International Journal of Modern Physics C

We study the traffic-driven epidemic spreading on scale-free networks with tunable degree distribution. The heterogeneity of networks is controlled by the exponent $\gamma$ of power-law degree distribution. It is found that the epidemic threshold is minimized at about $\gamma =2.2$. Moreover, we find that nodes with larger algorithmic betweenness are more likely to be infected. We expect our work to provide new insights in to the effect of network structures on traffic-driven epidemic spreading.

In this paper, to deal with the problem of modified function projective synchronization (MFPS) between two different networks with delayed couplings and delayed nodes of different dimensions, a hybrid control scheme combining adaptive control and nonlinear control is proposed. First, a more realistic drive-response complex network model is constructed by introducing double delays. Then, we design hybrid feedback controllers to synchronize up the drive and response networks of different dimensions to a scaling function matrix. Based on Lyapunov stability theory and the linear matrix inequality (LMI), we rigorously prove that the MFPS between the proposed drive-response networks can be achieved and meanwhile some sufficient conditions are derived by adopting an appropriate Lyapunov–Krasovskii energy function. Noteably, many existing synchronization settings can be regarded as special cases of the present synchronization framework. Numerical simulation experiments are employed to verify the correctness and the effectiveness of the proposed method.

Minesweeper is a famous computer game consisting usually in a two-dimensional lattice, where cells can be empty or mined and gamers are required to locate the mines without dying. Even if minesweeper seems to be a very simple system, it has some complex and interesting properties as NP-completeness. In this paper and for the one-dimensional case, given a lattice of n cells and m mines, we calculate the winning probability. By numerical simulations this probability is also estimated. We also find out by mean of these simulations that there exists a critical density of mines that minimize the probability of winning the game. Analytical results and simulations are compared showing a very good agreement.

Motivated by the way Japanese tatami mats are placed on the floor, we consider domino tilings with a constraint and estimate the number of such tilings of plane regions. We map the system onto a monomer-dimer model with a novel local interaction on the dual lattice. We make use of a variant of the Hamiltonian replica exchange Monte Carlo method where data for ferromagnetic and anti-ferromagnetic models are combined to make a single family of histograms. The properties of the density of states is studied beyond exact enumeration and combinatorial methods. The logarithm of the number of the tilings is linear in the boundary length of the region for all the regions studied.

A backstepping scheme is proposed for synchronization between two complex dynamical networks with different structures. The nodes of the networks are spatiotemporal chaotic systems. A recurrence relation containing the information from neighbors is established so that only one control input is needed to synchronize two spatiotemporal networks. The Lyapunov stability theory is applied to prove that the differences between the drive and response networks tend to zero asymptotically under the control. The proposed scheme is numerically implemented in the synchronization of two networks with the Fisher–Kolmogorov and the Burgers spatiotemporal chaotic systems as the nodes.

The pseudopotential lattice Boltzmann model has been widely used to solve multi-phase and multi-component flow problems. However, original pseudopotential model cannot be used in simulating diffusion flow with large pressure difference because of its limitation. In this paper, we incorporate pseudopotential model with a new form of effective mass to solve this problem based on the relationship between pressure difference and effective mass. The improved model is verified through Laplace’s law and binary immiscible Poiseuille flow. By simulating pipeline binary diffusion flow and two-inlet binary cavity jet flow, we show that the improved model can achieve larger pressure difference than pseudopotential model with traditional effective mass forms.

Cascading failures of loads in isolated networks have been studied extensively over the last decade. Since 2010, such research has extended to interdependent networks. In this paper, we study cascading failures with local load redistribution in interdependent Watts–Strogatz (WS) networks. The effects of rewiring probability and coupling strength on the resilience of interdependent WS networks have been extensively investigated. It has been found that, for small values of the tolerance parameter, interdependent networks are more vulnerable as rewiring probability increases. For larger values of the tolerance parameter, the robustness of interdependent networks firstly decreases and then increases as rewiring probability increases. Coupling strength has a different impact on robustness. For low values of coupling strength, the resilience of interdependent networks decreases with the increment of the coupling strength until it reaches a certain threshold value. For values of coupling strength above this threshold, the opposite effect is observed. Our results are helpful to understand and design resilient interdependent networks.

The statistical mechanics approach to wealth distribution is based on the conservative kinetic multi-agent model for money exchange, where the local interaction rule between the agents is analogous to the elastic particle scattering process. Here, we discuss the role of a class of conservative local operators, and we show that, depending on the values of their parameters, they can be used to generate all the relevant distributions. We also show numerically that in order to generate the power-law tail, an heterogeneous risk aversion model is required. By changing the parameters of these operators, one can also fine tune the resulting distributions in order to provide support for the emergence of a more egalitarian wealth distribution.

Relativistic generalization of path integral Monte Carlo (PIMC) method has been proposed. The problem of relativistic oscillator has been studied in the framework of this approach. Ultra-relativistic and nonrelativistic limits have been discussed. We show that PIMC method can be effectively used for investigation of relativistic systems.

We investigate the critical properties of the equilibrium and nonequilibrium systems on Solomon networks. The equilibrium and nonequilibrium systems studied here are the Ising and Majority-vote models, respectively. These systems are simulated by applying the Monte Carlo method. We calculate the critical points, as well as the critical exponents ratio $\gamma ∕\nu$, $\beta ∕\nu$ and $1∕\nu$. We find that both systems present identical exponents on Solomon networks and are of different universality class as the regular two-dimensional ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

Based on velocity-difference-separation model, the mixed traffic flow on two-lane road is investigated. For a fixed road length, the influence of bus and bus stops on traffic flow is studied with the increasing traffic density. Compared with the result without bus stops given by Li et al., a new traffic state is found, which is valuable for studying the impacts of public transport on urban traffic flow.

Opinion formation is a process through which interactions of individuals and dynamism of their opinions in effect of neighbors are modeled. In this paper, in an effort to model the opinion formation more realistically, we have introduced a model that considers the role of network structure in opinion dynamics. In this model, each individual changes his opinion in a way so as to decrease its difference with the opinion of trusted neighbors while he intensifies his dissention with the untrusted ones. Considering trust/distrust relations as a signed network, we have defined a structural indicator which shows the degree of instability in social structure and is calculated based on the structural balance theory. It is also applied as feedback to the opinion formation process affecting its dynamics. Our simulation results show formation of a set of clusters containing individuals holding opinions having similar values. Also, the opinion value of each individual is far from the ones of distrusted neighbors. Since this model considers distrust and instability of relations in society, it can offer a more realistic model of opinion formation.

Molecular motors are natural nanomachines that use the free energy released from ATP hydrolysis to generate mechanical forces. Cytoplasmic dynein motors often work collectively as a team to drive important processes such as axonal growth, proplatelet formation and mitosis, as forces generated by single motors are insufficient. A large team of dynein motors is used to slide cytoskeletal microtubules with respect to one another during the process of proplatelet formation and axonal growth. These motors attach to a cargo microtubule via their tail domains, undergo the process of detachment and reattachment of their head domains on another track microtubule, while sliding the cargo microtubule along the track. Traditional continuum/mean-field approaches used in the past are not ideal for studying the sliding mechanism of microtubules, as they ignore spatial and temporal fluctuations due to different possible distributions of motor tails on cargo filament, as well as binding/unbinding of motors from their track. Therefore, these models cannot be used to address important questions such as how the distribution of motor tails on microtubules, or how the mutual exclusion of motor heads on microtubule tracks affects the sliding velocity of cargo microtubule. To answer these, here we use a computational stochastic model where we model each dynein motor explicitly. In our model, we use both random as well as uniform distributions of dynein motors on cargo microtubule, as well as mutual exclusion of motors on microtubule tracks. We find that sliding velocities are least affected by the distribution of motor tails on microtubules, whereas they are greatly affected by mutual exclusion of motor heads on microtubule tracks. We also find that sliding velocity depends on the length of cargo microtubule if mutual exclusion among motor heads is considered.

In this paper, we introduce a modification of detrended fluctuation analysis (DFA), called multivariate DFA (MNDFA) method, based on the scaling of time series size $N$. In traditional DFA method, we obtained the influence of the sequence segmentation interval $s$, and it inspires us to propose a new model MNDFA to discuss the scaling of time series size towards DFA. The effectiveness of the procedure is verified by numerical experiments with both artificial and stock returns series. Results show that the proposed MNDFA method contains more significant information of series compared to traditional DFA method. The scaling of time series size has an influence on the auto-correlation (AC) in time series. For certain series, we obtain an exponential relationship, and also calculate the slope through the fitting function. Our analysis and finite-size effect test demonstrate that an appropriate choice of the time series size can avoid unnecessary influences, and also make the testing results more accurate.