Some remarks on exact methods for WL and 222Rn-daughter determination

International Nuclear Information System (INIS)

Groer, P.G.

1977-01-01

For an exact determination of the three 222 Rn-daughter concentrations (RaA, B and C) which properly weighted yield the Working Level, three equations relating observed counts (α or β) to these unknown concentrations have to be solved. The half-lives in the 222 Rn decay series, the type of decay and the counting errors, limit the suitable set of equations. Some aspects of two such exact methods are discussed

Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation

International Nuclear Information System (INIS)

Wang Dengshan; Zhang Hongqing

2005-01-01

In this paper, with the aid of the symbolic computation we improve the extended F-expansion method in [Chaos, Solitons and Fractals 2004; 22:111] and propose the further improved F-expansion method. Using this method, we have gotten many new exact solutions which we have never seen before within our knowledge of the (2 + 1)-dimensional Konopelchenko-Dubrovsky equation. In addition,the solutions we get are more general than the solutions that the extended F-expansion method gets.The solutions we get include Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions and so on. Our method can also apply to other partial differential equations and can also get many new exact solutions

New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods

International Nuclear Information System (INIS)

Saha Ray, S

2016-01-01

In this paper, new exact solutions of the time fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov (KdV–KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann–Liouville derivative is used to convert the nonlinear time fractional KdV–KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV–KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV–KZK equation. (paper)

A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods

Directory of Open Access Journals (Sweden)

Özkan Güner

2014-01-01

Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.

arXiv Integrable flows between exact CFTs

CERN Document Server

Georgiou, George

2017-11-14

We explicitly construct families of integrable σ-model actions smoothly inter-polating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels k$_{1}$ and k$_{2}$. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels k$_{1}$ and k$_{2}$ − k$_{1}$. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries.

Exact extraction method for road rutting laser lines

Science.gov (United States)

Hong, Zhiming

2018-02-01

This paper analyzes the importance of asphalt pavement rutting detection in pavement maintenance and pavement administration in today's society, the shortcomings of the existing rutting detection methods are presented and a new rutting line-laser extraction method based on peak intensity characteristic and peak continuity is proposed. The intensity of peak characteristic is enhanced by a designed transverse mean filter, and an intensity map of peak characteristic based on peak intensity calculation for the whole road image is obtained to determine the seed point of the rutting laser line. Regarding the seed point as the starting point, the light-points of a rutting line-laser are extracted based on the features of peak continuity, which providing exact basic data for subsequent calculation of pavement rutting depths.

Perturbation of an exact strong gravity solution

International Nuclear Information System (INIS)

Baran, S.A.

1982-10-01

Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)

Performance comparison of a new hybrid conjugate gradient method under exact and inexact line searches

Science.gov (United States)

Ghani, N. H. A.; Mohamed, N. S.; Zull, N.; Shoid, S.; Rivaie, M.; Mamat, M.

2017-09-01

Conjugate gradient (CG) method is one of iterative techniques prominently used in solving unconstrained optimization problems due to its simplicity, low memory storage, and good convergence analysis. This paper presents a new hybrid conjugate gradient method, named NRM1 method. The method is analyzed under the exact and inexact line searches in given conditions. Theoretically, proofs show that the NRM1 method satisfies the sufficient descent condition with both line searches. The computational result indicates that NRM1 method is capable in solving the standard unconstrained optimization problems used. On the other hand, the NRM1 method performs better under inexact line search compared with exact line search.

New method for the exact determination of the effective conductivity and the local field in RLC networks

International Nuclear Information System (INIS)

Zekri, L.; Zekri, N.; Bouamrane, R.

1999-10-01

We present a new numerical method for determining exactly the effective conductivity and the local field for random RLC networks. This method is compared to a real space renormalization group method and the Frank and Lobb method. Although our method is slower than the Frank and Lobb method, it also computes exactly the local field for large size systems. We also show that the renormalization group method fails in determining the local field. (author)

An Algebraic Method for Constructing Exact Solutions to Difference-Differential Equations

International Nuclear Information System (INIS)

Wang Zhen; Zhang Hongqing

2006-01-01

In this paper, we present a method to solve difference differential equation(s). As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions are obtained with the help of Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equation(s).

Short overview of PSA quantification methods, pitfalls on the road from approximate to exact results

International Nuclear Information System (INIS)

Banov, Reni; Simic, Zdenko; Sterc, Davor

2014-01-01

Over time the Probabilistic Safety Assessment (PSA) models have become an invaluable companion in the identification and understanding of key nuclear power plant (NPP) vulnerabilities. PSA is an effective tool for this purpose as it assists plant management to target resources where the largest benefit for plant safety can be obtained. PSA has quickly become an established technique to numerically quantify risk measures in nuclear power plants. As complexity of PSA models increases, the computational approaches become more or less feasible. The various computational approaches can be basically classified in two major groups: approximate and exact (BDD based) methods. In recent time modern commercially available PSA tools started to provide both methods for PSA model quantification. Besides availability of both methods in proven PSA tools the usage must still be taken carefully since there are many pitfalls which can drive to wrong conclusions and prevent efficient usage of PSA tool. For example, typical pitfalls involve the usage of higher precision approximation methods and getting a less precise result, or mixing minimal cuts and prime implicants in the exact computation method. The exact methods are sensitive to selected computational paths in which case a simple human assisted rearrangement may help and even switch from computationally non-feasible to feasible methods. Further improvements to exact method are possible and desirable which opens space for a new research. In this paper we will show how these pitfalls may be detected and how carefully actions must be done especially when working with large PSA models. (authors)

Exact Solutions for Fractional Differential-Difference Equations by an Extended Riccati Sub-ODE Method

International Nuclear Information System (INIS)

Feng Qinghua

2013-01-01

In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann—Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established. (general)

Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method

International Nuclear Information System (INIS)

Ebaid, A.

2007-01-01

Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV-mKdV equation are chosen to illustrate the effectiveness of the method

Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G-Expansion Method

Directory of Open Access Journals (Sweden)

Muhammad Shakeel

2014-01-01

Full Text Available The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method.

The Semianalytical Solutions for Stiff Systems of Ordinary Differential Equations by Using Variational Iteration Method and Modified Variational Iteration Method with Comparison to Exact Solutions

Directory of Open Access Journals (Sweden)

Mehmet Tarik Atay

2013-01-01

Full Text Available The Variational Iteration Method (VIM and Modified Variational Iteration Method (MVIM are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM and the Modified Variational Iteration Method (MVIM are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Directory of Open Access Journals (Sweden)

Rahmatullah

2018-03-01

Full Text Available We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation

A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation

International Nuclear Information System (INIS)

Ma Wenxiu; Lee, J.-H.

2009-01-01

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanh-function type methods, the homogeneous balance method, the exp-function method, the mapping method, and the F-expansion type methods. Its key point is to search for rational solutions to variable-coefficient ordinary differential equations transformed from given partial differential equations. As an application, the construction problem of exact solutions to the 3+1 dimensional Jimbo-Miwa equation is treated, together with a Baecklund transformation.

EXACT SOLITARY WAVE SOLUTIONS TO A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS USING DIRECT ALGEBRAIC METHOD

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.

The extended hyperbolic function method and exact solutions of the long-short wave resonance equations

International Nuclear Information System (INIS)

Shang Yadong

2008-01-01

The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions

Exact solution to the Coulomb wave using the linearized phase-amplitude method

Directory of Open Access Journals (Sweden)

Shuji Kiyokawa

2015-08-01

Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

Methods for constructing exact solutions of partial differential equations mathematical and analytical techniques with applications to engineering

CERN Document Server

Meleshko, Sergey V

2005-01-01

Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

Exact Methods for Solving the Train Departure Matching Problem

DEFF Research Database (Denmark)

Haahr, Jørgen Thorlund; Bull, Simon Henry

In this paper we consider the train departure matching problem which is an important subproblem of the Rolling Stock Unit Management on Railway Sites problem introduced in the ROADEF/EURO Challenge 2014. The subproblem entails matching arriving train units to scheduled departing trains at a railway...... site while respecting multiple physical and operational constraints. In this paper we formally define that subproblem, prove its NP- hardness, and present two exact method approaches for solving the problem. First, we present a compact Mixed Integer Program formulation which we solve using a MIP solver...

Use of exact albedo conditions in numerical methods for one-dimensional one-speed discrete ordinates eigenvalue problems

International Nuclear Information System (INIS)

Abreu, M.P. de

1994-01-01

The use of exact albedo boundary conditions in numerical methods applied to one-dimensional one-speed discrete ordinates (S n ) eigenvalue problems for nuclear reactor global calculations is described. An albedo operator that treats the reflector region around a nuclear reactor core implicitly is described and exactly was derived. To illustrate the method's efficiency and accuracy, it was used conventional linear diamond method with the albedo option to solve typical model problems. (author)

The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations

Directory of Open Access Journals (Sweden)

Yadong Shang

2012-01-01

Full Text Available This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E, the solitary wave solutions of kink-type for E and bell-type for n, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.

A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation

Science.gov (United States)

Ghanbari, Behzad; Inc, Mustafa

2018-04-01

The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.

General method and exact solutions to a generalized variable-coefficient two-dimensional KdV equation

International Nuclear Information System (INIS)

Chen, Yong; Shanghai Jiao-Tong Univ., Shangai; Chinese Academy of sciences, Beijing

2005-01-01

A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion

Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2

Science.gov (United States)

Weatherford, C. A.; Onda, K.; Temkin, A.

1985-01-01

The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.

Prepotential approach to exact and quasi-exact solvabilities

International Nuclear Information System (INIS)

Ho, C.-L.

2008-01-01

Exact and quasi-exact solvabilities of the one-dimensional Schroedinger equation are discussed from a unified viewpoint based on the prepotential together with Bethe ansatz equations. This is a constructive approach which gives the potential as well as the eigenfunctions and eigenvalues simultaneously. The novel feature of the present work is the realization that both exact and quasi-exact solvabilities can be solely classified by two integers, the degrees of two polynomials which determine the change of variable and the zeroth order prepotential. Most of the well-known exactly and quasi-exactly solvable models, and many new quasi-exactly solvable ones, can be generated by appropriately choosing the two polynomials. This approach can be easily extended to the constructions of exactly and quasi-exactly solvable Dirac, Pauli, and Fokker-Planck equations

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

Science.gov (United States)

Hesselmann, Andreas; Görling, Andreas

2011-01-21

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

New exact solutions of the mBBM equation

International Nuclear Information System (INIS)

Zhang Zhe; Li Desheng

2013-01-01

The enhanced modified simple equation method presented in this article is applied to construct the exact solutions of modified Benjamin-Bona-Mahoney equation. Some new exact solutions are derived by using this method. When some parameters are taken as special values, the solitary wave solutions can be got from the exact solutions. It is shown that the method introduced in this paper has general significance in searching for exact solutions to the nonlinear evolution equations. (authors)

An exact method for solving logical loops in reliability analysis

International Nuclear Information System (INIS)

Matsuoka, Takeshi

2009-01-01

This paper presents an exact method for solving logical loops in reliability analysis. The systems that include logical loops are usually described by simultaneous Boolean equations. First, present a basic rule of solving simultaneous Boolean equations. Next, show the analysis procedures for three-component system with external supports. Third, more detailed discussions are given for the establishment of logical loop relation. Finally, take up two typical structures which include more than one logical loop. Their analysis results and corresponding GO-FLOW charts are given. The proposed analytical method is applicable to loop structures that can be described by simultaneous Boolean equations, and it is very useful in evaluating the reliability of complex engineering systems.

Generalized WKB method through an appropriate canonical transformation giving an exact invariant

International Nuclear Information System (INIS)

Guyard, J.; Nadeau, A.

1976-01-01

The solution of differential equations of the type d 2 q/dtau 2 +ω 2 (tau)q=0 is of great interest in Physics. Authors often introduce an auxiliary function w, solution of a differential equation which can be solved by a perturbation method. In fact this approach is nothing but an extension of the well known WKB method. Lewis has found an exact invariant of the motion given in closed form in terms in a much easier way. This method can now be used as a natural way of introducing the WKB extension [fr

Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method

International Nuclear Information System (INIS)

Bekir Ahmet; Güner Özkan

2013-01-01

In this paper, we use the fractional complex transform and the (G′/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann—Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations

A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

NARCIS (Netherlands)

Bochev, Mikhail A.

2013-01-01

We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of

Exact milestoning

International Nuclear Information System (INIS)

Bello-Rivas, Juan M.; Elber, Ron

2015-01-01

A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied

Exact analysis of discrete data

CERN Document Server

Hirji, Karim F

2005-01-01

Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...

Exact solitary waves of the Fisher equation

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2005-01-01

New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given

Electrostatics of a Point Charge between Intersecting Planes: Exact Solutions and Method of Images

Science.gov (United States)

Mei, W. N.; Holloway, A.

2005-01-01

In this work, the authors present a commonly used example in electrostatics that could be solved exactly in a conventional manner, yet expressed in a compact form, and simultaneously work out special cases using the method of images. Then, by plotting the potentials and electric fields obtained from these two methods, the authors demonstrate that…

The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

Directory of Open Access Journals (Sweden)

Yusuf Pandir

2018-02-01

Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.

A general exact method for synthesizing parallel-beam projections from cone-beam projections via filtered backprojection

International Nuclear Information System (INIS)

Li Liang; Chen Zhiqiang; Xing Yuxiang; Zhang Li; Kang Kejun; Wang Ge

2006-01-01

In recent years, image reconstruction methods for cone-beam computed tomography (CT) have been extensively studied. However, few of these studies discussed computing parallel-beam projections from cone-beam projections. In this paper, we focus on the exact synthesis of complete or incomplete parallel-beam projections from cone-beam projections. First, an extended central slice theorem is described to establish a relationship between the Radon space and the Fourier space. Then, data sufficiency conditions are proposed for computing parallel-beam projection data from cone-beam data. Using these results, a general filtered backprojection algorithm is formulated that can exactly synthesize parallel-beam projection data from cone-beam projection data. As an example, we prove that parallel-beam projections can be exactly synthesized in an angular range in the case of circular cone-beam scanning. Interestingly, this angular range is larger than that derived in the Feldkamp reconstruction framework. Numerical experiments are performed in the circular scanning case to verify our method

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Science.gov (United States)

Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

2018-03-01

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

Exact Solution of Space-Time Fractional Coupled EW and Coupled MEW Equations Using Modified Kudryashov Method

International Nuclear Information System (INIS)

Raslan, K. R.; Ali, Khalid K.; EL-Danaf, Talaat S.

2017-01-01

In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels. (paper)

Exact Heat Kernel on a Hypersphere and Its Applications in Kernel SVM

Directory of Open Access Journals (Sweden)

Chenchao Zhao

2018-01-01

Full Text Available Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector machine compared to other competing similarity measures. Specifically, the idea of using heat diffusion on a hypersphere to measure similarity has been previously proposed and tested by Lafferty and Lebanon [1], demonstrating promising results based on a heuristic heat kernel obtained from the zeroth order parametrix expansion; however, how well this heuristic kernel agrees with the exact hyperspherical heat kernel remains unknown. This paper presents a higher order parametrix expansion of the heat kernel on a unit hypersphere and discusses several problems associated with this expansion method. We then compare the heuristic kernel with an exact form of the heat kernel expressed in terms of a uniformly and absolutely convergent series in high-dimensional angular momentum eigenmodes. Being a natural measure of similarity between sample points dwelling on a hypersphere, the exact kernel often shows superior performance in kernel SVM classifications applied to text mining, tumor somatic mutation imputation, and stock market analysis.

Bender-Dunne Orthogonal Polynomials, Quasi-Exact Solvability and Asymptotic Iteration Method for Rabi Hamiltonian

International Nuclear Information System (INIS)

Yahiaoui, S.-A.; Bentaiba, M.

2011-01-01

We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method (AIM). The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are deduced. We show (i) that orthogonal polynomials are generated from the upper limit (i.e., truncation limit) of polynomial solutions deduced from AIM, and (ii) prove to have nonpositive norm. (authors)

An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2017-11-01

Full Text Available In this article, a variety of solitary wave solutions are observed for microtubules (MTs. We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs involving parameters of special interest in nanobiosciences and biophysics. We determine hyperbolic, trigonometric, rational and exponential function solutions and obtain soliton-like pulse solutions for these equations. A comparative study against other methods demonstrates the validity of the technique that we developed and demonstrates that our method provides additional solutions. Finally, using suitable parameter values, we plot 2D and 3D graphics of the exact solutions that we observed using our method. Keywords: Analytical method, Exact solutions, Nonlinear evolution equations (NLEEs of microtubules, Nonlinear RLC transmission lines

Exact solution for the reflection and diffraction of atomic de Broglie waves by a travelling evanescent laser wave

International Nuclear Information System (INIS)

Witte, N.S.

1997-01-01

The exact solution to the problem of reflection and diffraction of atomic de Broglie waves by a travelling evanescent wave is found starting with a bare-state formulation. The solution for the wavefunctions, the tunnelling losses and the non-adiabatic losses are given exactly in terms of hyper-Bessel functions, and are valid for all detuning and Rabi frequencies, thus generalizing previous approximate methods. Furthermore we give the limiting cases of all amplitudes in the uniform semiclassical limit, which is valid in all regions including near the classical turning points, and in the large and weak coupling cases. Exact results for the zero detuning case are obtained in terms of Bessel functions. We find our uniform semiclassical limit to be closer to the exact result over the full range of parameter values than the previously reported calculations. The current knowledge of hyper-Bessel function properties is reviewed in order to apply this to the physical problems imposed

A fast exact simulation method for a class of Markov jump processes.

Science.gov (United States)

Li, Yao; Hu, Lili

2015-11-14

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.

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.)

Polygons of differential equations for finding exact solutions

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.; Demina, Maria V.

2007-01-01

A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given

New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

International Nuclear Information System (INIS)

Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

2009-01-01

In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

Exactly and quasi-exactly solvable 'discrete' quantum mechanics.

Science.gov (United States)

Sasaki, Ryu

2011-03-28

A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.

Exact Optimum Design of Segmented Thermoelectric Generators

Directory of Open Access Journals (Sweden)

M. Zare

2016-01-01

Full Text Available A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs. Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency.

Exact models for isotropic matter

Science.gov (United States)

Thirukkanesh, S.; Maharaj, S. D.

2006-04-01

We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.

Study of electron-molecule collision via finite-element method and r-matrix propagation technique: Exact exchange

International Nuclear Information System (INIS)

Abdolsalami, F.; Abdolsalami, M.; Perez, L.; Gomez, P.

1995-01-01

The authors have applied the finite-element method to electron-molecule collision with the exchange effect implemented rigorously. All the calculations are done in the body-frame within the fixed-nuclei approximation, where the exact treatment of exchange as a nonlocal effect results in a set of coupled integro-differential equations. The method is applied to e-H 2 and e-N 2 scatterings and the cross sections obtained are in very good agreement with the corresponding results the authors have generated from the linear-algebraic approach. This confirms the significant difference observed between their results generated by linear-algebraic method and the previously published e-N 2 cross sections. Their studies show that the finite-element method is clearly superior to the linear-algebraic approach in both memory usage and CPU time especially for large systems such as e-N 2 . The system coefficient matrix obtained from the finite-element method is often sparse and smaller in size by a factor of 12 to 16, compared to the linear-algebraic technique. Moreover, the CPU time required to obtain stable results with the finite-element method is significantly smaller than the linear-algebraic approach for one incident electron energy. The usage of computer resources in the finite-element method can even be reduced much further when (1) scattering calculations involving multiple electron energies are performed in one computer run and (2) exchange, which is a short range effect, is approximated by a sparse matrix. 17 refs., 7 figs., 5 tabs

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

Science.gov (United States)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

Exact solutions of some nonlinear partial differential equations using ...

Indian Academy of Sciences (India)

The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...

New Exact Solutions of Time Fractional Gardner Equation by Using New Version of F -Expansion Method

International Nuclear Information System (INIS)

Pandir, Yusuf; Duzgun, Hasan Huseyin

2017-01-01

In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are situated in the solution function. As a result, various exact analytical solutions consisting of single and combined Jacobi elliptic functions solutions are obtained. (paper)

Exactly energy conserving semi-implicit particle in cell formulation

International Nuclear Information System (INIS)

Lapenta, Giovanni

2017-01-01

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These

Exactly energy conserving semi-implicit particle in cell formulation

Energy Technology Data Exchange (ETDEWEB)

Lapenta, Giovanni, E-mail: giovanni.lapenta@kuleuven.be

2017-04-01

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These

Exact Solutions of Fractional Burgers and Cahn-Hilliard Equations Using Extended Fractional Riccati Expansion Method

Directory of Open Access Journals (Sweden)

Wei Li

2014-01-01

Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.

Exact traveling wave solutions of the Boussinesq equation

International Nuclear Information System (INIS)

Ding Shuangshuang; Zhao Xiqiang

2006-01-01

The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

Energy Technology Data Exchange (ETDEWEB)

Yu, Hua-Gen, E-mail: hgy@bnl.gov [Division of Chemistry, Department of Energy and Photon Sciences, Brookhaven National Laboratory, Upton, New York 11973-5000 (United States)

2016-08-28

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH{sub 4} and H{sub 2}CO are given, together with a comparison with previous results.

Elliptic equation rational expansion method and new exact travelling solutions for Whitham-Broer-Kaup equations

International Nuclear Information System (INIS)

Chen Yong; Wang Qi; Li Biao

2005-01-01

Based on a new general ansatz and a general subepuation, a new general algebraic method named elliptic equation rational expansion method is devised for constructing multiple travelling wave solutions in terms of rational special function for nonlinear evolution equations (NEEs). We apply the proposed method to solve Whitham-Broer-Kaup equation and explicitly construct a series of exact solutions which include rational form solitary wave solution, rational form triangular periodic wave solutions and rational wave solutions as special cases. In addition, the links among our proposed method with the method by Fan [Chaos, Solitons and Fractals 2004;20:609], are also clarified generally

Stochastic epidemic-type model with enhanced connectivity: exact solution

International Nuclear Information System (INIS)

Williams, H T; Mazilu, I; Mazilu, D A

2012-01-01

We present an exact analytical solution to a one-dimensional model of the susceptible–infected–recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming the master equation via a quantum spin operator formulation. We calculate exactly the time-dependent density of infected, recovered and susceptible populations for random initial conditions. Our results compare well with those of previous work, validating the model as a useful tool for additional and extended studies in this important area. Our model also provides exact solutions for the n-point correlation functions, and can be extended to more complex epidemic-type models

Eigenstates and dynamics of Hooke's atom: Exact results and path integral simulations

Science.gov (United States)

Gholizadehkalkhoran, Hossein; Ruokosenmäki, Ilkka; Rantala, Tapio T.

2018-05-01

The system of two interacting electrons in one-dimensional harmonic potential or Hooke's atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the "space splitting" arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke's atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.

Quasi-exact solvability

International Nuclear Information System (INIS)

Ushveridze, A.G.

1992-01-01

This paper reports that quasi-exactly solvable (QES) models realize principally new type of exact solvability in quantum physics. These models are distinguished by the fact that the Schrodinger equations for them can be solved exactly only for certain limited parts of the spectrum, but not for the whole spectrum. They occupy an intermediate position between the exactly the authors solvable (ES) models and all the others. The number of energy levels for which the spectral problems can be solved exactly refer below to as the order of QES model. From the mathematical point of view the existence of QES models is not surprising. Indeed, if the term exact solvability expresses the possibility of total explicit diagonalization of infinite Hamiltonian matrix, then the term quasi-exact solvability implies the situation when the Hamiltonian matrix can be reduced explicitly to the block-diagonal form with one of the appearing blocks being finite

Exact solution of a key equation in a finite stellar atmosphere by the method of Laplace transform and linear singular operators

International Nuclear Information System (INIS)

Das, R.N.

1980-01-01

The key equation which commonly appears for radiative transfer in a finite stellar atmosphere having ground reflection according to Lambert's law is considered in this paper. The exact solution of this equation is obtained for surface quantities in terms of the X-Y equations of Chandrasekhar by the method of Laplace transform and linear singular operators. This exact method is widely applicable for obtaining the solution for surface quantities in a finite atmosphere. (orig.)

Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient

International Nuclear Information System (INIS)

Cao Rui; Zhang Jian

2013-01-01

In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions. (general)

Dissociation between exact and approximate addition in developmental dyslexia.

Science.gov (United States)

Yang, Xiujie; Meng, Xiangzhi

2016-09-01

Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.

ExactPack Documentation

Energy Technology Data Exchange (ETDEWEB)

Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory

2016-05-09

For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.

New method for exact measurement of thermal neutron distribution in elementary cell

International Nuclear Information System (INIS)

Takac, S.M.; Krcevinac, S.B.

1966-06-01

Exact measurement of thermal neutron density distribution in an elementary cell necessitates the knowledge of the perturbations involved in the cell by the measuring device. A new method has been developed in which a special stress is made to evaluate these perturbations by measuring the response from the perturbations introduced in the elementary cell. The unperturbed distribution was obtained by extrapolation to zero perturbation. The final distributions for different lattice pitches were compared with a THERMOS-type calculation. As a pleasing fact a very good agreement has been reached, which dissolves the long existing disagreement between THERMOS calculations and measured density distribution (author)

New method for exact measurement of thermal neutron distribution in elementary cell

Energy Technology Data Exchange (ETDEWEB)

Takac, S M; Krcevinac, S B [Institute of nuclear sciences Boris Kidric, Vinca, Beograd (Yugoslavia)

1966-06-15

Exact measurement of thermal neutron density distribution in an elementary cell necessitates the knowledge of the perturbations involved in the cell by the measuring device. A new method has been developed in which a special stress is made to evaluate these perturbations by measuring the response from the perturbations introduced in the elementary cell. The unperturbed distribution was obtained by extrapolation to zero perturbation. The final distributions for different lattice pitches were compared with a THERMOS-type calculation. As a pleasing fact a very good agreement has been reached, which dissolves the long existing disagreement between THERMOS calculations and measured density distribution (author)

Exact rebinning methods for three-dimensional PET.

Science.gov (United States)

Liu, X; Defrise, M; Michel, C; Sibomana, M; Comtat, C; Kinahan, P; Townsend, D

1999-08-01

The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of three-dimensional (3-D) PET data. The first algorithm, FOREPROJ, is a fast-forward projection algorithm that allows calculation of the 3-D attenuation correction factors (ACF's) directly from a two-dimensional (2-D) transmission scan, without first reconstructing the attenuation map and then performing a 3-D forward projection. The use of FOREPROJ speeds up the estimation of the 3-D ACF's by more than a factor five. The second algorithm, FOREX, is a rebinning algorithm that is also more than five times faster, compared to the standard reprojection algorithm (3DRP) and does not suffer from the image distortions generated by the even faster approximate Fourier rebinning (FORE) method at large axial apertures. However, FOREX is probably not required by most existing scanners, as the axial apertures are not large enough to show improvements over FORE with clinical data. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30 degrees), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the excellent accuracy achieved by these algorithms and the important speedup when the sinogram sizes are powers of two.

An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2016-06-01

Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.

Exact solitary waves of the Korteveg - de Vries - Burgers equation

OpenAIRE

Kudryashov, N. A.

2004-01-01

New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.

A Lie-admissible method of integration of Fokker-Planck equations with non-linear coefficients (exact and numerical solutions)

International Nuclear Information System (INIS)

Fronteau, J.; Combis, P.

1984-08-01

A Lagrangian method is introduced for the integration of non-linear Fokker-Planck equations. Examples of exact solutions obtained in this way are given, and also the explicit scheme used for the computation of numerical solutions. The method is, in addition, shown to be of a Lie-admissible type

Implementing Families of Implicit Chebyshev Methods with Exact Coefficients for the Numerical Integration of First- and Second-Order Differential Equations

National Research Council Canada - National Science Library

Mitchell, Jason

2002-01-01

A method is presented for the generation of exact numerical coefficients found in two families of implicit Chebyshev methods for the numerical integration of first- and second-order ordinary differential equations...

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

Directory of Open Access Journals (Sweden)

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.

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.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

Science.gov (United States)

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Exact Synthesis of Reversible Circuits Using A* Algorithm

Science.gov (United States)

Datta, K.; Rathi, G. K.; Sengupta, I.; Rahaman, H.

2015-06-01

With the growing emphasis on low-power design methodologies, and the result that theoretical zero power dissipation is possible only if computations are information lossless, design and synthesis of reversible logic circuits have become very important in recent years. Reversible logic circuits are also important in the context of quantum computing, where the basic operations are reversible in nature. Several synthesis methodologies for reversible circuits have been reported. Some of these methods are termed as exact, where the motivation is to get the minimum-gate realization for a given reversible function. These methods are computationally very intensive, and are able to synthesize only very small functions. There are other methods based on function transformations or higher-level representation of functions like binary decision diagrams or exclusive-or sum-of-products, that are able to handle much larger circuits without any guarantee of optimality or near-optimality. Design of exact synthesis algorithms is interesting in this context, because they set some kind of benchmarks against which other methods can be compared. This paper proposes an exact synthesis approach based on an iterative deepening version of the A* algorithm using the multiple-control Toffoli gate library. Experimental results are presented with comparisons with other exact and some heuristic based synthesis approaches.

Quasi exact solution of the Rabi Hamiltonian

CERN Document Server

Koç, R; Tuetuencueler, H

2002-01-01

A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.

New exact travelling wave solutions for the Ostrovsky equation

International Nuclear Information System (INIS)

Kangalgil, Figen; Ayaz, Fatma

2008-01-01

In this Letter, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. In order to illustrate the validity and the advantages of the method we choose the Ostrovsky equation. As a result, many new and more general exact solutions have been obtained for the equation

A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation

International Nuclear Information System (INIS)

Sabry, R.; Zahran, M.A.; Fan Engui

2004-01-01

A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found

Exact solutions of nonlinear differential equations using continued fractions

International Nuclear Information System (INIS)

Ditto, W.L.; Pickett, T.J.

1990-01-01

The continued-fraction conversion method (J. Math. Phys. (N.Y.), 29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation φ(r) '' + 2φ(r)'/r + αφ(r) p = 0, for p=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form -φ '' (r) -2φ(r)'/r + αφ(r) 2p+1 + λφ(r) 4p+1 = 0 for arbitrary α, γ and p. A condition is established for the generation of exact solutions from the method

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

Science.gov (United States)

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

Accurate characterization of 3D diffraction gratings using time domain discontinuous Galerkin method with exact absorbing boundary conditions

KAUST Repository

Sirenko, Kostyantyn

2013-07-01

Exact absorbing and periodic boundary conditions allow to truncate grating problems\\' infinite physical domains without introducing any errors. This work presents exact absorbing boundary conditions for 3D diffraction gratings and describes their discretization within a high-order time-domain discontinuous Galerkin finite element method (TD-DG-FEM). The error introduced by the boundary condition discretization matches that of the TD-DG-FEM; this results in an optimal solver in terms of accuracy and computation time. Numerical results demonstrate the superiority of this solver over TD-DG-FEM with perfectly matched layers (PML)-based domain truncation. © 2013 IEEE.

Exact Green's function method of solar force-free magnetic-field computations with constant alpha. I - Theory and basic test cases

Science.gov (United States)

Chiu, Y. T.; Hilton, H. H.

1977-01-01

Exact closed-form solutions to the solar force-free magnetic-field boundary-value problem are obtained for constant alpha in Cartesian geometry by a Green's function approach. The uniqueness of the physical problem is discussed. Application of the exact results to practical solar magnetic-field calculations is free of series truncation errors and is at least as economical as the approximate methods currently in use. Results of some test cases are presented.

Exactly and completely integrable nonlinear dynamical systems

International Nuclear Information System (INIS)

Leznov, A.N.; Savel'ev, M.V.

1987-01-01

The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions

An Exact Solution of the Binary Singular Problem

Directory of Open Access Journals (Sweden)

Baiqing Sun

2014-01-01

Full Text Available Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method.

Comparison of exact, efron and breslow parameter approach method on hazard ratio and stratified cox regression model

Science.gov (United States)

Fatekurohman, Mohamat; Nurmala, Nita; Anggraeni, Dian

2018-04-01

Lungs are the most important organ, in the case of respiratory system. Problems related to disorder of the lungs are various, i.e. pneumonia, emphysema, tuberculosis and lung cancer. Comparing all those problems, lung cancer is the most harmful. Considering about that, the aim of this research applies survival analysis and factors affecting the endurance of the lung cancer patient using comparison of exact, Efron and Breslow parameter approach method on hazard ratio and stratified cox regression model. The data applied are based on the medical records of lung cancer patients in Jember Paru-paru hospital on 2016, east java, Indonesia. The factors affecting the endurance of the lung cancer patients can be classified into several criteria, i.e. sex, age, hemoglobin, leukocytes, erythrocytes, sedimentation rate of blood, therapy status, general condition, body weight. The result shows that exact method of stratified cox regression model is better than other. On the other hand, the endurance of the patients is affected by their age and the general conditions.

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

Science.gov (United States)

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

BOOK REVIEW: Structures in the Universe by Exact Methods: Formation, Evolutions, Interactions (Cambridge Monographs on Mathematical Physics) Structures in the Universe by Exact Methods: Formation, Evolutions, Interactions (Cambridge Monographs on Mathematical Physics)

Science.gov (United States)

Coley, Alan

2010-05-01

In this book the use of inhomogeneous models in cosmology, both in modelling structure formation and interpreting cosmological observations, is discussed. The authors concentrate on exact solutions, and particularly the Lemaitre-Tolman (LT) and Szekeres models (the important topic of averaging is not discussed). The book serves to demonstrate that inhomogeneous metrics can generate realistic models of cosmic structure formation and nonlinear evolution and shows that general relativity has a lot more to offer to cosmology than just the standard spatially homogeneous FLRW model. I would recommend this book to people working in theoretical cosmology. In the introduction (and in the concluding chapter and throughout the book) a reasonable discussion of the potential problems with the standard FLRW cosmology is presented, and a list of examples illustrating the limitations of standard FLRW cosmology are discussed (including potential problems with perturbation methods). In particular, the authors argue that the assumptions of isotropy and spatial homogeneity (and consequently the Copernican principle) must be properly challenged and revisited. Indeed, it is possible for `good old general relativity' to be used to explain cosmological observations without introducing speculative elements. In part I of the book the necessary background is presented (readers need a background in general relativity theory at an advanced undergraduate or graduate level). There is a good (and easy to read) review of the exact spherically symmetric dust Lemaitre-Tolman model (LT) (often denoted the LTB model) and the Lemaitre and Szekeres models. Light propogation (i.e. null geodesics, for both central and off-center observers) in exact inhomogeneous (LT) models is reviewed. In part II a number of applications of exact inhomogeneous models are presented (taken mainly from the authors' own work). In chapter 4, the evolution of exact inhomogeneous models (primarily the LT model, but also the

Comparing EFT and Exact One-Loop Analyses of Non-Degenerate Stops

CERN Document Server

Drozd, Aleksandra; Quevillon, Jeremie; You, Tevong

2015-01-01

We develop a universal approach to the one-loop effective field theory (EFT) using the Covariant Derivative Expansion (CDE) method. We generalise previous results to include broader classes of UV models, showing how expressions previously obtained assuming degenerate heavy-particle masses can be extended to non-degenerate cases. We apply our method to the general MSSM with non-degenerate stop squarks, illustrating our approach with calculations of the coefficients of dimension-6 operators contributing to the $hgg$ and $h\\gamma\\gamma$ couplings, and comparing with exact calculations of one-loop Feynman diagrams. We then use present and projected future sensitivities to these operator coefficients to obtain present and possible future indirect constraints on stop masses. The current sensitivity is already comparable to that of direct LHC searches, and future FCC-ee measurements could be sensitive to stop masses above a TeV. The universality of our one-loop EFT approach facilitates extending these constraints to...

New exact solutions for two nonlinear equations

International Nuclear Information System (INIS)

Wang Quandi; Tang Minying

2008-01-01

In this Letter, we investigate two nonlinear equations given by u t -u xxt +3u 2 u x =2u x u xx +uu xxx and u t -u xxt +4u 2 u x =3u x u xx +uu xxx . Through some special phase orbits we obtain four new exact solutions for each equation above. Some previous results are extended

Exact error estimation for solutions of nuclide chain equations

International Nuclear Information System (INIS)

Tachihara, Hidekazu; Sekimoto, Hiroshi

1999-01-01

The exact solution of nuclide chain equations within arbitrary figures is obtained for a linear chain by employing the Bateman method in the multiple-precision arithmetic. The exact error estimation of major calculation methods for a nuclide chain equation is done by using this exact solution as a standard. The Bateman, finite difference, Runge-Kutta and matrix exponential methods are investigated. The present study confirms the following. The original Bateman method has very low accuracy in some cases, because of large-scale cancellations. The revised Bateman method by Siewers reduces the occurrence of cancellations and thereby shows high accuracy. In the time difference method as the finite difference and Runge-Kutta methods, the solutions are mainly affected by the truncation errors in the early decay time, and afterward by the round-off errors. Even though the variable time mesh is employed to suppress the accumulation of round-off errors, it appears to be nonpractical. Judging from these estimations, the matrix exponential method is the best among all the methods except the Bateman method whose calculation process for a linear chain is not identical with that for a general one. (author)

Exact shock profile for the ASEP with sublattice-parallel update

International Nuclear Information System (INIS)

Jafarpour, F H; Ghafari, F E; Masharian, S R

2005-01-01

We analytically study the one-dimensional asymmetric simple exclusion process with open boundaries under sublattice-parallel updating scheme. We investigate the stationary state properties of this model conditioned on finding a given particle number in the system. Recent numerical investigations have shown that the model possesses three different phases in this case. Using a matrix product method we calculate both the exact canonical partition function and also density profiles of the particles in each phase. Application of the Yang-Lee theory reveals that the model undergoes two second-order phase transitions at critical points. These results confirm the correctness of our previous numerical studies

Exact solutions of the neutron slowing down equation

International Nuclear Information System (INIS)

Dawn, T.Y.; Yang, C.N.

1976-01-01

The problem of finding the exact analytic closed-form solution for the neutron slowing down equation in an infinite homogeneous medium is studied in some detail. The existence and unique properties of the solution of this equation for both the time-dependent and the time-independent cases are studied. A direct method is used to determine the solution of the stationary problem. The final result is given in terms of a sum of indefinite multiple integrals by which solutions of some special cases and the Placzek-type oscillation are examined. The same method can be applied to the time-dependent problem with the aid of the Laplace transformation technique, but the inverse transform is, in general, laborious. However, the solutions of two special cases are obtained explicitly. Results are compared with previously reported works in a variety of cases. The time moments for the positive integral n are evaluated, and the conditions for the existence of the negative moments are discussed

Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

Science.gov (United States)

Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

2017-11-01

In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

New explicit and exact solutions of the Benney–Kawahara–Lin equation

International Nuclear Information System (INIS)

Yuan-Xi, Xie

2009-01-01

In this paper, we present a combination method of constructing the explicit and exact solutions of nonlinear partial differential equations. And as an illustrative example, we apply the method to the Benney–Kawahara–Lin equation and derive its many explicit and exact solutions which are all new solutions. (general)

Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions

Directory of Open Access Journals (Sweden)

Weiguo Rui

2014-01-01

Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.

Exact geodesic distances in FLRW spacetimes

Science.gov (United States)

Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri

2017-11-01

Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

On a method of construction of exact solutions for equations of two-dimensional hydrodynamics of incompressible liquids

International Nuclear Information System (INIS)

Yurov, A.V.; Yurova, A.A.

2006-01-01

The simple algebraic method for construction of exact solutions of two-dimensional hydrodynamic equations of incompressible flow is proposed. This method can be applied both to nonviscous flow (Euler equations) and to viscous flow (Navier-Stokes equations). In the case of nonviscous flow, the problem is reduced to sequential solving of three linear partial differential equations. In the case of viscous flow, the Navier-Stokes equations are reduced to three linear partial differential equations and one differential equation of the first order [ru

Energy vs. density on paths toward more exact density functionals.

Science.gov (United States)

Kepp, Kasper P

2018-03-14

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a "path". Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness and "straying" from the "path" by separating errors in ρ and E[ρ]. A consistent path toward exactness involves minimizing both errors. Second, a suitably diverse test set of trial densities ρ' can be used to estimate the significance of errors in ρ without knowing the exact densities which are often inaccessible. To illustrate this, the systems previously studied by Medvedev et al., the first ionization energies of atoms with Z = 1 to 10, the ionization energy of water, and the bond dissociation energies of five diatomic molecules were investigated using CCSD(T)/aug-cc-pV5Z as benchmark at chemical accuracy. Four functionals of distinct designs was used: B3LYP, PBE, M06, and S-VWN. For atomic cations regardless of charge and compactness up to Z = 10, the energy effects of the different ρ are energy-wise insignificant. An interesting oscillating behavior in the density sensitivity is observed vs. Z, explained by orbital occupation effects. Finally, it is shown that even large "normal" problems such as the Co-C bond energy of cobalamins can use simpler (e.g. PBE) trial densities to drastically speed up computation by loss of a few kJ mol -1 in accuracy. The proposed method of using a test set of trial densities to estimate the sensitivity and significance of density errors of functionals may be useful for testing and designing new balanced functionals with more systematic improvement of densities and energies.

Exact analytic solutions generated from stipulated Morse and trigonometric Scarf potentials

International Nuclear Information System (INIS)

Saikia, N; Ahmed, S A S

2011-01-01

The extended transformation method has been applied to the exactly solvable stipulated Morse potential and trigonometric Scarf potential, to generate a set of exactly solvable quantum systems (QSs) in any chosen dimension. Bound state solutions of the exactly solvable potentials are given. The generated QSs are generally of Sturmian form. We also report a system case-specific regrouping technique to convert a Sturmian QS to a normal QS. A second-order application of the transformation method is given. The normalizability of the generated QSs is generally given in Sturmian form.

Symmetries and exact solutions of the nondiagonal Einstein-Rosen metrics

International Nuclear Information System (INIS)

Goyal, N; Gupta, R K

2012-01-01

We seek exact solutions of the nondiagonal Einstein-Rosen metrics. The method of Lie symmetry of differential equations is utilized to obtain new exact solutions of Einstein vacuum equations obtained from the nondiagonal Einstein-Rosen metric. Four cases arise depending on the nature of the Lie symmetry generator. In all cases, we find reductions in terms of ordinary differential equations and exact solutions of the nonlinear system of partial differential equations (PDEs) are derived. For this purpose, first we check the Painlevé property and then corresponding to the nonlinear system of PDEs, symmetries and exact solutions are obtained.

Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra

Science.gov (United States)

Sulc, Miroslav; Hernandez, Henar; Martinez, Todd J.; Vanicek, Jiri

2014-03-01

We recently showed that the Dephasing Representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that cellularization yields further acceleration [M. Šulc and J. Vaníček, Mol. Phys. 110, 945 (2012)]. Here we focus on increasing its accuracy by first implementing an exact Gaussian basis method (GBM) combining the accuracy of quantum dynamics and efficiency of classical dynamics. The DR is then derived together with ten other methods for computing time-resolved spectra with intermediate accuracy and efficiency. These include the Gaussian DR (GDR), an exact generalization of the DR, in which trajectories are replaced by communicating frozen Gaussians evolving classically with an average Hamiltonian. The methods are tested numerically on time correlation functions and time-resolved stimulated emission spectra in the harmonic potential, pyrazine S0 /S1 model, and quartic oscillator. Both the GBM and the GDR are shown to increase the accuracy of the DR. Surprisingly, in chaotic systems the GDR can outperform the presumably more accurate GBM, in which the two bases evolve separately. This research was supported by the Swiss NSF Grant No. 200021_124936/1 and NCCR Molecular Ultrafast Science & Technology (MUST), and by the EPFL.

Free Vibration Analysis for Shells of Revolution Using an Exact Dynamic Stiffness Method

Directory of Open Access Journals (Sweden)

Xudong Chen

2016-01-01

Full Text Available An exact generalised formulation for the free vibration of shells of revolution with general shaped meridians and arbitrary boundary conditions is introduced. Starting from the basic shell theories, the vibration governing equations are obtained in the Hamilton form, from which dynamic stiffness is computed using the ordinary differential equations solver COLSYS. Natural frequencies and modes are determined by employing the Wittrick-Williams (W-W algorithm in conjunction with the recursive Newton’s method, thus expanding the applications of the abovementioned techniques from one-dimensional skeletal structures to two-dimensional shells of revolution. A solution for solving the number of clamped-end frequencies J0 in the W-W algorithm is presented for both uniform and nonuniform shell segment members. Based on these theories, a FORTRAN program is written. Numerical examples on circular cylindrical shells, hyperboloidal cooling tower shells, and spherical shells are given, and error analysis is performed. The convergence of the proposed method on J0 is verified, and comparisons with frequencies from existing literature show that the dynamic stiffness method is robust, reliable, and accurate.

The asymptotic and exact Fisher information matrices of a vector ARMA process

NARCIS (Netherlands)

Klein, A.; Melard, G.; Saidi, A.

2008-01-01

The exact Fisher information matrix of a Gaussian vector autoregressive-moving average (VARMA) process has been considered for a time series of length N in relation to the exact maximum likelihood estimation method. In this paper it is shown that the Gaussian exact Fisher information matrix

New exact wave solutions for Hirota equation

Indian Academy of Sciences (India)

2Department of Engineering Sciences, Faculty of Technology and Engineering,. University ... of nonlinear partial differential equations (NPDEs) in mathematical physics. Keywords. ... This method has been successfully applied to obtain exact.

A class of exact solutions to the Einstein field equations

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R K

2012-01-01

The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

Science.gov (United States)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations

Science.gov (United States)

Subramanian, Ramanathan Vishnampet Ganapathi

Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvement. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs. Such methods have enabled sensitivity analysis and active control of turbulence at engineering flow conditions by providing gradient information at computational cost comparable to that of simulating the flow. They accelerate convergence of numerical design optimization algorithms, though this is predicated on the availability of an accurate gradient of the discretized flow equations. This is challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. We analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space--time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge--Kutta-like scheme

Exact Solutions to a Combined sinh-cosh-Gordon Equation

International Nuclear Information System (INIS)

Wei Long

2010-01-01

Based on a transformed Painleve property and the variable separated ODE method, a function transformation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions to the resulting equations by some methods. As an application, exact solutions for the combined sinh-cosh-Gordon equation are formally derived. (general)

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

Science.gov (United States)

Pont, Federico M.; Osenda, Omar; Serra, Pablo

2018-05-01

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.

Electronic properties of antiferromagnetic UBi2 metal by exact exchange for correlated electrons method

Directory of Open Access Journals (Sweden)

E Ghasemikhah

2012-03-01

Full Text Available This study investigated the electronic properties of antiferromagnetic UBi2 metal by using ab initio calculations based on the density functional theory (DFT, employing the augmented plane waves plus local orbital method. We used the exact exchange for correlated electrons (EECE method to calculate the exchange-correlation energy under a variety of hybrid functionals. Electric field gradients (EFGs at the uranium site in UBi2 compound were calculated and compared with the experiment. The EFGs were predicted experimentally at the U site to be very small in this compound. The EFG calculated by the EECE functional are in agreement with the experiment. The densities of states (DOSs show that 5f U orbital is hybrided with the other orbitals. The plotted Fermi surfaces show that there are two kinds of charges on Fermi surface of this compound.

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.

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

Science.gov (United States)

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Exact nonparametric confidence bands for the survivor function.

Science.gov (United States)

Matthews, David

2013-10-12

A method to produce exact simultaneous confidence bands for the empirical cumulative distribution function that was first described by Owen, and subsequently corrected by Jager and Wellner, is the starting point for deriving exact nonparametric confidence bands for the survivor function of any positive random variable. We invert a nonparametric likelihood test of uniformity, constructed from the Kaplan-Meier estimator of the survivor function, to obtain simultaneous lower and upper bands for the function of interest with specified global confidence level. The method involves calculating a null distribution and associated critical value for each observed sample configuration. However, Noe recursions and the Van Wijngaarden-Decker-Brent root-finding algorithm provide the necessary tools for efficient computation of these exact bounds. Various aspects of the effect of right censoring on these exact bands are investigated, using as illustrations two observational studies of survival experience among non-Hodgkin's lymphoma patients and a much larger group of subjects with advanced lung cancer enrolled in trials within the North Central Cancer Treatment Group. Monte Carlo simulations confirm the merits of the proposed method of deriving simultaneous interval estimates of the survivor function across the entire range of the observed sample. This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. It was begun while the author was visiting the Department of Statistics, University of Auckland, and completed during a subsequent sojourn at the Medical Research Council Biostatistics Unit in Cambridge. The support of both institutions, in addition to that of NSERC and the University of Waterloo, is greatly appreciated.

Exact Solutions of the Harry-Dym Equation

International Nuclear Information System (INIS)

Mokhtari, Reza

2011-01-01

The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He's variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation. (general)

New exact solutions of the(2+1-dimensional Broer-Kaup equation by the consistent Riccati expansion method

Directory of Open Access Journals (Sweden)

Jiang Ying

2017-01-01

Full Text Available In this work, we study the (2+1-D Broer-Kaup equation. The composite periodic breather wave, the exact composite kink breather wave and the solitary wave solutions are obtained by using the coupled degradation technique and the consistent Riccati expansion method. These results may help us to investigate some complex dynamical behaviors and the interaction between composite non-linear waves in high dimensional models

Exact theory of freeze-out

Science.gov (United States)

Cannoni, Mirco

2015-03-01

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature . The point , which coincides with the stationary point of the equation for the quantity , is where the maximum departure of the WIMPs abundance from the thermal value is reached. For each mass and total annihilation cross section , the temperature and the actual WIMPs abundance are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval . The matching of the two abundances at is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1-2 % in the case of -wave and -wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics.

On nonlinear differential equation with exact solutions having various pole orders

International Nuclear Information System (INIS)

Kudryashov, N.A.

2015-01-01

We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed

Exact model reduction of combinatorial reaction networks

Directory of Open Access Journals (Sweden)

Fey Dirk

2008-08-01

Full Text Available Abstract Background Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. Results We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs to a model with 87 ODEs. Conclusion The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.

New Exact Solutions for (1 + 1)-Dimensional Dispersion-Less System

International Nuclear Information System (INIS)

Naranmandula; Hu Jianguo; Bao Gang; Tubuxin

2008-01-01

Using improved homogeneous balance method, we obtain complex function form new exact solutions for the (1+1)-dimensional dispersion-less system, and from the exact solutions we derive real function form solution of the field u. Based on this real function form solution, we find some new interesting coherent structures by selecting arbitrary functions appropriately

Disease clusters, exact distributions of maxima, and P-values.

Science.gov (United States)

Grimson, R C

1993-10-01

This paper presents combinatorial (exact) methods that are useful in the analysis of disease cluster data obtained from small environments, such as buildings and neighbourhoods. Maxwell-Boltzmann and Fermi-Dirac occupancy models are compared in terms of appropriateness of representation of disease incidence patterns (space and/or time) in these environments. The methods are illustrated by a statistical analysis of the incidence pattern of bone fractures in a setting wherein fracture clustering was alleged to be occurring. One of the methodological results derived in this paper is the exact distribution of the maximum cell frequency in occupancy models.

AESS: Accelerated Exact Stochastic Simulation

Science.gov (United States)

Jenkins, David D.; Peterson, Gregory D.

2011-12-01

The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution

Incorporation of exact boundary conditions into a discontinuous galerkin finite element method for accurately solving 2d time-dependent maxwell equations

KAUST Repository

Sirenko, Kostyantyn; Liu, Meilin; Bagci, Hakan

2013-01-01

A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing

Exact, almost and delayed fault detection: An observer based approach

DEFF Research Database (Denmark)

Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.

1999-01-01

This paper consider the problem of fault detection and isolation in continuous- and discrete-time systems while using zero or almost zero threshold. A number of different fault detections and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability...... conditions are given for the formulated design problems together with methods for appropriate design of observer based fault detectors. The l-step delayed fault detection problem is also considered for discrete-time systems . Moreover, certain indirect fault detection methods such as unknown input observers...

Exact results for integrable asymptotically-free field theories

CERN Document Server

Evans, J M; Evans, Jonathan M; Hollowood, Timothy J

1995-01-01

An account is given of a technique for testing the equivalence between an exact factorizable S-matrix and an asymptotically-free Lagrangian field theory in two space-time dimensions. The method provides a way of resolving CDD ambiguities in the S-matrix and it also allows for an exact determination of the physical mass in terms of the Lambda parameter of perturbation theory. The results for various specific examples are summarized. (To appear in the Proceedings of the Conference on Recent Developments in Quantum Field Theory and Statistical Mechanics, ICTP, Trieste, Easter 1995).

New exact solutions of the generalized Zakharov–Kuznetsov ...

Indian Academy of Sciences (India)

In this paper, new exact solutions, including soliton, rational and elliptic integral function solutions, for the generalized Zakharov–Kuznetsov modified equal-width equation are obtained using a new approach called the extended trial equation method. In this discussion, a new version of the trial equation method for the ...

Exactly solvable position dependent mass schroedinger equation

International Nuclear Information System (INIS)

Koc, R.; Tuetuencueler, H.; Koercuek, E.

2002-01-01

Exact solution of the Schrodinger equation with a variable mass is presented. We have derived general expressions for the eigenstates and eigenvalues of the position dependent mass systems. We provide supersymmetric and Lie algebraic methods to discuss the position dependent mass systems

Exact thermal representation of multilayer rectangular structures by infinite plate structures using the method of images

Science.gov (United States)

Palisoc, Arthur L.; Lee, Chin C.

1988-12-01

Using the method of images and the analytical temperature solution to the multilayer infinite plate structure, the thermal profile over finite rectangular multilayer integrated circuit devices can be calculated exactly. The advantage of using the image method lies in the enhanced capability of arriving at an analytical solution for structures where analytical solutions do not apparently exist, e.g., circular or arbitrarily oriented rectangular sources over multilayered rectangular structures. The new approach results in large savings in computer CPU time especially for small sources over large substrates. The method also finds very important applications to integrated circuit devices with heat dissipating elements close to the edge boundaries. Results from two examples indicate that the edge boundaries of a device may also be utilized to remove heat from it. This additional heat removing capability should have important applications in high power devices.

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

Directory of Open Access Journals (Sweden)

Matthew J Simpson

Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i the rate at which the domain elongates, (ii the diffusivity associated with the spreading density profile, (iii the reaction rate, and (iv the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t.

Exact solutions of some coupled nonlinear diffusion-reaction ...

Indian Academy of Sciences (India)

certain coupled diffusion-reaction (D-R) equations of very general nature. In recent years, various direct methods have been proposed to find the exact solu- tions not only of nonlinear partial differential equations but also of their coupled versions. These methods include unified ansatz approach [3], extended hyperbolic func ...

Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics

International Nuclear Information System (INIS)

Niven, Robert K.

2005-01-01

The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a 'binary decision', exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems

Exact renormalization group as a scheme for calculations

International Nuclear Information System (INIS)

Mack, G.

1985-10-01

In this lecture I report on recent work to use exact renormalization group methods to construct a scheme for calculations in quantum field theory and classical statistical mechanics on the continuum. (orig./HSI)

Inverse Schroedinger equation and the exact wave function

International Nuclear Information System (INIS)

Nakatsuji, Hiroshi

2002-01-01

Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem

Exact norm-conserving stochastic time-dependent Hartree-Fock

International Nuclear Information System (INIS)

Tessieri, Luca; Wilkie, Joshua; Cetinbas, Murat

2005-01-01

We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method, we calculate the low energy spectrum of helium. An extension of the method to bosons is outlined

An Exact Method to Determine the Photonic Resonances of Quasicrystals Based on Discrete Fourier Harmonics of Higher-Dimensional Atomic Surfaces

Directory of Open Access Journals (Sweden)

Farhad A. Namin

2016-08-01

Full Text Available A rigorous method for obtaining the diffraction patterns of quasicrystals is presented. Diffraction patterns are an essential analytical tool in the study of quasicrystals, since they can be used to determine their photonic resonances. Previous methods for approximating the diffraction patterns of quasicrystals have relied on evaluating the Fourier transform of finite-sized super-lattices. Our approach, on the other hand, is exact in the sense that it is based on a technique that embeds quasicrystals into higher dimensional periodic hyper-lattices, thereby completely capturing the properties of the infinite structure. The periodicity of the unit cell in the higher dimensional space can be exploited to obtain the Fourier series expansion in closed-form of the corresponding atomic surfaces. The utility of the method is demonstrated by applying it to one-dimensional Fibonacci and two-dimensional Penrose quasicrystals. The results are verified by comparing them to those obtained by using the conventional super-lattice method. It is shown that the conventional super-cell approach can lead to inaccurate results due to the continuous nature of the Fourier transform, since quasicrystals have a discrete spectrum, whereas the approach introduced in this paper generates discrete Fourier harmonics. Furthermore, the conventional approach requires very large super-cells and high-resolution sampling of the reciprocal space in order to produce accurate results leading to a very large computational burden, whereas the proposed method generates accurate results with a relatively small number of terms. Finally, we propose how this approach can be generalized from the vertex model, which assumes identical particles at all vertices, to a more realistic case where the quasicrystal is composed of different atoms.

On the exact interpolating function in ABJ theory

Energy Technology Data Exchange (ETDEWEB)

Cavaglià, Andrea [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); Gromov, Nikolay [Mathematics Department, King’s College London,The Strand, London WC2R 2LS (United Kingdom); St. Petersburg INP,Gatchina, 188 300, St.Petersburg (Russian Federation); Levkovich-Maslyuk, Fedor [Mathematics Department, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Nordita, KTH Royal Institute of Technology and Stockholm University,Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden)

2016-12-16

Based on the recent indications of integrability in the planar ABJ model, we conjecture an exact expression for the interpolating function h(λ{sub 1},λ{sub 2}) in this theory. Our conjecture is based on the observation that the integrability structure of the ABJM theory given by its Quantum Spectral Curve is very rigid and does not allow for a simple consistent modification. Under this assumption, we revised the previous comparison of localization results and exact all loop integrability calculations done for the ABJM theory by one of the authors and Grigory Sizov, fixing h(λ{sub 1},λ{sub 2}). We checked our conjecture against various weak coupling expansions, at strong coupling and also demonstrated its invariance under the Seiberg-like duality. This match also gives further support to the integrability of the model. If our conjecture is correct, it extends all the available integrability results in the ABJM model to the ABJ model.

Exact cosmological solutions for MOG

International Nuclear Information System (INIS)

Roshan, Mahmood

2015-01-01

We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)

Exact theory of freeze-out

International Nuclear Information System (INIS)

Cannoni, Mirco

2015-01-01

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x * = m χ /T * . The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y 0 , is where the maximum departure of the WIMPs abundance Y from the thermal value Y 0 is reached. For each mass m χ and total annihilation cross section left angle σ ann υ r right angle, the temperature x * and the actual WIMPs abundance Y(x * ) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x * . The matching of the two abundances at x * is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)

Exact method for the simulation of Coulombic systems by spherically truncated, pairwise r-1 summation

International Nuclear Information System (INIS)

Wolf, D.; Keblinski, P.; Phillpot, S.R.; Eggebrecht, J.

1999-01-01

Based on a recent result showing that the net Coulomb potential in condensed ionic systems is rather short ranged, an exact and physically transparent method permitting the evaluation of the Coulomb potential by direct summation over the r -1 Coulomb pair potential is presented. The key observation is that the problems encountered in determining the Coulomb energy by pairwise, spherically truncated r -1 summation are a direct consequence of the fact that the system summed over is practically never neutral. A simple method is developed that achieves charge neutralization wherever the r -1 pair potential is truncated. This enables the extraction of the Coulomb energy, forces, and stresses from a spherically truncated, usually charged environment in a manner that is independent of the grouping of the pair terms. The close connection of our approach with the Ewald method is demonstrated and exploited, providing an efficient method for the simulation of even highly disordered ionic systems by direct, pairwise r -1 summation with spherical truncation at rather short range, i.e., a method which fully exploits the short-ranged nature of the interactions in ionic systems. The method is validated by simulations of crystals, liquids, and interfacial systems, such as free surfaces and grain boundaries. copyright 1999 American Institute of Physics

Nonlinear evolution-type equations and their exact solutions using inverse variational methods

International Nuclear Information System (INIS)

Kara, A H; Khalique, C M

2005-01-01

We present the role of invariants in obtaining exact solutions of differential equations. Firstly, conserved vectors of a partial differential equation (p.d.e.) allow us to obtain reduced forms of the p.d.e. for which some of the Lie point symmetries (in vector field form) are easily concluded and, therefore, provide a mechanism for further reduction. Secondly, invariants of reduced forms of a p.d.e. are obtainable from a variational principle even though the p.d.e. itself does not admit a Lagrangian. In this latter case, the reductions carry all the usual advantages regarding Noether symmetries and double reductions. The examples we consider are nonlinear evolution-type equations such as the Korteweg-deVries equation, but a detailed analysis is made on the Fisher equation (which describes reaction-diffusion waves in biology, inter alia). Other diffusion-type equations lend themselves well to the method we describe (e.g., the Fitzhugh Nagumo equation, which is briefly discussed). Some aspects of Painleve properties are also suggested

Exactly soluble problems in statistical mechanics

International Nuclear Information System (INIS)

Yang, C.N.

1983-01-01

In the last few years, a number of two-dimensional classical and one-dimensional quantum mechanical problems in statistical mechanics have been exactly solved. Although these problems range over models of diverse physical interest, their solutions were obtained using very similar mathematical methods. In these lectures, the main points of the methods are discussed. In this introductory lecture, an overall survey of all these problems without going into the detailed method of solution is given. In later lectures, they shall concentrate on one particular problem: the delta function interaction in one dimension, and go into the details of that problem

An optimized method for neurotransmitters and their metabolites analysis in mouse hypothalamus by high performance liquid chromatography-Q Exactive hybrid quadrupole-orbitrap high-resolution accurate mass spectrometry.

Science.gov (United States)

Yang, Zong-Lin; Li, Hui; Wang, Bing; Liu, Shu-Ying

2016-02-15

Neurotransmitters (NTs) and their metabolites are known to play an essential role in maintaining various physiological functions in nervous system. However, there are many difficulties in the detection of NTs together with their metabolites in biological samples. A new method for NTs and their metabolites detection by high performance liquid chromatography coupled with Q Exactive hybrid quadruple-orbitrap high-resolution accurate mass spectrometry (HPLC-HRMS) was established in this paper. This method was a great development of the applying of Q Exactive MS in the quantitative analysis. This method enabled a rapid quantification of ten compounds within 18min. Good linearity was obtained with a correlation coefficient above 0.99. The concentration range of the limit of detection (LOD) and the limit of quantitation (LOQ) level were 0.0008-0.05nmol/mL and 0.002-25.0nmol/mL respectively. Precisions (relative standard deviation, RSD) of this method were at 0.36-12.70%. Recovery ranges were between 81.83% and 118.04%. Concentrations of these compounds in mouse hypothalamus were detected by Q Exactive LC-MS technology with this method. Copyright © 2016 Elsevier B.V. All rights reserved.

Exact simulation of Brown-Resnick random fields at a finite number of locations

DEFF Research Database (Denmark)

Dieker, Ton; Mikosch, Thomas Valentin

2015-01-01

We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure.......We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure....

Quasi-exact solutions of nonlinear differential equations

OpenAIRE

Kudryashov, Nikolay A.; Kochanov, Mark B.

2014-01-01

The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.

Exact travelling wave solutions for some important nonlinear ...

Indian Academy of Sciences (India)

The study of nonlinear partial differential equations is an active area of research in applied mathematics, theoretical physics and engineering fields. In particular ... In [16–18], the author applied this method to construct the exact solutions of.

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

Symmetry and exact solutions of nonlinear spinor equations

International Nuclear Information System (INIS)

Fushchich, W.I.; Zhdanov, R.Z.

1989-01-01

This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differential equations for spinor, vector and scalar fields widely used in quantum field theory. Large classes of nonlinear spinor equations invariant under the Poincare group P(1, 3), Weyl group (i.e. Poincare group supplemented by a group of scale transformations), and the conformal group C(1, 3) are described. Ansaetze invariant under the Poincare and the Weyl groups are constructed. Using these we reduce the Poincare-invariant nonlinear Dirac equations to systems of ordinary differential equations and construct large families of exact solutions of the nonlinear Dirac-Heisenberg equation depending on arbitrary parameters and functions. In a similar way we have obtained new families of exact solutions of the nonlinear Maxwell-Dirac and Klein-Gordon-Dirac equations. The obtained solutions can be used for quantization of nonlinear equations. (orig.)

Erlotinib-induced rash spares previously irradiated skin

International Nuclear Information System (INIS)

Lips, Irene M.; Vonk, Ernest J.A.; Koster, Mariska E.Y.; Houwing, Ronald H.

2011-01-01

Erlotinib is an epidermal growth factor receptor inhibitor prescribed to patients with locally advanced or metastasized non-small cell lung carcinoma after failure of at least one earlier chemotherapy treatment. Approximately 75% of the patients treated with erlotinib develop acneiform skin rashes. A patient treated with erlotinib 3 months after finishing concomitant treatment with chemotherapy and radiotherapy for non-small cell lung cancer is presented. Unexpectedly, the part of the skin that had been included in his previously radiotherapy field was completely spared from the erlotinib-induced acneiform skin rash. The exact mechanism of erlotinib-induced rash sparing in previously irradiated skin is unclear. The underlying mechanism of this phenomenon needs to be explored further, because the number of patients being treated with a combination of both therapeutic modalities is increasing. The therapeutic effect of erlotinib in the area of the previously irradiated lesion should be assessed. (orig.)

Separable expansions of the NN t-matrix via exact half off the energy shell methods

International Nuclear Information System (INIS)

Pisent, G.; Amos, K.; Dortmans, P.J.

1992-01-01

Recently a method was proposed by which one can obtain rank 1 (for uncoupled channels) and rank 2 (for coupled channels), energy dependent t-matrix representations which are exact on- and half off of the energy shell. Fully off shell, this representation, though accurate at low energies, is flawed. For uncoupled channels, if the phase shift passes through zero, the representation has a pathology. Two methods which overcome this are investigated one due to Haberzettl which was extended to coupled channels, and the second which is based upon selective combination of the elements of Sturmian expansions. All methods of separation over a range of energies up to 250 MeV for the 1 S 0 and 3 S 1 channels are compared with the Paris interaction. Special attention is paid to the convergence of the higher order Haberzettl expansion and to the comparison of the extended methods for energies around the zero phase shift pathology for the 1 S 0 channel. The method describes well the fully off-shell properties of the t-matrices up to quite high energies, while keeping the rank of the separation as low as possible in order to be used in three or more body calculations. 39 refs., 10 figs

An exact approach for aggregated formulations

DEFF Research Database (Denmark)

Gamst, Mette; Spoorendonk, Simon; Røpke, Stefan

Aggregating formulations is a powerful approach for problems to take on tractable forms. Aggregation may lead to loss of information, i.e. the aggregated formulation may be an approximation of the original problem. In branch-and-bound context, aggregation can also complicate branching, e.g. when...... optimality cannot be guaranteed by branching on aggregated variables. We present a generic exact solution method to remedy the drawbacks of aggregation. It combines the original and aggregated formulations and applies Benders' decomposition. We apply the method to the Split Delivery Vehicle Routing Problem....

A low-dispersion, exactly energy-charge-conserving semi-implicit relativistic particle-in-cell algorithm

Science.gov (United States)

Chen, Guangye; Luis, Chacon; Bird, Robert; Stark, David; Yin, Lin; Albright, Brian

2017-10-01

Leap-frog based explicit algorithms, either ``energy-conserving'' or ``momentum-conserving'', do not conserve energy discretely. Time-centered fully implicit algorithms can conserve discrete energy exactly, but introduce large dispersion errors in the light-wave modes, regardless of timestep sizes. This can lead to intolerable simulation errors where highly accurate light propagation is needed (e.g. laser-plasma interactions, LPI). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce a low-dispersion, exactly energy-and-charge-conserving PIC algorithm. Specifically, we employ the leap-frog method for Maxwell equations, and the Crank-Nicolson method for particle equations. Such an algorithm admits exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm has been implemented in a code named iVPIC, based on the VPIC code developed at LANL. We will present numerical results that demonstrate the properties of the scheme with sample test problems (e.g. Weibel instability run for 107 timesteps, and LPI applications.

Exact boundary controllability of nodal profile for quasilinear hyperbolic systems

CERN Document Server

Li, Tatsien; Gu, Qilong

2016-01-01

This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyp...

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

Exact theory of freeze-out

Energy Technology Data Exchange (ETDEWEB)

Cannoni, Mirco [Universidad de Huelva, Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Huelva (Spain)

2015-03-01

We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x{sub *} = m{sub χ}/T{sub *}. The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y{sub 0}, is where the maximum departure of the WIMPs abundance Y from the thermal value Y{sub 0} is reached. For each mass m{sub χ} and total annihilation cross section left angle σ{sub ann}υ{sub r} right angle, the temperature x{sub *} and the actual WIMPs abundance Y(x{sub *}) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x{sub *}. The matching of the two abundances at x{sub *} is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)

Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method

Energy Technology Data Exchange (ETDEWEB)

Fatalov, Vadim R [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2011-08-31

We prove results on exact asymptotics as n{yields}{infinity} for the expectations E{sub a} exp{l_brace}-{theta}{Sigma}{sub k=0}{sup n-1}g(X{sub k}){r_brace} and probabilities P{sub a}{l_brace}(1/n {Sigma}{sub k=0}{sup n-1}g(X{sub k})=}1, is the corresponding random walk on R, g(x) is a positive continuous function satisfying certain conditions, and d>0, {theta}>0, a element of R are fixed numbers. Our results are obtained using a new method which is developed in this paper: the Laplace method for the occupation time of discrete-time Markov chains. For g(x) one can take |x|{sup p}, log (|x|{sup p}+1), p>0, |x| log (|x|+1), or e{sup {alpha}|x|}-1, 0<{alpha}<1/2, x element of R, for example. We give a detailed treatment of the case when g(x)=|x| using Bessel functions to make explicit calculations.

New exact travelling wave solutions of bidirectional wave equations

Indian Academy of Sciences (India)

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea. ∗ ... exact travelling wave solutions of system (1) using the modified tanh–coth function method ... The ordinary differential equation is then integrated.

Duality and self-duality (energy reflection symmetry) of quasi-exactly solvable periodic potentials

International Nuclear Information System (INIS)

Dunne, Gerald V.; Shifman, M.

2002-01-01

A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential. The self-dual point of this transformation corresponds to the energy-reflection symmetry found previously for certain QES systems. The duality transformation interchanges bands at the bottom (top) of the spectrum of one potential with gaps at the top (bottom) of the spectrum of the other, dual, potential. Thus, the duality transformation provides an exact mapping between the weak coupling (perturbative) and semiclassical (nonperturbative) sectors

Exact solutions to the time-fractional differential equations via local fractional derivatives

Science.gov (United States)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

A procedure to construct exact solutions of nonlinear evolution ...

Indian Academy of Sciences (India)

Exact solutions; the functional variable method; nonlinear wave equations. PACS Nos 02.30. ... computer science, directly searching for solutions of nonlinear differential equations has become more and ... Right after this pioneer work, this ...

Exact solutions of Lovelock-Born-Infeld black holes

International Nuclear Information System (INIS)

Aiello, Matias; Ferraro, Rafael; Giribet, Gaston

2004-01-01

The exact five-dimensional charged black hole solution in Lovelock gravity coupled to Born-Infeld electrodynamics is presented. This solution interpolates between the Hoffmann black hole for the Einstein-Born-Infeld theory and other solutions in the Lovelock theory previously studied in the literature. It is shown how the conical singularity of the metric around the origin can be removed by a proper choice of the black hole parameters. The differences existing with the Reissner-Nordstroem black holes are discussed. In particular, we show the existence of charged black holes with a unique horizon

Exactly solvable irreversible processes on one-dimensional lattices

International Nuclear Information System (INIS)

Wolf, N.O.; Evans, J.W.; Hoffman, D.K.

1984-01-01

We consider the kinetics of a process where the sites of an infinite 1-D lattice are filled irreversibly and, in general, cooperatively by N-mers (taking N consecutive sites at a time). We extend the previously available exact solution for nearest neighbor cooperative effects to range N cooperative effects. Connection with the continuous ''cooperative car parking problem'' is indicated. Both uniform and periodic lattices, and empty and certain partially filled lattice initial conditions are considered. We also treat monomer ''filling in stages'' for certain highly autoinhibitory cooperative effects of arbitrary range

Exact results relating spin-orbit interactions in two-dimensional strongly correlated systems

Science.gov (United States)

Kucska, Nóra; Gulácsi, Zsolt

2018-06-01

A 2D square, two-bands, strongly correlated and non-integrable system is analysed exactly in the presence of many-body spin-orbit interactions via the method of Positive Semidefinite Operators. The deduced exact ground states in the high concentration limit are strongly entangled, and given by the spin-orbit coupling are ferromagnetic and present an enhanced carrier mobility, which substantially differs for different spin projections. The described state emerges in a restricted parameter space region, which however is clearly accessible experimentally. The exact solutions are provided via the solution of a matching system of equations containing 74 coupled, non-linear and complex algebraic equations. In our knowledge, other exact results for 2D interacting systems with spin-orbit interactions are not present in the literature.

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

International Nuclear Information System (INIS)

Ugurlu, Yavuz; Kaya, Dogan

2008-01-01

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

New types of exact solutions for a breaking soliton equation

International Nuclear Information System (INIS)

Mei Jianqin; Zhang Hongqing

2004-01-01

In this paper based on a system of Riccati equations, we present a newly generally projective Riccati equation expansion method and its algorithm, which can be used to construct more new exact solutions of nonlinear differential equations in mathematical physics. A typical breaking soliton equation is chosen to illustrate our algorithm such that more families of new exact solutions are obtained, which contain soliton-like solutions and periodic solutions. This algorithm can also be applied to other nonlinear differential equations

Quasi-exact evaluation of time domain MFIE MOT matrix elements

KAUST Repository

Shi, Yifei; Bagci, Hakan; Shanker, Balasubramaniam; Lu, Mingyu; Michielssen, Eric

2013-01-01

A previously proposed quasi-exact scheme for evaluating matrix elements resulting from the marching-on-in-time (MOT) discretization of the time domain electric field integral equation (EFIE) is extended to matrix entries resulting from the discretization of its magnetic field integral equation (MFIE) counterpart. Numerical results demonstrate the accuracy of the scheme as well as the late-time stability of the resulting MOT-MFIE solver. © 2013 IEEE.

Quasi-exact evaluation of time domain MFIE MOT matrix elements

KAUST Repository

Shi, Yifei

2013-07-01

A previously proposed quasi-exact scheme for evaluating matrix elements resulting from the marching-on-in-time (MOT) discretization of the time domain electric field integral equation (EFIE) is extended to matrix entries resulting from the discretization of its magnetic field integral equation (MFIE) counterpart. Numerical results demonstrate the accuracy of the scheme as well as the late-time stability of the resulting MOT-MFIE solver. © 2013 IEEE.

Strong pairing approximation in comparison with the exact solutions to the pairing Hamiltonian

Directory of Open Access Journals (Sweden)

Lunyov A.V.

2016-01-01

Full Text Available Results of the Strong Pairing Approximation (SPA as a method with the exact particle number conservation are compared with those of the quasiparticle method (QM. It is shown that SPA comes to the same equations as QM for the gap parameter, chemical potential and one- and two-quasiparticle states. Calculations are performed for 14864Gd84 as an example, and compared with the exact solutions to the pairing Hamiltonian.

Exact results for Wilson loops in arbitrary representations

Energy Technology Data Exchange (ETDEWEB)

Fiol, Bartomeu; Torrents, Genís [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, 08028 Barcelona, Catalonia (Spain)

2014-01-08

We compute the exact vacuum expectation value of 1/2 BPS circular Wilson loops of N=4 U(N) super Yang-Mills in arbitrary irreducible representations. By localization arguments, the computation reduces to evaluating certain integrals in a Gaussian matrix model, which we do using the method of orthogonal polynomials. Our results are particularly simple for Wilson loops in antisymmetric representations; in this case, we observe that the final answers admit an expansion where the coefficients are positive integers, and can be written in terms of sums over skew Young diagrams. As an application of our results, we use them to discuss the exact Bremsstrahlung functions associated to the corresponding heavy probes.

Exact solution of matricial Φ23 quantum field theory

Science.gov (United States)

Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar

2017-12-01

We apply a recently developed method to exactly solve the Φ3 matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large- N limit to integral equations that we solve exactly for all correlation functions. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.

The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations

International Nuclear Information System (INIS)

Liu Chunping; Liu Xiaoping

2004-01-01

First, we investigate the solitary wave solutions of the Burgers equation and the KdV equation, which are obtained by using the hyperbolic function method. Then we present a theorem which will not only give us a clear relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations, but also provide us an approach to construct new exact solutions in complex scalar field. Finally, we apply the theorem to the KdV-Burgers equation and obtain its new exact solutions

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

Energy Technology Data Exchange (ETDEWEB)

Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya36@yahoo.com

2008-04-14

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories

Energy Technology Data Exchange (ETDEWEB)

Carvalho, P.R.S. [Universidade Federal do Piaui, Departamento de Fisica, Teresina, PI (Brazil); Sena-Junior, M.I. [Universidade de Pernambuco, Escola Politecnica de Pernambuco, Recife, PE (Brazil); Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil)

2017-11-15

In this work we evaluate analytically the ultraviolet divergences of Lorentz-violating massive O(N) λφ{sup 4} scalar field theories, which are exact in the Lorentz-violating mechanism, firstly explicitly at next-to-leading order and latter at any loop level through an induction procedure based on a theorem following from the exact approach, for computing the corresponding critical exponents. For attaining that goal, we employ three different and independent field-theoretic renormalization group methods. The results found for the critical exponents show that they are identical in the three distinct methods and equal to their Lorentz-invariant counterparts. Furthermore, we show that the results obtained here, based on the single concept of loop order of the referred terms of the corresponding β-function and anomalous dimensions, reduce to the ones obtained through the earlier non-exact approach based on a joint redefinition of the field and coupling constant of the theory, in the appropriate limit. (orig.)

Exact constants in approximation theory

CERN Document Server

Korneichuk, N

1991-01-01

This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Directory of Open Access Journals (Sweden)

Peng Jiang

2013-01-01

Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

CONDITIONS FOR EXACT CAVALIERI ESTIMATION

Directory of Open Access Journals (Sweden)

Mónica Tinajero-Bravo

2014-03-01

Full Text Available Exact Cavalieri estimation amounts to zero variance estimation of an integral with systematic observations along a sampling axis. A sufficient condition is given, both in the continuous and the discrete cases, for exact Cavalieri sampling. The conclusions suggest improvements on the current stereological application of fractionator-type sampling.

Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow

Science.gov (United States)

Saengow, C.; Giacomin, A. J.

2017-12-01

The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η∞ affects the normal stress differences in LAOS.

Incorporation of exact boundary conditions into a discontinuous galerkin finite element method for accurately solving 2d time-dependent maxwell equations

KAUST Repository

Sirenko, Kostyantyn

2013-01-01

A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing transient electromagnetic wave interactions on two-dimensional waveguides. Numerical results demonstrate the proposed method\\'s superiority over the TD-DG-FEM that employs approximate boundary conditions and perfectly matched layers. Additionally, it is shown that the proposed method can produce the solution with ten-eleven digit accuracy when high-order spatial basis functions are used to discretize the Maxwell equations as well as the EACs. © 1963-2012 IEEE.

Exact solutions for rotating charged dust

International Nuclear Information System (INIS)

Islam, J.N.

1984-01-01

Earlier work by the author on rotating charged dust is summarized. An incomplete class of exact solutions for differentially rotating charged dust in Newton-Maxwell theory for the equal mass and charge case that was found earlier is completed. A new global exact solution for cylindrically symmetric differentially rotating charged dust in Newton-Maxwell theory is presented. Lastly, a new exact solution for cylindrically symmetric rigidly rotating charged dust in general relativity is given. (author)

New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source

International Nuclear Information System (INIS)

Abdou, M.A.

2008-01-01

The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics

Quantum decay model with exact explicit analytical solution

Science.gov (United States)

Marchewka, Avi; Granot, Er'El

2009-01-01

A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.

Exact Outage Probability of Dual-Hop CSI-Assisted AF Relaying Over Nakagami-m Fading Channels

KAUST Repository

Xia, Minghua; Aissa, Sonia; Wu, Yik-Chung

2012-01-01

to evaluate the outage performance of the system under study. The analytical results of outage probability coincide exactly with Monte-Carlo simulation results and outperform the previously reported upper bounds in the low and medium SNR regions.

Exact exchange-correlation potential and approximate exchange potential in terms of density matrices

International Nuclear Information System (INIS)

Holas, A.; March, N.H.

1995-01-01

An exact expression in terms of density matrices (DM) is derived for δF[n]/δn(r), the functional derivative of the Hohenberg-Kohn functional. The derivation starts from the differential form of the virial theorem, obtained here for an electron system with arbitrary interactions, and leads to an expression taking the form of an integral over a path that can be chosen arbitrarily. After applying this approach to the equivalent system of noninteracting electrons (Slater-Kohn-Sham scheme) and combining the corresponding result with the previous one, an exact expression for the exchange-correlation potential v xc (r) is obtained which is analogous in character to that for δF[n]/δn(r), but involving, besides the interacting-system DMs, also the noninteracitng DMs. Equating the former DMs to the latter ones, we reduce the result for the exact v xc (r) to that for an approximate exchange-only potential v x (r). This leads naturally to the Harbola-Sahni exchange-only potential

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

Science.gov (United States)

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

On a revisit to the Painlevé test for integrability and exact solutions ...

Indian Academy of Sciences (India)

... the same equations and keeping the singularity manifold completely general in nature. It has been found that the equations, in real form, pass the Painlevé test for integrability. The truncation procedure of the same analysis leads to non-trivial exact solutions obtained previously and auto-Backlund transformation between ...

Exact analytical solutions for nonlinear reaction-diffusion equations

International Nuclear Information System (INIS)

Liu Chunping

2003-01-01

By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way

Exact Solutions to (2+1)-Dimensional Kaup-Kupershmidt Equation

International Nuclear Information System (INIS)

Lu Hailing; Liu Xiqiang

2009-01-01

In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup-Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+1)-dimensional KK equation by the symmetry method and the (G'/G)-expansion method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions. (general)

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

A computationally exact method of Dawson's model for hole dynamics of one-dimensional plasma

International Nuclear Information System (INIS)

Kitahara, Kazuo; Tanno, Kohki; Takada, Toshio; Hatori, Tadatsugu; Urata, Kazuhiro; Irie, Haruyuki; Nambu, Mitsuhiro; Saeki, Kohichi.

1990-01-01

We show a simple but computationally exact solution of the one-dimensional plasma model, so-called 'Dawson's model'. Using this solution, we can describe the evolution of the plasma and find the relative stabilization of a big hole after the instability of two streams. (author)

Exact renormalization group equation for the Lifshitz critical point

Science.gov (United States)

Bervillier, C.

2004-10-01

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

Run-to-Run Optimization Control Within Exact Inverse Framework for Scan Tracking.

Science.gov (United States)

Yeoh, Ivan L; Reinhall, Per G; Berg, Martin C; Chizeck, Howard J; Seibel, Eric J

2017-09-01

A run-to-run optimization controller uses a reduced set of measurement parameters, in comparison to more general feedback controllers, to converge to the best control point for a repetitive process. A new run-to-run optimization controller is presented for the scanning fiber device used for image acquisition and display. This controller utilizes very sparse measurements to estimate a system energy measure and updates the input parameterizations iteratively within a feedforward with exact-inversion framework. Analysis, simulation, and experimental investigations on the scanning fiber device demonstrate improved scan accuracy over previous methods and automatic controller adaptation to changing operating temperature. A specific application example and quantitative error analyses are provided of a scanning fiber endoscope that maintains high image quality continuously across a 20 °C temperature rise without interruption of the 56 Hz video.

A fast, exact code for scattered thermal radiation compared with a two-stream approximation

International Nuclear Information System (INIS)

Cogley, A.C.; Pandey, D.K.

1980-01-01

A two-stream accuracy study for internally (thermal) driven problems is presented by comparison with a recently developed 'exact' adding/doubling method. The resulting errors in external (or boundary) radiative intensity and flux are usually larger than those for the externally driven problems and vary substantially with the radiative parameters. Error predictions for a specific problem are difficult. An unexpected result is that the exact method is computationally as fast as the two-stream approximation for nonisothermal media

Nonlinear differential equations with exact solutions expressed via the Weierstrass function

NARCIS (Netherlands)

Kudryashov, NA

2004-01-01

A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear

On exact solutions of scattering problems

International Nuclear Information System (INIS)

Nikishov, P.Yu.; Plekhanov, E.B.; Zakhariev, B.N.

1982-01-01

Examples illustrating the quality of the reconstruction of potentials from single-channel scattering data by using exactly solvable models are given. Simple exact solutions for multi-channel systems with non-degenerated resonance singularities of the scattering matrix are derived

Exact solutions to sine-Gordon-type equations

International Nuclear Information System (INIS)

Liu Shikuo; Fu Zuntao; Liu Shida

2006-01-01

In this Letter, sine-Gordon-type equations, including single sine-Gordon equation, double sine-Gordon equation and triple sine-Gordon equation, are systematically solved by Jacobi elliptic function expansion method. It is shown that different transformations for these three sine-Gordon-type equations play different roles in obtaining exact solutions, some transformations may not work for a specific sine-Gordon equation, while work for other sine-Gordon equations

Exact solutions for the cubic-quintic nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Zhu Jiamin; Ma Zhengyi

2007-01-01

In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions

Exact collisional moments for plasma fluid theories

Science.gov (United States)

Pfefferle, David; Hirvijoki, Eero; Lingam, Manasvi

2017-10-01

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of the distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities, and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas, that relies on the Chapman-Enskog method, as well as to deriving collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rate.

Exact relations for energy transfer in self-gravitating isothermal turbulence.

Science.gov (United States)

Banerjee, Supratik; Kritsuk, Alexei G

2017-11-01

Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (S. Galtier and S. Banerjee, Phys. Rev. Lett. 107, 134501 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.134501; S. Banerjee and S. Galtier, Phys. Rev. E 87, 013019 (2013)PLEEE81539-375510.1103/PhysRevE.87.013019), the current exact relation shows that the pressure dilatation terms play practically no role in the energy cascade. Both the flux and source terms are written in terms of two-point differences. Sources enter the relation in a form of mixed second-order structure functions. Unlike the kinetic and thermodynamic potential energies, the gravitational contribution is absent from the flux term. An estimate shows that, for the isotropic case, the correlation between density and gravitational acceleration may play an important role in modifying the energy transfer in self-gravitating turbulence. The exact relation is also written in an alternative form in terms of two-point correlation functions, which is then used to describe scale-by-scale energy budget in spectral space.

New exact solutions of the KdV-Burgers-Kuramoto equation

International Nuclear Information System (INIS)

Zhang Sheng

2006-01-01

A generalized F-expansion method is proposed and applied to the KdV-Burgers-Kuramoto equation. As a result, many new and more general exact travelling wave solutions are obtained including combined non-degenerate Jacobi elliptic function solutions, solitary wave solutions and trigonometric function solutions. The method can be applied to other nonlinear partial differential equations in mathematical physics

Exact solutions to two higher order nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Xu Liping; Zhang Jinliang

2007-01-01

Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)

New exact approaches to the nuclear eigenvalue problem

International Nuclear Information System (INIS)

Andreozzi, F.; Lo Iudice, N.; Porrino, A.; Knapp, F.; Kvasil, J.

2005-01-01

In a recent past some of us have developed a new algorithm for diagonalizing the shell model Hamiltonian which consists of an iterative sequence of diagonalization of sub-matrices of small dimensions. The method, apart from being easy to implement, is robust, yielding always stable numerical solutions, and free of ghost eigenvalues. Subsequently, we have endowed the algorithm with an importance sampling, which leads to a drastic truncation of the shell model space, while keeping the accuracy of the solutions under control. Applications to typical nuclei show that the sampling yields also an extrapolation law to the exact eigenvalues. Complementary to the shell model algorithm is a method we are developing for studying collective and non collective excitations. To this purpose we solve the nuclear eigenvalue problem in a space which is the direct sum of Tamm-Dancoff n-phonon subspaces (n=0,1, ...N). The multiphonon basis is constructed by an iterative equation of motion method, which generates an over complete set of n-phonon states from the (n-1)-phonon basis. The redundancy is removed completely and exactly by a method based on the Choleski decomposition. The full Hamiltonian matrix comes out to have a simple structure and, therefore, can be drastically truncated before diagonalization by the mentioned importance sampling method. The phonon composition of the basis states allows removing naturally and maximally the spurious admixtures induced by the centre of mass motion. An application of the method to 16 O will be given for illustrative purposes. (authors)

Time measurement - technical importance of most exact clocks

International Nuclear Information System (INIS)

Goebel, E.O.; Riehle, F.

2004-01-01

The exactness of the best atomic clocks currently shows a temporal variation of 1 second in 30 million years. This means that we have reached the point of the most exact frequency and time measurement ever. In the past, there was a trend towards increasing the exactness in an increasingly fast sequence. Will this trend continue? And who will profit from it? This article is meant to give answers to these questions. This is done by presenting first the level reached currently with the best atomic clocks and describing the research activities running worldwide with the aim of achieving even more exact clocks. In the second part, we present examples of various areas of technical subjects and research in which the most exact clocks are being applied presently and even more exact ones will be needed in the future [de

MCNP HPGe detector benchmark with previously validated Cyltran model.

Science.gov (United States)

Hau, I D; Russ, W R; Bronson, F

2009-05-01

An exact copy of the detector model generated for Cyltran was reproduced as an MCNP input file and the detection efficiency was calculated similarly with the methodology used in previous experimental measurements and simulation of a 280 cm(3) HPGe detector. Below 1000 keV the MCNP data correlated to the Cyltran results within 0.5% while above this energy the difference between MCNP and Cyltran increased to about 6% at 4800 keV, depending on the electron cut-off energy.

Regarding on the exact solutions for the nonlinear fractional differential equations

Directory of Open Access Journals (Sweden)

Kaplan Melike

2016-01-01

Full Text Available In this work, we have considered the modified simple equation (MSE method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW and the modified equal width (mEW equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.

On the connection between the inverse transform method and the exact quantum eigenstates

International Nuclear Information System (INIS)

Honerkamp, J.; Weber, P.; Wiesler, A.

1979-01-01

The 'inverse scattering transformation', which has been used to solve certain nonlinear field theories classically, is discussed in the context of the quantized version of these theories. In particular the non-linear Schroedinger equation and the massive Thirring model are considered. It is found that certain Jost functions of the associated scattering problem lead already, in quantizing the theory, to creation operators for the exact eigenstates of the corresponding Hamiltonians. (Auth.)

Exact wavefunctions for a time-dependent Coulomb potential

International Nuclear Information System (INIS)

Menouar, S; Maamache, M; Saadi, Y; Choi, J R

2008-01-01

The one-dimensional Schroedinger equation associated with a time-dependent Coulomb potential is studied. The invariant operator method (Lewis and Riesenfeld) and unitary transformation approach are employed to derive quantum solutions of the system. We obtain an ordinary second-order differential equation whose analytical exact solution has been unknown. It is confirmed that the form of this equation is similar to the radial Schroedinger equation for the hydrogen atom in a (arbitrary) strong magnetic field. The qualitative properties for the eigenstates spectrum are described separately for the different values of the parameter ω 0 appearing in the x 2 term, x being the position, i.e., ω 0 > 0, ω 0 0 = 0. For the ω 0 = 0 case, the eigenvalue equation of invariant operator reduces to a solvable form and, consequently, we have provided exact eigenstates of the time-dependent Hamiltonian system

Implementation of nonseparable exact exchange effects in the first-order nondegenerate adiabatic theory

International Nuclear Information System (INIS)

Abdolsalami, M.; Abdolsalami, F.; Gonzalez, H.R.

1994-01-01

We have implemented nonlocal exchange effects rigorously in the first-order nondegenerate adiabatic (FONDA) theory. This implementation requires solving integrodifferential equations that involve double integrals. Separable and model exchange approximations that simplify the inclusion of exchange in the scattering calculations have been previously implemented in the FONDA theory. The discrepancy between the exact exchange FONDA cross sections and the separable and model exchange results suggests that one needs to include exchange rigorously to obtain accurate results over a wide range of energies. Specifically, a difference of up to 30% is observed between the exact and separable exchange FONDA cross sections at near-threshold energies. At higher energies the FONDA results from the rigorous and model exchange implementations disagree by as much as 10%

Thermodynamics of Rh nuclear spins calculated by exact diagonalization

DEFF Research Database (Denmark)

Lefmann, K.; Ipsen, J.; Rasmussen, F.B.

2000-01-01

We have employed the method of exact diagonalization to obtain the full-energy spectrum of a cluster of 16 Rh nuclear spins, having dipolar and RK interactions between first and second nearest neighbours only. We have used this to calculate the nuclear spin entropy, and our results at both positi...

The exact solution of self-consistent equations in the scanning near-field optic microscopy problem

DEFF Research Database (Denmark)

Lozovski, Valeri; Bozhevolnyi, Sergey I.

1999-01-01

The macroscopic approach that allows one to obtain an exact solution of the self-consistent equation of the Lippmann-Schwinger type is developed. The main idea of our method consist in usage of diagram technque for exact summation of the infinite series corresponding to the iteration procedure fo...

Exact discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2016-01-08

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data and exact analytical benchmark statistics

DEFF Research Database (Denmark)

Nørrelykke, Simon F; Flyvbjerg, Henrik

2011-01-01

The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...

Exact Sampling and Decoding in High-Order Hidden Markov Models

NARCIS (Netherlands)

Carter, S.; Dymetman, M.; Bouchard, G.

2012-01-01

We present a method for exact optimization and sampling from high order Hidden Markov Models (HMMs), which are generally handled by approximation techniques. Motivated by adaptive rejection sampling and heuristic search, we propose a strategy based on sequentially refining a lower-order language

Exact solutions for MHD flow of couple stress fluid with heat transfer

Directory of Open Access Journals (Sweden)

Najeeb Alam Khan

2016-01-01

Full Text Available This paper aims at presenting exact solutions for MHD flow of couple stress fluid with heat transfer. The governing partial differential equations (PDEs for an incompressible MHD flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. The methodology is implemented for linearizing the flow equations without extra transformation and restrictive assumptions. Comparison is made with the result obtained previously.

Exact results on diffusion in a piecewise linear potential with a time-dependent sink

Energy Technology Data Exchange (ETDEWEB)

Diwaker, E-mail: diwakerphysics@gmail.com [Central University of Himachal Pradesh, School of Physical and Astronomical Sciences (India); Chakraborty, Aniruddha [Indian Institute of Technology Mandi (India)

2016-02-15

The Smoluchowski equation with a time-dependent sink term is solved exactly. In this method, knowing the probability distribution P(0, s) at the origin, allows deriving the probability distribution P(x, s) at all positions. Exact solutions of the Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse, and exponential variation in time.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

Science.gov (United States)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

Geometrically exact nonlinear analysis of pre-twisted composite rotor blades

Directory of Open Access Journals (Sweden)

Li'na SHANG

2018-02-01

Full Text Available Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the anisotropic material properties. In this paper, the geometrically exact nonlinear modeling of a generalized Timoshenko beam with arbitrary cross-sectional shape, generally anisotropic material behavior and large deflections has been presented based on Hodges’ method. The concept of decomposition of rotation tensor was used to express the strain in the beam. The variational asymptotic method was used to determine the arbitrary warping of the beam cross section. The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy. The geometrically exact nonlinear equations of motion were established by Hamilton’s principle. The established modeling was used for the static and dynamic analysis of pre-twisted composite rotor blades, and the analytical results were validated based on experimental data. The influences of the transverse shear deformation on the pre-twisted composite rotor blade were investigated. The results indicate that the influences of the transverse shear deformation on the static deformation and the natural frequencies of the pre-twisted composite rotor blade are related to the length to chord ratio of the blade. Keywords: Geometrically exact, Nonlinear, Pre-twisted composite blade, Transverse shear deformation, Variational asymptotic, Warping

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

International Nuclear Information System (INIS)

Dubrovsky, V. G.; Topovsky, A. V.

2013-01-01

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u (n) , n= 1, …, N are constructed via Zakharov and Manakov ∂-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u (n) and calculated by ∂-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u (n) . It is shown that the sums u=u (k 1 ) +...+u (k m ) , 1 ⩽k 1 2 m ⩽N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

Products of composite operators in the exact renormalization group formalism

Science.gov (United States)

Pagani, C.; Sonoda, H.

2018-02-01

We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short-distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.

Exactly averaged equations for flow and transport in random media

International Nuclear Information System (INIS)

Shvidler, Mark; Karasaki, Kenzi

2001-01-01

It is well known that exact averaging of the equations of flow and transport in random porous media can be realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding the general form of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present a general form of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure non-local equations in general case of stochastically homogeneous fields. (author)

Mean field approximation versus exact treatment of collisions in few-body systems

International Nuclear Information System (INIS)

Lemm, J.; Weiguny, A.; Giraud, B.G.

1990-01-01

A variational principle for calculating matrix elements of the full resolvent operator for a many-body system is studied. Its mean field approximation results in non-linear equations of Hartree (-Fock) type, with initial and final channel wave functions as driving terms. The mean field equations will in general have many solutions whereas the exact problem being linear, has a unique solution. In a schematic model with separable forces the mean field equations are analytically soluble, and for the exact problem the resulting integral equations are solved numerically. Comparing exact and mean field results over a wide range of system parameters, the mean field approach proves to be a very reliable approximation, which is not plagued by the notorious problem of defining asymptotic channels in the time-dependent mean field method. (orig.)

Exact, almost and delayed fault detection

DEFF Research Database (Denmark)

Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.

1999-01-01

Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems....... The l-step delayed fault detection problem is also considered for discrete-time systems....

Exact solutions, numerical relativity and gravitational radiation

International Nuclear Information System (INIS)

Winicour, J.

1986-01-01

In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful

Exact invariants in the form of momentum resonances for particle motion in one-dimensional, time-dependent potentials

International Nuclear Information System (INIS)

Goedert, J.; Lewis, H.R.

1984-01-01

A momentum-resonance ansatz of Lewis and Leach was used to study exact invariants for time-dependent, one-dimensional potentials. This ansatz provides a framework for finding invariants admitted by a larger class of time-dependent potentials that was known previously. For a potential that admits an exact invariant in this resonance form, we have shown how to construct the invariant as a functional of the potential in terms of the solution of a definite linear algebraic system of equations. We have found a necessary and sufficient condition on the potential for the existence of an invariant with a given number of resonances. There exist more potentials that admit invariants with two resonances than were previously known and we have found an example in parametric form of such a potential. We have also found examples of potentials that admit invariants with three resonances

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.

Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form

Science.gov (United States)

Delzanno, G. L.

2015-11-01

A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.

Classes of exact Einstein Maxwell solutions

Science.gov (United States)

Komathiraj, K.; Maharaj, S. D.

2007-12-01

We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

Exact optics - III. Schwarzschild's spectrograph camera revised

Science.gov (United States)

Willstrop, R. V.

2004-03-01

Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.

Fingering patterns in magnetic fluids: Perturbative solutions and the stability of exact stationary shapes

Science.gov (United States)

Anjos, Pedro H. A.; Lira, Sérgio A.; Miranda, José A.

2018-04-01

We examine the formation of interfacial patterns when a magnetic liquid droplet (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. By using a vortex-sheet formalism, we find exact stationary solutions for the fluid-fluid interface in the form of n -fold polygonal shapes. A weakly nonlinear, mode-coupling method is then utilized to find time-evolving perturbative solutions for the interfacial patterns. The stability of such nonzero surface tension exact solutions is checked and discussed, by trying to systematically approach the exact stationary shapes through perturbative solutions containing an increasingly larger number of participating Fourier modes. Our results indicate that the exact stationary solutions of the problem are stable, and that a good matching between exact and perturbative shape solutions is achieved just by using a few Fourier modes. The stability of such solutions is substantiated by a linearization process close to the stationary shape, where a system of mode-coupling equations is diagonalized, determining the eigenvalues which dictate the stability of a fixed point.

Exact Solutions of the Hierarchical Korteweg-de Vries Equation of Micro structured Granular Materials

International Nuclear Information System (INIS)

Abourabia, A.M.; El-Danaf, T.S.; Morad, A.M.

2008-01-01

The problem under consideration are related to wave propagation in micro structured materials, characterized by higher-order nonlinear and higher-order dispersive effects; particularly, the wave propagation in dilatant granular materials. In the present paper the model equation is solved analytically by exact method called Jacobi elliptic method. The types of solutions are defined and discussed over a wide range of material parameters (two dispersion parameters and one microstructure parameter). The dispersion properties and the relation between group and phase velocities of the model equation are studied. The diagrams are drawn to illustrate the physical properties of the exact solutions

Exact solutions of the dirac equation for an electron in magnetic field with shape invariant method

International Nuclear Information System (INIS)

Setare, M.R.; Hatami, O.

2008-01-01

Based on the shape invariance property we obtain exact solutions of the Virac equation for an electron moving in the presence of a certain varying magnetic Geld, then we also show its non-relativistic limit. (authors)

Exact traveling wave solutions for a new nonlinear heat transfer equation

Directory of Open Access Journals (Sweden)

Gao Feng

2017-01-01

Full Text Available In this paper, we propose a new non-linear partial differential equation to de-scribe the heat transfer problems at the extreme excess temperatures. Its exact traveling wave solutions are obtained by using Cornejo-Perez and Rosu method.

Exact and approximate multiple diffraction calculations

International Nuclear Information System (INIS)

Alexander, Y.; Wallace, S.J.; Sparrow, D.A.

1976-08-01

A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation

Exact Outage Probability of Dual-Hop CSI-Assisted AF Relaying Over Nakagami-m Fading Channels

KAUST Repository

Xia, Minghua

2012-10-01

In this correspondence, considering dual-hop channel state information (CSI)-assisted amplify-and-forward (AF) relaying over Nakagami- m fading channels, the cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) is derived. In particular, when the fading shape factors m1 and m2 at consecutive hops take non-integer values, the bivariate H-function and G -function are exploited to obtain an exact analytical expression for the CDF. The obtained CDF is then applied to evaluate the outage performance of the system under study. The analytical results of outage probability coincide exactly with Monte-Carlo simulation results and outperform the previously reported upper bounds in the low and medium SNR regions.

The exact equation of motion of a simple pendulum of arbitrary amplitude: a hypergeometric approach

International Nuclear Information System (INIS)

Qureshi, M I; Rafat, M; Azad, S Ismail

2010-01-01

The motion of a simple pendulum of arbitrary amplitude is usually treated by approximate methods. By using generalized hypergeometric functions, it is however possible to solve the problem exactly. In this paper, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. A new and exact expression for the time of swinging of a simple pendulum from the vertical position to an arbitrary angular position θ is given by equation (3.10). The time period of such a pendulum is also exactly expressible in terms of hypergeometric functions. The exact expressions thus obtained are used to plot the graphs that compare the exact time period T(θ 0 ) with the time period T(0) (based on simple harmonic approximation). We also compare the relative difference between T(0) and T(θ 0 ) found from the exact equation of motion with the usual perturbation theory estimate. The treatment is intended for graduate students, who have acquired some familiarity with the hypergeometric functions. This approach may also be profitably used by specialists who encounter during their investigations nonlinear differential equations similar in form to the pendulum equation. Such nonlinear differential equations could arise in diverse fields, such as acoustic vibrations, oscillations in small molecules, turbulence and electronic filters, among others.

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

The exact probability law for the approximated similarity from the ...

African Journals Online (AJOL)

The exact probability law for the approximated similarity from the Minhashing method. Soumaila Dembele, Gane Samb Lo. Abstract. We propose a probabilistic setting in which we study the probability law of the Rajaraman and Ullman RU algorithm and a modied version of it denoted by RUM. These algorithms aim at ...

Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV Equation

International Nuclear Information System (INIS)

Aslan İsmail

2014-01-01

The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. (general)

Some exact solutions to the translation-invariant N-body problem

International Nuclear Information System (INIS)

Hall, R.L.

1978-01-01

It is shown that Schroedinger's equation for a translation-invariant system consisting of N particles with arbitrary masses interacting via Hooke's law pair potentials with the same coupling constant can be solved exactly; explicit solutions are found for the case N = 3. Exact solutions are also found explicitly for the translation-invariant problem in which a particle with mass m 0 interacts with N identical particles of mass m 1 via Hooke's law pair potential with coupling constant k 0 2 , and the identical particles interact with each other via Hooke's law pair potentials with coupling constant k 1 2 . The latter solution provides a basis problem for an energy lower-bound method for translation-invariant atom-like systems. (author)

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.

Extension of the KLI approximation toward the exact optimized effective potential.

Science.gov (United States)

Iafrate, G J; Krieger, J B

2013-03-07

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be

New Exact Solutions for New Model Nonlinear Partial Differential Equation

OpenAIRE

Maher, A.; El-Hawary, H. M.; Al-Amry, M. S.

2013-01-01

In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.

A method for acetylcholinesterase staining of brain sections previously processed for receptor autoradiography.

Science.gov (United States)

Lim, M M; Hammock, E A D; Young, L J

2004-02-01

Receptor autoradiography using selective radiolabeled ligands allows visualization of brain receptor distribution and density on film. The resolution of specific brain regions on the film often can be difficult to discern owing to the general spread of the radioactive label and the lack of neuroanatomical landmarks on film. Receptor binding is a chemically harsh protocol that can render the tissue virtually unstainable by Nissl and other conventional stains used to delineate neuroanatomical boundaries of brain regions. We describe a method for acetylcholinesterase (AChE) staining of slides previously processed for receptor binding. AChE staining is a useful tool for delineating major brain nuclei and tracts. AChE staining on sections that have been processed for receptor autoradiography provides a direct comparison of brain regions for more precise neuroanatomical description. We report a detailed thiocholine protocol that is a modification of the Koelle-Friedenwald method to amplify the AChE signal in brain sections previously processed for autoradiography. We also describe several temporal and experimental factors that can affect the density and clarity of the AChE signal when using this protocol.

A Large Class of Exact Solutions to the One-Dimensional Schrodinger Equation

Science.gov (United States)

Karaoglu, Bekir

2007-01-01

A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement. (Contains 1 table and 1 figure.)

Exact evaluation of the rates of electrostatic decay and scattering off thermal ions for an unmagnetized Maxwellian plasma

Energy Technology Data Exchange (ETDEWEB)

Layden, B.; Cairns, Iver H.; Robinson, P. A. [School of Physics, University of Sydney, Sydney, NSW 2006 (Australia)

2013-08-15

Electrostatic decay of Langmuir waves into Langmuir and ion sound waves (L→L′+S) and scattering of Langmuir waves off thermal ions (L+i→L′+i′, also called “nonlinear Landau damping”) are important nonlinear weak-turbulence processes. The rates for these processes depend on the quadratic longitudinal response function α{sup (2)} (or, equivalently, the quadratic longitudinal susceptibility χ{sup (2)}), which describes the second-order response of a plasma to electrostatic wave fields. Previous calculations of these rates for an unmagnetized Maxwellian plasma have relied upon an approximate form for α{sup (2)} that is valid where two of the wave fields are fast (i.e., v{sub φ}=ω/k≫V{sub e} where ω is the angular frequency, k is the wavenumber, and V{sub e} is the electron thermal speed) and one is slow (v{sub φ}≪V{sub e}). Recently, an exact expression was derived for α{sup (2)} that is valid for any phase speeds of the three waves in an unmagnetized Maxwellian plasma. Here, this exact α{sup (2)} is applied to the calculation of the three-dimensional rates for electrostatic decay and scattering off thermal ions, and the resulting exact rates are compared with the approximate rates. The calculations are performed using previously derived three-dimensional rates for electrostatic decay given in terms of a general α{sup (2)}, and newly derived three-dimensional rates for scattering off thermal ions; the scattering rate is derived assuming a Maxwellian ion distribution, and both rates are derived assuming arc distributions for the wave spectra. For most space plasma conditions, the approximate rate is found to be accurate to better than 20%; however, for sufficiently low Langmuir phase speeds (v{sub φ}/V{sub e}≈3) appropriate to some spatial domains of the foreshock regions of planetary bow shocks and type II solar radio bursts, the use of the exact rate may be necessary for accurate calculations. The relative rates of electrostatic decay

Exact solutions in three-dimensional gravity

CERN Document Server

Garcia-Diaz, Alberto A

2017-01-01

A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...

Exact solutions to operator differential equations

International Nuclear Information System (INIS)

Bender, C.M.

1992-01-01

In this talk we consider the Heisenberg equations of motion q = -i(q, H), p = -i(p, H), for the quantum-mechanical Hamiltonian H(p, q) having one degree of freedom. It is a commonly held belief that such operator differential equations are intractable. However, a technique is presented here that allows one to obtain exact, closed-form solutions for huge classes of Hamiltonians. This technique, which is a generalization of the classical action-angle variable methods, allows us to solve, albeit formally and implicitly, the operator differential equations of two anharmonic oscillators whose Hamiltonians are H = p 2 /2 + q 4 /4 and H = p 4 /4 + q 4 /4

Exact gravitational quasinormal frequencies of topological black holes

International Nuclear Information System (INIS)

Birmingham, Danny; Mokhtari, Susan

2006-01-01

We compute the exact gravitational quasinormal frequencies for massless topological black holes in d-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies

Finding optimal exact reducts

KAUST Repository

AbouEisha, Hassan M.

2014-01-01

The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts

Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism

Energy Technology Data Exchange (ETDEWEB)

Neto, J.F.S.; Lima, K.A.L.; Carvalho, P.R.S. [Universidade Federal do Piaui, Departamento de Fisica, Teresina, PI (Brazil); Sena-Junior, M.I. [Universidade de Pernambuco, Escola Politecnica de Pernambuco, Recife, PE (Brazil); Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil)

2017-12-15

We probe the two-scale-factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O(N)λφ{sup 4} scalar field theories with rotation symmetry breaking in three distinct and independent methods in which the rotation symmetry-breaking mechanism is treated exactly. We show that the rotation symmetry-breaking amplitude ratios turn out to be identical in the three methods and equal to their respective rotation symmetry-breaking ones, although the amplitudes themselves, in general, depend on the method employed and on the rotation symmetry-breaking parameter. At the end, we show that all these results can be generalized, through an inductive process based on a general theorem emerging from the exact calculation, to any loop level and physically interpreted based on symmetry ideas. (orig.)

Exact solutions of (3 + 1-dimensional generalized KP equation arising in physics

Directory of Open Access Journals (Sweden)

Syed Tauseef Mohyud-Din

Full Text Available In this work, we have obtained some exact solutions to (3 + 1-dimensional generalized KP Equation. The improved tanϕ(ξ2-expansion method has been introduced to construct the exact solutions of nonlinear evolution equations. The obtained solutions include hyperbolic function solutions, trigonometric function solutions, exponential solutions, and rational solutions. Our study has added some new varieties of solutions to already available solutions. It is also worth mentioning that the computational work has been reduced significantly. Keywords: Improved tanϕ(ξ2-expansion method, Hyperbolic function solution, Trigonometric function solution, Rational solution, (3 + 1-dimensional generalized KP equation

Exact Algorithm for the Capacitated Team Orienteering Problem with Time Windows

Directory of Open Access Journals (Sweden)

Junhyuk Park

2017-01-01

Full Text Available The capacitated team orienteering problem with time windows (CTOPTW is a problem to determine players’ paths that have the maximum rewards while satisfying the constraints. In this paper, we present the exact solution approach for the CTOPTW which has not been done in previous literature. We show that the branch-and-price (B&P scheme which was originally developed for the team orienteering problem can be applied to the CTOPTW. To solve pricing problems, we used implicit enumeration acceleration techniques, heuristic algorithms, and ng-route relaxations.

Bayesian noninferiority test for 2 binomial probabilities as the extension of Fisher exact test.

Science.gov (United States)

Doi, Masaaki; Takahashi, Fumihiro; Kawasaki, Yohei

2017-12-30

Noninferiority trials have recently gained importance for the clinical trials of drugs and medical devices. In these trials, most statistical methods have been used from a frequentist perspective, and historical data have been used only for the specification of the noninferiority margin Δ>0. In contrast, Bayesian methods, which have been studied recently are advantageous in that they can use historical data to specify prior distributions and are expected to enable more efficient decision making than frequentist methods by borrowing information from historical trials. In the case of noninferiority trials for response probabilities π 1 ,π 2 , Bayesian methods evaluate the posterior probability of H 1 :π 1 >π 2 -Δ being true. To numerically calculate such posterior probability, complicated Appell hypergeometric function or approximation methods are used. Further, the theoretical relationship between Bayesian and frequentist methods is unclear. In this work, we give the exact expression of the posterior probability of the noninferiority under some mild conditions and propose the Bayesian noninferiority test framework which can flexibly incorporate historical data by using the conditional power prior. Further, we show the relationship between Bayesian posterior probability and the P value of the Fisher exact test. From this relationship, our method can be interpreted as the Bayesian noninferior extension of the Fisher exact test, and we can treat superiority and noninferiority in the same framework. Our method is illustrated through Monte Carlo simulations to evaluate the operating characteristics, the application to the real HIV clinical trial data, and the sample size calculation using historical data. Copyright © 2017 John Wiley & Sons, Ltd.

Quaternionic formulation of the exact parity model

Energy Technology Data Exchange (ETDEWEB)

Brumby, S.P.; Foot, R.; Volkas, R.R.

1996-02-28

The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs.

Quaternionic formulation of the exact parity model

International Nuclear Information System (INIS)

Brumby, S.P.; Foot, R.; Volkas, R.R.

1996-01-01

The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs

New exact solutions of sixth-order thin-film equation

Directory of Open Access Journals (Sweden)

Wafaa M. Taha

2014-01-01

Full Text Available TheG′G-expansion method is used for the first time to find traveling-wave solutions for the sixth-order thin-film equation, where related balance numbers are not the usual positive integers. New types of exact traveling-wave solutions, such as – solitary wave solutions, are obtained the sixth-order thin-film equation, when parameters are taken at special values.

Comments on a direct approach to finding exact invariants for one-dimensional time-dependent classical hamiltonian

International Nuclear Information System (INIS)

Castro Moreira, I. de.

1983-01-01

A method introduced by Lewis and Leach for the obtention of exact invariants of the form I = Σ p sup(n) F sub(n) (q,t) for hamiltonian systems, is generalized and applied directly on the equations of motion. It gives us a general procedure to generates exact invariants also for non hamiltonian systems. (Author) [pt

Off-diagonal Bethe ansatz for exactly solvable models

CERN Document Server

Wang, Yupeng; Cao, Junpeng; Shi, Kangjie

2015-01-01

This book serves as an introduction of the off-diagonal Bethe Ansatz method, an analytic theory for the eigenvalue problem of quantum integrable models. It also presents some fundamental knowledge about quantum integrability and the algebraic Bethe Ansatz method. Based on the intrinsic properties of R-matrix and K-matrices, the book introduces a systematic method to construct operator identities of transfer matrix.  These identities allow one to establish the inhomogeneous T-Q relation formalism to obtain Bethe Ansatz equations and to retrieve corresponding eigenstates. Several longstanding models can thus be solved via this method since the lack of obvious reference states is made up. Both the exact results and the off-diagonal Bethe Ansatz method itself may have important applications in the fields of quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.

Precise calculation of the transmission coefficient of a potential barrier. Study of the error in the B K W approximation; Calcul exact du coefficient de transmission d'une barriere de potentiel. Etude de l'erreur de l'approximation B K W

Energy Technology Data Exchange (ETDEWEB)

Jamet, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1964-07-01

Following on to work started in a previous report, the author carries out in the case of few examples, the calculation of the transmission coefficient T using accurate methods. He then deduces from this the error in the B K W method. The calculations are carried out for values of T ranging down to 10{sup -200}. The use of modern computers makes it possible to obtain values of T to eight decimal places in a few seconds and the practical advantage of the B K W approximation appears therefore considerably reduced. The author gives also a method which may be used for an exact calculation of the energy levels of a potential well. (author) [French] Poursuivant une etude commencee dans une note anterieure, l'auteur effectue, sur quelques exemples, le calcul du coefficient de transmission T par des methodes exactes. Il en deduit ensuite l'erreur de la methode B K W. Les calculs sont faits pour des valeurs de T allant jusqu'a 10{sup -200}. L'utilisation des machines a calculer modernes permettant d'obtenir en quelques secondes, la valeur de T avec 8 decimales exactes, l'interet pratique de l'approximation B K W semble considerablement diminue. L'auteur indique egalement une methode qui peut servir a calculer exactement les niveaux d'energie d'un puits de potentiel. (auteur)

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

Energy Technology Data Exchange (ETDEWEB)

Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)

2013-03-15

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

The exact wavefunction factorization of a vibronic coupling system

International Nuclear Information System (INIS)

Chiang, Ying-Chih; Klaiman, Shachar; Otto, Frank; Cederbaum, Lorenz S.

2014-01-01

We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation

Exact folded-band chaotic oscillator.

Science.gov (United States)

Corron, Ned J; Blakely, Jonathan N

2012-06-01

An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

Approximate and exact hybrid algorithms for private nearest-neighbor queries with database protection

KAUST Repository

Ghinita, Gabriel; Kalnis, Panos; Kantarcioǧlu, Murâ t; Bertino, Elisa

2010-01-01

Mobile devices with global positioning capabilities allow users to retrieve points of interest (POI) in their proximity. To protect user privacy, it is important not to disclose exact user coordinates to un-trusted entities that provide location-based services. Currently, there are two main approaches to protect the location privacy of users: (i) hiding locations inside cloaking regions (CRs) and (ii) encrypting location data using private information retrieval (PIR) protocols. Previous work focused on finding good trade-offs between privacy and performance of user protection techniques, but disregarded the important issue of protecting the POI dataset D. For instance, location cloaking requires large-sized CRs, leading to excessive disclosure of POIs (O({pipe}D{pipe}) in the worst case). PIR, on the other hand, reduces this bound to O(√{pipe}D{pipe}), but at the expense of high processing and communication overhead. We propose hybrid, two-step approaches for private location-based queries which provide protection for both the users and the database. In the first step, user locations are generalized to coarse-grained CRs which provide strong privacy. Next, a PIR protocol is applied with respect to the obtained query CR. To protect against excessive disclosure of POI locations, we devise two cryptographic protocols that privately evaluate whether a point is enclosed inside a rectangular region or a convex polygon. We also introduce algorithms to efficiently support PIR on dynamic POI sub-sets. We provide solutions for both approximate and exact NN queries. In the approximate case, our method discloses O(1) POI, orders of magnitude fewer than CR- or PIR-based techniques. For the exact case, we obtain optimal disclosure of a single POI, although with slightly higher computational overhead. Experimental results show that the hybrid approaches are scalable in practice, and outperform the pure-PIR approach in terms of computational and communication overhead. © 2010

Approximate and exact hybrid algorithms for private nearest-neighbor queries with database protection

KAUST Repository

Ghinita, Gabriel

2010-12-15

Mobile devices with global positioning capabilities allow users to retrieve points of interest (POI) in their proximity. To protect user privacy, it is important not to disclose exact user coordinates to un-trusted entities that provide location-based services. Currently, there are two main approaches to protect the location privacy of users: (i) hiding locations inside cloaking regions (CRs) and (ii) encrypting location data using private information retrieval (PIR) protocols. Previous work focused on finding good trade-offs between privacy and performance of user protection techniques, but disregarded the important issue of protecting the POI dataset D. For instance, location cloaking requires large-sized CRs, leading to excessive disclosure of POIs (O({pipe}D{pipe}) in the worst case). PIR, on the other hand, reduces this bound to O(√{pipe}D{pipe}), but at the expense of high processing and communication overhead. We propose hybrid, two-step approaches for private location-based queries which provide protection for both the users and the database. In the first step, user locations are generalized to coarse-grained CRs which provide strong privacy. Next, a PIR protocol is applied with respect to the obtained query CR. To protect against excessive disclosure of POI locations, we devise two cryptographic protocols that privately evaluate whether a point is enclosed inside a rectangular region or a convex polygon. We also introduce algorithms to efficiently support PIR on dynamic POI sub-sets. We provide solutions for both approximate and exact NN queries. In the approximate case, our method discloses O(1) POI, orders of magnitude fewer than CR- or PIR-based techniques. For the exact case, we obtain optimal disclosure of a single POI, although with slightly higher computational overhead. Experimental results show that the hybrid approaches are scalable in practice, and outperform the pure-PIR approach in terms of computational and communication overhead. © 2010

Exact self-energy of the many-body problem from conserving approximations

International Nuclear Information System (INIS)

Takada, Y.

1995-01-01

A procedure is proposed to obtain the exact self-energy in the many-body problem. This algorithm is based on the formal analysis to reach the exact theory by repeated applications of an operator F to an arbitrarily chosen input self-energy represented as a functional of the dressed Green's function. The operator F is so defined that the microscopic conservation law for particle number is satisfied. The rigorous self-energy is obtained by the solution of an eigenfunction of F. Particular attention is paid to the relation between the present procedure and the Baym-Kadanoff framework of conserving approximations. By simplifying the procedure in F with use of the generalized Ward identity, we suggest a practical method to implement this algorithm rather easily in actual systems. In order to suggest future directions to improve on this practical method, the recently developed mean-field theory for the Hubbard model in the limit of high spatial dimensions is also discussed in the context of our theory

Effect of flux discontinuity on spatial approximations for discrete ordinates methods

International Nuclear Information System (INIS)

Duo, J.I.; Azmy, Y.Y.

2005-01-01

This work presents advances on error analysis of the spatial approximation of the discrete ordinates method for solving the neutron transport equation. Error norms for different non-collided flux problems over a two dimensional pure absorber medium are evaluated using three numerical methods. The problems are characterized by the incoming flux boundary conditions to obtain solutions with different level of differentiability. The three methods considered are the Diamond Difference (DD) method, the Arbitrarily High Order Transport method of the Nodal type (AHOT-N), and of the Characteristic type (AHOT-C). The last two methods are employed in constant, linear and quadratic orders of spatial approximation. The cell-wise error is computed as the difference between the cell-averaged flux computed by each method and the exact value, then the L 1 , L 2 , and L ∞ error norms are calculated. The results of this study demonstrate that the level of differentiability of the exact solution profoundly affects the rate of convergence of the numerical methods' solutions. Furthermore, in the case of discontinuous exact flux the methods fail to converge in the maximum error norm, or in the pointwise sense, in accordance with previous local error analysis. (authors)

Exact scattering solutions in an energy sudden (ES) representation

International Nuclear Information System (INIS)

Chang, B.; Eno, L.; Rabitz, H.

1983-01-01

In this paper, we lay down the theoretical foundations for computing exact scattering wave functions in a reference frame which moves in unison with the system internal coordinates. In this frame the (internal) coordinates appear to be fixed and its adoption leads very naturally (in zeroth order) to the energy sudden (ES) approximation [and the related infinite order sudden (IOS) method]. For this reason we call the new representation for describing the exact dynamics of a many channel scattering problem, the ES representation. Exact scattering solutions are derived in both time dependent and time independent frameworks for the representation and many interesting results in these frames are established. It is shown, e.g., that in a time dependent frame the usual Schroedinger propagator factorizes into internal Hamiltonian, ES, and energy correcting propagators. We also show that in a time independent frame the full Green's functions can be similarly factorized. Another important feature of the new representation is that it forms a firm foundation for seeking corrections to the ES approximation. Thus, for example, the singularity which arises in conventional perturbative expansions of the full Green's functions (with the ES Green's function as the zeroth order solution) is avoided in the ES representation. Finally, a number of both time independent and time dependent ES correction schemes are suggested

A Simple Exact Error Rate Analysis for DS-CDMA with Arbitrary Pulse Shape in Flat Nakagami Fading

Science.gov (United States)

Rahman, Mohammad Azizur; Sasaki, Shigenobu; Kikuchi, Hisakazu; Harada, Hiroshi; Kato, Shuzo

A simple exact error rate analysis is presented for random binary direct sequence code division multiple access (DS-CDMA) considering a general pulse shape and flat Nakagami fading channel. First of all, a simple model is developed for the multiple access interference (MAI). Based on this, a simple exact expression of the characteristic function (CF) of MAI is developed in a straight forward manner. Finally, an exact expression of error rate is obtained following the CF method of error rate analysis. The exact error rate so obtained can be much easily evaluated as compared to the only reliable approximate error rate expression currently available, which is based on the Improved Gaussian Approximation (IGA).

Exact Solutions for Einstein's Hyperbolic Geometric Flow

International Nuclear Information System (INIS)

He Chunlei

2008-01-01

In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow

A Class of Quasi-exact Solutions of Rabi Hamiltonian

International Nuclear Information System (INIS)

Pan Feng; Yao Youkun; Xie Mingxia; Han Wenjuan; Draayer, J.P.

2007-01-01

A class of quasi-exact solutions of the Rabi Hamiltonian, which describes a two-level atom interacting with a single-mode radiation field via a dipole interaction without the rotating-wave approximation, are obtained by using a wavefunction ansatz. Exact solutions for part of the spectrum are obtained when the atom-field coupling strength and the field frequency satisfy certain relations. As an example, the lowest exact energy level and the corresponding atom-field entanglement at the quasi-exactly solvable point are calculated and compared to results from the Jaynes-Cummings and counter-rotating cases of the Rabi Hamiltonian.

Long-term stable time integration scheme for dynamic analysis of planar geometrically exact Timoshenko beams

Science.gov (United States)

Nguyen, Tien Long; Sansour, Carlo; Hjiaj, Mohammed

2017-05-01

In this paper, an energy-momentum method for geometrically exact Timoshenko-type beam is proposed. The classical time integration schemes in dynamics are known to exhibit instability in the non-linear regime. The so-called Timoshenko-type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known Bernoulli-type model. The treatment of the Bernoulli-model has been recently addressed by the authors. In this present work, we extend our approach of using the strain rates to define the strain fields to in-plane geometrically exact Timoshenko-type beams. The large rotational degrees of freedom are exactly computed. The well-known enhanced strain method is used to avoid locking phenomena. Conservation of energy, momentum and angular momentum is proved formally and numerically. The excellent performance of the formulation will be demonstrated through a range of examples.

An exact method for computing the frustration index in signed networks using binary programming

OpenAIRE

Aref, Samin; Mason, Andrew J.; Wilson, Mark C.

2016-01-01

Computing the frustration index of a signed graph is a key step toward solving problems in many fields including social networks, physics, material science, and biology. The frustration index determines the distance of a network from a state of total structural balance. Although the definition of the frustration index goes back to 1960, its exact algorithmic computation, which is closely related to classic NP-hard graph problems, has only become a focus in recent years. We develop three new b...

Pure N=2 super Yang-Mills and exact WKB

International Nuclear Information System (INIS)

Kashani-Poor, Amir-Kian; Troost, Jan

2015-01-01

We apply exact WKB methods to the study of the partition function of pure N=2ϵ i -deformed gauge theory in four dimensions in the context of the 2d/4d correspondence. We study the partition function at leading order in ϵ 2 /ϵ 1 (i.e. at large central charge) and in an expansion in ϵ 1 . We find corrections of the form ∼exp [−((/tiny SW periods)/(ϵ 1 ))] to this expansion. We attribute these to the exchange of the order of summation over gauge instanton number and over powers of ϵ 1 when passing from the Nekrasov form of the partition function to the topological string theory inspired form. We conjecture that such corrections should be computable from a worldsheet perspective on the partition function. Our results follow upon the determination of the Stokes graphs associated to the Mathieu equation with complex parameters and the application of exact WKB techniques to compute the Mathieu characteristic exponent.

Generation of exact solutions to the Einstein field equations for homogeneous space--time

International Nuclear Information System (INIS)

Hiromoto, R.E.

1978-01-01

A formalism is presented capable of finding all homogeneous solutions of the Einstein field equations with an arbitrary energy-stress tensor. Briefly the method involves the classification of the four-dimensional Lie algebra over the reals into nine different broad classes, using only the Lorentz group. Normally the classification of Lie algebras means that one finds all essentially different solutions of the Jacobi identities, i.e., there exists no nonsingular linear transformation which transforms two sets of structure constants into the other. This approach is to utilize the geometrical considerations of the homogeneous spacetime and field equations to be solved. Since the set of orthonormal basis vectors is not only endowed with a Minkowskian metric, but also constitutes the vector space of our four-dimensional Lie algebras, the Lie algebras are classified against the Lorentz group restricts the linear group of transformations, denoting the essentially different Lie algebras, into nine different broad classes. The classification of the four-dimensional Lie algebras represents the unification of various methods previously introduced by others. Where their methods found only specific solutions to the Einstein field equations, systematic application of the nine different classes of Lie algebras guarantees the extraction of all solutions. Therefore, the methods of others were extended, and their foundations of formalism which goes beyond the present literature of exact homogeneous solutions to the Einstein field equations is built upon

Extremal black holes as exact string solutions

International Nuclear Information System (INIS)

Horowitz, G.T.; Tseytlin, A.A.

1994-01-01

We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in α' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five-dimensional background which is proved to be an exact string solution

Criteria for exact qudit universality

International Nuclear Information System (INIS)

Brennen, Gavin K.; O'Leary, Dianne P.; Bullock, Stephen S.

2005-01-01

We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 052309 (2000)] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H jk x =(ℎ/2π)Ω(vertical bar k> jk y =(ℎ/2π)Ω(i vertical bar k> jk x,y are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=(ℎ/2π)Ω vertical bar d-1,d-1> 87 Rb and construct an optimal gate sequence using Raman laser pulses

Quasitraces on exact C*-algebras are traces

DEFF Research Database (Denmark)

Haagerup, Uffe

2014-01-01

It is shown that all 2-quasitraces on a unital exact C ∗   -algebra are traces. As consequences one gets: (1) Every stably finite exact unital C ∗   -algebra has a tracial state, and (2) if an AW ∗   -factor of type II 1   is generated (as an AW ∗   -algebra) by an exact C ∗   -subalgebra, then i......, then it is a von Neumann II 1   -factor. This is a partial solution to a well known problem of Kaplansky. The present result was used by Blackadar, Kumjian and Rørdam to prove that RR(A)=0  for every simple non-commutative torus of any dimension...

Equivariant Homotopy Theory and K-Theory of Exact Categories with Duality

DEFF Research Database (Denmark)

Moi, Kristian Jonsson

This thesis has two main parts. The first part, which consists of two papers, is concerned with the role of equivariant loop spaces in the K-theory of exact categories with duality. We prove a group completion-type result for topological monoids with anti-involution. The methods in this proof als...

New exact solutions of the Dirac equation. 11

International Nuclear Information System (INIS)

Bagrov, V.G.; Noskov, M.D.

1984-01-01

Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found

Computing exact bundle compliance control charts via probability generating functions.

Science.gov (United States)

Chen, Binchao; Matis, Timothy; Benneyan, James

2016-06-01

Compliance to evidenced-base practices, individually and in 'bundles', remains an important focus of healthcare quality improvement for many clinical conditions. The exact probability distribution of composite bundle compliance measures used to develop corresponding control charts and other statistical tests is based on a fairly large convolution whose direct calculation can be computationally prohibitive. Various series expansions and other approximation approaches have been proposed, each with computational and accuracy tradeoffs, especially in the tails. This same probability distribution also arises in other important healthcare applications, such as for risk-adjusted outcomes and bed demand prediction, with the same computational difficulties. As an alternative, we use probability generating functions to rapidly obtain exact results and illustrate the improved accuracy and detection over other methods. Numerical testing across a wide range of applications demonstrates the computational efficiency and accuracy of this approach.

Exact Closed-form Solutions for Lamb's Problem

Science.gov (United States)

Feng, X.

2017-12-01

In this work, we report on an exact closedform solution for the displacement at the surfaceof an elastic halfspace elicited by a buried point source that acts at some point underneath thatsurface. This is commonly referred to as the 3D Lamb's problem, for which previous solutionswere restricted to sources and receivers placed at the free surface. By means of the reciprocitytheorem, our solution should also be valid as a means to obtain the displacements at interior pointswhen the source is placed at the free surface. We manage to obtain explicit results by expressingthe solution in terms of elementary algebraic expression as well as elliptic integrals. We anchorour developments on Poissons ratio 0.25 starting from Johnson's numerical, integral transformsolutions. Furthermore, the spatial derivatives of our solutions can be easily acquired in termsof our methods. In the end, our closed-form results agree perfectly with the numerical results ofJohnson, which strongly conrms the correctness of our explicit formulas. It is hoped that in duetime, these formulas may constitute a valuable canonical solution that will serve as a yardstickagainst which other numerical solutions can be compared and measured.In addition, we abstract some terms from our solutions as the generator of the Rayleigh waves.Some basic properties of the Rayleigh waves in the time domain will be indicated in terms of thegenerator. The fareld radiation patterns of P-wave and S-wave elicited by the double-couple forcein the uniform half-space medium could also be acquired from our results.

Exact ground-state correlation functions of one-dimenisonal strongly correlated electron models with resonating-valence-bond ground state

International Nuclear Information System (INIS)

Yamanaka, Masanori; Honjo, Shinsuke; Kohmoto, Mahito

1996-01-01

We investigate one-dimensional strongly correlated electron models which have the resonating-valence-bond state as the exact ground state. The correlation functions are evaluated exactly using the transfer matrix method for the geometric representations of the valence-bond states. In this method, we only treat matrices with small dimensions. This enables us to give analytical results. It is shown that the correlation functions decay exponentially with distance. The result suggests that there is a finite excitation gap, and that the ground state is insulating. Since the corresponding noninteracting systems may be insulating or metallic, we can say that the gap originates from strong correlation. The persistent currents of the present models are also investigated and found to be exactly vanishing

Exact method for numerically analyzing a model of local denaturation in superhelically stressed DNA

International Nuclear Information System (INIS)

Fye, R.M.; Benham, C.J.

1999-01-01

Local denaturation, the separation at specific sites of the two strands comprising the DNA double helix, is one of the most fundamental processes in biology, required to allow the base sequence to be read both in DNA transcription and in replication. In living organisms this process can be mediated by enzymes which regulate the amount of superhelical stress imposed on the DNA. We present a numerically exact technique for analyzing a model of denaturation in superhelically stressed DNA. This approach is capable of predicting the locations and extents of transition in circular superhelical DNA molecules of kilobase lengths and specified base pair sequences. It can also be used for closed loops of DNA which are typically found in vivo to be kilobases long. The analytic method consists of an integration over the DNA twist degrees of freedom followed by the introduction of auxiliary variables to decouple the remaining degrees of freedom, which allows the use of the transfer matrix method. The algorithm implementing our technique requires O(N 2 ) operations and O(N) memory to analyze a DNA domain containing N base pairs. However, to analyze kilobase length DNA molecules it must be implemented in high precision floating point arithmetic. An accelerated algorithm is constructed by imposing an upper bound M on the number of base pairs that can simultaneously denature in a state. This accelerated algorithm requires O(MN) operations, and has an analytically bounded error. Sample calculations show that it achieves high accuracy (greater than 15 decimal digits) with relatively small values of M (M<0.05N) for kilobase length molecules under physiologically relevant conditions. Calculations are performed on the superhelical pBR322 DNA sequence to test the accuracy of the method. With no free parameters in the model, the locations and extents of local denaturation predicted by this analysis are in quantitatively precise agreement with in vitro experimental measurements

The exact effects of radiation and joule heating on magnetohydrodynamic Marangoni convection over a flat surface

Directory of Open Access Journals (Sweden)

Khaled S.M.

2018-01-01

Full Text Available In this paper, we re-investigate the problem describing effects of radiation, Joule heating, and viscous dissipation on magnetohydrodynamic Marangoni convection boundary layer over a flat surface with suction/injection. The analytical solution obtained for the reduced system of non-linear-coupled differential equations governing the problem. Laplace transform successfully implemented to get the exact expression for the temperature profile. Furthermore, comparing the current exact results with approximate numerical results obtained using Runge-Kutta-Fehlberg method is introduced. These comparisons declare that the published numerical results agree with the current exact results. In addition, the effects of various parameters on the temperature profile are discussed graphically.

Exact travelling wave solutions of the (3+1)-dimensional mKdV-ZK ...

Indian Academy of Sciences (India)

In this paper, the new generalized (′/)-expansion method is executed to find the travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation. The efficiency of this method for finding exact and travelling wave solutions has been demonstrated. It is shown ...

Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations

DEFF Research Database (Denmark)

Garde, Henrik

2018-01-01

. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method...

INDEFINITE COPOSITIVE MATRICES WITH EXACTLY ONE POSITIVE EIGENVALUE OR EXACTLY ONE NEGATIVE EIGENVALUE

NARCIS (Netherlands)

Jargalsaikhan, Bolor

Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out

On exact correlation functions in SU(N) $ \\mathcal{N}=2 $ superconformal QCD

CERN Document Server

Baggio, Marco; Papadodimas, Kyriakos

2015-01-01

We consider the exact coupling constant dependence of extremal correlation functions of ${\\cal N} = 2$ chiral primary operators in 4d ${\\cal N} = 2$ superconformal gauge theories with gauge group SU(N) and N_f=2N massless fundamental hypermultiplets. The 2- and 3-point functions, viewed as functions of the exactly marginal coupling constant and theta angle, obey the tt* equations. In the case at hand, the tt* equations form a set of complicated non-linear coupled matrix equations. We point out that there is an ad hoc self-consistent ansatz that reduces this set of partial differential equations to a sequence of decoupled semi-infinite Toda chains, similar to the one encountered previously in the special case of SU(2) gauge group. This ansatz requires a surprising new non-renormalization theorem in ${\\cal N} = 2$ superconformal field theories. We derive a general 3-loop perturbative formula for 2- and 3-point functions in the ${\\cal N} = 2$ chiral ring of the SU(N) theory, and in all explicitly computed exampl...

Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares

International Nuclear Information System (INIS)

Gurin, Péter; Varga, Szabolcs

2015-01-01

We extend the transfer matrix method of one-dimensional hard core fluids placed between confining walls for that case where the particles can pass each other and at most two layers can form. We derive an eigenvalue equation for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between σ and 3σ (σ is the side length of the square). The exact equation of state and the nearest neighbor distribution functions show three different structures: a fluid phase with one layer, a fluid phase with two layers, and a solid-like structure where the fluid layers are strongly correlated. The structural transition between differently ordered fluids develops continuously with increasing density, i.e., no thermodynamic phase transition occurs. The high density structure of the system consists of clusters with two layers which are broken with particles staying in the middle of the pore

Exactly solvable models of two-dimensional dilaton cosmology with quantum backreaction

International Nuclear Information System (INIS)

Zaslavskii, O B

2003-01-01

We consider a general approach to exactly solvable 2D dilaton cosmology with one-loop backreaction from conformal fields taken into account. It includes as particular cases previous models discussed in the literature. We list different types of solutions and investigate their properties for simple models, typical for string theory. We find a rather rich class of everywhere-regular solutions, which exist practically in every type of analysed solution. They exhibit different kinds of asymptotic behaviour in the past and future, including inflation, superinflation, deflation, power expansion or contraction. In particular, for some models the dS spacetime with a time-dependent dilaton field is the exact solution of the field equations. For some kinds of solution the weak-energy condition is violated independently of a specific model. We also find the solutions with a singularity which is situated in an infinite past (or future), so at any finite moment of a comoving time the universe is singularity-free. It is pointed out that for some models the spacetime may be everywhere regular even in spite of infinitely large quantum backreaction in an infinite past

Analytic progress on exact lattice chiral symmetry

International Nuclear Information System (INIS)

Kikukawa, Y.

2002-01-01

Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional)

Exact periodic solutions of the sixth-order generalized Boussinesq equation

International Nuclear Information System (INIS)

Kamenov, O Y

2009-01-01

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u tt = u xx + 3(u 2 ) xx + u xxxx + αu xxxxxx , α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

A procedure to construct exact solutions of nonlinear fractional differential equations.

Science.gov (United States)

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy.

Science.gov (United States)

Ansumali, S; Karlin, I V; Arcidiacono, S; Abbas, A; Prasianakis, N I

2007-03-23

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.

Exact-exchange time-dependent density-functional theory for static and dynamic polarizabilities

International Nuclear Information System (INIS)

Hirata, So; Ivanov, Stanislav; Bartlett, Rodney J.; Grabowski, Ireneusz

2005-01-01

Time-dependent density-functional theory (TDDFT) employing the exact-exchange functional has been formulated on the basis of the optimized-effective-potential (OEP) method of Talman and Shadwick for second-order molecular properties and implemented into a Gaussian-basis-set, trial-vector algorithm. The only approximation involved, apart from the lack of correlation effects and the use of Gaussian-type basis functions, was the consistent use of the adiabatic approximation in the exchange kernel and in the linear response function. The static and dynamic polarizabilities and their anisotropy predicted by the TDDFT with exact exchange (TDOEP) agree accurately with the corresponding values from time-dependent Hartree-Fock theory, the exact-exchange counterpart in the wave function theory. The TDOEP is free from the nonphysical asymptotic decay of the exchange potential of most conventional density functionals or from any other manifestations of the incomplete cancellation of the self-interaction energy. The systematic overestimation of the absolute values and dispersion of polarizabilities that plagues most conventional TDDFT cannot be seen in the TDOEP

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.

Exact complexity: The spectral decomposition of intrinsic computation

International Nuclear Information System (INIS)

Crutchfield, James P.; Ellison, Christopher J.; Riechers, Paul M.

2016-01-01

We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full eigenvalue spectrum of the mixed-state presentation of a process's ϵ-machine causal-state dynamic. Measures include correlation functions, power spectra, past-future mutual information, transient and synchronization informations, and many others. As a result, a direct and complete analysis of intrinsic computation is now available for the temporal organization of finitary hidden Markov models and nonlinear dynamical systems with generating partitions and for the spatial organization in one-dimensional systems, including spin systems, cellular automata, and complex materials via chaotic crystallography. - Highlights: • We provide exact, closed-form expressions for a hidden stationary process' intrinsic computation. • These include information measures such as the excess entropy, transient information, and synchronization information and the entropy-rate finite-length approximations. • The method uses an epsilon-machine's mixed-state presentation. • The spectral decomposition of the mixed-state presentation relies on the recent development of meromorphic functional calculus for nondiagonalizable operators.

Large-scale exact diagonalizations reveal low-momentum scales of nuclei

Science.gov (United States)

Forssén, C.; Carlsson, B. D.; Johansson, H. T.; Sääf, D.; Bansal, A.; Hagen, G.; Papenbrock, T.

2018-03-01

Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding 1010 on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for 6Li in model spaces up to Nmax=22 and to reveal the 4He+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.

Analytical and exact solutions of the spherical and cylindrical diodes of Langmuir-Blodgett law

Science.gov (United States)

Torres-Cordoba, Rafael; Martinez-Garcia, Edgar

2017-10-01

This paper discloses the exact solutions of a mathematical model that describes the cylindrical and spherical electron current emissions within the context of a physics approximation method. The solution involves analyzing the 1D nonlinear Poisson equation, for the radial component. Although an asymptotic solution has been previously obtained, we present a theoretical solution that satisfies arbitrary boundary conditions. The solution is found in its parametric form (i.e., φ(r )=φ(r (τ)) ) and is valid when the electric field at the cathode surface is non-zero. Furthermore, the non-stationary spatial solution of the electric potential between the anode and the cathode is also presented. In this work, the particle-beam interface is considered to be at the end of the plasma sheath as described by Sutherland et al. [Phys. Plasmas 12, 033103 2005]. Three regimes of space charge effects—no space charge saturation, space charge limited, and space charge saturation—are also considered.

Exact exchange-correlation potentials of singlet two-electron systems

Science.gov (United States)

Ryabinkin, Ilya G.; Ospadov, Egor; Staroverov, Viktor N.

2017-10-01

We suggest a non-iterative analytic method for constructing the exchange-correlation potential, v XC ( r ) , of any singlet ground-state two-electron system. The method is based on a convenient formula for v XC ( r ) in terms of quantities determined only by the system's electronic wave function, exact or approximate, and is essentially different from the Kohn-Sham inversion technique. When applied to Gaussian-basis-set wave functions, the method yields finite-basis-set approximations to the corresponding basis-set-limit v XC ( r ) , whereas the Kohn-Sham inversion produces physically inappropriate (oscillatory and divergent) potentials. The effectiveness of the procedure is demonstrated by computing accurate exchange-correlation potentials of several two-electron systems (helium isoelectronic series, H2, H3 + ) using common ab initio methods and Gaussian basis sets.

Exactly soluble models for surface partition of large clusters

International Nuclear Information System (INIS)

Bugaev, K.A.; Bugaev, K.A.; Elliott, J.B.

2007-01-01

The surface partition of large clusters is studied analytically within a framework of the 'Hills and Dales Model'. Three formulations are solved exactly by using the Laplace-Fourier transformation method. In the limit of small amplitude deformations, the 'Hills and Dales Model' gives the upper and lower bounds for the surface entropy coefficient of large clusters. The found surface entropy coefficients are compared with those of large clusters within the 2- and 3-dimensional Ising models

Exactly solvable birth and death processes

International Nuclear Information System (INIS)

Sasaki, Ryu

2009-01-01

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q x (with x being the population) corresponding to the q-Racah polynomial.

Exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres

International Nuclear Information System (INIS)

Liu Chunping

2005-01-01

First, by using the generally projective Riccati equation method, many kinds of exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres are obtained in a unified way. Then, some relations among these solutions are revealed

Exact renormalization group equations: an introductory review

Science.gov (United States)

Bagnuls, C.; Bervillier, C.

2001-07-01

We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.

Exact closed form expressions for outage probability of GSC receivers over Rayleigh fading channel subject to self-interference

KAUST Repository

Nam, Sungsik

2010-11-01

Previous work on performance analyses of generalized selection combining (GSC) RAKE receivers based on the signal to noise ratio focused on the development of methodologies to derive exact closed-form expressions for various performance measures. However, some open problems related to the performance evaluation of GSC RAKE receivers still remain to be solved such that an assessment of the impact of self-interference on the performance of GSC RAKE receivers. To have a full and exact understanding of the performance of GSC RAKE receivers, the outage probability of GSC RAKE receivers needs to be analyzed as closed-form expressions. The major difficulty in this problem is to derive some joint statistics of ordered exponential variates. With this motivation in mind, we capitalize in this paper on some new order statistics results to derive exact closed-form expressions for outage probability of GSC RAKE receivers subject to self-interference over independent and identically distributed Rayleigh fading channels. © 2010 IEEE.

Exact association test for small size sequencing data.

Science.gov (United States)

Lee, Joowon; Lee, Seungyeoun; Jang, Jin-Young; Park, Taesung

2018-04-20

Recent statistical methods for next generation sequencing (NGS) data have been successfully applied to identifying rare genetic variants associated with certain diseases. However, most commonly used methods (e.g., burden tests and variance-component tests) rely on large sample sizes. Notwithstanding, due to its-still high cost, NGS data is generally restricted to small sample sizes, that cannot be analyzed by most existing methods. In this work, we propose a new exact association test for sequencing data that does not require a large sample approximation, which is applicable to both common and rare variants. Our method, based on the Generalized Cochran-Mantel-Haenszel (GCMH) statistic, was applied to NGS datasets from intraductal papillary mucinous neoplasm (IPMN) patients. IPMN is a unique pancreatic cancer subtype that can turn into an invasive and hard-to-treat metastatic disease. Application of our method to IPMN data successfully identified susceptible genes associated with progression of IPMN to pancreatic cancer. Our method is expected to identify disease-associated genetic variants more successfully, and corresponding signal pathways, improving our understanding of specific disease's etiology and prognosis.

Exact vacuum polarization in 1 + 1 dimensional finite nuclei

International Nuclear Information System (INIS)

Ferree, T.C.

1992-01-01

There is considerable interest in the use of renormalizable quantum field theories to describe nuclear structure. In particular, theories which employ hadronic degrees of freedom are used widely and lead to efficient models which allow self-consistent solutions of the many-body problem. An interesting feature inherent to relativistic field theories (like QHD) is the presence of an infinite sea of negative energy fermion (nucleon) states, which interact dynamically with positive energy fermions via other fields. Such interactions give rise to, for example, vacuum polarization effects, in which virtual particle-antiparticle pairs interact with positive energy valence nucleons as well as with each other, and can significantly influence the ground and excited states of nuclear systems. Several authors have addressed this question in various approximations for finite nuclei, mostly based on extensions of results derived for a uniform system of nucleons. Some attempts have also been made to include vacuum effects in finite systems exactly, but the presence of a vector potential can be problematic when working in a spectral representation. In this paper, the author presents a computational method by which vacuum polarization effects in finite nuclei can be calculated exactly in the RHA by employing matrix diagonalization methods in a discrete Fourier representation of the Dirac equation, and an approximate method for including deep negative energy states based on a derivative expansion of the effective action. This efficient approach is shown to provide well-behaved vacuum polarization densities which remain so even in the presence of strong vector potential

Exact solution for the generalized Telegraph Fisher's equation

International Nuclear Information System (INIS)

Abdusalam, H.A.; Fahmy, E.S.

2009-01-01

In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.

Exact solution of the hidden Markov processes

Science.gov (United States)

Saakian, David B.

2017-11-01

We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .

Dissipative motion perturbation theory and exact solutions

International Nuclear Information System (INIS)

Lodder, J.J.

1976-06-01

Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion

Exact Theory of Compressible Fluid Turbulence

Science.gov (United States)

Drivas, Theodore; Eyink, Gregory

2017-11-01

We obtain exact results for compressible turbulence with any equation of state, using coarse-graining/filtering. We find two mechanisms of turbulent kinetic energy dissipation: scale-local energy cascade and ``pressure-work defect'', or pressure-work at viscous scales exceeding that in the inertial-range. Planar shocks in an ideal gas dissipate all kinetic energy by pressure-work defect, but the effect is omitted by standard LES modeling of pressure-dilatation. We also obtain a novel inverse cascade of thermodynamic entropy, injected by microscopic entropy production, cascaded upscale, and removed by large-scale cooling. This nonlinear process is missed by the Kovasznay linear mode decomposition, treating entropy as a passive scalar. For small Mach number we recover the incompressible ``negentropy cascade'' predicted by Obukhov. We derive exact Kolmogorov 4/5th-type laws for energy and entropy cascades, constraining scaling exponents of velocity, density, and internal energy to sub-Kolmogorov values. Although precise exponents and detailed physics are Mach-dependent, our exact results hold at all Mach numbers. Flow realizations at infinite Reynolds are ``dissipative weak solutions'' of compressible Euler equations, similarly as Onsager proposed for incompressible turbulence.

Exact explicit travelling wave solutions for (n + 1)-dimensional Klein-Gordon-Zakharov equations

International Nuclear Information System (INIS)

Li Jibin

2007-01-01

Using the methods of dynamical systems for the (n + 1)-dimensional KGS nonlinear wave equations, five classes of exact explicit parametric representations of the bounded travelling solutions are obtained. To guarantee the existence of the above solutions, all parameter conditions are given

Exact Cover Problem in Milton Babbitt's All-partition Array

OpenAIRE

Bemman, Brian; Meredith, David

2015-01-01

One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set, A, and a collection of distinct subsets of this set, S, then a subset of S is an exact cover of A if it exhaustively and exclu- sively partitions A. We provide a backtracking algorithm for solving ...

Exact and analytic solutions of the Ernst equation governing axially symmetric stationary vacuum gravitational fields

International Nuclear Information System (INIS)

Baxter, Mathew; Van Gorder, Robert A

2013-01-01

We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions. (paper)

Exact ground-state phase diagrams for the spin-3/2 Blume-Emery-Griffiths model

Energy Technology Data Exchange (ETDEWEB)

Canko, Osman; Keskin, Mustafa [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Deviren, Bayram [Institute of Science, Erciyes University, 38039 Kayseri (Turkey)], E-mail: keskin@erciyes.edu.tr

2008-05-15

We have calculated the exact ground-state phase diagrams of the spin-3/2 Ising model using the method that was proposed and applied to the spin-1 Ising model by Dublenych (2005 Phys. Rev. B 71 012411). The calculated, exact ground-state phase diagrams on the diatomic and triangular lattices with the nearest-neighbor (NN) interaction have been presented in this paper. We have obtained seven and 15 topologically different ground-state phase diagrams for J>0 and J<0, respectively, on the diatomic lattice and have found the conditions for the existence of uniform and intermediate or non-uniform phases. We have also constructed the exact ground-state phase diagrams of the model on the triangular lattice and found 20 and 59 fundamental phase diagrams for J>0 and J<0, respectively, the conditions for the existence of uniform and intermediate phases have also been found.

Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

Science.gov (United States)

Adem, Abdullahi Rashid; Moawad, Salah M.

2018-05-01

In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

Exact-to-precision generalized perturbation theory for source-driven systems

International Nuclear Information System (INIS)

Wang Congjian; Abdel-Khalik, Hany S.

2011-01-01

Highlights: ► We present a new development in higher order generalized perturbation theory. ► The method addresses the explosion in the flux phase space, input parameters, and responses. ► The method hybridizes first-order GPT and proper orthogonal decomposition snapshots method. ► A simplified 1D and realistic 2D assembly models demonstrate applicability of the method. ► The accuracy of the method is compared to exact direct perturbations and first-order GPT. - Abstract: Presented in this manuscript are new developments to perturbation theory which are intended to extend its applicability to estimate, with quantifiable accuracy, the exact variations in all responses calculated by the model with respect to all possible perturbations in the model's input parameters. The new developments place high premium on reducing the associated computational overhead in order to enable the use of perturbation theory in routine reactor design calculations. By way of examples, these developments could be employed in core simulation to accurately estimate the few-group cross-sections variations resulting from perturbations in neutronics and thermal-hydraulics core conditions. These variations are currently being described using a look-up table approach, where thousands of assembly calculations are performed to capture few-group cross-sections variations for the downstream core calculations. Other applications include the efficient evaluation of surrogates for applications that require repeated model runs such as design optimization, inverse studies, uncertainty quantification, and online core monitoring. The theoretical background of these developments applied to source-driven systems and supporting numerical experiments are presented in this manuscript. Extension to eigenvalue problems will be presented in a future article.

Exact work

International Nuclear Information System (INIS)

Zeger, J.

1993-01-01

Organized criminals also tried to illegally transfer nuclear material through Austria. Two important questions have to be answered after the material is sized by police authorities: What is the composition of the material and where does it come from? By application of a broad range of analytical techniques, which were developed or refined by our experts, it is possible to measure the exact amount and isotopic composition of uranium and plutonium in any kind of samples. The criminalistic application is only a byproduct of the large scale work on controlling the peaceful application of nuclear energy, which is done in contract with the IAEA in the context of the 'Network of Analytical Laboratories'

Exact ground-state phase diagrams for the spin-3/2 Blume-Emery-Griffiths model

International Nuclear Information System (INIS)

Canko, Osman; Keskin, Mustafa; Deviren, Bayram

2008-01-01

We have calculated the exact ground-state phase diagrams of the spin-3/2 Ising model using the method that was proposed and applied to the spin-1 Ising model by Dublenych (2005 Phys. Rev. B 71 012411). The calculated, exact ground-state phase diagrams on the diatomic and triangular lattices with the nearest-neighbor (NN) interaction have been presented in this paper. We have obtained seven and 15 topologically different ground-state phase diagrams for J>0 and J 0 and J<0, respectively, the conditions for the existence of uniform and intermediate phases have also been found

Iterative optimized effective potential and exact exchange calculations at finite temperature

International Nuclear Information System (INIS)

Mattsson, Ann Elisabet; Modine, Normand Arthur; Muller, Richard Partain; Desjarlais, Michael Paul; Lippert, Ross A.; Sears, Mark P.; Wright, Alan Francis

2006-01-01

We report the implementation of an iterative scheme for calculating the Optimized Effective Potential (OEP). Given an energy functional that depends explicitly on the Kohn-Sham wave functions, and therefore, implicitly on the local effective potential appearing in the Kohn-Sham equations, a gradient-based minimization is used to find the potential that minimizes the energy. Previous work has shown how to find the gradient of such an energy with respect to the effective potential in the zero-temperature limit. We discuss a density-matrix-based derivation of the gradient that generalizes the previous results to the finite temperature regime, and we describe important optimizations used in our implementation. We have applied our OEP approach to the Hartree-Fock energy expression to perform Exact Exchange (EXX) calculations. We report our EXX results for common semiconductors and ordered phases of hydrogen at zero and finite electronic temperatures. We also discuss issues involved in the implementation of forces within the OEP/EXX approach.

Exact solution of nonsteady thermal boundary layer equation

International Nuclear Information System (INIS)

Dorfman, A.S.

1995-01-01

There are only a few exact solutions of the thermal boundary layer equation. Most of them are derived for a specific surface temperature distribution. The first exact solution of the steady-state boundary layer equation was given for a plate with constant surface temperature and free-stream velocity. The same problem for a plate with polynomial surface temperature distribution was solved by Chapmen and Rubesin. Levy gave the exact solution for the case of a power law distribution of both surface temperature and free-stream velocity. The exact solution of the steady-state boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution was given by the author in two forms: of series and of the integral with an influence function of unheated zone. A similar solution of the nonsteady thermal boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution is presented here. In this case, the coefficients of series depend on time, and in the limit t → ∞ they become the constant coefficients of a similar solution published before. This solution, unlike the one presented here, does not satisfy the initial conditions at t = 0, and, hence, can be used only in time after the beginning of the process. The solution in the form of a series becomes a closed-form exact solution for polynomial surface temperature and a power law free-stream velocity distribution. 7 refs., 2 figs

Previous medical history of diseases in children with attention deficit hyperactivity disorder and their parents

Directory of Open Access Journals (Sweden)

Ayyoub Malek

2014-02-01

Full Text Available Introduction: The etiology of Attention deficit hyperactivity disorder (ADHD is complex and most likely includes genetic and environmental factors. This study was conducted to evaluatethe role of previous medical history of diseases in ADHD children and their parents during theearlier years of the ADHD children's lives. Methods: In this case-control study, 164 ADHD children attending to Child and AdolescentPsychiatric Clinics of Tabriz University of Medical Sciences, Iran, compared with 166 normal children selected in a random-cluster method from primary and guidance schools. ADHDrating scale (Parents version and clinical interview based on schedule for Schedule forAffective Disorders and Schizophrenia for School-Age Children-Present and Lifetime Version(K-SADS were used to diagnose ADHD cases and to select the control group. Two groupswere compared for the existence of previous medical history of diseases in children andparents. Fisher's exact test and logistic regression model were used for data analysis. Results: The frequency of maternal history of medical disorders (28.7% vs. 12.0%; P = 0.001was significantly higher in children with ADHD compared with the control group. The frequency of jaundice, dysentery, epilepsy, asthma, allergy, and head trauma in the medicalhistory of children were not significantly differed between the two groups. Conclusion: According to this preliminary study, it may be concluded that the maternal historyof medical disorders is one of contributing risk factors for ADHD.

New Exact Solutions for the Wick-Type Stochastic Kudryashov–Sinelshchikov Equation

International Nuclear Information System (INIS)

Ray, S. Saha; Singh, S.

2017-01-01

In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space. (paper)

Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation

Directory of Open Access Journals (Sweden)

Hongwei Yang

2012-01-01

Full Text Available We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.

An exact fermion-pair to boson mapping

International Nuclear Information System (INIS)

Johnson, C.W.

1993-01-01

I derive in a novel fashion exact formulas for the calculation of general matrix elements, including the overlap (norm) matrix, between states constructed from fermion pairs. Mapping the fermion pairs to bosons, I show how to construct finite and exact (in the sense of preserving matrix elements) boson representations of the norm operator and one- and two-fermion operators. This may lead to a microscopic basis for the Interacting Boson Model, as well as new truncation schemes for the nuclear shell model

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

Science.gov (United States)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

The exact mass-gaps of the principal chiral models

CERN Document Server

Hollowood, Timothy J

1994-01-01

An exact expression for the mass-gap, the ratio of the physical particle mass to the $\\Lambda$-parameter, is found for the principal chiral sigma models associated to all the classical Lie algebras. The calculation is based on a comparison of the free-energy in the presence of a source coupling to a conserved charge of the theory computed in two ways: via the thermodynamic Bethe Ansatz from the exact scattering matrix and directly in perturbation theory. The calculation provides a non-trivial test of the form of the exact scattering matrix.

Occupation times and exact asymptotics of small deviations of Bessel processes for Lp-norms with p>0

International Nuclear Information System (INIS)

Fatalov, V R

2007-01-01

We prove theorems on exact asymptotics of the distributions of integral functionals of the occupation time of Bessel processes. Using these results, we obtain exact asymptotics of small deviations for Bessel processes in the L p -norm. We use Laplace's method for the occupation times of Markov processes with continuous time. Computations are carried out for p=2 and p=1. We also solve extremal problems for the action functional

Exact performance analysis of MIMO cognitive radio systems using transmit antenna selection

KAUST Repository

Tourki, Kamel

2014-03-01

We consider in this paper, a spectrum sharing cognitive radio system with a ratio selection scheme; where one out of N independent-and-identically- distributed transmit antennas is selected such that the ratio of the secondary transmitter (ST) to the secondary receiver (SR) channel gain to the interference from the ST to the primary receiver (PR) channel gain is maximized. Although previous works considered perfect, outdated, or partial channel state information at the transmitter, we stress that using such assumptions may lead to a feedback overhead for updating the SR with the ST-PR interference channel estimation. Considering only statistical knowledge of the ST-PR channel gain, we investigate a ratio selection scheme using a mean value (MV)-based power allocation strategy referred to as MV-based scheme. We first provide the exact statistics in terms of probability density function and cumulative distribution function of the secondary channel gain as well as of the interference channel gain. Furthermore, we derive exact cumulative density function of the received signal-to-noise ratio at the SR where the ST uses a power allocation based on instantaneous perfect channel state information (CSI) referred to as CSI-based scheme. These statistics are then used to derive exact closed form expressions of the outage probability, symbol error rate, and ergodic capacity of the secondary system when the interference channel from the primary transmitter (PT) to the SR is ignored. Furthermore, an asymptotical analysis is also carried out for the MV-based scheme as well as for the CSI-based scheme to derive the generalized diversity gain for each. Subsequently, we address the performance analysis based on exact statistics of the combined signal-to-interference-plus- noise ratio at the SR of the more challenging case; when the PT-SR interference channel is considered. Numerical results in a Rayleigh fading environment manifest that the MV-based scheme outperforms the CSI

Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability

Science.gov (United States)

Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.

2018-02-01

As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi-exactly

Exact, multiple soliton solutions of the double sine Gordon equation

International Nuclear Information System (INIS)

Burt, P.B.

1978-01-01

Exact, particular solutions of the double sine Gordon equation in n dimensional space are constructed. Under certain restrictions these solutions are N solitons, where N <= 2q - 1 and q is the dimensionality of space-time. The method of solution, known as the base equation technique, relates solutions of nonlinear partial differential equations to solutions of linear partial differential equations. This method is reviewed and its applicability to the double sine Gordon equation shown explicitly. The N soliton solutions have the remarkable property that they collapse to a single soliton when the wave vectors are parallel. (author)

Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

Science.gov (United States)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-06-01

In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.

Exact solution of the Ising model in a fully frustrated two-dimensional lattice

International Nuclear Information System (INIS)

Silva, N.R. da; Medeiros e Silva Filho, J.

1983-01-01

A straightforward extension of the Onsager method allows us to solve exactly the Ising problem in a fully frustated square lattice in the absence of external magnetic field. It is shown there is no singularity in the thermodynamic functions for non-zero temperature. (Author) [pt

Transversal magnetotransport in Weyl semimetals: Exact numerical approach

Science.gov (United States)

Behrends, Jan; Kunst, Flore K.; Sbierski, Björn

2018-02-01

Magnetotransport experiments on Weyl semimetals are essential for investigating the intriguing topological and low-energy properties of Weyl nodes. If the transport direction is perpendicular to the applied magnetic field, experiments have shown a large positive magnetoresistance. In this work we present a theoretical scattering matrix approach to transversal magnetotransport in a Weyl node. Our numerical method confirms and goes beyond the existing perturbative analytical approach by treating disorder exactly. It is formulated in real space and is applicable to mesoscopic samples as well as in the bulk limit. In particular, we study the case of clean and strongly disordered samples.

Stop: a fast procedure for the exact computation of the performance of complex probabilistic systems

International Nuclear Information System (INIS)

Corynen, G.C.

1982-01-01

A new set-theoretic method for the exact and efficient computation of the probabilistic performance of complex systems has been developed. The core of the method is a fast algorithm for disjointing a collection of product sets which is intended for systems with more than 1000 components and 100,000 cut sets. The method is based on a divide-and-conquer approach, in which a multidimensional problem is progressively decomposed into lower-dimensional subproblems along its dimensions. The method also uses a particular pointer system that eliminates the need to store the subproblems by only requiring the storage of pointers to those problems. Examples of the algorithm and the divide-and-conquer strategy are provided, and comparisons with other significant methods are made. Statistical complexity studies show that the expected time and space complexity of other methods is O(me/sup n/), but that our method is O(nm 3 log(m)). Problems which would require days of Cray-1 computer time with present methods can now be solved in seconds. Large-scale systems that can only be approximated with other techniques can now also be evaluated exactly

On symmetries and exact solutions of the Einstein–Maxwell field equations via the symmetry approach

International Nuclear Information System (INIS)

Kaur, Lakhveer; Gupta, R K

2013-01-01

Using the Lie symmetry approach, we have examined herein the system of partial differential equations corresponding to the Einstein–Maxwell equations for a static axially symmetric spacetime. The method used reduces the system of partial differential equations to a system of ordinary differential equations according to the Lie symmetry admitted. In particular, we found the relevant system of ordinary differential equations is all optimal subgroups. The system of ordinary differential equations is further solved in general to obtain exact solutions. Several new physically important families of exact solutions are derived. (paper)

Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory

Science.gov (United States)

Krüger, Matthias; Solon, Alexandre; Démery, Vincent; Rohwer, Christian M.; Dean, David S.

2018-02-01

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.

Exact periodic solutions of the sixth-order generalized Boussinesq equation

Energy Technology Data Exchange (ETDEWEB)

Kamenov, O Y [Department of Applied Mathematics and Informatics, Technical University of Sofia, PO Box 384, 1000 Sofia (Bulgaria)], E-mail: okam@abv.bg

2009-09-18

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u{sub tt} = u{sub xx} + 3(u{sup 2}){sub xx} + u{sub xxxx} + {alpha}u{sub xxxxxx}, {alpha} in R, depending on the positive parameter {alpha}. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

Exact soliton-like solutions of perturbed phi4-equation

International Nuclear Information System (INIS)

Gonzalez, J.A.

1986-05-01

Exact soliton-like solutions of damped, driven phi 4 -equation are found. The exact expressions for the velocities of solitons are given. It is non-perturbatively proved that the perturbed phi 4 -equation has stable kink-like solutions of a new type. (author)

Quasi-exactly solvable relativistic soft-core Coulomb models

Energy Technology Data Exchange (ETDEWEB)

Agboola, Davids, E-mail: davagboola@gmail.com; Zhang, Yao-Zhong, E-mail: yzz@maths.uq.edu.au

2012-09-15

By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein-Gordon and Dirac equations with the family of soft-core Coulomb potentials V{sub q}(r)=-Z/(r{sup q}+{beta}{sup q}){sup 1/q}, Z>0, {beta}>0, q{>=}1. We consider cases q=1 and q=2 and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derived in terms of the roots of a set of Bethe ansatz equations. - Highlights: Black-Right-Pointing-Pointer The relativistic bound-state solutions of the soft-core Coulomb models. Black-Right-Pointing-Pointer Quasi-exact treatments of the Dirac and Klein-Gordon equations for the soft-core Coulomb models. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer The hidden Lie algebraic structure discussed for the models. Black-Right-Pointing-Pointer Results useful in describing mesonic atoms and interaction of intense laser fields with atom.

Relativistic plasma dielectric tensor evaluation based on the exact plasma dispersion functions concept

International Nuclear Information System (INIS)

Castejon, F.; Pavlov, S. S.

2006-01-01

The fully relativistic plasma dielectric tensor for any wave and plasma parameter is estimated on the basis of the exact plasma dispersion functions concept. The inclusion of this concept allows one to write the tensor in a closed and compact form and to reduce the tensor evaluation to the calculation of those functions. The main analytical properties of these functions are studied and two methods are given for their evaluation. The comparison between the exact dielectric tensor with the weakly relativistic approximation, widely used presently in plasma waves calculations, is given as well as the range of plasma temperature, harmonic number, and propagation angle in which the weakly relativistic approximation is valid

A geometric method of constructing exact solutions in modified f(R,T)-gravity with Yang-Mills and Higgs interactions

CERN Document Server

Vacaru, Sergiu I.; Yazici, Enis

2014-01-01

We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.

Exact scattering and diffraction of antiplane shear waves by a vertical edge crack

Science.gov (United States)

Tsaur, Deng-How

2010-06-01

Scattering and diffraction problems of a vertical edge crack connected to the surface of a half space are considered for antiplane shear wave incidence. The method of separation of variables is adopted to derive an exact series solution. The total displacement field is expressed as infinite series containing products of radial and angular Mathieu functions with unknown coefficients. An exact analytical determination of unknown coefficients is carried out by insuring the vanishing of normal stresses on crack faces. Frequency-domain results are given for extremely near, near, and far fields, whereas time-domain ones are for horizontal surface and subsurface motions. Comparisons with published data for the dynamic stress intensity factor show good agreement. The exact analytical nature of proposed solutions can be applied very conveniently and rapidly to high-frequency steady-state cases, enhancing the computation efficiency in transient cases when performing the fast Fourier transform. A sampled set of time slices for underground wave propagation benefits the interpretation of scattering and diffraction phenomena induced by a vertical edge crack.

Bifurcations of Exact Traveling Wave Solutions for (2+1)-Dimensional HNLS Equation

International Nuclear Information System (INIS)

Xu Yuanfen

2012-01-01

For the (2+1)-Dimensional HNLS equation, what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems. Ten exact explicit parametric representations of the traveling wave solutions are given. (general)

Exactly marginal deformations from exceptional generalised geometry

Energy Technology Data Exchange (ETDEWEB)

Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford,Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Gabella, Maxime [Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Graña, Mariana [Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHE,75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)

2017-01-27

We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS{sub 5} flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS{sub 5} flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.

Exact Lattice Supersymmetry

Energy Technology Data Exchange (ETDEWEB)

Catterall, Simon; Kaplan, David B.; Unsal, Mithat

2009-03-31

We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.

Exact renormalization group for gauge theories

International Nuclear Information System (INIS)

Balaban, T.; Imbrie, J.; Jaffe, A.

1984-01-01

Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study

Upper bounds on minimum cardinality of exact and approximate reducts

KAUST Repository

Chikalov, Igor

2010-01-01

In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.

Electron transfer dynamics: Zusman equation versus exact theory

International Nuclear Information System (INIS)

Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing

2009-01-01

The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.

An exact solution of three interacting friendly walks in the bulk

International Nuclear Information System (INIS)

Tabbara, R; Owczarek, A L; Rechnitzer, A

2016-01-01

We find the exact solution of three interacting friendly directed walks on the square lattice in the bulk, modelling a system of homopolymers that can undergo a multiple polymer fusion or zipping transition by introducing two distinct interaction parameters that differentiate between the zipping of only two or all three walks. We establish functional equations for the model’s corresponding generating function that are subsequently solved exactly by means of the obstinate kernel method. We then proceed to analyse our model, first considering the case where triple-walk interaction effects are ignored, finding that our model exhibits two phases which we classify as free and gelated (or zipped) regions, with the system exhibiting a second-order phase transition. We then analyse the full model where both interaction parameters are incorporated, presenting the full phase diagram and highlighting the additional existence of a first-order gelation (zipping) boundary. (paper)

Exactly complete solutions of the Schroedinger equation with a spherically harmonic oscillatory ring-shaped potential

International Nuclear Information System (INIS)

Zhang Mincang; Sun Guohua; Dong Shihai

2010-01-01

A spherically harmonic oscillatory ring-shaped potential is proposed and its exactly complete solutions are presented by the Nikiforov-Uvarov method. The effect of the angle-dependent part on the radial solutions is discussed.

The fractional coupled KdV equations: Exact solutions and white noise functional approach

International Nuclear Information System (INIS)

Ghany, Hossam A.; El Bab, A. S. Okb; Zabel, A. M.; Hyder, Abd-Allah

2013-01-01

Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the modified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types. (general)

Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

Science.gov (United States)

Polyanin, A. D.; Sorokin, V. G.

2017-12-01

The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

Polymers undergoing inhomogeneous adsorption: exact results and Monte Carlo simulations

Energy Technology Data Exchange (ETDEWEB)

Iliev, G K [Department of Mathematics, University of Melbourne, Parkville, Victoria (Australia); Orlandini, E [Dipartimento di Fisica, CNISM, Universita di Padova, Via Marzolo 8, 35131 Padova (Italy); Whittington, S G, E-mail: giliev@yorku.ca [Department of Chemistry, University of Toronto, Toronto (Canada)

2011-10-07

We consider several types of inhomogeneous polymer adsorption. In each case, the inhomogeneity is regular and resides in the surface, in the polymer or in both. We consider two different polymer models: a directed walk model that can be solved exactly and a self-avoiding walk model which we investigate using Monte Carlo methods. In each case, we compute the phase diagram. We compare and contrast the phase diagrams and give qualitative arguments about their forms. (paper)

Exact Cover Problem in Milton Babbitt's All-partition Array

DEFF Research Database (Denmark)

Bemman, Brian; Meredith, David

2015-01-01

One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set...

Exact solution of a coupled spin–electron linear chain composed of localized Ising spins and mobile electrons

International Nuclear Information System (INIS)

Čisárová, Jana; Strečka, Jozef

2014-01-01

Exact solution of a coupled spin–electron linear chain composed of localized Ising spins and mobile electrons is found. The investigated spin–electron model is exactly solvable by the use of a transfer-matrix method after tracing out the degrees of freedom of mobile electrons delocalized over a couple of interstitial (decorating) sites. The exact ground-state phase diagram reveals an existence of five phases with different number of mobile electrons per unit cell, two of which are ferromagnetic, two are paramagnetic and one is antiferromagnetic. We have studied in particular the dependencies of compressibility and specific heat on temperature and electron density. - Highlights: • A coupled spin–electron chain composed of Ising spins and mobile electrons is exactly solved. • Quantum paramagnetic, ferromagnetic and antiferromagnetic ground states are found. • A compressibility shows a non-monotonous dependence on temperature and electron density. • Thermal dependences of specific heat display two distinct peaks

Parallel Implementation of Gamma-Point Pseudopotential Plane-Wave DFT with Exact Exchange

International Nuclear Information System (INIS)

Bylaska, Eric J.; Tsemekhman, Kiril L.; Baden, Scott B.; Weare, John H.; Jonsson, Hannes

2011-01-01

One of the more persistent failures of conventional density functional theory (DFT) methods has been their failure to yield localized charge states such as polarons, excitons and solitons in solid-state and extended systems. It has been suggested that conventional DFT functionals, which are not self-interaction free, tend to favor delocalized electronic states since self-interaction creates a Coulomb barrier to charge localization. Pragmatic approaches in which the exchange correlation functionals are augmented with small amount of exact exchange (hybrid-DFT, e.g. B3LYP and PBE0) have shown promise in localizing charge states and predicting accurate band gaps and reaction barriers. We have developed a parallel algorithm for implementing exact exchange into pseudopotential plane-wave density functional theory and we have implemented it in the NWChem program package. The technique developed can readily be employed in plane-wave DFT programs. Furthermore, atomic forces and stresses are straightforward to implement, making it applicable to both confined and extended systems, as well as to Car-Parrinello ab initio molecular dynamic simulations. This method has been applied to several systems for which conventional DFT methods do not work well, including calculations for band gaps in oxides and the electronic structure of a charge trapped state in the Fe(II) containing mica, annite.

Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

Science.gov (United States)

Rao, T. R. Ramesh

2018-04-01

In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.

Energy vs. density on paths toward exact density functionals

DEFF Research Database (Denmark)

Kepp, Kasper Planeta

2018-01-01

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness...

Exact braneworld cosmology induced from bulk black holes

International Nuclear Information System (INIS)

Gregory, James P; Padilla, Antonio

2002-01-01

We use a new, exact approach in calculating the energy density measured by an observer living on a brane embedded in a charged black-hole spacetime. We find that the bulk Weyl tensor gives rise to nonlinear terms in the energy density and pressure in the FRW equations for the brane. Remarkably, these take exactly the same form as the 'unconventional' terms found in the cosmology of branes embedded in pure AdS, with extra matter living on the brane. Black-hole-driven cosmologies have the benefit that there is no ambiguity in splitting the braneworld energy momentum into tension and additional matter. We propose a new, enlarged relationship between the two descriptions of braneworld cosmology. We also study the exact thermodynamics of the field theory and present a generalized Cardy-Verlinde formula in this set-up

Specification, construction, and exact reduction of state transition system models of biochemical processes.

Science.gov (United States)

Bugenhagen, Scott M; Beard, Daniel A

2012-10-21

Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction events. Since they often involve a large number of interactions, it can be difficult to construct such a model for a system, and since the resulting state-level model can involve a huge number of states, model analysis can be difficult or impossible. Here, we describe methods for the high-level specification of a system using hypergraphs, for the automated generation of a state-level model from a high-level model, and for the exact reduction of a state-level model using information from the high-level model. Exact reduction is achieved through the automated application to the high-level model of the symmetry reduction technique and reduction by decomposition by independent subsystems, allowing potentially significant reductions without the need to generate a full model. The application of the method to biochemical reaction systems is illustrated by models describing a hypothetical ion-channel at several levels of complexity. The method allows for the reduction of the otherwise intractable example models to a manageable size.

When is quasi-linear theory exact. [particle acceleration

Science.gov (United States)

Jones, F. C.; Birmingham, T. J.

1975-01-01

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.

Exact Lagrangian caps and non-uniruled Lagrangian submanifolds

Science.gov (United States)

Dimitroglou Rizell, Georgios

2015-04-01

We make the elementary observation that the Lagrangian submanifolds of C n , n≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov-Eliashberg algebra is acyclic.

Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields

Energy Technology Data Exchange (ETDEWEB)

Li, Yuan-Yuan; Cao, Junpeng [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Yang, Wen-Li [Institute of Modern Physics, Northwest University, Xian 710069 (China); Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048 (China); Shi, Kangjie [Institute of Modern Physics, Northwest University, Xian 710069 (China); Wang, Yupeng, E-mail: yupeng@iphy.ac.cn [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)

2014-02-15

The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.

Generalized exact holographic mapping with wavelets

Science.gov (United States)

Lee, Ching Hua

2017-12-01

The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic N -dimensional lattice system to a (N +1 )-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high-pass wavelet filter is revealed to be proportional to the radius of the dual anti-de Sitter space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.

Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities

Directory of Open Access Journals (Sweden)

Idris Addou

2000-01-01

Full Text Available We consider the boundary-value problem $$displaylines{ -(varphi_p (u'' =lambda f(u mbox{ in }(0,1 cr u(0 = u(1 =0,, }$$ where $p>1$, $lambda >0$ and $varphi_p (x =| x|^{p-2}x$. The nonlinearity $f$ is cubic-like with three distinct roots 0=a less than b less than c. By means of a quadrature method, we provide the exact number of solutions for all $lambda >0$. This way we extend a recent result, for $p=2$, by Korman et al. cite{KormanLiOuyang} to the general case $p>1$. We shall prove that when 1less than $pleq 2$ the structure of the solution set is exactly the same as that studied in the case $p=2$ by Korman et al. cite{KormanLiOuyang}, and strictly different in the case $p>2$.

Exact soliton-like solutions of the radial Gross–Pitaevskii equation

International Nuclear Information System (INIS)

Toikka, L A; Hietarinta, J; Suominen, K-A

2012-01-01

We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e. radial) Gross–Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlevé transcendent. In each case the potential can be chosen to be time independent. (paper)

Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results

Science.gov (United States)

Liu, Li; Mishchenko, Michael I.

2016-01-01

We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

The variational method in quantum mechanics: an elementary introduction

Science.gov (United States)

Borghi, Riccardo

2018-05-01

Variational methods in quantum mechanics are customarily presented as invaluable techniques to find approximate estimates of ground state energies. In the present paper a short catalogue of different celebrated potential distributions (both 1D and 3D), for which an exact and complete (energy and wavefunction) ground state determination can be achieved in an elementary way, is illustrated. No previous knowledge of calculus of variations is required. Rather, in all presented cases the exact energy functional minimization is achieved by using only a couple of simple mathematical tricks: ‘completion of square’ and integration by parts. This makes our approach particularly suitable for undergraduates. Moreover, the key role played by particle localization is emphasized through the entire analysis. This gentle introduction to the variational method could also be potentially attractive for more expert students as a possible elementary route toward a rather advanced topic on quantum mechanics: the factorization method. Such an unexpected connection is outlined in the final part of the paper.

Propagation of nuclear data uncertainty: Exact or with covariances

Directory of Open Access Journals (Sweden)

van Veen D.

2010-10-01

Full Text Available Two distinct methods of propagation for basic nuclear data uncertainties to large scale systems will be presented and compared. The “Total Monte Carlo” method is using a statistical ensemble of nuclear data libraries randomly generated by means of a Monte Carlo approach with the TALYS system. These libraries are then directly used in a large number of reactor calculations (for instance with MCNP after which the exact probability distribution for the reactor parameter is obtained. The second method makes use of available covariance files and can be done in a single reactor calculation (by using the perturbation method. In this exercise, both methods are using consistent sets of data files, which implies that covariance files used in the second method are directly obtained from the randomly generated nuclear data libraries from the first method. This is a unique and straightforward comparison allowing to directly apprehend advantages and drawbacks of each method. Comparisons for different reactions and criticality-safety benchmarks from 19F to actinides will be presented. We can thus conclude whether current methods for using covariance data are good enough or not.

Exact Relativistic `Antigravity' Propulsion

Science.gov (United States)

Felber, Franklin S.

2006-01-01

The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.

Exact solutions with solitary patterns for the Zakharov-Kuznetsov equations with fully nonlinear dispersion

International Nuclear Information System (INIS)

Inc, Mustafa

2007-01-01

In this paper, the nonlinear dispersive Zakharov-Kuznetsov ZK(m, n, k) equations are solved exactly by using the Adomian decomposition method. The two special cases, ZK(2, 2, 2) and ZK(3, 3, 3), are chosen to illustrate the concrete scheme of the decomposition method in ZK(m, n, k) equations. General formulas for the solutions of ZK(m, n, k) equations are established

Lattice sigma models with exact supersymmetry

International Nuclear Information System (INIS)

Simon Catterall; Sofiane Ghadab

2004-01-01

We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and twisted versions of conventional supersymmetric sigma models with N=2 supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built from the original supercharges. The lattice theories possess local actions and exhibit no fermion doubling. In the two and four dimensional theories we show that these lattice theories are invariant under additional discrete symmetries. We argue that the presence of these exact symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry in the continuum limit. As a concrete example we show preliminary numerical results from a simulation of the O(3) supersymmetric sigma model in two dimensions. (author)

Exact and useful optimization methods for microeconomics

NARCIS (Netherlands)

Balder, E.J.

2011-01-01

This paper points out that the treatment of utility maximization in current textbooks on microeconomic theory is deficient in at least three respects: breadth of coverage, completeness-cum-coherence of solution methods and mathematical correctness. Improvements are suggested in the form of a

Exact solutions and numerical simulation of longitudinal vibration of the Rayleigh-Love rods with variable cross-sections

CSIR Research Space (South Africa)

Shatalov, M

2012-09-01

Full Text Available Exact solutions of equations of longitudinal vibration of conical and exponential rod are analyzed for the Rayleigh-Love model. These solutions are used as reference results for checking accuracy of the method of lines. It is shown that the method...

SUSY non-Abelian gauge models: exact beta function from one loop of perturbation theory

International Nuclear Information System (INIS)

Shifman, M.A.; Vajnshtejn, A.I.; Zakharov, V.I.

1985-01-01

The method for calculating the exact β function (to all orders in the coupling constant) proposed earlier in supersymmetric electrodynamics is extended. The starting point is the observation that the low-energy effective action is exhausted by one loop provided that the theory is regularized supersymmetrically both in the ultraviolet and infrared domains in four dimensions. The Pouli-Villars method of the ultraviolet regularization is used. Two methods for the infrared regularization are considered. The first one - quantization in a box with a finite volume L 3 - is universally applicable to anygauge theory. The second method is based on the effective Higgs mechanism for mass generation and requires the presence of certain matter superfields in the lagrangian. Within this method the necessary condition is the existence of flat directions, so called valeys, along which the vacuum energy vanishes. The theory is quantized near epsilon non-vanishing value of the scalar field from the bottom of the valley. After calculating the one-loop effective action one and the same exact expression is obtained for the β function within the both approaches, and it also coincides with our earlier result extracted from instanton calculus. A few remarks on the problem of anomalies in SUSY gauge theories are presented

Explicit and exact solutions for a generalized long-short wave resonance equations with strong nonlinear term

International Nuclear Information System (INIS)

Shang Yadong

2005-01-01

In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions

Benchmarking GW against exact diagonalization for semiempirical models

DEFF Research Database (Denmark)

Kaasbjerg, Kristen; Thygesen, Kristian Sommer

2010-01-01

We calculate ground-state total energies and single-particle excitation energies of seven pi-conjugated molecules described with the semiempirical Pariser-Parr-Pople model using self-consistent many-body perturbation theory at the GW level and exact diagonalization. For the total energies GW capt...... (Hubbard models) where correlation effects dominate over screening/relaxation effects. Finally we illustrate the important role of the derivative discontinuity of the true exchange-correlation functional by computing the exact Kohn-Sham levels of benzene....

Semi-exact solution of elastic non-uniform thickness and density rotating disks by homotopy perturbation and Adomian's decomposition methods. Part I: Elastic solution

International Nuclear Information System (INIS)

Hojjati, M.H.; Jafari, S.

2008-01-01

In this work, two powerful analytical methods, namely homotopy perturbation method (HPM) and Adomian's decomposition method (ADM), are introduced to obtain distributions of stresses and displacements in rotating annular elastic disks with uniform and variable thicknesses and densities. The results obtained by these methods are then compared with the verified variational iteration method (VIM) solution. He's homotopy perturbation method which does not require a 'small parameter' has been used and a homotopy with an imbedding parameter p element of [0,1] is constructed. The method takes the full advantage of the traditional perturbation methods and the homotopy techniques and yields a very rapid convergence of the solution. Adomian's decomposition method is an iterative method which provides analytical approximate solutions in the form of an infinite power series for nonlinear equations without linearization, perturbation or discretization. Variational iteration method, on the other hand, is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. This study demonstrates the ability of the methods for the solution of those complicated rotating disk cases with either no or difficult to find fairly exact solutions without the need to use commercial finite element analysis software. The comparison among these methods shows that although the numerical results are almost the same, HPM is much easier, more convenient and efficient than ADM and VIM

Exact solutions for some discrete models of the Boltzmann equation

International Nuclear Information System (INIS)

Cabannes, H.; Hong Tiem, D.

1987-01-01

For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

Large-N limit of the two-Hermitian-matrix model by the hidden BRST method

International Nuclear Information System (INIS)

Alfaro, J.

1993-01-01

This paper discusses the large-N limit of the two-Hermitian-matrix model in zero dimensions, using the hidden Becchi-Rouet-Stora-Tyutin method. A system of integral equations previously found is solved, showing that it contained the exact solution of the model in leading order of large N

Exact Algorithms for Solving Stochastic Games

DEFF Research Database (Denmark)

Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels

2012-01-01

Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....

Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase

CERN Document Server

Bleher, P M

2005-01-01

The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on the Yang-Baxter equations and it represents the free energy in terms of an $N\\times N$ Hankel determinant. Paul Zinn-Justin observed that the Izergin-Korepin formula can be re-expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction. We use this observation to obtain the large $N$ asymptotics of the six-vertex model with DWBC in the disordered phase. The solution is based on the Riemann-Hilbert approach and the Deift-Zhou nonlinear steepest descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign matrices (the ASM problem) is a special case of the the six-vertex model. We compare the obtained exact solution of the six-vertex model with known exact results for the 1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called f...

Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins.

Science.gov (United States)

Ghose, R; Fushman, D; Cowburn, D

2001-04-01

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand. Copyright 2001 Academic Press.

Multilocus lod scores in large pedigrees: combination of exact and approximate calculations.

Science.gov (United States)

Tong, Liping; Thompson, Elizabeth

2008-01-01

To detect the positions of disease loci, lod scores are calculated at multiple chromosomal positions given trait and marker data on members of pedigrees. Exact lod score calculations are often impossible when the size of the pedigree and the number of markers are both large. In this case, a Markov Chain Monte Carlo (MCMC) approach provides an approximation. However, to provide accurate results, mixing performance is always a key issue in these MCMC methods. In this paper, we propose two methods to improve MCMC sampling and hence obtain more accurate lod score estimates in shorter computation time. The first improvement generalizes the block-Gibbs meiosis (M) sampler to multiple meiosis (MM) sampler in which multiple meioses are updated jointly, across all loci. The second one divides the computations on a large pedigree into several parts by conditioning on the haplotypes of some 'key' individuals. We perform exact calculations for the descendant parts where more data are often available, and combine this information with sampling of the hidden variables in the ancestral parts. Our approaches are expected to be most useful for data on a large pedigree with a lot of missing data. (c) 2007 S. Karger AG, Basel

Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

International Nuclear Information System (INIS)

Fu Jingli; Jimenez, Salvador; Tang Yifa; Vazquez, Luis

2008-01-01

In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out

Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Fu Jingli [Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018 (China)], E-mail: sqfujingli@163.com; Jimenez, Salvador [Departamento de Matematica Aplicada TTII, E.T.S.I. Telecomunicacion, Universidad Politecnica de Madrid, 28040 Madrid (Spain); Tang Yifa [State Key Laboratory of Scientific and Engineering Computing, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Vazquez, Luis [Departamento de Matematica Aplicada Facultad de Informatica, Universidad Complutense de Madrid, 28040 Madrid (Spain); Centro de Astrobiologia (CSIC-INTA), Torrejon de Ardoz, 28850 Madrid (Spain)

2008-03-03

In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

Science.gov (United States)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Exact 2-point function in Hermitian matrix model

International Nuclear Information System (INIS)

Morozov, A.; Shakirov, Sh.

2009-01-01

J. Harer and D. Zagier have found a strikingly simple generating function [1,2] for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.

Exact solutions in string-motivated scalar-field cosmology

International Nuclear Information System (INIS)

Oezer, M.; Taha, M.O.

1992-01-01

Two exact cosmological solutions to a scalar-field potential motivated by six-dimensional (6D) Einstein-Maxwell theory are given. The resulting pure scalar-field cosmology is free of singularity and causality problems but conserves entropy. These solutions are then extended into exact cosmological solutions for a decaying scalar field with an approximate two-loop 4D string potential. The resulting cosmology is, for both solutions, free of cosmological problems and close to the standard cosmology of the radiation era

Efficiently computing exact geodesic loops within finite steps.

Science.gov (United States)

Xin, Shi-Qing; He, Ying; Fu, Chi-Wing

2012-06-01

Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.

Exactly soluble matrix models

International Nuclear Information System (INIS)

Raju Viswanathan, R.

1991-09-01

We study examples of one dimensional matrix models whose potentials possess an energy spectrum that can be explicitly determined. This allows for an exact solution in the continuum limit. Specifically, step-like potentials and the Morse potential are considered. The step-like potentials show no scaling behaviour and the Morse potential (which corresponds to a γ = -1 model) has the interesting feature that there are no quantum corrections to the scaling behaviour in the continuum limit. (author). 5 refs

Exact solutions for a system of nonlinear plasma fluid equations

International Nuclear Information System (INIS)

Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

1991-04-01

A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

Linear orbit parameters for the exact equations of motion

International Nuclear Information System (INIS)

Parzen, G.

1995-01-01

This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The β, α and ψ functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittance. The differential equations for η = x/β 1/2 is found. New relationships between α, β, ψ and ν are derived

Universality in exact quantum state population dynamics and control

International Nuclear Information System (INIS)

Wu, Lian-Ao; Segal, Dvira; Brumer, Paul; Egusquiza, Inigo L.

2010-01-01

We consider an exact population transition, defined as the probability of finding a state at a final time that is exactly equal to the probability of another state at the initial time. We prove that, given a Hamiltonian, there always exists a complete set of orthogonal states that can be employed as time-zero states for which this exact population transition occurs. The result is general: It holds for arbitrary systems, arbitrary pairs of initial and final states, and for any time interval. The proposition is illustrated with several analytic models. In particular, we demonstrate that in some cases, by tuning the control parameters, a complete transition might occur, where a target state, vacant at t=0, is fully populated at time τ.

Fuzziness and Foundations of Exact and Inexact Sciences

CERN Document Server

Dompere, Kofi Kissi

2013-01-01

The monograph is an examination of the fuzzy rational foundations of the structure of exact and inexact sciences over the epistemological space which is distinguished from the ontological space. It is thus concerned with the demarcation problem. It examines exact science and its critique of inexact science. The role of fuzzy rationality in these examinations is presented. The driving force of the discussions is the nature of the information that connects the cognitive relational structure of the epistemological space to the ontological space for knowing. The knowing action is undertaken by decision-choice agents who must process information to derive exact-inexact or true-false conclusions. The information processing is done with a paradigm and laws of thought that constitute the input-output machine. The nature of the paradigm selected depends on the nature of the information structure that is taken as input of the thought processing. Generally, the information structure received from the ontological space i...

Polynomial conservation laws and exact solutions connected with isometrical and homothetic symmetries in the nonlinear sigma model

International Nuclear Information System (INIS)

Ivanov, G.G.

1985-01-01

In the non linear delta-model conserved tensor currents connected with the isometrical, homothetic and affine motions in the space Vsup(N) of the chiral field values are constructed. New classes of the exact solutions are obtained in the SO(3) and SO(5) invariant delta-models using the connection between the groups of isometrical and homothetic motions in the space-time and isometrical motions in Vsup(N). Some methods of obtaining exact solutions in 4-dimensional delta-model with non trivial topological charge are considered

Exact analysis of Packet Reversed Packet Combining Scheme and Modified Packet Combining Scheme; and a combined scheme

International Nuclear Information System (INIS)

Bhunia, C.T.

2007-07-01

Packet combining scheme is a well defined simple error correction scheme for the detection and correction of errors at the receiver. Although it permits a higher throughput when compared to other basic ARQ protocols, packet combining (PC) scheme fails to correct errors when errors occur in the same bit locations of copies. In a previous work, a scheme known as Packet Reversed Packet Combining (PRPC) Scheme that will correct errors which occur at the same bit location of erroneous copies, was studied however PRPC does not handle a situation where a packet has more than 1 error bit. The Modified Packet Combining (MPC) Scheme that can correct double or higher bit errors was studied elsewhere. Both PRPC and MPC schemes are believed to offer higher throughput in previous studies, however neither adequate investigation nor exact analysis was done to substantiate this claim of higher throughput. In this work, an exact analysis of both PRPC and MPC is carried out and the results reported. A combined protocol (PRPC and MPC) is proposed and the analysis shows that it is capable of offering even higher throughput and better error correction capability at high bit error rate (BER) and larger packet size. (author)

Fast Exact Euclidean Distance (FEED) Transformation

NARCIS (Netherlands)

Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.

2004-01-01

Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number

A k-space method for acoustic propagation using coupled first-order equations in three dimensions.

Science.gov (United States)

Tillett, Jason C; Daoud, Mohammad I; Lacefield, James C; Waag, Robert C

2009-09-01

A previously described two-dimensional k-space method for large-scale calculation of acoustic wave propagation in tissues is extended to three dimensions. The three-dimensional method contains all of the two-dimensional method features that allow accurate and stable calculation of propagation. These features are spectral calculation of spatial derivatives, temporal correction that produces exact propagation in a homogeneous medium, staggered spatial and temporal grids, and a perfectly matched boundary layer. Spectral evaluation of spatial derivatives is accomplished using a fast Fourier transform in three dimensions. This computational bottleneck requires all-to-all communication; execution time in a parallel implementation is therefore sensitive to node interconnect latency and bandwidth. Accuracy of the three-dimensional method is evaluated through comparisons with exact solutions for media having spherical inhomogeneities. Large-scale calculations in three dimensions were performed by distributing the nearly 50 variables per voxel that are used to implement the method over a cluster of computers. Two computer clusters used to evaluate method accuracy are compared. Comparisons of k-space calculations with exact methods including absorption highlight the need to model accurately the medium dispersion relationships, especially in large-scale media. Accurately modeled media allow the k-space method to calculate acoustic propagation in tissues over hundreds of wavelengths.

Exact Results in Non-Supersymmetric Large N Orientifold Field Theories

CERN Document Server

Armoni, Adi; Veneziano, Gabriele

2003-01-01

We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to N=1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the non-supersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1/N).

Previously unidentified changes in renal cell carcinoma gene expression identified by parametric analysis of microarray data

International Nuclear Information System (INIS)

Lenburg, Marc E; Liou, Louis S; Gerry, Norman P; Frampton, Garrett M; Cohen, Herbert T; Christman, Michael F

2003-01-01

Renal cell carcinoma is a common malignancy that often presents as a metastatic-disease for which there are no effective treatments. To gain insights into the mechanism of renal cell carcinogenesis, a number of genome-wide expression profiling studies have been performed. Surprisingly, there is very poor agreement among these studies as to which genes are differentially regulated. To better understand this lack of agreement we profiled renal cell tumor gene expression using genome-wide microarrays (45,000 probe sets) and compare our analysis to previous microarray studies. We hybridized total RNA isolated from renal cell tumors and adjacent normal tissue to Affymetrix U133A and U133B arrays. We removed samples with technical defects and removed probesets that failed to exhibit sequence-specific hybridization in any of the samples. We detected differential gene expression in the resulting dataset with parametric methods and identified keywords that are overrepresented in the differentially expressed genes with the Fisher-exact test. We identify 1,234 genes that are more than three-fold changed in renal tumors by t-test, 800 of which have not been previously reported to be altered in renal cell tumors. Of the only 37 genes that have been identified as being differentially expressed in three or more of five previous microarray studies of renal tumor gene expression, our analysis finds 33 of these genes (89%). A key to the sensitivity and power of our analysis is filtering out defective samples and genes that are not reliably detected. The widespread use of sample-wise voting schemes for detecting differential expression that do not control for false positives likely account for the poor overlap among previous studies. Among the many genes we identified using parametric methods that were not previously reported as being differentially expressed in renal cell tumors are several oncogenes and tumor suppressor genes that likely play important roles in renal cell

Development of Exact Matrix-Matching Inductively Coupled Plasma-Optical Emission Spectroscopy for the Analysis of Cu and K in Infant Formula

Energy Technology Data Exchange (ETDEWEB)

Lee, Ye-Ji; Yim, Yong-Hyeon [University of Science and Technology, Daejeon (Korea, Republic of); Heo, Sung Woo; Han, Myung-Sub; Lim, Youngran [Korea Research Institute of Standards and Science, Daejeon (Korea, Republic of)

2016-08-15

In the present study, we have developed an exact matrix-matching inductively coupled plasma-optical emission spectroscopy (ICP-OES) as a low-cost alternative to the isotope dilution inductively coupled plasma mass spectrometry (ICP-MS) method for accurate and precise measurements of nutrient elements K and Cu in infant formula. In spite of its high precision and accuracy, ICP-OES analysis of complex samples was not reliable due to biases originating from various matrix effects. The elaborated exact matrix-matching approach tested here demonstrated its potential to minimize biases due to matrix mismatch. The exact matrix-matching ICP-OES method was successfully validated by comparing the results with those from an isotope dilution ICP-M S method. Because the model provides reliable results without significant loss of precision, it will be an excellent choice for major element analysis in a complex sample, especially when isotope dilution is not applicable due to the l ck of alternative isotopes or the high cost of enriched isotopes.

Exact Solution of a Strongly Coupled Gauge Theory in 0 +1 Dimensions

Science.gov (United States)

Krishnan, Chethan; Kumar, K. V. Pavan

2018-05-01

Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the exact analytic solution of a specific example of such a theory: namely, the smallest colored tensor model due to Gurau and Witten that exhibits nonlinearities. We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory. The physics of the spectrum, despite the smallness of N , exhibits rudimentary signatures of chaos. This Letter is a summary of our main results: the technical details will appear in companion paper [C. Krishnan and K. V. Pavan Kumar, Complete solution of a gauged tensor model, arXiv:1804.10103].

Toward Exact Number: Young Children Use One-to-one Correspondence to Measure Set Identity but not Numerical Equality

Science.gov (United States)

Izard, Véronique; Streri, Arlette; Spelke, Elizabeth S.

2014-01-01

Exact integer concepts are fundamental to a wide array of human activities, but their origins are obscure. Some have proposed that children are endowed with a system of natural number concepts, whereas others have argued that children construct these concepts by mastering verbal counting or other numeric symbols. This debate remains unresolved, because it is difficult to test children’s mastery of the logic of integer concepts without using symbols to enumerate large sets, and the symbols themselves could be a source of difficulty for children. Here, we introduce a new method, focusing on large quantities and avoiding the use of words or other symbols for numbers, to study children’s understanding of an essential property underlying integer concepts: the relation of exact numerical equality. Children aged 32-36 months, who possessed no symbols for exact numbers beyond 4, were given one-to-one correspondence cues to help them track a set of puppets, and their enumeration of the set was assessed by a non-verbal manual search task. Children used one-to-one correspondence relations to reconstruct exact quantities in sets of 5 or 6 objects, as long as the elements forming the sets remained the same individuals. In contrast, they failed to track exact quantities when one element was added, removed, or substituted for another. These results suggest an alternative to both nativist and symbol-based constructivist theories of the development of natural number concepts: Before learning symbols for exact numbers, children have a partial understanding of the properties of exact numbers. PMID:24680885

Exact marginality in open string field theory. A general framework

International Nuclear Information System (INIS)

Kiermaier, M.

2007-07-01

We construct analytic solutions of open bosonic string field theory for any exactly marginal deformation in any boundary conformal field theory when properly renormalized operator products of the marginal operator are given. We explicitly provide such renormalized operator products for a class of marginal deformations which include the deformations of flat D-branes in flat backgrounds by constant massless modes of the gauge field and of the scalar fields on the D-branes, the cosine potential for a space-like coordinate, and the hyperbolic cosine potential for the time-like coordinate. In our construction we use integrated vertex operators, which are closely related to finite deformations in boundary conformal field theory, while previous analytic solutions were based on unintegrated vertex operators. We also introduce a modified star product to formulate string field theory around the deformed background. (orig.)

Momentum-space cluster dual-fermion method

Science.gov (United States)

Iskakov, Sergei; Terletska, Hanna; Gull, Emanuel

2018-03-01

Recent years have seen the development of two types of nonlocal extensions to the single-site dynamical mean field theory. On one hand, cluster approximations, such as the dynamical cluster approximation, recover short-range momentum-dependent correlations nonperturbatively. On the other hand, diagrammatic extensions, such as the dual-fermion theory, recover long-ranged corrections perturbatively. The correct treatment of both strong short-ranged and weak long-ranged correlations within the same framework is therefore expected to lead to a quick convergence of results, and offers the potential of obtaining smooth self-energies in nonperturbative regimes of phase space. In this paper, we present an exact cluster dual-fermion method based on an expansion around the dynamical cluster approximation. Unlike previous formulations, our method does not employ a coarse-graining approximation to the interaction, which we show to be the leading source of error at high temperature, and converges to the exact result independently of the size of the underlying cluster. We illustrate the power of the method with results for the second-order cluster dual-fermion approximation to the single-particle self-energies and double occupancies.

Exact approaches for scaffolding

OpenAIRE

Weller, Mathias; Chateau, Annie; Giroudeau, Rodolphe

2015-01-01

This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We ex...

Exact solutions of a nonpolynomially nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Parwani, R.; Tan, H.S.

2007-01-01

A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics

New exact solutions of the Einstein—Maxwell equations for magnetostatic fields

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R.K.

2012-01-01

The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein—Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions

Asymptotically exact localized expansions for signals in the time–frequency domain

International Nuclear Information System (INIS)

Muzhikyan, Aramazd H; Avanesyan, Gagik T

2012-01-01

Based on a unique waveform with strong exponential localization property, an exact mathematical method for solving problems in signal analysis in the time–frequency domain is presented. An analogue of the Gabor frame exposes the non-commutative geometry of the time–frequency plane. Signals are visualized using the constructed graphical representation. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

Exact computation of the 9-j symbols

International Nuclear Information System (INIS)

Lai Shantao; Chiu Jingnan

1992-01-01

A useful algebraic formula for the 9-j symbol has been rewritten for convenient use on a computer. A simple FORTRAN program for the exact computation of 9-j symbols has been written for the VAX with VMS version V5,4-1 according to this formula. The results agree with the approximate values in existing literature. Some specific values of 9-j symbols needed for the intensity and alignments of three-photon nonresonant transitions are tabulated. Approximate 9-j symbol values beyond the limitation of the computer can also be computed by this program. The computer code of the exact computation of 3-j, 6-j and 9-j symbols are available through electronic mail upon request. (orig.)

Exact deconstruction of the 6D (2,0) theory

Science.gov (United States)

Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodríguez-Gómez, D.

2017-06-01

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: in the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the "half-BPS" limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 × T 2. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

Exact deconstruction of the 6D (2,0) theory

International Nuclear Information System (INIS)

Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodriguez-Gomez, D.

2017-06-01

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2 , starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the ''half-BPS'' limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 x T 2 . In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

Exact Stiffness for Beams on Kerr-Type Foundation: The Virtual Force Approach

Directory of Open Access Journals (Sweden)

Suchart Limkatanyu

2013-01-01

Full Text Available This paper alternatively derives the exact element stiffness equation for a beam on Kerr-type foundation. The shear coupling between the individual Winkler-spring components and the peripheral discontinuity at the boundaries between the loaded and the unloaded soil surfaces are taken into account in this proposed model. The element flexibility matrix is derived based on the virtual force principle and forms the core of the exact element stiffness matrix. The sixth-order governing differential compatibility of the problem is revealed using the virtual force principle and solved analytically to obtain the exact force interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix based on the exact force interpolation functions. The so-called “natural” element stiffness matrix is obtained by inverting the exact element flexibility matrix. One numerical example is utilized to confirm the accuracy and the efficiency of the proposed beam element on Kerr-type foundation and to show a more realistic distribution of interactive foundation force.

Exact simulation of conditioned Wright-Fisher models.

Science.gov (United States)

Zhao, Lei; Lascoux, Martin; Waxman, David

2014-12-21

Forward and backward simulations play an increasing role in population genetics, in particular when inferring the relative importance of evolutionary forces. It is therefore important to develop fast and accurate simulation methods for general population genetics models. Here we present an exact simulation method that generates trajectories of an allele׳s frequency in a finite population, as described by a general Wright-Fisher model. The method generates conditioned trajectories that start from a known frequency at a known time, and which achieve a specific final frequency at a known final time. The simulation method applies irrespective of the smallness of the probability of the transition between the initial and final states, because it is not based on rejection of trajectories. We illustrate the method on several different populations where a Wright-Fisher model (or related) applies, namely (i) a locus with 2 alleles, that is subject to selection and mutation; (ii) a locus with 3 alleles, that is subject to selection; (iii) a locus in a metapopulation consisting of two subpopulations of finite size, that are subject to selection and migration. The simulation method allows the generation of conditioned trajectories that can be used for the purposes of visualisation, the estimation of summary statistics, and the development/testing of new inferential methods. The simulated trajectories provide a very simple approach to estimating quantities that cannot easily be expressed in terms of the transition matrix, and can be applied to finite Markov chains other than the Wright-Fisher model. Copyright © 2014 Elsevier Ltd. All rights reserved.

Novel correlations in two dimensions: Some exact solutions

International Nuclear Information System (INIS)

Murthy, M.V.; Bhaduri, R.K.; Sen, D.

1996-01-01

We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring. copyright 1996 The American Physical Society

Accelerating exact schedulability analysis for fixed-priority pre-emptive scheduling

NARCIS (Netherlands)

Hang, Y.; Jiale, Z.; Keskin, U.; Bril, R.J.

2010-01-01

The schedulability analysis for fixed-priority preemptive scheduling (FPPS) plays a significant role in the real-time systems domain. The so-called Hyperplanes Exact Test (HET) [1] is an example of an exact schedulability test for FPPS. In this paper, we aim at improving the efficiency of HET by

Exact WKB analysis and cluster algebras

International Nuclear Information System (INIS)

Iwaki, Kohei; Nakanishi, Tomoki

2014-01-01

We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schrödinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes automorphisms associated with periods of cluster algebras. The paper also includes an extensive introduction of the exact WKB analysis and the surface realization of cluster algebras for nonexperts. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)

A position-dependent mass model for the Thomas–Fermi potential: Exact solvability and relation to δ-doped semiconductors

Energy Technology Data Exchange (ETDEWEB)

Schulze-Halberg, Axel, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary IN 46408 (United States); García-Ravelo, Jesús; Pacheco-García, Christian [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, Zacatenco, 07738 México D.F. (Mexico); Juan Peña Gil, José [Universidad Autónoma Metropolitana - Azcapotzalco, CBI - Area de Física Atómica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 México D.F. (Mexico)

2013-06-15

We consider the Schrödinger equation in the Thomas–Fermi field, a model that has been used for describing electron systems in δ-doped semiconductors. It is shown that the problem becomes exactly-solvable if a particular effective (position-dependent) mass distribution is incorporated. Orthogonal sets of normalizable bound state solutions are constructed in explicit form, and the associated energies are determined. We compare our results with the corresponding findings on the constant-mass problem discussed by Ioriatti (1990) [13]. -- Highlights: ► We introduce an exactly solvable, position-dependent mass model for the Thomas–Fermi potential. ► Orthogonal sets of solutions to our model are constructed in closed form. ► Relation to delta-doped semiconductors is discussed. ► Explicit subband bottom energies are calculated and compared to results obtained in a previous study.

A position-dependent mass model for the Thomas–Fermi potential: Exact solvability and relation to δ-doped semiconductors

International Nuclear Information System (INIS)

Schulze-Halberg, Axel; García-Ravelo, Jesús; Pacheco-García, Christian; Juan Peña Gil, José

2013-01-01

We consider the Schrödinger equation in the Thomas–Fermi field, a model that has been used for describing electron systems in δ-doped semiconductors. It is shown that the problem becomes exactly-solvable if a particular effective (position-dependent) mass distribution is incorporated. Orthogonal sets of normalizable bound state solutions are constructed in explicit form, and the associated energies are determined. We compare our results with the corresponding findings on the constant-mass problem discussed by Ioriatti (1990) [13]. -- Highlights: ► We introduce an exactly solvable, position-dependent mass model for the Thomas–Fermi potential. ► Orthogonal sets of solutions to our model are constructed in closed form. ► Relation to delta-doped semiconductors is discussed. ► Explicit subband bottom energies are calculated and compared to results obtained in a previous study

Atypical extended electronic states in an infinite Vicsek fractal: An exact result

International Nuclear Information System (INIS)

Chakrabarti, A.; Bhattacharyya, B.

1996-01-01

We present a class of extended electronic wave functions on a Vicsek fractal. The transmittivity of arbitrarily large fractal lattices corresponding to these particular extended-state eigenvalues exhibits a power-law decay with increasing system size. The eigenvalues corresponding to the above extended states as well as the scaling law for the transmittivity have been exactly calculated using a real-space renormalization-group method. copyright 1996 The American Physical Society

Exact traveling wave solution of nonlinear variants of the RLW and the PHI-four equations

Energy Technology Data Exchange (ETDEWEB)

Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111 (Egypt); Department of Mathematics, Teacher' s College, Bisha, P.O. Box 551 (Saudi Arabia)], E-mail: asoliman_99@yahoo.com

2007-08-27

By means of the modified extended tanh-function (METF) method the multiple traveling wave solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system. The solutions for the nonlinear equations such as variants of the RLW and variant of the PHI-four equations are exactly obtained and so the efficiency of the method can be demonstrated.

Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations

Directory of Open Access Journals (Sweden)

Zhanhua Yu

2011-01-01

Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

Science.gov (United States)

Rivera, R.; Villarroel, D.

2002-10-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

International Nuclear Information System (INIS)

Rivera, R.; Villarroel, D.

2002-01-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics

Exact axially symmetric galactic dynamos

Science.gov (United States)

Henriksen, R. N.; Woodfinden, A.; Irwin, J. A.

2018-05-01

We give a selection of exact dynamos in axial symmetry on a galactic scale. These include some steady examples, at least one of which is wholly analytic in terms of simple functions and has been discussed elsewhere. Most solutions are found in terms of special functions, such as associated Lagrange or hypergeometric functions. They may be considered exact in the sense that they are known to any desired accuracy in principle. The new aspect developed here is to present scale-invariant solutions with zero resistivity that are self-similar in time. The time dependence is either a power law or an exponential factor, but since the geometry of the solution is self-similar in time we do not need to fix a time to study it. Several examples are discussed. Our results demonstrate (without the need to invoke any other mechanisms) X-shaped magnetic fields and (axially symmetric) magnetic spiral arms (both of which are well observed and documented) and predict reversing rotation measures in galaxy haloes (now observed in the CHANG-ES sample) as well as the fact that planar magnetic spirals are lifted into the galactic halo.

New version of PLNoise: a package for exact numerical simulation of power-law noises

Science.gov (United States)

Milotti, Edoardo

2007-08-01

installed on the target machine. No. of lines in distributed program, including test data, etc.:2975 No. of bytes in distributed program, including test data, etc.:194 588 Distribution format:tar.gz Catalogue identifier of previous version: ADXV_v1_0 Journal reference of previous version: Comput. Phys. Comm. 175 (2006) 212 Does the new version supersede the previous version?: Yes Nature of problem: Exact generation of different types of colored noise. Solution method: Random superposition of relaxation processes [E. Milotti, Phys. Rev. E 72 (2005) 056701], possibly followed by an integration step to produce noise with spectral index >2. Reasons for the new version: Extension to 1/f noises with spectral index 2<α⩽4: the new version generates both noises with spectral with spectral index 0<α⩽2 and with 2<α⩽4. Summary of revisions: Although the overall structure remains the same, one routine has been added and several changes have been made throughout the code to include the new integration step. Unusual features: The algorithm is theoretically guaranteed to be exact, and unlike all other existing generators it can generate samples with uneven spacing. Additional comments: The program requires an initialization step; for some parameter sets this may become rather heavy. Running time: Running time varies widely with different input parameters, however in a test run like the one in Section 3 in the long write-up, the generation routine took on average about 75 μs for each sample.

THE METHOD OF CONSTRUCTING A BOOLEAN FORMULA OF A POLYGON IN THE DISJUNCTIVE NORMAL FORM

Directory of Open Access Journals (Sweden)

A. A. Butov

2014-01-01

Full Text Available The paper focuses on finalizing the method of finding a polygon Boolean formula in disjunctive normal form, described in the previous article [1]. An improved method eliminates the drawback asso-ciated with the existence of a class of problems for which the solution is only approximate. The pro-posed method always allows to find an exact solution. The method can be used, in particular, in the systems of computer-aided design of integrated circuits topology.

Exact deconstruction of the 6D (2,0) theory

Energy Technology Data Exchange (ETDEWEB)

Hayling, J.; Papageorgakis, C. [Queen Mary Univ. of London (United Kingdom). CRST and School of Physics and Astronomy; Pomoni, E. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Rodriguez-Gomez, D. [Oviedo Univ. (Spain). Dept. of Physics

2017-06-15

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T{sup 2}, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the ''half-BPS'' limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S{sup 4} to the (2,0) partition function on S{sup 4} x T{sup 2}. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

5D Lovelock gravity: New exact solutions with torsion

Science.gov (United States)

Cvetković, B.; Simić, D.

2016-10-01

Five-dimensional Lovelock gravity is investigated in the first order formalism. A new class of exact solutions is constructed: the Bañados, Teitelboim, Zanelli black rings with and without torsion. We show that our solution with torsion exists in a different sector of the Lovelock gravity, as compared to the Lovelock Chern-Simons sector or the one investigated by Canfora et al. The conserved charges of the solutions are found using Nester's formula, and the results are confirmed by the canonical method. We show that the theory linearized around the background with torsion possesses two additional degrees of freedom with respect to general relativity.

Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

Science.gov (United States)

Tisdell, C. C.

2017-01-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

Exact route-length formulas and a storage location assignment heuristic for picker-to-parts warehouses

NARCIS (Netherlands)

Dijkstra, Arjan; Roodbergen, Kees Jan

2017-01-01

Order picking is one of the most time-critical processes in warehouses. We focus on the combined effects of routing methods and storage location assignment on process performance. We present exact formulas for the average route length under any storage location assignment for four common routing

An hp-adaptive strategy for the solution of the exact kernel curved wire Pocklington equation

NARCIS (Netherlands)

D.J.P. Lahaye (Domenico); P.W. Hemker (Piet)

2007-01-01

textabstractIn this paper we introduce an adaptive method for the numerical solution of the Pocklington integro-differential equation with exact kernel for the current induced in a smoothly curved thin wire antenna. The hp-adaptive technique is based on the representation of the discrete solution,

TVT-Exact and midurethral sling (SLING-IUFT) operative procedures: a randomized study.

Science.gov (United States)

Aniuliene, Rosita; Aniulis, Povilas; Skaudickas, Darijus

2015-01-01

The aim of the study is to compare results, effectiveness and complications of TVT exact and midurethral sling (SLING-IUFT) operations in the treatment of female stress urinary incontinence (SUI). A single center nonblind, randomized study of women with SUI who were randomized to TVT-Exact and SLING-IUFT was performed by one surgeon from April 2009 to April 2011. SUI was diagnosed on coughing and Valsalva test and urodynamics (cystometry and uroflowmetry) were assessed before operation and 1 year after surgery. This was a prospective randomized study. The follow up period was 12 months. 76 patients were operated using the TVT-Exact operation and 78 patients - using the SLING-IUFT operation. There was no statistically significant differences between groups for BMI, parity, menopausal status and prolapsed stage (no patients had cystocele greater than stage II). Mean operative time was significantly shorter in the SLING-IUFT group (19 ± 5.6 min.) compared with the TVT-Exact group (27 ± 7.1 min.). There were statistically significant differences in the effectiveness of both procedures: TVT-Exact - at 94.5% and SLING-IUFT - at 61.2% after one year. Hospital stay was statistically significantly shorter in the SLING-IUFT group (1. 2 ± 0.5 days) compared with the TVT-Exact group (3.5 ± 1.5 days). Statistically significantly fewer complications occurred in the SLING-IUFT group. the TVT-Exact and SLING-IUFT operations are both effective for surgical treatment of female stress urinary incontinence. The SLING-IUFT involved a shorter operation time and lower complications rate., the TVT-Exact procedure had statistically significantly more complications than the SLING-IUFT operation, but a higher effectiveness.

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025

Model checking exact cost for attack scenarios

DEFF Research Database (Denmark)

Aslanyan, Zaruhi; Nielson, Flemming

2017-01-01

Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support....... However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....

An Exactly Solvable Supersymmetric Model of Semimagic Nuclei

International Nuclear Information System (INIS)

Balantekin, A. B.; Gueven, Nurtac; Pehlivan, Yamac

2008-01-01

A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It is shown that such an interaction leads to an exactly solvable model whose (0 + ) eigenstates and energies can be computed very easily with the help of the algebraic Bethe ansatz method. It is also shown that the model has a supersymmetry which connects the spectra of some semimagic nuclei. The results obtained from this model for the semimagic Ni isotopes from 58 Ni to 68 Ni are given. In addition, a new and easier technique for calculating the energy eigenvalues from the Bethe ansatz equations is also presented.

Stability conditions for exact-exchange Kohn-Sham methods and their relation to correlation energies from the adiabatic-connection fluctuation-dissipation theorem.

Science.gov (United States)

Bleiziffer, Patrick; Schmidtel, Daniel; Görling, Andreas

2014-11-28

The occurrence of instabilities, in particular singlet-triplet and singlet-singlet instabilities, in the exact-exchange (EXX) Kohn-Sham method is investigated. Hessian matrices of the EXX electronic energy with respect to the expansion coefficients of the EXX effective Kohn-Sham potential in an auxiliary basis set are derived. The eigenvalues of these Hessian matrices determine whether or not instabilities are present. Similar as in the corresponding Hartree-Fock case instabilities in the EXX method are related to symmetry breaking of the Hamiltonian operator for the EXX orbitals. In the EXX methods symmetry breaking can easily be visualized by displaying the local multiplicative exchange potential. Examples (N2, O2, and the polyyne C10H2) for instabilities and symmetry breaking are discussed. The relation of the stability conditions for EXX methods to approaches calculating the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem is discussed. The existence or nonexistence of singlet-singlet instabilities in an EXX calculation is shown to indicate whether or not the frequency-integration in the evaluation of the correlation energy is singular in the EXX-ACFD method. This method calculates the Kohn-Sham correlation energy through the ACFD theorem theorem employing besides the Coulomb kernel also the full frequency-dependent exchange kernel and yields highly accurate electronic energies. For the case of singular frequency-integrands in the EXX-ACFD method a regularization is suggested. Finally, we present examples of molecular systems for which the self-consistent field procedure of the EXX as well as the Hartree-Fock method can converge to more than one local minimum depending on the initial conditions.

Stability conditions for exact-exchange Kohn-Sham methods and their relation to correlation energies from the adiabatic-connection fluctuation-dissipation theorem

International Nuclear Information System (INIS)

Bleiziffer, Patrick; Schmidtel, Daniel; Görling, Andreas

2014-01-01

The occurrence of instabilities, in particular singlet-triplet and singlet-singlet instabilities, in the exact-exchange (EXX) Kohn-Sham method is investigated. Hessian matrices of the EXX electronic energy with respect to the expansion coefficients of the EXX effective Kohn-Sham potential in an auxiliary basis set are derived. The eigenvalues of these Hessian matrices determine whether or not instabilities are present. Similar as in the corresponding Hartree-Fock case instabilities in the EXX method are related to symmetry breaking of the Hamiltonian operator for the EXX orbitals. In the EXX methods symmetry breaking can easily be visualized by displaying the local multiplicative exchange potential. Examples (N 2 , O 2 , and the polyyne C 10 H 2 ) for instabilities and symmetry breaking are discussed. The relation of the stability conditions for EXX methods to approaches calculating the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem is discussed. The existence or nonexistence of singlet-singlet instabilities in an EXX calculation is shown to indicate whether or not the frequency-integration in the evaluation of the correlation energy is singular in the EXX-ACFD method. This method calculates the Kohn-Sham correlation energy through the ACFD theorem theorem employing besides the Coulomb kernel also the full frequency-dependent exchange kernel and yields highly accurate electronic energies. For the case of singular frequency-integrands in the EXX-ACFD method a regularization is suggested. Finally, we present examples of molecular systems for which the self-consistent field procedure of the EXX as well as the Hartree-Fock method can converge to more than one local minimum depending on the initial conditions

Comparison between phase shift derived and exactly calculated nucleon--nucleon interaction matrix elements

International Nuclear Information System (INIS)

Gregersen, A.W.

1977-01-01

A comparison is made between matrix elements calculated using the uncoupled channel Sussex approach to second order in DWBA and matrix elements calculated using a square well potential. The square well potential illustrated the problem of the determining parameter independence balanced with the concept of phase shift difference. The super-soft core potential was used to discuss the systematics of the Sussex approach as a function of angular momentum as well as the relation between Sussex generated and effective interaction matrix elements. In the uncoupled channels the original Sussex method of extracting effective interaction matrix elements was found to be satisfactory. In the coupled channels emphasis was placed upon the 3 S 1 -- 3 D 1 coupled channel matrix elements. Comparison is made between exactly calculated matrix elements, and matrix elements derived using an extended formulation of the coupled channel Sussex method. For simplicity the potential used is a nonseparable cut-off oscillator. The eigenphases of this potential can be made to approximate the realistic nucleon--nucleon phase shifts at low energies. By using the cut-off oscillator test potential, the original coupled channel Sussex method of determining parameter independence was shown to be incapable of accurately reproducing the exact cut-off oscillator matrix elements. The extended Sussex method was found to be accurate to within 10 percent. The extended method is based upon more general coupled channel DWBA and a noninfinite oscillator wave function solution to the cut-off oscillator auxiliary potential. A comparison is made in the coupled channels between matrix elements generated using the original Sussex method and the extended method. Tables of matrix elements generated using the original uncoupled channel Sussex method and the extended coupled channel Sussex method are presented for all necessary angular momentum channels

Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions

Directory of Open Access Journals (Sweden)

Armando Martínez-Pérez

2017-10-01

Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.

Exact Boundary Controllability of Electromagnetic Fields in a General Region

International Nuclear Information System (INIS)

Eller, M. M.; Masters, J. E.

2002-01-01

We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which reduces the proof of exact controllability to the proof of continuous observability for the homogeneous adjoint system. There is no geometric restriction imposed on the domain

An Exact Confidence Region in Multivariate Calibration

OpenAIRE

Mathew, Thomas; Kasala, Subramanyam

1994-01-01

In the multivariate calibration problem using a multivariate linear model, an exact confidence region is constructed. It is shown that the region is always nonempty and is invariant under nonsingular transformations.

A unified form of exact-MSR codes via product-matrix frameworks

KAUST Repository

Lin, Sian Jheng

2015-02-01

Regenerating codes represent a class of block codes applicable for distributed storage systems. The [n, k, d] regenerating code has data recovery capability while possessing arbitrary k out of n code fragments, and supports the capability for code fragment regeneration through the use of other arbitrary d fragments, for k ≤ d ≤ n - 1. Minimum storage regenerating (MSR) codes are a subset of regenerating codes containing the minimal size of each code fragment. The first explicit construction of MSR codes that can perform exact regeneration (named exact-MSR codes) for d ≥ 2k - 2 has been presented via a product-matrix framework. This paper addresses some of the practical issues on the construction of exact-MSR codes. The major contributions of this paper include as follows. A new product-matrix framework is proposed to directly include all feasible exact-MSR codes for d ≥ 2k - 2. The mechanism for a systematic version of exact-MSR code is proposed to minimize the computational complexities for the process of message-symbol remapping. Two practical forms of encoding matrices are presented to reduce the size of the finite field.

A unified form of exact-MSR codes via product-matrix frameworks

KAUST Repository

Lin, Sian Jheng; Chung, Weiho; Han, Yunghsiangsam; Al-Naffouri, Tareq Y.

2015-01-01

Regenerating codes represent a class of block codes applicable for distributed storage systems. The [n, k, d] regenerating code has data recovery capability while possessing arbitrary k out of n code fragments, and supports the capability for code fragment regeneration through the use of other arbitrary d fragments, for k ≤ d ≤ n - 1. Minimum storage regenerating (MSR) codes are a subset of regenerating codes containing the minimal size of each code fragment. The first explicit construction of MSR codes that can perform exact regeneration (named exact-MSR codes) for d ≥ 2k - 2 has been presented via a product-matrix framework. This paper addresses some of the practical issues on the construction of exact-MSR codes. The major contributions of this paper include as follows. A new product-matrix framework is proposed to directly include all feasible exact-MSR codes for d ≥ 2k - 2. The mechanism for a systematic version of exact-MSR code is proposed to minimize the computational complexities for the process of message-symbol remapping. Two practical forms of encoding matrices are presented to reduce the size of the finite field.

On the exact solutions of high order wave equations of KdV type (I)

Science.gov (United States)

Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

2014-12-01

In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

Energy Technology Data Exchange (ETDEWEB)

Sharma, Pankaj, E-mail: psharma@rtu.ac.in; Parashar, Sandeep Kumar, E-mail: parashar2@yahoo.com [Mechanical Engineering Department, Rajasthan Technical University, Kota (India)

2016-05-06

The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.

Efficient exact optimization of multi-objective redundancy allocation problems in series-parallel systems

International Nuclear Information System (INIS)

Cao, Dingzhou; Murat, Alper; Chinnam, Ratna Babu

2013-01-01

This paper proposes a decomposition-based approach to exactly solve the multi-objective Redundancy Allocation Problem for series-parallel systems. Redundancy allocation problem is a form of reliability optimization and has been the subject of many prior studies. The majority of these earlier studies treat redundancy allocation problem as a single objective problem maximizing the system reliability or minimizing the cost given certain constraints. The few studies that treated redundancy allocation problem as a multi-objective optimization problem relied on meta-heuristic solution approaches. However, meta-heuristic approaches have significant limitations: they do not guarantee that Pareto points are optimal and, more importantly, they may not identify all the Pareto-optimal points. In this paper, we treat redundancy allocation problem as a multi-objective problem, as is typical in practice. We decompose the original problem into several multi-objective sub-problems, efficiently and exactly solve sub-problems, and then systematically combine the solutions. The decomposition-based approach can efficiently generate all the Pareto-optimal solutions for redundancy allocation problems. Experimental results demonstrate the effectiveness and efficiency of the proposed method over meta-heuristic methods on a numerical example taken from the literature.

Exact travelling wave solutions of the Whitham-Broer-Kaup and Broer-Kaup-Kupershmidt equations

International Nuclear Information System (INIS)

Xu Guiqiong; Li Zhibin

2005-01-01

In this paper, an interesting fact is found that the auxiliary equation method is also applicable to a coupled system of two different equations involving both even-order and odd-order partial derivative terms. Furthermore, singular travelling wave solutions can also be obtained by considering other types of exact solutions of auxiliary equation. The Whitham-Broer-Kaup and the (2 + 1)-dimensional Broer-Kaup-Kupershmidt equations are chosen as examples to illustrate the effectiveness of the auxiliary equation method

Exact ground and excited states of an antiferromagnetic quantum spin model

International Nuclear Information System (INIS)

Bose, I.

1989-08-01

A quasi-one-dimensional spin model which consists of a chain of octahedra of spins has been suggested for which a certain parameter regime of the Hamiltonian, the ground state, can be written down exactly. The ground state is highly degenerate and can be other than a singlet. Also, several excited states can be constructed exactly. The ground state is a local RVB state for which resonance is confined to rings of spins. Some exact numerical results for an octahedron of spins have also been reported. (author). 16 refs, 2 figs, 1 tab

Exact solutions for oscillatory shear sweep behaviors of complex fluids from the Oldroyd 8-constant framework

Science.gov (United States)

Saengow, Chaimongkol; Giacomin, A. Jeffrey

2018-03-01

In this paper, we provide a new exact framework for analyzing the most commonly measured behaviors in large-amplitude oscillatory shear flow (LAOS), a popular flow for studying the nonlinear physics of complex fluids. Specifically, the strain rate sweep (also called the strain sweep) is used routinely to identify the onset of nonlinearity. By the strain rate sweep, we mean a sequence of LAOS experiments conducted at the same frequency, performed one after another, with increasing shear rate amplitude. In this paper, we give exact expressions for the nonlinear complex viscosity and the corresponding nonlinear complex normal stress coefficients, for the Oldroyd 8-constant framework for oscillatory shear sweeps. We choose the Oldroyd 8-constant framework for its rich diversity of popular special cases (we list 18 of these). We evaluate the Fourier integrals of our previous exact solution to get exact expressions for the real and imaginary parts of the complex viscosity, and for the complex normal stress coefficients, as functions of both test frequency and shear rate amplitude. We explore the role of infinite shear rate viscosity on strain rate sweep responses for the special case of the corotational Jeffreys fluid. We find that raising η∞ raises the real part of the complex viscosity and lowers the imaginary. In our worked examples, we thus first use the corotational Jeffreys fluid, and then, for greater accuracy, we use the Johnson-Segalman fluid, to describe the strain rate sweep response of molten atactic polystyrene. For our comparisons with data, we use the Spriggs relations to generalize the Oldroyd 8-constant framework to multimode. Our generalization yields unequivocally, a longest fluid relaxation time, used to assign Weissenberg and Deborah numbers to each oscillatory shear flow experiment. We then locate each experiment in the Pipkin space.

Corollary from the Exact Expression for Enthalpy of Vaporization

OpenAIRE

A. A. Sobko

2011-01-01

A problem on determining effective volumes for atoms and molecules becomes actual due to rapidly developing nanotechnologies. In the present study an exact expression for enthalpy of vaporization is obtained, from which an exact expression is derived for effective volumes of atoms and molecules, and under certain assumptions on the form of an atom (molecule) it is possible to find their linear dimensions. The accuracy is only determined by the accuracy of measurements of thermodynamic paramet...

Exact penalty results for mathematical programs with vanishing constraints

Czech Academy of Sciences Publication Activity Database

Hoheisel, T.; Kanzow, Ch.; Outrata, Jiří

2010-01-01

Roč. 72, č. 5 (2010), s. 2514-2526 ISSN 0362-546X R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : Mathematical programs with vanishing constraints * Mathematical programs with equilibrium constraints * Exact penalization * Calmness * Subdifferential calculus * Limiting normal cone Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://library.utia.cas.cz/separaty/2010/MTR/outrata-exact penalty results for mathematical programs with vanishing constraints.pdf

Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach

Science.gov (United States)

Chen, Yusui; You, J. Q.; Yu, Ting

2014-11-01

A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.

Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

Directory of Open Access Journals (Sweden)

Emrullah Yaşar

Full Text Available In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI equation with Riemann–Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi–Kober sense. Furthermore, adapting the Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method. Keywords: Fractional Sawada–Kotera–Ito equation, Lie symmetry, Riemann–Liouville fractional derivative, Conservation laws, Exact solutions

Exact Slater integrals

International Nuclear Information System (INIS)

Golden, L.B.

1968-01-01

In atomic structure calculations, one has to evaluate the Slater integrals. In the present program, the authors evaluate exactly the Slater integral when hydrogenic wave functions are used for the bound-state orbitals. When hydrogenic wave functions are used, the Slater integrals involve integrands which can be written in the form of a product of an exponential, exp(ax) and a known analytic polynomial function, f(x). By repeated partial integration such an integral can be expressed in terms of a finite series involving the exponential, the polynomial function and its derivatives. PL/1-FORMAC has a built-in subroutine that will analytically find the derivatives of any multinomial. Thus, the finite series and hence the Slater integral can be evaluated analytically. (Auth.)

Exact matrix treatment of statistical mechanical lattice model of adsorption induced gate opening in metal-organic frameworks

International Nuclear Information System (INIS)

Dunne, Lawrence J; Manos, George

2015-01-01

Here we present a statistical mechanical lattice model which is exactly solvable using a matrix method and allows treatment of adsorption induced gate opening structural transformations of metal-organic frameworks which are nanoporous materials with exceptional adsorption properties. Modelling of these structural changes presents a serious theoretical challenge when the solid and gas species are treated in an even handed way. This exactly solvable model complements other simulation based approaches. The methodology presented here highlights the competition between the potential for adsorption and the energy required for structural transition as a driving force for the features in the adsorption isotherms. (paper)

Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system

Directory of Open Access Journals (Sweden)

Boris V. Kapitonov

2010-02-01

Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.

Hyperkaehlerian manifolds and exact β functions of two-dimensional N=4 supersymmetric σ models

International Nuclear Information System (INIS)

Morozov, A.Yu.; Perelomov, A.M.

1984-01-01

Two-dimensional supersymmetric sigma-models on cotangent bundles over CPsup(n) are investigated. These mannfolds are supplied with hyperkaehlerian metrics, and the corresponding σ-models possess N=4 supersymmetry. Also they admit instantonic solutions, which permits to apply the Novikov-Shifman-Vainshtein-Zakharov method and calculate exact β-functions. βsup(gsup(2)) = 0, as was expected

The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

Science.gov (United States)

Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.

2018-04-01

We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

THE INFLUENCE OF THE ASSESSMENT MODEL AND METHOD TOWARD THE SCIENCE LEARNING ACHIEVEMENT BY CONTROLLING THE STUDENTS? PREVIOUS KNOWLEDGE OF MATHEMATICS.

OpenAIRE

Adam rumbalifar; I. g. n. Agung; Burhanuddin tola.

2018-01-01

This research aims to study the influence of the assessment model and method toward the science learning achievement by controlling the students? previous knowledge of mathematics. This study was conducted at SMP East Seram district with the population of 295 students. This study applied a quasi-experimental method with 2 X 2 factorial design using the ANCOVA model. The findings after controlling the students\\' previous knowledge of mathematics show that the science learning achievement of th...

Exactly solvable models in many-body theory

CERN Document Server

March, N H

2016-01-01

The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.

Exact algorithms for haplotype assembly from whole-genome sequence data.

Science.gov (United States)

Chen, Zhi-Zhong; Deng, Fei; Wang, Lusheng

2013-08-15

Haplotypes play a crucial role in genetic analysis and have many applications such as gene disease diagnoses, association studies, ancestry inference and so forth. The development of DNA sequencing technologies makes it possible to obtain haplotypes from a set of aligned reads originated from both copies of a chromosome of a single individual. This approach is often known as haplotype assembly. Exact algorithms that can give optimal solutions to the haplotype assembly problem are highly demanded. Unfortunately, previous algorithms for this problem either fail to output optimal solutions or take too long time even executed on a PC cluster. We develop an approach to finding optimal solutions for the haplotype assembly problem under the minimum-error-correction (MEC) model. Most of the previous approaches assume that the columns in the input matrix correspond to (putative) heterozygous sites. This all-heterozygous assumption is correct for most columns, but it may be incorrect for a small number of columns. In this article, we consider the MEC model with or without the all-heterozygous assumption. In our approach, we first use new methods to decompose the input read matrix into small independent blocks and then model the problem for each block as an integer linear programming problem, which is then solved by an integer linear programming solver. We have tested our program on a single PC [a Linux (x64) desktop PC with i7-3960X CPU], using the filtered HuRef and the NA 12878 datasets (after applying some variant calling methods). With the all-heterozygous assumption, our approach can optimally solve the whole HuRef data set within a total time of 31 h (26 h for the most difficult block of the 15th chromosome and only 5 h for the other blocks). To our knowledge, this is the first time that MEC optimal solutions are completely obtained for the filtered HuRef dataset. Moreover, in the general case (without the all-heterozygous assumption), for the HuRef dataset our

Analysis of thin plates with holes by using exact geometrical representation within XFEM.

Science.gov (United States)

Perumal, Logah; Tso, C P; Leng, Lim Thong

2016-05-01

This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.

Exact solutions to chaotic and stochastic systems

Science.gov (United States)

González, J. A.; Reyes, L. I.; Guerrero, L. E.

2001-03-01

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.

Exact solution for a non-Markovian dissipative quantum dynamics.

Science.gov (United States)

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

Exact coefficients for higher dimensional operators with sixteen supersymmetries

Energy Technology Data Exchange (ETDEWEB)

Chen, Wei-Ming [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, R.O.C. (China); Huang, Yu-tin [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, R.O.C. (China); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Wen, Congkao [INFN Sezione di Roma “Tor Vergata' ,Via della Ricerca Scientifica, 00133 Roma (Italy)

2015-09-15

We consider constraints on higher-dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F{sup n} with MHV helicity configurations must satisfy a recursion relation, and are completely determined by that of F{sup 4}. As the F{sup 4} coefficient is known to be one-loop exact, this allows us to derive exact coefficients for all such operators. We also argue that the results are consistent with the SL(2,Z) duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb branch effective action, we again find an infinite class of operators whose coefficients are determined exactly. We also consider three-dimensional N=8 as well as six-dimensional N=(2,0),(1,0) and (1,1) theories. In all cases, we demonstrate that the coefficient of dimension-six operator must be proportional to the square of that of dimension-four.