International Journal of Modern Physics C

In this paper, the second-, third- and fourth-order Abel equations are solved. The differential transform method (DTM) is used to compute approximate solutions of the nonlinear ordinary Abel differential equations. The results are compared with the results obtained by the classical Runge–Kutta (RK4) method. Figures are presented to show the reliability and simplicity of the method.

A model of fission gas migration in nuclear fuel pellet is proposed. Diffusion process of fission gas in granular structure of nuclear fuel with presence of inter-granular bubbles in the fuel matrix is simulated by fractional diffusion model. The Grunwald–Letnikov derivative parameter characterizes the influence of porous fuel matrix on the diffusion process of fission gas. A finite-difference method for solving fractional diffusion equations is considered. Numerical solution of diffusion equation shows correlation of fission gas release and Grunwald–Letnikov derivative parameter. Calculated profile of fission gas concentration distribution is similar to that obtained in the experimental studies. Diffusion of fission gas is modeled for real RBMK-1500 fuel operation conditions. A functional dependence of Grunwald–Letnikov derivative parameter with fuel burn-up is established.

The main focus of this research is the contagion of a financial crisis on an interbank debt network. In order to simulate the crisis propagation a weighted community complex network based on growth strategy has been created. The contagion is described by a new way of disease propagation perspective based on the concept of a financial virus. The model reproduces the existence of TBTF banks and shows the impact that an initial TBTF bank crash produces in the interbank network depending on the magnitude of the initial crash and on the resistance that the network offers against the contagion propagation.

In complex network epidemiology, diseases spread along contacting edges between individuals and different edges may play different roles in epidemic outbreaks. Quantifying the efficiency of edges is an important step towards arresting epidemics. In this paper, we study the efficiency of edges in general susceptible-infected-recovered models, and introduce the transmission capability to measure the efficiency of edges. Results show that deleting edges with the highest transmission capability will greatly decrease epidemics on scale-free networks. Basing on the message passing approach, we get exact mathematical solution on configuration model networks with edge deletion in the large size limit.

One frequently observed congested traffic flow pattern is wide moving jam (WMJ), in which the average vehicle speed is very low and the density is very high. In some recent studies, variable speed limits (VSL) were proposed as effective measures to eliminate or abate the influence of jam waves. However, in most of these studies, the stochastic features of driving behaviors and the resulting uncertainty of traffic flow dynamics were not fully considered. In this paper, we use cellular automaton (CA) model-based simulations to test the performances of different VSL control strategies and apply the three-phase traffic theory to further analyze the obtained results. Based on the simulation results, we got two novel findings. Firstly, we observed seven, instead of the previously assumed six, states of traffic flow in the evolution process of WMJ, when VSL were applied. Secondly and more importantly, we found that inappropriate speed limit may induce new WMJ and exaggerate congestions in two ways: one way corresponds to an F → J transition and the other corresponds to an F → S → J transition. Based on these findings, the appropriate lower bound of VSL was finally discussed in this paper.

In this paper, we extend some ideas of statistical physics to describe the properties of human mobility. From a physical point of view, we consider the statistical empirical laws of private cars mobility, taking advantage of a GPS database which contains a sampling of the individual trajectories of 2% of the whole vehicle population in an Italian region. Our aim is to discover possible "universal laws" that can be related to the dynamical cognitive features of individuals. Analyzing the empirical trip length distribution we study if the travel time can be used as universal cost function in a mesoscopic model of mobility. We discuss the implications of the elapsed times distribution between successive trips that shows an underlying Benford's law, and we study the rank distribution of the average visitation frequency to understand how people organize their daily agenda. We also propose simple stochastic models to suggest possible explanations of the empirical observations and we compare our results with analogous results on statistical properties of human mobility presented in the literature.

In usual scale-free networks of Barabási–Albert type, a newly added node selects randomly m neighbors from the already existing network nodes, proportionally to the number of links these had before. Then the number n(k) of nodes with k links each decays as 1/k^γ where γ = 3 is universal, i.e. independent of m. Now we use a limited directedness in building the network, as a result of which the exponent γ decreases from 3 to 2 for increasing m.

One-directional traffic on two-lanes is modeled in the framework of a spring-block type model. A fraction q of the cars are allowed to change lanes, following simple dynamical rules, while the other cars keep their initial lane. The advance of cars, starting from equivalent positions and following the two driving strategies is studied and compared. As a function of the parameter q the winning probability and the average gain in the advancement for the lane-changing strategy is computed. An interesting phase-transition like behavior is revealed and conclusions are drawn regarding the conditions when the lane changing strategy is the better option for the drivers.