International Journal of Modern Physics C

In this work, the structural, mechanical and thermodynamic properties of CaLi₂ in the pressure range of 0–72GPa have been studied. It was found that CaLi₂ undergoes a phase transition from P$6_3$/mmc to C2/c phase at 25.37GPa and from C2/c to P$2_1$/c phase at 55.99GPa, which is consistent with previous experimental and partially theoretical results. Besides, at 0GPa, the lowest enthalpy appears in both P$6_3$/mmc and Fd-3m structures, showing the coexistence of these two phases. However, P$6_3$/mmc phase is not stable when the pressure is larger than 6GPa. Finally, the elastic of CaLi₂ at different pressures was investigated using the elastic stability criterion, and the thermodynamic properties under different pressures are investigated in detail.

In this paper, we introduce the heterogeneity in the parameter $\sigma$ to three coupled Lorenz oscillators and investigate the effects of parameter heterogeneity on the coupling dynamics. In the presence of parameter heterogeneity, the complete synchronous state is replaced by lag synchronous state which owns the largest Lyapunov exponent exactly the same as that of the complete synchronous chaos. We find two types of oscillation quenching states induced by the parameter heterogeneity, homogeneous nontrivial equilibria and heterogeneous equilibria. In the homogeneous nontrivial equilibria, all oscillators fall onto a same nontrivial equilibrium of the isolated Lorenz oscillator, which requires low coupling strength. Depending on the coupling function, the heterogeneous equilibria may appear at intermediate coupling strength or large coupling strength. We numerically show that the transitions among lag synchronous state and different types of quenching states are always discontinuous ones. The stability diagram of the lag synchronous chaos is presented theoretically, which is compatible with those based on the synchronization error and Lyapunov exponents.

This paper presents a detailed literature review on the studies carried out in the last three decades, for understanding the factors affecting the performance of the ejector. An ejector is one of the important components in many industrial applications in the field of refrigerant expansion, circulation of fluids, vacuum creation, etc. From the analysis of the reported works of the ejector, the CFD modeling has proved to be a convenient method for analyzing the complex phenomenon in the ejector like mixing process, turbulence characteristics, shock interactions, and condensation process. The first part of this paper discusses the operation of ejector, flow structure, parameters required for the computational modeling, governing equations, etc. The second part discusses the influence of geometrical parameters and various operating conditions on the ejector performance. The shape and position of shock waves in the ejector for various operating conditions are also narrated under the same section. Third part of this paper is devoted to discussions on advances in modeling to be considered for the performance improvement of ejectors. Finally, the paper concludes with clear guidelines for the effective ejector modeling. Future scope of ejector research, pathways to progress, etc., mentioned in the conclusion section should help researchers and designers in this field.

In this paper, we aim to study the role of hubs in the network coherence quantified by the Laplacian spectra and choose two families of unicyclic and bicyclic networks with the same network size as our network models. In order to investigate the influence of adding links on the coherence, we construct four types of bicyclic networks with the same average degree. Using the network’s regular structures and matrix theories, we obtain analytical solutions of the coherences regarding the degrees of hub nodes. Based on these exact results for the coherence, the network with one hub displays higher coherence compared to the network with two hubs. We then obtain exact relations for the coherences of the bicyclic networks with the same average degree and show that different adding links and hub’s positions are responsible for distinct performance of the consensus algorithms. Finally, we show that the coherence and average path length behave in a linear way meaning that smaller average path length results in better coherence.

Traffic flow affects the transmission and distribution of pathogens. The large-scale traffic flow that emerges with the rapid development of global economic integration plays a significant role in the epidemic spread. In order to more accurately indicate the time characteristics of the traffic-driven epidemic spread, new parameters are added to represent the change of the infection rate parameter over time on the traffic-driven Susceptible–Infected–Recovered (SIR) epidemic spread model. Based on the collected epidemic data in Hebei Province, a linear regression method is performed to estimate the infection rate parameter and an improved traffic-driven SIR epidemic spread dynamics model is established. The impact of different link-closure rules, traffic flow and average degree on the epidemic spread is studied. The maximum instantaneous number of infected nodes and the maximum number of ever infected nodes are obtained through simulation. Compared to the simulation results of the links being closed between large-degree nodes, closing the links between small-degree nodes can effectively inhibit the epidemic spread. In addition, reducing traffic flow and increasing the average degree of the network can also slow the epidemic outbreak. The study provides the practical scientific basis for epidemic prevention departments to conduct traffic control during epidemic outbreaks.

In today’s globalized world, grain is not only food, but also a strategic weapon, a trump card in the game of nations. As one of the three staple grains, international trade of wheat faces high supply risk. Each country should not only pay attention to the ways in which trade risks are spread, but also pay high attention to how resources are reallocated between countries to reduce losses from supply risks. Therefore, based on complex network theory and global wheat trade data, we construct an international wheat trade network (IWTN) and analyze the feedback of network robustness under random and targeted attacks. Then, we propose a global wheat trade redistribution model through the maximum entropy principle to simulate the resource redistribution among wheat trading countries under different supply risks. Finally, changes in trade relations among major countries are analyzed. The results of the study provide an important reference for the recovery of national resources after wheat supply risk and new ideas for researchers related to international trade.

This paper deals with the study of the reaction–diffusion epidemic model perturbed with time noise. It has various applications such as disease in population models of humans, wildlife, and many others. The stochastic SIR model is numerically investigated with the proposed stochastic backward Euler scheme and proposed stochastic implicit finite difference (IFD) scheme. The stability of the proposed methods is shown with Von Neumann criteria and both schemes are unconditionally stable. Both schemes are consistent with systems of the equations in the mean square sense. The numerical solution obtained by the proposed stochastic backward Euler scheme and solutions converges towards an equilibrium but it has negative and divergent behavior for some values. The numerical solution gained by the proposed IFD scheme preserves the positivity and also solutions converge towards endemic and disease-free equilibrium. We have used two problems to check our findings. The graphical behavior of the stochastic SIR model is much adjacent to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The results show the efficacy of the proposed stochastic IFD scheme.

We have studied the magnetic relaxation behavior of a two-dimensional Ising ferromagnet by Monte Carlo simulation. Our primary goal is to investigate the effects of the system’s geometry (area preserving), boundary conditions and dynamical rules on the relaxation behavior. The Glauber and Metropolis dynamical rules have been employed. The systems with periodic and open boundary conditions are studied. The major findings are the exponential relaxation and the dependence of relaxation time ($\tau$) on the aspect ratio $R$ (length over breadth having fixed area). A power law dependence ($\tau \sim R^{-s}$) has been observed for larger values of aspect ratio ($R$). The exponent ($s$) has been found to depend linearly ($s=aT+b$) on the system’s temperature ($T$). The transient behaviors of the spin-flip density have been investigated for both surface and bulk/core. The size dependencies of saturated spin-flip density significantly differ for the surface and the bulk/core. Both the saturated bulk/core and saturated surface spin-flip density was found to follow the logarithmic dependence $f_d=a+blog(L)$ with the system size. The faster relaxation was observed for open boundary condition with any kind (Metropolis/Glauber) of dynamical rule. Similarly, Metropolis algorithm yields faster relaxation for any kind (open/periodic) of boundary condition.

This paper concerns the issue of fixed-time synchronization (FXTS) for complex networks composed of dynamical nodes with discontinuous dynamics, abbreviated as discontinuous dynamic networks, under the concept of Filippov solution. In terms of $1$-norm and $2$-norm, two types of simple control schemes without the linear feedback part are, respectively, designed to compel the considered discontinuous dynamic network to fixed-timely synchronize with a desired trajectory. By utilizing a novel two-stage analysis approach, some new FXTS criteria are derived. Compared with the existing research works, the established theoretical results not only are more relaxed, but also improve the estimation accuracy of synchronous settling time. Finally, the validity of the analytical results is verified via numerical simulations.

This paper aims to simulate an immiscible two-phase flow in two-dimensional T-shaped, modified T-shaped, cross-shaped, and modified cross-shaped micromixers numerically. The effects of various parameters, including Capillary number, phase flow rate ratio, and channel width ratio, on the generation of droplets were studied. Also, modification of T-shaped and cross-shaped micromixers was proposed. The results reveal that equidistant tiny droplets are generated in the modified micromixers compared to ordinary geometry under the same conditions. Three types of squeezing regime, laminar regime, and jetting regime were observed in different values of the capillary number. It was also observed that the droplet size decreases with the increase in capillary number. Moreover, this study demonstrates that the multiphase flows in micro-devices are very sensitive to even small changes in the channel geometry.

In this paper, an adaptive endogenous model is introduced to explain the formation and evolution mechanism of interbank lending market with central bank. We investigate the evolution of structure of interbank lending market and the impact of structure of bank assets, bank adaptive behaviors, liquidity and dispersion on the resilience of interbank lending market, respectively. Simulation results demonstrate that the structure of the initial interbank lending market has scale-free and small-world features, which keeps in the evolution of the network. Moreover, we find risk gathering requires relatively long time but the outbreak is concentrated and percentage of defaults is a nonmonotonic function of percentage of initial liquid assets. Furthermore, we discover that moderate liquidity hoarding helps to reduce risk contagion effect in the initial stage of contagion while excessive hoarding of liquidity increases the fragility of the network.

The forecast of tropical cyclone (TC) seasons remains an elusive subject of study. In order to characterize their complexity, the energy of North Atlantic (NA) TC seasons is studied in this research work. The time evolution of the accumulated cyclone energy probability distribution is analyzed using mobile windows to calculate the statistical parameters: mean, standard deviation, kurtosis and skewness. A nonstationary distribution with clear excess of extreme energetic seasons when compared to a Gaussian distribution was found for the most recent years. The data also show a clear correlation between variability and mean, i.e. more energetic periods are more variable. Finally, the dynamics is analyzed using several techniques such as the lag plot, Hurst exponent and fractal dimension. A stochastic but persistent behavior was found. It is finally concluded that the NA TC season energy seems to be increasing both in magnitude and variability. This helps to elucidate the possible effect of global warming into increasing hurricane hazards.

Numerical procedure plays a key role in tackling the solutions of nonlinear dynamical systems. With the advent of the age of big data and high-power computing, developing efficient and fast numerical algorithms is an urgent task. This paper extends the Lie derivative discretization algorithm to the nonautonomous nonlinear systems and investigates the numerical solutions of the systems. The periodic solutions of three different classical nonlinear systems are calculated, and the results are compared to those values calculated from the Runge–Kutta fourth-order algorithm, which demonstrated that the Lie derivative algorithm has the advantages of large time step and short computation time.

In this paper, we investigate the one-electron propagation in a nonlinear chain with electron–lattice interaction. The model contains standard cubic nonlinear terms, and we introduce the coupling between the electron and the lattice through the hopping distribution. We solve the coupled equation set to electron and lattice and calculate the electronic position as a function of time. We provide a detailed investigation of the electron and lattice dynamics for a wide range of electron–lattice coupling intensities. Our results demonstrate that depending on the initial condition we consider and the intensity of the electron–lattice interaction, we can obtain (or not) an electron–phonon pair formation. Our results reveal that, depending on the initial velocity of the lattice and the degree of electron–lattice term, we can observe a repulsion between electron and lattice deformations.