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Zhonghuai Hou

Zhonghuai Hou appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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cond-mat.stat-mechcond-mat.dis-nncond-mat.softphysics.soc-phphysics.chem-phnlin.AOBiological Physicscond-mat.mtrl-sciPopulations and EvolutionApplicationscond-mat.mes-hallMethodologyNeurons and Cognitionnlin.CDphysics.comp-phSocial and Information NetworksSubcellular Processes

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Published work

34 published item(s)

preprint2026arXiv

Hierarchical Reconstruction of Time-arrow from Multi-time Correlations

The entropy production rate (EPR), a key measure of thermodynamic irreversibility in stochastic thermodynamics, is difficult to determine directly in experiments, motivating lower-bound-based estimation from observations. However, a systematic framework for organizing increasing amounts of the irreversibility information in experimental state observables into progressively tighter bounds remains lacking. Here, we show that multi-time correlations of a class of state observations naturally encode this information to provide a hierarchy. By defining a reconstruction operation as a combination of correlations, we obtain a sequence of lower bounds on the EPR. Correlations of higher order capture the thermodynamic information at greater temporal depth, thereby capturing more irreversibility and yielding tighter bounds. Under ideal conditions, this hierarchy converges to the full EPR in the limit of infinitely dense observations over a finite time window.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Activity-induced Nonequilibrium Vaporization Leads to Reentrant Phase Separation

Active Brownian particles (ABPs) with pure repulsion is an ideal model to understand the effect of nonequilibrium on collective behaviors. It has long been established that activity can create effective attractions leading to motility-induced phase separation (MIPS), whose role is similar to that of (inverse) temperature in the simplest equilibrium system with attractive inter-particle interactions. Here, our theoretical analysis based on a kinetic theory of MIPS shows that a new type of activity-induced nonequilibrium vaporization is able to hinder the formation of dense phase when activity is large enough. Such nonequilibrium vaporization along with the activity-induced effective attraction thus lead to a MIPS reentrance. Numerical simulations verify such nonequilibrium effect induced solely by activity on phase behaviors of ABPs, and further demonstrate the dependence of MIPS on activity and the strength of inter-particle interaction predicted by our theoretical analysis. Our findings highlight the unique role played by the nonequilibrium nature of activity on phase behaviors of active systems, which may inspire deep insights into the essential difference between equilibrium and nonequilibrium systems.

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preprint2022arXiv

Effective Entropy Production and Thermodynamic Uncertainty Relation of Active Brownian Particles

Understanding stochastic thermodynamics of active Brownian particles (ABPs) system has been an important topic in very recent years. In this article we study a general model of active Brownian particle systems by introducing a coarse-grained Fokker-Planck equation, which allows us to identify an effective entropy production along a stochastic trajectory, wherein an activity and configuration dependent diffusion coefficient comes into play with an important role. Although the hidden component between the true entropy production and the effective one is dominant, the effective entropy production still act as a reliable measure to quantify the dynamical irreversibility, capturing important phenomenon such as the interface and defects of motility induced phase separation (MIPS). Furthermore, in this framework, we are able to obtain the entropic bound as well as TUR associated with any generalized currents in the systems. We expect the new conceptual quantities proposed here to be broadly used in the context of active matter.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Improved estimation for energy dissipation in biochemical oscillations

Biochemical oscillations, regulating the timing of life processes, need consume energy to achieve good performance on crucial functions, such as high accuracy of phase period and high sensitivity to external signals. However, it is a great challenge to precisely estimate the energy dissipation in such systems. Here, based on the stochastic normal form theory (SNFT), we calculate the Pearson correlation coefficient between the oscillatory amplitude and phase, and a trade-off relation between transport efficiency and phase sensitivity can then be derived, which serves as a tighter form than the estimator resulting from the conventional thermodynamic uncertainty relation (TUR). Our findings demonstrate that a more precise energy dissipation estimation can be obtained by enhancing the sensitivity of the biochemical oscillations. Moreover, the internal noise and amplitude power effects have also been discovered.

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preprint2020arXiv

Design principles for biochemical oscillations with limited energy resources

As biochemical systems may frequently suffer from limited energy resources so that internal molecular fluctuation has to be utilized to induce random rhythm, it is still a great theoretical challenge to understand the elementary principles for biochemical systems with limited energy resources to maintain phase accuracy and phase sensitivity. Here, we address the issue by deriving the energy accuracy and the sensitivity-accuracy trade-off relations for a general biochemical model, analytically and numerically. We find that, biochemical systems consume much lower energy cost by noise-induced oscillations to keep almost equal efficiency to maintain precise processes than that by normal oscillations, elucidating clearly the survival mechanism when energy resources are limited. Moreover, an optimal system size is predicted where both the highest sensitivity and accuracy can be reached at the same time, providing a new strategy for the design of biological networks with limited energy sources.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Inertial Effects on Kinetics of Motility-Induced Phase Separation

Motility-induced phase separation (MIPS) is of great importance and has been extensively researched in overdamped systems, nevertheless, what impacts inertia will bring on kinetics of MIPS is lack of investigation. Here, we find that, not only the phase transition changes from continuous to discontinuous, but also the formation of clusters exhibits a nucleation-like process without any coarsening regime, different from spinodal decomposition in the overdamped case. This remarkable kinetics stems from a competition between activity-induced accumulation of particles and inertia-induced suppression of clustering process. More interestingly, the discontinuity of MIPS still exists even when the ratio of particle mass to the friction coefficient reduces to be very small such as 0.0001. Our findings emphasize the importance of inertia in kinetics of MIPS, and may open a new perspective on understanding the nature of MIPS in active systems.

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preprint2019arXiv

Configuration Dynamics of a Flexible Polymer Chain in a Bath of Chiral Active Particles

We investigate configuration dynamics of a flexible polymer chain in a bath of active particles with dynamic chirality, i.e., particles rotate with a deterministic angular velocity $ω$ besides self-propulsion,by Langevin dynamics simulations in two dimensional space. Particular attentions are paid to how the gyration radius $R_{g}$ changes with the propulsion velocity $v_{0}$,angular velocity $ω$ and chain length. We find that in a chiral bath with a typical nonzero $ω$, the chain first collapses into a small compact cluster and swells again with increasing $v_{0}$, in quite contrast to the case for a normal achiral bath $(ω=0)$ wherein a flexible chain swells with increasing $v_{0}$. More interestingly, the polymer can even form a closed ring if the chain length is large enough,which may oscillate with the cluster if $v_{0}$ is large. Consequently, the gyration radius $R_{g}$ shows nontrivial non-monotonic dependences on $v_{0}$, i.e., it undergoes a minimum for relatively short chains, and two minima with a maximum in between for longer chains. Our analysis shows that such interesting phenomena are mainly due to the competition between two roles played by the chiral active bath: while the persistence motion due to particle activity tends to stretch the chain, the circular motion of the particle may lead to an effective osmotic pressure that tends to collapse the chain. In addition, the size of the circular motion $R_{0}=v_{0}/ω$ shows an important role in that the compact clusters and closed-rings are both observed at nearly the same values of $R_{0}$ for different $ω$.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Self-assembly of active core corona particles into highly ordered and self-healing structures

Formation of highly ordered structures usually needs to overcome a high free-energy barrier that is greatly beyond the ability of thermodynamic fluctuation, such that the system would be easily trapped into a state with many defects and the annealing process of which often occurs on unreachable long time-scales. Here we report a fascinating example theoretically that active core corona particles can successfully self-assemble into a large-scaled and highly ordered stripe or trimer lattice, which is hardly achieved in a non-driven equilibrium system. Besides, such an activity-induced ordered structure shows an interesting self-healing feature of defects. In addition, there exists an optimal level of activity that most favorably enhance the formation of ordered self-assembly structures. Since core corona particles act as important units for self-assembly in real practice, we believe our study opens a new design-strategy for highly ordered materials.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A hybrid multiscale coarse-grained method for dynamics on complex networks

Brute-force simulations for dynamics on very large networks are quite expensive. While phenomenological treatments may capture some macroscopic properties, they often ignore important microscopic details. Fortunately, one may be only interested in the property of local part and not in the whole network. Here, we propose a hybrid multiscale coarse-grained(HMCG) method which combines a fine Monte Carlo(MC) simulation on the part of nodes of interest with a more coarse Langevin dynamics on the rest part. We demonstrate the validity of our method by analyzing the equilibrium Ising model and the nonequilibrium susceptible-infected-susceptible model. It is found that HMCG not only works very well in reproducing the phase transitions and critical phenomena of the microscopic models, but also accelerates the evaluation of dynamics with significant computational savings compared to microscopic MC simulations directly for the whole networks. The proposed method is general and can be applied to a wide variety of networked systems just adopting appropriate microscopic simulation methods and coarse graining approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Critical noise of majority-vote model on complex networks

The majority-vote model with noise is one of the simplest nonequilibrium statistical model that has been extensively studied in the context of complex networks. However, the relationship between the critical noise where the order-disorder phase transition takes place and the topology of the underlying networks is still lacking. In the paper, we use the heterogeneous mean-field theory to derive the rate equation for governing the model's dynamics that can analytically determine the critical noise $f_c$ in the limit of infinite network size $N\rightarrow \infty$. The result shows that $f_c$ depends on the ratio of ${\left\langle k \right\rangle }$ to ${\left\langle k^{3/2} \right\rangle }$, where ${\left\langle k \right\rangle }$ and ${\left\langle k^{3/2} \right\rangle }$ are the average degree and the $3/2$ order moment of degree distribution, respectively. Furthermore, we consider the finite size effect where the stochastic fluctuation should be involved. To the end, we derive the Langevin equation and obtain the potential of the corresponding Fokker-Planck equation. This allows us to calculate the effective critical noise $f_c(N)$ at which the susceptibility is maximal in finite size networks. We find that the $f_c-f_c(N)$ decays with $N$ in a power-law way and vanishes for $N\rightarrow \infty$. All the theoretical results are confirmed by performing the extensive Monte Carlo simulations in random $k$-regular networks, Erdös-Rényi random networks and scale-free networks.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Heterogeneous nucleation on complex networks with mobile impurities

We study the heterogeneous nucleation of Ising model on complex networks under a non-equilibrium situation where the impurities perform degree-biased motion controlled by a parameter α. Through the forward flux sampling and detailed analysis on the nucleating clusters, we find that the nucleation rate shows a nonmonotonic dependence on αfor small number of impurities, in which a maximal nucleation rate occurs at α=0 corresponding to the degree-uncorrelated random motion. Furthermore, we demonstrate the distinct features of the nucleating clusters along the pathway for different preference of impurities motion, which may be used to understand the resonance-like dependence of nucleation rate on the motion bias of impurities. Our theoretical analysis shows that the nonequilibrium diffusion of impurities can always induce a positive energy flux that can facilitate the barrier-crossing nucleation process. The nonmonotonic feature of the average value of the energy flux with αmay be the origin of our simulation results.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Large-scale Epitaxial Growth Kinetics of Graphene: A Kinetic Monte Carlo Study

Epitaxial growth via chemical vapor deposition is considered to be the most promising way towards synthesizing large area graphene with high quality. However, it remains a big theoretical challenge to reveal growth kinetics with atomically energetic and large-scale spatial information included. Here, we propose a minimal kinetic Monte Carlo model to address such an issue on an active catalyst surface with graphene/substrate lattice mismatch, which facilitates us to perform large scale simulations of the growth kinetics over two dimensional surface with growth fronts of complex shapes. A geometry-determined large-scale growth mechanism is revealed, where the rate-dominating event is found to be $C_{1}$-attachment for concave growth front segments and $C_{5}$-attachment for others. This growth mechanism leads to an interesting time-resolved growth behavior which is well consistent with that observed in a recent scanning tunneling microscopy experiment.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Nonequilibrium Glass Transition in Mixtures of Active-Passive Particles

We develop a mode coupling theory(MCT) to study the nonequilibrium glass transition behavior of a mono-disperse mixture of active-passive hard-sphere particles. The MCT equations clearly demonstrate that the glass transition is shifted to higher values of total volume fraction when doping a passive system with active particles. Interestingly, we find that the glass transition point may show a non-monotonic dependence on the effective diffusivity of the active component, indicating a nontrivial type of activity induced reentrance behavior. Analysis based on the nonergodic parameters suggest that the glassy state at small activity is due to the caging effect, while that at high activity could result from activity induced dynamic clustering.

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preprint2014arXiv

Complex activated transition in a system of two coupled bistable oscillators

We study the fluctuation-activated transition process in a system of two coupled bistable oscillators, in which each oscillator is driven by one constant force and an independent Gaussian white noise. The transition pathway has been identified and the transition rate has been computed as the coupling strength $μ$ and the mismatch $σ$ in the force constants are varied. For identical oscillators ($σ=0$), the transition undergoes a change from a two-step process with two candidate pathways to a one-step process with also two candidate pathways to a one-step process with a single pathway as $μ$ is increased. For nonidentical oscillators ($σ\neq0$), a novel transition emerges that is a mixture of a two-step pathway and a one-step pathway. Interestingly, we find that the total transition rate depends nonmonotonically on $μ$: a maximal rate appears in an intermediate magnitude of $μ$. Moreover, in the presence of weak coupling the rate also exhibits an unexpected maximum as a function of $σ$. The results are in an excellent agreement with our numerical simulations by forward flux sampling.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

An Efficient Self-optimized Sampling Method for Rare Events in Nonequilibrium Systems

Rare events such as nucleation processes are of ubiquitous importance in real systems. The most popular method for nonequilibrium systems, forward flux sampling (FFS), samples rare events by using interfaces to partition the whole transition process into sequence of steps along an order parameter connecting the initial and final states. FFS usually suffers from two main difficulties: low computational efficiency due to bad interface locations and even being not applicable when trapping into unknown intermediate metastable states. In the present work, we propose an approach to overcome these difficulties, by self-adaptively locating the interfaces on the fly in an optimized manner. Contrary to the conventional FFS which set the interfaces with euqal distance of the order parameter, our approach determines the interfaces with equal transition probability which is shown to satisfy the optimization condition. This is done by firstly running long local trajectories starting from the current interface $ł_i$ to get the conditional probability distribution $P_c$, and then determining $ł_{i+1}$ by equalling $P_c$ to a give value $p_0$. With these optimized interfaces, FFS can be run in a much efficient way. In addition, our approach can conveniently find the intermediate metastable states by monitoring some special long trajectories that nither end at the initial state nor reach the next interface, the number of which will increase sharply from zero if such metastable states are encountered. We apply our approach to a model two-state system and a two-dimensional lattice gas Ising model. Our approach is shown to be much more efficient than the conventional FFS method without losing accuracy, and it can also well reproduce the two-step nucleation scenario of the Ising model with easy identification of the intermidiate metastable state.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Explosive synchronization transitions in complex neural network

It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [Gómez-Gardeñes \emph{et al.} Phys.Rev.Letts. 106, 128701 (2011)] and chaotic oscillators [Leyva \emph{et al.} Phys.Rev.Letts. 108, 168702 (2012)]. Here, we investigate the effect of a microscopic correlation between the dynamics and the interacting topology of coupled FitzHugh-Nagumo oscillators on phase synchronization transition in Barabási-Albert (BA) scale-free networks and Erdös-Rényi (ER) random networks. We show that, if the width of distribution of natural frequencies of the oscillations is larger than a threshold value, a strong hysteresis loop arises in the synchronization diagram of BA networks due to the positive correlation between node degrees and natural frequencies of the oscillations, indicating the evidence of an explosive transition towards synchronization of relaxation oscillators system. In contrast to the results in BA networks, in more homogeneous ER networks the synchronization transition is always of continuous type regardless of the the width of the frequency distribution. Moreover, we consider the effect of degree-mixing patterns on the nature of the synchronization transition, and find that the degree assortativity is unfavorable for the occurrence of such an explosive transition.

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preprint2013arXiv

How does degree heterogeneity affect nucleation of Ising model on complex networks?

We investigate the nucleation of Ising model on complex networks and focus on the role played by the heterogeneity of degree distribution on nucleation rate. Using Monte Carlo simulation combined with forward flux sampling, we find that for a weak external field the nucleation rate decreases monotonically as degree heterogeneity increases. Interestingly, for a relatively strong external field the nucleation rate exhibits a nonmonotonic dependence on degree heterogeneity, in which there exists a maximal nucleation rate at an intermediate level of degree heterogeneity. Furthermore, we develop a heterogeneous mean-field theory for evaluating the free-energy barrier of nucleation. The theoretical estimations are qualitatively consistent with the simulation results. Our study suggests that degree heterogeneity plays a nontrivial role in the dynamics of phase transition in networked Ising systems.

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preprint2013arXiv

Mobility and density induced amplitude death in metapopulation networks of coupled oscillators

We investigate the effects of mobility and density on the amplitude death of coupled oscillators in metapopulation networks, wherein each node represents a subpopulation with any number of mobile individuals. We perform stochastic simulations of the dynamical reaction-diffusion processes associated with the Landau-Stuart oscillators in scale-free networks. Interestingly, we find that, with increasing the mobility rate or density, the system may undergo phase transitions from incoherent state to amplitude death, and then to frequency synchronization. Especially, there exists an extent of intermediate mobility rate and density leading to global oscillator death. In addition, we show this nontrivial phenomenon is robust to different network topologies. Our findings may invoke further efforts and attentions to explore the underlying mechanism of collective behaviors in metapopulation coupled systems.

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preprint2013arXiv

Mobility-enhanced signal response in metapopulation networks of coupled oscillators

We investigate the effect of mobility on the response of coupled oscillators to a subthreshold external signal in metapopulation networks, wherein each node represents a subpopulation with overdamped bistable oscillators that can randomly diffuse between nodes. With increasing mobility rate, the oscillators undergo transitions from intrawell to interwell motion, demonstrating clearly mobility-enhanced signal amplification. Moreover, the response shows nonmonotonic dependence on the mobility rate, i.e., a maximal gain occurs at a moderate level of mobility. This interesting phenomenon is robust against variations in the overall density, network size, as well as network topology. In addition, a simple mean-field analysis is carried out to qualitatively illustrate the simulation results.

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preprint2013arXiv

Orientation Sensitive Nonlinear Growth of Graphene: A Geometry-determined Epitaxial Growth Mechanism

Although the corresponding carbon-metal interactions can be very different, a similar nonlinear growth behavior of graphene has been observed for different metal substrates. To understand this interesting experimental observation, a multiscale $\lq\lq$standing-on-the-front" kinetic Monte Carlo study is performed. An extraordinary robust geometry effect is identified, which solely determines the growth kinetics and makes the details of carbon-metal interaction not relevant at all. Based on such a geometry-determined mechanism, epitaxial growth behavior of graphene can be easily predicted in many cases. As an example, an orientation-sensitive growth kinetics of graphene on Ir(111) surface has been studied. Our results demonstrate that lattice mismatch pattern at the atomic level plays an important role for macroscopic epitaxial growth.

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preprint2012arXiv

An efficient strategy to suppress epidemic explosion in heterogeneous metapopulation networks

We propose an efficient strategy to suppress epidemic explosion in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals and is assigned a curing rate that is proportional to $k^α$ with $k$ the node degree and $α$ an adjustable parameter. We have performed stochastic simulations of the dynamical reaction-diffusion processes associated with the susceptible-infected-susceptible model in scale-free networks. We found that the epidemic threshold reaches a maximum when the exponent $α$ is tuned to be $α_{opt}\simeq 1.3$. This nontrivial phenomenon is robust to the change of the network size and the average degree. In addition, we have carried out a mean field analysis to further validate our scheme, which also demonstrates that epidemic explosion follows different routes for $α$ larger or less than $α_{opt}$. Our work suggests that in order to effectively suppress epidemic spreading on heterogeneous complex networks, subpopulations with higher degrees should be allocated more resources than just being linearly dependent on the degree $k$.

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preprint2012arXiv

Delay induced bifurcation of dominant transition pathways

We investigate delay effects on dominant transition pathways (DTP) between metastable states of stochastic systems. A modified version of the Maier-Stein model with linear delayed feedback is considered as an example. By a stability analysis of the {"on-axis"} DTP in trajectory space, we find that a bifurcation of DTPs will be induced when time delay $τ$ is large enough. This finding is soon verified by numerically derived DTPs which are calculated by employing a recently developed minimum action method extended to delayed stochastic systems. Further simulation shows that, the delay-induced bifurcation of DTPs also results in a nontrivial dependence of the transition rate constant on the delay time. Finally, the bifurcation diagram is given on the $τ-β$ plane, where $β$ measures the non-conservation of the original Maier-Stein model.

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preprint2012arXiv

Flexibility Induced Motion Transition of Active Filament: Rotation without Long-range Hydrodynamic Interaction

We investigate the motion of active semiflexible filament with shape kinematics and hydrodynamic interaction including. Three types of filament motion are found: Translation, snaking and rotation. Change of flexibility will induce instability of shape kinematics and further result in asymmetry of shape kinematics respect to the motion of mass center, which are responsible to a continuous-like transition from translation to snaking and a first-order-like transition from snaking to rotation, respectively. Of particular interest, we find that long-range hydrodynamic interaction is not necessary for filament rotation, but can enhance remarkably the parameter region for its appearance. This finding may provide an evidence that the experimentally found collective rotation of active filaments is more likely to arise from the individual property even without the long-range hydrodynamic interaction.

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preprint2012arXiv

Noise-induced vortex reversal of self-propelled particles

We report an interesting phenomenon of noise-induced vortex reversal in a two-dimensional system of self-propelled particles (SPP) with soft-core interactions. With the aid of forward flux sampling, we analyze the configurations along the reversal pathway and thus identify the mechanism of vortex reversal. We find that statistically the reversal exhibits a hierarchical process: those particles at the periphery first change their motion directions, and then more inner layers of particles reverse later on. Furthermore, we calculate the dependence of the average reversal rate on noise intensity $D$ and the number $N$ of SPP. We find that the rate decreases exponentially with the reciprocal of $D$. Interestingly, the rate varies nonmonotonically with $N$ and a minimal rate exists for an intermediate value of $N$.

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preprint2012arXiv

Nucleation pathways on complex networks

Identifying nucleation pathway is important for understanding the kinetics of first-order phase transitions in natural systems. In the present work, we study nucleation pathway of the Ising model in homogeneous and heterogeneous networks using the forward flux sampling method, and find that the nucleation processes represent distinct features along pathways for different network topologies. For homogeneous networks, there always exists a dominant nucleating cluster to which relatively small clusters are attached gradually to form the critical nucleus. For heterogeneous ones, many small isolated nucleating clusters emerge at the early stage of the nucleation process, until suddenly they form the critical nucleus through a sharp merging process. By analyzing the properties of the nucleating clusters along the pathway, we show that the main reason behind the different routes is the heterogeneous character of the underlying networks.

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preprint2011arXiv

Atomistic Mechanisms of Nonlinear Graphene Growth on Ir Surface

As a two-dimensional material, graphene can be naturally obtained via epitaxial growth on a suitable substrate. Growth condition optimization usually requires an atomistic level understanding of the growth mechanism. In this article, we perform a mechanistic study about graphene growth on Ir(111) surface by combining first principles calculations and kinetic Monte Carlo (kMC) simulations. Small carbon clusters on the Ir surface are checked first. On terraces, arching chain configurations are favorable in energy and they are also of relatively high mobilities. At steps, some magic two-dimensional compact structures are identified, which show clear relevance to the nucleation process. Attachment of carbon species to a graphene edge is then studied. Due to the effect of substrate, at some edge sites, atomic carbon attachment becomes thermodynamically unfavorable. Graphene growth at these difficult sites has to proceed via cluster attachment, which is the growth rate determining step. Based on such an inhomogeneous growth picture, kMC simulations are made possible by successfully separating different timescales, and they well reproduce the experimentally observed nonlinear kinetics. Different growth rates and nonlinear behaviors are predicted for different graphene orientations, which is consistent with available experimental results. Importantly, as a phenomenon originated from lattice mismatch, inhomogeneity revealed in this case is expected to be quite universal and it should also make important roles in many other hetero-epitaxial systems.

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preprint2011arXiv

Coarse-grained Monte Carlo simulations of the phase transition of Potts model on weighted networks

Developing effective coarse grained (CG) approach is a promising way for studying dynamics on large size networks. In the present work, we have proposed a strength-based CG (\sCG) method to study critical phenomena of the Potts model on weighted complex networks. By merging nodes with close strength together, the original network is reduced to a CG-network with much smaller size, on which the CG-Hamiltonian can be well-defined. In particular, we make error analysis and show that our strength-based CG approach satisfies the condition of statistical consistency, which demands that the equilibrium probability distribution of the CG-model matches that of the microscopic counterpart. Extensive numerical simulations are performed on scale-free networks, without or with strength-correlation, showing that this \sCG approach works very well in reproducing the phase diagrams, fluctuations, and finite size effects of the microscopic model, while the \dCG approach proposed in our recent work [Phys. Rev. E 82, 011107(2010)] does not.

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preprint2011arXiv

Coarse-grained Simulations of Chemical Oscillation in a Lattice Brusselator System

Accelerated coarse-graining (CG) algorithms for simulating heterogeneous chemical reactions on surface systems have recently gained much attention. In the present paper, we consider such an issue by investigating the oscillation behavior of a two-dimension (2D) lattice-gas Brusselator model. We have adopted a coarse-grained Kinetic Monte Carlo (CG-KMC) procedure, where $m \times m$ microscopic lattice sites are grouped together to form a CG cell, upon which CG processes take place with well-defined CG rates. We find that, however, such a CG approach almost fails if the CG rates are obtained by a simple local mean field ($s$-LMF) approximation, due to the ignorance of correlation among adjcent cells resulted from the trimolecular reaction in this nonlinear system. By properly incorporating such boundary effects, we thus introduce the so-called $b$-LMF CG approach. Extensive numerical simulations demonstrate that the $b$-LMF method can reproduce the oscillation behavior of the system quite well, given that the diffusion constant is not too small. In addition, we find that the deviation from the KMC results reaches a nearly zero minimum level at an intermediate cell size, which lies in between the effective diffusion length and the minimal size required to sustain a well-defined temporal oscillation.

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preprint2011arXiv

Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics

Stochastic thermodynamics of chemical reaction systems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalytic oxidation of carbon monoxide on the surface of platinum crystal as an example. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the time averaged entropy productionP on the system sizeN in a parameter region close to the deterministic Hopf bifurcation.In the large system size (weak noise) limit, we find that P N^β with β=0 or 1 when the system is below or abovethe Hopf bifurcation, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly,P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system parameter approaches the so-called CANARD point where the maximum disappears.This phenomenon could be qualitativelyunderstood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.

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preprint2011arXiv

Optimal modularity for nucleation in network-organized Ising model

We study nucleation dynamics of Ising model in a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in real-world networks. By introducing a variant of a recently developed forward flux sampling method, we efficiently calculate the rate and elucidate the pathway for nucleation process. It is found that as the network modularity becomes worse the nucleation undergoes a transition from two-step to one-step process. Interestingly, the nucleation rate shows a nonmonotonic dependency on the modularity, in which a maximal nucleation rate occurs at a moderate level of modularity. A simple mean field analysis is proposed to qualitatively illustrate the simulation results.

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preprint2011arXiv

Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling

We investigate temporal coherence and spatial synchronization on small-world networks consisting of noisy Terman-Wang (TW) excitable neurons in dependence on two types of time-delayed coupling: $\{x_j(t-τ)-x_i (t)\}$ and $\{x_j(t-τ)-x_i(t-τ)\}$. For the former case, we show that time delay in the coupling can dramatically enhance temporal coherence and spatial synchrony of the noise-induced spike trains. In addition, if the delay time $τ$ is tuned to nearly match the intrinsic spike period of the neuronal network, the system dynamics reaches a most ordered state, which is both periodic in time and nearly synchronized in space, demonstrating an interesting resonance phenomenon with delay. For the latter case, however, we can not achieve a similar spatiotemporal ordered state, but the neuronal dynamics exhibits interesting synchronization transition with time delay from zigzag fronts of excitations to dynamic clustering anti-phase synchronization (APS), and further to clustered chimera states which have spatially distributed anti-phase coherence separated by incoherence. Furthermore, we also show how these findings are influenced by the change of the noise intensity and the rewiring probability. Finally, qualitative analysis is given to illustrate the numerical results.

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preprint2010arXiv

Nucleation in scale-free networks

We have studied nucleation dynamics of the Ising model in scale-free networks with degree distribution $P(k)\sim k^{-γ}$ by using forward flux sampling method, focusing on how the network topology would influence the nucleation rate and pathway. For homogeneous nucleation, the new phase clusters grow from those nodes with smaller degree, while the cluster sizes follow a power-law distribution. Interestingly, we find that the nucleation rate $R_{Hom}$ decays exponentially with the network size $N$, and accordingly the critical nucleus size increases linearly with $N$, implying that homogeneous nucleation is not relevant in the thermodynamic limit. These observations are robust to the change of $γ$ and also present in random networks. In addition, we have also studied the dynamics of heterogeneous nucleation, wherein $w$ impurities are initially added, either to randomly selected nodes or to targeted ones with largest degrees. We find that targeted impurities can enhance the nucleation rate $R_{Het}$ much more sharply than random ones. Moreover, $\ln (R_{Het}/R_{Hom})$ scales as $w^{γ-2/γ-1}$ and $w$ for targeted and random impurities, respectively. A simple mean field analysis is also present to qualitatively illustrate above simulation results.

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preprint2010arXiv

Statistically consistent coarse-grained simulations for critical phenomena in complex networks

We propose a degree-based coarse graining approach that not just accelerates the evaluation of dynamics on complex networks, but also satisfies the consistency conditions for both equilibrium statistical distributions and nonequilibrium dynamical flows. For the Ising model and susceptible-infected-susceptible epidemic model, we introduce these required conditions explicitly and further prove that they are satisfied by our coarse-grained network construction within the annealed network approximation. Finally, we numerically show that the phase transitions and fluctuations on the coarse-grained network are all in good agreements with those on the original one.

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preprint2009arXiv

Resonant response of forced complex networks: the role of topological disorder

We investigate the effect of topological disorder on a system of forced threshold elements, where each element is arranged on top of complex heterogeneous networks. Numerical results indicate that the response of the system to a weak signal can be amplified at an intermediate level of topological disorder, thus indicating the occurrence of topological-disorder-induced resonance. Using mean field method, we obtain an analytical understanding of the resonant phenomenon by deriving the effective potential of the system. Our findings might provide further insight into the role of network topology in signal amplification in biological networks.

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