International Journal of Modern Physics C

The problem of Complex Modified Projective Synchronization (CMPS) for fractional-order complex-valued dynamic networks (FOCDNs) is investigated in this paper. Compared with real-valued dynamic networks, complex-valued dynamic networks have expansive application space. First, coupling weight has been generally considered as static constant in most situations, we consider time-varying coupling weight and the unknown parameters in the FOCDNs. Meanwhile, several parameter update laws are designed to estimate unknown parameters and an adaptive coupling weight is defined to adjust coupling nodes in order to solve CMPS problem of the network. Second, some effective criteria for CMPS of FOCDNs are derived by fractional calculus and Lyapunov stability theory. According to the theoretical analysis, FOCDNs with time-varying delay can achieve CMPS via adaptive controller. Finally, the effectiveness of the modified projective strategy for fractional-order complex networks is illustrated via two numerical examples in the complex-valued space.

The quality of air is closely related to people’s life. When the concentration of pollutants in the atmosphere reaches a harmful level, it will damage the ecosystem and threaten the survival of human beings. To study the internal transmission mechanism of air pollutants, a model named Uncontaminated–Emissive–Contaminated–Recovered (UECR) is proposed in this paper. This model considers the influence of various control measures of air diffusion, and the heterogeneity of the underlying network. First, based on the mean-field theory, the basic reproductive rate $R_0$ was calculated, the relationship between $R_0$ and equilibrium points was proved, and the stability of the model was also demonstrated. Then, combined with three existing air pollutant propagation networks, the model’s effectiveness was illustrated through simulation experiments. From the proof and experiments, it was concluded that the propagation of air pollutants is related to the basic reproductive rate, so some suggestions were given on pollution prevention and control for accelerating the ending process of pollutant propagation.

The dynamical Brusselator reaction–diffusion system of time-fractional is used to describe chemical models and chemical processes with nonlinear oscillation. In this study, the Laplace optimized decomposition scheme is proposed for approximating solutions of three applications of the two-dimensional (2D) reaction–diffusion Brusselator model with the noninteger derivative proposed in the Caputo approach. Complete descriptions of the scheme and solution steps are utilized and mentioned. By applying the procedures of the Laplace inversion operator and truncating the optimized series, the approximate solutions are drawn, tabulated and sketched. Numerical results show the efficiency, reliability and accuracy of the technique for the nonlinear systems of partial differential equations of noninteger-different order derivatives. Finally, focused notes and futures planning works are mentioned with the most-used references.

Abnormal event detection is a popular research direction in the field of intelligent transportation and public safety. The features that characterize abnormal events are extracted from given video sequence through computer vision technology. Then the abnormal events in the video are automatically detected through the classification model. In order to describe the motion characteristics of events more accurately, a new feature based on motion entropy is proposed in this paper. The entropy value of motion pixels in the video frame is calculated as the input feature of the classification model. Motion entropy is suitable to regard as a feature to distinguish normal events from abnormal events due to the big differences between normal and abnormal events. In addition, an abnormal event detection model based on motion entropy and dual support vector data description (ME-DSVDD) is presented to solve the problem of insufficient sample diversity. The standard data set is tested to analyze the performance of the proposed model. The experimental results show that the proposed method can effectively improve the performance of the abnormal event detection model.

We investigate the external field effect on opinion formation based on the majority rule and $q$-voter models on a complete graph. The external field can be considered as the mass media in the social system, with the probability $p$ agents following the mass media opinion. Based on our Monte Carlo simulation, the mass media effect is not strong enough to make the system reach a homogeneous state (complete consensus) with the magnetization $m=1$ for all values of $p$, indicating the existence of a usual phase transition for all values of $p$. In the $q$-voter model, the mass media eliminates the usual phase transition at $p\approx 0.21$. We obtain the model’s critical point and scaling parameters using the finite-size scaling analysis and obtain that both models have the same scaling parameters. The external field effect decreases both models’ relaxation time and the relaxation time following the power-law relation such as $\tau \sim N^{\beta }$, where $N$ is the population size and $\beta$ depends on the probability $p$. In the majority rule model, $\beta$ follows a linear relation, and in the q-voter model, $\beta$ follows a power-law relation.

This paper proposes a new cooperative driving model for the platooning of connected and automated vehicles on basic freeway sections. We introduce the desired speed, consider the communication delay between vehicles in the actual environment and employ the constant time headway policy as the spacing policy. In the model, the position error, the speed error, the difference between the desired speed and the speed of the considered vehicle and the acceleration are taken into account. The information obtained by vehicle communication is fully utilized, and the control effect of the control strategy is improved. We apply the Lyapunov–Krasovskii theorem to investigate the stability of the system. The effectiveness of the proposed model is verified by several traffic simulation scenarios.

This paper deals with the design of a CPU cooling system using a novel numerical modelling approach based on automatic calculation in a commercial software. A research object is an aluminium CPU heat sink with a thermal design power of 50 W with a new fin design. A numerical model of the cooling process has been developed, and the heat sink efficiency has been investigated. The main goal of optimization was to get the minimum temperature of the CPU processor at the minimum mass of the heat sink. The comparative analysis of the results that obtained via three methods (screening, adaptive multiple-objective, multi-objective genetic algorithm) was performed. This analysis showed that screening was the least time-consuming method, but it did not provide the required solution. Adaptive multiple-objective and multi-objective genetic algorithm solutions show similar results but significantly differ in time. It was established that the adaptive multiple-objective method is the best method for the heat sink optimization task. At the determined optimal design parameter, the CPU temperature is in the range 304–307 K, while the mass was 81–87 g. In comparison, the heat sink mass before optimization of the design parameters was 93 g at the CPU temperature of 309–311 K.

In the research of network structure, long ties are considered to be a hidden but valuable interaction. In this paper, we innovatively interpret the long ties structure in traditional research as a higher-order information spreading path. It effectively avoids the homogenization of information level and redundancy of network structure. The spreading bridge model based on high-order long ties structure is established accordingly. Modern online social behavior is modeled by establishing spreading expansion rate and spreading diffusion rate to improve model adaptability. The spread dynamics model based on multivariate interactions is developed by combining direct-linked spread as a binary interaction relationship in traditional research with bridge-linked spread. The validity of the model is verified by comparing the model simulation results with real cases.

Agent’s learning behavior usually presents biased judgments influenced by many internal and external reasons, we incorporate an improved $Q$-learning algorithm in the reinforcement learning which is examined with the prisoner’s dilemma game in an activity-driven networks. The heterogeneous learning rate and $ϵ$-greedy exploration mechanism are taken into account while modeling decision-making of agents. Simulation results show the proposed reinforcement learning mechanism is conducive to the emergence of defective behavior, i.e. it could maximize one’s expected payoff regardless of its neighbors’ strategy. In addition, we find the temptation gain, vision level and the number of connected edges of activated agents are proportional to the density of defectors. Interestingly, when the inherent learning rate is small, the increase of exploration rate can demote the appearance of defectors, and the decrease of defectors is insignificant by increasing of exploration rate conversely.

This work is based on a numerical simulation to study the flow pattern and heat transfer characteristics inside a cavity in the form of an Islamic knot. The effect of height and length of the obstacle are investigated. Nine different obstacles with different lengths (a) and heights (b) are considered. It can be found that the variation in length and height of the hot obstacle leads to the obvious change in the flow field and temperature field. In addition, the small gap inside the cavity has a limited effect on the flow motion. Besides, the small gap between the cold and hot surfaces leads to higher conduction heat transport. For high Ra, the flow and heat transfer characteristics can be described in two situations. The first is included in the cases of $(a,b)=(10,1)$, (10, 2) and (10, 3), where the primary vortices are located on the top and bottom of the cavity. The second one consists of cases $(a,b)=(3,3)$, (4, 3), (5, 3), (6, 3), (7, 3) and (8, 3), where the primary flow circulations are established on the left and right sides. For all the cases, the average Nu increases by rising the Ra. By increasing the Ra, the average Nu in the second situation increases more significantly than that in the first one. The cases in the second situation always have better heat transfer performance than those in the first one, especially at higher Ra.

A solid–solid contact model of a rough surface with a single peak was established to explore the thermal effect of interfacial friction. From the perspective of friction force, temperature and energy, the law of the thermal effect was revealed. The results showed that the temperature of the asperities gradually increased during the shearing process, and a stress concentration formed in the shearing zone. After contact, the asperities had undergone unrecoverable plastic deformation. At each indentation depth, as the rotation angle of the crystal increased, the friction force, average temperature, and the sum of the changes in thermal kinetic and thermal potential energy first increased and then decreased; the trends of the three parameters changing with the rotation angle of the crystal were consistent. The average decreases in the friction force, average temperature, and the sum of the changes in thermal kinetic and thermal potential energy were 52.47%, 30.91% and 56.75%, respectively, for a crystal structure with a rotation angle of 45^∘ compared to a crystal structure with a rotation angle of 0^∘. The methods used in this study provide a reference for the design of frictional pairs and the reduction of the thermal effect of interfacial friction.

The pulse widening in fiber communications causes a significant restriction of bit rate. The intermodal dispersion occurs not only in grade-index multimode fibers but also in the two-core single-mode fiber. The Goos–Hänchen (GH) shift is not considered in the conventional analysis based on geometric optics. The GH shift is calculated in the step-index fiber in this paper. The analytic expression is derived for calculating the pulse widening from intermodal dispersion in the multimode fiber. The analytic and numerical results show that GH shift has an important effect on the intermodal dispersion. The positive GH shift can decrease the pulse widening. The maximum transmission distance of a multimode fiber can be greatly increased when light propagates near the maximum critical propagation angle.

This paper focuses on numerical solutions of time fractional nonlinear Korteweg–de Vries–Burgers equation formulated with Caputo’s fractional derivative. For this purpose, a framework of combinations of collocation method with the finite-element method is provided using trigonometric quintic B-spline basis. The method consists of both spatial discretization and temporal discretization using approximate solution and Crank–Nicolson approach. Discretizing fractional derivative is made using $L1(0<\gamma \le 1)$ algorithm which is derived from the definition of Caputo derivative using an approximate function. The stability analysis is established using von-Neumann stability technique. The numerical results obtained using the collocation method are presented via tables and graphics. The novel results demonstrate the efficiency and reliability of the method.

Early warning signs of the outbreak of pandemic disease become a high profile from the beginning and they remind more susceptible individuals to keep social distance on social occasions. However, these signs have no way to the Susceptible–Infected–Recovered (SIR) models which have been concerned by medical scientists. Warning signs imply the risk level of the pandemic disease evaluated by the government. The response of susceptible population ($S$-population) to the warning signs is represented by a chicken game. In order to get a better payoff, the more beneficial behavior of the $S$-population may be induced in the autonomous society based on the SIR model. We emphasize that participants can choose their strategies whether to follow the health rules or not without coercion in the chicken game while the warning signs released by the policy makers can encourage $S$-population to choose beneficial behavior, instead of purely following the healthy rules or not. The agile policy helps $S$-population to make a choice on the basis of risk interests but without losing to protect themselves in a serious pandemic situation. Comparing the classic SIR model with our signal-SIR model, the serious pandemic signal released by the policy makers and the disease awareness to it together play an important role in the outbreak period of the pandemic disease.