Abstract: In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain in time and fourth-order in space. We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space. Based on the - approximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Applications using two model problems demonstrate the theoretical results. PubDate: Wed, 21 Aug 2019 13:05:11 +000

Abstract: Using a resonance nonlinear Schrödinger equation as a bridge, we explore a direct connection of cold plasma physics to two-dimensional black holes. Namely, we compute and diagonalize a metric attached to the propagation of magnetoacoustic waves in a cold plasma subject to a transverse magnetic field, and we construct an explicit change of variables by which this metric is transformed exactly to a Jackiw-Teitelboim black hole metric. PubDate: Mon, 19 Aug 2019 08:05:13 +000

Abstract: In this paper, a prey-predator model and weak Allee effect in prey growth and its dynamical behaviors are studied in detail. The existence, boundedness, and stability of the equilibria of the model are qualitatively discussed. Bifurcation analysis is also taken into account. After incorporating the searching delay and digestion delay, we establish a delayed predator-prey system with Allee effect. The results show that there exist stability switches and Hopf bifurcation occurs while the delay crosses a set of critical values. Finally, we present some numerical simulations to illustrate our theoretical analysis. PubDate: Tue, 06 Aug 2019 10:05:17 +000

Abstract: The Davey-Stewartson Equation (DSE) is an equation system that reflects the evolution in finite depth of soft nonlinear packets of water waves that move in one direction but in which the waves’ amplitude is modulated in spatial directions. This paper uses the Generalized Elliptic Equation Rational Expansion (GEERE) technique to extract fresh exact solutions for the DSE. As a consequence, solutions with parameters of trigonometric, hyperbolic, and rational function are achieved. To display the physical characteristics of this model, the solutions obtained are graphically displayed. Modulation instability assessment of the outcomes acquired is also discussed and it demonstrates that all the solutions built are accurate and stable. PubDate: Tue, 06 Aug 2019 10:05:13 +000

Abstract: The principal pivoting algorithm is a popular direct algorithm in solving the linear complementarity problem, and its block forms had also been studied by many authors. In this paper, relying on the characteristic of block principal pivotal transformations, a block principal pivoting algorithm is proposed for solving the linear complementarity problem with an -matrix. By this algorithm, the linear complementarity problem can be solved in some block principal pivotal transformations. Besides, both the lower-order and the higher-order experiments are presented to show the effectiveness of this algorithm. PubDate: Tue, 30 Jul 2019 10:05:11 +000

Abstract: Solving nonclassical symmetry of partial differential equations (PDEs) is a challenging problem in applications of symmetry method. In this paper, an alternative method is proposed for computing the nonclassical symmetry of PDEs. The method consists of the following three steps: firstly, a relationship between the classical and nonclassical symmetries of PDEs is established; then based on the link, we give three principles to obtain additional equations (constraints) to extend the system of the determining equations of the nonclassical symmetry. The extended system is more easily solved than the original one; thirdly, we use Wu’s method to solve the extended system. Consequently, the nonclassical symmetries are determined. Due to the fact that some constraints may produce trivial results, we name the candidate constraints as “potential” ones. The method gives a new way to determine a nonclassical symmetry. Several illustrative examples are given to show the efficiency of the presented method. PubDate: Thu, 18 Jul 2019 13:05:14 +000

Abstract: Let be a -Jordan Lie supertriple system. We first introduce the notions of generalized derivations and representations of and present some properties. Also, we study the low-dimensional cohomology and the coboundary operator of , and then we investigate the deformations and Nijenhuis operators of by choosing some suitable cohomologies. PubDate: Thu, 11 Jul 2019 09:05:15 +000

Abstract: In this paper, we present a corresponding fractional order three-dimensional autonomous chaotic system based on a new class of integer order chaotic systems. We found that the fractional order chaotic system belongs to the generalized Lorenz system family by analyzing its linear term and topological structure. We also found that the equilibrium point generated by the fractional order system belongs to the unstable saddle point through the prediction correction method and the fractional order stability theory. The complexity of fractional order chaotic system is given by spectral entropy algorithm and algorithm. We concluded that the fractional order chaotic system has a higher complexity. The fractional order system can generate rich dynamic behavior phenomenon with the values of the parameters and the order changed. We applied the finite time stability theory to design the finite time synchronous controller between drive system and corresponding system. The numerical simulations demonstrate that the controller provides fast and efficient method in the synchronization process. PubDate: Wed, 03 Jul 2019 08:05:08 +000

Abstract: We analyze the appearance of delta shock wave and vacuum state in the vanishing pressure limit of Riemann solutions to the non-isentropic generalized Chaplygin gas equations. As the pressure vanishes, the Riemann solution including two shock waves and possible one contact discontinuity converges to a delta shock wave solution. Both the density and the internal energy simultaneously present a Dirac delta singularity. And the Riemann solution involving two rarefaction waves and possible one contact discontinuity converges to a solution involving vacuum state of the transport equations. PubDate: Wed, 03 Jul 2019 08:05:06 +000

Abstract: In this paper, the existence of random attractors for nonautonomous stochastic reversible Selkov system with multiplicative noise has been proved through Ornstein-Uhlenbeck transformation. Furthermore, the upper semicontinuity of random attractors is discussed when the intensity of noise approaches zero. The main difficulty is to prove the asymptotic compactness for establishing the existence of tempered pullback random attractor. PubDate: Thu, 27 Jun 2019 15:05:07 +000

Abstract: Fictitious domain method (FDM) is a commonly accepted direct numerical simulation technique for moving boundary problems. Indicator function used to distinguish the solid zone and the fluid zone is an essential part concerning the whole prediction accuracy of FDM. In this work, a new indicator function through volume intersection is developed for FDM. In this method, the arbitrarily polyhedral cells across the interface between fluid and solid are located and subdivided into tetrahedrons. The fraction of the solid volume in each cell is accurately computed to achieve high precision of integration calculation in the particle domain, improving the accuracy of the whole method. The quadrature over the solid domain shows that the newly developed indicator function can provide results with high accuracy for variable integration in both stationary and moving boundary problems. Several numerical tests, including flow around a circular cylinder, a single sphere in a creeping shear flow, settlement of a circular particle in a closed container, and in-line oscillation of a circular cylinder, have been performed. The results show good accuracy and feasibility in dealing with the stationary boundary problem as well as the moving boundary problem. This method is accurate and conservative, which can be a feasible tool for studying problems with moving boundaries. PubDate: Wed, 26 Jun 2019 10:05:15 +000

Abstract: In this paper, we establish extensive form of the fractional kinetic equation involving generalized Galué type Struve function using the technique of Laplace transforms. The results are expressed in terms of Mittag-Leffler function. Further, numerical values of the results and their graphical interpretation are interpreted to study the behaviour of these solutions. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably) new results. PubDate: Tue, 04 Jun 2019 11:05:35 +000

Abstract: Based on Hirota’s bilinear structure, we evolute a new protuberance type arrangement of the (3+1)-dimensional Boiti-Boiti-Leon-Manna-Pempinelli equation, which depicts nonlinear wave spreads in incompressible fluid. New lump arrangement is built by applying the bilinear strategy and picking appropriate polynomial. Under various parameter settings, this lump arrangement has three sorts of numerous irregularity waves, blended arrangements including lump waves and solitons are additionally developed. Association practices are seen between lump soliton and soliton. Research demonstrates that soliton can somewhat swallow or release lump waves. The shape and highlights for these subsequent arrangements are portrayed by exploiting the three-dimensional plots and comparing shape plots by picking suitable parameters. The physical significance of these charts is given. PubDate: Mon, 03 Jun 2019 12:05:12 +000

Abstract: In this work, a generalization of continuous time random walk is considered, where the waiting times among the subsequent jumps are power-law correlated with kernel function . In a continuum limit, the correlated continuous time random walk converges in distribution a subordinated process. The mean square displacement of the proposed process is computed, which is of the form . The anomy exponent varies from to when and from to when . The generalized diffusion equation of the process is also derived, which has a unified form for the above two cases. PubDate: Sun, 02 Jun 2019 00:00:00 +000

Abstract: The discrete Gel’fand–Yaglom theorem was studied several years ago. In the present paper, we generalize the discrete Gel’fand–Yaglom method to obtain the determinants of mass matrices which appear in current works in particle physics, such as dimensional deconstruction and clockwork theory. Using the results, we show the expressions for vacuum energies in such various models. PubDate: Sun, 02 Jun 2019 00:00:00 +000

Abstract: This paper considers a new method based on the law of energy conservation for the study of thermo-stress-strain state of a rod of limited length with simultaneous presence of local heat fluxes, heat exchanges, and thermal insulation. The method allows determining the field of temperature distribution and the three components of deformations and stresses, as well as the magnitude of the rod elongation and the resulting axial force with an accuracy of satisfying the energy conservation laws. For specific initial data, all the sought-for ones are determined numerically with high accuracy. We found that all solutions satisfy the laws of energy conservation. PubDate: Sun, 02 Jun 2019 00:00:00 +000

Abstract: We used the complex method and the exp(-)-expansion method to find exact solutions of the (2+1)-dimensional mKdV equation. Through the maple software, we acquire some exact solutions. We have faith in that this method exhibited in this paper can be used to solve some nonlinear evolution equations in mathematical physics. Finally, we show some simulated pictures plotted by the maple software to illustrate our results. PubDate: Thu, 16 May 2019 08:05:09 +000

Abstract: In this manuscript, a computational paradigm of technique shooting is exploited for investigation of the three-dimensional Eyring-Powell fluid with activation energy over a stretching sheet with slip arising in the field of fluid dynamics. The problem is modeled and resulting nonlinear system of PDEs is transformed into nonlinear system of ODEs using well-known similarity transformations. The strength of shooting based computing approach is employed to analyze the dynamics of the system. The proposed technique is well-designed for different scenarios of the system based on three-dimensional non-Newtonian fluid with activation energy over a stretching sheet. Slip condition is also incorporated to enhance the physical and dynamical analysis of the system. The proposed results are compared with the bvp4C method for the correctness of the solver. Graphical and numerical illustrations are used to envisage the behavior of different proficient physical parameters of interest including magnetic parameter, stretching rate parameter, velocity slip parameter, Biot number on velocity, and Lewis number on temperature and concentration. PubDate: Mon, 06 May 2019 09:05:21 +000

Abstract: The motivation of this study is to construct the truncated solution of space-time fractional differential equations by the homotopy analysis method (HAM). The first space-time fractional differential equation is transformed into a space fractional differential equation or a time fractional differential equation before the HAM. Then the power series solution is constructed by the HAM. Finally, taking the illustrative examples into consideration we reach the conclusion that the HAM is applicable and powerful technique to construct the solution of space-time fractional differential equations. PubDate: Mon, 06 May 2019 09:05:19 +000

Abstract: The angular momentum content and propagation of linearly polarized Hermite-Gaussian modes are analyzed. The helicity gauge invariant continuity equation reveals that the helicity and flow in the direction of propagation are zero. However, the helicity flow exhibits nonvanishing transverse components. These components have been recently described as photonic wheels. These intrinsic angular momentum terms, depending on the criterion, can be associated with spin or orbital momentum. The electric and magnetic contributions to the optical helicity will be shown to cancel out for Hermite-Gaussian modes. The helicity here derived is consistent with the interpretation that it represents the projection of the angular momentum onto the direction of motion. PubDate: Sun, 05 May 2019 12:05:08 +000

Abstract: In this study, we introduce a new modification of fractional reduced differential transform method (m-FRDTM) to find exact and approximate solutions for nonhomogeneous linear multiterm time-fractional diffusion equations (MT-TFDEs) of constant coefficients in a bounded domain with suitable initial conditions. Different applications in two and three fractional order terms are given to illustrate our new modification. The approximate solutions are given in the form of series solutions. The results show that the m-FRDTM for MT-TFDEs is a powerful method and can be generalized to other types of multiterm time-fractional equations. PubDate: Thu, 02 May 2019 00:08:53 +000

Abstract: Multiple-pole soliton solutions to a semidiscrete modified Korteweg-de Vries equation are derived by virtue of the Riemann-Hilbert problem with higher-order zeros. A different symmetry condition is introduced to build the nonregular Riemann-Hilbert problem. The simplest multiple-pole soliton solution is presented. The dynamics of the solitons are studied. PubDate: Thu, 02 May 2019 00:00:00 +000

Abstract: By requiring and substituting into the -family equation and Novikov equation, we can obtain Alice-Bob peakon systems, where and are the arbitrary shifted parity transformation and delayed time reversal transformation, respectively. The nonlocal integrable Camassa-Holm equation and Degasperis-Procesi equation can be derived from the Alice-Bob -family equations by choosing different parameters. Some new types of interesting solutions are solved including explicit one-peakons, two-peakons, and -peakons solutions. PubDate: Thu, 02 May 2019 00:00:00 +000

Abstract: The Sawada-Kotera equation with a nonvanishing boundary condition, which models the evolution of steeper waves of shorter wavelength than those depicted by the Korteweg de Vries equation, is analyzed and also the perturbed Korteweg de Vries (pKdV) equation. For this goal, a capable method known as the multiple exp-function scheme (MEFS) is formally utilized to derive the multiple soliton solutions of the models. The MEFS as a generalization of Hirota’s perturbation method actually suggests a systematic technique to handle nonlinear evolution equations (NLEEs). PubDate: Thu, 02 May 2019 00:00:00 +000

Abstract: We prove that the moduli space of the pseudo holomorphic curves in the A-model on a symplectic torus is homeomorphic to a moduli space of Feynman diagrams in the configuration space of the morphisms in the B-model on the corresponding elliptic curve. These moduli spaces determine the structure of the both models. PubDate: Tue, 30 Apr 2019 10:05:26 +000

Abstract: It is shown that the application of theorems of induced representations method, namely, Frobenius reciprocity theorem, transitivity of induction theorem, and Mackey theorem on symmetrized squares, makes simplifying standard techniques in the theory of electron structure and constructing Cooper pair wavefunctions on the basis of one-electron solid-state wavefunctions possible. It is proved that the nodal structure of topological superconductors in the case of multidimensional irreducible representations is defined by additional quantum numbers. The technique is extended on projective representations in the case of nonsymmorphic space groups and examples of applications for topological superconductors UPt3 and Sr2RuO4 are considered. PubDate: Tue, 09 Apr 2019 13:05:12 +000

Abstract: In order to meet the filtration separation of hazardous materials on hazardous materials collection truck, the most popular separation devices, such as the cyclone separator and the filter cartridge, are combined to form a new filtration device in this study. The advantages of the two devices are utilized to achieve effective separation of solid particles and prevent secondary pollution. Among the various structural influence factors of filtration equipment, four structural parameters that affect the separation performance significantly are selected as optimization variables. The response surface methodology was used to design the simulation experiment. Using fluid mechanics analysis software, multiple sets of parameters were simulated. Then, the simulation data was used to establish a mathematical model of separation efficiency, and structural optimization analysis was performed based on the mathematical model. Finally, the results show that the inner exhaust pipe diameter and the cone height have more influence on the efficiency of the cyclone separation structure. The interaction between the diameter and insertion depth of the inner exhaust pipe is also obvious. Among the four optimization variables, there is an optimum value for the inner exhaust pipe insertion depth, and the effect of the other three factors on the separation efficiency is monotonic. In the case of a total separation efficiency of 99.9% and after optimizing the combined model within a reasonable interval, 81.25% of the 1-μm particles can be removed by the cyclone separation part, and only 18.75% are removed by the filter cartridge. PubDate: Mon, 08 Apr 2019 12:05:04 +000

Abstract: In this paper, we investigate the existence of infinitely many solutions to a fractional -Kirchhoff-type problem satisfying superlinearity with homogeneous Dirichlet boundary conditions as follows: where is a nonlocal integrodifferential operator with a singular kernel . We only consider the non-Ambrosetti-Rabinowitz condition to prove our results by using the symmetric mountain pass theorem. PubDate: Sun, 07 Apr 2019 08:05:16 +000

Abstract: The problem of a massive taut string, traveled by a heavy point mass, moving with an assigned law, is formulated in a linear context. Displacements are assumed to be transverse, and the dynamic tension is neglected. The equations governing the moving boundary problem are derived via a variational principle, in which the geometric compatibility between the point mass and the string is enforced via a Lagrange multiplier, having the meaning of transverse reactive force. The equations are rearranged in the form of a unique Volterra integral equation in the reactive force, which is solved numerically. A classical Galerkin solution is implemented for comparison. Numerical results throw light on the physics of the phenomenon and confirm the effectiveness of the algorithm. PubDate: Sun, 07 Apr 2019 07:05:25 +000

Abstract: The -expansion method is improved by presenting a new auxiliary ordinary differential equation for . By using this method, new exact traveling wave solutions of two important nonlinear evolution equations, i.e., the ill-posed Boussinesq equation and the unstable nonlinear Schrödinger equation, are constructed. The obtained solutions contain Jacobi elliptic function solutions which can be degenerated to the hyperbolic function solutions and the trigonometric function solutions. The present method is very concise and effective and can be applied to other types of nonlinear evolution equations. PubDate: Thu, 04 Apr 2019 09:05:15 +000