Application of a Chimera Full Potential Algorithm for Solving Aerodynamic Problems

Science.gov (United States)

Holst, Terry L.; Kwak, Dochan (Technical Monitor)

1997-01-01

A numerical scheme utilizing a chimera zonal grid approach for solving the three dimensional full potential equation is described. Special emphasis is placed on describing the spatial differencing algorithm around the chimera interface. Results from two spatial discretization variations are presented; one using a hybrid first-order/second-order-accurate scheme and the second using a fully second-order-accurate scheme. The presentation is highlighted with a number of transonic wing flow field computations.

Perturbed Coulomb Potentials in the Klein-Gordon Equation: Quasi-Exact Solution

Science.gov (United States)

Baradaran, M.; Panahi, H.

2018-05-01

Using the Lie algebraic approach, we present the quasi-exact solutions of the relativistic Klein-Gordon equation for perturbed Coulomb potentials namely the Cornell potential, the Kratzer potential and the Killingbeck potential. We calculate the general exact expressions for the energies, corresponding wave functions and the allowed values of the parameters of the potential within the representation space of sl(2) Lie algebra. In addition, we show that the considered equations can be transformed into the Heun's differential equations and then we reproduce the results using the associated special functions. Also, we study the special case of the Coulomb potential and show that in the non-relativistic limit, the solution of the Klein-Gordon equation converges to that of Schrödinger equation.

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

International Nuclear Information System (INIS)

Arum Sari, Resita; Suparmi, A; Cari, C

2016-01-01

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number n r causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function. (paper)

Asymptotic analysis of the local potential approximation to the Wetterich equation

Science.gov (United States)

Bender, Carl M.; Sarkar, Sarben

2018-06-01

This paper reports a study of the nonlinear partial differential equation that arises in the local potential approximation to the Wetterich formulation of the functional renormalization group equation. A cut-off-dependent shift of the potential in this partial differential equation is performed. This shift allows a perturbative asymptotic treatment of the differential equation for large values of the infrared cut-off. To leading order in perturbation theory the differential equation becomes a heat equation, where the sign of the diffusion constant changes as the space-time dimension D passes through 2. When D    2 one obtains a backward heat equation whose initial-value problem is ill-posed. For the special case D  =  1 the asymptotic series for cubic and quartic models is extrapolated to the small infrared-cut-off limit by using Padé techniques. The effective potential thus obtained from the partial differential equation is then used in a Schrödinger-equation setting to study the stability of the ground state. For cubic potentials it is found that this Padé procedure distinguishes between a -symmetric theory and a conventional Hermitian theory (g real). For an theory the effective potential is nonsingular and has a stable ground state but for a conventional theory the effective potential is singular. For a conventional Hermitian theory and a -symmetric theory (g  >  0) the results are similar; the effective potentials in both cases are nonsingular and possess stable ground states.

STEADY STATE AND PSEUDO-TRANSIENT ELECTRIC POTENTIAL USING THE POISSONBOLTZMANN EQUATION

Directory of Open Access Journals (Sweden)

L. C. dos Santos

2015-03-01

Full Text Available A method for analysis of the electric potential profile in saline solutions was developed for systems with one or two infinite flat plates. A modified Poisson-Boltzmann equation, taking into account nonelectrostatic interactions between ions and surfaces, was used. To solve the stated problem in the steady-state approach the finite-difference method was used. For the formulated pseudo-transient problem, we solved the set of ordinary differential equations generated from the algebraic equations of the stationary case. A case study was also carried out in relation to temperature, solution concentration, surface charge and salt-type. The results were validated by the stationary problem solution, which had also been used to verify the ionic specificity for different salts. The pseudo-transient approach allowed a better understanding of the dynamic behavior of the ion-concentration profile and other properties due to the surface charge variation.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

Science.gov (United States)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Supersymmetric approach for Killingbeck radial potential plus noncentral potential in Schrodinger equation

International Nuclear Information System (INIS)

Cari, C.; Suparmi, A.; Yunianto, M.; Pratiwi, B. N.

2016-01-01

Killingbeck radial potential, which consists of harmonic oscillator, linier and Coulomb potentials, is combined with non-central potential. The solution of three dimensional Schrodinger equation for Killingbeck potential is combined with Poschl-Teller potential and Symmetrical Top non-central potentials are investigated using supersymmetry (SUSY) operator. The non-relativistic energy is obtained which is infuenced by potentials and the wave functions are produced by using SUSY operator. (paper)

Solvable linear potentials in the Dirac equation

International Nuclear Information System (INIS)

Dominguez-Adame, F.; Gonzalez, M.A.

1990-01-01

The Dirac equation for some linear potentials leading to Schroedinger-like oscillator equations for the upper and lower components of the Dirac spinor have been solved. Energy levels for the bound states appear in pairs, so that both particles and antiparticles may be bound with the same energy. For weak coupling, the spacing between levels is proportional to the coupling constant while in the strong limit those levels are depressed compared to the nonrelativistic ones

Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code

Energy Technology Data Exchange (ETDEWEB)

Haverkort, J.W. [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090 GB Amsterdam (Netherlands); Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Blank, H.J. de [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Huysmans, G.T.A. [ITER Organization, Route de Vinon sur Verdon, 13115 Saint Paul Lez Durance (France); Pratt, J. [Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven (Netherlands); Koren, B., E-mail: b.koren@tue.nl [Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands)

2016-07-01

Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. A rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.

Analysis and classification of nonlinear dispersive evolution equations in the potential representation

International Nuclear Information System (INIS)

Eichmann, U.A.; Draayer, J.P.; Ludu, A.

2002-01-01

A potential representation for the subset of travelling solutions of nonlinear dispersive evolution equations is introduced. The procedure involves reduction of a third-order partial differential equation to a first-order ordinary differential equation. The potential representation allows us to deduce certain properties of the solutions without the actual need to solve the underlying evolution equation. In particular, the paper deals with the so-called K(n, m) equations. Starting from their respective potential representations it is shown that these equations can be classified according to a simple point transformation. As a result, e.g., all equations with linear dispersion join the same equivalence class with the Korteweg-deVries equation being its representative, and all soliton solutions of higher order nonlinear equations are thus equivalent to the KdV soliton. Certain equations with both linear and quadratic dispersions can also be treated within this equivalence class. (author)

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

Science.gov (United States)

Liu, Xianglin; Wang, Yang; Eisenbach, Markus; Stocks, G. Malcolm

2018-03-01

The Green function plays an essential role in the Korringa-Kohn-Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn-Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. By using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.

Equation of motion method in appearance potential spectra of simple metals

International Nuclear Information System (INIS)

Tay, G.

2004-01-01

Full Text. The equation of motion method is applied to function Tk 1 K 2 K 3 K 4 which describes, the propagation of two particles in the presence of the core hole. Neglecting final state interactions and assuming constant matrix elements, X-ray yield and the associated appearance potential spectrum is found to depend on the convolution of the empty density of states above the Fermi level of the metal. (author)

Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

Science.gov (United States)

Franz, Delbert D.; Melching, Charles S.

1997-01-01

The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The

A Potential Method for Body and Surface Wave Propagation in Transversely Isotropic Half- and Full-Spaces

Directory of Open Access Journals (Sweden)

Mehdi Raoofian Naeeni

2016-12-01

Full Text Available The problem of propagation of plane wave including body and surface waves propagating in a transversely isotropic half-space with a depth-wise axis of material symmetry is investigated in details. Using the advantage of representation of displacement fields in terms of two complete scalar potential functions, the coupled equations of motion are uncoupled and reduced to two independent equations for potential functions. In this paper, the secular equations for determination of body and surface wave velocities are derived in terms of both elasticity coefficients and the direction of propagation. In particular, the longitudinal, transverse and Rayleigh wave velocities are determined in explicit forms. It is also shown that in transversely isotropic materials, a Rayleigh wave may propagate in different manner from that of isotropic materials. Some numerical results for synthetic transversely isotropic materials are also illustrated to show the behavior of wave motion due to anisotropic nature of the problem.

Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

International Nuclear Information System (INIS)

Onate, C.A.; Onyeaju, M.C.; Ikot, A.N.

2016-01-01

The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.

Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

Energy Technology Data Exchange (ETDEWEB)

Onate, C.A., E-mail: oaclems14@physicist.net [Physics Department, University of Benin (Nigeria); Onyeaju, M.C.; Ikot, A.N. [Theoretical Physics Group, Physics Department, University of Port Harcourt (Nigeria)

2016-12-15

The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.

Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function

Science.gov (United States)

Durmus, Aysen

2018-03-01

The time independent Dirac equation is solved analytically for equal scalar and vector hyperbolic potential function in the presence of Greene and Aldrich approximation scheme. The bound state energy equation and spinor wave functions expressed by the hypergeometric function have been obtained in detail with asymptotic iteration approach. In order to indicate the accuracy of this different approach proposed to solve second order linear differential equations, we present that in the non-relativistic limit, analytical solutions of the Dirac equation converge to those of the Schrödinger one. We introduce numerical results of the theoretical analysis for hyperbolic potential function. Bound states corresponding to arbitrary values of n and l are reported for potential parameters covering a wide range of interaction. Also, we investigate relativistic vibrational energy spectra of alkali metal diatomic molecules in the different electronic states. It is observed that theoretical vibrational energy values are consistent with experimental Rydberg-Klein-Rees (RKR) results and vibrational energies of NaK, K_2 and KRb diatomic molecules interacting with hyperbolic potential smoothly converge to the experimental dissociation limit D_e=2508cm^{-1}, 254cm^{-1} and 4221cm^{-1}, respectively.

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schoedinger equation admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The admissible potentials come into families evolved from equations having a fixed number of elementary singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

Algebraic solution for the vector potential in the Dirac equation

Energy Technology Data Exchange (ETDEWEB)

Booth, H.S. [School of Mathematics and Physics, University of Tasmania, Hobart Tas (Australia); Centre for Mathematics and its Applications, Australian National University (Australia)]. E-mail: hbooth@wintermute.anu.edu.au; Legg, G.; Jarvis, P.D. [School of Mathematics and Physics, University of Tasmania, Hobart Tas (Australia)

2001-07-20

The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with attention to the additional constraints arising from non-maximality of the rank. The extension of the method to general spacetimes is illustrated by examples in diverse dimensions with both c- and a-number wavefunctions. (author)

Infinitely many solutions for sublinear fractional Schrodinger-type equations with general potentials

Directory of Open Access Journals (Sweden)

Gang-Ling Hou

2018-04-01

Full Text Available This article concerns the fractional Schrodinger type equations $$ (-\\Delta^\\alpha u+V(xu =f(x,u \\quad\\text{in } \\mathbb{R}^N, $$ where $N\\geq 2$, $\\alpha\\in(0,1$, $(-\\Delta^\\alpha$ stands for the fractional Laplacian, $V$ is a positive continuous potential, $f\\in C(\\mathbb{R}^N\\times\\mathbb{R},\\mathbb{R}$. We establish criteria that guarantee the existence of infinitely many solutions by using the genus properties in critical point theory.

Imaginary Time Step Method to Solve the Dirac Equation with Nonlocal Potential

International Nuclear Information System (INIS)

Zhang Ying; Liang Haozhao; Meng Jie

2009-01-01

The imaginary time step (ITS) method is applied to solve the Dirac equation with nonlocal potentials in coordinate space. Taking the nucleus 12 C as an example, even with nonlocal potentials, the direct ITS evolution for the Dirac equation still meets the disaster of the Dirac sea. However, following the recipe in our former investigation, the disaster can be avoided by the ITS evolution for the corresponding Schroedinger-like equation without localization, which gives the convergent results exactly the same with those obtained iteratively by the shooting method with localized effective potentials.

The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials

International Nuclear Information System (INIS)

Contreras-Astorga, Alonso; Schulze-Halberg, Axel

2014-01-01

We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, “Intertwining technique for the one-dimensional stationary Dirac equation,” Ann. Phys. 305, 151–189 (2003)

The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials

Energy Technology Data Exchange (ETDEWEB)

Contreras-Astorga, Alonso, E-mail: aloncont@iun.edu; Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

2014-10-15

We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, “Intertwining technique for the one-dimensional stationary Dirac equation,” Ann. Phys. 305, 151–189 (2003)].

Full information estimations of a system of simultaneous equations with error component structure

OpenAIRE

Balestra, Pietro; Krishnakumar, Jaya

1987-01-01

In this paper we develop full information methods for estimating the parameters of a system of simultaneous equations with error component struc-ture and establish relationships between the various structural estimat

Some exact solutions to the potential Kadomtsev-Petviashvili equation and to a system of shallow water wave equations

International Nuclear Information System (INIS)

Inan, Ibrahim E.; Kaya, Dogan

2006-01-01

In this Letter by considering an improved tanh function method, we found some exact solutions of the potential Kadomtsev-Petviashvili equation. Some exact solutions of the system of the shallow water wave equation were also found

Solution of Schroedinger equation for particle moving in two-well potential

International Nuclear Information System (INIS)

Ivanova, O.I.; Sabirov, R.Kh.

2000-01-01

The solution of the Schroedinger equation for the particle, moving in the two-well potential is given on the basis of a single variational method. This potential constitutes the sum of the harmonic potential and the Gaussian addition. The analytical expression for the wave function of the particle basic state is obtained. The dependence of the obtained solutions on the potential barrier height and width is studied. It is shown that the better separation of the potential barrier provides for higher accuracy of the calculations. The values of the two-well potential, whereby good agreement between the calculations and exact numerical solution of the Schroedinger equation may be expected, are presented [ru

Computational Challenge of Fractional Differential Equations and the Potential Solutions: A Survey

Directory of Open Access Journals (Sweden)

Chunye Gong

2015-01-01

Full Text Available We present a survey of fractional differential equations and in particular of the computational cost for their numerical solutions from the view of computer science. The computational complexities of time fractional, space fractional, and space-time fractional equations are O(N2M, O(NM2, and O(NM(M + N compared with O(MN for the classical partial differential equations with finite difference methods, where M, N are the number of space grid points and time steps. The potential solutions for this challenge include, but are not limited to, parallel computing, memory access optimization (fractional precomputing operator, short memory principle, fast Fourier transform (FFT based solutions, alternating direction implicit method, multigrid method, and preconditioner technology. The relationships of these solutions for both space fractional derivative and time fractional derivative are discussed. The authors pointed out that the technologies of parallel computing should be regarded as a basic method to overcome this challenge, and some attention should be paid to the fractional killer applications, high performance iteration methods, high order schemes, and Monte Carlo methods. Since the computation of fractional equations with high dimension and variable order is even heavier, the researchers from the area of mathematics and computer science have opportunity to invent cornerstones in the area of fractional calculus.

Global representations of the Heat and Schrodinger equation with singular potential

Directory of Open Access Journals (Sweden)

Jose A. Franco

2013-07-01

Full Text Available The n-dimensional Schrodinger equation with a singular potential $V_lambda(x=lambda |x|^{-2}$ is studied. Its solution space is studied as a global representation of $widetilde{SL(2,mathbb{R}}imes O(n$. A special subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. The space of K-finite vectors is calculated, obtaining conditions for $lambda$ so that this space is non-empty. The direct sum of solution spaces over such admissible values of $lambda$ is studied as a representation of the (2n+1-dimensional Heisenberg group.

On the classical theory of ordinary linear differential equations of the second order and the Schroedinger equation for power law potentials

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1983-01-01

The power law potentials in the Schroedinger equation solved recently are shown to come from the classical treatment of the singularities of a linear, second order differential equation. This allows to enlarge the class of solvable power law potentials. (Author) [pt

Position-Dependent Mass Schrödinger Equation for the Morse Potential

International Nuclear Information System (INIS)

Ovando, G; Peña, J J; Morales, J; López-Bonilla, J

2017-01-01

The position dependent mass Schrödinger equation (PDMSE) has a wide range of quantum applications such as the study of semiconductors, quantum wells, quantum dots and impurities in crystals, among many others. On the other hand, the Morse potential is one of the most important potential models used to study the electronic properties of diatomic molecules. In this work, the solution of the effective mass one-dimensional Schrödinger equation for the Morse potential is presented. This is done by means of the canonical transformation method in algebraic form. The PDMSE is solved for any model of the proposed kinetic energy operators as for example the BenDaniel-Duke, Gora-Williams, Zhu-Kroemer or Li-Kuhn. Also, in order to solve the PDMSE with Morse potential, we consider a superpotential leading to a special form of the exactly solvable Schrödinger equation of constant mass for a class of multiparameter exponential-type potential along with a proper mass distribution. The proposed approach is general and can be applied in the search of new potentials suitable on science of materials by looking into the viable choices of the mass function. (paper)

Overcritical PT-symmetric square well potential in the Dirac equation

OpenAIRE

Cannata, Francesco; Ventura, Alberto

2007-01-01

We study scattering properties of a PT-symmetric square well potential with real depth larger than the threshold of particle-antiparticle pair production as the time component of a vector potential in the (1+1)-dimensional Dirac equation.

Approximate Solution of Schrödinger Equation with Pseudo-Gaussian Potential Viewed as a Perturbation

Directory of Open Access Journals (Sweden)

Iacob Theodor-Felix

2015-12-01

Full Text Available We consider the Schrödinger equation with pseudo-Gaussian potential and point out that it is basically made up by a term representing the harmonic oscillator potential and an additional term, which is actually a power series that converges rapidly. Based on this observation the system can be considered as a perturbation of harmonic oscillator. The perturbation method is used to approximate the energy levels of pseudo- Gaussian oscillator. The results are compared with those obtained in the analytic and numeric case.

Solution of Effective-Mass Dirac Equation with Scalar-Vector and Pseudoscalar Terms for Generalized Hulthén Potential

Directory of Open Access Journals (Sweden)

Altuğ Arda

2017-01-01

Full Text Available We find the exact bound state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulthén potential in the case where we have a particular mass function m(x. We also search the solutions for the constant mass where the obtained results correspond to the ones when the Dirac equation has spin and pseudospin symmetry, respectively. After giving the obtained results for the nonrelativistic case, we search then the energy spectra and corresponding upper and lower components of Dirac spinor for the case of PT-symmetric forms of the present potential.

Darboux Transformations for Energy-Dependent Potentials and the Klein–Gordon Equation

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2013-01-01

We construct explicit Darboux transformations for a generalized Schrödinger-type equation with energy-dependent potential, a special case of which is the stationary Klein–Gordon equation. Our results complement and generalize former findings (Lin et al., Phys Lett A 362:212–214, 2007).

Integrable motion of curves in self-consistent potentials: Relation to spin systems and soliton equations

Energy Technology Data Exchange (ETDEWEB)

Myrzakulov, R.; Mamyrbekova, G.K.; Nugmanova, G.N.; Yesmakhanova, K.R. [Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Lakshmanan, M., E-mail: lakshman@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024 (India)

2014-06-13

Motion of curves and surfaces in R{sup 3} lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self-consistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials or soliton equations with self-consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota–Maxwell–Bloch equations, all in the presence of self-consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability. - Highlights: • Geometry of continuum spin chain with self-consistent potentials explored. • Mapping on moving space curves in R{sup 3} in the presence of potential fields carried out. • Equivalent generalized nonlinear Schrödinger (NLS) family of equations identified. • Integrability of identified nonlinear systems proved by deducing appropriate Lax pairs.

Generating potentially nilpotent full sign patterns

NARCIS (Netherlands)

Kim, I.J.; Olesky, D.D.; Shader, B.L.; Driessche, van den P.; Holst, van der H.; Vander Meulen, K.N.

2009-01-01

A sign pattern is a matrix with entries in {+,-, 0}. A full sign pattern has no zero entries. The refined inertia of a matrix pattern is defined and techniques are developed for constructing potentially nilpotent full sign patterns. Such patterns are spectrally arbitrary. These techniques can also

Gravitational and electromagnetic potentials of the stationary Einstein-Maxwell field equations

International Nuclear Information System (INIS)

Jones, T.C.

1979-01-01

Associated with the stationary Einstein-Maxwell field equations is an infinite hierarchy of potentials. The basic characteristics of these potentials are examined in general and then in greater detail for the particular case of the Reissner-Nordstrom metric. Thier essential utility in the process of solution generation is elucidated, and the necessary equations for solution generation are developed. Appropriate generating functions, which contain the complete infinite hierarchy of potentials, are developed and analyzed. Particular attention is paid to the inherent gauge freedom of these generating functions. Two methods of solution generation, which yield asymptotically flat solutions in vacuum, are generalized to include electromagnetism. One method, using potentials consistent with the Harrison transformation and the Reissner-Nordstrom metric, is discussed in detail, and its resultant difficulties are explored

The nonlinear heat equation with state–dependent parameters and its connection to the Burgers’ and the potential Burgers’ equation

DEFF Research Database (Denmark)

Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John-Josef

2014-01-01

In this work the stability properties of a nonlinear partial differential equation (PDE) with state–dependent parameters is investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (Potential) Burgers’ Equation. We show that for certain forms of coe...

Approximate analytical solutions of Klein-Gordon equation with Hulthen potentials for nonzero angular momentum

International Nuclear Information System (INIS)

Chen Changyuan; Sun Dongsheng; Lu Falin

2007-01-01

Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of bound states are attained for different l. The analytical energy equation and the unnormalized radial wave functions expressed in terms of hypergeometric polynomials are given

A Relation Between the Eikonal Equation Associated to a Potential Energy Surface and a Hyperbolic Wave Equation.

Science.gov (United States)

Bofill, Josep Maria; Quapp, Wolfgang; Caballero, Marc

2012-12-11

The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.

Transport coefficients of Quark-Gluon plasma with full QCD potential

Science.gov (United States)

J. P., Prasanth; Bannur, Vishnu M.

2018-05-01

The shear viscosity η, bulk viscosity ζ and their ratio with the entropy density, η / s, ζ / s have been studied in a quark-gluon plasma (QGP) within the cluster expansion method. The cluster expansion method allows us to include the interaction between the partons in the deconfined phase and to calculate the equation of state of quark-gluon plasma. It has been argued that the interactions present in the equation of state, the modified Cornell potential significantly contributes to the viscosity. The results obtained within our approaches agree with lattice quantum chromodynamics (LQCD) equation of state. We obtained η / s ≈ 0 . 128 within the temperature range T /Tc ∈ [ 0 . 9 , 1 . 5 ] which is very close to the theoretical lower bound η / s ≥ 1 /(4 π) in Yang-Mills theory. We also demonstrate that the effects of ζ / s at freezeout are possibly large.

Field differential equations for a potential flow from a Hamilton type variational principle

International Nuclear Information System (INIS)

Fierros Palacios, A.

1992-01-01

The same theoretical frame that was used to solve the problem of the field equations for a viscous fluid is utilized in this work. The purpose is to obtain the differential field equations for a potential flow from the Lagrangian formalism as in classical field theory. An action functional is introduced as a space-time integral over a region of three-dimensional Euclidean space, of a Lagrangian density as a function of certain field variables. A Hamilton type extremum action principle is postulated with adequate boundary conditions, and a set of differential field equations is derived. A particular Lagrangian density of the T-V type leads to the wave equation for the velocity potential. (Author)

Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation

International Nuclear Information System (INIS)

Shi, Ying; Zhang, Da-jun; Nimmo, Jonathan J C

2014-01-01

The Hirota–Miwa equation can be written in ‘nonlinear’ form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equation, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations. (paper)

A limit of the confluent Heun equation and the Schroedinger equation for an inverted potential and for an electric dipole

International Nuclear Information System (INIS)

El-Jaick, Lea Jaccoud; Figueiredo, Bartolomeu D.B.

2009-01-01

We reexamine and extend a group of solutions in series of Bessel functions for a limiting case of the confluent Heun equation and, then, apply such solutions to the one-dimensional Schroedinger equation with an inverted quasi-exactly solvable potential as well as to the angular equation for an electron in the field of a point electric dipole. For the first problem we find finite and infinite-series solutions which are convergent and bounded for any value of the independent variable. For the angular equation, we also find expansions in series of Jacobi polynomials. (author)

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

Science.gov (United States)

Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

2014-01-01

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

Application of Exp-function method to potential Kadomtsev-Petviashvili equation

International Nuclear Information System (INIS)

Xian Daquan; Dai Zhengde

2009-01-01

Exact periodic kink-wave solution, periodic soliton and doubly periodic solutions for the potential Kadomtsev-Petviashvii (PKP) equation are obtained using Exp-function method with the help of Maple computation.

On conserved densities and asymptotic behaviour for the potential Kadomtsev-Petviashvili equation

International Nuclear Information System (INIS)

Rosenhaus, V

2006-01-01

We study local conservation laws with non-vanishing conserved densities and corresponding boundary conditions for the potential Kadomtsev-Petviashvili equation. We analyse an infinite symmetry group of the equation, and generate a finite number of conserved densities corresponding to infinite symmetries through appropriate boundary conditions

Solution of Dirac equation for modified Poschl Teller plus trigonometric Scarf potential using Romanovsky polynomials method

International Nuclear Information System (INIS)

Prastyaningrum, I.; Cari, C.; Suparmi, A.

2016-01-01

The approximation analytical solution of Dirac equation for Modified Poschl Teller plus Trigonometric Scarf Potential are investigated numerically in terms of finite Romanovsky Polynomial. The combination of two potentials are substituted into Dirac Equation then the variables are separated into radial and angular parts. The Dirac equation is solved by using Romanovsky Polynomial Method. The equation that can reduce from the second order of differential equation into the differential equation of hypergeometry type by substituted variable method. The energy spectrum is numerically solved using Matlab 2011. Where the increase in the radial quantum number nr and variable of modified Poschl Teller Potential causes the energy to decrease. The radial and the angular part of the wave function also visualized with Matlab 2011. The results show, by the disturbance of a combination between this potential can change the wave function of the radial and angular part. (paper)

New lumps of Veselov-Novikov integrable nonlinear equation and new exact rational potentials of two-dimensional stationary Schroedinger equation via ∂-macron-dressing method

International Nuclear Information System (INIS)

Dubrovsky, V.G.; Formusatik, I.B.

2003-01-01

The scheme for calculating via Zakharov-Manakov ∂-macron-dressing method of new rational solutions with constant asymptotic values at infinity of the famous two-dimensional Veselov-Novikov (VN) integrable nonlinear evolution equation and new exact rational potentials of two-dimensional stationary Schroedinger (2DSchr) equation with multiple pole wave functions is developed. As examples new lumps of VN nonlinear equation and new exact rational potentials of 2DSchr equation with multiple pole of order two wave functions are calculated. Among the constructed rational solutions are as nonsingular and also singular

The exact solutions of the Schroedinger equation with the Morse potential via Laplace transforms

International Nuclear Information System (INIS)

Chen Gang

2004-01-01

In this Letter, we reduce the second-order differential equation about the one-dimensional Schroedinger equation with the Morse potential reduced to the first-order differential equation in terms of Laplace transforms and then obtain the exact bound state solutions

The Analytic Solution of Schroedinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

International Nuclear Information System (INIS)

Hu Xianquan; Luo Guang; Cui Lipeng; Niu Lianbin; Li Fangyu

2009-01-01

The analytic solution of the radial Schroedinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schroedinger equation is V(r) = α 1 r 8 + α 2 r 3 + α 3 r 2 + β 3 r -1 + β 2 r -3 + β 1 r -4 . Generally speaking, there is only an approximate solution, but not analytic solution for Schroedinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schroedinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schroedinger equation; and lastly, they discuss the solutions and make conclusions. (general)

Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

Directory of Open Access Journals (Sweden)

K. Atifi

2017-01-01

Full Text Available A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient. Some numerical experiments are given.

Stability study of pre-stack seismic inversion based on the full Zoeppritz equation

Science.gov (United States)

Liang, Lifeng; Zhang, Hongbing; Guo, Qiang; Saeed, Wasif; Shang, Zuoping; Huang, Guojiao

2017-10-01

Pre-stack seismic inversion is highly important and complicated. Its result is non-unique, and the process is unstable because pre-stack seismic inversion is an ill-posed problem that simultaneously obtains the results of multiple parameters. Combining the full Zoeppritz equation and additional assumptions with edge-preserving regularization (EPR) can help mitigate the problem. To achieve this combination, we developed an inversion method by constructing a new objective function, which includes the EPR and the Markov random field. The method directly gains reflectivity R PP by the full Zoeppritz equation instead of its approximations and effectively controls the stability of simultaneous inversion by two additional assumptions: the sectional constant V S/V P and the generalized Gardner equation. Thus, the simultaneous inversion of multiple parameters is directed toward to V P, ΔL S (the fitting deviation of V S) and density, and the generalized Gardner equation is regarded as a constraint from which the fitting relationship is derived. We applied the fast simulated annealing algorithm to solve the nonlinear optimization problem. The test results on 2D synthetic data indicated that the stability of simultaneous inversion for V P, ΔL S and density is better than these for V P, V S, and density. The inverted result of density gradually worsens as the deviation ΔL D (the fitting deviation of the density) increases. Moreover, the inverted results were acceptable when using the fitting relationships with error, although they showed varying degrees of influence. We constructed time-varying and space-varying fitting relationships using the logging data in pre-stack inversion of the field seismic data. This improved the inverted results of the simultaneous inversion for complex geological models. Finally, the inverted results of the field data distinctly revealed more detailed information about the layers and matched well with the logging data along the wells over most

Some blow-up problems for a semilinear parabolic equation with a potential

Science.gov (United States)

Cheng, Ting; Zheng, Gao-Feng

The blow-up rate estimate for the solution to a semilinear parabolic equation u=Δu+V(x)|u in Ω×(0,T) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x,0)=Mφ(x) as M goes to infinity, which have been found in [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006], is improved under some reasonable and weaker conditions compared with [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006].

Solution of Wheeler-De Witt Equation, Potential Well and Tunnel Effect

International Nuclear Information System (INIS)

Huang Yongchang; Weng Gang

2005-01-01

This paper uses the relation of the cosmic scale factor and scalar field to solve Wheeler-De Witt equation, gives the tunnel effect of the cosmic scale factor a and quantum potential well of scalar field, and makes it fit with the physics of cosmic quantum birth. By solving Wheeler-De Witt equation we achieve a general probability distribution of the cosmic birth, and give the analysis of cosmic quantum birth.

Orbital stability of standing waves for a class of Schrödinger equations with unbounded potential

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available This paper is concerned with the nonlinear Schrödinger equation with an unbounded potential i ϕ t = − Δ ϕ + V ( x ϕ − μ | ϕ | p − 1 ϕ − λ | ϕ | q − 1 ϕ , x ∈ ℝ N , t ≥ 0 , where 0$"> μ > 0 , 0,$"> λ > 0 , and 1 < p < q < 1 + 4 / N . The potential V ( x is bounded from below and satisfies V ( x → ∞ as | x | → ∞ . From variational calculus and a compactness lemma, the existence of standing waves and their orbital stability are obtained.

Standard electrode potential, Tafel equation, and the solvation thermodynamics.

Science.gov (United States)

Matyushov, Dmitry V

2009-06-21

Equilibrium in the electronic subsystem across the solution-metal interface is considered to connect the standard electrode potential to the statistics of localized electronic states in solution. We argue that a correct derivation of the Nernst equation for the electrode potential requires a careful separation of the relevant time scales. An equation for the standard metal potential is derived linking it to the thermodynamics of solvation. The Anderson-Newns model for electronic delocalization between the solution and the electrode is combined with a bilinear model of solute-solvent coupling introducing nonlinear solvation into the theory of heterogeneous electron transfer. We therefore are capable of addressing the question of how nonlinear solvation affects electrochemical observables. The transfer coefficient of electrode kinetics is shown to be equal to the derivative of the free energy, or generalized force, required to shift the unoccupied electronic level in the bulk. The transfer coefficient thus directly quantifies the extent of nonlinear solvation of the redox couple. The current model allows the transfer coefficient to deviate from the value of 0.5 of the linear solvation models at zero electrode overpotential. The electrode current curves become asymmetric in respect to the change in the sign of the electrode overpotential.

Quantum Gross-Pitaevskii Equation

Directory of Open Access Journals (Sweden)

Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete

2017-07-01

Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

A new approach to the Schrödinger equation with rational potentials

Science.gov (United States)

Dong, Ming-de; Chu, Jue-Hui

1984-04-01

A new analytic theory is established for the Schrödinger equation with a rational potential, including a complete classification of the regular eigenfunctions into three different types, an exact method of obtaining wavefunctions, an explicit formulation of the spectral equation (3 x 3 determinant) etc. All representations are exhibited in a unifying way via function-theoretic methods and therefore given in explicit form, in contrast to the prevailing discussion appealing to perturbation or variation methods or continued-fraction techniques. The irregular eigenfunctions at infinity can be obtained analogously and will be discussed separately as another solvable case for singular potentials.

Computational study on full-wave inversion based on the elastic wave-equation; Dansei hado hoteishiki full wave inversion no model keisan ni yoru kento

Energy Technology Data Exchange (ETDEWEB)

Uesaka, S [Kyoto University, Kyoto (Japan). Faculty of Engineering; Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan)

1997-05-27

Algorithm is constructed and a program developed for a full-wave inversion (FWI) method utilizing the elastic wave equation in seismic exploration. The FWI method is a method for obtaining a physical property distribution using the whole observed waveforms as the data. It is capable of high resolution which is several times smaller than the wavelength since it can handle such phenomena as wave reflection and dispersion. The method for determining the P-wave velocity structure by use of the acoustic wave equation does not provide information about the S-wave velocity since it does not consider S-waves or converted waves. In an analysis using the elastic wave equation, on the other hand, not only P-wave data but also S-wave data can be utilized. In this report, under such circumstances, an inverse analysis algorithm is constructed on the basis of the elastic wave equation, and a basic program is developed. On the basis of the methods of Mora and of Luo and Schuster, the correction factors for P-wave and S-wave velocities are formulated directly from the elastic wave equation. Computations are performed and the effects of the hypocenter frequency and vibration transmission direction are examined. 6 refs., 8 figs.

DEVELOPMENT OF SCIENTIFIC AND INFORMATIVE POTENTIAL OF STUDENTS IN THE TEACHING OF THE INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS

Directory of Open Access Journals (Sweden)

Виктор Семенович Корнилов

2017-12-01

Full Text Available In article attention that when training in the inverse problems for differential equations at students scientific and cognitive potential develops is paid. Students realize that mathematical models of the inverse problems for differential equations find the application in economy, the industries, ecology, sociology, biology, chemistry, mathematician, physics, in researches of the processes and the phenomena occurring in water and earth’s environment, air and space.Attention of the reader that in training activity to the inverse problems for differential equations at students the scientific outlook, logical, algorithmic, information thinking, creative activity, independence and ingenuity develop is focused. Students acquire skills to apply knowledge of many physical and mathematical disciplines, to carry out the analysis of the received decision of the reverse task and to formulate logical outputs of application-oriented character. Solving the inverse problems for differential equations, students acquire new knowledge in the field of applied and calculus mathematics, informatics, natural sciences and other knowledge.

Numerical solution of the Schroedinger equation with a polynomial potential

International Nuclear Information System (INIS)

Campoy, G.; Palma, A.

1986-01-01

A numerical method for solving the Schroedinger equation for a potential expressed as a polynomial is proposed. The basic assumption relies on the asymptotic properties of the solution of this equation. It is possible to obtain the energies and the stationary state functions simultaneously. They analyze, in particular, the cases of the quartic anharmonic oscillator and a hydrogen atom perturbed by a quadratic term, obtaining its energy eigenvalues for some values of the perturbation parameter. Together with the Hellmann-Feynman theorem, they use their algorithm to calculate expectation values of x'' for arbitrary positive values of n. 4 tables

A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

Energy Technology Data Exchange (ETDEWEB)

Liu, Chang, E-mail: cliuaa@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Xu, Kun, E-mail: makxu@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Sun, Quanhua, E-mail: qsun@imech.ac.cn [State Key Laboratory of High-temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuan Xi Rd, Beijing 100190 (China); Cai, Qingdong, E-mail: caiqd@mech.pku.edu.cn [Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871 (China)

2016-06-01

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region

Nonlocal integrable PDEs from hierarchies of symmetry laws: The example of Pohlmeyer-Lund-Regge equation and its reflectionless potential solutions

Science.gov (United States)

Demontis, F.; Ortenzi, G.; van der Mee, C.

2018-04-01

By following the ideas presented by Fukumoto and Miyajima in Fukumoto and Miyajima (1996) we derive a generalized method for constructing integrable nonlocal equations starting from any bi-Hamiltonian hierarchy supplied with a recursion operator. This construction provides the right framework for the application of the full machinery of the inverse scattering transform. We pay attention to the Pohlmeyer-Lund-Regge equation coming from the nonlinear Schrödinger hierarchy and construct the formula for the reflectionless potential solutions which are generalizations of multi-solitons. Some explicit examples are discussed.

Solution of Duffin-Kemmer-Petiau equations for finite and infinite square well potential

International Nuclear Information System (INIS)

Boztosun, I.; Taskin, F.; Burtebayev, N.

2002-01-01

The solution of the Duffin-Kemmer-Petiau relativistic equation for spinless boson in a central field has a long standing problem and the mathematical difficulty in attempting to reach the solution even for simple problems has caused the use this equation to be regarded as quite unattractive among scientists. In this paper we first derive the system of the first-order coupled differential equation which enable the energy eigenvalues to be evaluated and show that these equations can be reduced to the second-order Schroedinger type radial differential equation. We then consider some of the properties of this equation, which are needed for practical calculations, and show that using this the second-order radial equation, the physical observables can be found in a very simple way. As an example, we consider a pionic atoms in the finite and infinite square-well potentials and calculate the eigen-energies as well as the wave functions using the relativistic Duffin-Kemmer-Petiau equation. We show that our findings are in excellent agreement with the results of the Klein-Gordon equation

On invariant measures for the Vlasov equation with a regular potential

International Nuclear Information System (INIS)

Zhidkov, P.E.

2003-01-01

We consider a Vlasov equation with a smooth bounded potential of interaction between particles in a class of measure-valued solutions and construct a measure which is invariant for this problem in a sense

Algebraic inversion of the Dirac equation for the vector potential in the non-Abelian case

International Nuclear Information System (INIS)

Inglis, S M; Jarvis, P D

2012-01-01

We study the Dirac equation for spinor wavefunctions minimally coupled to an external field, from the perspective of an algebraic system of linear equations for the vector potential. By analogy with the method in electromagnetism, which has been well-studied, and leads to classical solutions of the Maxwell–Dirac equations, we set up the formalism for non-Abelian gauge symmetry, with the SU(2) group and the case of four-spinor doublets. An extended isospin-charge conjugation operator is defined, enabling the hermiticity constraint on the gauge potential to be imposed in a covariant fashion, and rendering the algebraic system tractable. The outcome is an invertible linear equation for the non-Abelian vector potential in terms of bispinor current densities. We show that, via application of suitable extended Fierz identities, the solution of this system for the non-Abelian vector potential is a rational expression involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial vector current densities, albeit in the non-closed form of a Neumann series. (paper)

The auxiliary field method and approximate analytical solutions of the Schroedinger equation with exponential potentials

Energy Technology Data Exchange (ETDEWEB)

Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be

2009-06-19

The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies of the Schroedinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schroedinger equation with exponential potentials of the form -{alpha}r{sup {lambda}}exp(-{beta}r) can also be analytically solved by using the auxiliary field method. Closed formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn to the Yukawa potential and the pure exponential potential.

The auxiliary field method and approximate analytical solutions of the Schroedinger equation with exponential potentials

International Nuclear Information System (INIS)

Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien

2009-01-01

The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies of the Schroedinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schroedinger equation with exponential potentials of the form -αr λ exp(-βr) can also be analytically solved by using the auxiliary field method. Closed formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn to the Yukawa potential and the pure exponential potential

Inhomogeneous critical nonlinear Schroedinger equations with a harmonic potential

International Nuclear Information System (INIS)

Cao Daomin; Han Pigong

2010-01-01

In this paper, we study the Cauchy problem of the inhomogeneous nonlinear Schroedinger equation with a harmonic potential: i∂ t u=-div(f(x)∇u)+|x| 2 u-k(x)|u| 4/N u, x is an element of R N , N≥1, which models the remarkable Bose-Einstein condensation. We discuss the existence and nonexistence results and investigate the limiting profile of blow-up solutions with critical mass.

Efficient construction of exchange and correlation potentials by inverting the Kohn-Sham equations.

Science.gov (United States)

Kananenka, Alexei A; Kohut, Sviataslau V; Gaiduk, Alex P; Ryabinkin, Ilya G; Staroverov, Viktor N

2013-08-21

Given a set of canonical Kohn-Sham orbitals, orbital energies, and an external potential for a many-electron system, one can invert the Kohn-Sham equations in a single step to obtain the corresponding exchange-correlation potential, vXC(r). For orbitals and orbital energies that are solutions of the Kohn-Sham equations with a multiplicative vXC(r) this procedure recovers vXC(r) (in the basis set limit), but for eigenfunctions of a non-multiplicative one-electron operator it produces an orbital-averaged potential. In particular, substitution of Hartree-Fock orbitals and eigenvalues into the Kohn-Sham inversion formula is a fast way to compute the Slater potential. In the same way, we efficiently construct orbital-averaged exchange and correlation potentials for hybrid and kinetic-energy-density-dependent functionals. We also show how the Kohn-Sham inversion approach can be used to compute functional derivatives of explicit density functionals and to approximate functional derivatives of orbital-dependent functionals.

Variational and potential formulation for stochastic partial differential equations

International Nuclear Information System (INIS)

Munoz S, A G; Ojeda, J; Sierra D, P; Soldovieri, T

2006-01-01

Recently there has been interest in finding a potential formulation for stochastic partial differential equations (SPDEs). The rationale behind this idea lies in obtaining all the dynamical information of the system under study from one single expression. In this letter we formally provide a general Lagrangian formalism for SPDEs using the Hojman et al method. We show that it is possible to write the corresponding effective potential starting from an s-equivalent Lagrangian, and that this potential is able to reproduce all the dynamics of the system once a special differential operator has been applied. This procedure can be used to study the complete time evolution and spatial inhomogeneities of the system under consideration, and is also suitable for the statistical mechanics description of the problem. (letter to the editor)

The investigation of relativistic microscopic optical potential based on RBBG equation

International Nuclear Information System (INIS)

Chen Baoqiu; Ma Zhongyu

1992-01-01

The relativistic microscopic optical potential is derived from the RBBG equation. The nucleon complex effective mass is determined phenomenologically by a fit to 200 MeV proton-nucleus scattering data. Then the relativistic microscopic optical potentials of proton scattered from different targets: 16 O, 40 Ca, 90 Zr and 208 Pb in the energies range from 160 to 800 MeV have been got. The relativistic microscopic optical potentials have been used to study proton- 40 Ca scattering at 200 MeV. Theoretical predictions for cross section and spin observables are compared with experimental data and phenomenological Dirac optical potential

Rational Solutions and Lump Solutions of the Potential YTSF Equation

Science.gov (United States)

Sun, Hong-Qian; Chen, Ai-Hua

2017-07-01

By using of the bilinear form, rational solutions and lump solutions of the potential Yu-Toda-Sasa-Fukuyama (YTSF) equation are derived. Dynamics of the fundamental lump solution, n1-order lump solutions, and N-lump solutions are studied for some special cases. We also find some interaction behaviours of solitary waves and one lump of rational solutions.

Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials

Science.gov (United States)

Finster, Felix; Smoller, Joel

2010-09-01

A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtained by gluing together WKB and Airy solutions of corresponding one-dimensional Schrödinger equations. Our method is motivated by, and has applications to, the analysis of linear wave equations in the geometry of a rotating black hole.

New exact travelling wave solutions for two potential coupled KdV equations with symbolic computation

International Nuclear Information System (INIS)

Yang Zonghang

2007-01-01

We find new exact travelling wave solutions for two potential KdV equations which are presented by Foursov [Foursov MV. J Math Phys 2000;41:6173-85]. Compared with the extended tanh-function method, the algorithm used in our paper can obtain some new kinds of exact travelling wave solutions. With the aid of symbolic computation, some novel exact travelling wave solutions of the potential KdV equations are constructed

Solution of Schroedinger Equation for Two-Dimensional Complex Quartic Potentials

International Nuclear Information System (INIS)

Singh, Ram Mehar; Chand, Fakir; Mishra, S. C.

2009-01-01

We investigate the quasi-exact solutions of the Schroedinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x 1 + ip 3 , y = x 2 + ip 4 , p x = p 1 + ix 3 , p y = p 2 + ix 4 . Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including PT-symmetric one, are also worked out. (general)

Computational study on full-wave inversion based on the acoustic wave-equation; Onkyoha hado hoteishiki full wave inversion no model keisan ni yoru kento

Energy Technology Data Exchange (ETDEWEB)

Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan); Uesaka, S [Kyoto University, Kyoto (Japan). Faculty of Engineering

1996-10-01

The effect of initial models on full-wave inversion (FWI) analysis based on acoustic wave-equation was studied for elastic wave tomography of underground structures. At present, travel time inversion using initial motion travel time is generally used, and inverse analysis is conducted using the concept `ray,` assuming very high wave frequency. Although this method can derive stable solutions relatively unaffected by initial model, it uses only the data of initial motion travel time. FWI calculates theoretical waveform at each receiver using all of observed waveforms as data by wave equation modeling where 2-D underground structure is calculated by difference calculus under the assumption that wave propagation is described by wave equation of P wave. Although it is a weak point that FWI is easily affected by noises in an initial model and data, it is featured by high resolution of solutions. This method offers very excellent convergence as a proper initial model is used, resulting in sufficient performance, however, it is strongly affected by initial model. 2 refs., 7 figs., 1 tab.

D-Dimensional Dirac Equation for Energy-Dependent Pseudoharmonic and Mie-type Potentials via SUSYQM

International Nuclear Information System (INIS)

Ikot, A.N.; Hassanabadi, H.; Maghsoodi, E.; Zarrinkamar, S.

2014-01-01

We investigate the approximate solution of the Dirac equation for energy-dependent pseudoharmonic and Mie-type potentials under the pseudospin and spin symmetries using the supersymmetry quantum mechanics. We obtain the bound-state energy equation in an analytical manner and comment on the system behavior via various figures and tables

A separable approximation of the NN-Paris-potential in the framework of the Bethe-Salpeter equation

International Nuclear Information System (INIS)

Schwarz, K.; Haidenbauer, J.; Froehlich, J.

1985-09-01

The Bethe-Salpeter equation is solved with a separable kernel for the most important nucleon-nucleon partial wave states. We employ the Ernst Shakin-Thaler method in the framework of minimal relativity (Blankenbeckler-Sugar equation) to generate a separable representation of the meson-theoretical Paris potential. These separable interactions, which closely approximate the on-shell- and half-off-shell behaviour of the Paris potential, are then cast into a covariant form for application in the Bethe-Salpeter equation. The role of relativistic effects is discussed with respect to on-shell and off-shell properties of the NN-system. (Author)

Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials

International Nuclear Information System (INIS)

Hartwig, J. T.; Stokman, J. V.

2013-01-01

We realize an extended version of the trigonometric Cherednik algebra as affine Dunkl operators involving Heaviside functions. We use the quadratic Casimir element of the extended trigonometric Cherednik algebra to define an explicit nonstationary Schrödinger equation with delta-potential. We use coordinate Bethe ansatz methods to construct solutions of the nonstationary Schrödinger equation in terms of generalized Bethe wave functions. It is shown that the generalized Bethe wave functions satisfy affine difference Knizhnik-Zamolodchikov equations as functions of the momenta. The relation to the vector valued root system analogs of the quantum Bose gas on the circle with delta-function interactions is indicated.

Stability of Planar Rarefaction Wave to 3D Full Compressible Navier-Stokes Equations

Science.gov (United States)

Li, Lin-an; Wang, Teng; Wang, Yi

2018-05-01

We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier-Stokes equations with the heat-conductivities in an infinite long flat nozzle domain {R × T^2} . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x 2 and x 3 and its interactions with the planar rarefaction wave in x 1 direction.

Chemical-potential flow equations for graphene with Coulomb interactions

Science.gov (United States)

Fräßdorf, Christian; Mosig, Johannes E. M.

2018-06-01

We calculate the chemical potential dependence of the renormalized Fermi velocity and static dielectric function for Dirac quasiparticles in graphene nonperturbatively at finite temperature. By reinterpreting the chemical potential as a flow parameter in the spirit of the functional renormalization group (fRG) we obtain a set of flow equations, which describe the change of these functions upon varying the chemical potential. In contrast to the fRG the initial condition of the flow is nontrivial and has to be calculated separately. Our results are consistent with a charge carrier-independent Fermi velocity v (k ) for small densities n ≲k2/π , supporting the comparison of the zero-density fRG calculation of Bauer et al. [Phys. Rev. B 92, 121409 (2015), 10.1103/PhysRevB.92.121409], with the experiment of Elias et al. [Nat. Phys. 7, 701 (2011), 10.1038/nphys2049].

On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging

KAUST Repository

Antonelli, Paolo

2014-01-14

We analyse a nonlinear Schrödinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree-Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray free electron laser. We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schrödinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential. © 2014 Springer-Verlag Berlin Heidelberg.

Analysis of wave equation in electromagnetic field by Proca equation

International Nuclear Information System (INIS)

Pamungkas, Oky Rio; Soeparmi; Cari

2017-01-01

This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

Exact solution of nonrelativistic Schrodinger equation for certain central physical potential

International Nuclear Information System (INIS)

Bose, S.K.; Gupta, N.

1998-01-01

It is obtained here a class/classes of exact solution of the nonrelativistic Schrodinger equation for certain central potentials of physical interest by using proper ansatz/ansatze. The explicit expressions of energy eigenvalue and eigenfunction are obtained for each solution. These solutions are valid when for, in general, each solutions an interrelation between the parameters of the potential and the orbital-angular-momentum quantum number l is satisfied. These solutions, besides having an aesthetic appeal, can be used as benchmark to test the accuracy of nonperturbative methods, which sometimes yield wrong results, of solving the Schrodinger equation. The exact solution for the following central potentials, which are relevant in different areas of physics, have been obtained: 1) V(r)=ar 6 + br 4 + cr 2 ; 2) V(r)=ar 2 + br + c/r; 3) V(r)=r 2 + λr 2 /(1+gr 2 ); 4) V(r)= a/r + b/(r+λ); 5a) V(r)=a/r + b/r 2 +c/r 3 +d/r 4 ; 5)b V(r)=a/r 2 + b/r 2 + c/r 4 + d/r 6 ; 6a) V(r)=a/r 1/2 + b/r 3/2 ; 6b) V(r)=ar 2/3 + br -2/3 + cr -4/3

Solution Of Schrödinger Equation For Poschl-Teller Plus Scarf Non-Central Potential Using Supersymmetry Quantum Mechanics Aproach

Directory of Open Access Journals (Sweden)

Antomi Saregar

2015-04-01

Full Text Available In this paper, we show that the exact energy eigenvalues and eigenfunctions of the Schrödinger equation for charged particles moving in a certain class of noncentral potentials can be easily calculated analytically in a simple and elegant manner by using Supersymmetric method (SUSYQM. We discuss the Poschl-Teller plus Scarf non-central potential systems. Then, by operating the lowering operator we get the ground state wave function, and the excited state wave functions are obtained by operating raising operator repeatedly. The energy eigenvalue is expressed in the closed form obtained using the shape invariant properties. The results are in exact agreement with other methods. Keyword: supersymmetry, non-central potentials, poschl teller plus scarf.

New equations for density, entropy, heat capacity, and potential temperature of a saline thermal fluid

Science.gov (United States)

Sun, Hongbing; Feistel, Rainer; Koch, Manfred; Markoe, Andrew

2008-10-01

A set of fitted polynomial equations for calculating the physical variables density, entropy, heat capacity and potential temperature of a thermal saline fluid for a temperature range of 0-374 °C, pressure range of 0.1-100 MPa and absolute salinity range of 0-40 g/kg is established. The freshwater components of the equations are extracted from the recently released tabulated data of freshwater properties of Wagner and Pruß [2002. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Journal of Physical and Chemical Reference Data 31, 387-535]. The salt water component of the equation is based on the near-linear relationship between density, salinity and specific heat capacity and is extracted from the data sets of Feistel [2003. A new extended Gibbs thermodynamic potential of seawater. Progress in Oceanography 58, 43-114], Bromley et al. [1970. Heat capacities and enthalpies of sea salt solutions to 200 °C. Journal of Chemical and Engineering Data 15, 246-253] and Grunberg [1970. Properties of sea water concentrates. In: Third International Symposium on Fresh Water from the Sea, vol. 1, pp. 31-39] in a temperature range 0-200 °C, practical salinity range 0-40, and varying pressure and is also calibrated by the data set of Millero et al. [1981. Summary of data treatment for the international high pressure equation of state for seawater. UNESCO Technical Papers in Marine Science 38, 99-192]. The freshwater and salt water components are combined to establish a workable multi-polynomial equation, whose coefficients were computed through standard linear regression analysis. The results obtained in this way for density, entropy and potential temperature are comparable with those of existing models, except that our new equations cover a wider temperature—(0-374 °C) than the traditional (0-40 °C) temperature range. One can apply these newly established equations to the calculation of in-situ or

Salpeter equation in position space: Numerical solution for arbitrary confining potentials

International Nuclear Information System (INIS)

Nickisch, L.J.; Durand, L.; Durand, B.

1984-01-01

We present and test two new methods for the numerical solution of the relativistic wave equation [(-del 2 +m 1 2 )/sup 1/2/+(-del 2 +m 2 2 )/sup 1/2/+V(r)-M]psi( r ) = 0, which appears in the theory of relativistic quark-antiquark bound states. Our methods work directly in position space, and hence have the desirable features that we can vary the potential V(r) locally in fitting the qq-bar mass spectrum, and can easily build in the expected behavior of V for r→0,infinity. Our first method converts the nonlocal square-root operators to mildly singular integral operators involving hyperbolic Bessel functions. The resulting integral equation can be solved numerically by matrix techniques. Our second method approximates the square-root operators directly by finite matrices. Both methods converge rapidly with increasing matrix size (the square-root matrix method more rapidly) and can be used in fast-fitting routines. We present some tests for oscillator and Coulomb interactions, and for the realistic Coulomb-plus-linear potential used in qq-bar phenomenology

Beam stabilization in the two-dimensional nonlinear Schrodinger equation with an attractive potential by beam splitting and radiation

DEFF Research Database (Denmark)

leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich

2004-01-01

The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...... losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials....

Multiple solutions to some singular nonlinear Schrodinger equations

Directory of Open Access Journals (Sweden)

Monica Lazzo

2001-01-01

Full Text Available We consider the equation $$ - h^2 Delta u + V_varepsilon(x u = |u|^{p-2} u $$ which arises in the study of standing waves of a nonlinear Schrodinger equation. We allow the potential $V_varepsilon$ to be unbounded below and prove existence and multiplicity results for positive solutions.

Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion

International Nuclear Information System (INIS)

Bajnok, Zoltán; Balog, János; Correa, Diego H.; Hegedűs, Árpád; Massolo, Fidel I. Schaposnik; Tóth, Gábor Zsolt

2014-01-01

The boundary thermodynamic Bethe Ansatz (BTBA) equations introduced in http://dx.doi.org/10.1007/JHEP08(2012)134http://dx.doi.org/10.1007/JHEP10(2013)135 to describe the cusp anomalous dimension contain imaginary chemical potentials and singular boundary fugacities, which make its systematic expansion problematic. We propose an alternative formulation based on real chemical potentials and additional source terms. We expand our equations to double wrapping order and find complete agreement with the direct two-loop gauge theory computation of the cusp anomalous dimension

Solutions of Navier-Stokes Equation with Coriolis Force

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Sunggeun Lee

2017-01-01

Full Text Available We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.

Hydrodynamic parameters estimation from self-potential data in a controlled full scale site

Science.gov (United States)

Chidichimo, Francesco; De Biase, Michele; Rizzo, Enzo; Masi, Salvatore; Straface, Salvatore

2015-03-01

A multi-physical approach developed for the hydrodynamic characterization of porous media using hydrogeophysical information is presented. Several pumping tests were performed in the Hydrogeosite Laboratory, a controlled full-scale site designed and constructed at the CNR-IMAA (Consiglio Nazionale delle Ricerche - Istituto di Metodologia per l'Analisi Ambientale), in Marsico Nuovo (Basilicata Region, Southern Italy), in order to obtain an intermediate stage between laboratory experiments and field survey. The facility consists of a pool, used to study water infiltration processes, to simulate the space and time dynamics of subsurface contamination phenomena, to improve and to find new relationship between geophysical and hydrogeological parameters, to test and to calibrate new geophysical techniques and instruments. Therefore, the Hydrogeosite Laboratory has the advantage of carrying out controlled experiments, like in a flow cell or sandbox, but at field comparable scale. The data collected during the experiments have been used to estimate the saturated hydraulic conductivity ks [ms-1] using a coupled inversion model working in transient conditions, made up of the modified Richards equation describing the water flow in a variably saturated porous medium and the Poisson equation providing the self-potential ϕ [V], which naturally occurs at points of the soil surface owing to the presence of an electric field produced by the motion of underground electrolytic fluids through porous systems. The result obtained by this multi-physical numerical approach, which removes all the approximations adopted in previous works, makes a useful instrument for real heterogeneous aquifer characterization and for predictive analysis of its behavior.

Stability of stationary states of non-local equations with singular interaction potentials

KAUST Repository

Fellner, Klemens

2011-04-01

We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin.For locally attractive singular interaction potentials we prove under a linear stability condition local non-linear stability of stationary states consisting of a finite sum of Dirac masses. For singular repulsive interaction potentials we show the stability of stationary states of uniformly bounded solutions under a convexity condition.Finally, we present numerical simulations to illustrate our results. © 2010 Elsevier Ltd.

Exact solutions of the Dirac equation with a Coulomb plus scalar potential in 2 + 1 dimensions

International Nuclear Information System (INIS)

Dong, Shihai; Gu, Xiaoyan; Ma, Zhongqi; Dong, Shishan

2002-01-01

The exact solutions of the (2+1)-dimensional Dirac equation with a Coulomb potential and a scalar one are analytically presented by studying the second-order differential equations obtained from a pair of coupled first-order ones. The eigenvalues are studied in some detail. (author)

Approximate analytical solution of the Dirac equation for pseudospin symmetry with modified Po schl-Teller potential and trigonometric Scarf II non-central potential using asymptotic iteration method

International Nuclear Information System (INIS)

Pratiwi, B N; Suparmi, A; Cari, C; Yunianto, M; Husein, A S

2016-01-01

We apllied asymptotic iteration method (AIM) to obtain the analytical solution of the Dirac equation in case exact pseudospin symmetry in the presence of modified Pcischl- Teller potential and trigonometric Scarf II non-central potential. The Dirac equation was solved by variables separation into one dimensional Dirac equation, the radial part and angular part equation. The radial and angular part equation can be reduced into hypergeometric type equation by variable substitution and wavefunction substitution and then transform it into AIM type equation to obtain relativistic energy eigenvalue and wavefunctions. Relativistic energy was calculated numerically by Matlab software. And then relativistic energy spectrum and wavefunctions were visualized by Matlab software. The results show that the increase in the radial quantum number n_r causes decrease in the relativistic energy spectrum. The negative value of energy is taken due to the pseudospin symmetry limit. Several quantum wavefunctions were presented in terms of the hypergeometric functions. (paper)

Tokamak m = 1 magnetohydrodynamic calculations in toroidal geometry using a full set of nonlinear resistive magnetohydrodynamic equations

International Nuclear Information System (INIS)

Charlton, L.A.; Carreras, B.A.; Holmes, J.A.; Lynch, V.E.

1988-01-01

The linear stability and nonlinear evolution of the resistive m = 1 mode in tokamaks is studied using a full set of resistive magnetohydrodynamic (MHD) equations in toroidal geometry. The modification of the linear and nonlinear properties of the mode by a combination of strong toroidal effects and low resistivity is the focus of this work. Linearly there is a transition from resistive kink to resistive tearing behavior as the aspect ratio and resistivity are reduced, and there is a corresponding modification of the nonlinear behavior, including a slowing of the island growth and development of a Rutherford regime, as the tearing regime is approached. In order to study the sensitivity of the stability and evolution to assumptions concerning the equation of state, two sets of full nonlinear resistive MHD equations (a pressure convection set and an incompressible set) are used. Both sets give more stable nonlinear behavior as the aspect ratio is reduced. The pressure convection set shows a transition from a Kadomtsev reconnection at large aspect ratio to a saturation at small aspect ratio. The incompressible set yields Kadomtsev reconnection for all aspect ratios, but with a significant lengthening of the reconnection time and development of a Rutherford regime at an aspect ratio approaching the transition from a resistive kink mode to a tearing mode. The pressure convection set gives an incomplete reconnection similar to that sometimes seen experimentally. The pressure convection set is, however, strictly justified only at high beta

Singular potentials and analytic regularization in classical Yang-Mills equations

International Nuclear Information System (INIS)

Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.

1978-10-01

The class of instanton solutions with 'extension' parameter Λ 2 positive is extended to Λ 2 negative. The nature of the singular sphere of radius |Λ| is analized in the light of the analytical regularization method. This leads to well defined solutions of the Yang - Mills equations. Some of them are sourceless ('+- i o' and 'Vp'), others correspond to currents concentrated on the sphere of singularity ('+' and '-'). Although the equations are non-linear, the 'Vp' solutions turns out to be the real part of the '+- i o' solutions. The anzats of t'Hooft for the superposition of instantons is used to sum the contributions corresponding to Λ 2 with positive and negative signs. A subsequent limiting process allows then the construction of solutions of the 'multipole' type. The general situation of potentials having a denominator D, with a corresponding surface of singularity at D=0, is also considered in the same light. (Author) [pt

On solving the Schrödinger equation for a complex deictic potential ...

Indian Academy of Sciences (India)

Making use of an ansatz for the eigenfunction, we investigate closed-form solutions of the Schrödinger equation for an even power complex deictic potential and its variant in one dimension. For this purpose, extended complex phase-space approach is utilized and nature of the eigenvalue and the corresponding ...

Applying the Nernst equation to simulate redox potential variations for biological nitrification and denitrification processes.

Science.gov (United States)

Chang, Cheng-Nan; Cheng, Hong-Bang; Chao, Allen C

2004-03-15

In this paper, various forms of Nernst equations have been developed based on the real stoichiometric relationship of biological nitrification and denitrification reactions. Instead of using the Nernst equation based on a one-to-one stoichiometric relation for the oxidizing and the reducing species, the basic Nernst equation is modified into slightly different forms. Each is suitable for simulating the redox potential (ORP) variation of a specific biological nitrification or denitrification process. Using the data published in the literature, the validity of these developed Nernst equations has been verified by close fits of the measured ORP data with the calculated ORP curve. The simulation results also indicate that if the biological process is simulated using an incorrect form of Nernst equation, the calculated ORP curve will not fit the measured data. Using these Nernst equations, the ORP value that corresponds to a predetermined degree of completion for the biochemical reaction can be calculated. Thus, these Nernst equations will enable a more efficient on-line control of the biological process.

Application of zero eigenvalue for solving the potential, heat, and wave equations using a sequence of special functions

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available In the solution of boundary value problems, usually zero eigenvalue is ignored. This case also happens in calculating the eigenvalues of matrices, so that we would often like to find the nonzero solutions of the linear system A X = λ X when λ ≠ 0 . But λ = 0 implies that det A = 0 for X ≠ 0 and then the rank of matrix A is reduced at least one degree. This comment can similarly be stated for boundary value problems. In other words, if at least one of the eigens of equations related to the main problem is considered zero, then one of the solutions will be specified in advance. By using this note, first we study a class of special functions and then apply it for the potential, heat, and wave equations in spherical coordinate. In this way, some practical examples are also given.

Numerical soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method

International Nuclear Information System (INIS)

Kaya, Dogan; El-Sayed, Salah M.

2003-01-01

In this Letter we present an Adomian's decomposition method (shortly ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions

Stability equation and two-component Eigenmode for domain walls in scalar potential model

International Nuclear Information System (INIS)

Dias, G.S.; Graca, E.L.; Rodrigues, R. de Lima

2002-08-01

Supersymmetric quantum mechanics involving a two-component representation and two-component eigenfunctions is applied to obtain the stability equation associated to a potential model formulated in terms of two coupled real scalar fields. We investigate the question of stability by introducing an operator technique for the Bogomol'nyi-Prasad-Sommerfield (BPS) and non-BPS states on two domain walls in a scalar potential model with minimal N 1-supersymmetry. (author)

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

Science.gov (United States)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

A maximum principle for the first-order Boltzmann equation, incorporating a potential treatment of voids

International Nuclear Information System (INIS)

Schofield, S.L.

1988-01-01

Ackroyd's generalized least-squares method for solving the first-order Boltzmann equation is adapted to incorporate a potential treatment of voids. The adaptation comprises a direct least-squares minimization allied with a suitably-defined bilinear functional. The resulting formulation gives rise to a maximum principle whose functional does not contain terms of the type that have previously led to difficulties in treating void regions. The maximum principle is derived without requiring continuity of the flux at interfaces. The functional of the maximum principle is concluded to have an Euler-Lagrange equation given directly by the first-order Boltzmann equation. (author)

Hs solutions for nonlinear Schrodinger equations with potentials superquadratic at infinity

International Nuclear Information System (INIS)

Zhang Guoping; Yajima, Kenji; Liu Fengshan

2006-01-01

In this Letter we study the initial value problem for the nonlinear Schrodinger equation with the potential V superquadratic at infinity. With the local smoothing property and Strichartz inequality obtained by the authors, we prove the existence and the uniqueness of the solution for H s -valued initial data and fractional s by combining the L 2 boundedness theory of pseudo differential operators and the fractional derivatives estimate

A second eigenvalue bound for the Dirichlet Schrodinger equation wtih a radially symmetric potential

Directory of Open Access Journals (Sweden)

Craig Haile

2000-01-01

Full Text Available We study the time-independent Schrodinger equation with radially symmetric potential $k|x|^alpha$, $k ge 0$, $k in mathbb{R}, alpha ge 2$ on a bounded domain $Omega$ in $mathbb{R}^n$, $(n ge 2$ with Dirichlet boundary conditions. In particular, we compare the eigenvalue $lambda_2(Omega$ of the operator $-Delta + k |x|^alpha $ on $Omega$ with the eigenvalue $lambda_2(S_1$ of the same operator $-Delta +kr^alpha$ on a ball $S_1$, where $S_1$ has radius such that the first eigenvalues are the same ($lambda_1(Omega = lambda_1(S_1$. The main result is to show $lambda_2(Omega le lambda_2(S_1$. We also give an extension of the main result to the case of a more general elliptic eigenvalue problem on a bounded domain $Omega$ with Dirichlet boundary conditions.

On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation

KAUST Repository

Wang, Y.; Sun, S.; Yu, B.

2013-01-01

A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy's law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.

Inverse scattering scheme for the Dirac equation at fixed energy

International Nuclear Information System (INIS)

Leeb, H.; Lehninger, H.; Schilder, C.

2001-01-01

Full text: Based on the concept of generalized transformation operators a new hierarchy of Dirac equations with spherical symmetric scalar and fourth component vector potentials is presented. Within this hierarchy closed form expressions for the solutions, the potentials and the S-matrix can be given in terms of solutions of the original Dirac equation. Using these transformations an inverse scattering scheme has been constructed for the Dirac equation which is the analog to the rational scheme in the non-relativistic case. The given method provides for the first time an inversion scheme with closed form expressions for the S-matrix for non-relativistic scattering problems with central and spin-orbit potentials. (author)

Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

International Nuclear Information System (INIS)

Litvinets, F N; Shapovalov, A V; Trifonov, A Yu

2007-01-01

A countable set of asymptotic space-localized solutions is constructed for a 3D Hartree-type equation with a quadratic potential by the complex germ method in the adiabatic approximation. The asymptotic parameter is 1/T, where T >> 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schroedinger equation is formulated for the Hartree-type equation. For the solutions constructed, the Berry phases are found in an explicit form

Equation of state of asymmetric nuclear matter using re-projected nucleon–nucleon potentials

Science.gov (United States)

Asadi Aghbolaghi, Z.; Bigdeli, M.

2018-06-01

In this paper, we have calculated the equation of state of asymmetric nuclear matter using the lowest order constrained variational approach and Argonne family potentials with and without three-nucleon interaction (TNI) contribution. In particular, we have used the AV18 potential and the re-projected potentials, AV8‧, and AV6‧. We have also calculated the saturation properties of symmetric nuclear matter, and the nuclear symmetry energy using AV18+TNI, AV8‧+TNI and AV6‧+TNI potentials. The inclusion of TNI has modified the agreement with experiment. We have also made a comparison between our results and those of other many-body calculations.

Euler-Lagrange Equations of Networks with Higher-Order Elements

Directory of Open Access Journals (Sweden)

Z. Biolek

2017-06-01

Full Text Available The paper suggests a generalization of the classic Euler-Lagrange equation for circuits compounded of arbitrary elements from Chua’s periodic table. Newly defined potential functions for general (α, β elements are used for the construction of generalized Lagrangians and generalized dissipative functions. Also procedures of drawing the Euler-Lagrange equations are demonstrated.

Remarks on a Class of Nonlinear Schrödinger Equations with Potential Vanishing at Infinity

Directory of Open Access Journals (Sweden)

Hongbo Zhu

2013-01-01

Full Text Available We study the following nonlinear Schrödinger equation −Δu+V(xu=K(xf(u,  x∈ℝN,  u∈H1(ℝN, where the potential V(x vanishes at infinity. Working in weighted Sobolev space, we obtain the ground states of problem ( under a Nahari type condition. Furthermore, if V(x,K(x are radically symmetric with respect to x∈ℝN, it is shown that problem ( has a positive solution with some more general growth conditions of the nonlinearity. Particularly, if f(u=up, then the growth restriction σ≤p≤N+2/N-2 in Ambrosetti et al. (2005 can be relaxed to σ~≤p≤N+2/N-2, where σ~<σ if 0<β<α<2.

On separable Pauli equations

International Nuclear Information System (INIS)

Zhalij, Alexander

2002-01-01

We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

Semiclassical Klein-Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential

International Nuclear Information System (INIS)

Coffey, W T; Kalmykov, Yu P; Titov, S V; Mulligan, B P

2007-01-01

The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(ℎ 4 ) and in the classical limit, ℎ → 0, reduces to the Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived. (fast track communication)

Solution of Full Wave Equation for Global Modes in Small Aspect Ratio Tokamaks with Non-Circular Cross-Section

International Nuclear Information System (INIS)

Burma, C.; Cuperman, S.; Komoshvili, K.

1998-01-01

The wave equation for strongly toroidal small aspect ratio (spherical) tokamaks with non-circular cross-section is properly formulated and solved for global waves, in the Alfven frequency range. The current-carrying toroidal plasma is surrounded by a helical sheet-current antenna, which is enclosed within a perfectly conducting wall. The problem is formulated in terms of the vector and scalar potentials (A,Φ), thus avoiding the numerical solution occurring in the case of (E,B) formulation. Adequate boundary conditions are applied at the vacuum - metallic wall interface and the magnetic axis. A recently derived dielectric tensor-operator, able to describe the anisotropic plasma response in spherical tokamaks, is used for this purpose; except for its linear character, no physical or geometrical limitations are imposed on it. The equilibrium profiles (magnetic field, pressure and current) are obtained from a numerical solution of the Grad-Shafranov equation. Specifically, the wave equation is solved by the aid of a numerical code we developed for the present problem, based on the well documented 2(1/2)D finite element solver proposed by E.G. Sewell. With the definitions V i (θ,ρ) = U i (-θ,ρ) (V i U i = A j , Φ; j = ρ,φ,θ), our code solves simultaneously 16 second order partial differential equations (eight equations for each of real and imaginary set of functions V i , U i ). A systematic analysis of the solutions obtained for various values and combinations of wavenumbers and frequencies in the Alfven range is presented

Impact of wall potential on the fluid-wall interaction in a cylindrical capillary and a generalized Kelvin equation

International Nuclear Information System (INIS)

Jakubov, T.S.; Mainwaring, D.E.

2006-01-01

In the present work a generalized Kelvin equation for a fluid confined in thick-walled cylindrical capillary is developed. This has been accomplished by including the potential energy function for interaction between a solid wall of a capillary and a confined fluid into the Kelvin equation. Using the Lennard-Jones 12-6 potential, an explicit form of the potential energy functions as expressed by hypergeometrical functions have been derived-firstly, for the interaction between a solid wall and a test atom placed at an arbitrary point in a long open-end capillary, and thereafter for the body-body interaction between the solid wall and a confined Lennard-Jones fluid. Further, this generalized Kelvin equation has been applied to detailed description hysteresis phenomena in such capillaries. All numerical calculations have been carried out for the model argon-graphite system at 90 K

Relativistic energy eigenvalues for the Dirac equation in the presence of vector and scalar potentials via the simple similarity transformation

International Nuclear Information System (INIS)

Barakat, T

2012-01-01

Based on the simple similarity transformation, we were able to transform the Dirac equation whose potential contains vector V (r) = -A/r + B 1 r and scalar S(r) = B 2 r types into a form nearly identical to the Schrödinger equation. The transformed equation is so simple that one can solve it by means of the asymptotic iteration method. Moreover, within the same framework we were able to obtain the relativistic energy eigenvalues for the Dirac equation with vector Coulomb plus scalar linear, and with pure scalar linear potentials; V (r) = -A/r, S(r) = B 2 r, and V (r) = 0, S(r) = B 2 r, respectively.

On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation

KAUST Repository

Wang, Y.

2013-01-01

A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy\\'s law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.

Current-Voltage and Floating-Potential characteristics of cylindrical emissive probes from a full-kinetic model based on the orbital motion theory

Science.gov (United States)

Chen, Xin; Sánchez-Arriaga, Gonzalo

2018-02-01

To model the sheath structure around an emissive probe with cylindrical geometry, the Orbital-Motion theory takes advantage of three conserved quantities (distribution function, transverse energy, and angular momentum) to transform the stationary Vlasov-Poisson system into a single integro-differential equation. For a stationary collisionless unmagnetized plasma, this equation describes self-consistently the probe characteristics. By solving such an equation numerically, parametric analyses for the current-voltage (IV) and floating-potential (FP) characteristics can be performed, which show that: (a) for strong emission, the space-charge effects increase with probe radius; (b) the probe can float at a positive potential relative to the plasma; (c) a smaller probe radius is preferred for the FP method to determine the plasma potential; (d) the work function of the emitting material and the plasma-ion properties do not influence the reliability of the floating-potential method. Analytical analysis demonstrates that the inflection point of an IV curve for non-emitting probes occurs at the plasma potential. The flat potential is not a self-consistent solution for emissive probes.

Potential pathways by which maternal second-hand smoke exposure during pregnancy causes full-term low birth weight.

Science.gov (United States)

Niu, Zhongzheng; Xie, Chuanbo; Wen, Xiaozhong; Tian, Fuying; Yuan, Shixin; Jia, Deqin; Chen, Wei-Qing

2016-04-29

It is well documented that maternal exposure to second-hand smoke (SHS) during pregnancy causes low birth weight (LBW), but its mechanism remains unknown. This study explored the potential pathways. We enrolled 195 pregnant women who delivered full-term LBW newborns, and 195 who delivered full-term normal birth weight newborns as the controls. After controlling for maternal age, education level, family income, pre-pregnant body mass index, newborn gender and gestational age, logistic regression analysis revealed that LBW was significantly and positively associated with maternal exposure to SHS during pregnancy, lower placental weight, TNF-α and IL-1β, and that SHS exposure was significantly associated with lower placental weight, TNF-α and IL-1β. Structural equation modelling identified two plausible pathways by which maternal exposure to SHS during pregnancy might cause LBW. First, SHS exposure induced the elevation of TNF-α, which might directly increase the risk of LBW by transmission across the placenta. Second, SHS exposure first increased maternal secretion of IL-1β and TNF-α, which then triggered the secretion of VCAM-1; both TNF-α and VCAM-1 were significantly associated with lower placental weight, thus increasing the risk of LBW. In conclusion, maternal exposure to SHS during pregnancy may lead to LBW through the potential pathways of maternal inflammation and lower placental weight.

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Science.gov (United States)

Guarnieri, F.; Moon, W.; Wettlaufer, J. S.

2017-09-01

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with a negative constant drift, described by a Fokker-Planck equation with a potential V (x ) =-[b ln(x ) +a x ] , for b >0 and a finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schrödinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a constant negative drift. We conclude with a comparison to other analytical methods and with numerical solutions.

Arbitrary l-wave solutions of the Schroedinger equation for the screen Coulomb potential

International Nuclear Information System (INIS)

Dong, Shishan; Sun, Guohua; Dong, Shihai

2013-01-01

Using improved approximate schemes for centrifugal term and the singular factor 1/r appearing in potential itself, we solve the Schroedinger equation with the screen Coulomb potential for arbitrary angular momentum state l. The bound state energy levels are obtained. A closed form of normalization constant of the wave functions is also found. The numerical results show that our results are in good agreement with those obtained by other methods. The key issue is how to treat two singular points in this quantum system. (author)

Analysis of D Dimensional Dirac equation for q -deformed Posch-Teller combined with q -deformed trigonometric Manning Rosen Non-Central potential using Asymptotic Iteration Method (AIM)

International Nuclear Information System (INIS)

Alam, Y.; Suparmi; Cari; Anwar, F.

2016-01-01

In this study, we used asymptotic iteration method (AIM) to obtain the relativistic energy spectra and wavefunctions for D Dimensional Dirac equation. Solution of the D Dimensional Dirac equation using asymptotic iteration method was done by four steps. The first step, we substitutied q deformed Poschl-Teller potential plus q-deformed Manning Rosen Non-Central potential into D dimensional Dirac equation. And then, general term of D dimensioanl Dirac equation for q deformed Poschl-Teller potential plus q-deformed Manning Rosen Non-Central potential was reduced into one dimensioanal Dirac equation, consist of radial part and angular part. The second step, both of one dimensional part must be reduced to hypergeometric type differential equation by suitable parameter change. And then, hypergeometric type differential equation was transformed into AIM type differential equation. For the last step, AIM type differential equation can be solved to obtain the relativistic energy and wavefunctions of Dirac equation. Relativistic energy and wavefunctions were visualized by using Matlab software. (paper)

Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft

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Yuma Fukushima

2015-01-01

Full Text Available The linearized Euler equations (LEEs solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.

Supersymmetric Solution of the Schroedinger Equation for Woods-Saxon Potential by Using the Pekeris Approximation

International Nuclear Information System (INIS)

Feizi, H.; Rajabi, A.A.; Shojaei, M.R.

2011-01-01

In this work, the three dimensional Woods-Saxon potential is studied within the context of Supersymmetry Quantum Mechanics. We have applied the SUSY method by using the Pekeris approximation to the centrifugal potential l ≠ 0 states. By application of this method, it is possible to solve the Schroedinger equation for this potential. We obtain exactly bound state spectrum and wave function of Woods-Saxon potential for nonzero angular momentum. Hamiltonian hierarchy method and the shape invariance property are used in the calculations. (authors)

Self-consistent field theory of collisions: Orbital equations with asymptotic sources and self-averaged potentials

Energy Technology Data Exchange (ETDEWEB)

Hahn, Y.K., E-mail: ykhahn22@verizon.net

2014-12-15

The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model. - Highlights: • First extension of HF to scattering states, with proper asymptotic conditions. • Orbital equations with asymptotic sources and integrable orbital solutions. • Construction of self-averaged potentials, and orbital energy fixing. • Channel coupling and configuration mixing, involving the new orbitals. • Critical evaluation of the

Particle resonance in the Dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential

International Nuclear Information System (INIS)

Villalba, Victor M.; Gonzalez-Diaz, Luis A.

2009-01-01

We show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing weak electric field associated with a hyperbolic tangent potential. We solve the Dirac equation in terms of Gauss hyper-geometric functions and show explicitly how the resonant behavior depends on the strength of the electric field evaluated at the support of the point interaction. We derive an approximate expression for the value of the resonances and compare the results calculated for the hyperbolic potential with those obtained for a linear perturbative potential. Finally, we characterize the resonances with the help of the phase shift and the Wigner delay time. (orig.)

Solutions of the Dirac Equation with the Shifted DENG-FAN Potential Including Yukawa-Like Tensor Interaction

Science.gov (United States)

Yahya, W. A.; Falaye, B. J.; Oluwadare, O. J.; Oyewumi, K. J.

2013-08-01

By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schr\\"{o}dinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.

Bound state solution of Dirac equation for Hulthen plus trigonometric Rosen Morse non-central potential using Romanovski polynomial

Energy Technology Data Exchange (ETDEWEB)

Suparmi, A., E-mail: suparmiuns@gmail.com; Cari, C., E-mail: suparmiuns@gmail.com [Physics Department, Post Graduate Study, Sebelas Maret University (Indonesia); Angraini, L. M. [Physics Department, Mataram University (Indonesia)

2014-09-30

The bound state solutions of Dirac equation for Hulthen and trigonometric Rosen Morse non-central potential are obtained using finite Romanovski polynomials. The approximate relativistic energy spectrum and the radial wave functions which are given in terms of Romanovski polynomials are obtained from solution of radial Dirac equation. The angular wave functions and the orbital quantum number are found from angular Dirac equation solution. In non-relativistic limit, the relativistic energy spectrum reduces into non-relativistic energy.

Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

Science.gov (United States)

Wang, D.

2017-12-01

The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

Simple equation method for nonlinear partial differential equations and its applications

Directory of Open Access Journals (Sweden)

Taher A. Nofal

2016-04-01

Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.

equate: An R Package for Observed-Score Linking and Equating

Directory of Open Access Journals (Sweden)

Anthony D. Albano

2016-10-01

Full Text Available The R package equate contains functions for observed-score linking and equating under single-group, equivalent-groups, and nonequivalent-groups with anchor test(s designs. This paper introduces these designs and provides an overview of observed-score equating with details about each of the supported methods. Examples demonstrate the basic functionality of the equate package.

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials.

Science.gov (United States)

Chen, Yong; Yan, Zhenya

2016-03-22

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.

Bound state solution of Dirac equation for 3D harmonics oscillator plus trigonometric scarf noncentral potential using SUSY QM approach

Energy Technology Data Exchange (ETDEWEB)

Cari, C., E-mail: carinln@yahoo.com; Suparmi, A., E-mail: carinln@yahoo.com [Physics Department, Sebelas Maret University, Jl. Ir. Sutami no 36A Kentingan Surakarta 57126 (Indonesia)

2014-09-30

Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.

Examining Potential Boundary Bias Effects in Kernel Smoothing on Equating: An Introduction for the Adaptive and Epanechnikov Kernels.

Science.gov (United States)

Cid, Jaime A; von Davier, Alina A

2015-05-01

Test equating is a method of making the test scores from different test forms of the same assessment comparable. In the equating process, an important step involves continuizing the discrete score distributions. In traditional observed-score equating, this step is achieved using linear interpolation (or an unscaled uniform kernel). In the kernel equating (KE) process, this continuization process involves Gaussian kernel smoothing. It has been suggested that the choice of bandwidth in kernel smoothing controls the trade-off between variance and bias. In the literature on estimating density functions using kernels, it has also been suggested that the weight of the kernel depends on the sample size, and therefore, the resulting continuous distribution exhibits bias at the endpoints, where the samples are usually smaller. The purpose of this article is (a) to explore the potential effects of atypical scores (spikes) at the extreme ends (high and low) on the KE method in distributions with different degrees of asymmetry using the randomly equivalent groups equating design (Study I), and (b) to introduce the Epanechnikov and adaptive kernels as potential alternative approaches to reducing boundary bias in smoothing (Study II). The beta-binomial model is used to simulate observed scores reflecting a range of different skewed shapes.

Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials

Science.gov (United States)

Cameron, Stephen; Silvestre, Luis; Snelson, Stanley

2018-05-01

We establish a priori upper bounds for solutions to the spatially inhomogeneous Landau equation in the case of moderately soft potentials, with arbitrary initial data, under the assumption that mass, energy and entropy densities stay under control. Our pointwise estimates decay polynomially in the velocity variable. We also show that if the initial data satisfies a Gaussian upper bound, this bound is propagated for all positive times.

On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

Directory of Open Access Journals (Sweden)

Nikolai N. Bogoliubov (Jr.

2007-01-01

Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

Mathematical analysis of the dimensional scaling technique for the Schroedinger equation with power-law potentials

International Nuclear Information System (INIS)

Ding Zhonghai; Chen, Goong; Lin, Chang-Shou

2010-01-01

The dimensional scaling (D-scaling) technique is an innovative asymptotic expansion approach to study the multiparticle systems in molecular quantum mechanics. It enables the calculation of ground and excited state energies of quantum systems without having to solve the Schroedinger equation. In this paper, we present a mathematical analysis of the D-scaling technique for the Schroedinger equation with power-law potentials. By casting the D-scaling technique in an appropriate variational setting and studying the corresponding minimization problem, the D-scaling technique is justified rigorously. A new asymptotic dimensional expansion scheme is introduced to compute asymptotic expansions for ground state energies.

Solution of Schrodinger equation for Three Dimensional Harmonics Oscillator plus Rosen-Morse Non-central potential using NU Method and Romanovski Polynomials

International Nuclear Information System (INIS)

Cari, C; Suparmi, A

2013-01-01

The energy eigenvalues and eigenfunctions of Schrodinger equation for three dimensional harmonic oscillator potential plus Rosen-Morse non-central potential are investigated using NU method and Romanovski polynomial. The bound state energy eigenvalues are given in a closed form and corresponding radial wave functions are expressed in associated Laguerre polynomials while angular eigen functions are given in terms of Romanovski polynomials. The Rosen-Morse potential is considered to be a perturbation factor to the three dimensional harmonic oscillator potential that causes the increase of radial wave function amplitude and decrease of angular momentum length. Keywords: Schrodinger Equation, Three dimensional Harmonic Oscillator potential, Rosen-morse non-central potential, NU method, Romanovski Polynomials

Scattering state solutions of the Duffin-Kemmer-Petiau equation with the Varshni potential model

Energy Technology Data Exchange (ETDEWEB)

Oluwadare, O.J. [Federal University Oye-Ekiti, Department of Physics, Oye-Ekiti, Ekiti State (Nigeria); Oyewumi, K.J. [Federal University of Technology, Department of Physics, Minna, Niger State (Nigeria)

2017-02-15

The scattering state of the Duffin-Kemmer-Petiau equation with the Varshni potential was studied. The asymptotic wave function, the scattering phase shift and normalization constant were obtained for any J states by dealing with the centrifugal term using a suitable approximation. The analytical properties of the scattering amplitude and the bound state energy were obtained and discussed. Our numerical and graphical results indicate that the scattering phase shift depends largely on total angular momentum J, screening parameter β and potential strengths a and b. (orig.)

equateIRT: An R Package for IRT Test Equating

Directory of Open Access Journals (Sweden)

Michela Battauz

2015-12-01

Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

Science.gov (United States)

Yuan, Na

2018-04-01

With the aid of the symbolic computation, we present an improved ( G ‧ / G ) -expansion method, which can be applied to seek more types of exact solutions for certain nonlinear evolution equations. In illustration, we choose the (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation to demonstrate the validity and advantages of the method. As a result, abundant explicit and exact nontraveling wave solutions are obtained including two solitary waves solutions, nontraveling wave solutions and dromion soliton solutions. Some particular localized excitations and the interactions between two solitary waves are researched. The method can be also applied to other nonlinear partial differential equations.

Solution of the two- dimensional heat equation for a rectangular plate

Directory of Open Access Journals (Sweden)

Nurcan BAYKUŞ SAVAŞANERİL

2015-11-01

Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.

Integral equation for Coulomb problem

International Nuclear Information System (INIS)

Sasakawa, T.

1986-01-01

For short range potentials an inhomogeneous (homogeneous) Lippmann-Schwinger integral equation of the Fredholm type yields the wave function of scattering (bound) state. For the Coulomb potential, this statement is no more valid. It has been felt difficult to express the Coulomb wave function in a form of an integral equation with the Coulomb potential as the perturbation. In the present paper, the author shows that an inhomogeneous integral equation of a Volterra type with the Coulomb potential as the perturbation can be constructed both for the scattering and the bound states. The equation yielding the binding energy is given in an integral form. The present treatment is easily extended to the coupled Coulomb problems

Quantum Potential and Symmetries in Extended Phase Space

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Sadollah Nasiri

2006-06-01

Full Text Available The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space representation followed by the generalization of this concept to extended phase space. It is shown that there exists an extended canonical transformation that removes the expression for the quantum potential in the dynamical equation. The situation, mathematically, is similar to disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates that changes the physical potential to an effective one. The representation where the quantum potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form, is one in which the dynamical equation turns out to be the Wigner equation.

Study of the 3D Euler equations using Clebsch potentials: dual mechanisms for geometric depletion

Science.gov (United States)

Ohkitani, Koji

2018-02-01

After surveying analyses of the 3D Euler equations using the Clebsch potentials scattered over the literature, we report some preliminary new results. 1. Assuming that flow fields are free from nulls of the impulse and the vorticity fields, we study how constraints imposed by the Clebsch potentials lead to a degenerate geometrical structure, typically in the form of depletion of nonlinearity. We consider a vorticity surface spanned by \\boldsymbol ω and another material vector \\boldsymbol {W} such that \\boldsymbol γ=\\boldsymbol ω× \\boldsymbol {W}, where \\boldsymbol γ is the impulse variable in geometric gauge. We identify dual mechanism for geometric depletion and show that at least of one them is acting if \\boldsymbol {W} does not develop a null. This suggests that formation of singularity in flows endowed with Clebsch potentials is less likely to happen than in more general flows. Some arguments are given towards exclusion of ‘type I’ blowup. A mathematical challenge remains to rule out singularity formation for flows which have Clebsch potentials everywhere. 2. We exploit classical differential geometry kinematically to write down the Gauss-Weingarten equations for the vorticity surface of the Clebsch potential in terms of fluid dynamical variables, as are the first, second and third fundamental forms. In particular, we derive a constraint on the size of the Gaussian curvature near the point of a possible singularity. On the other hand, an application of the Gauss-Bonnet theorem reveals that the tangential curvature of the surface becomes large in the neighborhood of near-singularity. 3. Using spatially-periodic flows with highly-symmetry, i.e. initial conditions of the Taylor-Green vortex and the Kida-Pelz flow, we present explicit formulas of the Clebsch potentials with exceptional singular surfaces where the Clebsch potentials are undefined. This is done by connecting the known expressions with the solenoidal impulse variable (i.e. the

Prolongation Loop Algebras for a Solitonic System of Equations

Directory of Open Access Journals (Sweden)

Maria A. Agrotis

2006-11-01

Full Text Available We consider an integrable system of reduced Maxwell-Bloch equations that describes the evolution of an electromagnetic field in a two-level medium that is inhomogeneously broadened. We prove that the relevant Bäcklund transformation preserves the reality of the n-soliton potentials and establish their pole structure with respect to the broadening parameter. The natural phase space of the model is embedded in an infinite dimensional loop algebra. The dynamical equations of the model are associated to an infinite family of higher order Hamiltonian systems that are in involution. We present the Hamiltonian functions and the Poisson brackets between the extended potentials.

Bound states of the Dirac equation with some physical potentials by the Nikiforov-Uvarov method

Energy Technology Data Exchange (ETDEWEB)

Setare, Mohammad R; Haidari, S [Department of Physics, University of Kurdistan, Pasdaran Avenue, Sanandaj (Iran, Islamic Republic of)], E-mail: rezakord@ipm.ir, E-mail: heidary.somayeh@gmail.com

2010-01-15

Exact analytical solutions for the s-wave Dirac equation with the reflectionless-type, Rosen-Morse and Manning-Rosen potentials are obtained, under the condition of spin symmetry. We obtained bound state energy eigenvalues and corresponding spinor wave function in the framework of the Nikiforov-Uvarov (NU) method.

Averaged RMHD equations

International Nuclear Information System (INIS)

Ichiguchi, Katsuji

1998-01-01

A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Directory of Open Access Journals (Sweden)

Hamidreza Rezazadeh

2014-05-01

Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

Bethe-Salpeter equation for non-self conjugate mesons in a power-law potential

International Nuclear Information System (INIS)

Ikhdair, S.M.

1992-07-01

We develop an approach to the solution of the spinless Bethe-Salpeter equation for the different-mass case. Although the calculations are developed for spin-zero particles in any arbitrary spherically symmetric potential, the non-Coulombic effective power-law potential is used as a kernel to produce the spin-averaged bound states of the non-self-conjugate mesons. The analytical formulae are also applicable to the self-conjugate mesons in the equal-mass case. The flavor-independent case is investigated in this work. The calculations are carried out to the third-order correction of the energy series. Results are consistent with those obtained before. (author). 14 refs, 1 tab

On a model for baryons based on a Dirac equation with confining potentials

International Nuclear Information System (INIS)

Ferreira, P.L.

1977-06-01

An independent particle model for baryons is studied in which the quarks obey a Dirac equation with an average potential of the form V(r) = 1/2 (1 + β)(V 0 + lambda r - γ/r). A numerical solution is obtained for S-waves. Several properties of the 1/2 + baryons such as the ratio (G sub(A)/G sub(V)) sub (N) for nucleons and baryon magnetic moments are analysed in terms of the model. A comparison with the case of a pure linear potential and with a pure harmonic oscillator is made, showing that it is possible to obtain a better agreement with the data in the present case

A composite velocity procedure for the compressible Navier-Stokes equations

Science.gov (United States)

Khosla, P. K.; Rubin, S. G.

1982-01-01

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Analytical Solution of the Schrödinger Equation with Spatially Varying Effective Mass for Generalised Hylleraas Potential

International Nuclear Information System (INIS)

Debnath, S.; Maji, Smarajit; Meyur, Sanjib

2014-01-01

We have obtained exact solution of the effective mass Schrödinger equation for the generalised Hylleraas potential. The exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunctions are obtained in terms of the hypergeometric functions. Results are also given for the special case of potential parameter.

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

International Nuclear Information System (INIS)

Sirendaoreji

2006-01-01

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

Approximate Solutions to the Dirac Equation with Effective Mass for the Manning-Rosen Potential in N Dimensions

International Nuclear Information System (INIS)

Bahar, M.K.; Yasuk, F.

2012-01-01

The solutions of the effective mass Dirac equation for the Manning-Rosen potential with the centrifugal term are studied approximately in N dimension. The relativistic energy spectrum and two-component spinor eigenfunctions are obtained by the asymptotic iteration method. We have also investigated eigenvalues of the effective mass Dirac-Manning-Rosen problem for α = 0 or α = 1. In this case, the Manning-Rosen potential reduces to the Hulthen potential. (author)

Inversion transformation in the Schroedinger equation

International Nuclear Information System (INIS)

Demkov, Yu.N.; Semenova, N.V.

1984-01-01

Using the inversion with respect to a sphere in the coordinate space, the equivalence between the Schroedinger equations with different potentials is established. It is shown that the zero-energy equation for a spherically symmetric potential is equivalent to the equation with an axially symmetric potential of a special form. The particular exact solutions of the zero-energy problem for the motion of a particle in the field of two Maxwell ''fish-eye'' potentials and potentials with the two Coulomb singularities are found

The equation of state and ionization equilibrium of dense aluminum plasma with conductivity verification

International Nuclear Information System (INIS)

Wang, Kun; Shi, Zongqian; Shi, Yuanjie; Bai, Jun; Wu, Jian; Jia, Shenli

2015-01-01

The equation of state, ionization equilibrium, and conductivity are the most important parameters for investigation of dense plasma. The equation of state is calculated with the non-ideal effects taken into consideration. The electron chemical potential and pressure, which are commonly used thermodynamic quantities, are calculated by the non-ideal free energy and compared with results of a semi-empirical equation of state based on Thomas-Fermi-Kirzhnits model. The lowering of ionization potential, which is a crucial factor in the calculation of non-ideal Saha equation, is settled according to the non-ideal free energy. The full coupled non-ideal Saha equation is applied to describe the ionization equilibrium of dense plasma. The conductivity calculated by the Lee-More-Desjarlais model combined with non-ideal Saha equation is compared with experimental data. It provides a possible approach to verify the accuracy of the equation of state and ionization equilibrium

Ordinary differential equations

CERN Document Server

Greenberg, Michael D

2014-01-01

Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

An investigation of relativistic microscopic optical potential in terms of relativistic Brueckner-Bethe-Goldstone equation

International Nuclear Information System (INIS)

Chen Baoqiu; Ma Zhongyu

1992-01-01

Relativistic microscopic optical potential of nucleon-nucleus is derived from the relativistic Brueckner-Bethe-Goldstone (RBBG) equation. The complex effective mass of a nucleon is determined by a fit to 200 MeV p- 40 Ca scattering data. The relativistic microscopic optical potentials with this effective mass are obtained from RBBG for p- 16O , 40 Ca, 90 Zr and 208 Pb scattering in energy range from 160 to 800 MeV. The microscopic optical potential is used to study the proton- 40 Ca scattering problem at 200 MeV. The results, such as differential cross section, analyzing power and spin rotation function are compared with those calculated from phenomenological relativistic optical potential

Self-Similar Solutions of Variable-Coefficient Cubic-Quintic Nonlinear Schroedinger Equation with an External Potential

International Nuclear Information System (INIS)

Wu Hongyu; Fei Jinxi; Zheng Chunlong

2010-01-01

An improved homogeneous balance principle and an F-expansion technique are used to construct exact self-similar solutions to the cubic-quintic nonlinear Schroedinger equation. Such solutions exist under certain conditions, and impose constraints on the functions describing dispersion, nonlinearity, and the external potential. Some simple self-similar waves are presented. (general)

Transport of momentum in full f gyrokinetics

International Nuclear Information System (INIS)

Parra, Felix I.; Catto, Peter J.

2010-01-01

Full f electrostatic gyrokinetic formulations employ two gyrokinetic equations, one for ions and the other for electrons, and quasineutrality to obtain the ion and electron distribution functions and the electrostatic potential. We demonstrate with several examples that the long wavelength radial electric field obtained with full f approaches is extremely sensitive to errors in the ion and electron density since small deviations in density give rise to large, nonphysical deviations in the conservation of toroidal angular momentum. For typical tokamak values, a relative error of 10 -7 in the ion or electron densities is enough to obtain the incorrect toroidal rotation. Based on the insights gained with the examples considered, three simple tests to check transport of toroidal angular momentum in full f simulations are proposed.

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

Energy Technology Data Exchange (ETDEWEB)

Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com [Physics Department, Faculty of Mathematics and Science, Sebelas Maret University, Jl. Ir. Sutami 36A Kentingan Surakarta 57126 (Indonesia); Deta, U. A. [Physics Department, Faculty of Science and Mathematics Education and Teacher Training, Surabaya State University, Surabaya (Indonesia)

2016-02-08

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy. The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.

Introduction to partial differential equations

CERN Document Server

Greenspan, Donald

2000-01-01

Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

Analytic perturbation theory for screened Coulomb potential: full continuum wave function

International Nuclear Information System (INIS)

Bechler, A.; Ennan, Mc J.; Pratt, R.H.

1979-01-01

An analytic perturbation theory developed previously is used to find a continuum screened-Coulomb wave function characterized by definite asymptotic momentum. This wave function satisfies an inhomogeneous partial differential equation which is solved in parabolic coordinates; the solution depends on both parabolic variables. We calculate partial wave projections of this solution and show that we can choose to add a solution of the homogeneous equation such that the partial wave projections become equal to the normalized continuum radial function found previously. However, finding the unique solution with given asymptotic linear momentum will require either using boundary conditions to determine the unique needed solution of the homogeneous equation or equivalently specifying the screened-Coulomb phase-shifts. (author)

Quantization of Equations of Motion

Directory of Open Access Journals (Sweden)

D. Kochan

2007-01-01

Full Text Available The Classical Newton-Lagrange equations of motion represent the fundamental physical law of mechanics. Their traditional Lagrangian and/or Hamiltonian precursors when available are essential in the context of quantization. However, there are situations that lack Lagrangian and/or Hamiltonian settings. This paper discusses a description of classical dynamics and presents some irresponsible speculations about its quantization by introducing a certain canonical two-form ?. By its construction ? embodies kinetic energy and forces acting within the system (not their potential. A new type of variational principle employing differential two-form ? is introduced. Variation is performed over “umbilical surfaces“ instead of system histories. It provides correct Newton-Lagrange equations of motion. The quantization is inspired by the Feynman path integral approach. The quintessence is to rearrange it into an “umbilical world-sheet“ functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, the new approach reduces to the standard quantum mechanics. As an example, Quantum Mechanics with friction is analyzed in detail. 

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Directory of Open Access Journals (Sweden)

Vitanov Nikolay K.

2018-03-01

Full Text Available We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Integrable discretizations of the short pulse equation

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

2010-01-01

In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.

REALIZATION OF SCIENTIFIC AND EDUCATIONAL POTENTIAL OF TRAINING IN THE INVERSE PROBLEMSFOR THE DIFFERENTIAL EQUATIONS

Directory of Open Access Journals (Sweden)

В С Корнилов

2016-12-01

Full Text Available In article methodical aspects of training for the inverse problems for differential equations of students of higher education institutions of the physical and mathematical and natural-science directions of preparation are stated. The attention to expediency of development in students of scientific outlook allowing to acquire fundamental knowledge of methods and methodology of research of mathematical models of the inverse problems, to master the principles of the organization of theoretical and practical researches of the inverse problem, to create ideas of the inverse problems as universal tools of knowledge of world around is paid.In article attention that development of scientific outlook in training activity to the inverse problems for differential equations allows students to deep understanding of idea of integrity of the world, assimilation of disciplines of applied mathematics, disciplines from other data domains is paid. It is marked that in the course of such training in students lines of humanitarization take root. Students acquire skills to analyze the received solutions of the inverse problems for differential equations, to formulate logical outputs about an ecological status of air space, earth’s environment or the water environment, to apply results of solutions of the inverse problems for differential equations in the humanitarian analysis of applied researches.

Numerical solution of the potential problem by integral equations without Green's functions

International Nuclear Information System (INIS)

De Mey, G.

1977-01-01

An integral equation technique will be presented to solve Laplace's equation in a two-dimensional area S. The Green's function has been replaced by a particular solution of Laplace equation in order to establish the integral equation. It is shown that accurate results can be obtained provided the pivotal elimination method is used to solve the linear algebraic set

Numerical implementation and oceanographic application of the thermodynamic potentials of liquid water, water vapour, ice, seawater and humid air – Part 1: Background and equations

Directory of Open Access Journals (Sweden)

R. Feistel

2010-07-01

Full Text Available A new seawater standard referred to as the International Thermodynamic Equation of Seawater 2010 (TEOS-10 was adopted in June 2009 by UNESCO/IOC on its 25th General Assembly in Paris, as recommended by the SCOR/IAPSO Working Group 127 (WG127 on Thermodynamics and Equation of State of Seawater. To support the adoption process, WG127 has developed a comprehensive source code library for the thermodynamic properties of liquid water, water vapour, ice, seawater and humid air, referred to as the Sea-Ice-Air (SIA library. Here we present the background information and equations required for the determination of the properties of single phases and components as well as of phase transitions and composite systems as implemented in the library. All results are based on rigorous mathematical methods applied to the Primary Standards of the constituents, formulated as empirical thermodynamic potential functions and, except for humid air, endorsed as Releases of the International Association for the Properties of Water and Steam (IAPWS. Details of the implementation in the TEOS-10 SIA library are given in a companion paper.

Quaternionic potentials and CP-violation

International Nuclear Information System (INIS)

Nishi, Celso Chikahiro

2000-01-01

Full text follows: In the formulation of Quantum Mechanics by using a non-commutative ring of quaternions, we attempt to solve the Schroedinger equation with quaternionic potentials. Decay processes can easily be modeled by including complex imaginary potentials. Although, it could be explained as a transition between states under action of a perturbation. Purely imaginary quaternionic potentials can be used to describe CP-violation effects. The neutral kaon system, K 0 - K-bar 0 or K L - K S , represents an example of CP-violation phenomenon. The inclusion of quaternionic potentials imply a reformulation of the whole quantum theory. The use of a quaternionic algebra in discussing the Schroedinger equation leads to the lost of time reversal invariance (T), closely connected to CP violation by the well-known CPT theorem. In particular, we study the Schroedinger equation in presence of a quaternionic potential barrier given in terms of V, real potential acting in the region of width a, and jW, purely quaternionic potential acting in the region of width b. Different cases, |W|/V and b/a, are discussed in view of possible deviations of standard Quantum Mechanics. The complex linear Schroedinger equation is solved for stationary states. The explicit solution contains complex and quaternionic transmission/reflection coefficients. A wave packet treatment needs to make a more realistic and physical description. We briefly discuss possible interpretations and remaining questions. (author)

A new formulation of equations of compressible fluids by analogy with Maxwell's equations

International Nuclear Information System (INIS)

Kambe, Tsutomu

2010-01-01

A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.

About potential of double layer and boundary value problems for Laplace equation

International Nuclear Information System (INIS)

Aleshin, M.V.

1991-01-01

An integral operator raisen by a kernel of the double layer's potential is investigated. The kernel is defined on S (S - two-digit variety of C 2 class presented by a boundary of the finite domain in R 3 ). The operator is considered on C(S). Following results are received: the operator's spectrum belongs to [-1,1]; it's eigenvalues and eigenfunctions may be found by Kellog's method; knowledge of the operator's spectrum is enough to construct it's resolvent. These properties permit to point out the determined interation processes, solving boundary value problems for Laplace equation. One of such processes - solving of Roben problem - is generalized on electrostatic problems. 6 refs

Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

DEFF Research Database (Denmark)

Guo, Hairun; Zeng, Xianglong; Zhou, Binbin

2013-01-01

We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

Moving potential for Dirac and Klein–Gordon equations

Indian Academy of Sciences (India)

and according to our knowledge the mathematical treatment of relativistic ..... the equation with step + Coulomb is soluble in principle, the time-dependent term ... and A R Hibbs, Quantum mechanics and path integrals (McGraw Hill, New.

Scattering states of the Klein-Gordon equation with Coulomb-like scalar plus vector potentials in arbitrary dimension

International Nuclear Information System (INIS)

Chen Changyuan; Sun Dongsheng; Lu Falin

2004-01-01

Properties of scattering states of the Klein-Gordon equation with Coulomb-like scalar plus vector potentials are investigated in an arbitrary dimension. Exact results of normalized wave functions of scattering states in the 'k/2π scale' and formula of phase shifts are presented

The trajectory-coherent approximation and the system of moments for the Hartree type equation

Directory of Open Access Journals (Sweden)

V. V. Belov

2002-01-01

Full Text Available The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter ℏ (ℏ→0, are constructed with a power accuracy of O(ℏ N/2, where N is any natural number. In constructing the semiclassically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for centered moments is essentially used. The nonlinear superposition principle has been formulated for the class of semiclassically concentrated solutions of Hartree type equations. The results obtained are exemplified by a one-dimensional Hartree type equation with a Gaussian potential.

Nonlinear Dirac Equations

Directory of Open Access Journals (Sweden)

Wei Khim Ng

2009-02-01

Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

Generalized Freud's equation and level densities with polynomial potential

Science.gov (United States)

Boobna, Akshat; Ghosh, Saugata

2013-08-01

We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.

Exact solutions for the quintic nonlinear Schroedinger equation with time and space modulated nonlinearities and potentials

International Nuclear Information System (INIS)

Belmonte-Beitia, Juan; Calvo, Gabriel F.

2009-01-01

In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions

Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model

Directory of Open Access Journals (Sweden)

Nikola V. Georgiev

2003-01-01

Full Text Available An analytic time series in the form of numerical solution (in an appropriate finite time interval of the Hodgkin-Huxley current clamped (HHCC system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN type, having as a solution the given single component (action potential of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation and a specific modification of least squares method for identifying unknown coefficients are developed and applied.

The inverse problem for the one-dimensional Schroedinger equation with an energy-dependent potential. II

International Nuclear Information System (INIS)

Jaulent, M.; Jean, C.

1976-01-01

The one-dimensional Schroedinger equation y + ''+ ) 7k 2 -V + (k,x){y + =0, x belonging to R, was previously considered when the potential V + (k,x) depends on the energy k 2 in the following way: V + (k,x)=U(x)+2kQ(x), (U(x), Q(x)) belonging to a large class of pairs of real potentials admitting no bound state). The two systems of differential and integral equations then introduced are solved. Then, investigating the inverse scattering problem it is found that a necessary and sufficient condition for one of the functions S + (k) and Ssub(-1)sup(+)(k) to be the scattering matrix associated with a pair (U(x), Q(x)) is that S + (k) (or equivalently Ssub(-1)sup(+)(k) belongs to the class S introduced. This pair is the only one admitting this function as its scattering matrix. Investigating the inverse reflection problem, it is found that a necessary and sufficient condition for a function S 21 + (k) to be the reflection coefficient to the right associated with a pair (U(x), Q(x)) is that S 21 + (k) belongs to the class R introduced. This pair is the only one admitting this function as

Making full use of wind power potential in North America -- possibilities

Energy Technology Data Exchange (ETDEWEB)

Guillaud, Christian

2010-09-15

The anticipated increase in electrical load in North America up to the year 2050 will be at least 50%. Wind potential in North America is enormous, well in excess of the expected requirements. However, the amount of wind capacity, which can be directly connected to a grid is limited to 20% of the installed capacity because of technical constraints. Technologies to enable full wind potential to be harnessed still need to be developed; they will consist in storing wind energy in hydroelectric reservoirs or generating hydrogen. However, the resulting cost of electricity will be somewhat higher than present.

Generation of matter-wave solitons of the Gross-Pitaevskii equation with a time-dependent complicated potential

Energy Technology Data Exchange (ETDEWEB)

Mohamadou, Alidou [Condensed Matter Laboratory, Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala (Cameroon); Abdus Salam International Centre for Theoretical Physics, P.O. Box 538, Strada Costiera 11, I-34014 Trieste (Italy); Wamba, Etienne; Kofane, Timoleon C. [Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon); Doka, Serge Y. [Higher Teacher Training College, University of Maroua, P.O. Box 55, Maroua (Cameroon); Ekogo, Thierry B. [Departement de Physique, Universite des Sciences et Techniques de Masuku, B.P. 943, Franceville (Gabonese Republic)

2011-08-15

We examine the generation of bright matter-wave solitons in the Gross-Pitaevskii equation describing Bose-Einstein condensates with a time-dependent complex potential, which is composed of a repulsive parabolic background potential and a gravitational field. By performing a modified lens-type transformation, an explicit expression for the growth rate of a purely growing modulational instability is presented and analyzed. We point out the effects of the gravitational field, as well as of the parameter related to the feeding or loss of atoms in the condensate, on the instability growth rate. It is evident from numerical simulations that the feeding with atoms and the magnetic trap have opposite effects on the dynamics of the system. It is shown that the feeding or loss parameter can be well used to control the instability domain. Our study shows that the gravitational field changes the condensate trail of the soliton trains during the propagation. We also perform a numerical analysis to solve the Gross-Pitaevskii equation with a time-dependent complicated potential. The numerical results on the effect of both the gravitational field and the parameter of feeding or loss of atoms in the condensate agree well with predictions of the linear stability analysis. Another result of the present work is the modification of the background wave function in the Thomas-Fermi approximation during the numerical simulations.

Uncertain differential equations

CERN Document Server

Yao, Kai

2016-01-01

This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

Retarded potentials and time domain boundary integral equations a road map

CERN Document Server

Sayas, Francisco-Javier

2016-01-01

This book offers a thorough and self-contained exposition of the mathematics of time-domain boundary integral equations associated to the wave equation, including applications to scattering of acoustic and elastic waves. The book offers two different approaches for the analysis of these integral equations, including a systematic treatment of their numerical discretization using Galerkin (Boundary Element) methods in the space variables and Convolution Quadrature in the time variable. The first approach follows classical work started in the late eighties, based on Laplace transforms estimates. This approach has been refined and made more accessible by tailoring the necessary mathematical tools, avoiding an excess of generality. A second approach contains a novel point of view that the author and some of his collaborators have been developing in recent years, using the semigroup theory of evolution equations to obtain improved results. The extension to electromagnetic waves is explained in one of the appendices...

On the Potential of Full Duplex Communication in 5G Small Cell Networks

DEFF Research Database (Denmark)

Mahmood, Nurul Huda; Berardinelli, Gilberto; Tavares, Fernando Menezes Leitão

2015-01-01

, the potential throughput gain may not be 100% as promised. In this study, we evaluate the performance of full duplex communication in a dense small cell scenario as targeted by future 5th Generation (5G) radio access technology under the ideal assumptions of a full buffer, always active traffic model...

New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

International Nuclear Information System (INIS)

Chen Huaitang; Zhang Hongqing

2004-01-01

A generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. More new multiple soliton solutions are obtained for the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

The generalized effective potential and its equations of motion

International Nuclear Information System (INIS)

Ananikyan, N.S.; Savvidy, G.K.

1980-01-01

By means ot the Legendre transformations a functional GITA(PHI, G, S) is constructed which depends on PHI -a possible expectation value of the quantum field, G -a possible expectation value of the 2-point connected Green function and S= - a possible expectation value of the classical action. The motion equations for the functional GITA are derived on the example of the gPHI 3 theory and an iteration technique is suggested to solve them. A basic equation for GITA which is solved by means of iteration techniques is an ordinary and not a variation one, as it is the case at usual Legendre transformations. The developed formalism can be easily generalized as to other theories

Exact solutions of the Schrodinger equation with the position-dependent mass for a hard-core potential

International Nuclear Information System (INIS)

Dong Shihai; Lozada-Cassou, M.

2005-01-01

The exact solutions of two-dimensional Schrodinger equation with the position-dependent mass for a hard-core potential are obtained. The eigenvalues related to the position-dependent masses μ 1 and μ 2 , the potential well depth V 0 and the effective range r 0 can be calculated by the boundary condition. We generalize this quantum system to three-dimensional case. The special cases for l=0,1 are studied in detail. For l=0 and c=0, we find that the energy levels will increase with the parameters μ 2 , V 0 and r 0 if μ 1 >μ 2

Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation

Directory of Open Access Journals (Sweden)

Mostafa M.A. Khater

Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions

Combined Helmholtz Integral Equation - Fourier series formulation of acoustical radiation and scattering problems

CSIR Research Space (South Africa)

Fedotov, I

2006-07-01

Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...

True amplitude wave equation migration arising from true amplitude one-way wave equations

Science.gov (United States)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

International Nuclear Information System (INIS)

Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

2014-01-01

By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained

Universal Critical Power for Nonlinear Schroedinger Equations with a Symmetric Double Well Potential

International Nuclear Information System (INIS)

Sacchetti, Andrea

2009-01-01

Here we consider stationary states for nonlinear Schroedinger equations in any spatial dimension n with symmetric double well potentials. These states may bifurcate as the strength of the nonlinear term increases and we observe two different pictures depending on the value of the nonlinearity power: a supercritical pitchfork bifurcation, and a subcritical pitchfork bifurcation with two asymmetric branches occurring as the result of saddle-node bifurcations. We show that in the semiclassical limit, or for a large barrier between the two wells, the first kind of bifurcation always occurs when the nonlinearity power is less than a critical value; in contrast, when the nonlinearity power is larger than such a critical value then we always observe the second scenario. The remarkable fact is that such a critical value is a universal constant in the sense that it does not depend on the shape of the double well potential and on the dimension n.

Master equations for degenerate systems: electron radiative cascade in a Coulomb potential

International Nuclear Information System (INIS)

Uskov, D B; Pratt, R H

2004-01-01

We examine the effects of degeneracy and its lifting for the problem of electron radiative cascade, described by master equations of the Lindblad form (quantum optical master equations). A weak external field approximation is used to study the resulting gradual transformation of cascade dynamics between degenerate and non-degenerate forms. Exploiting the spherical symmetry properties of the system we demonstrate significant difference between perturbations commuting with angular momentum and perturbations breaking the spherical symmetry, such as a homogeneous external field. We discuss the possibility and the general approach for reduction of the Lindblad master equations in the case of spectral degeneracy to the Pauli balance equations. This determines the appropriate choice of basis as, for example, spherical or parabolic

Some physical applications of fractional Schroedinger equation

International Nuclear Information System (INIS)

Guo Xiaoyi; Xu Mingyu

2006-01-01

The fractional Schroedinger equation is solved for a free particle and for an infinite square potential well. The fundamental solution of the Cauchy problem for a free particle, the energy levels and the normalized wave functions of a particle in a potential well are obtained. In the barrier penetration problem, the reflection coefficient and transmission coefficient of a particle from a rectangular potential wall is determined. In the quantum scattering problem, according to the fractional Schroedinger equation, the Green's function of the Lippmann-Schwinger integral equation is given

Bimolecular Master Equations for a Single and Multiple Potential Wells with Analytic Solutions.

Science.gov (United States)

Ghaderi, Nima

2018-04-12

The analytic solutions, that is, populations, are derived for the K-adiabatic and K-active bimolecular master equations, separately, for a single and multiple potential wells and reaction channels, where K is the component of the total angular momentum J along the axis of least moment of inertia of the recombination products at a given energy E. The analytic approach provides the functional dependence of the population of molecules on its K-active or K-adiabatic dissociation, association rate constants and the intermolecular energy transfer, where the approach may complement the usual numerical approaches for reactions of interest. Our previous work, Part I, considered the solutions for a single potential well, whereby an assumption utilized there is presently obviated in the derivation of the exact solutions and farther discussed. At the high-pressure limit, the K-adiabatic and K-active bimolecular master equations may each reduce, respectively, to the K-adiabatic and K-active bimolecular Rice-Ramsperger-Kassel-Marcus theory (high-pressure limit expressions) for bimolecular recombination rate constant, for a single potential well, and augmented by isomerization terms when multiple potential wells are present. In the low-pressure limit, the expression for population above the dissociation limit, associated with a single potential well, becomes equivalent to the usual presumed detailed balance between the association and dissociation rate constants, where the multiple well case is also considered. When the collision frequency of energy transfer, Z LJ , between the chemical intermediate and bath gas is sufficiently less than the dissociation rate constant k d ( E' J' K') for postcollision ( E' J' K), then the solution for population, g( EJK) + , above the critical energy further simplifies such that depending on Z LJ , the dissociation and association rate constant k r ( EJK), as g( EJK) + = k r ( EJK)A·BC/[ Z LJ + k d ( EJK)], where A and BC are the reactants, for

Dynamics of wide and snake-like pulses in coupled Schrödinger equations with full-modulated nonlinearities

Energy Technology Data Exchange (ETDEWEB)

Yomba, Emmanuel, E-mail: emmanuel.yomba@csun.edu; Zakeri, Gholam-Ali, E-mail: ali.zakeri@csun.edu

2016-02-05

We investigate the existence of various solitary wave solutions in coupled Schrödinger equations with specific cubic and quintic nonlinearities. This system arises in wave propagation in fiber optics with focusing and defocusing with modulated nonlinearities. We obtain front–front, bright–bright, dark–dark, and dark–bright like solitons using a direct approach, and then, by reducing the system of equations to a single auxiliary equation of a Duffing-type ordinary differential equation, we provide a large class of Jacobi-elliptic solutions. These solutions are presented in the exact form and analyzed. We find a class of wide localized and snake-like (in both space and time) vector solitons. One of the novel aspects of this study is that we have shown that the qualitative behavior of the solutions is independent of the choice of similarity variables. Numerical results show that the solutions of the above system are stable with up to 10% white noises. - Highlights: • Dynamics of wide and snake-like pulses is analyzed for coupled Schrödinger equations. • Qualitative appearance of solutions is analyzed using various similarity variables. • Effect of change in parameter-values on dynamics of the solutions is investigated. • Vectors front–front, bright–bright, dark–dark and dark–bright solitons are obtained.

Magnetopause boundary structure deduced from the high-time resolution particle experiment on the Equator-S spacecraft

Directory of Open Access Journals (Sweden)

G. K. Parks

1999-12-01

Full Text Available An electrostatic analyser (ESA onboard the Equator-S spacecraft operating in coordination with a potential control device (PCD has obtained the first accurate electron energy spectrum with energies ≈7 eV–100 eV in the vicinity of the magnetopause. On 8 January, 1998, a solar wind pressure increase pushed the magnetopause inward, leaving the Equator-S spacecraft in the magnetosheath. On the return into the magnetosphere approximately 80 min later, the magnetopause was observed by the ESA and the solid state telescopes (the SSTs detected electrons and ions with energies ≈20–300 keV. The high time resolution (3 s data from ESA and SST show the boundary region contains of multiple plasma sources that appear to evolve in space and time. We show that electrons with energies ≈7 eV–100 eV permeate the outer regions of the magnetosphere, from the magnetopause to ≈6Re. Pitch-angle distributions of ≈20–300 keV electrons show the electrons travel in both directions along the magnetic field with a peak at 90° indicating a trapped configuration. The IMF during this interval was dominated by Bx and By components with a small Bz.Key words. Magnetospheric physics (magnetopause · cusp · and boundary layers; magnetospheric configuration and dynamics; solar wind · magnetosphere interactions

Probabilistic delay differential equation modeling of event-related potentials.

Science.gov (United States)

Ostwald, Dirk; Starke, Ludger

2016-08-01

"Dynamic causal models" (DCMs) are a promising approach in the analysis of functional neuroimaging data due to their biophysical interpretability and their consolidation of functional-segregative and functional-integrative propositions. In this theoretical note we are concerned with the DCM framework for electroencephalographically recorded event-related potentials (ERP-DCM). Intuitively, ERP-DCM combines deterministic dynamical neural mass models with dipole-based EEG forward models to describe the event-related scalp potential time-series over the entire electrode space. Since its inception, ERP-DCM has been successfully employed to capture the neural underpinnings of a wide range of neurocognitive phenomena. However, in spite of its empirical popularity, the technical literature on ERP-DCM remains somewhat patchy. A number of previous communications have detailed certain aspects of the approach, but no unified and coherent documentation exists. With this technical note, we aim to close this gap and to increase the technical accessibility of ERP-DCM. Specifically, this note makes the following novel contributions: firstly, we provide a unified and coherent review of the mathematical machinery of the latent and forward models constituting ERP-DCM by formulating the approach as a probabilistic latent delay differential equation model. Secondly, we emphasize the probabilistic nature of the model and its variational Bayesian inversion scheme by explicitly deriving the variational free energy function in terms of both the likelihood expectation and variance parameters. Thirdly, we detail and validate the estimation of the model with a special focus on the explicit form of the variational free energy function and introduce a conventional nonlinear optimization scheme for its maximization. Finally, we identify and discuss a number of computational issues which may be addressed in the future development of the approach. Copyright © 2016 Elsevier Inc. All rights reserved.

Reduction of infinite dimensional equations

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Zhongding Li

2006-02-01

Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.

Nonlocal constitutive equations of elasto-visco-plasticity coupled with damage and temperature

Directory of Open Access Journals (Sweden)

Liu Weijie

2016-01-01

Full Text Available In this paper, the nonlocal anisothermal elasto-visco-plastic constitutive equations strongly coupled with ductile isotropic damage, nonlinear isotropic hardening and kinematic hardening are developed to model the material behaviour under finite strain. The new micromorphic variable of damage is introduced into the principle of virtual power and new additional balance equations are obtained. Thermodynamically-consistent nonlocal constitutive equations are then deduced. The evolution equations are deduced from the generalized normality rule for the Norton-Hoff visco-plastic potential. This model is used to simulate various material responses under different velocities at high temperature. The micromorphic parameters of damage: micromorphic density and H moduli are studied to examine the effects of micromorphic damage. Biaxial tension is performed to make a comparison between the local damage model and the micromorphic damage model.

Neutron optical potentials in unstable nuclei and the equation of state of asymmetric nuclear matter

International Nuclear Information System (INIS)

Oyamatsu, K.; Iida, K.

2003-01-01

Neutron single particle potential is one of the basic macroscopic properties to describe structure and reactions of nuclei in nuclear reactors and in the universe. However, the potential is quite uncertain for unstable nuclei primarily because the equation of state (EOS) of asymmetric nuclear matter is not known well. The present authors studied systematically the empirical EOS of asymmetric nuclear matter using a macroscopic nuclear model; about two hundred EOS's having empirically allowed values of L (symmetry energy density derivative coefficient) and K 0 (incompressibility) were obtained from the fittings to masses and radii of stable nuclei. It was suggested that the L value could be determined from global (Z, A) dependence of nuclear radii. In the present study, the single particle potential is examined assuming kinetic energies of non-interacting Fermi gases. The potential in a nucleus can be calculated easily, once the density distribution is solved using the effective nuclear interaction (EOS). Neutron and proton single particle potentials are calculated systematically for 80 Ni using the two hundred EOS's. It is found that the neutron-proton potential difference has clear and appreciable L dependence, while the potential for each species does not show such simple dependence on L. (author)

Darboux transformations and linear parabolic partial differential equations

International Nuclear Information System (INIS)

Arrigo, Daniel J.; Hickling, Fred

2002-01-01

Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n+1) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation. This matrix equation is solved using a generalized Hopf-Cole transformation. The solutions for the original equation are given in terms of solutions of the heat equation. These results are applied to the (1+1)-dimensional Schroedinger equation where all bound state solutions are obtained for a 2n-parameter family of potentials. As a special case, the solutions for integral members of the regular and modified Poeschl-Teller potentials are recovered. (author). Letter-to-the-editor

Mathematical and physical aspects of controlling the exact solutions of the 3D Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Fedele, Renato; Jovanovic, Dusan; De Nicola, Sergio; Eliasson, Bengt; Shukla, Padma K.

2010-01-01

The possibility of the decomposition of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schroedinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, it is possible to construct the exact controlled solutions of the 3D GPE from the solutions of a linear 2D Schroedinger equation coupled with a 1D nonlinear Schroedinger equation (the transverse and longitudinal components of the GPE, respectively). The coupling between these two equations is the functional of the transverse and the longitudinal profiles. The applied method of nonlinear decomposition, called the controlling potential method (CPM), yields the full 3D solution in the form of the product of the solutions of the transverse and longitudinal components of the GPE. It is shown that the CPM constitutes a variational principle and sets up a condition on the controlling potential well. Its physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control. The method is applied to the case of a parabolic external potential to construct analytically an exact BEC state in the form of a bright soliton, for which the quantitative comparison between the external and controlling potentials is presented.

Two particles interacting via the Yukawa potential in the frame of a truly nonrelativistic wave equation

International Nuclear Information System (INIS)

Kukhtin, V.V.; Kuzmenko, M.V.

2000-01-01

Complete text of publication follows. Recent studies (1) have shown that the Schroedinger nonrelativistic wave equation for a system of interacting particles is not a rigorously nonrelativistic one since it is based on the implicit assumption that the interaction propagation velocity is a finite value, which implies commutativity of the operators of coordinates and momenta of different particles. The refusal from this assumption implies their noncommutativity, which allows one to construct a truly nonrelativistic nonlinear self-consistent wave equation for a system of interacting particles. In the frame of the advanced wave equation, we investigate the spectrum of bound states for the two-body problem with the Yukawa potential V(r) = -V 0 a exp(-r/a)/r as a function of parameters of the potential. A peculiar feature of the spectrum is the presence of a critical value of V 0 (with the fixed parameter a), above which the given bound state cannot exist. In the ground state with l = 0 at a critical value of V 0 , the mean distance between particles takes the least value equal to the Compton wavelength of the particle with reduced mass. We estimate the parameter of noncommutativity ε for the operators of the coordinate of one particle and of the momentum of other one ([χ 1 , p 2x ] = i(h/2π)m 2 /M x ε) for the bound state of a deuteron, for which we consider the lowest state with l = 0 as its ground state. The parameter a of the Yukawa potential is taken to be equal to the Compton wavelength of a pion, 1.41 fm. In order to obtain the binding energy of a deuteron E = -2.22452 MeV, the parameter V 0 has to equal 51.23 MeV. In this case, the parameter of noncommutativity ε for the operators of the coordinate of one particle and of the momentum of other one ε = 0.0011, i.e., the commutator is nonzero even for such a weakly bound system as a deuteron where particles are located outside the region of action of nuclear forces for a significant fraction of time. Moreover

Generation of membrane potential beyond the conceptual range of Donnan theory and Goldman-Hodgkin-Katz equation.

Science.gov (United States)

Tamagawa, Hirohisa; Ikeda, Kota

2017-09-01

Donnan theory and Goldman-Hodgkin-Katz equation (GHK eq.) state that the nonzero membrane potential is generated by the asymmetric ion distribution between two solutions separated by a semipermeable membrane and/or by the continuous ion transport across the semipermeable membrane. However, there have been a number of reports of the membrane potential generation behaviors in conflict with those theories. The authors of this paper performed the experimental and theoretical investigation of membrane potential and found that (1) Donnan theory is valid only when the macroscopic electroneutrality is sufficed and (2) Potential behavior across a certain type of membrane appears to be inexplicable on the concept of GHK eq. Consequently, the authors derived a conclusion that the existing theories have some limitations for predicting the membrane potential behavior and we need to find a theory to overcome those limitations. The authors suggest that the ion adsorption theory named Ling's adsorption theory, which attributes the membrane potential generation to the mobile ion adsorption onto the adsorption sites, could overcome those problems.

Relations between nonlinear Riccati equations and other equations in fundamental physics

International Nuclear Information System (INIS)

Schuch, Dieter

2014-01-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown

ALTERNATIVE EQUATIONS FOR DYNAMIC BEHAVIOR OF IONIC CHANNEL ACTIVATION AND INACTIVATION GATES

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Mahmut ÖZER

2003-03-01

Full Text Available In this paper, alternative equations for dynamics of ionic channel activation and inactivation gates are proposed based on the path probability method. Dynamic behavior of a voltage-gated ionic channel is modeled by the conventional Hodgkin-Huxley (H-H mathematical formalism. In that model, conductance of the channel is defined in terms of activation and inactivation gates. Dynamics of the activation and inactivation gates is modeled by first-order differential equations dependent on the gate variable and the membrane potential. In the new approach proposed in this study, dynamic behavior of activation and inactivation gates is modeled by a firstorder differential equation dependent on internal energy and membrane potential by using the path probability method which is widely used in statistical physics. The new model doesn't require the time constant and steadystate values which are used explicitly in the H-H model. The numerical results show validity of the proposed method.

Analyses of pion-40Ca elastic scattering data using the Klein–Gordon equation

International Nuclear Information System (INIS)

Shehadeh, Z.F.

2009-01-01

The elastic scattering data for incident pion energies of 130, 163.3, 180, and 230 MeV on 40 Ca have been analyzed using the full Klein–Gordon equation (KGE), as opposed to its approximate form which renders it to the format of a Schroedinger equation with an energy-dependent potential (RSE). Calculated angular distributions, using KGE and RSE, for all four cases are nearly the same up to about 70° but differ significantly at larger angles. To fit the large-angle data of 163.3 MeV, the nature of the old potential determined by using RSE needs to be revised. The new potentials in four cases are presented and they are compatible with those determined from the inverse scattering theory at a fixed energy in the surface region. (author)

Gross-Pitaevskii equation for Bose particles in a double-well potential: Two-mode models and beyond

International Nuclear Information System (INIS)

Ananikian, D.; Bergeman, T.

2006-01-01

In this work, our primary goal has been to explore the range of validity of two-mode models for Bose-Einstein condensates in double-well potentials. Our derivation, like others, uses symmetric and antisymmetric condensate basis functions for the Gross-Pitaevskii equation. In what we call an 'improved two-mode model' (I2M), the tunneling coupling energy explicitly includes a nonlinear interaction term, which has been given previously in the literature but not widely appreciated. We show that when the atom number (and hence the extent of the wave function) in each well vary appreciably with time, the nonlinear interaction term produces a temporal change in the tunneling energy or rate, which has not previously been considered to our knowledge. In addition, we obtain a parameter, labeled ''interaction tunneling,'' that produces a decrease of the tunneling energy when the wave functions in the two wells overlap to some extent. Especially for larger values of the nonlinear interaction term, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in one and three dimensions, as compared with models that have no interaction term in the tunneling energy. The usefulness of this model is demonstrated by good agreement with recent experimental results for the tunneling oscillation frequency [Albiez et al., Phys. Rev. Lett. 95, 010402 (2005)]. We also present equations and results for a multimode approach, and use the I2M model to obtain modified equations for the second-quantized version of the Bose-Einstein double-well problem

Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method

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Ituen B. Okon

2017-01-01

Full Text Available We used a tool of conventional Nikiforov-Uvarov method to determine bound state solutions of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP. We obtained the energy eigenvalues and the total normalized wave function. We employed Hellmann-Feynman Theorem (HFT to compute expectation values r-2, r-1, T, and p2 for four different diatomic molecules: hydrogen molecule (H2, lithium hydride molecule (LiH, hydrogen chloride molecule (HCl, and carbon (II oxide molecule. The resulting energy equation reduces to three well-known potentials which are as follows: Hulthen potential, Yukawa potential, and inversely quadratic potential. The bound state energies for Hulthen and Yukawa potentials agree with the result reported in existing literature. We obtained the numerical bound state energies of the expectation values by implementing MATLAB algorithm using experimentally determined spectroscopic constant for the different diatomic molecules. We developed mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number.

An ordinary differential equation model for full thickness wounds and the effects of diabetes.

Science.gov (United States)

Bowden, L G; Maini, P K; Moulton, D E; Tang, J B; Wang, X T; Liu, P Y; Byrne, H M

2014-11-21

Wound healing is a complex process in which a sequence of interrelated phases contributes to a reduction in wound size. For diabetic patients, many of these processes are compromised, so that wound healing slows down. In this paper we present a simple ordinary differential equation model for wound healing in which attention focusses on the dominant processes that contribute to closure of a full thickness wound. Asymptotic analysis of the resulting model reveals that normal healing occurs in stages: the initial and rapid elastic recoil of the wound is followed by a longer proliferative phase during which growth in the dermis dominates healing. At longer times, fibroblasts exert contractile forces on the dermal tissue, the resulting tension stimulating further dermal tissue growth and enhancing wound closure. By fitting the model to experimental data we find that the major difference between normal and diabetic healing is a marked reduction in the rate of dermal tissue growth for diabetic patients. The model is used to estimate the breakdown of dermal healing into two processes: tissue growth and contraction, the proportions of which provide information about the quality of the healed wound. We show further that increasing dermal tissue growth in the diabetic wound produces closure times similar to those associated with normal healing and we discuss the clinical implications of this hypothesised treatment. Copyright © 2014 Elsevier Ltd. All rights reserved.

The generalized Airy diffusion equation

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Frank M. Cholewinski

2003-08-01

Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.

Exact solution of the Klein-Gordon equation for the PT-symmetric generalized Woods-Saxon potential by the Nikiforov-Uvarov method

International Nuclear Information System (INIS)

Ikhdair, S.M.; Sever, R.

2007-01-01

The exact solution of the one-dimensional Klein-Gordon equation of the PT-symmetric generalized Woods-Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s-states are also investigated for different types of complex generalized Woods-Saxon potentials. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

The magnetic field experiment onboard Equator-S and its scientific possibilities

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K.-H. Fornacon

1999-12-01

Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

The magnetic field experiment onboard Equator-S and its scientific possibilities

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K.-H. Fornacon

Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.

Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

New solitons connected to the Dirac equation

International Nuclear Information System (INIS)

Grosse, H.

1984-01-01

Imposing isospectral invariance for the one dimensional Dirac operator leads to systems of nonlinear partial differential equations. By constructing reflectionless potentials of the Dirac equation we obtain a new type of solitons for a system of modified Korteweg-de Vries equations. (Author)

Non-markovian boltzmann equation

International Nuclear Information System (INIS)

Kremp, D.; Bonitz, M.; Kraeft, W.D.; Schlanges, M.

1997-01-01

A quantum kinetic equation for strongly interacting particles (generalized binary collision approximation, ladder or T-matrix approximation) is derived in the framework of the density operator technique. In contrast to conventional kinetic theory, which is valid on large time scales as compared to the collision (correlation) time only, our approach retains the full time dependencies, especially also on short time scales. This means retardation and memory effects resulting from the dynamics of binary correlations and initial correlations are included. Furthermore, the resulting kinetic equation conserves total energy (the sum of kinetic and potential energy). The second aspect of generalization is the inclusion of many-body effects, such as self-energy, i.e., renormalization of single-particle energies and damping. To this end we introduce an improved closure relation to the Bogolyubov endash Born endash Green endash Kirkwood endash Yvon hierarchy. Furthermore, in order to express the collision integrals in terms of familiar scattering quantities (Mo/ller operator, T-matrix), we generalize the methods of quantum scattering theory by the inclusion of medium effects. To illustrate the effects of memory and damping, the results of numerical simulations are presented. copyright 1997 Academic Press, Inc

Some Aspects of Extended Kinetic Equation

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Dilip Kumar

2015-09-01

Full Text Available Motivated by the pathway model of Mathai introduced in 2005 [Linear Algebra and Its Applications, 396, 317–328] we extend the standard kinetic equations. Connection of the extended kinetic equation with fractional calculus operator is established. The solution of the general form of the fractional kinetic equation is obtained through Laplace transform. The results for the standard kinetic equation are obtained as the limiting case.

Dirac equation in low dimensions: The factorization method

Energy Technology Data Exchange (ETDEWEB)

Sánchez-Monroy, J.A., E-mail: antosan@if.usp.br [Instituto de Física, Universidade de São Paulo, 05508-090, São Paulo, SP (Brazil); Quimbay, C.J., E-mail: cjquimbayh@unal.edu.co [Departamento de Física, Universidad Nacional de Colombia, Bogotá, D. C. (Colombia); CIF, Bogotá (Colombia)

2014-11-15

We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein–Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials. - Highlights: • The low-dimensional Dirac equation in the presence of static potentials is solved. • The factorization method is generalized for energy-dependent Hamiltonians. • The shape invariance is generalized for energy-dependent Hamiltonians. • The stability of the Dirac sea is related to the existence of supersymmetric partner Hamiltonians.

Multiple solutions and stability of the steady transonic small-disturbance equation

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Ya Liu

2017-09-01

Full Text Available Numerical solutions of the steady transonic small-disturbance (TSD potential equation are computed using the conservative Murman−Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data.

Comparison of the Schrodinger and Salpeter equations

International Nuclear Information System (INIS)

Jacobs, S.; Olsson, M.G.

1985-01-01

A unified approach to the solution of the Schrodinger and spinless Salpeter equations is presented. Fits to heavy quark bound state energies using various potential models are employed to determine whether the Salpeter equation provides a better description of heavy quark systems than the Schrodinger equation

Modified Darboux transformations with foreign auxiliary equations

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2011-01-01

We construct a new type of first-order Darboux transformations for the stationary Schroedinger equation. In contrast to the conventional case, our Darboux transformations support arbitrary (foreign) auxiliary equations. We show that among other applications, our formalism can be used to systematically construct Darboux transformations for Schroedinger equations with energy-dependent potentials, including a recent result (Lin et al., 2007) as a special case. -- Highlights: → We generalize the Darboux transformation for the Schroedinger equation. → By admitting arbitrary auxiliary functions, we provide a new tool for generating solutions. → As a special case we recover a recent result on energy-dependent potentials. → We extend the latter result to very general energy-dependence.

A connection between the Einstein and Yang-Mills equations

International Nuclear Information System (INIS)

Mason, L.J.; Newman, E.T.

1989-01-01

It is our purpose here to show an unusual relationship between the Einstein equations and the Yang-Mills equations. We give a correspondence between solutions of the self-dual Einstein vacuum equations and the self-dual Yang-Mills equations with a special choice of gauge group. The extension of the argument to the full Yang-Mills equations yields Einstein's unified equations. We try to incorporate the full Einstein vacuum equations, but the approach is incomplete. We first consider Yang-Mills theory for an arbitrary Lie-algebra with the condition that the connection 1-form and curvature are constant on Minkowski space. This leads to a set of algebraic equations on the connection components. We then specialize the Lie-algebra to be the (infinite dimensional) Lie algebra of a group of diffeomorphisms of some manifold. The algebraic equations then become differential equations for four vector fields on the manifold on which the diffeomorphisms act. In the self-dual case, if we choose the connection components from the Lie-algebra of the volume preserving 4-dimensional diffeomorphism group, the resulting equations are the same as those obtained by Ashtekar, Jacobsen and Smolin, in their remarkable simplification of the self-dual Einstein vacuum equations. (An alternative derivation of the same equations begins with the self-dual Yang-Mills connection now depending only on the time, then choosing the Lie-algebra as that of the volume preserving 3-dimensional diffeomorphisms). When the reduced full Yang-Mills equations are used in the same context, we get Einstein's equations for his unified theory based on absolute parallelism. To incorporate the full Einstein vacuum equations we use as the Lie group the semi-direct product of the diffeomorphism group of a 4-dimensional manifold with the group of frame rotations of an SO(1, 3) bundle over the 4-manifold. This last approach, however, yields equations more general than the vacuum equations. (orig.)

Projection potentials and angular momentum convergence of total energies in the full-potential Korringa–Kohn–Rostoker method

International Nuclear Information System (INIS)

Zeller, Rudolf

2013-01-01

Although the full-potential Korringa–Kohn–Rostoker Green function method yields accurate results for many physical properties, the convergence of calculated total energies with respect to the angular momentum cutoff is usually considered to be less satisfactory. This is surprising because accurate single-particle energies are expected if they are calculated by Lloyd’s formula and because accurate densities and hence accurate double-counting energies should result from the total energy variational principle. It is shown how the concept of projection potentials can be used as a tool to analyse the convergence behaviour. The key factor blocking fast convergence is identified and it is illustrated how total energies can be improved with only a modest increase of computing time. (paper)

Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method

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Ying Wang

2014-06-01

Full Text Available We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of superfluid wave function. We also eliminate the interdependence between variable coefficients of the equation terms avoiding the restrictions that occur in some other works. The exact soliton solutions of the GGPE are obtained through the delicate combined utilization of modified lens-type transformation and F-expansion method with dominant features like soliton type properties highlighted.

On Delay-Independent Criteria for Oscillation of Higher-Order Functional Differential Equations

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Yuangong Sun

2011-01-01

Full Text Available We investigate the oscillation of the following higher-order functional differential equation: x(n(t+q(t|x(t-τ|λ-1x(t-τ=e(t, where q(t and e(t are continuous functions on [t0,∞, 1>λ>0 and τ≠0 are constants. Unlike most of delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the case τ>0 and the case τ<0 under the assumption that the potentials q(t and e(t change signs on [t0,∞.

SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

Science.gov (United States)

Collier, D.M.; Meeks, L.A.; Palmer, J.P.

1960-05-10

A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

An inverse problem in a parabolic equation

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Zhilin Li

1998-11-01

Full Text Available In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed. A regularization approach for constructing an approximate solution to the ill-posed integral equation is proposed. Theoretical analysis and numerical experiment are provided to support the method.

Minimal solution for inconsistent singular fuzzy matrix equations

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M. Nikuie

2013-10-01

Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.

Spectral bisection algorithm for solving Schrodinger equation using upper and lower solutions

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Qutaibeh Deeb Katatbeh

2007-10-01

Full Text Available This paper establishes a new criteria for obtaining a sequence of upper and lower bounds for the ground state eigenvalue of Schr"odinger equation $ -Deltapsi(r+V(rpsi(r=Epsi(r$ in $N$ spatial dimensions. Based on this proposed criteria, we prove a new comparison theorem in quantum mechanics for the ground state eigenfunctions of Schrodinger equation. We determine also lower and upper solutions for the exact wave function of the ground state eigenfunctions using the computed upper and lower bounds for the eigenvalues obtained by variational methods. In other words, by using this criteria, we prove that the substitution of the lower(upper bound of the eigenvalue in Schrodinger equation leads to an upper(lower solution. Finally, two proposed iteration approaches lead to an exact convergent sequence of solutions. The first one uses Raielgh-Ritz theorem. Meanwhile, the second approach uses a new numerical spectral bisection technique. We apply our results for a wide class of potentials in quantum mechanics such as sum of power-law potentials in quantum mechanics.

Stochastic Levy Divergence and Maxwell's Equations

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B. O. Volkov

2015-01-01

Full Text Available One of the main reasons for interest in the Levy Laplacian and its analogues such as Levy d'Alembertian is a connection of these operators with gauge fields. The theorem proved by Accardi, Gibillisco and Volovich stated that a connection in a bundle over a Euclidean space or over a Minkowski space is a solution of the Yang-Mills equations if and only if the corresponding parallel transport to the connection is a solution of the Laplace equation for the Levy Laplacian or of the d'Alembert equation for the Levy d'Alembertian respectively (see [5, 6]. There are two approaches to define Levy type operators, both of which date back to the original works of Levy [7]. The first is that the Levy Laplacian (or Levy d'Alembertian is defined as an integral functional generated by a special form of the second derivative. This approach is used in the works [5, 6], as well as in the paper [8] of Leandre and Volovich, where stochastic Levy-Laplacian is discussed. Another approach to the Levy Laplacian is defining it as the Cesaro mean of second order derivatives along the family of vectors, which is an orthonormal basis in the Hilbert space. This definition of the Levy Laplacian is used for the description of solutions of the Yang-Mills equations in the paper [10].The present work shows that the definitions of the Levy Laplacian and the Levy d'Alembertian based on Cesaro averaging of the second order directional derivatives can be transferred to the stochastic case. In the article the values of these operators on a stochastic parallel transport associated with a connection (vector potential are found. In this case, unlike the deterministic case and the stochastic case of Levy Laplacian from [8], these values are not equal to zero if the vector potential corresponding to the stochastic parallel transport is a solution of the Maxwell's equations. As a result, two approaches to definition of the Levy Laplacian in the stochastic case give different operators. This

A Model for Solving the Maxwell Quasi Stationary Equations in a 3-Phase Electric Reduction Furnace

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S. Ekrann

1982-10-01

Full Text Available A computer code has been developed for the approximate computation of electric and magnetic fields within an electric reduction furnace. The paper describes the numerical methods used to solve Maxwell's quasi-stationary equations, which are the governing equations for this problem. The equations are discretized by a staggered grid finite difference technique. The resulting algebraic equations are solved by iterating between computations of electric and magnetic quantities. This 'outer' iteration converges only when the skin depth is larger or of about the same magnitude as the linear dimensions of the computational domain. In solving for electric quantities with magnetic quantities being regarded as known, and vice versa, the central computational task is the solution of a Poisson equation for a scalar potential. These equations are solved by line successive overrelaxation combined with a rebalancing technique.

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods - Part 1: Derivation and properties

Science.gov (United States)

Eldred, Christopher; Randall, David

2017-02-01

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restricted to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.

The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2005-01-01

An extended Fan's sub-equation method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (NLPDEs). The key idea of this method is to take full advantage of the general elliptic equation involving five parameters which has more new solutions and whose degeneracies can lead to special sub-equations involving three parameters. More new solutions are obtained for KdV-MKdV, Broer-Kaup-Kupershmidt (BKK) and variant Boussinesq equations. Then we present a technique which not only gives us a clear relation among this general elliptic equation and other sub-equations involving three parameters (Riccati equation, first kind elliptic equation, auxiliary ordinary equation, generalized Riccati equation and so on), but also provides an approach to construct new exact solutions to NLPDEs

Solving equations by topological methods

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Lech Górniewicz

2005-01-01

Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.

Complex centers of polynomial differential equations

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Mohamad Ali M. Alwash

2007-07-01

Full Text Available We present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.

Capillary-gravity waves and the Navier-Stokes equation

International Nuclear Information System (INIS)

Behroozi, F.; Podolefsky, N.

2001-01-01

Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation. (author)

Effective action and the quantum equation of motion

International Nuclear Information System (INIS)

Branchina, V.; Faivre, H.; Zappala, D.

2004-01-01

We carefully analyze the use of the effective action in dynamical problems, in particular the conditions under which the equation (δΓ)/(δφ) = 0 can be used as a quantum equation of motion and illustrate in detail the crucial relation between the asymptotic states involved in the definition of Γ and the initial state of the system. Also, by considering the quantum-mechanical example of a double-well potential, where we can get exact results for the time evolution of the system, we show that an approximation to the effective potential in the quantum equation of motion that correctly describes the dynamical evolution of the system is obtained with the help of the wilsonian RG equation (already at the lowest order of the derivative expansion), while the commonly used one-loop effective potential fails to reproduce the exact results. (orig.)

The construction of partner potential from the general potential anharmonic in D-dimensional Schrodinger system

Science.gov (United States)

Suparmi; Cari, C.; Wea, K. N.; Wahyulianti

2018-03-01

The Schrodinger equation is the fundamental equation in quantum physics. The characteristic of the particle in physics potential field can be explained by using the Schrodinger equation. In this study, the solution of 4 dimensional Schrodinger equation for the anharmonic potential and the anharmonic partner potential have done. The method that used to solve the Schrodinger equation was the ansatz wave method, while to construction the partner potential was the supersymmetric method. The construction of partner potential used to explain the experiment result that cannot be explained by the original potential. The eigenvalue for anharmonic potential and the anharmonic partner potential have the same characteristic. Every increase of quantum orbital number the eigenvalue getting smaller. This result corresponds to Bohrn’s atomic theory that the eigenvalue is inversely proportional to the atomic shell. But the eigenvalue for the anharmonic partner potential higher than the eigenvalue for the anharmonic original potential.

Solutions of the linearized Bach-Einstein equation in the static spherically symmetric case

International Nuclear Information System (INIS)

Schmidt, H.J.

1985-01-01

The Bach-Einstein equation linearized around Minkowski space-time is completely solved. The set of solutions depends on three parameters; a two-parameter subset of it becomes asymptotically flat. In that region the gravitational potential is of the type phi = -m/r + epsilon exp (-r/l). Because of the different asymptotic behaviour of both terms, it became necessary to linearize also around the Schwarzschild solution phi = -m/r. The linearized equation resulting in this case is discussed using qualitative methods. The result is that for m = 2l phi = -m/r + epsilon r -2 exp (-r/l) u, where u is some bounded function; m is arbitrary and epsilon again small. Further, the relation between the solution of the linearized and the full equation is discussed. (author)

On an analytical formulation for the mono-energetic neutron space-kinetic equation in full cylinder symmetry

International Nuclear Information System (INIS)

Oliveira, F.R.; Bodmann, B.E.J.; Vilhena, M.T.; Carvalho, F.

2017-01-01

Highlights: • The present work presents an exact solution to neutron spatial kinetic equation. • It is an exact solution in a heterogeneous cylinder with temporal dependence. • The solution was constructed through the separation of variables method. - Abstract: In the present work we discuss a system of partial differential equations that model neutron space-kinetics in cylindrical geometry and are defined by two sectionally homogeneous cylinder cells, mono-energetic neutrons and one group of delayed neutron precursors. The solution is determined using the technique of variable separation. The associated complete spectra with respect to each variable separation are analysed and truncated such as to allow a parameterized global solution. For the obtained solution we present some numerical results for the scalar neutron flux and its time dependence and projection on the cylinder axis z and the radial and cylinder axis projection. As a case study we consider an insertion of an absorbing medium in the upper cylinder cell. Continuity of the scalar flux at the interface between the two cylinder elements and conserved current density is explained and related to scale invariance of the partial differential equation system together with the initial and boundary conditions. Some numerical results for the scalar angular neutron flux and associated current densities are shown.

The Balescu kinetic equation with exchange interaction

International Nuclear Information System (INIS)

Belyi, V V; Kukharenko, Yu A

2009-01-01

Starting with the quantum BBGKY hierarchy for the distribution functions, we have obtained the quantum kinetic equation including the dynamical screening of the interaction potential, which exactly takes into account the exchange scattering in the plasma. The collision integral is expressed in terms of the Green function of the linearized Hartree–Fock equation. The potential energy takes into account the polarization and exchange interaction too

Quantum-mechanical few-body scattering equations with half-on-shell energy-independent subsystem input

International Nuclear Information System (INIS)

Zeiger, E.M.

1978-01-01

New equations are presented for three- and four-body scattering, within the context of nonrelativistic quantum mechanics and a Hamiltonian scattering theory. For the three-body case Faddeev-type equations are presented which, although obtained from the rigorous Faddeev theory, only require two-body bound state wave functions and half-off-shell transition amplitudes as input. In addition, their effective potentials are independent of the three-body energy, and can easily be made real after an angular momentum decomposition. The equations are formulated in terms of physical transition amplitudes for three-body processes, except that in the breakup case the partial-wave amplitudes differ from the corresponding full amplitudes by a Watson final-state-interaction factor. Also presented are new equations for four-body scattering, obtained by generalizing our three-body formalism to the four-body case. These equations, although equivalent to those of Faddeev--Yakubovskii, are expressed in terms of singularity-free transition amplitudes, and their energy-independent effective potentials require only half-on-shell subsystem transition amplitudes (and bound state wave functions) as input. However, due to the detailed index structure of the Faddeev--Yakubovskii formalsim, the result of the generalization is considerably more complicated than in the three-body case

4He binding energy calculation including full tensor-force effects

Science.gov (United States)

Fonseca, A. C.

1989-09-01

The four-body equations of Alt, Grassberger, and Sandhas are solved in the version where the (2)+(2) subamplitudes are treated exactly by convolution, using one-term separable Yamaguchy nucleon-nucleon potentials in the 1S0 and 3S1-3D1 channels. The resulting jp=1/2+ and (3/2+ three-body subamplitudes are represented in a separable form using the energy-dependent pole expansion. Converged bound-state results are calculated for the first time using the full interaction, and are compared with those obtained from a simplified treatment of the tensor force. The Tjon line that correlates three-nucleon and four-nucleon binding energies is shown using different nucleon-nucleon potentials. In all calculations the Coulomb force has been neglected.

New solutions of the confluent Heun equation

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Harold Exton

1998-05-01

Full Text Available New compact triple series solutions of the confluent Heun equation (CHE are obtained by the appropriate applications of the Laplace transform and its inverse to a suitably constructed system of soluble differential equations. The computer-algebra package MAPLE V is used to tackle an auxiliary system of non-linear algebraic equations. This study is partly motivated by the relationship between the CHE and certain Schrödininger equations.

Generalised master equations for wave equation separation in a Kerr or Kerr-Newman black hole background

International Nuclear Information System (INIS)

Carter, B.; McLenaghan, R.G.

1982-01-01

It is shown how previous general formulae for the separated radial and angular parts of the massive, charged scalar (Klein, Gordon) wave equation on one hand, and of the zero mass, neutral, but higher spin (neutrino, electromagnetic and gravitational) wave equations on the other hand may be combined in a more general formula which also covers the case of the full massive charged Dirac equation in a Kerr or Kerr-Newman background space. (Auth.)

The what and where of adding channel noise to the Hodgkin-Huxley equations.

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Joshua H Goldwyn

2011-11-01

Full Text Available Conductance-based equations for electrically active cells form one of the most widely studied mathematical frameworks in computational biology. This framework, as expressed through a set of differential equations by Hodgkin and Huxley, synthesizes the impact of ionic currents on a cell's voltage--and the highly nonlinear impact of that voltage back on the currents themselves--into the rapid push and pull of the action potential. Later studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional description than the original Hodgkin-Huxley equations or their counterparts. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the equations of Hodgkin-Huxley type. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic equations of Hodgkin-Huxley type as well as to more modern models of ion channel dynamics. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly MATLAB simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950 and http://www.amath.washington.edu/~etsb/tutorials.html.

Solutions manual to accompany Ordinary differential equations

CERN Document Server

Greenberg, Michael D

2014-01-01

Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

Fermat type differential and difference equations

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Kai Liu

2015-06-01

Full Text Available This article we explore the relationship between the number of differential and difference operators with the existence of meromorphic solutions of Fermat type differential and difference equations. Some Fermat differential and difference equations of certain types are also considered.

On matrix fractional differential equations

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Adem Kılıçman

2017-01-01

Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

A Note of Extended Proca Equations and Superconductivity

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Christianto V.

2009-01-01

Full Text Available It has been known for quite long time that the electrodynamics of Maxwell equations can be extended and generalized further into Proca equations. The implications of in- troducing Proca equations include an alternative description of superconductivity, via extending London equations. In the light of another paper suggesting that Maxwell equations can be written using quaternion numbers, then we discuss a plausible exten- sion of Proca equation using biquaternion number. Further implications and experi- ments are recommended.

Group-theoretical interpretation of the Korteweg-de Vries type equations

International Nuclear Information System (INIS)

Berezin, F.A.; Perelomov, A.M.

1978-01-01

The Korteweg-de Vries equation is studied within the group-theoretical framework. Analogous equations are obtained for which the many-dimensional Schroedinger equation (with nonlocal potential) plays the same role as the one-dimensional Schroedinger equation does in the theory of the Korteweg-de Vries equation

Darboux transformation for the NLS equation

International Nuclear Information System (INIS)

Aktosun, Tuncay; Mee, Cornelis van der

2010-01-01

We analyze a certain class of integral equations associated with Marchenko equations and Gel'fand-Levitan equations. Such integral equations arise through a Fourier transformation on various ordinary differential equations involving a spectral parameter. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution in terms of the unperturbed quantities and the finite-rank perturbation. We show that this result provides a fundamental approach to derive Darboux transformations for various systems of ordinary differential operators. We illustrate our theory by providing the explicit Darboux transformation for the Zakharov-Shabat system and show how the potential and wave function change when a simple discrete eigenvalue is added to the spectrum, and thus we also provide a one-parameter family of Darboux transformations for the nonlinear Schroedinger equation.

The solution of the Poisson-Boltzmann's equation for self-consistent potential of infinite, random, nonlinear and non-uniform system

International Nuclear Information System (INIS)

Rasulova, M.Yu

1998-01-01

A study has been made of a system of charged particles and inhomogeneities randomly distributed in accordance with the same law in the neighborhoods of corresponding sites of a planar crystal lattice. The existence and uniqueness of the solution of the generalized Poisson-Boltzmann's equation for the average self-consistent potential and average density of surface charges are proved. (author)

Wave Functions for Time-Dependent Dirac Equation under GUP

Science.gov (United States)

Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

2018-04-01

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

Lattice Wigner equation

Science.gov (United States)

Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

Global solutions for 3D nonlocal Gross-Pitaevskii equations with rough data

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Hartmut Pecher

2012-10-01

Full Text Available We study the Cauchy problem for the Gross-Pitaevskii equation with a nonlocal interaction potential of Hartree type in three space dimensions. If the potential is even and positive definite or a positive function and its Fourier transform decays sufficiently rapidly the problem is shown to be globally well-posed for large rough data which not necessarily have finite energy and also in a situation where the energy functional is not positive definite. The proof uses a suitable modification of the I-method.

Discrete Riccati equation solutions: Distributed algorithms

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D. G. Lainiotis

1996-01-01

Full Text Available In this paper new distributed algorithms for the solution of the discrete Riccati equation are introduced. The algorithms are used to provide robust and computational efficient solutions to the discrete Riccati equation. The proposed distributed algorithms are theoretically interesting and computationally attractive.

Analytical solutions of time-fractional models for homogeneous Gardner equation and non-homogeneous differential equations

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Olaniyi Samuel Iyiola

2014-09-01

Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

Correct Linearization of Einstein's Equations

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Rabounski D.

2006-06-01

Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.

Solution of the Korteweg--de Vries equation in a half-space bounded by a wall

International Nuclear Information System (INIS)

Moses, H.E.

1976-01-01

A solution of the Korteweg--de Vries equation in the half-space 0 less than r less than infinity with the boundary condition V(0) = 0 is given. The boundary condition may be interpreted as the requirement that the plane which bounds the half-space be a rigid wall. Aside from possible physical interest, this solution, which is obtained from one of the potentials for the radial Schroedinger equation which do not scatter, appears to indicate that the radial Schroedinger equation and the corresponding Gel'fand--Levitan equation play a role in the case of the half-space bounded by a wall similar to that of the one-dimensional Schroedinger equation (-- infinity less than x less than infinity) and its corresponding Gel'fand--Levitan equation in the more usual full space treatment of the KdV equation. A possible interpretation of the solution presented is that it corresponds to the reflection of a wave by a wall, in which the incident wave is singular and the reflected wave is nonsingular but highly dispersive

The Nonrelativistic Scattering States of the Deng-Fan Potential

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Bentol Hoda Yazarloo

2013-01-01

Full Text Available The approximately analytical scattering state solution of the Schrodinger equation is obtained for the Deng-Fan potential by using an approximation scheme to the centrifugal term. Energy eigenvalues, normalized wave functions, and scattering phase shifts are calculated. We consider and verify two special cases: the l=0 and the s-wave Hulthén potential.

Meson spectra from two-body dirac equations with minimal interactions

International Nuclear Information System (INIS)

Crater, H.W.; Becker, R.L.; Wong, C.Y.

1991-01-01

Many authors have used two-body relativistic wave equations with spin in nonperturbative numerical quark model calculations of the meson spectrum. Usually, they adopt a truncation of the Bethe-Salpeter equation of QED and/or scalar. QED and replace the static Coulomb interactions of those field theories with a semiphenomenological Q bar Q potential whose insertion in the Breit terms give the corresponding spin corrections. However, the successes of these wave equations in QED have invariably depended on perturbative treatment of the terms in each beyond the Coulomb terms. There have been no successful nonperturbative numerical test of two-body quantum wave equations in QED, because in most equations the effective potentials beyond the Coulomb are singular and can only be treated perturbatively. This is a glaring omission that we rectify here for the case of the two-body Dirac equations of constraint dynamics. We show in this paper that a nonperturbative numerical treatment of these equations for QED yields the same spectral results as a perturbative treatment of them which in turn agrees with the standard spectral results for positronium and muonium. This establishes that the vector and scalar interaction structures of our equations accurately incorporate field theoretic interactions in a bone fide relativistic wave equation. The last portion of this work will report recent quark model calculations using these equations with the Adler-Piran static Q bar Q potential

Reaction diffusion equations with boundary degeneracy

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Huashui Zhan

2016-03-01

Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.

The gBL transport equations

International Nuclear Information System (INIS)

Mynick, H.E.

1989-05-01

The transport equations arising from the ''generalized Balescu- Lenard'' (gBL) collision operator are obtained, and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases, having the same structure. The resultant theory offers potential explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/ΓT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy to neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest. 10 refs

Imaging of the internal structure of comet 67P/Churyumov-Gerasimenko from radiotomography CONSERT Data (Rosetta Mission) through a full 3D regularized inversion of the Helmholtz equations on functional spaces

Science.gov (United States)

Barriot, Jean-Pierre; Serafini, Jonathan; Sichoix, Lydie; Benna, Mehdi; Kofman, Wlodek; Herique, Alain

We investigate the inverse problem of imaging the internal structure of comet 67P/ Churyumov-Gerasimenko from radiotomography CONSERT data by using a coupled regularized inversion of the Helmholtz equations. A first set of Helmholtz equations, written w.r.t a basis of 3D Hankel functions describes the wave propagation outside the comet at large distances, a second set of Helmholtz equations, written w.r.t. a basis of 3D Zernike functions describes the wave propagation throughout the comet with avariable permittivity. Both sets are connected by continuity equations over a sphere that surrounds the comet. This approach, derived from GPS water vapor tomography of the atmosphere,will permit a full 3D inversion of the internal structure of the comet, contrary to traditional approaches that use a discretization of space at a fraction of the radiowave wavelength.

Exactly solvable energy-dependent potentials

International Nuclear Information System (INIS)

Garcia-Martinez, J.; Garcia-Ravelo, J.; Pena, J.J.; Schulze-Halberg, A.

2009-01-01

We introduce a method for constructing exactly-solvable Schroedinger equations with energy-dependent potentials. Our method is based on converting a general linear differential equation of second order into a Schroedinger equation with energy-dependent potential. Particular examples presented here include harmonic oscillator, Coulomb and Morse potentials with various types of energy dependence.

PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS

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Korhan KARABULUT

1998-03-01

Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.

Scattering of a two skyrmion configuration on potential holes or barriers in a model Landau-Lifshitz equation

International Nuclear Information System (INIS)

Collins, J C; Zakrzewski, W J

2009-01-01

The dynamics of a baby-skyrmion configuration, in a model Landau-Lifshitz equation, was studied in the presence of various potential obstructions. The baby-skyrmion configuration was constructed from two Q = 1 hedgehog solutions to the baby-skyrme model in (2+1) dimensions. The potential obstructions were created by introducing a new term into the Lagrangian which resulted in a localized inhomogeneity in the potential terms' coefficient. In the barrier system, the normal circular path was deformed as the skyrmions traversed the barrier. During the same period, it was seen that the skyrmions sped up as they went over the barrier. For critical values of the barrier height and width, the skyrmions were no longer bound and were free to separate. In the case of a potential hole, the baby skyrmions no longer formed a bound state and moved asymptotically along the axis of the hole. It is shown how to modify the definition of the angular momentum to include the effects of the obstructions, so that it is conserved

Effect of quantity and composition of waste on the prediction of annual methane potential from landfills.

Science.gov (United States)

Cho, Han Sang; Moon, Hee Sun; Kim, Jae Young

2012-04-01

A study was conducted to investigate the effect of waste composition change on the methane production in landfills. An empirical equation for the methane potential of the mixed waste is derived based on the methane potential values of individual waste components and the compositional ratio of waste components. A correction factor was introduced in the equation and was determined from the BMP and lysimeter tests. The equation and LandGEM were applied for a full size landfill and the annual methane potential was estimated. Results showed that the changes in quantity of waste affected the annual methane potential from the landfill more than the changes of waste composition. Copyright © 2012 Elsevier Ltd. All rights reserved.

Canonical reduction of self-dual Yang-Mills equations to Fitzhugh-Nagumo equation and exact solutions

International Nuclear Information System (INIS)

Sayed, S.M.; Gharib, G.M.

2009-01-01

The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills theory to two-dimensional Fitzhugh-Nagumo and the real Newell-Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh-Nagumo and Newell-Whitehead equations. The corresponding gauge potential A μ and the gauge field strengths F μν are also obtained. New explicit and exact traveling wave and solitary solutions (for Fitzhugh-Nagumo and Newell-Whitehead equations) are obtained by using an improved sine-cosine method and the Wu's elimination method with the aid of Mathematica.

VOLUME AND TAPER EQUATIONS FOR COMMERCIAL STEMS OF Nothofagus obliqua AND N. alpina

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Hernan Attis Beltran

2017-09-01

Full Text Available Timber volume of standing trees is essential information for management decisions. The increasing need to optimize the potential capacity of forests maintaining their conservation, requires the quantification of the different potential possible timber products. The aim was to adjust taper equations to determine volumes of different timber products for commercial stems of Nothofagus alpina and N. obliqua. Trees of both species were randomly selected in harvesting areas of Lanin National Park (Argentina. Trees were felled and cut into commercial logs, measuring diameter with bark at different heights up to the beginning of the crown, and for each tree the diameter at breast height and total height. Five taper equations were selected and non-linear regression processes were employed for the fittings. We obtained the volume through the integration of the stem profile equation and the rotation in the space thereof through solid of revolution. The Bennet and Swindel (1972 model was selected for both Nothofagus species, obtaining similar equation parameters and differences were observed at the top of the stems of larger trees. For this the use of an integrated model is not recommended. With the obtained equations it is possible to: (i estimatevolume at different heights and for different commercial diameters, and (ii predict the height at which both species reach to a certain diameter. The model presented some statistical limitations (e.g. multicollinearity, however, the fitting of the equation and the easy understanding of the outputs support it as a useful tool in a broad range of forest applications.

Dunkl Hyperbolic Equations

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Hatem Mejjaoli

2008-12-01

Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.

Minimally coupled N-particle scattering integral equations

International Nuclear Information System (INIS)

Kowalski, K.L.

1977-01-01

A concise formalism is developed which permits the efficient representation and generalization of several known techniques for deriving connected-kernel N-particle scattering integral equations. The methods of Kouri, Levin, and Tobocman and Bencze and Redish which lead to minimally coupled integral equations are of special interest. The introduction of channel coupling arrays is characterized in a general manner and the common base of this technique and that of the so-called channel coupling scheme is clarified. It is found that in the Bencze-Redish formalism a particular coupling array has a crucial function but one different from that of the arrays employed by Kouri, Levin, and Tobocman. The apparent dependence of the proof of the minimality of the Bencze-Redish integral equations upon the form of the inhomogeneous term in these equations is eliminated. This is achieved by an investigation of the full (nonminimal) Bencze-Redish kernel. It is shown that the second power of this operator is connected, a result which is needed for the full applicability of the Bencze-Redish formalism. This is used to establish the relationship between the existence of solutions to the homogeneous form of the minimal equations and eigenvalues of the full Bencze-Redish kernel

Investigating the potential of e-Learning in healthcare postgraduate curricula: a structural equation model.

Science.gov (United States)

Katharaki, Maria; Daskalakis, Stelios; Mantas, John

2010-01-01

The objective of this paper is to assess the future adaptability of e-Learning platforms within postgraduate modules. An ongoing empirical assessment was conducted amongst postgraduate students, based on the Technology Acceptance Model (TAM). The current paper presents the outcomes from the second phase of a survey, involving fifty six participants. Data analysis was performed using a structural equation model, based on partial least squares. Results highlighted the very strong effect of perceived usefulness and perceived ease of use to attitude towards using e-Learning platforms. Consequently, attitude towards use proved to be a very strong predictor of behavioral intention. Perceived usefulness, on the contrary, did not prove to have an effect to behavioral intention. Implications on the potential of using e-Learning platforms are discussed along with limitations and future directions of the study.

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

Science.gov (United States)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSGLRR full second-moment Reynolds stress models are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST) two-equation models.

Differential Equations Compatible with KZ Equations

International Nuclear Information System (INIS)

Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

2000-01-01

We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

Isomorphism of Intransitive Linear Lie Equations

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Jose Miguel Martins Veloso

2009-11-01

Full Text Available We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.

Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation

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V. O. Vakhnenko

2016-01-01

Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.

Influencing Mechanism of Potential Factors on Passengers’ Long-Distance Travel Mode Choices Based on Structural Equation Modeling

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Yun Wang

2017-10-01

Full Text Available Understanding the public transportation users’ preferences to long-distance travel modes would contribute to reasonable developing policies and resource allocation. This paper aims to explore the influencing mechanism of potential factors on the long-distance travel mode choice. A survey was conducted to collect the data. The analysis of variance (ANOVA approach was applied to analyze the correlation relationship between potential factors and travel mode choice behavior. The results showed that, except gender, service demand for safety and departure time, all of the other factors significantly influenced the travel mode choice behavior. Specifically, passengers with higher education level and income level were more likely to choose high-speed railway (HSR and plane; passengers caring about travel expense were more likely to choose ordinary train, whereas plane and HSR may be chosen more by passengers caring more about comfort, punctuality and efficiency; the more passengers were satisfied with travel modes’ service performance, the more they would be likely to choose them; the most competitive distance ranges for coach, ordinary train, HSR and plane were below 500 km, 500–1000 km, 500–1500 km and over 1500 km, respectively. Besides, the structural equation modeling (SEM technique was applied to investigate the influencing mechanism of factors on the long-distance travel mode choice. The results revealed that travel distance was the most significant variable directly influencing passengers’ mode choices, followed by the service demand, performance evaluation, and personal attributes. Furthermore, personal attributes were verified to have an indirect effect on travel mode choice behavior by significantly affecting the service demand and performance evaluation.

Equation for the superfluid gap obtained by coarse graining the Bogoliubov-de Gennes equations throughout the BCS-BEC crossover

Science.gov (United States)

Simonucci, S.; Strinati, G. C.

2014-02-01

We derive a nonlinear differential equation for the gap parameter of a superfluid Fermi system by performing a suitable coarse graining of the Bogoliubov-de Gennes (BdG) equations throughout the BCS-BEC crossover, with the aim of replacing the time-consuming solution of the original BdG equations by the simpler solution of this novel equation. We perform a favorable numerical test on the validity of this new equation over most of the temperature-coupling phase diagram, by an explicit comparison with the full solution of the original BdG equations for an isolated vortex. We also show that the new equation reduces both to the Ginzburg-Landau equation for Cooper pairs in weak coupling close to the critical temperature and to the Gross-Pitaevskii equation for composite bosons in strong coupling at low temperature.

Solutions for confluent and double-confluent Heun equations and some applications

Energy Technology Data Exchange (ETDEWEB)

El-Jaick, Lea Jaccoud; Figueiredo, Bartolomeu D.B. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

2008-07-01

This paper examines some solutions for confluent and double-confluent Heun equations and their applications to the Schroedinger equation with quasi-exactly solvable potentials. In the first place, we review two Leaver's solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)] and introduce an additional expansion in series of irregular confluent hypergeometric functions. Then, we find the conditions under which one of these solutions can be written as a linear combination of the others. In the second place, by means of limiting procedures we generate solutions for the double-confluent equation as well as for special limits of both the confluent and double-confluent equations. In the third place, solutions of the Heun equations are used to solve the one-dimensional Schroedinger equation for quasi-exactly solvable potentials. We consider a symmetric and an asymmetric double-Morse potentials which appear in the theory of quantum spin systems [O. B. Zaslavskii and V. V. Ulyanov, Sov. Phys. JETP 60, 991 (1984)], a bottomless volcano-type potential which gives degenerate eigenstates [S. Kar and R. R. Parwani, Europhys. Lett., 80, 30004 (2007)], and a potential which leads to quasi normal modes, that is, to solutions presenting complex energies [H. T. Cho and C. L. Ho, J. Phys. A: Math. Theor. 40, 1325 (2007)]. (author)

Solutions for confluent and double-confluent Heun equations and some applications

International Nuclear Information System (INIS)

El-Jaick, Lea Jaccoud; Figueiredo, Bartolomeu D.B.

2008-01-01

This paper examines some solutions for confluent and double-confluent Heun equations and their applications to the Schroedinger equation with quasi-exactly solvable potentials. In the first place, we review two Leaver's solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)] and introduce an additional expansion in series of irregular confluent hypergeometric functions. Then, we find the conditions under which one of these solutions can be written as a linear combination of the others. In the second place, by means of limiting procedures we generate solutions for the double-confluent equation as well as for special limits of both the confluent and double-confluent equations. In the third place, solutions of the Heun equations are used to solve the one-dimensional Schroedinger equation for quasi-exactly solvable potentials. We consider a symmetric and an asymmetric double-Morse potentials which appear in the theory of quantum spin systems [O. B. Zaslavskii and V. V. Ulyanov, Sov. Phys. JETP 60, 991 (1984)], a bottomless volcano-type potential which gives degenerate eigenstates [S. Kar and R. R. Parwani, Europhys. Lett., 80, 30004 (2007)], and a potential which leads to quasi normal modes, that is, to solutions presenting complex energies [H. T. Cho and C. L. Ho, J. Phys. A: Math. Theor. 40, 1325 (2007)]. (author)

Construction of alternative Hamiltonian structures for field equations

Energy Technology Data Exchange (ETDEWEB)

Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

2001-08-10

We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)

A quark-antiquark potential from a superconducting model of confinement

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J.W. Alcock

1983-10-01

Full Text Available The Landau-Ginzburg phenomenological theory of superconductivity is used as a model of flux confinement. A monopole pair of sources is included to simulate a quark-antiquark system. The interaction energy is found in the static approximation appropriate for heavy quark systems, and equated with the interquark potential. This potential is compared with other suggested phenomenological potentials and succeeds in reproducing heavy quark spectra.

Complex nonlinear Lagrangian for the Hasegawa-Mima equation

International Nuclear Information System (INIS)

Dewar, R.L.; Abdullatif, R.F.; Sangeetha, G.G.

2005-01-01

The Hasegawa-Mima equation is the simplest nonlinear single-field model equation that captures the essence of drift wave dynamics. Like the Schroedinger equation it is first order in time. However its coefficients are real, so if the potential φ is initially real it remains real. However, by embedding φ in the space of complex functions a simple Lagrangian is found from which the Hasegawa-Mima equation may be derived from Hamilton's Principle. This Lagrangian is used to derive an action conservation equation which agrees with that of Biskamp and Horton. (author)

Time-dependent field equations for paraxial relativistic electron beams: Beam Research Program

International Nuclear Information System (INIS)

Sharp, W.M.; Yu, S.S.; Lee, E.P.

1987-01-01

A simplified set of field equations for a paraxial relativistic electron beam is presented. These equations for the beam electrostatic potential phi and pinch potential Phi identical to A/sub z/ - phi retain previously neglected time-dependent terms and for axisymmetric beams reduce exactly to Maxwell's equations

A physics-based potential and electric field model of a nanoscale ...

Indian Academy of Sciences (India)

... paper, we have developed a physics-based model for surface potential, channel potential, electric field and drain current for AlGaN/GaN high electron mobility transistor with high-K gate dielectric using two-dimensional Poisson equation under full depletion approximation with the inclusion of effect of polarization charges.

On Fractional Order Hybrid Differential Equations

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Mohamed A. E. Herzallah

2014-01-01

Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

Stationary localized modes of the quintic nonlinear Schroedinger equation with a periodic potential

International Nuclear Information System (INIS)

Alfimov, G. L.; Konotop, V. V.; Pacciani, P.

2007-01-01

We consider localized modes (bright solitons) of the one-dimensional quintic nonlinear Schroedinger equation with a periodic potential, describing several mean-field models of low-dimensional condensed gases. In the case of attractive nonlinearity we deduce sufficient conditions for collapse. We show that there exist spatially localized modes with arbitrarily large numbers of particles. We study such solutions in the semi-infinite gap (attractive case) and in the first gap (attractive and repulsive cases), and show that a nonzero minimum value of the number of particles is necessary for a localized mode to be created. In the limit of large negative frequencies (attractive case) we observe quantization of the number of particles of the stationary modes. Such solutions can be interpreted as coupled Townes solitons and appear to be stable. The modes in the first gap have numbers of particles infinitely growing with frequencies approaching one of the gap edges, which is explained by the power decay of the modes. Stability of the localized modes is discussed

A Greenian approach to the solution of the Schroedinger equation for periodic lattice potentials

International Nuclear Information System (INIS)

Minelli, T.A.

1976-01-01

A modified structural Green's function (MSGF), exploiting all the information contained in the previously solved Schroedinger equation for the electron interacting with a single lattice site, has been introduced and used in order to obtain, from a Dyson-type equation, a kernel whose poles and residues give the E-vs.-k relation and, respectively, the Bloch functions. Such a formulation suggests an alternative technique for the approximate solution of the KKR equations. The MSGF formalism has been also used in order to determine the structure constants of a one-dimensional lattice in a general representation

Riccati and Ermakov Equations in Time-Dependent and Time-Independent Quantum Systems

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Dieter Schuch

2008-05-01

Full Text Available The time-evolution of the maximum and the width of exact analytic wave packet (WP solutions of the time-dependent Schrödinger equation (SE represents the particle and wave aspects, respectively, of the quantum system. The dynamics of the maximum, located at the mean value of position, is governed by the Newtonian equation of the corresponding classical problem. The width, which is directly proportional to the position uncertainty, obeys a complex nonlinear Riccati equation which can be transformed into a real nonlinear Ermakov equation. The coupled pair of these equations yields a dynamical invariant which plays a key role in our investigation. It can be expressed in terms of a complex variable that linearizes the Riccati equation. This variable also provides the time-dependent parameters that characterize the Green's function, or Feynman kernel, of the corresponding problem. From there, also the relation between the classical and quantum dynamics of the systems can be obtained. Furthermore, the close connection between the Ermakov invariant and the Wigner function will be shown. Factorization of the dynamical invariant allows for comparison with creation/annihilation operators and supersymmetry where the partner potentials fulfil (real Riccati equations. This provides the link to a nonlinear formulation of time-independent quantum mechanics in terms of an Ermakov equation for the amplitude of the stationary state wave functions combined with a conservation law. Comparison with SUSY and the time-dependent problems concludes our analysis.

Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems

Directory of Open Access Journals (Sweden)

Florian Thüroff

2014-11-01

Full Text Available Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system’s dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system’s ordered state nematic, despite purely polar interactions on the level of single particles.

New exact solutions of the Dirac equation

International Nuclear Information System (INIS)

Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Lavrov, P.M.; Shapovalov, V.N.

1980-01-01

Search for new exact solutions of the Dirac and Klein-Gordon equations are in progress. Considered are general properties of the Dirac equation solutions for an electron in a purely magnetic field, in combination with a longitudinal magnetic and transverse electric fields. New solutions for the equations of charge motion in an electromagnetic field of axial symmetry and in a nonstationary field of a special form have been found for potentials selected concretely

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian

2015-01-01

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean

2015-02-03

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

Canonical reduction of self-dual Yang-Mills equations to Fitzhugh-Nagumo equation and exact solutions

Energy Technology Data Exchange (ETDEWEB)

Sayed, S.M. [Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef (Egypt); Mathematics Department, P.O. Box 1144, Tabouk Teacher College, Ministry of Education (Saudi Arabia)], E-mail: eaashour@lycos.com; Gharib, G.M. [Mathematics Department, P.O. Box 1144, Tabouk Teacher College, Ministry of Education (Saudi Arabia)

2009-01-30

The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills theory to two-dimensional Fitzhugh-Nagumo and the real Newell-Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh-Nagumo and Newell-Whitehead equations. The corresponding gauge potential A{sub {mu}} and the gauge field strengths F{sub {mu}}{sub {nu}} are also obtained. New explicit and exact traveling wave and solitary solutions (for Fitzhugh-Nagumo and Newell-Whitehead equations) are obtained by using an improved sine-cosine method and the Wu's elimination method with the aid of Mathematica.

Ultradiscrete sine-Gordon Equation over Symmetrized Max-Plus Algebra, and Noncommutative Discrete and Ultradiscrete sine-Gordon Equations

Directory of Open Access Journals (Sweden)

Kenichi Kondo

2013-11-01

Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.

Magnetism of hexagonal close-packed nickel calculated by full-potential linearized augmented plane wave method

International Nuclear Information System (INIS)

Tian, F.; Tian, H.; Whitmore, L.; Ye, L.Y.

2015-01-01

The energy dependent on volume of hexagonal close-packed (hcp) nickel with different magnetism is calculated by full-potential linearized augmented plane wave method. Based on the calculation ferromagnetic state is found to be the most stable state. The magnetic moment of hcp Ni is calculated and compared to those calculated by different pseudo-potential methods. Furthermore, it is also compared to that of face-centered cubic (fcc) one with the reason discussed

Solving Partial Differential Equations Using a New Differential Evolution Algorithm

Directory of Open Access Journals (Sweden)

Natee Panagant

2014-01-01

Full Text Available This paper proposes an alternative meshless approach to solve partial differential equations (PDEs. With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm (EA is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced.

On the Potential of Full Duplex Performance in 5G Ultra-Dense Small Cell Networks

DEFF Research Database (Denmark)

Gatnau, Marta; Fleischer, Marko; Berardinelli, Gilberto

2016-01-01

inter-cell interference and traffic constraints. In this paper, we first study the self-interference cancellation capabilities by using a real demonstrator. Results show that achieving ~110 dB of cancellation is already possible with the current available technology, thus providing the required level...... of isolation to build an operational full duplex node. Secondly, we investigate the inter-cell interference and traffic constraints impact on the full duplex performance in 5th generation systems. System level results show that both the traffic and the inter-cell interference can significantly reduce...... the potential gain of full duplex with respect to half duplex. However, for large traffic asymmetry, full duplex can boost the performance of the lightly loaded link....

A physics-based potential and electric field model of a nanoscale ...

Indian Academy of Sciences (India)

In this paper, we have developed a physics-based model for surface potential, channel potential, electric field and drain current for AlGaN/GaN high electron mobility transistor with high-K gate dielectric using two-dimensional Poisson equation under full depletion approximation with the inclusion of effect of polarization ...

Diffusion-equation representations of landform evolution in the simplest circumstances: Appendix C

Science.gov (United States)

Hanks, Thomas C.

2009-01-01

The diffusion equation is one of the three great partial differential equations of classical physics. It describes the flow or diffusion of heat in the presence of temperature gradients, fluid flow in porous media in the presence of pressure gradients, and the diffusion of molecules in the presence of chemical gradients. [The other two equations are the wave equation, which describes the propagation of electromagnetic waves (including light), acoustic (sound) waves, and elastic (seismic) waves radiated from earthquakes; and LaPlace’s equation, which describes the behavior of electric, gravitational, and fluid potentials, all part of potential field theory. The diffusion equation reduces to LaPlace’s equation at steady state, when the field of interest does not depend on t. Poisson’s equation is LaPlace’s equation with a source term.

The one-dimensional Gross-Pitaevskii equation and its some excitation states

Energy Technology Data Exchange (ETDEWEB)

Prayitno, T. B., E-mail: trunk-002@yahoo.com [Physics Department, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta, Jl. Pemuda Rawamangun no. 10, Jakarta, 13220 (Indonesia)

2015-04-16

We have derived some excitation states of the one-dimensional Gross-Pitaevskii equation coupled by the gravitational potential. The methods that we have used here are taken by pursuing the recent work of Kivshar et. al. by considering the equation as a macroscopic quantum oscillator. To obtain the states, we have made the appropriate transformation to reduce the three-dimensional Gross-Pitaevskii equation into the one-dimensional Gross-Pitaevskii equation and applying the time-independent perturbation theory in the general solution of the one-dimensional Gross-Pitaevskii equation as a linear superposition of the normalized eigenfunctions of the Schrödinger equation for the harmonic oscillator potential. Moreover, we also impose the condition by assuming that some terms in the equation should be so small in order to preserve the use of the perturbation method.

Derivation of the Gross-Pitaevskii equation for condensed bosons from the Bogoliubov-de Gennes equations for superfluid fermions

International Nuclear Information System (INIS)

Pieri, P.; Strinati, G.C.

2003-01-01

We derive the time-independent Gross-Pitaevskii equation at zero temperature for condensed bosons, which form as bound-fermion pairs when the mutual fermionic attractive interaction is sufficiently strong, from the strong-coupling limit of the Bogoliubov-de Gennes equations that describe superfluid fermions in the presence of an external potential. Three-body corrections to the Gross-Pitaevskii equation are also obtained by our approach. Our results are relevant to the recent advances with ultracold fermionic atoms in a trap

Roy–Steiner equations for πN scattering

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Ruiz de Elvira J.

2014-06-01

Full Text Available In this talk, we present a coupled system of integral equations for the πN → πN (s-channel and ππ → N̅N (t-channel lowest partial waves, derived from Roy–Steiner equations for pion–nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili–Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy–Steiner equations.

FDTD for Hydrodynamic Electron Fluid Maxwell Equations

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Yingxue Zhao

2015-05-01

Full Text Available In this work, we develop a numerical method for solving the three dimensional hydrodynamic electron fluid Maxwell equations that describe the electron gas dynamics driven by an external electromagnetic wave excitation. Our numerical approach is based on the Finite-Difference Time-Domain (FDTD method for solving the Maxwell’s equations and an explicit central finite difference method for solving the hydrodynamic electron fluid equations containing both electron density and current equations. Numerical results show good agreement with the experiment of studying the second-harmonic generation (SHG from metallic split-ring resonator (SRR.

Dynamics of bright solitons and soliton arrays in the nonlinear Schrödinger equation with a combination of random and harmonic potentials

International Nuclear Information System (INIS)

Chen Qianyong; Kevrekidis, Panayotis G; Malomed, Boris A

2012-01-01

We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schrödinger equation, which includes the harmonic oscillator potential and a random potential. The equation models experimentally relevant spatially disordered settings in Bose-Einstein condensates (BECs) and nonlinear optics. First, the generation of soliton arrays from a broad initial quasi-uniform state by the modulational instability (MI) is considered following a sudden switch of the nonlinearity from repulsive to attractive. Then, we study oscillations of a single soliton in this setting, which models a recently conducted experiment in a BEC. The basic characteristics of the MI-generated array, such as the number of solitons and their mobility, are reported as functions of the strength and correlation length of the disorder, and of the total norm. For the single oscillating soliton, its survival rate is found. The main features of these dependences are explained qualitatively. (paper)

Regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations.

Science.gov (United States)

Gibbon, John D; Pal, Nairita; Gupta, Anupam; Pandit, Rahul

2016-12-01

We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter ϕ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984)CMPHAY0010-361610.1007/BF01212349]. By taking an L^{∞} norm of the energy of the full binary system, designated as E_{∞}, we have shown that ∫_{0}^{t}E_{∞}(τ)dτ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with 128^{3} to 512^{3} collocation points and over the duration of our DNSs confirm that E_{∞} remains bounded as far as our computations allow.

Mathematical modeling and the two-phase constitutive equations

International Nuclear Information System (INIS)

Boure, J.A.

1975-01-01

The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr

On the reduction of the multidimensional stationary Schroedinger equation to a first-order equation and its relation to the pseudoanalytic function theory

Energy Technology Data Exchange (ETDEWEB)

Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)

2005-01-28

class of potentials in the Schroedinger equation (which includes for instance all radial potentials), this new approach gives us a simple procedure allowing us to obtain an infinite sequence of solutions of the Schroedinger equation from one known particular solution.

Cellular solutions for the Poisson equation in extended systems

International Nuclear Information System (INIS)

Zhang, X.; Butler, W.H.; MacLaren, J.M.; van Ek, J.

1994-01-01

The Poisson equation for the electrostatic potential in a solid is solved using three different cellular techniques. The relative merits of these different approaches are discussed for two test charge densities for which an analytic solution to the Poisson equation is known. The first approach uses full-cell multiple-scattering theory and results in the famililar structure constant and multipole moment expansion. This solution is shown to be valid everywhere inside the cell, although for points outside the muffin-tin sphere but inside the cell the sums must be performed in the correct order to yield meaningful results. A modification of the multiple-scattering-theory approach yields a second method, a Green-function cellular method, which only requires the solution of a nearest-neighbor linear system of equations. A third approach, a related variational cellular method, is also derived. The variational cellular approach is shown to be the most accurate and reliable, and to have the best convergence in angular momentum of the three methods. Coulomb energies accurate to within 10 -6 hartree are easily achieved with the variational cellular approach, demonstrating the practicality of the approach in electronic structure calculations

Extension of Gibbs-Duhem equation including influences of external fields

Science.gov (United States)

Guangze, Han; Jianjia, Meng

2018-03-01

Gibbs-Duhem equation is one of the fundamental equations in thermodynamics, which describes the relation among changes in temperature, pressure and chemical potential. Thermodynamic system can be affected by external field, and this effect should be revealed by thermodynamic equations. Based on energy postulate and the first law of thermodynamics, the differential equation of internal energy is extended to include the properties of external fields. Then, with homogeneous function theorem and a redefinition of Gibbs energy, a generalized Gibbs-Duhem equation with influences of external fields is derived. As a demonstration of the application of this generalized equation, the influences of temperature and external electric field on surface tension, surface adsorption controlled by external electric field, and the derivation of a generalized chemical potential expression are discussed, which show that the extended Gibbs-Duhem equation developed in this paper is capable to capture the influences of external fields on a thermodynamic system.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions.

Science.gov (United States)

Latella, Ivan; Pérez-Madrid, Agustín

2013-10-01

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Thermodynamic quantities for the Klein–Gordon equation

Indian Academy of Sciences (India)

We study some thermodynamic quantities for the Klein–Gordon equation with a linear plus inverselinear, scalar potential. We obtain the energy eigenvalues with the help of the quantization rule from the biconfluent Heun's equation.We use a method based on the Euler–MacLaurin formula to analytically compute thethermal ...

Infinitely many solutions for fractional Schr\\"odinger equations in R^N

Directory of Open Access Journals (Sweden)

Caisheng Chen

2016-03-01

Full Text Available Using variational methods we prove the existence of infinitely many solutions to the fractional Schrodinger equation $$ (-\\Delta^su+V(xu=f(x,u, \\quad x\\in\\mathbb{R}^N, $$ where $N\\ge 2, s\\in (0,1$. $(-\\Delta^s$ stands for the fractional Laplacian. The potential function satisfies $V(x\\geq V_0>0$. The nonlinearity f(x,u is superlinear, has subcritical growth in u, and may or may not satisfy the (AR condition.

Variational Integrals of a Class of Nonhomogeneous -Harmonic Equations

Directory of Open Access Journals (Sweden)

Guanfeng Li

2014-01-01

Full Text Available We introduce a class of variational integrals whose Euler equations are nonhomogeneous -harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous -harmonic equations by applying direct methods of the calculus of variations. Besides, we establish some interesting results on variational integrals.

Reduction of the Breit Coulomb equation to an equivalent Schroedinger equation, and investigation of the behavior of the wave function near the origin

International Nuclear Information System (INIS)

Malenfant, J.

1988-01-01

The Breit equation for two equal-mass spin-1/2 particles interacting through an attractive Coulomb potential is separated into its angular and radial parts, obtaining coupled sets of first-order differential equations for the radial wave functions. The radial equations for the 1 J/sub J/, 3 J/sub J/, and 3 P 0 states are further reduced to a single, one-dimensional Schroedinger equation with a relatively simple effective potential. No approximations, other than the initial one of an instantaneous Coulomb interaction, are made in deriving this equation; it accounts for all relativistic effects, as well as for mixing between different components of the wave function. Approximate solutions are derived for this Schroedinger equation, which gives the correct O(α 4 ) term for the 1 1 S 0 energy and for the n 1 J/sub J/ energies, for J>0. The radial equations for the 3 (J +- 1)/sub J/ states are reduced to two second-order coupled equations. At small r, the Breit Coulomb wave functions behave as r/sup ν//sup -1/, where ν is either √J(J+1)+1-α 2 /4 or √J(J+1)-α 2 /4 . The 1 S 0 and 3 P 0 wave functions therefore diverge at the origin as r/sup //sup √//sup 1-//sup α//sup <2//4 -1$. This divergence of the J = 0 states, however, does not occur when the spin-spin interaction, -(α/r)αxα, is added to the Coulomb potential

Flow fields in the supersonic through-flow fan. Comparison of the solutions of the linear potential theory and the numerical solution of the Euler equations; Choonsoku tsukaryu fan nai no nagareba. Senkei potential rironkai to Euler hoteishiki no suchikai no hikaku

Energy Technology Data Exchange (ETDEWEB)

Yamasaki, N; Nanba, M; Tashiro, K [Kyushu University, Fukuoka (Japan). Faculty of Engineering

1996-03-27

Comparison study between solutions of a linear potential theory and numerical solution of Euler equations was made for flow in a supersonic through-flow fan. In numerical fluid dynamic technique, Euler equations are solved by finite difference method under the assumption of air and perfect gas fluid, and neglected viscosity and thermal conductivity of fluid. As a result, in a linear potential theory, expansion wave was regarded as equipotential discontinuous surface, while in Euler numerical solution, it was regarded as finite pressure gradient where a wave front fans out toward downstream. The latter reflection point of shock wave on a wing existed upstream as compared with the former reflection point. The shock wave angle was dominated by Euler equations, and different from the Mach line of a linear potential theory in both angle and discontinuous quantities in front and behind. Both calculated solutions well agreed with each other until the first reflection point of the Mach line, however, thereafter the difference between them increased toward downstream. 5 refs., 5 figs., 1 tab.

Generalized Freud's equation and level densities with polynomial

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 81; Issue 2. Generalized Freud's equation and level densities with polynomial potential. Akshat Boobna Saugata Ghosh. Research Articles Volume 81 ... Keywords. Orthogonal polynomial; Freud's equation; Dyson–Mehta method; methods of resolvents; level density.

Hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit

International Nuclear Information System (INIS)

Suárez, Abril; Chavanis, Pierre-Henri

2015-01-01

Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with an arbitrary potential of the form V(|ϕ| 2 ). We compare the results with simplified models in which the gravitational potential is introduced by hand in the Klein-Gordon equation, and assumed to satisfy a (generalized) Poisson equation. Nonrelativistic hydrodynamic equations based on the Schrodinger-Poisson equations or on the Gross-Pitaevskii-Poisson equations are recovered in the limit c → +∞. (paper)

The ground state of long-range Schrödinger equations and static qq̄ potential

Energy Technology Data Exchange (ETDEWEB)

Beccaria, Matteo [Dipartimento di Matematica e Fisica Ennio De Giorgi,Università del Salento, Via Arnesano, 73100 Lecce (Italy); INFN, Via Arnesano, 73100 Lecce (Italy); Metafune, Giorgio [Dipartimento di Matematica e Fisica Ennio De Giorgi,Università del Salento, Via Arnesano, 73100 Lecce (Italy); Pallara, Diego [Dipartimento di Matematica e Fisica Ennio De Giorgi,Università del Salento, Via Arnesano, 73100 Lecce (Italy); INFN, Via Arnesano, 73100 Lecce (Italy)

2016-05-06

Motivated by the recent results in http://arxiv.org/abs/1601.05679 about the quark-antiquark potential in N=4 SYM, we reconsider the problem of computing the asymptotic weak-coupling expansion of the ground state energy of a certain class of 1d Schrödinger operators −((d{sup 2})/(dx{sup 2}))+λ V(x) with long-range potential V(x). In particular, we consider even potentials obeying ∫{sub ℝ}dx V(x)<0 with large x asymptotics V∼−a/x{sup 2}−b/x{sup 3}+⋯. The associated Schrödinger operator is known to admit a bound state for λ→0{sup +}, but the binding energy is rigorously non-analytic at λ=0. Its asymptotic expansion starts at order O(λ), but contains higher corrections λ{sup n} log{sup m} λ with all 0≤m≤n−1 and standard Rayleigh-Schrödinger perturbation theory fails order by order in λ. We discuss various analytical tools to tame this problem and provide the general expansion of the binding energy at O(λ{sup 3}) in terms of quadratures. The method is tested on a soluble potential that is fully under control, and on various non-soluble cases as well. A supersymmetric case, arising in the study of the quark-antiquark potential in N=6 ABJ(M) theory, is also exploited to provide a further non-trivial consistency check. Our analytical results confirm at third order a remarkable exponentiation of the leading infrared logarithms, first noticed in N=4 SYM where it may be proved by Renormalization Group arguments. We prove this interesting feature at all orders at the level of the Schrödinger equation for general potentials in the considered class.

Picone-type inequalities for nonlinear elliptic equations and their applications

Directory of Open Access Journals (Sweden)

Takaŝi Kusano

2001-01-01

Full Text Available Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are also obtained.

A Coordinate Transformation for Unsteady Boundary Layer Equations

Directory of Open Access Journals (Sweden)

Paul G. A. CIZMAS

2011-12-01

Full Text Available This paper presents a new coordinate transformation for unsteady, incompressible boundary layer equations that applies to both laminar and turbulent flows. A generalization of this coordinate transformation is also proposed. The unsteady boundary layer equations are subsequently derived. In addition, the boundary layer equations are derived using a time linearization approach and assuming harmonically varying small disturbances.

Bipartite Fuzzy Stochastic Differential Equations with Global Lipschitz Condition

Directory of Open Access Journals (Sweden)

Marek T. Malinowski

2016-01-01

Full Text Available We introduce and analyze a new type of fuzzy stochastic differential equations. We consider equations with drift and diffusion terms occurring at both sides of equations. Therefore we call them the bipartite fuzzy stochastic differential equations. Under the Lipschitz and boundedness conditions imposed on drifts and diffusions coefficients we prove existence of a unique solution. Then, insensitivity of the solution under small changes of data of equation is examined. Finally, we mention that all results can be repeated for solutions to bipartite set-valued stochastic differential equations.

Effective Schroedinger equations on submanifolds

Energy Technology Data Exchange (ETDEWEB)

Wachsmuth, Jakob

2010-02-11

In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.

Special solutions of neutral functional differential equations

Directory of Open Access Journals (Sweden)

Győri István

2001-01-01

Full Text Available For a system of nonlinear neutral functional differential equations we prove the existence of an -parameter family of "special solutions" which characterize the asymptotic behavior of all solutions at infinity. For retarded functional differential equations the special solutions used in this paper were introduced by Ryabov.

Potential scattering of Dirac particles

International Nuclear Information System (INIS)

Thaller, B.

1981-01-01

A quantum mechanical interpretation of the Dirac equation for particles in external electromagnetic potentials is discussed. It is shown that a consequent development of the Stueckelberg-Feynman theory into a probabilistic interpretation of the Dirac equation corrects some prejudices concerning negative energy states, Zitterbewegung and bound states in repulsive potentials and yields the connection between propagator theory and scattering theory. Limits of the Dirac equation, considered as a wave mechanical equation, are considered. (U.K.)

A hierarchy of Liouville integrable discrete Hamiltonian equations

Energy Technology Data Exchange (ETDEWEB)

Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn

2008-05-12

Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.

New material equations for electromagnetism with toroid polarizations

International Nuclear Information System (INIS)

Dubovik, V.M.; Martsenyuk, M.A.; Saha, B.

1999-09-01

With regard to the toroid contributions, a modified system of equations of electrodynamics moving continuous media has been obtained. Alternative formalisms to introduce the toroid moment contributions in the equations of electromagnetism has been worked out. The two four-potential formalism has been developed. Lorentz transformation laws for the toroid polarizations has been given. Covariant form of equations of electrodynamics of continuous media with toroid polarizations has been written. (author)

Self-dual solutions to Euclidean Yang-Mills equations

International Nuclear Information System (INIS)

Corrigan, E.

1979-01-01

The paper provides an introduction to two approaches towards understanding the classical Yang-Mills field equations. On the one hand, the work of Atiyah and Ward showed that the self-dual equations, which are non-linear, could be regarded as a set of linear equations which turned out to be related to each other by Baecklund transformations. Fundamental to their procedure was the observation that the information carried by the vector potential could be coded into the structure of certain analytic vector bundles over a three dimensional projective space. The classification of these bundles and the subsequent recovery of the gauge field led to the infinite set of ansaetze, corresponding to the sets of linear equation mentioned already. On the other hand, Atiyah, Hitchin, Drinfeld and Manin have recently constructed, completely algebraically, the bundles of interest and indicated how the Yang-Mills potential may be obtained. Remarkably, their construction differs very little as the gauge group is changed (to any of the classical compact groups) and, uses only the elementary operations of linear algebra to yield potentials as rational functions of the spatial coordinates. (Auth.)

Developing a generalized allometric equation for aboveground biomass estimation

Science.gov (United States)

Xu, Q.; Balamuta, J. J.; Greenberg, J. A.; Li, B.; Man, A.; Xu, Z.

2015-12-01

A key potential uncertainty in estimating carbon stocks across multiple scales stems from the use of empirically calibrated allometric equations, which estimate aboveground biomass (AGB) from plant characteristics such as diameter at breast height (DBH) and/or height (H). The equations themselves contain significant and, at times, poorly characterized errors. Species-specific equations may be missing. Plant responses to their local biophysical environment may lead to spatially varying allometric relationships. The structural predictor may be difficult or impossible to measure accurately, particularly when derived from remote sensing data. All of these issues may lead to significant and spatially varying uncertainties in the estimation of AGB that are unexplored in the literature. We sought to quantify the errors in predicting AGB at the tree and plot level for vegetation plots in California. To accomplish this, we derived a generalized allometric equation (GAE) which we used to model the AGB on a full set of tree information such as DBH, H, taxonomy, and biophysical environment. The GAE was derived using published allometric equations in the GlobAllomeTree database. The equations were sparse in details about the error since authors provide the coefficient of determination (R2) and the sample size. A more realistic simulation of tree AGB should also contain the noise that was not captured by the allometric equation. We derived an empirically corrected variance estimate for the amount of noise to represent the errors in the real biomass. Also, we accounted for the hierarchical relationship between different species by treating each taxonomic level as a covariate nested within a higher taxonomic level (e.g. species contribution of each different covariate in estimating the AGB of trees. Lastly, we applied the GAE to an existing vegetation plot database - Forest Inventory and Analysis database - to derive per-tree and per-plot AGB estimations, their errors, and how

Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials

Science.gov (United States)

Liu, Lei; Tian, Bo; Wu, Xiao-Yu; Sun, Yan

2018-02-01

Under investigation in this paper is the higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials which can be applied in the nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation. Based on the Kadomtsev-Petviashvili hierarchy reduction, we construct the Nth order rogue wave-like solutions in terms of the Gramian under the integrable constraint. With the help of the analytic and graphic analysis, we exhibit the first-, second- and third-order rogue wave-like solutions through the different dispersion, nonlinearity and linear potential coefficients. We find that only if the dispersion and nonlinearity coefficients are proportional to each other, heights of the background of those rogue waves maintain unchanged with time increasing. Due to the existence of complex parameters, such nonautonomous rogue waves in the higher-order cases have more complex features than those in the lower.

Properties of meromorphic solutions to certain differential-difference equations

Directory of Open Access Journals (Sweden)

Xiaoguang Qi

2013-06-01

Full Text Available We consider the properties of meromorphic solutions to certain type of non-linear difference equations. Also we show the existence of meromorphic solutions with finite order for differential-difference equations related to the Fermat type functional equation. This article extends earlier results by Liu et al [12].

Modeling and analysis of surface potential of single gate fully depleted SOI MOSFET using 2D-Poisson's equation

Science.gov (United States)

Mani, Prashant; Tyagi, Chandra Shekhar; Srivastav, Nishant

2016-03-01

In this paper the analytical solution of the 2D Poisson's equation for single gate Fully Depleted SOI (FDSOI) MOSFET's is derived by using a Green's function solution technique. The surface potential is calculated and the threshold voltage of the device is minimized for the low power consumption. Due to minimization of threshold voltage the short channel effect of device is suppressed and after observation we obtain the device is kink free. The structure and characteristics of SingleGate FDSOI MOSFET were matched by using MathCAD and silvaco respectively.

MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE

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Francisco Frutos Alfaro

2017-04-01

Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.

The GUP and quantum Raychaudhuri equation

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Elias C. Vagenas

2018-06-01

Full Text Available In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalised uncertainty principle, with the corrections from the quantum Raychaudhuri equation. The reason for this comparison is to connect the deformation parameters β0 and α0 with η which is the parameter that characterises the quantum Raychaudhuri equation. The derived relation between the parameters appears to depend on the relative scale of the system (black hole, which could be read as a beta function equation for the quadratic deformation parameter β0. This study shows a correspondence between the two phenomenological approaches and indicates that quantum Raychaudhuri equation implies the existence of a crystal-like structure of spacetime.

Solitons in Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Lopes, E.

1985-01-01

It is observed that, when the potential is integrable and repulsive, the Gross-Pitaevskii Equation, with non-vanishing boundary conditions, describes a family of planar solitons. A method is presented which provides an exact soliton field to the Dirac Delta potential and an approximation solution to any other kind of potential. As an example the method is then applied to the case of a repulsive Yukawa potential. A brief discuss the relation between these solitons and Anderson's superfluidity mechanism, is also presented. (author) [pt

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

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Thomas Gomez

2018-04-01

Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

Interior Gradient Estimates for Nonuniformly Parabolic Equations II

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Lieberman Gary M

2007-01-01

Full Text Available We prove interior gradient estimates for a large class of parabolic equations in divergence form. Using some simple ideas, we prove these estimates for several types of equations that are not amenable to previous methods. In particular, we have no restrictions on the maximum eigenvalue of the coefficient matrix and we obtain interior gradient estimates for so-called false mean curvature equation.

Relativistic n-body wave equations in scalar quantum field theory

International Nuclear Information System (INIS)

Emami-Razavi, Mohsen

2006-01-01

The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields

Emmy Noether and Linear Evolution Equations

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P. G. L. Leach

2013-01-01

Full Text Available Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have an equivalent in the Schrödinger Equation corresponding to the Lagrangian and by extension to linear evolution equations in general. The implications of these connections are investigated.

Integrodifferential equation approach. Pt. 1

International Nuclear Information System (INIS)

Oehm, W.; Sofianos, S.A.; Fiedeldey, H.; South Africa Univ., Pretoria. Dept. of Physics); Fabre de la Ripelle, M.; South Africa Univ., Pretoria. Dept. of Physics)

1990-02-01

A single integrodifferential equation in two variables, valid for A nucleons interacting by pure Wigner forces, which has previously only been solved in the extreme and uncoupled adiabatic approximations is now solved exactly for three- and four-nucleon systems. The results are in good agreement with the values obtained for the binding energies by means of an empirical interpolation formula. This validates all our previous conclusions, in particular that the omission of higher (than two) order correlations in our four-body equation only produces a rather small underbinding. The integrodifferential equation approach (IDEA) is here also extended to spin-dependent forces of the Malfliet-Tjon type, resulting in two coupled integrodifferential equations in two variables. The exact solution and the interpolated adiabatic approximation are again in good agreement. The inclusion of the hypercentral part of the two-body interaction in the definition of the Faddeev-type components again leads to substantial improvement for fully local potentials, acting in all partial waves. (orig.)

General Navier–Stokes-like momentum and mass-energy equations

Energy Technology Data Exchange (ETDEWEB)

Monreal, Jorge, E-mail: jmonreal@mail.usf.edu

2015-03-15

A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors.

Dirac equation on a curved surface

Energy Technology Data Exchange (ETDEWEB)

Brandt, F.T., E-mail: fbrandt@usp.br; Sánchez-Monroy, J.A., E-mail: antosan@usp.br

2016-09-07

The dynamics of Dirac particles confined to a curved surface is examined employing the thin-layer method. We perform a perturbative expansion to first-order and split the Dirac field into normal and tangential components to the surface. In contrast to the known behavior of second order equations like Schrödinger, Maxwell and Klein–Gordon, we find that there is no geometric potential for the Dirac equation on a surface. This implies that the non-relativistic limit does not commute with the thin-layer method. Although this problem can be overcome when second-order terms are retained in the perturbative expansion, this would preclude the decoupling of the normal and tangential degrees of freedom. Therefore, we propose to introduce a first-order term which rescues the non-relativistic limit and also clarifies the effect of the intrinsic and extrinsic curvatures on the dynamics of the Dirac particles. - Highlights: • The thin-layer method is employed to derive the Dirac equation on a curved surface. • A geometric potential is absent at least to first-order in the perturbative expansion. • The effects of the extrinsic curvature are included to rescue the non-relativistic limit. • The resulting Dirac equation is consistent with the Heisenberg uncertainty principle.

Abundant Interaction Solutions of Sine-Gordon Equation

Directory of Open Access Journals (Sweden)

DaZhao Lü

2012-01-01

Full Text Available With the help of computer symbolic computation software (e.g., Maple, abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equations. Such interaction solutions are difficultly obtained via other methods. And the method can be automatically carried out in computer.

Nested variant of the method of moments of coupled cluster equations for vertical excitation energies and excited-state potential energy surfaces.

Science.gov (United States)

Kowalski, Karol

2009-05-21

In this article we discuss the problem of proper balancing of the noniterative corrections to the ground- and excited-state energies obtained with approximate coupled cluster (CC) and equation-of-motion CC (EOMCC) approaches. It is demonstrated that for a class of excited states dominated by single excitations and for states with medium doubly excited component, the newly introduced nested variant of the method of moments of CC equations provides mathematically rigorous way of balancing the ground- and excited-state correlation effects. The resulting noniterative methodology accounting for the effect of triples is tested using its parallel implementation on the systems, for which iterative CC/EOMCC calculations with full inclusion of triply excited configurations or their most important subset are numerically feasible.

Eulerian derivations of non-inertial Navier-Stokes equations

CSIR Research Space (South Africa)

Combrinck, MA

2014-09-01

Full Text Available The paper presents an Eulerian derivation of the non-inertial Navier-Stokes equations as an alternative to the Lagrangian fluid parcel approach. This work expands on the work of Kageyama and Hyodo [1] who derived the incompressible momentum equation...

New optical solitons of space-time conformable fractional perturbed Gerdjikov-Ivanov equation by sine-Gordon equation method

Science.gov (United States)

Yaşar, Elif; Yıldırım, Yakup; Yaşar, Emrullah

2018-06-01

This paper devotes to conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation which appears in nonlinear fiber optics and photonic crystal fibers (PCF). We consider the model with full nonlinearity in order to give a generalized flavor. The sine-Gordon equation approach is carried out to model equation for retrieving the dark, bright, dark-bright, singular and combined singular optical solitons. The constraint conditions are also reported for guaranteeing the existence of these solitons. We also present some graphical simulations of the solutions for better understanding the physical phenomena of the behind the considered model.

From the Hartree dynamics to the Vlasov equation

DEFF Research Database (Denmark)

Benedikter, Niels Patriz; Porta, Marcello; Saffirio, Chiara

2016-01-01

We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large N, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise...

Bound-state Dirac eigenvalues for scalar potentials

International Nuclear Information System (INIS)

Ram, B.; Arafah, M.

1981-01-01

The Dirac equation is solved with a linear and a quadratic scalar potential using an approach in which the Dirac equation is first transformed to a one-dimensional Schroedinger equation with an effective potential. The WKB method is used to obtain the energy eigenvalues. The eigenvalues for the quadratic scalar potential are real just as they are for the linear potential. The results with the linear potential agree well with those obtained by Critchfield. (author)

Asymptotic Expansions for Higher-Order Scalar Difference Equations

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Pituk Mihály

2007-01-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Positive Solutions for Coupled Nonlinear Fractional Differential Equations

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Wenning Liu

2014-01-01

Full Text Available We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones K1, K2 and computing the fixed point index in product cone K1×K2, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.

Generalization of the Dirac’s Equation and Sea

DEFF Research Database (Denmark)

Javadi, Hossein; Forouzbakhsh, Farshid; Daei Kasmaei, Hamed

2016-01-01

Newton's second law is motion equation in classic mechanics that does not say anything about the nature of force. The equivalent formulations and their extensions such as Lagrangian and Hamiltonian do not explain about mechanism of converting Potential energy to Kinetic energy and Vice versa....... In quantum mechanics, Schrodinger equation is similar to Newton's second law in classic mechanics. Quantum mechanics is also extension of Newtonian mechanics to atomic and subatomic scales and relativistic mechanics is extension of Newtonian mechanics to high velocities near to velocity of light too....... Schrodinger equation is not a relativistic equation, because it is not invariant under Lorentz transformations. Dirac expanded The Schrodinger equation by presenting Dirac Sea and founded relativistic quantum mechanics. In this paper by reconsidering the Dirac Sea and his equation, the structure of photon...

Estimating order-picking times for return heuristic - equations and simulations

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Grzegorz Tarczyński

2015-09-01

Full Text Available Background: A key element of the evaluation of warehouse operation is the average order-picking time. In warehouses where the order-picking process is carried out according to the "picker-to-part" rule the order-picking time is usually proportional to the distance covered by the picker while picking items. This distance can by estimated by simulations or using mathematical equations. In the paper only the best described in the literature one-block rectangular warehouses are considered. Material and methods: For the one-block rectangular warehouses there are well known five routing heuristics. In the paper the author considers the return heuristic in two variants. The paper presents well known Hall's and De Koster's equations for the average distance traveled by the picker while completing items from one pick list. The author presents own proposals for calculating the expected distance. Results: the results calculated by the use of mathematical equations (the formulas of Hall, De Koster and own propositions were compared with the average values obtained using computer simulations. For the most cases the average error does not exceed 1% (except for Hall's equations. To carry out simulation the computer software Warehouse Real-Time Simulator was used. Conclusions: the order-picking time is a function of many variables and its optimization is not easy. It can be done in two stages: firstly using mathematical equations the set of the potentially best variants is established, next the results are verified using simulations. The results calculated by the use of equations are not precise, but possible to achieve immediately. The simulations are more time-consuming, but allow to analyze the order-picking process more accurately.

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

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Tieshan He

2011-01-01

Full Text Available This paper is concerned with the existence of nontrivial periodic solutions and positive periodic solutions to a nonlinear second-order difference equation. Under some conditions concerning the first positive eigenvalue of the linear equation corresponding to the nonlinear second-order equation, we establish the existence results by using the topological degree and fixed point index theories.

On some perturbation techniques for quasi-linear parabolic equations

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Igor Malyshev

1990-01-01

Full Text Available We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in “explicit” form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.

Iterative solution of the semiconductor device equations

Energy Technology Data Exchange (ETDEWEB)

Bova, S.W.; Carey, G.F. [Univ. of Texas, Austin, TX (United States)

1996-12-31

Most semiconductor device models can be described by a nonlinear Poisson equation for the electrostatic potential coupled to a system of convection-reaction-diffusion equations for the transport of charge and energy. These equations are typically solved in a decoupled fashion and e.g. Newton`s method is used to obtain the resulting sequences of linear systems. The Poisson problem leads to a symmetric, positive definite system which we solve iteratively using conjugate gradient. The transport equations lead to nonsymmetric, indefinite systems, thereby complicating the selection of an appropriate iterative method. Moreover, their solutions exhibit steep layers and are subject to numerical oscillations and instabilities if standard Galerkin-type discretization strategies are used. In the present study, we use an upwind finite element technique for the transport equations. We also evaluate the performance of different iterative methods for the transport equations and investigate various preconditioners for a few generalized gradient methods. Numerical examples are given for a representative two-dimensional depletion MOSFET.

INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS

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Elena N. Kushner

2018-01-01

Full Text Available For the generalized Rapoport-Leas equations, algebra of differential invariants is constructed with respect to point transformations, that is, transformations of independent and dependent variables. The finding of a general transformation of this type reduces to solving an extremely complicated functional equation. Therefore, following the approach of Sophus Lie, we restrict ourselves to the search for infinitesimal transformations which are generated by translations along the trajectories of vector fields. The problem of finding these vector fields reduces to the redefined system decision of linear differential equations with respect to their coefficients. The Rapoport-Leas equations arise in the study of nonlinear filtration processes in porous media, as well as in other areas of natural science: for example, these equations describe various physical phenomena: two-phase filtration in a porous medium, filtration of a polytropic gas, and propagation of heat at nuclear explosion. They are vital topic for research: in recent works of Bibikov, Lychagin, and others, the analysis of the symmetries of the generalized Rapoport-Leas equations has been carried out; finite-dimensional dynamics and conditions of attractors existence have been found. Since the generalized RapoportLeas equations are nonlinear partial differential equations of the second order with two independent variables; the methods of the geometric theory of differential equations are used to study them in this paper. According to this theory differential equations generate subvarieties in the space of jets. This makes it possible to use the apparatus of modern differential geometry to study differential equations. We introduce the concept of admissible transformations, that is, replacements of variables that do not derive equations outside the class of the Rapoport-Leas equations. Such transformations form a Lie group. For this Lie group there are differential invariants that separate

Solution of Einstein's Geometrical Gravitational Field Equations Exterior to Astrophysically Real or Hypothetical Time Varying Distributions of Mass within Regions of Spherical Geometry

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Chifu E. N.

2009-07-01

Full Text Available Here, we present a profound and complete analytical solution to Einstein’s gravitational field equations exterior to astrophysically real or hypothetical time varying distribu- tions of mass or pressure within regions of spherical geometry. The single arbitrary function f in our proposed exterior metric tensor and constructed field equations makes our method unique, mathematically less combersome and astrophysically satisfactory. The obtained solution of Einstein’s gravitational field equations tends out to be a gen- eralization of Newton’s gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration

General solutions of second-order linear difference equations of Euler type

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Akane Hongyo

2017-01-01

Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

Introduction to the Yang-Baxter Equation with Open Problems

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Florin Nichita

2012-04-01

Full Text Available The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C. N. Yang, and in statistical mechanics, in R. J. Baxter’s work. Later, it turned out that this equation plays a crucial role in: quantum groups, knot theory, braided categories, analysis of integrable systems, quantum mechanics, non-commutative descent theory, quantum computing, non-commutative geometry, etc. Many scientists have found solutions for the Yang-Baxter equation, obtaining qualitative results (using the axioms of various algebraic structures or quantitative results (usually using computer calculations. However, the full classification of its solutions remains an open problem. In this paper, we present the (set-theoretical Yang-Baxter equation, we sketch the proof of a new theorem, we state some problems, and discuss about directions for future research.

Nonlinear q-Generalizations of Quantum Equations: Homogeneous and Nonhomogeneous Cases—An Overview

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Fernando D. Nobre

2017-01-01

Full Text Available Recent developments on the generalizations of two important equations of quantum physics, namely the Schroedinger and Klein–Gordon equations, are reviewed. These generalizations present nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard linear equations are recovered in the limit q → 1 . Interestingly, these equations present a common, soliton-like, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In both cases, the corresponding well-known Einstein energy-momentum relations, as well as the Planck and the de Broglie ones, are preserved for arbitrary values of q. In order to deal appropriately with the continuity equation, a classical field theory has been developed, where besides the usual Ψ ( x → , t , a new field Φ ( x → , t must be introduced; this latter field becomes Ψ * ( x → , t only when q → 1 . A class of linear nonhomogeneous Schroedinger equations, characterized by position-dependent masses, for which the extra field Φ ( x → , t becomes necessary, is also investigated. In this case, an appropriate transformation connecting Ψ ( x → , t and Φ ( x → , t is proposed, opening the possibility for finding a connection between these fields in the nonlinear cases. The solutions presented herein are potential candidates for applications to nonlinear excitations in plasma physics, nonlinear optics, in structures, such as those of graphene, as well as in shallow and deep water waves.

Controllability of the moments for Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation

OpenAIRE

Rozanova-Pierrat , Anna

2006-01-01

Recalling the proprieties of the Khokhlov-Zabolotskaya-Kuznetsov(KZK) equation, we prove the controllability of moments result for the linear part of KZK equation. Then we prove the local controllability result for the full KZK equation applying a known method of perturbation for the nonlinear inverse problem.

Communication: A benchmark-quality, full-dimensional ab initio potential energy surface for Ar-HOCO

International Nuclear Information System (INIS)

Conte, Riccardo; Bowman, Joel M.; Houston, Paul L.

2014-01-01

A full-dimensional, global ab initio potential energy surface (PES) for the Ar-HOCO system is presented. The PES consists of a previous intramolecular ab initio PES for HOCO [J. Li, C. Xie, J. Ma, Y. Wang, R. Dawes, D. Xie, J. M. Bowman, and H. Guo, J. Phys. Chem. A 116, 5057 (2012)], plus a new permutationally invariant interaction potential based on fitting 12 432 UCCSD(T)-F12a/aVDZ counterpoise-corrected energies. The latter has a total rms fitting error of about 25 cm −1 for fitted interaction energies up to roughly 12 000 cm −1 . Two additional fits are presented. One is a novel very compact permutational invariant representation, which contains terms only involving the Ar-atom distances. The rms fitting error for this fit is 193 cm −1 . The other fit is the widely used pairwise one. The pairwise fit to the entire data set has an rms fitting error of 427 cm −1 . All of these potentials are used in preliminary classical trajectory calculations of energy transfer with a focus on comparisons with the results using the benchmark potential

Communication: A benchmark-quality, full-dimensional ab initio potential energy surface for Ar-HOCO

Energy Technology Data Exchange (ETDEWEB)

Conte, Riccardo, E-mail: riccardo.conte@emory.edu, E-mail: jmbowma@emory.edu; Bowman, Joel M., E-mail: riccardo.conte@emory.edu, E-mail: jmbowma@emory.edu [Department of Chemistry and Cherry L. Emerson Center for Scientific Calculation, Emory University, Atlanta, Georgia 30322 (United States); Houston, Paul L., E-mail: paul.houston@cos.gatech.edu [School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)

2014-04-21

A full-dimensional, global ab initio potential energy surface (PES) for the Ar-HOCO system is presented. The PES consists of a previous intramolecular ab initio PES for HOCO [J. Li, C. Xie, J. Ma, Y. Wang, R. Dawes, D. Xie, J. M. Bowman, and H. Guo, J. Phys. Chem. A 116, 5057 (2012)], plus a new permutationally invariant interaction potential based on fitting 12 432 UCCSD(T)-F12a/aVDZ counterpoise-corrected energies. The latter has a total rms fitting error of about 25 cm{sup −1} for fitted interaction energies up to roughly 12 000 cm{sup −1}. Two additional fits are presented. One is a novel very compact permutational invariant representation, which contains terms only involving the Ar-atom distances. The rms fitting error for this fit is 193 cm{sup −1}. The other fit is the widely used pairwise one. The pairwise fit to the entire data set has an rms fitting error of 427 cm{sup −1}. All of these potentials are used in preliminary classical trajectory calculations of energy transfer with a focus on comparisons with the results using the benchmark potential.

Solving Differential Equations in R: Package deSolve

Directory of Open Access Journals (Sweden)

Karline Soetaert

2010-02-01

Full Text Available In this paper we present the R package deSolve to solve initial value problems (IVP written as ordinary differential equations (ODE, differential algebraic equations (DAE of index 0 or 1 and partial differential equations (PDE, the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR, DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1 to demonstrate the potential of using R for dynamic modeling, (2 to highlight typical uses of the different methods implemented and (3 to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to R’s high-level procedures. deSolve is the successor of package odesolve which will be deprecated in

Realizing the full potential of a RITA spectrometer

DEFF Research Database (Denmark)

Lefmann, K.; Niedermayer, C.; Abrahamsen, A.B.

2006-01-01

The “re-invented triple-axis spectrometer (RITA) concept has existed for a decade. Recent developments at RITA-2 at PSI, have revealed more of the potential of this instrument class. We demonstrate the performance of the multi-blade imaging mode, which has been applied e.g. to studies of dispersion...... relations and emphasize the power of this mode in combination with the low background of RITA-2. In addition, we present other ways of utilizing the position sensitive detector in a RITA instrument. Simulations of a planned upgrade of the guide-monochromator system at RITA-2 have shown a potential...

Numerical investigation of action potential transmission in plants

Directory of Open Access Journals (Sweden)

Mariusz Pietruszka

2014-01-01

Full Text Available In context of a fairly concise review of recent literature and well established experimental results we reconsider the problem of action potential propagating steadily down the plant cell(s. Having adopted slightly modified Hodgkin-Huxley set of differential equations for the action potential we carried out the numerical investigation of these equations in the course of time. We argue that the Hodgkin-Huxley-Katz model for the nerve impulse can be used to describe the phenomena which take place in plants - this point of view seems to be plausible since the mechanisms involving active ionic transport across membranes from the mathematical point of view are similar. Besides, we compare in a qualitative way our theoretical outcomes with typical experimental results for the action potentials which arise as the reaction of plants to electrical, mechanical and light stimuli. Moreover, we point out the relevance of the sequence of events during the pulse with the appropriate ionic fluxes.

An implicit spectral formula for generalized linear Schroedinger equations

International Nuclear Information System (INIS)

Schulze-Halberg, A.; Garcia-Ravelo, J.; Pena Gil, Jose Juan

2009-01-01

We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schroedinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schroedinger equation or the Schroedinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form. (author)

Equation Discovery for Financial Forcasting in Context of Islamic Banking

Institute of Scientific and Technical Information of China (English)

Amer Alzaidi; Dimitar Kazakov

2010-01-01

This paper describes an equation discovery approach based on machine leamng using LAGdtAMGE as an equation discovery tool,with two sources of input,a dataset and model presented in context-free gammar.The approach is searching a large range of potential equations by a specific model.The parameters of the equation are fitted to find the best equations.The The experiments are illustratedwith commodity prices from the London Metal Exchange for the period of January-October 2009.The outputs of the experiments are a large number of equations;same of the equations display that the predicted rakes are following the market trends in perfect patterns.

Bogomolny equations in certain generalized baby BPS Skyrme models

Science.gov (United States)

Stępień, Ł. T.

2018-01-01

By using the concept of strong necessary conditions (CSNCs), we derive Bogomolny equations and Bogomol’nyi-Prasad-Sommerfield (BPS) bounds for two certain modifications of the baby BPS Skyrme model: the nonminimal coupling to the gauge field and the k-deformed ungauged model. In particular, we study how the Bogomolny equations and the equation for the potential reflect these two modifications. In both examples, the CSNC method appears to be a very useful tool. We also find certain localized solutions of these Bogomolny equations.

Integro-differential equation approach extended to larger nuclei

International Nuclear Information System (INIS)

Adam, R.M.; Sofianos, S.A.; Fiedeldey, H.; Fabre de la Ripelle, M.

1992-01-01

We extend the integro-differential equation approach (IDEA) from few-nucleon to closed-shell and closed-subshell nuclei and outline the analytical methods required for the calculation of the density functions, which enter into the integro-differential equations. These contain all the physics for a system of fermions associated with the Pauli principle. In order to test the accuracy of the IDEA comparisons are made of the binding energies of 4 He, 12 C and 16 O obtained with effective potentials using the hypercentral approximation (HCA) providing a variational solution without correlations, the IDEA which fully includes the two-body correlations, the S-states integro-differential equation (SIDE) valid for potentials operating only on pairs in the S-state and those calculated by several variational or perturbative methods in the literature. (author)

Asymptotic Expansions for Higher-Order Scalar Difference Equations

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Ravi P. Agarwal

2007-04-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Wave-equation dispersion inversion

KAUST Repository

Li, Jing

2016-12-08

We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

Equivalence of two alternative approaches to Schroedinger equations

International Nuclear Information System (INIS)

Goenuel, B; Koeksal, K

2006-01-01

A recently developed simple approach for the exact/approximate solution of Schroedinger equations with constant/position-dependent mass, in which the potential is considered as in the perturbation theory, is shown to be equivalent to the one leading to the construction of exactly solvable potentials via the solution of second-order differential equations in terms of known special functions. The formalism in the former solves difficulties encountered in the latter in revealing the corrections explicitly to the unperturbed piece of the solutions whereas the other obviates cumbersome procedures used in the calculations of the former

Maxwell-Like Equations for Free Dirac Electrons

Science.gov (United States)

Bruce, S. A.

2018-03-01

In this article, we show that the wave equation for a free Dirac electron can be represented in a form that is analogous to Maxwell's electrodynamics. The electron bispinor wavefunction is explicitly expressed in terms of its real and imaginary components. This leads us to incorporate into it appropriate scalar and pseudo-scalar fields in advance, so that a full symmetry may be accomplished. The Dirac equation then takes on a form similar to that of a set of inhomogeneous Maxwell's equations involving a particular self-source. We relate plane wave solutions of these equations to waves corresponding to free Dirac electrons, identifying the longitudinal component of the electron motion, together with the corresponding Zitterbewegung ("trembling motion").

SCIENTIFIC AND METHODICAL ASPECTS OF FORMATION OF SUBJECT CONTENT OF TRAINING COURSESFOR INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS

Directory of Open Access Journals (Sweden)

В С Корнилов

2016-12-01

Full Text Available The article presents scientific and methodical aspects of forming the content of education inverse problems for differential equations for students of higher educational institutions of physical, mathematical and natural science training areas. The goals are formulated and the principles of training are the content of learning inverse problems for differential equations. Attention is drawn to the particular issues of teaching courses inverse problems. Describes the classification criteria and target modules that play the role of tools to create and analyze the model and curriculum, forming learning content inverse problems for differential equations. The content classification features and target modules. Formulate conclusions that learning the inverse problems for differential equations has scientific, educational and humanitarian potential of students and as a result of this training they gain the fundamental knowledge in the applied and computational mathematics, and also develop scientific worldview, applied, environmental, information thinking.

An alternative form of the Darcy equation

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Awad Mohamed M.

2014-01-01

Full Text Available This study presents an alternative form of the Darcy equation. This alternative form will be presented with the use of Bejan number (Be in the Left Hand Side (LHS of the equation. The main advantage in this alternative form of the Darcy equation is presenting both the Left Hand Side (LHS and the Right Hand Side (RHS as dimensionless quantities. For instance, this is similar to the relation of Fanning friction factor with Reynolds number for Hagen-Poiseuille flow (fully developed laminar flow in a circular pipe.

Solutions and Conservation Laws of a (2+1-Dimensional Boussinesq Equation

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Letlhogonolo Daddy Moleleki

2013-01-01

Full Text Available We study a nonlinear evolution partial differential equation, namely, the (2+1-dimensional Boussinesq equation. For the first time Lie symmetry method together with simplest equation method is used to find the exact solutions of the (2+1-dimensional Boussinesq equation. Furthermore, the new conservation theorem due to Ibragimov will be utilized to construct the conservation laws of the (2+1-dimensional Boussinesq equation.

Quarkonia from charmonium and renormalization group equations

International Nuclear Information System (INIS)

Ditsas, P.; McDougall, N.A.; Moorhouse, R.G.

1978-01-01

A prediction of the upsilon and strangeonium spectra is made from the charmonium spectrum by solving the Salpeter equation using an identical potential to that used in charmonium. Effective quark masses and coupling parameters αsub(s) are functions of the inter-quark distance according to the renormalization group equations. The use of the Fermi-Breit Hamiltonian for obtaining the charmonium hyperfine splitting is criticized. (Auth.)

BCS @ 50: derivation of gap equations in different lattice geometries

International Nuclear Information System (INIS)

Saurabh Basu

2007-07-01

We rigorously derive BCS gap equations for a square, triangular and a honeycomb lattice using a two-dimensional t-J model. The gap equations in all the three lattice geometries look usual, with band indices appearing and a minor modification in the separable pair potential for the (two band) honeycomb lattice. In each case, the gap equation is solved (self consistently with the number equation) at low densities assuming singlet pairing. (author)

Determination of quark-antiquark potentials and meson spectra

International Nuclear Information System (INIS)

Semay, C.; Silvestre-Brac, B.

1999-01-01

We determine two different sets of quark-antiquark potential to be used in a Schroedinger or a Salpeter type of equation. The central part contains QCD inspired components: the Coulomb like interaction, the confinement potential and an instanton interaction. It is supplemented with phenomenological relativistic corrections. The constituent quarks are characterized by a colour charge density. The parameters are determined by a minimization procedure on representative samples of mesons and the full spectra are calculated. Refs. 6, tabs. 2 (author)

Contact Geometry of Hyperbolic Equations of Generic Type

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Dennis The

2008-08-01

Full Text Available We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6, Goursat (class 6-7 and generic (class 7-7 hyperbolic equations, we use Cartan's equivalence method to study the generic case. An intriguing feature of this class of equations is that every generic hyperbolic equation admits at most a nine-dimensional contact symmetry algebra. The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric generic hyperbolic equations are derived and explicit symmetry algebras are presented. Moreover, these maximally symmetric equations are Darboux integrable. An enumeration of several submaximally symmetric (eight and seven-dimensional generic hyperbolic structures is also given.

Relativistic wave equations and compton scattering

International Nuclear Information System (INIS)

Sutanto, S.H.; Robson, B.A.

1998-01-01

Full text: Recently an eight-component relativistic wave equation for spin-1/2 particles was proposed.This equation was obtained from a four-component spin-1/2 wave equation (the KG1/2 equation), which contains second-order derivatives in both space and time, by a procedure involving a linearisation of the time derivative analogous to that introduced by Feshbach and Villars for the Klein-Gordon equation. This new eight-component equation gives the same bound-state energy eigenvalue spectra for hydrogenic atoms as the Dirac equation but has been shown to predict different radiative transition probabilities for the fine structure of both the Balmer and Lyman a-lines. Since it has been shown that the new theory does not always give the same results as the Dirac theory, it is important to consider the validity of the new equation in the case of other physical problems. One of the early crucial tests of the Dirac theory was its application to the scattering of a photon by a free electron: the so-called Compton scattering problem. In this paper we apply the new theory to the calculation of Compton scattering to order e 2 . It will be shown that in spite of the considerable difference in the structure of the new theory and that of Dirac the cross section is given by the Klein-Nishina formula

Saha's ionization equation for high Z elements

International Nuclear Information System (INIS)

Godwal, B.K.; Sikka, S.K.

1977-01-01

Saha's ionization equation has been solved for high Z elements with the aim of providing input for opacity calculations. Results are presented for two elements, tungsten and uranium. The ionization potentials have been evaluated using the simple Bhor's formula with suitable effective charges for ions. The reliability of the free electron density, ion concentrations, etc., obtained from the Saha's equation solutions has been checked by comparing the P and E computed from them with those given by the Thomas-Fermi-Dirac equation of state. The agreement between the two is good from temperatures above 0.2 keV. (author)

Parametrically Excited Oscillations of Second-Order Functional Differential Equations and Application to Duffing Equations with Time Delay Feedback

Directory of Open Access Journals (Sweden)

Mervan Pašić

2014-01-01

Full Text Available We study oscillatory behaviour of a large class of second-order functional differential equations with three freedom real nonnegative parameters. According to a new oscillation criterion, we show that if at least one of these three parameters is large enough, then the main equation must be oscillatory. As an application, we study a class of Duffing type quasilinear equations with nonlinear time delayed feedback and their oscillations excited by the control gain parameter or amplitude of forcing term. Finally, some open questions and comments are given for the purpose of further study on this topic.

Ventilation equations for improved exothermic process control.

Science.gov (United States)

McKernan, John L; Ellenbecker, Michael J

2007-04-01

Exothermic or heated processes create potentially unsafe work environments for an estimated 5-10 million American workers each year. Excessive heat and process contaminants have the potential to cause acute health effects such as heat stroke, and chronic effects such as manganism in welders. Although millions of workers are exposed to exothermic processes, insufficient attention has been given to continuously improving engineering technologies for these processes to provide effective and efficient control. Currently there is no specific occupational standard established by OSHA regarding exposure to heat from exothermic processes, therefore it is important to investigate techniques that can mitigate known and potential adverse occupational health effects. The current understanding of engineering controls for exothermic processes is primarily based on a book chapter written by W. C. L. Hemeon in 1955. Improvements in heat transfer and meteorological theory necessary to design improved process controls have occurred since this time. The research presented involved a review of the physical properties, heat transfer and meteorological theories governing buoyant air flow created by exothermic processes. These properties and theories were used to identify parameters and develop equations required for the determination of buoyant volumetric flow to assist in improving ventilation controls. Goals of this research were to develop and describe a new (i.e. proposed) flow equation, and compare it to currently accepted ones by Hemeon and the American Conference of Governmental Industrial Hygienists (ACGIH). Numerical assessments were conducted to compare solutions from the proposed equations for plume area, mean velocity and flow to those from the ACGIH and Hemeon. Parameters were varied for the dependent variables and solutions from the proposed, ACGIH, and Hemeon equations for plume area, mean velocity and flow were analyzed using a randomized complete block statistical

Embedded solitons in the third-order nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Pal, Debabrata; Ali, Sk Golam; Talukdar, B

2008-01-01

We work with a sech trial function with space-dependent soliton parameters and envisage a variational study for the nonlinear Schoedinger (NLS) equation in the presence of third-order dispersion. We demonstrate that the variational equations for pulse evolution in this NLS equation provide a natural basis to derive a potential model which can account for the existence of a continuous family of embedded solitons supported by the third-order NLS equation. Each member of the family is parameterized by the propagation velocity and co-efficient of the third-order dispersion

Isostable reduction with applications to time-dependent partial differential equations.

Science.gov (United States)

Wilson, Dan; Moehlis, Jeff

2016-07-01

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

Exact solutions of the Schrödinger equation with a coulomb ring-shaped potential in the cosmic string spacetime

Science.gov (United States)

Wang, Zhi; Long, Zheng-wen; Long, Chao-yun; Teng, Jing

2015-05-01

We study the Schrödinger equation with a Coulomb ring-shaped potential in the spacetime of a cosmic string, and the solutions of the system are obtained by using the generalized parametric Nikiforov-Uvarov (NU) method. They show that the quantum dynamics of a physical system depend on the non-trivial topological features of the cosmic string spacetime and the energy levels of the considered quantum system depend explicitly on the angular deficit α which characterizes the global structure of the metric in the cosmic string spacetime.

Novel Exponentially Fitted Two-Derivative Runge-Kutta Methods with Equation-Dependent Coefficients for First-Order Differential Equations

Directory of Open Access Journals (Sweden)

Yanping Yang

2016-01-01

Full Text Available The construction of exponentially fitted two-derivative Runge-Kutta (EFTDRK methods for the numerical solution of first-order differential equations is investigated. The revised EFTDRK methods proposed, with equation-dependent coefficients, take into consideration the errors produced in the internal stages to the update. The local truncation errors and stability of the new methods are analyzed. The numerical results are reported to show the accuracy of the new methods.

A heat equation for freezing processes with phase change

DEFF Research Database (Denmark)

Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John-Josef

2016-01-01

In this work, the stability properties as well as possible applications of a partial differential equation (PDE) with state-dependent parameters are investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (potential) Burgers’ equation. We show that...

Realizing the full potential of a RITA spectrometer

International Nuclear Information System (INIS)

Lefmann, K.; Niedermayer, Ch.; Abrahamsen, A.B.; Bahl, C.R.H.; Christensen, N.B.; Jacobsen, H.S.; Larsen, T.L.; Haefliger, P.; Filges, U.; Ronnow, H.M.

2006-01-01

The 're-invented triple-axis spectrometer (RITA) concept has existed for a decade. Recent developments at RITA-2 at PSI, have revealed more of the potential of this instrument class. We demonstrate the performance of the multi-blade imaging mode, which has been applied e.g. to studies of dispersion relations and emphasize the power of this mode in combination with the low background of RITA-2. In addition, we present other ways of utilizing the position sensitive detector in a RITA instrument. Simulations of a planned upgrade of the guide-monochromator system at RITA-2 have shown a potential to increase the flux at the sample position by a factor 5

Realizing the full potential of a RITA spectrometer

Energy Technology Data Exchange (ETDEWEB)

Lefmann, K. [Riso National Laboratory, Frederiksborgvej 399, DK-4000 Roskilde (Denmark)]. E-mail: kim.lefmann@risoe.dk; Niedermayer, Ch. [Laboratory for Neutron Scattering, ETH-Zuerich and Paul Scherrer Institut, CH-5232 Villilgen (Switzerland); Abrahamsen, A.B. [Riso National Laboratory, Frederiksborgvej 399, DK-4000 Roskilde (Denmark); Bahl, C.R.H. [Riso National Laboratory, Frederiksborgvej 399, DK-4000 Roskilde (Denmark); Christensen, N.B. [Riso National Laboratory, Frederiksborgvej 399, DK-4000 Roskilde (Denmark): Laboratory for Neutron Scattering, ETH-Zuerich and Paul Scherrer Institut, CH-5232 Villilgen (Switzerland); Jacobsen, H.S. [Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen O (Denmark); Larsen, T.L. [Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen O (Denmark); Haefliger, P. [Laboratory for Neutron Scattering, ETH-Zuerich and Paul Scherrer Institut, CH-5232 Villilgen (Switzerland); Filges, U. [Laboratory for Neutron Scattering, ETH-Zuerich and Paul Scherrer Institut, CH-5232 Villilgen (Switzerland); Ronnow, H.M. [Laboratory for Neutron Scattering, ETH-Zuerich and Paul Scherrer Institut, CH-5232 Villilgen (Switzerland)

2006-11-15

The 're-invented triple-axis spectrometer (RITA) concept has existed for a decade. Recent developments at RITA-2 at PSI, have revealed more of the potential of this instrument class. We demonstrate the performance of the multi-blade imaging mode, which has been applied e.g. to studies of dispersion relations and emphasize the power of this mode in combination with the low background of RITA-2. In addition, we present other ways of utilizing the position sensitive detector in a RITA instrument. Simulations of a planned upgrade of the guide-monochromator system at RITA-2 have shown a potential to increase the flux at the sample position by a factor 5.

A functional-analytic method for the study of difference equations

Directory of Open Access Journals (Sweden)

Siafarikas Panayiotis D

2004-01-01

Full Text Available We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the and spaces, p∈ℕ, . The method will be illustrated by use of two examples concerning a nonlinear ordinary difference equation known as the Putnam equation, and a linear partial difference equation of three variables describing the discrete Newton law of cooling in three dimensions.

Neutron Star masses from the Field Correlator Method Equation of State

Directory of Open Access Journals (Sweden)

Zappalà D.

2014-04-01

Full Text Available We analyse the hadron-quark phase transition in neutron stars by confronting the hadronic Equation of State (EoS obtained according to the microscopic Brueckner-Hartree-Fock many body theory, with the quark matter EoS derived within the Field Correlator Method. In particular, the latter EoS is only parametrized in terms of the gluon condensate and the large distance quark-antiquark potential, so that the comparison of the results of this analysis with the most recent measurements of heavy neutron star masses provides some physical constraints on these two parameters.

Nuclear structure information studied through Dirac equation with deformed mean fields

International Nuclear Information System (INIS)

Dudek, J.

2000-01-01

Complete text of publication follows. Relativistic mean-field theory provides a formal expression for the Dirac equation for the nucleonic motion in an atomic nucleus. The 'potentials' within such a formalism are given in terms of the meson fields, the latter obtained through a coupled system of equations of the Klein-Grodon type. Usually the whole system is being solved by using a Hartree approximation by employing an iterative selfonsistent algorithms. On a more phenomenological level one can parametrize the potentials that enter into a Dirac equation rather than obtain the selfconsistently; such a simplification was suggested some time ago by the Munich group. We introduce a Woods-Saxon type parametrisation and verify by a non-linear search routine what are the 'best fit potential parameters' that reproduce the single particle excitations in the double-magic spherical nuclei as well as the band-head properties in some hundreds of deformed nuclei. Next, by introducing a low-energy reduction of the Dirac equation, one may obtain in a natural way a Pauli Schrodinger type equation with a position dependent effective mass. The role of the corresponding term in a description of single particle energies of the nucleons is illustrated and the implications for the cranking equation are discussed in some detail. (author)

Maximal Regularity of the Discrete Harmonic Oscillator Equation

Directory of Open Access Journals (Sweden)

Airton Castro

2009-01-01

Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.

p-Euler equations and p-Navier-Stokes equations

Science.gov (United States)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Existence and concentration of positive solutions for a quasilinear elliptic equation in R

Directory of Open Access Journals (Sweden)

Elisandra Gloss

2010-05-01

Full Text Available We study the existence and concentration of positive solutions for the quasilinear elliptic equation $$ -varepsilon^2u'' -varepsilon^2(u^2''u+V(x u = h(u $$ in $mathbb{R}$ as $varepsilono 0$, where the potential $V:mathbb{R}o mathbb{R}$ has a positive infimum and $inf_{partial Omega}V>inf_{ Omega}V$ for some bounded domain $Omega$ in $mathbb{R}$, and $h$ is a nonlinearity without having growth conditions such as Ambrosetti-Rabinowitz.

Equating error in observed-score equating

NARCIS (Netherlands)

van der Linden, Willem J.

2006-01-01

Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of

Hot electrons in superlattices: quantum transport versus Boltzmann equation

DEFF Research Database (Denmark)

Wacker, Andreas; Jauho, Antti-Pekka; Rott, S.

1999-01-01

A self-consistent solution of the transport equation is presented for semiconductor superlattices within different approaches: (i) a full quantum transport model based on nonequilibrium Green functions, (ii) the semiclassical Boltzmann equation for electrons in a miniband, and (iii) Boltzmann...

Extending the precision and efficiency of the all-electron full-potential linearized augmented plane-wave density-functional theory method

International Nuclear Information System (INIS)

Michalicek, Gregor

2015-01-01

Density functional theory (DFT) is the most widely-used first-principles theory for analyzing, describing and predicting the properties of solids based on the fundamental laws of quantum mechanics. The success of the theory is a consequence of powerful approximations to the unknown exchange and correlation energy of the interacting electrons and of sophisticated electronic structure methods that enable the computation of the density functional equations on a computer. A widely used electronic structure method is the full-potential linearized augmented plane-wave (FLAPW) method, that is considered to be one of the most precise methods of its kind and often referred to as a standard. Challenged by the demand of treating chemically and structurally increasingly more complex solids, in this thesis this method is revisited and extended along two different directions: (i) precision and (ii) efficiency. In the full-potential linearized augmented plane-wave method the space of a solid is partitioned into nearly touching spheres, centered at each atom, and the remaining interstitial region between the spheres. The Kohn-Sham orbitals, which are used to construct the electron density, the essential quantity in DFT, are expanded into a linearized augmented plane-wave basis, which consists of plane waves in the interstitial region and angular momentum dependent radial functions in the spheres. In this thesis it is shown that for certain types of materials, e.g., materials with very broad electron bands or large band gaps, or materials that allow the usage of large space-filling spheres, the variational freedom of the basis in the spheres has to be extended in order to represent the Kohn-Sham orbitals with high precision over a large energy spread. Two kinds of additional radial functions confined to the spheres, so-called local orbitals, are evaluated and found to successfully eliminate this error. A new efficient basis set is developed, named linearized augmented lattice

Applying homotopy analysis method for solving differential-difference equation

International Nuclear Information System (INIS)

Wang Zhen; Zou Li; Zhang Hongqing

2007-01-01

In this Letter, we apply the homotopy analysis method to solving the differential-difference equations. A simple but typical example is applied to illustrate the validity and the great potential of the generalized homotopy analysis method in solving differential-difference equation. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the differential-difference equations

Ab initio/interpolated quantum dynamics on coupled electronic states with full configuration interaction wave functions

International Nuclear Information System (INIS)

Thompson, K.; Martinez, T.J.

1999-01-01

We present a new approach to first-principles molecular dynamics that combines a general and flexible interpolation method with ab initio evaluation of the potential energy surface. This hybrid approach extends significantly the domain of applicability of ab initio molecular dynamics. Use of interpolation significantly reduces the computational effort associated with the dynamics over most of the time scale of interest, while regions where potential energy surfaces are difficult to interpolate, for example near conical intersections, are treated by direct solution of the electronic Schroedinger equation during the dynamics. We demonstrate the concept through application to the nonadiabatic dynamics of collisional electronic quenching of Li(2p). Full configuration interaction is used to describe the wave functions of the ground and excited electronic states. The hybrid approach agrees well with full ab initio multiple spawning dynamics, while being more than an order of magnitude faster. copyright 1999 American Institute of Physics

A New Factorisation of a General Second Order Differential Equation

Science.gov (United States)

Clegg, Janet

2006-01-01

A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…

A Variational Approach to Perturbed Discrete Anisotropic Equations

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Amjad Salari

2016-01-01

Full Text Available We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory.

Semianalytic Solution of Space-Time Fractional Diffusion Equation

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A. Elsaid

2016-01-01

Full Text Available We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM. Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.

Using the charge-stabilization technique in the double ionization potential equation-of-motion calculations with dianion references.

Science.gov (United States)

Kuś, Tomasz; Krylov, Anna I

2011-08-28

The charge-stabilization method is applied to double ionization potential equation-of-motion (EOM-DIP) calculations to stabilize unstable dianion reference functions. The auto-ionizing character of the dianionic reference states spoils the numeric performance of EOM-DIP limiting applications of this method. We demonstrate that reliable excitation energies can be computed by EOM-DIP using a stabilized resonance wave function instead of the lowest energy solution corresponding to the neutral + free electron(s) state of the system. The details of charge-stabilization procedure are discussed and illustrated by examples. The choice of optimal stabilizing Coulomb potential, which is strong enough to stabilize the dianion reference, yet, minimally perturbs the target states of the neutral, is the crux of the approach. Two algorithms of choosing optimal parameters of the stabilization potential are presented. One is based on the orbital energies, and another--on the basis set dependence of the total Hartree-Fock energy of the reference. Our benchmark calculations of the singlet-triplet energy gaps in several diradicals show a remarkable improvement of the EOM-DIP accuracy in problematic cases. Overall, the excitation energies in diradicals computed using the stabilized EOM-DIP are within 0.2 eV from the reference EOM spin-flip values. © 2011 American Institute of Physics

Singular multiparameter dynamic equations with distributional ...

African Journals Online (AJOL)

Singular multiparameter dynamic equations with distributional potentials on time scales. ... In this paper, we consider both singular single and several multiparameter ... multiple function which is of one sign and nonzero on the given time scale.

Full particle simulations of quasi-perpendicular shocks

Science.gov (United States)

Lembège, B.

This tutorial-style review is dedicated to the different strategies and constraints used for analysing the dynamics of a collisionless shocks with full particle simulations. Main results obtained with such simulations can be found in published materials (recent references are provided in this text); these will be only quoted herein in order to illustrate a few aspects of these simulations. Thanks to the large improvement of super computers, full particle simulations reveal to be quite helpful for analyzing in details the dynamics of collisionless shocks. The main characteristics of such codes can be shortly reminded as follows: one resolves the full set of Poisson and Maxwell's equations without any approximation. Two approaches are commonly used for resolving this equation's set, more precisely the space derivatives: (i) the finite difference approach and (ii) the use of FFT's (Fast Fourier Transform). Two advantages of approach (ii) are that FFT's are highly optimized in supercomputers libraries, and these allow to separate all fields components into two groups: the longitudinal electrostatic component El (solution of Poisson equation) and the transverse electromagnetic components Et and Bt solutions of the Maxwell's equations (so called "fields pusher"). Such a separation is quite helpful in the post processing stage necessary for the data analysis, as will be explained in the presentation. both ions and electrons populations are treated as individual finite-size particles and suffer the effects of all fields via the Lorentz force, so called "particle pusher", which is applied to each particle. Because of the large number of particles commonly used, the particle pusher represents the most expensive part of the calculations on which most efforts of optimisation needs to be performed (in terms of "vectorisation" or of "parallelism"). Relativistic effects may be included in this force via the use of particle momemtum. Each particle has three velocity components (vx

Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

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Khaled A. Gepreel

2013-01-01

Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.