be used to characterize any multinetwork emerging as a nontrivial aggregation of several interdependent layers.
TL;DR: This paper derives a convenient and asymptotically optimal maximum likelihood estimator for the diffusion coefficient and for the magnitude of localization noise together with the corresponding Fisher information, which bounds the performance of all unbiased estimators.
Abstract: Camera-based single-particle tracking enables quantitative determination of transport properties and provides nanoscale information about material characteristics such as viscosity and elasticity. However, static localization noise and the blurring of a particle's position over camera integration times introduce artifacts into measurement results even for a particle executing simple diffusion. Common data analysis methods based on the mean-square displacement do not properly account for these effects. In this paper, we analyze the statistics of tracking data for freely diffusing particles in realistic experimental scenarios. We derive a convenient and asymptotically optimal maximum likelihood estimator for the diffusion coefficient and for the magnitude of localization noise together with the corresponding Fisher information, which bounds the performance of all unbiased estimators. We find that the effect of varying the illumination profile during the camera integration time is quantified by a motion blur coefficient, R . We also find that a double-pulse illumination sequence maximizes the information content in some common experimental scenarios. Our results provide a rigorous theoretical framework and practical experimental recipe for achieving optimal performance in camera-based single-particle tracking.
TL;DR: An exceptionally accurate spin-glass-type Potts model for community detection that is at least as accurate as the best currently available algorithms and robust to the effects of noise and competitive with the best current algorithms in terms of speed and size of solvable systems.
Abstract: We report on an exceptionally accurate spin-glass-type Potts model for community detection. With a simple algorithm, we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of noise. It is also competitive with the best currently available algorithms in terms of speed and size of solvable systems. We find that the computational demand often exhibits superlinear scaling $O({L}^{1.3})$ where $L$ is the number of edges in the system, and we have applied the algorithm to synthetic systems as large as $40\ifmmode\times\else\texttimes\fi{}{10}^{6}$ nodes and over $1\ifmmode\times\else\texttimes\fi{}{10}^{9}$ edges. A previous stumbling block encountered by popular community detection methods is the so-called ``resolution limit.'' Being a ``local'' measure of community structure, our Potts model is free from this resolution-limit effect, and it further remains a local measure on weighted and directed graphs. We also address the mitigation of resolution-limit effects for two other popular Potts models.
TL;DR: The total entropy production is the sum of two contributions, the so-called adiabatic and nonadiabatic entropy productions, each of which is non-negative, and these are derived for continuous Markovian processes.
Abstract: The total entropy production is the sum of two contributions, the so-called adiabatic and nonadiabatic entropy productions, each of which is non-negative. We derive their explicit expressions for continuous Markovian processes, discuss their properties, and illustrate their behavior on two exactly solvable models.
TL;DR: The rheological function of N cycles and force chains is elucidated, suggesting that the three-force cycles are called upon for reinforcements to ward off failure via shear banding in the lead up to failure.
Abstract: We examine the coevolution of $N$ cycles and force chains as part of a broader study which is designed to quantitatively characterize the role of the laterally supporting contact network to the evolution of force chains. Here, we elucidate the rheological function of these coexisting structures, especially in the lead up to failure. In analogy to force chains, we introduce the concept of force cycles: $N$ cycles whose contacts each bear above average force. We examine their evolution around force chains in a discrete element simulation of a dense granular material under quasistatic biaxial loading. Three-force cycles are shown to be stabilizing structures that inhibit relative particle rotations and provide strong lateral support to force chains. These exhibit distinct behavior from other cycles. Their population decreases rapidly during the initial stages of the strain-hardening regime---a trend that is suddenly interrupted and reversed upon commencement of force chain buckling prior to peak shear stress. Results suggest that the three-force cycles are called upon for reinforcements to ward off failure via shear banding. Ultimately though, the resistance to buckling proves futile; buckling wins under the combined effects of dilatation and increasing compressive load. The sudden increase in three-force cycles may thus be viewed as an indicator of imminent failure via shear bands.
TL;DR: An alternate model for rumor spreading over networks is suggested, in which two rumors with different probabilities of acceptance may propagate among nodes, and it is found that preferred rumor 1 is dominant in the network when the degree of nodes is high enough and/or when the network contains large clustered groups of nodes, expelling rumor 2.
Abstract: An alternate model for rumor spreading over networks is suggested, in which two rumors (termed rumor 1 and rumor 2) with different probabilities of acceptance may propagate among nodes. The propagation is not symmetric in the sense that when deciding which rumor to adopt, nodes always consider rumor 1 first. The model is a natural generalization of the well-known epidemic SIS (susceptible-infective-susceptible) model and reduces to it when some of the parameters of this model are zero. We find that preferred rumor 1 is dominant in the network when the degree of nodes is high enough and/or when the network contains large clustered groups of nodes, expelling rumor 2. However, numerical simulations on synthetic networks show that it is possible for rumor 2 to occupy a nonzero fraction of the nodes in many cases as well. Specifically, in the Watts-Strogatz small-world model a moderate level of clustering supports its adoption, while increasing randomness reduces it. For Erdos-Renyi networks, a low average degree allows the coexistence of the two types of rumors. In Barabasi-Albert networks generated with a low $m$, where $m$ is the number of links when a new node is added, it is also possible for rumor 2 to spread over the network.
TL;DR: This work addresses the issue of the self energy of the mobile ions in electrolyte solutions within a general Gaussian renormalized fluctuation theory using a field-theoretic approach and introduces the Born radii of the ions in the form of a charge distribution allowing for different born radii between the cations and anions.
Abstract: We address the issue of the self energy of the mobile ions in electrolyte solutions within a general Gaussian renormalized fluctuation theory using a field-theoretic approach. We introduce the Born radii of the ions in the form of a charge distribution allowing for different Born radii between the cations and anions. The model thus automatically yields a theory free of divergences and accounts for the solvation of the ions at the level of continuous dielectric media. In an inhomogeneous dielectric medium, the self energy is in general position dependent and differences in the self energy between cations and anions can give rise to local charge separation in a macroscopically neutral system. Treating the Born radius a as a smallness parameter, we show that the self energy can be split into an O(a^(−1)) nonuniversal contribution and an O(a^0) universal contribution that depends only on the ion concentration, valency, and the spatially varying dielectric constant. For a weakly inhomogeneous dielectric medium, the nonuniversal part of the self energy is shown to have the form of the Born energy with the local dielectric constant. This self energy is incorporated into the Poisson-Boltzmann equation as a simple means of including this local fluctuation effect in a mean-field theory. We illustrate the phenomenon of charge separation by considering cations and anions of difference sizes and valencies in a periodic dielectric medium.
TL;DR: The efficiency at maximum power of a quantum-dot Carnot heat engine is evaluated and Curzon-Ahlborn efficiency is recovered in the limit of weak dissipation.
Abstract: We evaluate the efficiency at maximum power of a quantum-dot Carnot heat engine. The universal values of the coefficients at the linear and quadratic order in the temperature gradient are reproduced. Curzon-Ahlborn efficiency is recovered in the limit of weak dissipation.
TL;DR: An improved compartmental formalism able to handle the simultaneous time evolution of the disease and the underlying network topology successfully is introduced and the interplay and outcomes of both dynamical elements, process and structure, on adaptive networks featuring different degree distributions at the initial stage are analyzed.
Abstract: Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have been analyzed using low complexity analytical formalisms, revealing nevertheless some novel dynamical features. However, current methods have failed to reproduce with accuracy the simultaneous time evolution of the disease and the underlying network topology. In the framework of the adaptive susceptible-infectious-susceptible (SIS) model of Gross et al. [Phys. Rev. Lett. 96, 208701 (2006)], we introduce an improved compartmental formalism able to handle this coevolutionary task successfully. With this approach, we analyze the interplay and outcomes of both dynamical elements, process and structure, on adaptive networks featuring different degree distributions at the initial stage.
TL;DR: A generalization of the detailed fluctuation theorem is derived, modified by the addition of a term that quantifies the change in uncertainty about the microscopic state of the system upon making measurements of physical observables during feedback.
Abstract: We extend the framework of forward and reverse processes commonly utilized in the derivation and analysis of the nonequilibrium work relations to thermodynamic processes with repeated discrete feedback. Within this framework, we derive a generalization of the detailed fluctuation theorem, which is modified by the addition of a term that quantifies the change in uncertainty about the microscopic state of the system upon making measurements of physical observables during feedback. As an application, we extend two nonequilibrium work relations: the nonequilibrium work fluctuation theorem and the relative-entropy work relation.
TL;DR: It was found that the solitons are delayed after the collision, andsolitons with higher amplitude experience longer delays.
Abstract: The interaction of two counterpropagating solitons of equal amplitudes has been studied experimentally and numerically in a monolayer strongly coupled complex plasma. Complex plasmas are microparticle suspensions in ion-electron plasmas. It was found that the solitons are delayed after the collision. Solitons with higher amplitude experience longer delays. The amplitude of the overlapping solitons during the collision was less than the sum of the initial soliton amplitudes.
TL;DR: Systematic high-resolution calorimetric studies reveal thatblue phase III is effectively stabilized in a wide temperature range by mixing surface-functionalized nanoparticles with chiral liquid crystals, yielding a robust method to stabilize blue phases, especially blue phase III.
Abstract: Liquid-crystalline blue phases exhibit exceptional properties for applications in the display and sensor industry. However, in single component systems, they are stable only for very narrow temperature range between the isotropic and the chiral nematic phase, a feature that severely hinders their applicability. Systematic high-resolution calorimetric studies reveal that blue phase III is effectively stabilized in a wide temperature range by mixing surface-functionalized nanoparticles with chiral liquid crystals. This effect is present for two liquid crystals, yielding a robust method to stabilize blue phases, especially blue phase III. Theoretical arguments show that the aggregation of nanoparticles at disclination lines is responsible for the observed effects.
TL;DR: The crux of the theory is a dissipative variant of WKB (Wentzel-Kramers-Brillouin) approximation which assumes that the typical population size in the metastable state is large, and yields both entropic barriers to extinction and pre-exponential factors.
Abstract: We investigate the phenomenon of extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state $n=0$ is a repelling (scenario A) or attracting (scenario B) point of the deterministic rate equation. In scenario A the metastable stochastic population resides in the vicinity of an attracting fixed point next to the repelling point $n=0$. In scenario B there is an intermediate repelling point $n={n}_{1}$ between the attracting point $n=0$ and another attracting point $n={n}_{2}$ in the vicinity of which the metastable population resides. The crux of the theory is a dissipative variant of WKB (Wentzel-Kramers-Brillouin) approximation which assumes that the typical population size in the metastable state is large. Starting from the master equation, we calculate the quasistationary probability distribution of the population sizes and the (exponentially long) mean time to extinction for each of the two scenarios. When necessary, the WKB approximation is complemented (i) by a recursive solution of the quasistationary master equation at small $n$ and (ii) by the van Kampen system-size expansion, valid near the fixed points of the deterministic rate equation. The theory yields both entropic barriers to extinction and pre-exponential factors, and holds for a general set of multistep processes when detailed balance is broken. The results simplify considerably for single-step processes and near the characteristic bifurcations of scenarios A and B.