International Journal of Modern Physics C

To illustrate the role of Lorentz force on migration of nanopowders, CVFEM simulation has been reported in current research. The chamber contains hybrid nanomaterial and made up form porous media. Momentum equations have been modified for present paper with adding new source terms. The mentioned method works based on FEM in generation of mesh and calculation of gradient of scalars while it uses FVM approach for employing source terms. Testing with benchmark article shows the nice accuracy. Increase of permeability can enhance the speed of nanopowders and iso-temperature lines shapes become complicated. Impose of MHD creates new force against buoyancy and declines the velocity of the nanomaterial. Also, complication of isotherms declines with rise of Ha. With growth of Da, value of $\mathrm{\Psi }$ increases about 111% and 64.2% when $\mathrm{\text{Ha}}=0$ and 20, respectively. Also, augment of Ha results in reduction of velocity about 30% and 47.6% when $\mathrm{\text{Da}}=0.01$ and 100. Given $\mathrm{\text{Da}}=5\mathrm{\text{Ha}}=100$, Nu for $\mathrm{\text{Ra}}=\mathrm{\text{1e}}5$ is 6.83 times bigger than case with $log(\mathrm{\text{Ra}})=3$. Nu decreases to about 67.28% with increase of Ha when $\mathrm{\text{Da}}=100$, $\mathrm{\text{Ra}}=\mathrm{\text{1e}}5$. As Da increases, Nu rises about 62% when $\mathrm{\text{Ha}}=0$, $\mathrm{\text{Ra}}=\mathrm{\text{1e}}3$.

Community structure detection is one of the fundamental problems in complex network analysis towards understanding the topology structure and function of the network. Modularity is a criterion to evaluate the quality of community structures, and optimization of this quality function over the possible divisions of a network is a sensitive detection method for community structure. However, the direct application of this method is computationally costly. Nonnegative matrix factorization (NMF) is a widely used method for community detection. In this paper, we show that modularity maximization can be approximately reformulated under the framework of NMF with Frobenius norm, especially when $n$ is large. A new algorithm for detecting community structure is proposed based on the above finding. The new method is compared with four state-of-the-art methods on both synthetic and real-world networks, showing its higher clustering quality over the existing methods.

In recent decades, cardiovascular disease and stroke are recognized as the most important reason for the high death rate. Irregular bloodstream and the circulatory system are the main reason for this issue. In this paper, Computational Fluid dynamic method is employed to study the impacts of the flow pattern inside the cerebral aneurysm for detection of the hemorrhage of the aneurysm. To achieve a reliable outcome, blood flow is considered as a non-Newtonian fluid with a power-law model. In this study, the influence of the blood viscosity and velocity on the pressure distribution and average wall shear stress (AWSS) are comprehensively studied. Moreover, the flow pattern inside the aneurysm is investigated to obtain the high-risk regions for the rupture of the aneurysm. Our results indicate that the wall shear stress (WSS) increases with increasing blood flow velocity. Furthermore, the risk of aneurysm rupture is considerably increased when the AWSS increases more than 0.6. Indeed, the blood flow with high viscosity expands the high-risk region on the wall of the aneurysm. Blood flow indicates that the angle of the incoming bloodstream is substantially effective in the high-risk region on the aneurysm wall. The augmentation of the blood velocity and vortices considerably increases the risk of hemorrhage of the aneurysm.

Text as a complex system is commonly studied by various methods, like complex networks or time series analysis, in order to discover its properties. One of the most important properties of each text is its keywords, which are extracted by word ranking methods. There are various methods to rank words of a text. Each method differently ranks words according to their frequency, spatial distribution or other word properties. Here, we aimed to explore how similar various word ranking methods are. For this purpose, we studied the rank correlation of some important word ranking methods for number of sample texts with different subjects and text sizes. We found that by increasing text size the correlation between ranking methods grows. It means that as the text size increases, the associated word ranks calculated by different ranking methods converge. Also, we found out that the rank correlations of word ranking methods approach their maximum value in the case of large enough texts.

The mapping is a useful technique for improving the performance of WENO method. However, for the existed mapped WENO methods, two weaknesses still need to be overcome. First, too much computational cost is used, the computational cost of mapped WENO method is around $\frac{4}{3}$ of the original WENO method. Second, on the nonuniform meshes, too much memory space is used. We can take the WENO-RM method on nonuniform rectangle meshes for example, which is one of the famous mapped WENO methods. Comparing to original WENO method, the WENO-RM needs to store $128\times M$ additional parameters, where $M$ is the cell number. In order to overcome these weaknesses, we propose a new strategy for implementing the mapped WENO method. Different from the previous works, the new strategy is based on the average weight. The new strategy has following major advantages: first, it can give the solution which is as accurate as the original mapped WENO method; second, it can save the computational cost, because it only uses slightly more computational cost than the original WENO method; third, it can save the memory space because it only needs to store a little additional parameter compared to the original WENO method.

In this paper, effects of nondimensional distance between two square cylinders on the dissipation characteristics of the complex flow are investigated. The viscosity entropy generation rates around two serial square cylinders and the lift coefficient are analyzed to fully reveal the statistical features of the flow dissipation. Numerical results mainly show that the major viscosity entropy generation rate appears in the shear intersection region of the main flow and local stationary vortex. The viscosity entropy generation rate increases with increasing nondimensional distance ($S^{\ast }$). The increasing slope of the viscosity entropy generation rate at a range of $S^{\ast }\le 2$ is greater than that of $2\le S^{\ast }\le 5$. It is also found that the viscosity entropy generation rate is kept as a constant when the nondimensional distance $S^{\ast }$ is greater than 5. At $S^{\ast }\ge 5$, the effect of downstream square cylinder becomes negligible on the viscosity entropy generation rate. The fluctuating amplitude increases with increasing the nondimensional distance $S^{\ast }$. The high-frequency peak is ascribed to the strong vortex shedding around the downstream square cylinder, and the low-frequency peak is ascribed to the weak vortex shedding around the up square cylinder at $S^{\ast }=1$. Although our focus is mainly on the complex flow around two square cylinders, this work demonstrates the viscosity entropy generation rate with increasing nondimensional distance, which provides nice physical insight into understanding the local flow dissipation characteristics around the two serial square cylinders.

In this paper, the forced convection heat transfer of Ag–MgO/water hybrid micropolar nanofluid in a channel is studied numerically which the top wall of channel is smooth and bottom of it is in stairway form. The lattice Boltzmann method (LBM) is used for solving the fluid flow and heat transfer equations. The effects of Reynolds numbers ($Re=100$–400), volume fraction of nanofluid ($\varphi =0$, 0.01 and 0.02) and stairway aspect ratio ($a∕H=0.1$, 0.2 and 0.3) on the velocity, temperature and local and average Nusselt number profiles are investigated. The results show that by incrementing the Reynolds number and solid volume fraction and decreasing the $a$/$H$ simultaneously, the average Nusselt number increases.

The nanofluids are a recent challenging task in a nanotechnology field used in heat transfer enhancement for base fluids. The major purpose of this research is to examine the influences of Hall current on the non-Newtonian power-law nanofluid on an exponentially extending surface. Implementation in the Cattaneo–Christov heat flux and the free stream is performed to analyze the thermal relaxation features. Entropy generation evaluation and Bejan number during the convection flow are investigated. The Runge–Kutta–Fehlberg method is employed to resolve the transformed governing nonlinear equations. The impacts of the key physical factors on the profiles of primary and secondary velocities, temperature and entropy generation are discussed across the graphs. The local skin-friction coefficients, Nusselt and Sherwood numbers are demonstrated in a tabular form under the impacts of key physical parameters. Two different types of power-law indicators including pseudoplastic fluid $(n=0.7)$ and dilatant fluid $(n=1.2)$ are conducted. The results indicated that the flow speed decreases at dilatant fluid compared to pseudoplastic fluid due to higher viscosity. Increasing Hall current parameter powers the axial and secondary velocity profiles. Thermophoresis parameter powers the profiles of the temperature, nanoparticle volume fraction and local entropy generation. The dilatant fluid $(n=1.2)$ gives higher values of $C_{fx},C_{fz},{\mathrm{\text{Nu}}}_x$ and ${\mathrm{\text{Sh}}}_x$ compared to the pseudoplastic fluid $(n=0.7)$.

In this paper, we use the multiple exp-function method to explicity present traveling wave solutions, double-traveling wave (DTW) solutions and triple-traveling wave solutions (TWs) which include one-soliton, double-soliton and triple-soliton solutions for nonlinear partial differential equations (NPDEs) via, the (2+1)-dimensional and (3+1)-dimensional nonlinear Burgers PDEs in mathematical physics. In this work, we build some series of straightforward and new solutions successfully with the help of a computerized symbol computational software package like Maple or Mathematica. We will make some drawings in some cases with specific values for the relevant parameters for each obtained solutions such as the one-traveling wave solutions, double-traveling wave solutions and TWs. This method is efficient and powerful in solving a wide class of NPDEs.

We consider a compartmental model adapted to the case of COVID-19 that takes into account the detection of ill individuals and the cost of medical treatment and investigate the effect of a budget constraint. Our analysis shows how the collapse of the budget can drastically change the outcome of an epidemics. We see how with a good testing policy the epidemic might be controllable. By introducing a lockdown period, we show that the final number of deaths can be reduced substantially and observe that a budget collapse introduces rather extreme effects. We find that there exists a well-defined optimal starting point for a lockdown. We also looked at the consequences of a loss of immunity and found that then a budget collapse can occur for smaller costs of medical treatment.

We systematically study a concealed voter model with heterogeneous reaction rates including the copying rate, externalization rate and internalization rate of each voter, which corresponds to the heterogeneity of activity of real people. By means of heterogeneous mean-field treatment, we derive the evolution equations of the system which allow us to construct a conserved quantity that governs the dynamical process. And furthermore, we also obtain the analytical expressions for the consensus time along with the exit probability. Our studies suggest that the heterogeneous copying rate and internalization rate can decelerate the consensus process, whereas the heterogeneous externalization rate does the opposite but slightly. All the analytical predictions are validated by extensive computer simulations.

In this work, a mathematical model of the fractional-order in non-Newtonian Powell–Eyring fluid flow (PEFF) and heat transfer is presented and solved numerically. The set of nonlinear differential equations in terms of velocity, temperature which describes our proposed problem is tackled through the spectral collocation method based on Chebyshev polynomials of the third kind. This method reduces the presented model to a nonlinear system of algebraic equations. This system is constructed as a constrained optimization problem and optimized to get the unknown coefficients of the series solution. The effects of the thermal radiation, Powell–Eyring parameters; suction parameter and Prandtl number on the PEFF are discussed. The numerical values of the dimensionless velocity and temperature are depicted graphically. The results show that the given procedure is an easy and efficient tool to investigate the solution of such models. Some of findings of this important work help to govern the velocity and the rate of heat transportation through the boundary layer. At the same time, this study highlights many applications in fields of engineering and industry, where the quality of the desired product depends on the rate of heat transfer, thermal radiation phenomenon, and the composition of the material used, and manufacturing processes.

Network reliability plays an important role in analysis, synthesis and detection of real-world networks. In this paper, we first propose the concept of hypernetwork reliability, which generalizes the concept of network reliability. The model for hypernetwork reliability studies consists of a hypergraph with perfect reliable vertices and equal and independent hyperedge failure probability $1-p$. The measure of reliability is defined as the probability that a hypergraph is connected. Let $H$ be an $r$-uniform hypergraph with the number of vertices $n$ and the number of hyperedges $m$, where every hyperedge connects $r$ vertices. We confirm the possibility of the existence of a fixed hypergraph that is optimal or least for all hyperedges same survival possible $p$. It is simple to verify that such hypergraph exists if $m=[\frac{n-1}{r-1}]$. For a kind of 2-regular 3-uniform hypergraphs, we calculate the upper and lower bounds on the all-terminal reliability, and describe the class of hypergraphs that reach the boundary.

Asymmetrical influence of population is ubiquitous in human and animal societies. Based on this fact, we construct a setup of asymmetric influence of structured population, which is often put with the combination mechanism of tolerance and punishment when the dispute of unfair outcome happens, to investigate the evolution of cooperation. In detail, the structured populations are classified into two types: A-type players (strong players) and B-type players (weak players). A-type players are capable to decide whether or not to lower the fitness of B-type neighbors with punitive action due to the tolerance limits. This action affects the behavior of B-type neighbors in the evolutionary game. Based on our simulations, it is noted that the mechanism of punishment combining with tolerance in an asymmetrical environment can promote the evolution of cooperation. Furthermore, the lower threshold of tolerance with the looser punishment, the higher the level of cooperation; and the higher degree of tolerance with the stricter punishment will maintain the survival of cooperators. It is also worth mentioning that if A-type population is the key minority impacting the majority of B-type, they can favor affecting and further promoting the evolution of cooperation in the evolutionary game.