International Journal of Modern Physics C

The extremely accurate findings of ninth-order linear and nonlinear BVPs are described in this paper. CNPS and CPS are used to find out the numerical roots of linear and nonlinear, ninth-order BVPs. The proposed methods transform the ninth-order BVPs into a system of linear equations. The algorithms developed in this study not only provide approximate solutions to the BVPs using CNPS and CPS, but they also estimate the derivatives from the first to the ninth-order of the analytical solution simultaneously. These approaches are implemented across five diverse problems, showcasing the effectiveness of these techniques by utilizing step sizes of $h=1/10$ and $h=1/5$. In order to gauge the accuracy of the methods, a comparison is drawn between the outcomes and the exact solutions, which are then presented in tabular and graphical format. The precision of these techniques is demonstrated through a detailed investigation and is found to be superior to the CBS, the Petrov–Galerkin Method (PGM) using Splines functions as basis functions and Septic B Splines functions as weight functions, the collocation method for ninth-order BVPs by Quintic B Splines and Sextic B Splines as evidenced by the comparison of AEs of CPS and CNPS with these alternative methods.

This paper aims at the PCM-based heat sink for electronic cooling. In the present analysis, paraffin wax-based phase change material (PCM), in 3-fin and 4-fin hollow heat sinks with the proper volume of PCM in the temperature of the electronic components can be controlled. The PCM-filled heat sinks are placed on top of the high heat-generating integrated circuit (IC) components. The aim is to reduce the maximum temperature of the electronic components and keep them below their critical temperature, hence increasing the life of the IC chips. A correlation is put forward for dimensionless temperature ($\theta$) in terms of heat flux ($q^{\ast }$), volume content ($v^{\ast }$) and size of the IC chips ($\delta$). It has been found that there will be a 4–$6^{\circ }$C drop in temperature when compared to solid fins heat sinks. It is confirmed that the temperature of the IC chip is a strong function of heat flux, size and volume content of PCM.

In recent years, the frequent occurrence of extreme weather and national conflicts has highlighted the necessity of enhancing the robustness of the grain trade network. In this paper, we study the evolution of major trading countries, and the network robustness under random and different attack strategies. The results show that the heterogeneity of the Global Soybean Trade Network (GSTN) and trade connections among countries are increasing. The soybean trade network has strong resistance to random attacks, while subjected to targeted attacks, the stability of the network is significantly affected and damaged.

This paper reports the splitting morphology of low-viscous fingers in the microchannels that are associated with flat T-shaped, curved T-shaped, and Y-shaped junctions. The numerical simulations are based on the finite volume approach and the volume of the fluid model. In this study, microchannels are filled with silicon oil. Perfluorodecalin is used to displace silicon oil from the microchannels. Due to viscosity differences, the low-viscous finger (LVF)-shaped instability evolves at the interface of fluids. A single LVF propagates in the parent channel, and at the junction, it splits into two identical LVFs. It is noted that the splitting morphology of LVF depends upon the shape of the junction and its wettability. Therefore, there are three different junctions, i.e. flat T-shaped, curved T-shaped, and Y-shaped, with three different wettability conditions $(\theta )$, i.e. hydrophilic ($60^{\circ }$), hydrophobic ($120^{\circ }$), and superhydrophobic ($150^{\circ }$) are used for numerical investigation. It is found that a LVF splits symmetrically at all three different junctions but tips of LVFs are found to be convex in superhydrophobic conditions. The LVFs-shaped are curved in the limbs of curved T-shaped microchannel and straight in the limbs of flat T-shaped and Y-shaped microchannels. The findings of this paper may be used in lung biomechanics, respiratory diseases, biochemical testing, and many more.

In this paper, we investigate the phenomena of order-disorder phase transition and the universality of the majority-rule model defined on three complex networks, namely the Barabási–Albert, Watts–Strogatz and Erdős–Rényi networks. Assume each agent holds two possible opinions randomly distributed across the networks’ nodes. Agents adopt anticonformity and independence behaviors, represented by the probability p, where with a probability p, agents adopt anticonformity or independence behavior. Based on our numerical simulation results and finite-size scaling analysis, it is found that the model undergoes a continuous phase transition for all networks, with critical points for the independence model greater than those for the anticonformity model in all three networks. We obtain critical exponents identical to the opinion dynamics model defined on a complete graph, indicating that the model exhibits the same universality class as the mean-field Ising model.

This paper investigates the effects of introducing wavy cylinders of appropriate wavelength into tube bundles for the passive control of flow-induced vibration. The Reynolds-averaged Navier–Stokes approach RANS was used to study the turbulent flow characteristics within staggered tube bundles having transverse and longitudinal pitch-to-diameter ratios of 3.8 and 2.1, respectively. Two wavy models are tested with different wavelength-to-mean diameter ratios, namely: Model-A with $\lambda /D_m=2$ and Model-B with $\lambda /D_m=1$, and their performances are compared with those of a smooth circular tube bundle Model-C ($\lambda /D=\infty$), in a range of subcritical Reynolds numbers $0.5\times 10^4\le \mathrm{\text{Re}}\le 4.1\times 10^4$. Mean velocity and pressure fields as well as aerodynamic coefficients are presented and compared. According to the obtained results, the wavy tube bundle with $\lambda /D_m=2$ exhibits the best performance, with slightly smaller $C_D$ values than the smooth tube bundle. However, results show that the wavy model with $\lambda /D_m=1$ is clearly the worst with an increase of $C_D$ up to 40%. Numerical outcomes also reveal that the interaction of neighboring rows and columns affects the fluctuation of $C_D$ values relative to each tube position. Moreover, $C_D$ evolutions depend significantly on the variation of Re as well, where drag reduction is more substantial by increasing Re. Thus, wavy-shaped tubes with optimum parameters could be more suitable for flow control by enhancing the secondary flow, turbulence and fluid mixing.

The utilization of latent heat storage units with their high energy density and isothermal heat transfer behavior can enhance the performance of thermal energy systems. This study aims to investigate the effect of fin placement on the melting time of a wire and tube-based Phase Change Material (PCM) heat exchanger using numerical simulations. The study introduces a new complex geometry for the heat exchanger, and numerical analysis of heat transfer was conducted in Ansys Fluent software using an established solidification and melting model. The numerical results were validated against experimental data, and it was found that the position of the tubes and fins had a significant impact on heat transfer within the PCM. The model was able to predict temperature data with a maximum discrepancy of 3%.

The development of the micro-gas sensor for the pressure measurement of the different gas species in the low-pressure domain is an important phenomenon. This paper has investigated the importance of molecular characteristics of the eight different gas species in various pressure domains. Impacts of molecular weight, molecular diameter and viscosity of the selected eight gas species on the induced Knudsen force have been analyzed. This study has employed Direct simulation Monte Carlo (DSMC) results of simulations of the micro-gas sensors for the evaluation of the micro-sensor performance in different gas species. Our investigation shows that the influence of molecular diameter change in the high-pressure domain would result in higher significant Knudsen force change. Knudsen force is also reduced when the value of the gas viscosity is increased.

Compound channels are a common hydraulic section of many alluvial and fluvial systems, serving as conduits for the flow of water and sediment. The proper design of these structures requires an understanding of the entrainment and mixing mechanisms in them. This paper presents a three-dimensional numerical study of lock-exchange flow in a compound channel covering the Reynolds numbers (Re) range of 17000–39000. This study investigates flow structures and mixing patterns for various geometries and flow characteristics. The results show that the entrainment coefficient decreases as the dense flow progresses, and the amplitude of instantaneous mixing fluctuations decreases with an increase in the width of the floodplain and reduced gravity. The averaged flux entrainment profiles show a minimum at $\mathrm{\text{Re}}=27000$ at different times in the front area. In the head area also, a downward concavity can be seen in the profiles around $\mathrm{\text{Re}}=27000$. This study also reveals that changes in floodplain height do not affect the establishment of lobe-and-cleft instability. The wider the floodplain channel, the larger the lobe-and-cleft instability created. Small-scale mixing dominates at high Reynolds numbers, leading to higher fluid mixing.

Accurate prediction of industrial electricity consumption is not only beneficial to maintaining the steady development of the economy but also to conserving energy. To improve the prediction accuracy of industrial electricity consumption, a grey cluster weighted Markov model is proposed. It is applied to predict the industrial electricity consumption in four different regions in China. The prediction results are compared with the traditional discrete grey prediction model, which shows that the present model is more effective in these aspects of prediction accuracy, stability and extensibility. The research can provide theoretical references for the “West-East electricity transmission project” in China.

Parameter estimation is important in the study of control and synchronization of fractional-order nonlinear systems (FONSs). This paper proposes an improved Sparrow Search Algorithm (ISSA) for the parameter estimation problem of FONSs. The algorithm improves the population initialization, position update method of discoverers and warning sparrows based on Sparrow Search Algorithm (SSA), and the parameter estimation simulation experiment for fractional-order financial nonlinear system and fractional-order L nonlinear system is conducted to demonstrate this method. The experimental results show that the proposed ISSA is superior to the SSA, Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA) and Harris Hawks Optimization (HHO) in terms of parameter optimization accuracy and convergence speed, which validates the advantages of the ISSA.

This paper presents a numerical procedure for handling delay fractional differential problems where the derivative is defined using the M-fractional approach. The proposed scheme modus operandi is based on the shifted Legendre–Galerkin procedure, which is a powerful tool for solving complex differential models of generalized fractional derivatives. The method involves constructing a series of Legendre polynomials that form the basis functions for approximating the solution of the required problem. The coefficients of the series are obtained after solving an algebraic system of linear types that results from the application of the Galerkin practice. The numerical accuracy and convergence assessment are also presented together with various results. Simulations-based analyses are realized to validate the truthfulness and exactness of the process. The results manifest that the M-derivatives and the Galerkin practice provide alternative innovative approaches for handling M-delay fractional problems. Several keynotes and future recommendations are exhibited at the last with some selected references.

Studies have indicated that focusing solely on pairwise interactions between two nodes disregards the associativity among multi-nodes in the network’s local structure. This associativity can be seen as dependencies among nodes, where certain edges’ presence depends on the path leading to it. Examinations on diverse datasets have approved that the variable order of chained dependencies allows for the preservation of structure information, which enables the reconstruction of the original network into a Higher-Order Network (HON) with improved quality of network representation. This paper proposes a Density-based Higher-Order Network Embedding (DHONE) algorithm, which integrates the concept of higher-order density into the network-embedding process in order to classify the contribution of different orders of dependencies. Through the construction of a novel and effective higher-order adjacency matrix, DHONE steadily improves the accuracy of network representation learning. Experimental results demonstrate DHONEs proficiency in improving embedding accuracy and overall algorithm robustness. Furthermore, grounded in the concept of higher-order density proposed herein, numerous dependencies have been discerned within the network generated from trajectories, potentially indicating the role of multi-node structures in networks.

Birds have traits that can induce better aerodynamic efficiency along with high manoeuvring capability during its flight, which could be shared with unmanned aerial vehicles for improving their aerodynamic performances. One such feature of the wing tip, i.e. the primary feathers of the birds could be an effective geometrical feature to reduce the wing tip vortices. This paper presents the bio-inspired wing tip devices, i.e. three-and four-tipped multiple winglets in reducing the strength of vortices emanating from the wing tip of the wing operating in the Reynolds number (Re) of $0.9794\times 10^5$ and $0.9794\times 10^6$. Different combinations of both three- and four-tipped multiple winglets have been designed by varying the cant angle of each tip. Numerical simulations were carried out using Ansys-Fluent by solving three-dimensional Reynolds averaged Navier–Stokes formulations coupled with k-$ϵ$ turbulence model to resolve the features of tip vortices. The simulation clearly indicates that there is a strong correlation between the size of the vortices and the aerodynamic performance parameters such as $C_L/C_D$, ${(C_L)}_{max,}$ $C_L{}^{0.5}/C_D$, $C_L{}^{1.5}/{\mathrm{\text{C}}}_D$. The three- and four-tipped multiple winglets are effective in reducing vortex drag by disintegrating large strength vortex which occurs in the tip of straight wing, into few numbers of small strength vortices. When compared to straight wing, three-tipped multiple winglet with the cant angle combination of 50, 30, 10 improves the aerodynamic efficiency by 22% to 23% and the four-tipped winglet with the cant angle combination of 60, 50, 40, 30 enhances the same by 21% to 22% in the Re of $0.9794\times 10^5$. Even the longitudinal static stability has seen considerable improvement for four-tipped multiple winglets than three-tipped multiple winglets and straight wing.