Search

This paper focuses on developing and analyzing a new AR-iterative scheme designed for estimating fixed points of generalized non-expansive mappings of the Suzuki kind. The scheme’s stability and convergence properties are rigorously proven, highlighting its superior convergence rate for non-expansive mappings when compared to existing schemes in the literature. Additionally, an application of the AR-iterative scheme to differential equations is presented. These findings underscore the effectiveness and versatility of the proposed scheme in numerical analysis and computational mathematics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a novel approach for estimating the fixed points of multi-valued non-expansive mappings using the AR-iteration scheme in the context of uniformly convex Banach spaces. We establish strong and weak convergence results, providing rigorous analytical proofs and illustrating the results with a detailed example. Our approach showcases the potential of the AR-iteration scheme in solving real-world problems, particularly in addressing two-point boundary value problems. We demonstrate the applicability and effectiveness of the AR-iteration scheme in numerical analysis and computational mathematics. Our results contribute significantly to the advancement of numerical methods in solving boundary value problems, offering new insights and directions for future research in this area. Furthermore, we provide a detailed explanation of Green’s function approach and its implications for various scientific and engineering applications, paving the way for future research in this area. [ABSTRACT FROM AUTHOR]

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]

The aim of this paper is to show numerically the semi-ideal way of transferring energy in the non-steady supersonic mechanism. Energy can be transferred between two fluids in semi-ideal process if the two fluids are brought together for a direct contact. This paper shows the energy transfer between two fluids via the direct fluid-fluid interaction in a non-steady supersonic flow. This was shown by using two fluids one with higher energy than the other. Results including contour plots of static pressure, static temperature, and total pressure and velocity vectors show the structure of flow of the energy-transfer-mechanism in a supersonic flow. [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]

We have investigated in detail the effects of the depth and range of the limiting potential, the quantum size parameter, temperature and hydrostatic pressure on the nonlinear optical rectification (NOR) coefficient in GaAs/GaAlAs parabolic quantum dots (QDs) with a tangent square potential. Firstly, we add the tangent-square potential of the system along the z-axis to the original parabolic QD, and then the corresponding Schrödinger equation of the modified system can be solved to find the analytical forms of different splitting energy levels and envelope wave functions. Finally, the analysis and conclusions of the numerical simulations indicate that the above parameters have significant effects on the nonlinear optical properties of the modified system. [ABSTRACT FROM AUTHOR]

A numerical method of aerodynamic heating with material thermal ablation effects for hypersonic half-sphere is presented. A surface material ablation model is provided to analyze the ablation effects on aero-thermal properties and structural heat conduction for thermal protection system (TPS) of hypersonic vehicles. To demonstrate its capability, applications for thermal analysis of hypersonic vehicles using carbonaceous ceramic ablators are performed and discussed. The numerical results show the high efficiency and validation of the method developed in thermal characteristics analysis of hypersonic aerodynamic heating. [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]

The Pseudo-Shock Wave (PSW), which appears when supersonic flow in duct decelerates to subsonic, is a complicated process due to the interaction between boundary layer and shock wave. It significantly affects the performance and efficiency of flow devices. In this paper, PSW in two kinds of variable cross-section ducts, edge-varied and corner-varied, was investigated through CFD numerical simulation. Compared to the rectangular duct, a shorter and wider separation region is appeared in the corner of the edge-varied duct while the strongest separation is laterally propagated across the entire plane of the corner-varied duct's side wall. This makes the performances of varied ducts different from traditional constant cross-section ducts. [ABSTRACT FROM AUTHOR]

The simulation comparison research of two types of high-order triangular finite element methods for the numerical simulation of two-dimensional nonlinear electromagnetic fields is presented in this paper. The comparative study has been done in many ways, such as the accuracy of computation, the computation time and computer storage requirement. The comparative results obtained in this paper are very useful to calculation methods used in electromagnetic fields in modern physics fields. [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, 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]

In this paper, we establish a nanothermoelectric engine consisting of two discrete energy levels embedded between two reservoirs at different temperatures and chemical potentials. Based on master equation, the expressions for the power output and efficiency of the nanothermoelectric engine are derived. The characteristic curves between the power output and the efficiency are plotted. Moreover, the optimal performance parameters are obtained by the numerical calculation. The influence of the strength of variations in electron-electron interactions on the optimal performance parameters is analyzed in detail. [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]

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, numerical investigation was conducted for an oscillating NACA0012 foil combining the pitching and plunging motions. The plunging follows a sinusoidal motion while the pitching trajectory is controlled by achieving the resultant effective angle of attack (AOA) to be a harmonic cosine form. Computations were conducted over a range of the Strouhal number (St), different maximum effective AOA and different phase difference between pitching and plunging (ψ). Results show that, at higher St, significant improvement on propulsion performance has been achieved when the effective AOA profile maintains a harmonic cosine form by controlling the pitching motion of the foil. [ABSTRACT FROM AUTHOR]

The present paper studies the cavitation characteristics in thermodynamic condition. The present work modifies thermodynamic cavitation mass transfer expression based on the Rayleigh-Plesset equation. The pressure difference, surface tension and thermodynamic effects are considered in new mass transfer expression on the basics of the evaporation and condensation mechanics according to the micro-kinetic theory. The hydrofoil NACA0015's thermal cavitation characteristic is calculated at 25°C, 50°C, 70°C with the improved model. The shear stress transport model is adopted as turbulence kinetic energy transport equation. The pressure coefficient is compared with experiment data at different temperatures to validate the model. The temperature difference between local temperature and ambient temperature is obtained and the cavitation volume fraction is calculated. [ABSTRACT FROM AUTHOR]

In this paper, we study the ultracold atoms in optical lattice with a weak random external potential by an extended Bose–Hubbard model. When the on-site interaction is strong enough, the model can be mapped to the XXZ model. Then the mean-field theory is applied and we get the zero- and finite-temperature phase diagrams in different optical parameters. The differences between the systems with and without disorder were found, and the Bose-glass phase may exist in the system with disorder. [ABSTRACT FROM AUTHOR]

Most of finite volume schemes in the Arbitrary Lagrangian–Eulerian (ALE) method are constructed on the staggered mesh, where the momentum is defined at the nodes and the other variables (density, pressure and specific internal energy) are cell-centered. However, this kind of schemes must use a cell-centered remapping algorithm twice which is very inefficient. Furthermore, there is inconsistent treatment of the kinetic and internal energies.1 Recently, a new class of cell-centered Lagrangian scheme for two-dimensional compressible flow problems has been proposed in Ref. 2. The main new feature of the algorithm is the introduction of four pressures on each edge, two for each node on each side of the edge. This scheme is only first-order accurate. In this paper, a second-order cell-centered conservative ENO Lagrangian scheme is constructed by using an ENO-type approach to extend the spatial second-order accuracy. Time discretization is based on a second-order Runge–Kutta scheme. Combining a conservative interpolation (remapping) method3,4 with the second-order Lagrangian scheme, a kind of cell-centered second-order ALE methods can be obtained. Some numerical experiments are made with this method. All results show that our method is effective and have second-order accuracy. At last, in order to further increase the resolution of shock regions, we use an adaptive mesh generation based on the variational principle5 as a rezoned strategy for developing a class of adaptive ALE methods. Numerical experiments are also presented to valid the performance of the proposed method. [ABSTRACT FROM AUTHOR]

A parallel Navier-Stokes solver based on dynamic overset unstructured grids method is presented to simulate the unsteady turbulent flow field around helicopter in forward flight. The grid method has the advantages of unstructured grid and Chimera grid and is suitable to deal with multiple bodies in relatively moving. Unsteady Navier-Stokes equations are solved on overset unstructured grids by an explicit dual time-stepping, finite volume method. Preconditioning method applied to inner iteration of the dual-time stepping is used to speed up the convergence of numerical simulation. The Spalart-Allmaras one-equation turbulence model is used to evaluate the turbulent viscosity. Parallel computation is based on the dynamic domain decomposition method in overset unstructured grids system at each physical time step. A generic helicopter Robin with a four-blade rotor in forward flight is considered to validate the method presented in this paper. Numerical simulation results show that the parallel dynamic overset unstructured grids method is very efficient for the simulation of helicopter flow field and the results are reliable. [ABSTRACT FROM AUTHOR]

This paper studies the dynamical behavior of the Newton–Leipnik system and its trajectory-transformation control problem to multiple attractors. A simple linear state feedback controller for the Newton–Leipnik system based on the Lyapunov stability theory and applying the inverse optimal control method is designed. We stabilize asymptotically the chaotic attractors to unstable equilibriums of the system, so that the transformation of one attractor to another for the trajectory of the Newton–Leipnik system is realized. Theoretical analyses and numerical simulations both indicate the effectiveness of the controller. At last, the inverse optimal control method is proven effective for the chaotic systems with multiple attractors by the example on the unified chaotic system. [ABSTRACT FROM AUTHOR]

In order to increase greatly the calculation accuracy and the computation speed for complex electromagnetic fields in modern physics, a new finite element method, which has the high computation accuracy, fast computation speed and less computer storage requirements, is presented in this paper. The new method with a high-order finite element without internal nodes is introduced to compute and analyze some complex electromagnetic fields in the electron accelerators. In this paper, the complex electromagnetic field in an electromagnetic device has been calculated successfully by the finite elements, and the electromagnetic properties of the electromagnetic device under the specific work condition is analyzed and evaluated. Good agreement is found between the computed values and the experimental values. [ABSTRACT FROM AUTHOR]

In this paper, a solution-adaptive finite difference method is presented for the simulation of flow past a pair of side-by-side circular cylinders. The method consists of an adaptive 5-point stencil algorithm, a central-difference spatial discretization and an immersed boundary representation of complex geometry. Numerical results indicate that the method is capable of solving the flow problems with complex geometry in a multilevel manner. [ABSTRACT FROM AUTHOR]

The shock wave is reflected when it meets the boundary, and the boundary suffers an impulsive force simultaneously. The interaction between shock wave and boundary surface is related with their shapes. Many researches focused on the problems that a planar or a spherical shock wave is reflected by plate surface in the past. Recently, some researchers indicated that the interaction effect of spherical shock wave with a parabolic surface may be used for propulsion technique. But detailed work was not reported. In this paper, by using the numerical method, we study the interaction effect between a spherical shock wave and the parabolic surface. The propagation of reflected shock wave and the impulsive force that the parabolic surface sustains are computed. [ABSTRACT FROM AUTHOR]

In this paper we apply the unified coordinate system developed by Hui and his co-workers to the steady compressible flow computation in such a way that the grid is generated physically and automatically. At the beginning of computation one only needs to build a narrow layer of grids near the left boundary. It is demonstrated that by continuously injecting layers of grid in the inflow boundary, the grid will gradually fill up the entire flow domain. [ABSTRACT FROM AUTHOR]

In this paper, a Newton-Multigrid method is presented to solve the numerical simulation of the slider air bearing. For each fixed attitude in the specified grid, the Newton method is used to achieve the pressure distribution of the slider by solving the generalized Reynolds equations discretized by the least square finite difference (LSFD) method. Between the different sizes of grids, full approximation multigrid method is used to accelerate the convergence rate by eliminating the dominating low frequency error mode in the late stages of convergence. From the case study of the slider air bearing, it shows that the Newton-Multigrid method is accurate and efficient for the numerical simulation problem. [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]

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]

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]

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]

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 study, the coupling and the relative sensitivity characteristics of a Dual-Core photonic crystal fiber (DC-PCF)-based liquid sensor are evaluated by employing the full-vectorial finite element method (FV-FEM). The simulation results demonstrate that coupling length of the proposed sensor varies between 2 mm and 0.2 mm length at wide wavelength range (800–1600 nm) for low index analytes (1.33–1.36). Besides, birefringence of order ≈ 1 0 − 4 is reported. It is found that analyte with 1.36 index reaches higher sensitivity levels. On the other hand, the coupling length of the proposed sensor can be optimized with the ellipticity ratio of the central core hole. Bending analysis on coupling length and optical power fluctuations is also reported. It is found that the power flow in one core is increasing almost 90% towards the bending direction. The proposed structure with simple design parameters has a great potential in various biomedical applications including DNA detection and can also be employed as fiber-based refractometer in various sensing applications. [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]

The emission spectrum of a single atom inside an optomechanical cavity is studied in this paper. Our model consists of a single two-level atom coupled to a cavity with a moving end mirror. We numerically calculate the emission spectrum of the atom, taking the effect of the moving mirror into account. The dependence of the spectrum peak on the coupling between the moving mirror and the cavity field is analyzed. For weak cavity-mirror couplings, we expand the spectrum up to the first order of the coupling constant. [ABSTRACT FROM AUTHOR]

In this paper, we present numerical calculations based on the full potential augmented plane wave (FP-LAPW) method within the local density approximation (LDA) to study the optical properties of the ternary alloy AlxGa1-xN. The shape of the dielectric function, the refractive index, and the absorption coefficient versus photon energy were presented. From the results, we deduce the possibility of this alloy to be used in the optoelectronic and photovololtaic area. [ABSTRACT FROM AUTHOR]

In this paper, the effective capacitance between the origin (0, 0, 0) and any other lattice site (l1, l2, l3), in an infinite simple cubic (SC) network consisting of identical capacitors each of capacitance C, has been expressed rationally in terms of the known value go and π. The asymptotic behavior is also investigated, and some numerical values for the effective capacitance are presented. [ABSTRACT FROM AUTHOR]

In this paper, we studied the electromagnetic wave scattered by a time reversal symmetry broken topological insulator circular cylinder. According to the constitutive relations of topological insulator and Maxwell's equation, we derived the scattered electromagnetic fields and scattered coefficients. Numerical results show that the scattered width of the time reversal symmetry topological insulator circular cylinder is extraordinarily different from the width produced by the time reversal symmetry broken topological insulator. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the transport properties of /-based topological insulator quantum dots (TIQDs) under magnetic field. Both disk and square shaped TIQDs are considered and the magneto-conductance are calculated numerically for various magnetic field strength. The magnetic field lifts the spin degeneracy, leading to spin polarized current at given Fermi energy. Meanwhile, the magneto-conductance demonstrates the Aharonov-Bohm (AB) oscillation with a period of one flux quantum . Numerical results for AB oscillation features indicate the mismatch between electron (e) and hole (h) doping conditions, which can be attributed to the e-h asymmetry in the full band Hamiltonian. Further, interference effect emerges around bulk and edge energy degenerate points, subsequently suppressing the magneto-conductance in both shaped systems. All these physical characteristics are qualitatively consistent for disk and square shaped TIQDs due to the topological nature of edge modes. [ABSTRACT FROM AUTHOR]

In this paper, we prove that an H theorem exists for the discrete velocity direction model and provide a set of sufficient conditions, in which the speed distribution functions can be both at equilibrium state and at nonequilibrium state in all flow regimes. To enhance the numerical stability, we simplify the governing equations of the discrete velocity direction model by these sufficient conditions and apply these sufficient conditions to boundary conditions and initial conditions. [ABSTRACT FROM AUTHOR]

MOS-like transistors are one of the transistor topologies based on the carbon nanotubes. Some modified structures have been proposed to improve their electrical characteristics, such as band to band tunneling (BTBT) and switching behavior. Unfortunately, most of them increase the transistor length due to the use of additional regions. In this paper, we propose a structure that improves the OFF state and switching behavior of the transistor without increase in the transistor length. The proposed structure is constructed by a modification of the conventional structure in a way that its drain high-doped extension part is replaced by a lightly linear doped region. Then, the proposed structure has a Schottky contact at the drain side. With a nonequilibrium Green's function (NEGF) formalism, we have studied the characteristics of the proposed device and compared them with those obtained by a conventional structure with the same channel length. The results show that the proposed structure enjoys from better switching characteristics and OFF-state behavior, especially at low currents, in comparison to the main structure and, as a result, can be a good candidate for the low-power applications. [ABSTRACT FROM AUTHOR]

In the paper, the thermodynamic parameters of the superconducting state for Calcium under the pressure at 120 GPa have been determined. The numerical analysis has been made in the framework of the Eliashberg approach. In particular, the free energy difference between the superconducting and normal state has been calculated. On the basis of the obtained results, the specific heat for the superconducting (CS) and normal (CN) state, as well as the thermodynamic critical field (HC) have been determined. It has been shown that the characteristic values of the considered thermodynamic functions do not obey the BCS universal laws: ΔC(TC)/CN(TC) = 2.48 and $T_{C}C^{N}(T_{C})/H^{2}_{C}(0) = 0.154$. [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 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]

A Monte Carlo simulation program was developed to calculate the variations of the channeled to random electronic stopping powers of He+ in an energy 4 MeV in silicon single crystal along the major 〈100〉, 〈110〉 and 〈111〉 axes. This paper discusses both simulation and experimental results that shed light on the contribution of these factors. Results obtained by our simulation are in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we study the coexistence of the vortex and the FF state by using the generalized Ginzburg-Landau (GL) functional with the applied magnetic field, and obtain the numeric solutions. Furthermore, we investigate the topological structure of the vortex and find that the property of vortices relies heavily on the modulation q along z-axis. There is no topological vortex when q < qp, and the value $q=\sqrt{\frac{\beta}{-2\delta}}$ is more favorable for the topological vortex. Moreover the magnetic field at the core of the vortex is obtained for the topological vortex. [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]

The sub-cell-fix (SCF) method proposed by Russo and Smereka3 computes the distance function of the cells adjacent to the zero level-set without disturbing the original zero level-set. A modified sub-cell-fix scheme independent of local curvature is developed in this paper, which makes use of a combination of the points adjacent to zero level-set surfaces and preserves the interface in a second-order accuracy. The new sub-cell-fix scheme is capable of handling large local curvature, and as a result it demonstrates satisfactory performance on several challenging test cases. The limitations of the modified scheme on stretched grids are tested and it is found that the highly stretched grid causes large numerical errors, and needs further assessment and modification. [ABSTRACT FROM AUTHOR]

In this paper, we present a coupled fluid flow and geomechanics model for simulating coalbed methane recovery. In the model, the fluid flow process is simulated with a triple porosity/dual permeability representation, and the coupling effects of effective stress and matrix swelling/shrinkage approach are simulated with a coupled fluid flow, geomechanics and gas adsorption/desorption model. The mathematical model is implemented with a fully implicit finite volume method and simulation is conducted to evaluate the effect of coupled fluid flow, geomechanics, and gas adsorption/desorption. [ABSTRACT FROM AUTHOR]