International Journal of Modern Physics C

This paper investigates the well-posedness of a class of FSIDEs utilizing the fractional Caputo–Fabrizio derivative. Herein, the well-posedness proofs are constructed by considering some applicable conditions and combining theories of Banach space, AAT, and FPST. Approximating the solutions of such equations is still challenging for many mathematicians today due to their randomness and the hardness of finding the exact one. For the numerical aim, we introduce some useful properties of the Legendre-shifted polynomials and employ them as a basis of the collocation spectral method. The idea of this scheme is to convert such stochastic equations into algebraic systems subject to ${ℱ}_0$-measurable independent parameters. The stochastic term is driven by one-dimensional standard Brownian motion which is the most familiar type and for simulating its trajectories we discuss an easy method. We rigorously analyze the convergence of the proposed technique and other error behavior-bound results. Finally, various tangible numerical applications are performed to verify the present scheme’s accuracy and great feasibility and support theoretical results. The acquired results reveal that the methodology used is effective and appropriate to deal with various issues in light of the fractional Caputo–Fabrizio derivative.

Understanding the effect of alloying elements on the retention and clustering behavior of Helium (He) in Aluminum (Al) is a great help to study the radiation damage process of Al-based nuclear structure materials under He irradiation. Based on the first-principles calculations, we investigated the influence of Gallium (Ga) dopant on the formation of ${\mathrm{\text{He}}}_{\mathrm{\text{n}}}$ and ${\mathrm{\text{He}}}_{\mathrm{\text{n}}}\mathrm{\text{V}}$ clusters in Al and Al-0.9at% Ga (Al-Ga) alloy. We found that Ga dopant could influence the formation and growth of He clusters. In addition, the presence of Ga reduces the binding energy of both ${\mathrm{\text{He}}}_{\mathrm{\text{n}}}$ and ${\mathrm{\text{He}}}_{\mathrm{\text{n}}}\mathrm{\text{V}}$ clusters, resulting in He dissociation from the clusters more easily. Moreover, Ga could serve as a trapping center by reducing the charge density in its vicinity to induce He nucleation in Al-Ga alloy compared to that in pure Al. Furthermore, the binding energy of He to vacancy around Ga is weaker than that around Al, suggesting that Ga will decrease the trapping capability of vacancy to He. We thus propose that Ga plays a key role in He clustering behavior. Our results are significant to understand the effect of dopant on He bubbling behavior and the distribution of damages in Al-Ga alloy under He irradiation.

In this research, we analyze the air transportation network of the United States of America using databases with passenger activity containing detailed records of domestic flights between airports. Different properties obtained from the origin-destination matrix in the air transport network are studied from 2011 to 2020. The results are compared with a model based on the gravity law for human mobility defined in terms of transition probabilities and travel distances. The predictions of this model are confirmed through Monte Carlo simulations. Our findings reproduce the dynamics of passengers in the airport transportation network.

The spectrum of normalized Laplacian matrix of a network has attracted more and more attention because it is related to the structural properties and dynamical aspects of the network, specially in random walks. In this paper, we study the spectra and their applications of normalized Laplacian matrices for weighted level-3 Sierpiński graphs that are constructed in an iterative way. We analytically obtain all the spectra from two successive generations by applying the decimation method. Using the obtained spectra, we then derive closed-form expressions for their eigentime identity and number of spanning trees.

The impetus of this study is to provide an in-depth insight into the unsteady hydrodynamic characteristics of the cavitating flow, effects of the wavy leading edge (WLE) on the noise suppression mechanism due to a cavity cloud formation, which contains condensation, detachment, collapse, spanwise flow, streamwise velocity fluctuation, and shedding phenomenon. NACA 63₄-021 hydrofoil was considered with WLE having a wavelength of 25% and an amplitude of 5% of the mean chord length and was compared to a straight-leading-edge (SLE) hydrofoil at cavitation numbers of $\sigma =0.8$ and a chord-based Reynolds number of $7.2\times 10^5$. Counter-rotation vortices were produced between the peaks of the WLE hydrofoil by destroying the horseshoe vortex and delaying the tail vortex, changing the frequency. Here, the hydrodynamic forces have also been discussed in addition to the noise. The results showed that the leading-edge vortex formation and flow separation dynamics fundamentally differed between the SLE and the WLE hydrofoil. The main difference between the WLE and SLE hydrofoil turbulent flow is the formation of counter-rotating streamwise vortices pairs. We solved the cavitating flow using the large eddy simulation (LES) approach, as well as the Kunz mass transfer model, which is performed under the framework of the OpenFOAM package.

Noise widely exists in the nervous system, and plays an extremely important role in the information processing of the nervous system, which can enhance or weaken the ability of the nervous system to process information. Nerve cells exist in complex and changeable electromagnetic fields, and their potential changes are significantly regulated by electromagnetic induction. In response to this, first, a memristor is used to simulate the electromagnetic field environment where the nervous system is located, when using different weak periodic signals as the input of the neuron system, the rich stochastic resonance behavior of the FitzHugh–Nagumo neuron system is analyzed under the drive of phase noise. Second, taking the amplitude, period and intensity of phase noise as the main change parameters, and the changes of the parameters of the memristor and the period of the external signal as auxiliary conditions, the stochastic resonance dynamics analysis is carried out from three perspectives: the amplitude and period of phase noise, the amplitude and intensity of phase noise and the intensity and period of phase noise.

This study implements a new solver (reactiveInterFoam) to simulate the component mass transfer alongside deformable gas–liquid interfaces. Mass transfer from the rising bubble in a quiescent Newtonian fluid is simulated. An effect of bubble hydrodynamics on the simultaneous diffusion reaction and selectivity of the cyclohexane oxidation process is investigated on a two-dimensional axisymmetric domain. The color function volume of fluid (CF-VoF) technique is applied to capture the deformable interface, and the continuous species transfer method is used to monitor the gas–liquid mass transfer behavior. Several simulations have been conducted to validate the model reliability to forecast component mass transfer from the bubble to the liquid phase, bubble shape, and flow field. Simulation findings approved that the rate of mass transfer is a function of boundary’s concentration, layer thickness, and bubble surface area. Furthermore, the selectivity increases by decreasing bubble diameter in both spherical and ellipsoidal regimes. The small bubbles with a lower Reynolds number have higher average selectivity. Comparing the simulated bubble shape and the grace chart indicates that the suggested numerical method can perfectly predict bubble regimes. The absolute average relative deviation (AARD%) of 14.59% has been observed between the terminal velocities predicted by the numerical simulation and six experimental measurements.

In this paper, density functional theory (DFT) is used to study the structure, electron and absorption properties of 6-Amino crystal in the pressure range of 0–300GPa. The variations of the lattice constants, bond lengths and bond angles show that they undergo complex transformations under different pressures. More narrowly, the covalent bonds of the benzene ring and the uracil ring in the planar intramolecular structure are broken, and then the new covalent bonds between the adjacent intermolecular structure are reshaped at about 80, 100 and 160GPa. The analysis results of band gap and DOS of 6-Amino indicate that the electronic properties of 6-Amino repeatedly transform from the semiconductor system into the metal phase at 80, 180 and 260GPa. The absorption spectra show two important structural changes at 100 and 180GPa, and present the high optical activity with the change of pressure.

This study explores heat and mass transport in natural convection of Casson fluid in a vertical annulus via porous medium. Impacts of thermal radiation, heat source and chemical reaction are taken into consideration. The equations representing the model reduced into nondimensional ordinary differential equations under adequate transformations are solved analytically. Closed form solutions are obtained for the problem in terms of Bessel’s functions. Influences of various arising parameters such as porous medium parameter, heat generation, thermal radiation, thermal Grashof number, solutal Grashof number, etc. on flow, temperature and concentration fields are exhibited by graphs and discussed. Also, we have solved the problem numerically on MATLAB software employing the bvp4c technique along with shooting technique. The exact and numerical solutions compared found a good match. Moreover, the effects of numerous parameters on quantities of physical importance such as skin-friction coefficient, Nusselt number and Sherwood number are also portrayed and discussed. Heat exchangers, energy storage systems such as batteries and inverters, thermal storage and thermal protection systems are some examples of applications of the study.

Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation results for very large lattices with linear lattice sizes up to $L=3456$. Our estimated values of the correction-to-scaling exponent $\omega$ tend to decrease below the usually accepted value about 0.83 when the smallest lattice sizes, i.e. $L<L_{\mathrm{\text{min}}}$ with $L_{\mathrm{\text{min}}}\in [6,64]$, are discarded from the fits. This behavior apparently confirms some of the known estimates of the Monte Carlo renormalization group (MCRG) method, i.e. $\omega \approx 0.7$ and $\omega =0.75(5)$. We discuss the possibilities that $\omega$ is either really smaller than usually expected or these values of $\omega$ describe some transient behavior which, eventually, turns into the correct asymptotic behavior at $L_{\mathrm{\text{min}}}>64$. We propose refining MCRG simulations and analysis to resolve this issue. Our actual MC estimations of the critical exponents $\eta$ and $\nu$ provide stable values $\eta =0.03632(13)$ and $\nu =0.63017(31)$, which well agree with those of the conformal bootstrap method, i.e. $\eta =0.0362978(20)$ and $\nu =0.6299709(40)$.

In this paper, the variable camber morphing strategy is adopted in a NACA airfoil through computational investigation to enhance the lift to drag ratio ($L∕D)$ specifically for military UAV applications. The typical mission profile is also focused on enhancing the aerodynamic performance of the UAV during various flight segments by variable camber morphing. The airfoil camber is changed dynamically at different instances based on the mission profile requirements thereby altering the $L∕D$ characteristics. The concept of bio-inspired aerodynamics has received a greater attention in recent years because of the proven nature oriented real-time application. Hence, the concept of bio-inspired variable camber morphing is proposed herein that minimizes the use of unconventional control surfaces to attain the required performance at different segments of flight. MQ9 Reaper UAV model is chosen to implement the proposed variable camber morphing strategy at the mission flight segments. NACA 4412 cambered airfoil has been considered as the baseline model airfoil for the present study because of its higher zero lift angle characteristics. The lower camber of the airfoil section is changed from 1% to 3% at different angles of attack (AoA) for the time instances such as 1s, 2s and 3s, respectively. The lift coefficient ($C_l)$ of the airfoil is also significantly increased through camber morphing at different flight segments during each time step with negligible flow separation as observed through streamline patterns. Hence, the friction drag coefficient is also retained under optimum level as concluded through the boundary layer profiles.

In this work, a fifth-order weighted essentially nonoscillatory scheme based on Legendre polynomials is constructed for simulating Hamilton–Jacobi (HJ) equations in a finite difference framework. The new reconstruction is a convex combination of a fourth-degree polynomial and two quadratic polynomials in WENO-Z fashion. This reconstruction uses the same six-point information as the original fifth-order WENO scheme [G.-S. Jiang and D. Peng, SIAM J. Sci. Comput. 21, 2126 (2000)] and could obtain smaller absolute truncation errors and the same accuracy order in the smooth region, while it has less computational time. A detailed analysis of the approximation order of the designed WENO scheme is prepared. Some benchmark tests in one-dimensional and multi-dimensional space are considered to display the capability of the new proposed scheme.

The recently developed physics-informed machine learning has made great progress for solving nonlinear partial differential equations (PDEs), however, it may fail to provide reasonable approximations to the PDEs with discontinuous solutions. In this paper, we focus on the discrete time physics-informed neural network (PINN), and propose a hybrid PINN (hPINN) scheme for the nonlinear PDEs. In this approach, the local solution structures are classified as smooth and nonsmooth scales by introducing a discontinuity indicator, and then the automatic differentiation technique is employed for resolving smooth scales, while an improved weighted essentially nonoscillatory (WENO) scheme is adopted to capture discontinuities. We then test the present approach by considering the viscous and inviscid Burgers equations, and it is shown that compared with original discrete time PINN, the present hPINN approach has a better performance in approximating the discontinuous solution even at a relatively larger time step.

The implications and contagion effect of emotion cannot be ignored in rumor spreading. This paper sheds light on how decision makers’ (DMs) emotion type and intensity affect rumor spreading. Based on the rank-dependent expected utility (RDEU) and evolutionary game theory (EGT), we construct an evolutionary game model between rumormongers (RMs) and managers (Ms) by considering emotions. We use MATLAB to simulate and reveal the influencing mechanism of DMs’ emotion type and intensity on rumor spreading. The results indicate that the DMs’ strategy choice is not only affected by their own emotion preference and intensity, but also by the other players in rumor spreading. Moreover, pessimism has a more significant influence than optimism on the stability of the evolutionary game, Ms’ emotion is more sensitive to the game results than RMs’ emotion and the emotion intensity is proportional to the evolution speed. More significantly, some earthshaking emotional thresholds are found, which can be used to predict RMs’ behavior, help Ms gain critical time to deal with rumors, and avoid the Tacitus Trap crisis. Furthermore, the evolution results fall into five categories: risk, opportunity, ideal, security and hostility. The results of this work can benefit Ms’ public governance.