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This paper deals with the numerical solution of the time-fractional Gilson–Pickering equation using the Kansa method, in which the multiquadrics were utilized as the radial basis function. To achieve this, a meshless numerical scheme based on the finite difference along with the Kansa method has been presented. First, the finite difference approach has been utilized to discretize the temporal derivative, and subsequently, the Kansa method is employed to discretize the spatial derivatives. The stability and convergence analysis of the numerical scheme are also elucidated in this paper. Furthermore, the soliton solutions have been acquired by implementing the Kudryashov method for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme. [ABSTRACT FROM AUTHOR]

Memristor, as a nonlinear element, provides many advantages thanks to its superior properties to design different chaotic circuits. Thus, a novel four-dimensional double-scroll chaotic system with line equilibria as well as two unstable equilibria based on the flux-memristor model is proposed in this paper. The effects of initial values and parameters on the dynamic characteristics of the system are studied in detail by means of phase diagrams, Lyapunov exponent spectrums, bifurcation diagrams, two-parameter bifurcation diagrams and basins of attraction. Besides, a series of complex phenomena in the system, such as sustained chaos, bistability, transient chaos and coexisting attractors are observed, proving that the chaotic system has rich dynamic characteristics. Also, spectral entropy (SE) complexity algorithm and C 0 complexity algorithm based on structure complexity are adopted to analyze the complexity of the system. Additionally, PSPICE circuit simulation and Micro-Controller Unit (MCU) hardware experiment are carried out to verify the correctness of theoretical analysis and numerical simulation. Finally, the pulse chaos synchronization is achieved from the perspective of maximum Lyapunov exponent, and numerical simulations demonstrate the occurrence of the proposed system and practicability of the pulse synchronization control. [ABSTRACT FROM AUTHOR]

Through the Z m -KP hierarchy, we present a new (3+1)-dimensional equation called weakly coupled generalized Kadomtsev–Petviashvili (wc-gKP) equation. Based on Hirota bilinear differential equations, we get rational solutions to wc-gKP equation, and further we obtain lump solutions by searching for a symmetric positive semi-definite matrix. We do some numerical analysis on the trajectory of rational solutions and fit the trajectory equation of wave crest. Some graphics are illustrated to describe the properties of rational solutions and lump solutions. The method used in this paper to get lump solutions by constructing a symmetric positive semi-definite matrix can be applied to other integrable equations as well. The results expand the understanding of lump and rational solutions in soliton theory. [ABSTRACT FROM AUTHOR]

This paper constructs a novel memristive hyperchaotic system by introducing the flux-controlled memristor to an extended jerk system. The memristive system has two equilibria and coexists two symmetric hyperchaotic attractors. The dynamic behaviors of the system are studied through bifurcation analysis. The analog circuit design and microcontroller-based experimental implementation of the system are presented. The synchronization of the system is realized by using the adaptive control technique. The sufficient conditions for synchronization are established via theoretical and numerical analysis. [ABSTRACT FROM AUTHOR]

During the last three decades, nonstandard statistics for indistinguishable quantum particles has attracted wide attention and research interests from many institutions. Among these new types of statistics, the q -deformed Bose and Fermi statistics, originated from the study of quantum algebra, are being applied in more and more physical systems. In this paper, we construct a q -deformed generalization of the BCS-Leggett theory for ultracold Fermi gases based on our previously constructed q -deformed BCS theory. Some interesting features of this q -deformed interacting quantum gas are obtained by numerical analysis. For example, in the ordinary Bose–Einstein Condensation regime, the gas presents a fermionic feature instead of bosonic feature if the deformation parameter is tuned suitably, which might be referred to as the q -induced "Bose–Fermi" crossover. Conversely, a weak sign of the "Fermi–Bose" crossover is also found in the ordinary weak fermionic regime. [ABSTRACT FROM AUTHOR]

In the paper, the fixed-time and finite-time synchronizations of multi-links complex network are investigated. Compared with finite-time synchronization, the settling time of fixed-time synchronization is independent of initial conditions. For uncertain multi-links complex networks, this paper further analyzes synchronization mechanism and unknown parameters based on the drive-response concept and finite-time stability theory. Novel synchronization control criteria and the result of parameters identification are, respectively, obtained in a finite time by utilizing Lyapunov function and linear matrix inequality (LMI). Besides, we give other two versions of finite-time synchronization and parameters identification for uncertain multi-links complex network with impulsive control input. Finally, numerical examples are given to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, both the local region and sub-Monte Carlo steps were introduced to study the non-equilibrium steady state of two-dimensional Ising model. As the size of local region can vary on a large scale, it is very important to determine the effective local region size. In our studies, a series of local regions with different sizes were taken into consideration, and the results show that, when the temperature of a local region is far away from the critical temperature of the system, no matter the local region size is large or small, the results obtained by our calculations are almost the same; however, when the temperature of the local region is near to the critical point, the difference between the calculated results is very large if the local region size is very small, but this difference will decrease quickly when the local region size is enlarged, and the calculation results will tend to be the same when the local region size is larger than a certain value. Furthermore, the numerical results show that the effective local region size is almost unaffected by the temperature gradient of the system. It is clear that the local region and expanded Monte Carlo method provide us an efficient numerical method to study the non-equilibrium steady state. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to present a method for dynamic modeling and simulation of the translational joint with friction and clearance. The sizes of the clearances and the impacts between the slider and the guide in the translational joint can be neglected when the clearance sizes are very small. The geometric constraints of the translational joint are treated as bilateral constraints. The contact forces acting on the slider are reduced to the forces on the slider corners. The LuGre friction model is used to describe friction between slider and guide, because it can capture the variation of the friction force with slip velocity and the slider motion with stick–slip phenomenon. The problem of computing the normal forces on the slider is formulated and solved as a horizontal linear complementarity problem (HLCP), which is embedded in the event-driven method. Finally, a numerical example is considered and numerical results are presented to show the feasibility and the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, the group classification is presented for Fisher equation with time-dependent coefficients. The analysis provided many new solutions that take the form of doubly periodic-like solutions and soliton-like solutions. [ABSTRACT FROM AUTHOR]

In this paper, a generalized (3+1)-dimensional B-type Kadomtsev–Petviashvili (gBKP) equation is investigated by using the Hirota’s bilinear method. With the aid of symbolic computation, some new lump, mixed lump kink and periodic lump solutions are derived. Based on the derived solutions, some novel interaction phenomena like the fission and fusion interactions between one lump soliton and one kink soliton, the fission and fusion interactions between one lump soliton and a pair of kink solitons and the interactions between two periodic lump solitons are discussed graphically. Results might be helpful for understanding the propagation of the shallow water wave. [ABSTRACT FROM AUTHOR]

This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data. [ABSTRACT FROM AUTHOR]

In this paper, an aircraft model was tested in the wind tunnel with different degrees of yaw-roll coupling at different angles of attack. The dynamic increments of yawing and rolling moments are compared to study the coupling effects on damping characteristics. The characteristic time constants are calculated to study the changes of flow field structure related to coupling ratios. The damping characteristics and time lag effects of aerodynamic loads calculated by dynamic derivative method are also compared with experimental results to estimate the applicability of linear superposition principle at large angles of attack. [ABSTRACT FROM AUTHOR]

In this paper, a numerical study of the interaction between transverse cold jets on slender body in front of or between X-shape rudders with rudders in the oncoming free stream is presented. Firstly, the flow field at different jet conditions is simulated and analyzed. Then, the total force and moment amplification factors of the corresponding slender body with jet at different locations are analyzed and compared with those results of non-jet flow. Numerical results show that interactions take a great effect to the configuration of the flow field around rudders and the pressure distribution on slender surface. Moreover, the force and moment amplification changes regularly along with the location of jet nozzle. [ABSTRACT FROM AUTHOR]

To understand the interaction between the oscillated body and oncoming vortex, some numerical studies have been conducted on a system including two parallel D-cylinder and one oscillated foil in this paper. It is found that the distance between parallel D- cylinder and oscillated foil would play a key role in affecting the change regulation of thrust generation of oscillated foil, and the kinematics of oscillated foil would determine the value of propulsive thrust, the gap between two parallel D-cylinder would only affect the hydrodynamic performance of oscillated foil at intermediate conditions. [ABSTRACT FROM AUTHOR]

In this paper, a class of difference equations with variable-time impulses is considered. By applying comparison principle, we shall show that difference equations with variable-time impulse can be reduced to the corresponding difference equations with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the difference equations with variable-time impulses. Furthermore, we use a series of sufficient criteria to illustrate the same stability properties between variable-time impulsive difference equations and the fixed-time ones. We then establish several sufficient conditions guaranteeing the global exponential stability of variable-time impulsive difference equations by comparison principle. As an application, global exponential stability of discrete-time neural networks with variable-time impulses is discussed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, a vector Ramani equation is proposed by using the bilinear approach. With the help of the bilinear exchange formulae, bilinear Bäcklund transformation and the corresponding Lax pair for the vector Ramani equation are derived. Besides, multi-soliton solution expressed by pfaffian is given and proved by pfaffian techniques. [ABSTRACT FROM AUTHOR]

In this paper, the memristor-based fractional-order neural networks (MFNN) with delay and with two types of stabilizing control are described in detail. Based on the Lyapunov direct method, the theories of set-value maps, differential inclusions and comparison principle, some sufficient conditions and assumptions for global stabilization of this neural network model are established. Finally, two numerical examples are presented to demonstrate the effectiveness and practicability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a pair of symmetric three-terminal refrigerator models with a hot cavity connected to two colder reservoirs via ideal tunneling quantum dots. The cooling of the refrigerators is achieved by investing thermal power from a hot reservoir and electric power from an applied voltage. Based on the model proposed, we numerically analyze the performance of the refrigerators with different half width of energy levels, and particularly discuss the coefficient of performance for zero applied voltage in the limit of a small half level width. Finally, we optimize with half width of energy levels and get the optimal region of the refrigerators. [ABSTRACT FROM AUTHOR]

With the aim of providing an analytical approach (not accurate numerical results), for the first time, the sensitivity to the partial pressure of oxygen of the shift in the energy band gap experienced by cadmium-oxide thin films is evaluated for the visible region by introducing a suitable parameter. The sensitivity to the above pressure of the spatial carrier density is determined and compared with the sensitivity relative to the band gap shift. The gradient of the CdO carrier concentration as a function of the partial pressure of oxygen appears in the expressions for the two above sensitivity functions but the goal of this paper is not computing numerically this gradient so only qualitative estimations are done. In relation to the above results, the kinetics relative to the formation of CdO thin films are investigated. In addition, the sensitivity to the pressure in question of the corresponding optical-absorption shift in the visible range is calculated. [ABSTRACT FROM AUTHOR]

In PEM fuel cells, during electrochemical generation of electricity more than half of the chemical energy of hydrogen is converted to heat. This heat of reactions, if not exhausted properly, would impair the performance and durability of the cell. In general, large scale PEM fuel cells are cooled by liquid water that circulates through coolant flow channels formed in bipolar plates or in dedicated cooling plates. In this paper, a numerical method has been presented to study cooling and temperature distribution of a polymer membrane fuel cell stack. The heat flux on the cooling plate is variable. A three-dimensional model of fluid flow and heat transfer in cooling plates with 15 cm × 15 cm square area is considered and the performances of four different coolant flow field designs, parallel field and serpentine fields are compared in terms of maximum surface temperature, temperature uniformity and pressure drop characteristics. By comparing the results in two cases, the constant and variable heat flux, it is observed that applying constant heat flux instead of variable heat flux which is actually occurring in the fuel cells is not an accurate assumption. The numerical results indicated that the straight flow field model has temperature uniformity index and almost the same temperature difference with the serpentine models, while its pressure drop is less than all of the serpentine models. Another important advantage of this model is the much easier design and building than the spiral models. [ABSTRACT FROM AUTHOR]

In this paper, we use car-following theory to study the traditional vehicle's running cost and the electric vehicle's running cost. The numerical results illustrate that the traditional vehicle's running cost is larger than that of the electric vehicle and that the system's total running cost drops with the increase of the electric vehicle's proportion, which shows that the electric vehicle is better than the traditional vehicle from the perspective of the running cost. [ABSTRACT FROM AUTHOR]

In this paper, by adopting a fifth-order weighted essentially non-oscillatory (WENO) scheme with a third-order TVD Runge-Kutta time stepping method for two-dimensional reactive Euler equations, a parallel code is developed, and reignition behavior after a self-sustaining detonation from the tube into free space filled with H2/O2 mixtures is investigated. The numerical results show that the initial pressure has a great influence on the detonation cellular width, and that as the initial pressure increases, the cellular width gradually decreases and the cellular shape changes from irregular structure to regular structure, demonstrating the detonation instability to stability transition. When the initial pressure is larger than 1.2 atm, the detonation wave expands over the edge of the splitter plate, reignition can come into being because enough transverse waves collide with each other at the leading edge of the expanding front. When the initial pressure is 1.2 atm, hot spots appear on the front, and ignite the combustible gas near the hot spots after detonation diffraction. When the initial pressure is 1.0 atm, reignition fails. These findings hint that a critical initial pressure exists between 1.0-1.2 atm for direct reignition after detonation diffraction. [ABSTRACT FROM AUTHOR]

In this paper, we have designed, simulated and analyzed a new generation chiral metamaterials (MTMs) with two geometries. There are various types of chiral MTM structures in the literature and almost all of them are indented to be designed for high level of chirality. In fact, small chirality and its application areas were mostly ignored by researchers. In this sense, our study is one of the pioneer works for this type of research. Each structure based on omega resonators (ORs) with small chirality value is investigated both numerically and experimentally. The results are in very good agreement which will lead us to conclude that our structures can be easily used as devices for controlling polarization, EM wave transmission filtering, antireflection and so on for a wide range of the EM spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we apply car-following model to explore each person's travel time and the system's total travel time on an open road. The analytical and numerical results illustrate that each person's travel time and the system's total cost are directly related to each person's time headway at the origin when the road is long enough and the number of persons is large enough in the traffic system. The above results can help traffic engineers to optimize each person's arrival rate and help readers to understand the relationship between each person's travel time and his arrival rate. [ABSTRACT FROM AUTHOR]

In this paper, we propose an extended helicopter's rescuing model to explore the effects of multiple rescuing points on each helicopter's flying behavior during the whole rescuing process from the numerical perspective. The numerical results show that the proposed model can describe the qualitative effects of multiple rescuing points on each helicopter's speed, running trail and safe region. [ABSTRACT FROM AUTHOR]

The wavefunction method provides us with a useful tool to describe electron correlations in solids at the ground state. In this paper we review the recent development of the momentum-dependent local ansatz (MLA) wavefunction. It is constructed by taking into account two-particle excited states projected onto the local orbitals, and the momentum-dependent amplitudes of these states are chosen as variational parameters. The MLA describes accurately correlated electron states from the weak to the intermediate Coulomb interaction regime in infinite dimensions, and works well even in the strongly correlated region by introducing a new starting wavefunction called the hybrid (HB) wavefunction. The MLA-HB is therefore shown to overcome the limitation of the original local ansatz (LA) wavefunction as well as the Gutzwiller wavefunction. In particular, the calculated quasiparticle weight versus Coulomb interaction curve is shown to be close to that obtained by the numerical renormalization group approach. It is also shown that the MLA is applicable to the first-principles Hamiltonian. [ABSTRACT FROM AUTHOR]