Abstract: The Laplace-Adomian Decomposition Method (LADM) and Homotopy Perturbation Method (HPM) are both utilized in this research in order to obtain an approximate analytical solution to the nonlinear Schrödinger equation with harmonic oscillator. Accordingly, nonlinear Schrödinger equation in both one and two dimensions is provided to illustrate the effects of harmonic oscillator on the behavior of the wave function. The available literature does not provide an exact solution to the problem presented in this paper. Nevertheless, approximate analytical solutions are provided in this paper using LADM and HPM methods, in addition to comparing and analyzing both solutions. PubDate: Wed, 05 Dec 2018 06:09:18 +000

Abstract: A flat Friedmann-Robertson-Walker (FRW) multiscalar field cosmology is studied with a particular potential of the form , which emerges as a relation between the time derivatives of the scalars field momenta. Classically, by employing the Hamiltonian formalism of two scalar fields with standard kinetic energy, exact solutions are found for the Einstein-Klein-Gordon (EKG) system for different scenarios specified by the parameter , as well as the e-folding function which is also computed. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solved by applying an appropriate change of variables. PubDate: Tue, 04 Dec 2018 07:20:25 +000

Abstract: The conditions for the occurrence of the so-called macroscopic irreversibility property and the related phenomenon of decay to kinetic equilibrium which may characterize the 1-body probability density function (PDF) associated with hard-sphere systems are investigated. The problem is set in the framework of the axiomatic “ab initio” theory of classical statistical mechanics developed recently and the related establishment of an exact kinetic equation realized by the Master equation for the same kinetic PDF. As shown in the paper the task involves the introduction of a suitable functional of the 1-body PDF, identified here with the Master kinetic information. It is then proved that, provided the same PDF is prescribed in terms of suitably smooth, i.e., stochastic, solution of the Master kinetic equation, the two properties indicated above are indeed realized. PubDate: Sun, 02 Dec 2018 00:00:00 +000

Abstract: We have constructed a new sequence of positive linear operators with two variables by using Szasz-Kantorovich-Chlodowsky operators and Brenke polynomials. We give some inequalities for the operators by means of partial and full modulus of continuity and obtain a Lipschitz type theorem. Furthermore, we study the convergence of Szasz-Kantorovich-Chlodowsky-Brenke operators in weighted space of function with two variables and estimate the rate of approximation in terms of the weighted modulus of continuity. PubDate: Sun, 02 Dec 2018 00:00:00 +000

Abstract: We obtain exact expressions for the first three moments of the heat conductance of a quantum chain that crosses over from a superconducting quantum dot to a superconducting disordered quantum wire. Our analytic solution provides exact detailed descriptions of all crossovers that can be observed in the system as a function of its length, which include ballistic-metallic and metallic-insulating crossovers. The two Bogoliubov-de Gennes (BdG) symmetry classes with time-reversal symmetry are accounted for. The striking effect of total suppression of the insulating regime in systems with broken spin-rotation invariance is observed at large length scales. For a single channel system, this anomalous effect can be interpreted as a signature of the presence of the elusive Majorana fermion in a condensed matter system. PubDate: Sun, 02 Dec 2018 00:00:00 +000

Abstract: In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota-Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra. In the end, we give all Rota-Baxter operators of weight and on solvable and nilpotent Leibniz algebras of dimension 3, respectively. PubDate: Sun, 02 Dec 2018 00:00:00 +000

Abstract: In this paper, we investigate the existence and uniqueness of solutions for a boundary value problem for second-order quantum -difference equations with separated boundary conditions, by using classical fixed point theorems. Examples illustrating the main results are also presented. PubDate: Sun, 02 Dec 2018 00:00:00 +000

Abstract: This paper investigates the problem of identifying unknown coefficient of time dependent in heat conduction equation by new iteration method. In order to use new iteration method, we should convert the parabolic heat conductive equation into an integral equation by integral calculus and initial condition. This method constructs a convergent sequence of function, which approximates the exact solution with a few iterations and does not need complex calculation. Illustrative examples are given to demonstrate the efficiency and validity. PubDate: Wed, 14 Nov 2018 00:00:00 +000

Abstract: In this paper, we study the noise-induced truth seeking for heterogeneous Hegselmann-Krause (HK) model in opinion dynamics. It has been proved that small noise could induce the group to achieve truth in homogeneous HK model; however, for the more practical heterogeneous HK model, the theoretical conclusion is absent. Here, we prove that small noise could also induce the group to achieve truth in heterogenous HK model, and, moreover, we first theoretically prove that large noise could drive some agents to deviate from the truth. These theoretical findings evidently reveal how the free information flow spreading in the media determines the social truth seeking. PubDate: Sun, 11 Nov 2018 09:10:23 +000

Abstract: We consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank (namely, ,,, and ) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically symmetric gravitational configuration in dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions () of squared radial coordinate obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers for Lie algebras ,,, and , respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued matrix connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in case) the matrix representing a generator of the -group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances. We also calculate 2-form flux integrals over -dimensional discs and corresponding Wilson loop factors over their boundaries. PubDate: Wed, 07 Nov 2018 00:00:00 +000

Abstract: The original Bessel differential equation that describes, among many others, cylindrical acoustic or vortical waves, is a particular case of zero degree of the generalized Bessel differential equation that describes coupled acoustic-vortical waves. The solutions of the generalized Bessel differential equation are obtained for all possible combinations of the two complex parameters, order and degree, and finite complex variable, as Frobenius-Fuchs series around the regular singularity at the origin; the series converge in the whole complex plane of the variable, except for the point-at-infinity, that is, the only other singularity of the differential equation. The regular integral solutions of the first and second kinds lead, respectively, to the generalized Bessel and Neumann functions; these reduce to the original Bessel and Neumann functions for zero degree and have alternative expressions for nonzero degree. PubDate: Sun, 04 Nov 2018 00:00:00 +000

Abstract: In this paper, we consider the regularity problem of the solutions to the axisymmetric, inviscid, and incompressible Hall-magnetohydrodynamics (Hall-MHD) equations. First, we obtain the local-in-time existence of sufficiently regular solutions to the axisymmetric inviscid Hall-MHD equations without resistivity. Second, we consider the inviscid axisymmetric Hall equations without fluids and prove that there exists a finite time blow-up of a classical solution due to the Hall term. Finally, we obtain some blow-up criteria for the axisymmetric resistive and inviscid Hall-MHD equations. PubDate: Thu, 01 Nov 2018 00:00:00 +000

Abstract: This article addresses the inherent heat irreversibility in the flow of a couple stress thin film along a moving vertical belt subjected to free and adiabatic surface. Mathematical analysis for the fluid-governing-equations is performed in detail. For maximum thermal performance and efficiency, the present analysis follows the second law of thermodynamics approach for the evaluation of entropy generation rate in the moving film. With this thermodynamic process, the interconnectivity between variables responsible for energy wastage is accounted for in the thermo-fluid equipment. Results of the analysis revealed the fluid properties that contribute more to energy loss and how the exergy of the system can be restored. PubDate: Thu, 01 Nov 2018 00:00:00 +000

Abstract: Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar purposes in computer science and biology. As noted by Doi and others, techniques from quantum physics, such as second quantization, can be adapted to apply to such systems. Here we use these techniques to study how the “master equation” describing stochastic time evolution for a reaction network is related to the “rate equation” describing the deterministic evolution of the expected number of particles of each species in the large-number limit. We show that the relation is especially strong when a solution of master equation is a “coherent state”, meaning that the numbers of entities of each kind are described by independent Poisson distributions. Remarkably, in this case the rate equation and master equation give the exact same formula for the time derivative of the expected number of particles of each species. PubDate: Thu, 01 Nov 2018 00:00:00 +000

Abstract: This paper is devoted to the study of lump solutions to the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation. First we use a direct method to construct a class of exact solutions which contain six arbitrary real constants. Then we use these solutions to generate lump solutions with four real parameters. We also determine the amplitude and velocity of these lumps. PubDate: Thu, 01 Nov 2018 00:00:00 +000

Abstract: We investigate the existence of multivortex states in a superconducting mesoscopic sphere with a magnetic dipole placed at the center. We obtain analytic solutions for the order parameter inside the sphere through the linearized Ginzburg-Landau (GL) model, coupled with mixed boundary conditions, and under regularity conditions and decoupling coordinates approximation. The solutions of the linear GL equation are obtained in terms of Heun double confluent functions, in dipole coordinates symmetry. The analyticity of the solutions and the associated eigenproblem are discussed thoroughly. We minimize the free energy for the fully nonlinear GL system by using linear combinations of linear analytic solutions, and we provide the conditions of occurring multivortex states. The results are not restricted to the particular spherical geometry, since the present formalism can be extended for large samples, up to infinite superconducting space plus magnetic dipole. PubDate: Thu, 01 Nov 2018 00:00:00 +000

Abstract: We construct algebras for general “initial data” given by a vector space equipped with an antisymmetric bracket not necessarily satisfying the Jacobi identity. We prove that any such bracket can be extended to a 2-term algebra on a graded vector space of twice the dimension, with the 3-bracket being related to the Jacobiator. While these algebras always exist, they generally do not realize a nontrivial symmetry in a field theory. In order to define algebras with genuine field theory realizations, we prove the significantly more general theorem that if the Jacobiator takes values in the image of any linear map that defines an ideal there is a 3-term algebra with a generally nontrivial 4-bracket. We discuss special cases such as the commutator algebra of octonions, its contraction to the “R-flux algebra,” and the Courant algebroid. PubDate: Thu, 01 Nov 2018 00:00:00 +000

Abstract: In this paper, the controllability issue of complex network is discussed. A new quantitative index using knowledge of control centrality and condition number is constructed to measure the controllability of given networks. For complex networks with different controllable subspace dimensions, their controllability is mainly determined by the control centrality factor. For the complex networks that have the equal controllable subspace dimension, their different controllability is mostly determined by the condition number of subnetworks’ controllability matrix. Then the effect of this index is analyzed based on simulations on various types of network topologies, such as ER random network, WS small-world network, and BA scale-free network. The results show that the presented index could reflect the holistic controllability of complex networks. Such an endeavour could help us better understand the relationship between controllability and network topology. PubDate: Mon, 22 Oct 2018 00:00:00 +000

Abstract: We give a purely combinatorial proof of the Glaisher-Crofton identity which is derived from the analysis of discrete structures generated by the iterated action of the second derivative. The argument illustrates the utility of symbolic and generating function methodology of modern enumerative combinatorics. The paper is meant for nonspecialists as a gentle introduction to the field of graphical calculus and its applications in computational problems. PubDate: Mon, 22 Oct 2018 00:00:00 +000

Abstract: Vibration dynamics of elastic beams that are used in nanotechnology, such as atomic force microscope modeling and carbon nanotubes, are considered in terms of a fundamental response within a matrix framework. The modeling equations with piezoelectric and surface scale effects are written as a matrix differential equation subject to tip-sample general boundary conditions and to compatibility conditions for the case of multispan beams. We considered a quadratic and a cubic eigenvalue problem related to the inclusion of smart materials and surface effects. Simulations were performed for a two stepped beam with a piezoelectric patch subject to pulse forcing terms. Results with Timoshenko models that include surface effects are presented for micro- and nanoscale. It was observed that the effects are significant just in nanoscale. We also simulate the frequency effects of a double-span beam in which one segment includes rotatory inertia and shear deformation and the other one neglects both phenomena. The proposed analytical methodology can be useful in the design of micro- and nanoresonator structures that involve deformable flexural models for detecting and imaging of physical and biochemical quantities. PubDate: Thu, 18 Oct 2018 09:32:27 +000

Abstract: When two Newtonian liquid droplets are brought into contact on a solid substrate, a highly curved meniscus neck is established between the two which transforms the bihemispherically shaped fluid domain to a hemispherically shaped domain. The rate at which such topological transformation, called coalescence phenomenon, evolves results from a competition between the inertial force which resists the transformation, the interfacial force which promotes the rate, and the viscous force which arrests it. Depending on the behaviour of these forces, different scaling laws describing the neck growth can be observed, predicted theoretically, and proved numerically. The twofold objective of the present contribution is to propose a simple theoretical framework which leads to an Ordinary Differential Equation, the solution of which predicts the different scaling laws in various limits, and to validate these theoretical predictions numerically by modelling the phenomenon in the commercial Finite Element software COMSOL Multiphysics. PubDate: Thu, 18 Oct 2018 08:35:23 +000

Abstract: The harmonic vibration characteristics of a deeply buried spherical methane tank in viscoelastic soil subjected to cyclic loading in the frequency domain are investigated. The dynamic behavior of the soil is described based on the theory of fractional derivatives. By introducing potential functions, the closed-form expressions for the displacement and the stress of the viscoelastic soil surrounding the deeply buried spherical methane tank are obtained. Two die structures are considered: a homogeneous elastic medium and a shell structure. Based on the theory of elastic motion and the Flügge theory, analytic solutions for the dynamic responses of the spherical methane tank in a fractional-derivative viscoelastic soil are derived explicitly. Analytic solution expressions of the undetermined coefficients are determined by using the continuum boundary conditions. The system dynamic responses to the homogeneous elastic medium and the shell structure and the influences of the parameters of the fractional derivative, soil, and die on the dynamic characteristic of the system are compared and analyzed. The results indicate a significant difference between the dynamic responses of the die structures for the two models. PubDate: Thu, 18 Oct 2018 00:00:00 +000

Abstract: The spectral properties of two special classes of Jacobi operators are studied. For the first class represented by the -dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new polynomial identity relating the eigenvalues of such matrices with their matrix entries is obtained. In the limit this identity induces some requirements, which should satisfy the scattering data of the resulting infinite-dimensional Jacobi operator in the half-line, of which super- and subdiagonal matrix elements are equal to . We obtain such requirements in the simplest case of the discrete Schrödinger operator acting in , which does not have bound and semibound states and whose potential has a compact support. PubDate: Tue, 16 Oct 2018 08:15:49 +000

Abstract: In this article, we investigate an integrable weakly coupled nonlocal nonlinear Schrödinger (WCNNLS) equation including its Lax pair. Afterwards, Darboux transformation (DT) of the weakly coupled nonlocal NLS equation is constructed, and then the degenerated Darboux transformation can be got from Darboux transformation. Applying the degenerated Darboux transformation, the new solutions (,) and self-potential function are created from the known solutions (,). The (,) satisfy the parity-time (PT) symmetry condition, and they are rational solutions with two free phase parameters of the weakly coupled nonlocal nonlinear Schrödinger equation. From the plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution are produced. PubDate: Sun, 14 Oct 2018 00:00:00 +000

Abstract: A new theoretical approach has been established to define transport coefficients of charge and mass transport in porous materials directly from impedance data; thus four transport coefficients could be determined. In case of ammonia adsorption on sulfated zirconia, the diffusion coefficient was figured out to be approximately the mobility diffusion coefficient of ammonium ions: 1.2 x 10-7 cm2/s. The transport of carbon dioxide was examined for samples of zeolite type 5A in different hydration states. By impedance spectroscopy measurements, the diffusion coefficient of water vapor at 373 K is estimated to be about 7 x 10-6 cm2/s. The influence of carbon dioxide adsorption on diffusion coefficients is studied based on two pellet types of zeolite 5A. The difference between polar and non-polar gas adsorption in porous solids is considered as changed characteristic of impedance. PubDate: Thu, 04 Oct 2018 06:37:48 +000

Abstract: In the present study a particular case of Gross-Pitaevskii or nonlinear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case. PubDate: Mon, 01 Oct 2018 00:00:00 +000

Abstract: The presence and propagation of dust-acoustic solitary waves in dusty plasma contains four components such as negative and positive dust species beside ions and electrons are studied. Both the ions and electrons distributions are represented applying nonextensive formula. Employing the reductive perturbation method, an evolution equation is derived to describe the small-amplitude dust-acoustic solitons in the considered plasma system. The used reductive perturbation stretches lead to the nonlinear KdV and modified KdV equations with nonlinear and dispersion coefficients that depend on the parameters of the plasma. This study represents that the presence of compressive or/and rarefactive solitary waves depends mainly on the value of the first-order nonlinear coefficient. The structure of envelope wave is undefined for first-order nonlinear coefficient tends to vanish. The coexistence of the two types of solitary waves appears by increasing the strength of nonlinearity to the second order using the modified KdV equation. PubDate: Thu, 27 Sep 2018 07:41:22 +000

Abstract: We introduce the generalized q-deformed Sinh-Gordon equation and derive analytical soliton solutions for some sets of parameters. This new defined equation could be useful for modeling physical systems with violated symmetries. PubDate: Tue, 25 Sep 2018 10:26:54 +000

Abstract: The nonlinear phenomena which associate with magnetoacoustic waves in a plasma are analytically studied. A plasma is an open system with external inflow of energy and radiation losses. A plasma’s flow may be isentropically stable or unstable. The nonlinear phenomena occur differently in dependence on stability or instability of a plasma’s flow. The nonlinear instantaneous equation which describes dynamics of nonwave entropy mode in the field of intense magnetoacoustic perturbations is the result of special projecting of the conservation equations in the differential form. It is analyzed in some physically meaningful cases; those are periodic magnetoacoustic perturbations and particular cases of heating-cooling function. A plasma is situated in the straight magnetic field with constant equilibrium magnetic strength which form constant angle with the direction of wave propagation. A plasma is initially uniform and equilibrium. The conclusions concern nonlinear effects of fast and slow magnetoacoustic perturbations and may be useful in direct and inverse problems. PubDate: Mon, 24 Sep 2018 00:00:00 +000