International Journal of Modern Physics C

In this paper, the natural convection flow in a square cavity filled with nanofluid water-${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$ with a hot circular cylinder in the center of the cavity is numerically analyzed. All the walls are in lower temperatures than the circular cylinder. The Navier–Stokes and energy equations in the primitive variable form are discretized and solved by the finite element method (FEM). The effect of the volume fraction, the radius of the circular cylinder, the temperature and Rayleigh number is considered on the average Nusselt number. For the calculation of the viscosity coefficient and thermal conductivity coefficient of water-${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$ nanofluid, an experimental model is used which is the function of the volume fraction, temperature and nanoparticles diameter. This model is compared to the Brinkman model for viscosity and Maxwell model for thermal conductivity which are only the functions of volume fraction and are used by many researchers. The results show the experimental model leads to different results in comparison with the Brinkman model and Maxwell model, and indicate that the rate of the heat transfer can increase or decrease with the increase in volume fraction and temperature.

Quantum mechanical states are normally described by the Schrödinger equation, which generates real eigenvalues and quantizable solutions which form a basis for the estimation of quantum mechanical observables, such as momentum and kinetic energy. Studying transition in the realm of quantum physics and continuum physics is however more difficult and requires different models. We present here a new equation which bears similarities to the Korteweg–DeVries (KdV) equation and we generate a description of transitions in physics. We describe here the two- and three-dimensional form of the KdV like model dependent on the Plank constant $\hslash$ and generate soliton solutions. The results suggest that transitions are represented by soliton solutions which arrange in a spiral-fashion. By helicity, we propose a conserved pattern of transition at all levels of physics, from quantum physics to macroscopic continuum physics.

To explore the high-temperature superconductor at low pressures, we have investigated the crystal structures, electronic properties, and possible superconductivity in the case of methane (CH₄) doped by lithium in the pressure range of $0-100$GPa, based on the first-principles calculations. The results show that Li-intercalated CH₄ (Li_x(CH₄)${}_{1-x}$) can realize metallization and superconductivity at low pressures, even 5GPa. We find that there is a charge transfer between Li and CH₄, but the metallization is driven by the change of crystal field induce by doping instead of charge transfer. The critical temperture is predicted from 3.8K at 5GPa for LiCH₄ to 12.1K at 100GPa for Li(CH₄)₄. The low-pressure superconductivity of Li_x(CH₄)${}_{1-x}$ can be further optimized by adjusting component and pressure.

The robustness of complex networks responding to attacks has long been the focus of network science researching. Nonetheless, the precious studies mostly focus on network performance when facing malicious attacks and random failures while rarely pay attention to the influences of scales of attacking. It is wondering if it is an actual fact that the network is more fragile when attacking scale is exacerbated. In this paper, we are committed to exploring the influences related to the very factor of attacking scale from the perspective of cascading failure problem of dynamic network theory. We construct the model with a regular ranking edge deletion method by simulating attacking scale with $N_a$ and $a$ is denoted as attacked edge number. To be specific, we rank the edges according to initial distributed loads and delete edges in the ranked list, and subsequently observe the changes of robustness in the networks, including BA scale-free network, WS small-world network and several real traffic networks. During the process, an unusual counterintuitive phenomenon captures our attention that the network damages caused by attacks do not always grow with the increase of attacked edges number. We specifically demonstrate and analyze this abnormal cascading propagation phenomenon, ascribing this paradox to the dynamics of the load and the connections of the network structure. Our work may offer a new angle on better controlling the spread of cascading failure and remind the importance of effectively protecting networks from underlying dangers.

This study focuses on the characteristics of flow past three side-by-side rectangular cylinders under the effect of aspect ratios (AR) and Reynolds numbers (Re) at two different gap ratios ($g$) using the lattice Boltzmann method. For this purpose, AR is varied in the range of 0.25–4, the Re values are 100, 140 and 180 and the two different values of $g$ taken into account are $g=0.5$ and 3. The results are presented in the form of vorticity contours, temporal histories of drag and lift coefficients and power spectrum of lift coefficients. Also, the variation of physical parameters like mean drag coefficient, Strouhal number and the root-mean-square values of drag and lift coefficients with Re and AR is presented for $g=0.5$ and 3. The current numerical computations yield that for both gap ratios and all Re, there exist four different flow regimes depending on AR: (a) steady flow, (b) modulated flow, (c) symmetric flow and (d) periodic flow. At narrow gap ratios, the jet flow emerging within the gaps of cylinders altered the flow structures and fluid forces abruptly. The aspect ratio is found to have more influence on the flow characteristics of cylinders as compared to the Reynolds numbers at large gap ratios.

Rumor is an unauthenticated statement that gives significant changes in the social life of the people, financial markets (stocks and trades), etc. By incorporating the dissemination of rumor through groups in social, mobile networks and by considering the people’s cognitive factor (hesitate and forget), a new model on the rumor spreading process is presented in this paper. The spreading dynamics of rumor in homogeneous and heterogeneous networks is analyzed by using mean-field theory. The reproduction number is obtained by using the next-generation matrix. The global stability of the rumor-free equilibrium for the homogeneous and heterogeneous model is proved elaborately. An optimal control problem is developed to minimize the hesitators and infected persons and the existence of optimality is shown using Pontryagin’s Minimum Principle. The hesitating and forgetting mechanism has a great impact on the model and is similar to the real-life. Further, the control parameters work superior in controlling the spreading of rumors. Finally, the numerical results are verified by the analytical results.

The vortex in the branching microchannel enhances the mixing and heat transfer performance. To investigate the vortex intensity quantitatively, a lattice Boltzmann model for incompressible power-law fluid is developed by setting the range of lattice viscosity (0.001 $\le \nu \le$ 1). The validation of the current model is carried out by modeling the vortex in a T-shaped branching channel and the Poiseuille flow of power-law fluids. Then the vortex intensity in the $\psi$-shaped microchannel is numerically studied in terms of Reynolds number, branching angle and power-law index. The result indicates that both the recirculation length and height increase with the increase of the Reynolds number. The branching angle has a negative impact on the recirculation length, and it has little effect on the recirculation height. The influence of the power-law index on recirculation length and height depends on the Reynolds number.

Epidemics usually spread widely and can cause a great deal of loss to humans. In the real world, vaccination is the principal method for suppressing the spread of infectious diseases. The Susceptible-Infected-Susceptible (SIS) model suggests that voluntary vaccination may affect the spread of an epidemic. Most studies to date have argued that the infection rates of nodes in the SIS model are not heterogeneous. However, in reality, there exist differences in the neighbor network structure and the number of contacts, which may affect the spread of infectious diseases in society. As a consequence, it can be reasonably assumed that the infection rate of the nodes is heterogeneous because of the amount of contact among people. Here, we propose an improved SIS model with heterogeneity in infection rates, proportional to the degree of nodes. By conducting simulations, we illustrate that almost all vaccinated nodes have high degrees when the infection rate is positively correlated with the degree of a node. These vaccinated nodes can divide the whole network into many connected sub-graphs, which significantly slows down the propagation of an epidemic; the heterogeneity of infection rates has a strong inhibitory effect on epidemic transmission. On the other hand, when the infection rate is negatively related to the degrees of the infection rate nodes, it is difficult for most nodes to meet the inoculation conditions, and the number of inoculations is close to zero.

In this paper, we address a two-dimensional unsteady MHD mixed convective boundary layer flow past a flat surface of an electrically conducting Casson fluids taking radiative heat transfer. The partial slip boundary condition is imposed in the presence of suction/blowing. By adopting the continuous group of symmetry transformations, the symmetries and scaling laws are determined for the governing nonlinear partial differential equations along with boundary conditions. Finally, the set of coupled self-similar nonlinear ODEs is obtained. These equations are solved numerically for finding similar velocity and temperature for different parameter values. The effects of physical parameters on velocity and temperature are determined. The main findings are that the velocity profiles grow concavely and after reaching a critical point, the profiles overshoot by decreasing the velocity. This is due to the change of stress behavior which is an intrinsic property of the Casson fluid model. The imposition of partial slip condition on the flat surface leads to enhancement of the velocity overshoot.

We propose a nonlinear age-structured model of tumor cell population with proliferating and quiescent phases. We apply the discontinuous Galerkin (DG) method to study its dynamical behavior. The DG numerical approximation is used for the spatial discretization and then the strong-stability-preserving explicit Runge–Kutta (SSPERK) method is performed for the temporal discretization. This paper aims to establish more efficient results in the sense of computational approach and compare these with analogous estimates for Weighted Essentially and Non-Oscillatory (WENO) scheme. Finally, some test examples and numerical simulations are given to illustrate theoretical results and to examine the behavior of the solution.

We investigate the spreading of SARS-CoV-2 in the state of Alagoas, northeast of Brazil, via an adaptive susceptible-infected-removed (SIR) model featuring dynamic recuperation and propagation rates. Input parameters are defined based on data made available by Alagoas Secretary of Health from April 19, 2020 on. We provide with the evolution of the basic reproduction number $R_0$ and reproduce the historical series of the number of confirmed cases with less than $10\%$ error. We offer predictions, from November 16 forward, over the epidemic situation in the near future and show that it will keep decelerating. Furthermore, the same model can be used to study the epidemic dynamics in other countries with great easiness and accuracy.

In the last three decades, a lot of research has been devoted to the optical response of an atomic media in near-to-resonant conditions and to how nonlinear optical properties are enhanced in these systems. However, as current research turns its attention towards multi-level and multidimensional systems interacting with several electromagnetic fields, the ever-increasing complexity of these problems makes it difficult to treat the semiclassical model of the Maxwell–Bloch equations analytically without any strongly-limiting approximations. Thus, numerical methods and particularly robust and fast computational tools, capable of addressing such class of modern and future problems in photonics, are mandatory. In this paper, we describe the development and implementation of a Maxwell–Bloch numerical solver that exploits the massive parallelism of the GPUs to tackle efficiently problems in multidimensional settings or featuring Doppler broadening effects. This constitutes a simulation tool that is capable of addressing a vast class of problems with considerable reduction of simulation time, featuring speedups up to 15 compared with the same codes running on a CPU.

In this study, three-dimensional computational analysis is performed to investigate the magnetoconvection of ferrofluid ($F{e}_3{O}_4$-water) within a cubical enclosure heated by an inner spherical hot block. The ferrofluid, considered as a working fluid, is modeled as a single-phase fluid. The inner spherical block is put at high temperature while all the remaining walls of the enclosure are exposed to low temperature. Two radii values ($\mathrm{\text{rs}}=0.1$ and $0.2$) of the inner hot sphere are examined. Governing equations with corresponding boundary conditions are solved numerically applying a second-order accurate finite volume method on a staggered grid system, using an accelerated multigrid model. Simulations are carried out based on various flow-governing parameters such as Rayleigh number $(10^3<\text{Ra}<10^7)$, Hartmann number $(0<\text{Ha}<50)$ and ferrofluid nanoparticle volume fraction $(0<\varphi <4\%)$. The effects of the pertinent parameters in the performance of the system are also studied. The flow and thermal fields, the local and surface-averaged Nusselt numbers on the sphere and the enclosure for both configurations are detailed. The flow remains steady and laminar for all Rayleigh numbers regardless of the sphere radius. Obviously, heat transfer rate improves with $\text{Ra}$ augmentation and minimizes with Ha decrease. At the highest Ra and lowest Ha, higher inner sphere radius shows significantly better heat transfer rate (more than $30\%$). Useful correlations are presented to quantify the surface-averaged heat transfer rate through the cubical enclosure.

The efficient fuel injection system is a vital part of scramjet for a high-speed flight. In this scientific study, the effects of the multi fuel jets on the inclined surface are investigated at the supersonic air stream with Mach$=4$. This study employed the CFD technique for the simulation of the interaction of multi hydrogen-jets with free stream airflow. The impressions of inclined surface angle and hydrogen jet total pressure on the fuel mixing zone are disclosed. The Mach contour on the jet plane is presented to describe the chief terms on the distribution and penetration of hydrogen jet inside the combustion chamber. To perform a 3D computational study, the RANS equation with the SST turbulence model is used. Our study shows that the mixing performance of multi jets enhances in high jet pressure when the angle of the tending exterior is raised. Our findings also demonstrate that power and slant of the separation shock is highly effective on the size of the mixing zone.