International Journal of Modern Physics C

We show that several orbital equations and orbital clusters of the quadratic (logistic) map coincide surprisingly with cyclotomic period equations, polynomials whose roots are Gaussian periods. An analytical expression for the field discriminant of period equations is obtained and applied to discover and to fill gaps in number field databases constructed by numerical search processes. Such expression allows easy assess to inessential divisors of conventional discriminants and sheds light into why numerical construction of databases is a hard problem. It also provides significant information about the organization of periodic orbits of the quadratic map.

Identifying influential nodes in complex networks continues to be an open and vital issue, which is of great significance to the robustness and vulnerability of networks. In order to accurately identify influential nodes in complex networks and avoid the deviation in the evaluation of node influence by single measure, a novel method based on improved Technology for Order Preference by Similarity to an Ideal Solution (TOPSIS) is proposed to integrate multiple measures and identify influential nodes. Our method takes into account degree centrality (DC), closeness centrality (CC) and betweenness centrality (BC), and uses the information of the decision matrix to objectively assign weight to each measure, and takes the closeness degree from each node to be the ideal solution as the basis for comprehensive evaluation. At last, four experiments based on the Susceptible-Infected (SI) model are carried out, and the superiority of our method can be demonstrated.

The chronic traffic congestion undermines the level of satisfaction within a society. This study proposes a departure time model for estimating the temporal distribution of morning rush-hour traffic congestion over urban road networks. The departure time model is developed based on the point queue model that is used for estimating travel time. First, we prove the effectiveness of the travel time model (i.e. point queue), showing that it gives the same travel time estimation as the kinematic wave model does for a road with successive bottlenecks. Then, a variant of the bottleneck model is developed accordingly, aiming to capture travelers’ departure time choice for commute trips. The proposed departure time model relaxes a traditional assumption that the last commuter experiences the free flow travel time and considers travelers’ unwillingness of late arrivals for work. Numerical experiments show that the morning rush-hour generally starts at 7:29 am and ends at 8:46 am with a traffic congestion delay index (TCDI) of 2.164 for Beijing, China. Furthermore, the estimation of rush-hour start and end time is insensitive to most model parameters including the proportion of travelers who tend to arrive at work earlier than their schedules.

We first perform a complete Lie symmetry classification of the generalized convective Cahn–Hilliard equation. Then using the obtained symmetries, we mainly study the convective Cahn–Hilliard equation, of which a new power series solution is constructed. In particular for the crystal surface growth processes, the truncated series solution shows that the surface structures include peaks and valleys, and can exhibit different evolution trends with the driving force varying from compressive force to tensile force. Moreover, there exist several critical points for the driving force, where the surface configurations take the jump changes and show different features on the both sides of such critical points. According to the effects of driving forces, we analyze the dynamical features of crystal growth.

In this paper, the structural, electronic and absorption properties of 2,2′-iminobis (acetamide oxime) (IBO) under pressure of 0–300GPa are calculated by the density functional theory (DFT) calculations. Analysis of the variation trend of lattice constant, bond length and bond angle of IBO under compression conditions, shows there are complex transformations under different pressure. In addition, it is found that the structure of IBO in the $a$-axis is stiffer than that along the $b$- and $c$-axes, which indicates that the crystal has anisotropic compressibility. By analyzing the band structure and the density of states of IBO, it is seen that at 120GPa, the electronic structure of IBO changes into metallic system, and becomes more sensitive under compression conditions. The transition between metal and semiconductor occurs again at 150Gpa. Finally, at 180GPa, the crystal transforms into metal again. The three obvious phase transitions indicate that the structure of IBO becomes more unstable with the increase of pressure. The absorption spectra show that with the increase of pressure, the optical activity of IBO crystal grows higher, and three obvious structural transitions are, respectively, observed at 120, 150 and 180GPa.

In this study, hybrid nanofluid free convection has been simulated within a permeable domain involving Lorentz effect. To solve and simulate the problem, Control Volume-based Finite Element Method (CVFEM) method is applied. In addition, the non-Darcy model has been used to apply permeable condition in equations. The influence of hybrid nanoparticles (Fe₃O₄$+$MWCNT) inside water as base fluid has been studied. Meanwhile, source term of radiation impact has been described for different nanoparticle shapes. The impacts of substantial variables such as Darcy number, radiation factor, magnetic strength and Rayleigh number on nanofluid behavior were fully revealed. It can be concluded that enhancing permeability factor can improve the Nusselt number but reverse behavior can be reported for Lorentz forces.

The mechanical properties of irradiated iron are studied by molecular dynamics simulation. The initial models are irradiated with the energy of primary knocked-on atoms (PKA) of 10keV at 100, 300, 500 and 600 K, and then all the irradiated models are subjected to tensile test. The results reveal that the mechanical properties of irradiated iron are changed compared with un-irradiated iron, the yield stress and strain decrease after irradiation, and the irradiation causes the hardening of micro-structure at low temperature and high temperature, but it results in the softening of structure at room temperature. The plastic reduces for irradiated iron under tensile test, more stacking faults are formed in the crystal structure as the temperature increases.

In a nuclear reactor, the Zr–$x$Nb alloy, which is used as a structural material in the core region, is irradiated by energetic particles that cause the atoms to be displaced from their lattice sites and giving rise to crystal defects. The local changes in the atomic arrangements lead to local deformations of the solid and thereby changes of its local mechanical properties. Understanding the mechanisms behind this evolution in the core region of a reactor, and its monitoring or controlling is a critical task in nuclear industry. In this work, using extensive molecular dynamics simulations, we have studied the effects of radiation damage on the local mechanical properties of Zr–$x$Nb alloy. In the first step, the effect of Nb-concentration on the mechanical stability of homogeneous Zr–$x$Nb alloy is investigated. In the second step, we have studied the local changes of the elastic constants due to local changes of the microstructure. These local changes include presence and accumulation of vacancies in the form of dislocation loops or voids, accumulation of Nb atoms in the form of clusters of different morphologies. This study covers both cases of $T=0^{\circ }$K and finite temperatures up to $T=600^{\circ }$K.

The traffic dynamics of complex networks are largely determined by the node’s resource distribution. In this paper, based on the shortest path routing strategy, a node delivering capacity distribution mechanism is proposed into the traffic dynamics in Barabási and Albert (BA) scale-free networks; the efficiency of the mechanism on the network capacity measured by the critical point ($R_c$) of phase transition from free flow to congestion is primarily explored. Based on the proposed strategy, the total delivering capacity is reallocated according to both degree and betweenness of each node, and an optimal value of parameter ${\alpha }_c$ is found, leading to the maximum traffic capacity. The results of numerical experiments on scale-free networks suggest that the resource allocation strategy proposed here is capable of effectively enhancing the transmission capacity of networks. Furthermore, this study may provide novel insights into research on networked traffic systems.

Synchronization between cerebral and peripheral circulation at the pre-stroke stage is discussed in newborn rats using a model of stress-induced hemorrhagic stroke. It is considered how the degree of coherence between the rhythmic components of the blood flow velocity is varied under normal and pathological conditions. It is shown that the degree of entrainment changes significantly after severe stress, provoking the transformation of normal vascular dynamics into pathological ones. Strong increase in the coherence measure is revealed, characterizing the entrainment in the dynamics of blood flow in the microvascular network surrounding the sagittal sinus and in the vein of the neck. Such changes can be considered as a precursor of the latent stage of stroke development in risk groups.

Understanding the pedestrian behavior contributes to traffic simulation and facility design/redesign. In practice, the interactions between individual pedestrians can lead to virtual honk effect, such as urging surrounding pedestrians to walk faster in a crowded environment. To better reflect the reality, this paper proposes a new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect. To this end, the concept of critical density is introduced to define the occurrence of pedestrians’ honk event. In the linear stability analysis, the stability condition of the new bidirectional pedestrian flow model is given based on the perturbation method, and the neutral stability curve is also obtained. Based on this, it is found that the honk effect has a significant impact on the stability of pedestrian flow. In the nonlinear stability analysis, the modified Korteweg–de Vries (mKdV) equation of the model is obtained based on the reductive perturbation method. By solving the mKdV equation, the kink-antikink soliton wave is obtained to describe the propagation mechanism and rules of pedestrian congestion near the neutral stability curve. The simulation example shows that the pedestrians’ honk effect can mitigate the pedestrians crowding efficiently and improve the stability of the bidirectional pedestrian flow.

This paper presents an analytical solution for transient natural convection heat and mass transfer flow in a vertical channel with Soret and Dufour effects. Due to the presence of these two effects, energy and concentration equations are coupled. The dimensionless governing equations for momentum, energy and concentration are first decoupled using perturbation method and then solved using Laplace Transform Technique (LTT) under relevant initial and boundary conditions. The expressions for temperature, concentration, velocity, rate of heat transfer, rate of mass transfer and skin-friction are obtained. Numerical solutions are also obtained using pdepe in MATLAB so as to validate the accuracy of the proposed analytical method. The effects of Soret parameter, Dufour parameter, Grashof number, modified Grashof number, Prandtl number, Schmidt number and dimensionless time are presented graphically and discussed. It is observed that the temperature and velocity increase with increase in Dufour number, while concentration decreases with increase of Dufour number. The Dufour effect is more significant on the temperature and velocity in comparison to concentration. Moreover, it is observed that the concentration and velocity increase with increase in Soret number while the impact of Soret number is just contrast on temperature variation.

The network topology structure has great impact on its traffic capacity. Most of the biological and technological networks have been proved to exhibit scale-free feature. In real networks, the hub links, which usually bear large traffic loads, have restricted transport efficiency of the complex networks. In this paper, we focus on the bandwidth congestion and propose a rewiring link strategy to optimize traffic dynamics on scale-free networks. Two link rewiring strategies are compared and the simulation results on scale-free networks show that our strategy has more advantages, which makes the degree distribution of the network more uniform, reducing the average path length of different nodes, balancing the resources of the network and increasing the traffic capacity of the network. This work will be beneficial for designing network topology and optimizing network performances.

The spread of rumors has caused serious social and economic problems, especially during emergencies. Reducing the harm caused by rumors requires understanding the dynamical mechanism by which they propagate. To include the influence of time-dependent psychological factors, this paper proposes an improved rumor spreading model and derives mean-field equations describing the dynamics of rumor spreading. The psychological factors considered are the attenuation of individual interest, the cumulative effect of memory, and changes in sensory intensity with time. We also obtain the threshold condition of rumor spreading. Numerical simulations are used to verify our theoretical results. It is proved that the extremum of the cumulative effect of memory and the rumor attraction rate are positively correlated with the peak number of rumor spreaders, and negatively with the time required to reach the final rumor size. Time grows geometrically, while sensory intensity grows arithmetically. The initial approval rate of the memory accumulation effect and the stifling mechanism have little effect on the final rumor size. Finally, it is found that increasing the attenuation of interest coefficient reduces the time needed for the rumor to reach its final size.