Non-Fermi-liquid behavior: Exact results for ensembles of magnetic impurities

CERN Document Server

Zvyagin, A A

2002-01-01

In this work we consider several exactly solvable models of magnetic impurities in critical quantum antiferromagnetic spin chains and multichannel Kondo impurities. Their ground state properties are studied and the finite set of nonlinear integral equations, which exactly describe the thermodynamics of the models, is constructed. We obtain several analytic low-energy expressions for the temperature, magnetic field, and frequency dependences of important characteristics of exactly solvable disordered quantum spin models and disordered multichannel Kondo impurities with essential many-body interactions. We show that the only low-energy parameter that gets renormalized is the velocity of the low-lying excitations (or the effective crossover scale connected with each impurity); the others appear to be universal. In our study several kinds of strong disorder important for experiments were used. Some of them produce low divergences in certain characteristics of our strongly disordered critical systems (compared wit...

Integrable perturbed magnetic fields in toroidal geometry: An exact analytical flux surface label for large aspect ratio

Energy Technology Data Exchange (ETDEWEB)

Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E. [Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece)

2014-06-15

An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label.

Integrable perturbed magnetic fields in toroidal geometry: An exact analytical flux surface label for large aspect ratio

Science.gov (United States)

Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E.

2014-06-01

An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label.

Integrable perturbed magnetic fields in toroidal geometry: An exact analytical flux surface label for large aspect ratio

International Nuclear Information System (INIS)

Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E.

2014-01-01

An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label

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)

Double Potts chain and exact results for some two-dimensional models

International Nuclear Information System (INIS)

Yurishchev, M.A.

2000-11-01

A closed-form exact analytical solution for the q-state Potts model on a ladder 2x∞ with arbitrary two-, three-, and four-site interactions in a unit cell is presented. Using the obtained solution it is shown that the finite-size internal energy equation [J. Wosiek, Phys. Rev. B 49, 15 023 (1994)] yields an accurate value of the critical temperature for the triangular Potts lattice with three-site interactions in alternate triangular faces. (author)

Tunneling dynamics in open ultracold bosonic systems. Numerically exact dynamics - Analytical models - Control schemes

International Nuclear Information System (INIS)

Lode, Axel U.J.

2013-01-01

This thesis explores the quantum many-body tunneling dynamics of open ultracold bosonic systems with the recently developed multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. The capabilities of MCTDHB to provide solutions to the full time-dependent many-body problem are assessed in a benchmark using the analytically solvable harmonic interaction Hamiltonian and a generalization of it with time-dependent both one- and two-body potentials. In a comparison with numerically exact MCTDHB results, it is shown that e.g. lattice methods fail qualitatively to describe the tunneling dynamics. A model assembling the many-body physics of the process from basic simultaneously happening single-particle processes is derived and verified with a numerically exact MCTDHB description. The generality of the model is demonstrated even for strong interactions and large particle numbers. The ejection of the bosons from the source occurs with characteristic velocities. These velocities are defined by the chemical potentials of systems with different particle numbers which are converted to kinetic energy. The tunneling process is accompanied by fragmentation: the ejected bosons lose their coherence with the source and among each other. It is shown that the various aspects of the tunneling dynamics' can be controlled well with the interaction and the potential threshold.

Tunneling dynamics in open ultracold bosonic systems. Numerically exact dynamics - Analytical models - Control schemes

Energy Technology Data Exchange (ETDEWEB)

Lode, Axel U.J.

2013-06-03

This thesis explores the quantum many-body tunneling dynamics of open ultracold bosonic systems with the recently developed multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. The capabilities of MCTDHB to provide solutions to the full time-dependent many-body problem are assessed in a benchmark using the analytically solvable harmonic interaction Hamiltonian and a generalization of it with time-dependent both one- and two-body potentials. In a comparison with numerically exact MCTDHB results, it is shown that e.g. lattice methods fail qualitatively to describe the tunneling dynamics. A model assembling the many-body physics of the process from basic simultaneously happening single-particle processes is derived and verified with a numerically exact MCTDHB description. The generality of the model is demonstrated even for strong interactions and large particle numbers. The ejection of the bosons from the source occurs with characteristic velocities. These velocities are defined by the chemical potentials of systems with different particle numbers which are converted to kinetic energy. The tunneling process is accompanied by fragmentation: the ejected bosons lose their coherence with the source and among each other. It is shown that the various aspects of the tunneling dynamics' can be controlled well with the interaction and the potential threshold.

Exact one-loop results for l_i → l_jγ in 3-3-1 models

Science.gov (United States)

Hue, L. T.; Ninh, L. D.; Thuc, T. T.; Dat, N. T. T.

2018-02-01

We investigate the decays l_i→ l_j γ , with l_i=e,μ ,τ in a general class of 3-3-1 models with heavy exotic leptons with arbitrary electric charges. We present full and exact analytical results keeping external lepton masses. As a by product, we perform numerical comparisons between exact results and approximate ones where the external lepton masses are neglected. As expected, we found that branching fractions can reach the current experimental limits if mixings and mass differences of the exotic leptons are large enough. We also found unexpectedly that, depending on the parameter values, there can be huge destructive interference between the gauge and Higgs contributions when the gauge bosons connecting the Standard Model leptons to the exotic leptons are light enough. This mechanism should be taken into account when using experimental constraints on the branching fractions to exclude the parameter space of the model.

Arnol'd tongues for a resonant injection-locked frequency divider: analytical and numerical results

DEFF Research Database (Denmark)

Bartuccelli, Michele; Deane, Jonathan H.B.; Gentile, Guido

2010-01-01

’d tongues in the frequency–amplitude plane. In particular, we provide exact analytical formulae for the widths of the tongues, which correspond to the plateaux of the devil’s staircase picture. The results account for numerical and experimental findings presented in the literature for special driving terms...

Exact analytical modeling of magnetic vector potential in surface inset permanent magnet DC machines considering magnet segmentation

Science.gov (United States)

Jabbari, Ali

2018-01-01

Surface inset permanent magnet DC machine can be used as an alternative in automation systems due to their high efficiency and robustness. Magnet segmentation is a common technique in order to mitigate pulsating torque components in permanent magnet machines. An accurate computation of air-gap magnetic field distribution is necessary in order to calculate machine performance. An exact analytical method for magnetic vector potential calculation in surface inset permanent magnet machines considering magnet segmentation has been proposed in this paper. The analytical method is based on the resolution of Laplace and Poisson equations as well as Maxwell equation in polar coordinate by using sub-domain method. One of the main contributions of the paper is to derive an expression for the magnetic vector potential in the segmented PM region by using hyperbolic functions. The developed method is applied on the performance computation of two prototype surface inset magnet segmented motors with open circuit and on load conditions. The results of these models are validated through FEM method.

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.

Exact analytic expressions for the evolution of polarization for radiation propagating in a plasma with non uniformly sheared magnetic field

International Nuclear Information System (INIS)

Segre, S. E.

2001-01-01

The known analytic expressions for the evolution of the polarization of electromagnetic waves propagating in a plasma with uniformly sheared magnetic field are extended to the case where the shear is not constant. Exact analytic expressions are found for the case when the space variations of the medium are such that the magnetic field components and the plasma density satisfy a particular condition (eq. 13), possibly in a convenient reference frame of polarization space [it

Exact statistical results for binary mixing and reaction in variable density turbulence

Science.gov (United States)

Ristorcelli, J. R.

2017-02-01

We report a number of rigorous statistical results on binary active scalar mixing in variable density turbulence. The study is motivated by mixing between pure fluids with very different densities and whose density intensity is of order unity. Our primary focus is the derivation of exact mathematical results for mixing in variable density turbulence and we do point out the potential fields of application of the results. A binary one step reaction is invoked to derive a metric to asses the state of mixing. The mean reaction rate in variable density turbulent mixing can be expressed, in closed form, using the first order Favre mean variables and the Reynolds averaged density variance, ⟨ρ2⟩ . We show that the normalized density variance, ⟨ρ2⟩ , reflects the reduction of the reaction due to mixing and is a mix metric. The result is mathematically rigorous. The result is the variable density analog, the normalized mass fraction variance ⟨c2⟩ used in constant density turbulent mixing. As a consequence, we demonstrate that use of the analogous normalized Favre variance of the mass fraction, c″ ⁣2˜ , as a mix metric is not theoretically justified in variable density turbulence. We additionally derive expressions relating various second order moments of the mass fraction, specific volume, and density fields. The central role of the density specific volume covariance ⟨ρ v ⟩ is highlighted; it is a key quantity with considerable dynamical significance linking various second order statistics. For laboratory experiments, we have developed exact relations between the Reynolds scalar variance ⟨c2⟩ its Favre analog c″ ⁣2˜ , and various second moments including ⟨ρ v ⟩ . For moment closure models that evolve ⟨ρ v ⟩ and not ⟨ρ2⟩ , we provide a novel expression for ⟨ρ2⟩ in terms of a rational function of ⟨ρ v ⟩ that avoids recourse to Taylor series methods (which do not converge for large density differences). We have derived

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 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).

Exact analytical solution of time-independent neutron transport equation, and its applications to systems with a point source

International Nuclear Information System (INIS)

Mikata, Y.

2014-01-01

Highlights: • An exact solution for the one-speed neutron transport equation is obtained. • This solution as well as its derivation are believed to be new. • Neutron flux for a purely absorbing material with a point neutron source off the origin is obtained. • Spherically as well as cylindrically piecewise constant cross sections are studied. • Neutron flux expressions for a point neutron source off the origin are believed to be new. - Abstract: An exact analytical solution of the time-independent monoenergetic neutron transport equation is obtained in this paper. The solution is applied to systems with a point source. Systematic analysis of the solution of the time-independent neutron transport equation, and its applications represent the primary goal of this paper. To the best of the author’s knowledge, certain key results on the scalar neutron flux as well as their derivations are new. As an application of these results, a scalar neutron flux for a purely absorbing medium with a spherically piecewise constant cross section and an isotropic point neutron source off the origin as well as that for a cylindrically piecewise constant cross section with a point neutron source off the origin are obtained. Both of these results are believed to be new

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.

Analytic results for asymmetric random walk with exponential transition probabilities

International Nuclear Information System (INIS)

Gutkowicz-Krusin, D.; Procaccia, I.; Ross, J.

1978-01-01

We present here exact analytic results for a random walk on a one-dimensional lattice with asymmetric, exponentially distributed jump probabilities. We derive the generating functions of such a walk for a perfect lattice and for a lattice with absorbing boundaries. We obtain solutions for some interesting moment properties, such as mean first passage time, drift velocity, dispersion, and branching ratio for absorption. The symmetric exponential walk is solved as a special case. The scaling of the mean first passage time with the size of the system for the exponentially distributed walk is determined by the symmetry and is independent of the range

Watermelon configurations with wall interaction: exact and asymptotic results

Energy Technology Data Exchange (ETDEWEB)

Krattenthaler, C [Institut Camille Jordan, Universite Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622 Villeurbanne Cedex (France)

2006-06-15

We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.

Watermelon configurations with wall interaction: exact and asymptotic results

International Nuclear Information System (INIS)

Krattenthaler, C

2006-01-01

We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature

Watermelon configurations with wall interaction: exact and asymptotic results

Science.gov (United States)

Krattenthaler, C.

2006-06-01

We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.

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 results for the Boltzmann equation and Smoluchowski's coagulation equation

International Nuclear Information System (INIS)

Hendriks, E.M.

1983-01-01

Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)

Exact results for the behavior of the thermodynamic Casimir force in a model with a strong adsorption

Science.gov (United States)

Dantchev, Daniel M.; Vassilev, Vassil M.; Djondjorov, Peter A.

2016-09-01

When massless excitations are limited or modified by the presence of material bodies one observes a force acting between them generally called Casimir force. Such excitations are present in any fluid system close to its true bulk critical point. We derive exact analytical results for both the temperature and external ordering field behavior of the thermodynamic Casimir force within the mean-field Ginzburg-Landau Ising type model of a simple fluid or binary liquid mixture. We investigate the case when under a film geometry the boundaries of the system exhibit strong adsorption onto one of the phases (components) of the system. We present analytical and numerical results for the (temperature-field) relief map of the force in both the critical region of the film close to its finite-size or bulk critical points as well as in the capillary condensation regime below but close to the finite-size critical point.

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 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).

Exact one-loop results for l{sub i} → l{sub j}γ in 3-3-1 models

Energy Technology Data Exchange (ETDEWEB)

Hue, L.T. [Duy Tan University, Institute for Research and Development, Da Nang (Viet Nam); Vietnam Academy of Science and Technology, Institute of Physics, Hanoi (Viet Nam); Ninh, L.D. [Institute for Interdisciplinary Research in Science and Education, ICISE, Ghenh Rang, Quy Nhon (Viet Nam); Humboldt-Universitaet zu Berlin, Institut fuer Physik, Berlin (Germany); Thuc, T.T. [Department of Education and Training of Ca Mau, Ca Mau (Viet Nam); Dat, N.T.T. [Universita di Trieste, Dipartimento di Fisica, Theoretical Section, Trieste (Italy); International Center for Theoretical Physics, Trieste (Italy)

2018-02-15

We investigate the decays l{sub i} → l{sub j}γ, with l{sub i} = e, μ, τ in a general class of 3-3-1 models with heavy exotic leptons with arbitrary electric charges. We present full and exact analytical results keeping external lepton masses. As a by product, we perform numerical comparisons between exact results and approximate ones where the external lepton masses are neglected. As expected, we found that branching fractions can reach the current experimental limits if mixings and mass differences of the exotic leptons are large enough. We also found unexpectedly that, depending on the parameter values, there can be huge destructive interference between the gauge and Higgs contributions when the gauge bosons connecting the Standard Model leptons to the exotic leptons are light enough. This mechanism should be taken into account when using experimental constraints on the branching fractions to exclude the parameter space of the model. (orig.)

Exact capacity analysis of multihop transmission over amplify-and-forward relay fading channels

KAUST Repository

Yilmaz, Ferkan; Kucur, Oǧuz; Alouini, Mohamed-Slim

2010-01-01

In this paper, we propose an analytical framework on the exact computation of the average capacity of multihop transmission over amplify-and-forward relay fading channels. Our approach relies on the algebraic combination of Mellin and Laplace transforms to obtain exact single integral expressions which can be easily computed by Gauss-Chebyshev Quadrature (GCQ) rule. As such, the derived results are a convenient tool to analyze the average capacity of multihop transmission over amplify-and-forward relay fading channels. As an application of the analytical framework on the exact computation of the average capacity of multihop transmission, some examples are accentuated for generalized Nakagami-m fading channels. Numerical and simulation results, performed to verify the correctness of the proposed formulation, are in perfect agreement. ©2010 IEEE.

Exact capacity analysis of multihop transmission over amplify-and-forward relay fading channels

KAUST Repository

Yilmaz, Ferkan

2010-09-01

In this paper, we propose an analytical framework on the exact computation of the average capacity of multihop transmission over amplify-and-forward relay fading channels. Our approach relies on the algebraic combination of Mellin and Laplace transforms to obtain exact single integral expressions which can be easily computed by Gauss-Chebyshev Quadrature (GCQ) rule. As such, the derived results are a convenient tool to analyze the average capacity of multihop transmission over amplify-and-forward relay fading channels. As an application of the analytical framework on the exact computation of the average capacity of multihop transmission, some examples are accentuated for generalized Nakagami-m fading channels. Numerical and simulation results, performed to verify the correctness of the proposed formulation, are in perfect agreement. ©2010 IEEE.

New exact solutions of coupled Boussinesq–Burgers equations by Exp-function method

Directory of Open Access Journals (Sweden)

L.K. Ravi

2017-03-01

Full Text Available In the present paper, we build the new analytical exact solutions of a nonlinear differential equation, specifically, coupled Boussinesq–Burgers equations by means of Exp-function method. Then, we analyze the results by plotting the three dimensional soliton graphs for each case, which exhibit the simplicity and effectiveness of the proposed method. The primary purpose of this paper is to employ a new approach, which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq–Burgers equations.

Numerical Uncertainty Analysis for Computational Fluid Dynamics using Student T Distribution -- Application of CFD Uncertainty Analysis Compared to Exact Analytical Solution

Science.gov (United States)

Groves, Curtis E.; Ilie, marcel; Shallhorn, Paul A.

2014-01-01

Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.

On the exact conservation laws in thermal models and the analysis of AGS and SIS experimental results

International Nuclear Information System (INIS)

Keraenen, A.; Suhonen, E.; Cleymans, J.

1999-01-01

The production of hadrons in relativistic heavy ion collisions is studied using a statistical ensemble with thermal and chemical equilibrium. Special attention is given to exact conservation laws, i.e. certain charges are treated canonically instead of using the usual grand canonical approach. For small systems, the exact conservation of baryon number, strangeness and electric charge is to be taken into account. We have derived compact, analytical expressions for particle abundances in such ensemble. As an application, the change in K/π ratios in AGS experiments with different interaction system sizes is well reproduced. The canonical treatment of three charges becomes impractical very quickly with increasing system size. Thus, we focus our attention on exact conservation of strangeness, and treat baryon number and electric charge grand canonically. We present expressions for particle abundances in such ensemble as well, and apply them to reproduce the large variety of particle ratios in GSI SIS 2 A GeV Ni-Ni experiments. At the energies considered here, the exact strangeness conservation fully accounts for strange particle suppression, and no extra chemical factor is needed. (author)

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 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'

The exact analytical form for the box diagram with one heavy external quark

International Nuclear Information System (INIS)

He Xiao-Gang; McKellar, B.H.J.; Pallaghy, P.K.

1989-01-01

The exact analytical form for the box-diagram amplitude with one non-vanishing external quark mass is presented. The consequences of this work for meson mixing and the CP violating charge asymmetry are investigated in heavy quark systems. In the T 0 - T -0 system with the three generation model the charge asymmetry is typically of order (∼10 -4 ) but the mixing is extremely small ( -18 ). In the four generation case, the mixing can be greatly enhanced. With a normal KM matrix, the mixing is still very small ( -10 ) but with a flavour-flipped KM matrix, the mixing can be as large as a few percent while the charge asymmetry is still small ( -4 ). In the B '0 - B -'0 system, the mixing and charge asymmetry can be of order a few percent whereas in the T '0 - T -'0 system, the mixing is small. 13 refs., 4 figs

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

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 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.

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.

Coalescence of two equal cylinders: exact results for creeping viscous plane flow driven by capillarity

International Nuclear Information System (INIS)

Hopper, R.W.

1984-01-01

The coalescence of two equal viscous cylinders under the influence of capillarity is of interest in the theory of sintering. Although the flow in typical cylinder coalescence experiments is not planar, the plane-flow case is of general interest and is a good approximation in the early stage. An essentially exact analytic solution giving the shape as a function of time for slow plane flow is presented in simple closed form. 16 references, 2 figures, 1 table

Exact Results on Quantum Interference and Magnetoconductance in Variable-Range Hopping

Science.gov (United States)

Lin, Yeong-Lieh; Nori, Franco

1997-03-01

We study quantum interference effects on the transition strength for strongly localized electrons hopping on 2D square and 3D cubic lattices in a magnetic field B. In 2D, we obtain closed-form expressions for the tunneling probability between two arbitrary sites by exactly summing the corresponding phase factors of all directed paths connecting them. An analytic expression for the magnetoconductance, as an explicit function of the magnetic flux, is derived. A positive MC is clearly observed when turning on the magnetic field. When the strength of B reaches a certain value, which is inversely proportional to twice the hopping length, the MC is increased by a factor of two compared to that at zero field. The periodicity in the flux of the MC is found to be equal to hc/2e. In the experimentally important 3D case, we show how the interference patterns and the small-B behavior of the magnetoconductance vary according to the orientation of B. Furthermore, for a 3D sample, the effect on the low-flux MC due to the randomness of the angles between the hopping direction and the orientation of B is examined analytically.(Y.-L. Lin and F. Nori, Phys. Rev. Lett. 76), 4580 (1996); Phys. Rev. B 53, 15543 (1996).

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 protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

Science.gov (United States)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

Science.gov (United States)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Exact outage analysis of incremental decode-and-forward opportunistic relaying

KAUST Repository

Tourki, Kamel; Yang, Hongchuan; Alouini, Mohamed-Slim

2010-01-01

In this paper, we investigate a dual-hop decode-andforward opportunistic relaying scheme where the selected relay chooses to cooperate only if the source-destination channel is of an unacceptable quality. In our study, we derive exact closed-form expression for the outage probability based on the exact statistics of each hop. Furthermore, we perform asymptotic analysis and we deduce the diversity order of the scheme. We validate our analysis by showing that performance simulation results coincide with our analytical results over different network architectures. © 2010 IEEE.

Exact outage analysis of incremental decode-and-forward opportunistic relaying

KAUST Repository

Tourki, Kamel

2010-11-01

In this paper, we investigate a dual-hop decode-andforward opportunistic relaying scheme where the selected relay chooses to cooperate only if the source-destination channel is of an unacceptable quality. In our study, we derive exact closed-form expression for the outage probability based on the exact statistics of each hop. Furthermore, we perform asymptotic analysis and we deduce the diversity order of the scheme. We validate our analysis by showing that performance simulation results coincide with our analytical results over different network architectures. © 2010 IEEE.

Exact properties of spin glasses. I. 2D supersymmetry and Nishimori's result

International Nuclear Information System (INIS)

Georges, A.; Le Doussal, P.; Hansel, D.

1985-01-01

We introduce an effective theory of interacting fermions and bosons in order to express the quenched internal energy of the 2D Ising spin glass. We show that an exact result derived by Nishimori appears, in this formulation, as a dimensional reduction due to the apparition of a supersymmetry. For a general Ising spin glass, this suggests new insights into the physical meaning of this exact result

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 results for quantum chaotic systems and one-dimensional fermions from matrix models

International Nuclear Information System (INIS)

Simons, B.D.; Lee, P.A.; Altshuler, B.L.

1993-01-01

We demonstrate a striking connection between the universal parametric correlations of the spectra of quantum chaotic systems and a class of integrable quantum hamiltonians. We begin by deriving a non-perturbative expression for the universal m-point correlation function of the spectra of random matrix ensembles in terms of a non-linear supermatrix σ-model. These results are shown to coincide with those from previous studies of weakly disordered metallic systems. We then introduce a continuous matrix model which describes the quantum mechanics of the Sutherland hamiltonian describing particles interacting through an inverse-square pairwise potential. We demonstrate that a field theoretic approach can be employed to determine exact analytical expressions for correlations of the quantum hamiltonian. The results, which are expressed in terms of a non-linear σ-model, are shown to coincide with those for analogous correlation functions of random matrix ensembles after an appropriate change of variables. We also discuss possible generalizations of the matrix model to higher dimensions. These results reveal a common mathematical structure which underlies branches of theoretical physics ranging from continuous matrix models to strongly interacting quantum hamiltonians, and universalities in the spectra of quantum chaotic systems. (orig.)

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

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.

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.

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

Exact analytic solutions for Mikheyev-Smirnov-Wolfenstein level crossings

International Nuclear Information System (INIS)

Noetzold, D.

1987-01-01

An exact formula for the transition probability in level-crossing phenomena is derived for a general case, ranging from adiabatic to sudden crossings. This is done in the context of neutrino flavor oscillations for the Mikheyev-Smirnov-Wolfenstein (MSW) effect, where hitherto only numerical or approximate solutions were obtained. The matter density or level splitting is assumed to be governed by a hyperbolic-tangent function which, however, can change arbitrarily fast between two constant values. For example, in context of the MSW effect this furnishes a nice fit to the solar density determining the level crossing of solar neutrinos. In the quasiadiabatic limit the exact Landau-Zener factor can be read off, correcting some expressions obtained so far. Even in the opposite limit of a sudden level crossing a conversion is found, which can have far-reaching consequences for neutrino detection on Earth

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.

Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle

International Nuclear Information System (INIS)

Salazar, Domingos S P; Lira, Sérgio A

2016-01-01

In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system’s energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of N noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions. (paper)

Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

Science.gov (United States)

Martirosyan, A; Saakian, David B

2011-08-01

We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

Piecewise linear emulator of the nonlinear Schroedinger equation and the resulting analytic solutions for Bose-Einstein condensates

International Nuclear Information System (INIS)

Theodorakis, Stavros

2003-01-01

We emulate the cubic term Ψ 3 in the nonlinear Schroedinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a δ function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Ψ 3 one. In particular, it can be used for the nonlinear Schroedinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions

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.

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.)

One-dimensional Schrodinger equation with non-analytic potential V(x) = -g(2) exp (- vertical bar x vertical bar) and its exact Bessel-function solvability

Czech Academy of Sciences Publication Activity Database

Sasaki, R.; Znojil, Miloslav

2016-01-01

Roč. 49, č. 44 (2016), č. článku 445303. ISSN 1751-8113 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : non-analytic potentials * bound states * reflection and transmission * exactly solvable * orthogonality theorems * associated Hamiltonians * supersymmetry Subject RIV: BE - Theoretical Physics Impact factor: 1.857, year: 2016

Exact solutions, energy, and charge of stable Q-balls

Energy Technology Data Exchange (ETDEWEB)

Bazeia, D.; Marques, M.A. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)

2016-05-15

In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We use the analytic results to investigate how to control the energy and charge to make the Q-balls stable. (orig.)

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.

Complex dynamics of memristive circuits: Analytical results and universal slow relaxation

Science.gov (United States)

Caravelli, F.; Traversa, F. L.; Di Ventra, M.

2017-02-01

Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to models of the brain. However, analytical results that highlight the role of the graph connectivity on the memory dynamics are still few, thus limiting our understanding of these important dynamical systems. In this paper, we derive an exact matrix equation of motion that takes into account all the network constraints of a purely memristive circuit, and we employ it to derive analytical results regarding its relaxation properties. We are able to describe the memory evolution in terms of orthogonal projection operators onto the subspace of fundamental loop space of the underlying circuit. This orthogonal projection explicitly reveals the coupling between the spatial and temporal sectors of the memristive circuits and compactly describes the circuit topology. For the case of disordered graphs, we are able to explain the emergence of a power-law relaxation as a superposition of exponential relaxation times with a broad range of scales using random matrices. This power law is also universal, namely independent of the topology of the underlying graph but dependent only on the density of loops. In the case of circuits subject to alternating voltage instead, we are able to obtain an approximate solution of the dynamics, which is tested against a specific network topology. These results suggest a much richer dynamics of memristive networks than previously considered.

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 results for the one dimensional asymmetric exclusion model

International Nuclear Information System (INIS)

Derrida, B.; Evans, M.R.; Pasquier, V.

1993-01-01

The asymmetric exclusion model describes a system of particles hopping in a preferred direction with hard core repulsion. These particles can be thought of as charged particles in a field, as steps of an interface, as cars in a queue. Several exact results concerning the steady state of this system have been obtained recently. The solution consists of representing the weights of the configurations in the steady state as products of non-commuting matrices. (author)

Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins

Science.gov (United States)

Tschirhart, Hugo; Platini, Thierry

2018-05-01

In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals (PPA-mapping) can lead to exact solutions for previously unsolved problems. While the approach can be used in general when the model involves Poisson processes corresponding to creation or degradation, current applications of the method and new results derived using it have been limited to date. In this paper, we present the exact solution of a variation of the two-stage model of gene expression (with time dependent transition rates) describing the arbitrary partitioning of proteins. The methodology proposed makes full use of the PPA-mapping by transforming the original problem into a new process describing the evolution of three biological switches. Based on a succession of transformations, the method leads to a hierarchy of reduced models. We give an integral expression of the time dependent generating function as well as explicit results for the mean, variance, and correlation function. Finally, we discuss how results for time dependent parameters can be extended to the three-stage model and used to make inferences about models with parameter fluctuations induced by hidden stochastic variables.

Exact result in strong wave turbulence of thin elastic plates

Science.gov (United States)

Düring, Gustavo; Krstulovic, Giorgio

2018-02-01

An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5 -Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛ ℓ , where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Rapid Communication are valid for both weak and strong wave turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

Exact performance analysis of decode-and-forward opportunistic relaying

KAUST Repository

Tourki, Kamel

2010-06-01

In this paper, we investigate a dual-hop decode-and-forward opportunistic relaying scheme where the source may or may not be able to communicate directly with the destination. In our study, we consider a regenerative relaying scheme in which the decision to cooperate takes into account the effect of the possible erroneously detected and transmitted data at the best relay. We derive an exact closed-form expression for the end-to-end bit-error rate (BER) of binary phase-shift keying (BPSK) modulation based on the exact statistics of each hop. Unlike existing works where the analysis focused on high signal-to-noise ratio (SNR) regime, such results are important to enable the designers to take decisions regarding practical systems that operate at low SNR regime. We show that performance simulation results coincide with our analytical results.

Solar neutrino masses and mixing from bilinear R-parity broken supersymmetry: Analytical versus numerical results

Science.gov (United States)

Díaz, M.; Hirsch, M.; Porod, W.; Romão, J.; Valle, J.

2003-07-01

We give an analytical calculation of solar neutrino masses and mixing at one-loop order within bilinear R-parity breaking supersymmetry, and compare our results to the exact numerical calculation. Our method is based on a systematic perturbative expansion of R-parity violating vertices to leading order. We find in general quite good agreement between the approximate and full numerical calculations, but the approximate expressions are much simpler to implement. Our formalism works especially well for the case of the large mixing angle Mikheyev-Smirnov-Wolfenstein solution, now strongly favored by the recent KamLAND reactor neutrino data.

An Exact Solution of the Gamma Ray Burst Arrival Time Analysis ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

An Exact Solution of the Gamma Ray Burst Arrival Time Analysis. Problem. S. Sinha ISRO Satellite Center, Bangalore 560 017, India. Abstract. An analytical solution of the GRB arrival time analysis is presented. The errors in the position of the GRB resulting from timing and position errors of different satellites are calculated.

Communication: An exact bound on the bridge function in integral equation theories.

Science.gov (United States)

Kast, Stefan M; Tomazic, Daniel

2012-11-07

We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.

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 combinatorial approach to finite coagulating systems

Science.gov (United States)

Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr

2018-02-01

This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

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 asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application

Energy Technology Data Exchange (ETDEWEB)

Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2016-08-15

Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innovative generalization of the BP solution for an anisotropic ferromagnet, based on a physically motivated geometric (in-)equality, which takes the exact Skyrmion to a new class of functions beyond analyticity. The possibility of stabilizing such metastable states in helimagnets is discussed with the construction of individual Skyrmion, Skyrmion crystal and lattice with asymmetry, likely to be detected in precision experiments.

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)

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.

Non-local energy density functionals: models plus some exact general results

International Nuclear Information System (INIS)

March, N.H.

2001-02-01

Holas and March (Phys. Rev. A51, 2040, 1995) gave a formally exact expression for the force - δV xc (r-tilde)/δr-tilde associated with the exchange-correlation potential V xc (r-tilde) of density functional theory. This forged a precise link between first- and second-order density matrices and V xc (r-tilde). Here models are presented in which these low-order matrices can be related to the ground-state electron density. This allows non-local energy density functionals to be constructed within the framework of such models. Finally, results emerging from these models have led to the derivation of some exact 'nuclear cusp' relations for exchange and correlation energy densities in molecules, clusters and condensed phases. (author)

Some exact velocity profiles for granular flow in converging hoppers

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Cox, Grant M.; Hill, James M.

2005-01-01

Gravity flow of granular materials through hoppers occurs in many industrial processes. For an ideal cohesionless granular material, which satisfies the Coulomb-Mohr yield condition, the number of known analytical solutions is limited. However, for the special case of the angle of internal friction δ equal to ninety degrees, there exist exact parametric solutions for the governing coupled ordinary differential equations for both two-dimensional wedges and three-dimensional cones, both of which involve two arbitrary constants of integration. These solutions are the only known analytical solutions of this generality. Here, we utilize the double-shearing theory of granular materials to determine the velocity field corresponding to these exact parametric solutions for the two problems of gravity flow through converging wedge and conical hoppers. An independent numerical solution for other angles of internal friction is shown to coincide with the analytical solution.

Efficient implementation of one- and two-component analytical energy gradients in exact two-component theory

Science.gov (United States)

Franzke, Yannick J.; Middendorf, Nils; Weigend, Florian

2018-03-01

We present an efficient algorithm for one- and two-component analytical energy gradients with respect to nuclear displacements in the exact two-component decoupling approach to the one-electron Dirac equation (X2C). Our approach is a generalization of the spin-free ansatz by Cheng and Gauss [J. Chem. Phys. 135, 084114 (2011)], where the perturbed one-electron Hamiltonian is calculated by solving a first-order response equation. Computational costs are drastically reduced by applying the diagonal local approximation to the unitary decoupling transformation (DLU) [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to the X2C Hamiltonian. The introduced error is found to be almost negligible as the mean absolute error of the optimized structures amounts to only 0.01 pm. Our implementation in TURBOMOLE is also available within the finite nucleus model based on a Gaussian charge distribution. For a X2C/DLU gradient calculation, computational effort scales cubically with the molecular size, while storage increases quadratically. The efficiency is demonstrated in calculations of large silver clusters and organometallic iridium complexes.

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.)

Analytical exact solution of the non-linear Schroedinger equation

International Nuclear Information System (INIS)

Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da

2011-01-01

Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

Dichotomous Markov Noise:. Exact Results for Out-Of Systems

Science.gov (United States)

Bena, Ioana

Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on analytically-solvable situations. In particular, it has escaped attention till recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present a few relevant applications — the hypersensitive transport, the rocking ratchet, and the stochastic Stokes' drift. These results reinforce the impression that dichotomous noise can be put on par with Gaussian white noise as far as obtaining analytical results is concerned. They convincingly illustrate the interplay between noise and nonlinearity in generating nontrivial behaviors of nonequilibrium systems and point to various practical applications.

Exact analytical solution of the convolution integral equation for a general profile fitting function and Gaussian detector kernel

International Nuclear Information System (INIS)

Garcia-Vicente, F.; Rodriguez, C.

2000-01-01

One of the most important aspects in the metrology of radiation fields is the problem of the measurement of dose profiles in regions where the dose gradient is large. In such zones, the 'detector size effect' may produce experimental measurements that do not correspond to reality. Mathematically it can be proved, under some general assumptions of spatial linearity, that the disturbance induced in the measurement by the effect of the finite size of the detector is equal to the convolution of the real profile with a representative kernel of the detector. In this work the exact relation between the measured profile and the real profile is shown, through the analytical resolution of the integral equation for a general type of profile fitting function using Gaussian convolution kernels. (author)

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.

Intermittency inhibited by transport: An exactly solvable model

Science.gov (United States)

Zanette, Damián H.

1994-04-01

Transport is incorporated in a discrete-time stochastic model of a system undergoing autocatalytic reactions of the type A-->2A and A-->0, whose population field is known to exhibit spatiotemporal intermittency. The temporal evolution is exactly solved, and it is shown that if the transport process is strong enough, intermittency is inhibited. This inhibition is nonuniform, in the sense that, as transport is strengthened, low-order population moments are affected before the high-order ones. Numerical simulations are presented to support the analytical results.

Multijet final states: exact results and the leading pole approximation

International Nuclear Information System (INIS)

Ellis, R.K.; Owens, J.F.

1984-09-01

Exact results for the process gg → ggg are compared with those obtained using the leading pole approximation. Regions of phase space where the approximation breaks down are discussed. A specific example relevant for background estimates to W boson production is presented. It is concluded that in this instance the leading pole approximation may underestimate the standard QCD background by more than a factor of two in certain kinematic regions of physical interest

Exact solutions of continuous states for Hartmann potential

International Nuclear Information System (INIS)

Chen Changyuan; Lu Falin; Sun Dongsheng

2004-01-01

In this Letter, we obtain the exact solutions of continuous states for the Hartmann potential. The normalized wave functions of continuous states on the 'k/2π scale' and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed

An exactly solvable model for first- and second-order transitions

International Nuclear Information System (INIS)

Klushin, L I; Skvortsov, A M; Gorbunov, A A

1998-01-01

The possibility of an exact analytical description of first-order and second-order transitions is demonstrated using a specific microscopic model. Predictions using the exactly calculated partition function are compared with those based on the Landau and Yang-Lee approaches. The model employed is an adsorbed polymer chain with an arbitrary number of links and an external force applied to its end, for which the variation of the partition function with the adsorption interaction parameter and the magnitude of the applied force is calculated. In the thermodynamic limit, the system has one isotropic and two anisotropic, ordered phases, each of which is characterized by two order parameters and between which first-order and second-order transitions occur and a bicritical point exists. The Landau free energy is found exactly as a function of each order parameter separately and, near the bicritical point, as a function of both of them simultaneously. An exact analytical formula is found for the distribution of the complex zeros of the partition function in first-order and second-order phase transitions. Hypotheses concerning the way in which the free energy and the positions of the complex zeros scale with the number of particles N in the system are verified. (reviews of topical problems)

Exact master equations for the non-Markovian decay of a qubit

International Nuclear Information System (INIS)

Vacchini, Bassano; Breuer, Heinz-Peter

2010-01-01

Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. By employing the exact solution for the model, analytical expressions are determined for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows an explicit comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, the structure of widely used phenomenological master equations with a memory kernel may be incompatible with a nonperturbative treatment of the underlying microscopic model. Several physical implications of the results on the microscopic analysis and the phenomenological modeling of non-Markovian quantum dynamics of open systems are discussed.

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.

Some exact solutions for maximally symmetric topological defects in Anti de Sitter space

Science.gov (United States)

Alvarez, Orlando; Haddad, Matthew

2018-03-01

We obtain exact analytical solutions for a class of SO( l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = ( p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects ( p = 0 , 1 , 2 , . . . ; l = 1), vortex-like defects ( p = 1 , 2 , 3; l = 2), and the 't Hooft-Polyakov monopole ( p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

Cryptography based on neural networks - analytical results

International Nuclear Information System (INIS)

Rosen-Zvi, Michal; Kanter, Ido; Kinzel, Wolfgang

2002-01-01

The mutual learning process between two parity feed-forward networks with discrete and continuous weights is studied analytically, and we find that the number of steps required to achieve full synchronization between the two networks in the case of discrete weights is finite. The synchronization process is shown to be non-self-averaging and the analytical solution is based on random auxiliary variables. The learning time of an attacker that is trying to imitate one of the networks is examined analytically and is found to be much longer than the synchronization time. Analytical results are found to be in agreement with simulations. (letter to the editor)

Ageing without detailed balance in the bosonic contact and pair-contact processes: exact results

International Nuclear Information System (INIS)

Baumann, Florian; Henkel, Malte; Pleimling, Michel; Richert, Jean

2005-01-01

Ageing in systems without detailed balance is studied in the exactly solvable bosonic contact process and the critical bosonic pair-contact process. The two-time correlation function and the two-time response function are explicitly found. In the ageing regime, the dynamical scaling of these is analysed and exact results for the ageing exponents and the scaling functions are derived. For the critical bosonic pair-contact process, the autocorrelation and autoresponse exponents agree but the ageing exponents a and b are shown to be distinct

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].

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

Quasinormal modes of the BTZ black hole under scalar perturbations with a non-minimal coupling: exact spectrum

Science.gov (United States)

Panotopoulos, Grigoris

2018-06-01

We perturb the non-rotating BTZ black hole with a non-minimally coupled massless scalar field, and we compute the quasinormal spectrum exactly. We solve the radial equation in terms of hypergeometric functions, and we obtain an analytical expression for the quasinormal frequencies. In addition, we compare our analytical results with the 6th order semi-analytical WKB method, and we find an excellent agreement. The impact of the nonminimal coupling as well as of the cosmological constant on the quasinormal spectrum is briefly discussed.

Multishell method: Exact treatment of a cluster in an effective medium

International Nuclear Information System (INIS)

Gonis, A.; Garland, J.W.

1977-01-01

A method is presented for the exact determination of the Green's function of a cluster embedded in a given effective medium. This method, the multishell method, is applicable even to systems with off-diagonal disorder, extended-range hopping, multiple bands, and/or hybridization, and is computationally practicable for any system described by a tight-binding or interpolation-scheme Hamiltonian. It allows one to examine the effects of local environment on the densities of states and site spectral weight functions of disordered systems. For any given analytic effective medium characterized by a non-negative density of states the method yields analytic cluster Green's functions and non-negative site spectral weight functions. Previous methods used for the calculation of the Green's function of a cluster embedded in a given effective medium have not been exact. The results of numerical calculations for model systems show that even the best of these previous methods can lead to substantial errors, at least for small clusters in two- and three-dimensional lattices. These results also show that fluctuations in local environment have large effects on site spectral weight functions, even in cases in which the single-site coherent-potential approximation yields an accurate overall density of states

Some Exact Solutions of Boundary Layer Flows along a Vertical Plate with Buoyancy Forces Combined with Lorentz Forces under Uniform Suction

Directory of Open Access Journals (Sweden)

Asterios Pantokratoras

2008-01-01

Full Text Available Exact analytical solutions of boundary layer flows along a vertical porous plate with uniform suction are derived and presented in this paper. The solutions concern the Blasius, Sakiadis, and Blasius-Sakiadis flows with buoyancy forces combined with either MHD Lorentz or EMHD Lorentz forces. In addition, some exact solutions are presented specifically for water in the temperature range of 0∘C≤≤8∘C, where water density is nearly parabolic. Except for their use as benchmarking means for testing the numerical solution of the Navier-Stokes equations, the presented exact solutions with EMHD forces have use in flow separation control in aeronautics and hydronautics, whereas the MHD results have applications in process metallurgy and fusion technology. These analytical solutions are valid for flows with strong suction.

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 $p>2$.

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.

Pre-analytical and analytical aspects affecting clinical reliability of plasma glucose results.

Science.gov (United States)

Pasqualetti, Sara; Braga, Federica; Panteghini, Mauro

2017-07-01

The measurement of plasma glucose (PG) plays a central role in recognizing disturbances in carbohydrate metabolism, with established decision limits that are globally accepted. This requires that PG results are reliable and unequivocally valid no matter where they are obtained. To control the pre-analytical variability of PG and prevent in vitro glycolysis, the use of citrate as rapidly effective glycolysis inhibitor has been proposed. However, the commercial availability of several tubes with studies showing different performance has created confusion among users. Moreover, and more importantly, studies have shown that tubes promptly inhibiting glycolysis give PG results that are significantly higher than tubes containing sodium fluoride only, used in the majority of studies generating the current PG cut-points, with a different clinical classification of subjects. From the analytical point of view, to be equivalent among different measuring systems, PG results should be traceable to a recognized higher-order reference via the implementation of an unbroken metrological hierarchy. In doing this, it is important that manufacturers of measuring systems consider the uncertainty accumulated through the different steps of the selected traceability chain. In particular, PG results should fulfil analytical performance specifications defined to fit the intended clinical application. Since PG has tight homeostatic control, its biological variability may be used to define these limits. Alternatively, given the central diagnostic role of the analyte, an outcome model showing the impact of analytical performance of test on clinical classifications of subjects can be used. Using these specifications, performance assessment studies employing commutable control materials with values assigned by reference procedure have shown that the quality of PG measurements is often far from desirable and that problems are exacerbated using point-of-care devices. Copyright © 2017 The Canadian

Analytical eigenstates for the quantum Rabi model

International Nuclear Information System (INIS)

Zhong, Honghua; Xie, Qiongtao; Lee, Chaohong; Batchelor, Murray T

2013-01-01

We develop a method to find analytical solutions for the eigenstates of the quantum Rabi model. These include symmetric, anti-symmetric and asymmetric analytic solutions given in terms of the confluent Heun functions. Both regular and exceptional solutions are given in a unified form. In addition, the analytic conditions for determining the energy spectrum are obtained. Our results show that conditions proposed by Braak (2011 Phys. Rev. Lett. 107 100401) are a type of sufficiency condition for determining the regular solutions. The well-known Judd isolated exact solutions appear naturally as truncations of the confluent Heun functions. (paper)

Mathematical modeling and exact solutions to rotating flows of a Burgers' fluid

International Nuclear Information System (INIS)

Hayat, T.

2005-12-01

The aim of this study is to provide the modeling and exact analytic solutions for hydromagnetic oscillatory rotating flows of an incompressible Burgers' fluid bounded by a plate. The governing time-dependent equation for the Burgers' fluid is different than those from the Navier-Stokes' equation. The entire system is assumed to rotate around an axis normal to the plate. The governing equations for this investigation are solved analytically for two physical problems. The solutions for the three cases, when the two times angular velocity is greater than the frequency of oscillation or it is smaller than the frequency or it is equal to the frequency (resonant case), are discussed in second problem. In Burgers' fluid, it is also found that hydromagnetic solution in the resonant case satisfies the boundary condition at infinity. Moreover, the obtained analytical results reduce to several previously published results as the special cases. (author)

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 results on the one-dimensional Potts lattice gas

International Nuclear Information System (INIS)

Riera, R.; Chaves, C.M.G.F.

1982-12-01

An exact calculation of the Potts Lattice Gas in one dimension is presented. Close to T=O 0 K, the uniform susceptibility presents an essencial singularity, when the excharge parameter is positive, and a power law behaviour with critical exponent γ=1, when this parameter is negative. (Author) [pt

Exact results on the one-dimensional Potts lattice gas

International Nuclear Information System (INIS)

Riera, R.; Chaves, C.M.G.F.

1983-01-01

An exact calculation of the Potts Lattice Gas in one dimension is presented. Close to T=O 0 K, the uniform susceptibility presents an essential singularity, when the exchange parameter is positive, and a power law behaviour with critical exponent γ=1, when this parameter is negative. (Author) [pt

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

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.

An Exact Solution of The Neutron Slowing Down Equation

Energy Technology Data Exchange (ETDEWEB)

Stefanovic, D [Boris Kidric Vinca Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1970-07-01

The slowing down equation for an infinite homogeneous monoatomic medium is solved exactly. The cross sections depend on neutron energy. The solution is given in analytical form within each of the lethargy intervals. This analytical form is the sum of probabilities which are given by the Green functions. The calculated collision density is compared with the one obtained by Bednarz and also with an approximate Wigner formula for the case of a resonance not wider than one collision interval. For the special case of hydrogen, the present solution reduces to Bethe's solution. (author)

New analytic solutions of stochastic coupled KdV equations

International Nuclear Information System (INIS)

Dai Chaoqing; Chen Junlang

2009-01-01

In this paper, firstly, we use the exp-function method to seek new exact solutions of the Riccati equation. Then, with the help of Hermit transformation, we employ the Riccati equation and its new exact solutions to find new analytic solutions of the stochastic coupled KdV equation in the white noise environment. As some special examples, some analytic solutions can degenerate into these solutions reported in open literatures.

Exact analytical thermodynamic expressions for a Brownian heat engine

Science.gov (United States)

Taye, Mesfin Asfaw

2015-09-01

The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time t . Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed form expressions for the free energy, the rate of entropy production, and the rate of entropy flow from the system to the outside. We show that when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long time limit, the rate of entropy production balances the rate of entropy extraction, and at equilibrium both entropy production and extraction rates become zero. Furthermore, via the present model, many thermodynamic theories can be checked.

Exact analysis of the response of quantum systems to two-photons using a QSDE approach

International Nuclear Information System (INIS)

Pan, Yu; Dong, Daoyi; Zhang, Guofeng

2016-01-01

We introduce the quantum stochastic differential equation (QSDE) approach to exactly analyze the response of quantum systems to a continuous-mode two-photon input. The QSDE description of the two-photon process allows us to integrate the input–output analysis with the quantum network theory, and so the analytical computability of the output state of a general quantum system can be addressed within this framework. We show that the time-domain two-photon output states can be exactly calculated for a large class of quantum systems including passive linear networks, optomechanical oscillators and two-level emitter in waveguide systems. In particular, we propose to utilise the results for the exact simulation of the stimulated emission as well as the study of the scattering of two-mode photon wave packets. (paper)

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 results for ABJ Wilson loops and open-closed duality

Energy Technology Data Exchange (ETDEWEB)

Hatsuda, Yasuyuki [Département de Physique Théorique et section de Mathématiques, Université de Genève,Genève, CH-1211 (Switzerland); Okuyama, Kazumi [Department of Physics, Shinshu University,Matsumoto 390-8621 (Japan)

2016-10-24

We find new exact relations between the partition function and vacuum expectation values (VEVs) of 1/2 BPS Wilson loops in ABJ theory, which allow us to predict the large N expansions of the 1/2 BPS Wilson loops from known results of the partition function. These relations are interpreted as an open-closed duality where the closed string background is shifted by the insertion of Wilson loops due to a back-reaction. Using the connection between ABJ theory and the topological string on local ℙ{sup 1}×ℙ{sup 1}, we explicitly write down non-trivial relations between open and closed string amplitudes.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

International Nuclear Information System (INIS)

Freericks, J. K.; Krishnamurthy, H. R.; Kato, Yasuyuki; Kawashima, Naoki; Trivedi, Nandini

2009-01-01

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator-to-superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Analytical relativistic self-consistent-field calculations for atoms

International Nuclear Information System (INIS)

Barthelat, J.C.; Pelissier, M.; Durand, P.

1980-01-01

A new second-order representation of the Dirac equation is presented. This representation which is exact for a hydrogen atom is applied to approximate analytical self-consistent-field calculations for atoms. Results are given for the rare-gas atoms from helium to radon and for lead. The results compare favorably with numerical Dirac-Hartree-Fock solutions

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

Science.gov (United States)

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

Exact solutions for the static bending of Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model

International Nuclear Information System (INIS)

Wang, Y. B.; Zhu, X. W.; Dai, H. H.

2016-01-01

Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.

Exact solutions for the static bending of Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model

Energy Technology Data Exchange (ETDEWEB)

Wang, Y. B. [Department of Mathematics, ShaoXing University, No.900, ChengNan Avenue 312000, ShaoXing, Zhejiang (China); Zhu, X. W., E-mail: xiaowuzhu1026@znufe.edu.cn [School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073 (China); Dai, H. H. [Department of Mathematics, City University of HongKong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong (China)

2016-08-15

Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.

Exact interior solutions in 2 + 1-dimensional spacetime

Energy Technology Data Exchange (ETDEWEB)

Rahaman, Farook; Bhar, Piyali [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Biswas, Ritabrata [Indian Institute of Engineering Sceince and Technology Shibpur, Howrah, West Bengal (India); Usmani, A.A. [Aligarh Muslim University, Department of Physics, Aligarh, Uttar Pradesh (India)

2014-04-15

We provide a new class of exact solutions for the interior in 2 + 1-dimensional spacetime. The solutions obtained for the perfect fluid model both with and without cosmological constant (Λ) are found to be regular and singularity free. It assumes very simple analytical forms that help us to study the various physical properties of the configuration. Solutions without Λ are found to be physically acceptable. (orig.)

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

Some exact results for the three-layer Zamolodchikov model

International Nuclear Information System (INIS)

Boos, H.E.; Mangazeev, V.V.

2001-01-01

In this paper we continue the study of the three-layer Zamolodchikov model started in our previous works (H.E. Boos, V.V. Mangazeev, J. Phys. A 32 (1999) 3041-3054 and H.E. Boos, V.V. Mangazeev, J. Phys. A 32 (1999) 5285-5298). We analyse numerically the solutions to the Bethe ansatz equations obtained in H.E. Boos, V.V. Mangazeev, J. Phys. A 32 (1999) 5285-5298. We consider two regimes I and II which differ by the signs of the spherical sides (a 1 ,a 2 ,a 3 )→(-a 1 ,-a 2 ,-a 3 ). We accept the two-line hypothesis for the regime I and the one-line hypothesis for the regime II. In the thermodynamic limit we derive integral equations for distribution densities and solve them exactly. We calculate the partition function for the three-layer Zamolodchikov model and check a compatibility of this result with the functional relations obtained in H.E. Boos, V.V. Mangazeev, J. Phys. A 32 (1999) 5285-5298. We also do some numeric checkings of our results

Analytic approaches to relativistic hydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Hatta, Yoshitaka

2016-12-15

I summarize our recent work towards finding and utilizing analytic solutions of relativistic hydrodynamic. In the first part I discuss various exact solutions of the second-order conformal hydrodynamics. In the second part I compute flow harmonics v{sub n} analytically using the anisotropically deformed Gubser flow and discuss its dependence on n, p{sub T}, viscosity, the chemical potential and the charge.

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 BPS bound for noncommutative baby Skyrmions

International Nuclear Information System (INIS)

Domrin, Andrei; Lechtenfeld, Olaf; Linares, Román; Maceda, Marco

2013-01-01

The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory

Exactly soluble two-state quantum models with linear couplings

International Nuclear Information System (INIS)

Torosov, B T; Vitanov, N V

2008-01-01

A class of exact analytic solutions of the time-dependent Schroedinger equation is presented for a two-state quantum system coherently driven by a nonresonant external field. The coupling is a linear function of time with a finite duration and the detuning is constant. Four special models are considered in detail, namely the shark, double-shark, tent and zigzag models. The exact solution is derived by rotation of the Landau-Zener propagator at an angle of π/4 and is expressed in terms of Weber's parabolic cylinder function. Approximations for the transition probabilities are derived for all four models by using the asymptotics of the Weber function; these approximations demonstrate various effects of physical interest for each model

Exact results for survival probability in the multistate Landau-Zener model

International Nuclear Information System (INIS)

Volkov, M V; Ostrovsky, V N

2004-01-01

An exact formula is derived for survival probability in the multistate Landau-Zener model in the special case where the initially populated state corresponds to the extremal (maximum or minimum) slope of a linear diabatic potential curve. The formula was originally guessed by S Brundobler and V Elzer (1993 J. Phys. A: Math. Gen. 26 1211) based on numerical calculations. It is a simple generalization of the expression for the probability of diabatic passage in the famous two-state Landau-Zener model. Our result is obtained via analysis and summation of the entire perturbation theory series

Exact self-similar solutions of the Korteweg de Vries equation

International Nuclear Information System (INIS)

Nakach, R.

1975-12-01

It is shown that the exact analytic self-similar solution of the Korteweg de Vries equation is connected with the second Painleve transcendent. When the self-similar independant variable tends to infinity the asymptotic solutions are given by a nonlinear differential equation which can be integrated to yield Jacobian elliptic functions [fr

Exact extreme-value statistics at mixed-order transitions.

Science.gov (United States)

Bar, Amir; Majumdar, Satya N; Schehr, Grégory; Mukamel, David

2016-05-01

We study extreme-value statistics for spatially extended models exhibiting mixed-order phase transitions (MOT). These are phase transitions that exhibit features common to both first-order (discontinuity of the order parameter) and second-order (diverging correlation length) transitions. We consider here the truncated inverse distance squared Ising model, which is a prototypical model exhibiting MOT, and study analytically the extreme-value statistics of the domain lengths The lengths of the domains are identically distributed random variables except for the global constraint that their sum equals the total system size L. In addition, the number of such domains is also a fluctuating variable, and not fixed. In the paramagnetic phase, we show that the distribution of the largest domain length l_{max} converges, in the large L limit, to a Gumbel distribution. However, at the critical point (for a certain range of parameters) and in the ferromagnetic phase, we show that the fluctuations of l_{max} are governed by novel distributions, which we compute exactly. Our main analytical results are verified by numerical simulations.

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.

Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity

International Nuclear Information System (INIS)

Lai, S K; Chow, K W

2012-01-01

Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)

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 Local Correlations and Full Counting Statistics for Arbitrary States of the One-Dimensional Interacting Bose Gas

Science.gov (United States)

Bastianello, Alvise; Piroli, Lorenzo; Calabrese, Pasquale

2018-05-01

We derive exact analytic expressions for the n -body local correlations in the one-dimensional Bose gas with contact repulsive interactions (Lieb-Liniger model) in the thermodynamic limit. Our results are valid for arbitrary states of the model, including ground and thermal states, stationary states after a quantum quench, and nonequilibrium steady states arising in transport settings. Calculations for these states are explicitly presented and physical consequences are critically discussed. We also show that the n -body local correlations are directly related to the full counting statistics for the particle-number fluctuations in a short interval, for which we provide an explicit analytic result.

A novel framework on exact average symbol error probabilities of multihop transmission over amplify-and-forward relay fading channels

KAUST Repository

Yilmaz, Ferkan; Kucur, Oǧuz; Alouini, Mohamed-Slim

2010-01-01

In this paper, we propose an analytical framework on the exact computation of the average symbol error probabilities (ASEP) of multihop transmission over generalized fading channels when an arbitrary number of amplify-and-forward relays is used. Our approach relies on moment generating function (MGF) framework to obtain exact single integral expressions which can be easily computed by Gauss-Chebyshev Quadrature (GCQ) rule. As such, the derived results are a convenient tool to analyze the ASEP performance of multihop transmission over amplify-and-forward relay fading channels. Numerical and simulation results, performed to verify the correctness of the proposed formulation, are in perfect agreement. © 2010 IEEE.

A novel framework on exact average symbol error probabilities of multihop transmission over amplify-and-forward relay fading channels

KAUST Repository

Yilmaz, Ferkan

2010-09-01

In this paper, we propose an analytical framework on the exact computation of the average symbol error probabilities (ASEP) of multihop transmission over generalized fading channels when an arbitrary number of amplify-and-forward relays is used. Our approach relies on moment generating function (MGF) framework to obtain exact single integral expressions which can be easily computed by Gauss-Chebyshev Quadrature (GCQ) rule. As such, the derived results are a convenient tool to analyze the ASEP performance of multihop transmission over amplify-and-forward relay fading channels. Numerical and simulation results, performed to verify the correctness of the proposed formulation, are in perfect agreement. © 2010 IEEE.

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.

An exact approach for studying cargo transport by an ensemble of molecular motors

International Nuclear Information System (INIS)

Materassi, Donatello; Roychowdhury, Subhrajit; Hays, Thomas; Salapaka, Murti

2013-01-01

Intracellular transport is crucial for many cellular processes where a large fraction of the cargo is transferred by motor-proteins over a network of microtubules. Malfunctions in the transport mechanism underlie a number of medical maladies. Existing methods for studying how motor-proteins coordinate the transfer of a shared cargo over a microtubule are either analytical or are based on Monte-Carlo simulations. Approaches that yield analytical results, while providing unique insights into transport mechanism, make simplifying assumptions, where a detailed characterization of important transport modalities is difficult to reach. On the other hand, Monte-Carlo based simulations can incorporate detailed characteristics of the transport mechanism; however, the quality of the results depend on the number and quality of simulation runs used in arriving at results. Here, for example, it is difficult to simulate and study rare-events that can trigger abnormalities in transport. In this article, a semi-analytical methodology that determines the probability distribution function of motor-protein behavior in an exact manner is developed. The method utilizes a finite-dimensional projection of the underlying infinite-dimensional Markov model, which retains the Markov property, and enables the detailed and exact determination of motor configurations, from which meaningful inferences on transport characteristics of the original model can be derived. Under this novel probabilistic approach new insights about the mechanisms of action of these proteins are found, suggesting hypothesis about their behavior and driving the design and realization of new experiments. The advantages provided in accuracy and efficiency make it possible to detect rare events in the motor protein dynamics, that could otherwise pass undetected using standard simulation methods. In this respect, the model has allowed to provide a possible explanation for possible mechanisms under which motor proteins could

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

Compact tokamak reactors. Part 1 (analytic results)

International Nuclear Information System (INIS)

Wootton, A.J.; Wiley, J.C.; Edmonds, P.H.; Ross, D.W.

1996-01-01

We discuss the possible use of tokamaks for thermonuclear power plants, in particular tokamaks with low aspect ratio and copper toroidal field coils. Three approaches are presented. First we review and summarize the existing literature. Second, using simple analytic estimates, the size of the smallest tokamak to produce an ignited plasma is derived. This steady state energy balance analysis is then extended to determine the smallest tokamak power plant, by including the power required to drive the toroidal field, and considering two extremes of plasma current drive efficiency. The analytic results will be augmented by a numerical calculation which permits arbitrary plasma current drive efficiency; the results of which will be presented in Part II. Third, a scaling from any given reference reactor design to a copper toroidal field coil device is discussed. Throughout the paper the importance of various restrictions is emphasized, in particular plasma current drive efficiency, plasma confinement, plasma safety factor, plasma elongation, plasma beta, neutron wall loading, blanket availability and recirculating electric power. We conclude that the latest published reactor studies, which show little advantage in using low aspect ratio unless remarkably high efficiency plasma current drive and low safety factor are combined, can be reproduced with the analytic model

Exact results in a lattice model of a binary reactant mixture

International Nuclear Information System (INIS)

Thomas, P.B.

1995-01-01

We study phase separation in a binary mixture of two particles, which can react with each other and form a third compound. We determine the exact phase boundaries for a restricted range of the interaction parameters

An Exact Solution to the Central Core Model of the Renal Medulla

Science.gov (United States)

Mickens, Ronald E.

1998-11-01

The central core model of the renal medulla provides a mathematical representation of the urine concentration mechanism. The model consists of eight coupled, nonlinear ODE's subject to certain initial and boundary conditions. Many investigators have studied the properties of the solutions to these equations, however no general analytic solution is known to exist. Thus, special exact solutions assume a position of significance by providing a basis for insight into the understanding of more realistic models used to analyze actual data. We calculate an exact solution for the case in which the water permeabilities are zero and a particular, but realistic, functional form is used for the metabolic pump. A detailed discussion will be given for the results obtained on the four cencentration and four flux functions that define the model. If invited to do so, the author is willing to expand the talk for the above abstract to twenty minutes.

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)

Median of patient results as a tool for assessment of analytical stability

DEFF Research Database (Denmark)

Jørgensen, Lars Mønster; Hansen, Steen Ingemann; Petersen, Per Hyltoft

2015-01-01

BACKGROUND: In spite of the well-established external quality assessment and proficiency testing surveys of analytical quality performance in laboratory medicine, a simple tool to monitor the long-term analytical stability as a supplement to the internal control procedures is often needed. METHOD......: Patient data from daily internal control schemes was used for monthly appraisal of the analytical stability. This was accomplished by using the monthly medians of patient results to disclose deviations from analytical stability, and by comparing divergences with the quality specifications for allowable...... analytical bias based on biological variation. RESULTS: Seventy five percent of the twenty analytes achieved on two COBASs INTEGRA 800 instruments performed in accordance with the optimum and with the desirable specifications for bias. DISCUSSION: Patient results applied in analytical quality performance...

Exact solution of the neutron transport equation in spherical geometry

Energy Technology Data Exchange (ETDEWEB)

Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters

2017-03-15

Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.

Exact quasinormal modes for a special class of black holes

International Nuclear Information System (INIS)

Oliva, Julio; Troncoso, Ricardo

2010-01-01

Analytic exact expressions for the quasinormal modes of scalar and electromagnetic perturbations around a special class of black holes are found in d≥3 dimensions. It is shown that the size of the black hole provides a lower bound for the angular momentum of the perturbation. Quasinormal modes appear when this bound is fulfilled; otherwise the excitations become purely damped.

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 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

Analytical results for Abelian projection

International Nuclear Information System (INIS)

Ogilivie, Michael C.

1999-01-01

Analytic methods for Abelian projection are developed, and a number of results related to string tension measurements are obtained. It is proven that even without gauge fixing, Abelian projection yields string tensions of the underlying non-Abelian theory. Strong arguments are given for similar results in the case where gauge fixing is employed. The subgroup used for projection need only contain the center of the gauge group, and need not be Abelian. While gauge fixing is shown to be in principle unnecessary for the success of Abelian projection, it is computationally advantageous for the same reasons that improved operators, e.g., the use of fat links, are advantageous in Wilson loop measurements

Exact solutions to nonlinear symmetron theory: One- and two-mirror systems

Science.gov (United States)

Brax, Philippe; Pitschmann, Mario

2018-03-01

We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one- or two-mirror system. The one-dimensional equations of motion are integrated exactly for both systems and their solutions can be expressed in terms of Jacobi elliptic functions. Surprisingly, in the case of two parallel mirrors, the equations of motion generically provide not a unique solution but a discrete set of solutions with increasing number of nodes and energies. The solutions obtained herein can be applied to q BOUNCE experiments, neutron interferometry and for the calculation of the symmetron-field-induced "Casimir force" in the CANNEX experiment.

Comparison of approximate formulas for decision levels and detection limits for paired counting with the exact results

International Nuclear Information System (INIS)

Potter, W.E.

2005-01-01

The exact probability density function for paired counting can be expressed in terms of modified Bessel functions of integral order when the expected blank count is known. Exact decision levels and detection limits can be computed in a straightforward manner. For many applications perturbing half-integer corrections to Gaussian distributions yields satisfactory results for decision levels. When there is concern about the uncertainty for the expected value of the blank count, a way to bound the errors of both types using confidence intervals for the expected blank count is discussed. (author)

Analytical BPS Maxwell-Higgs Vortices

International Nuclear Information System (INIS)

Hora, E. da; Ferreira, M. M. Jr.; Santos, C. dos; Casana, R.

2014-01-01

We have established a prescription for the calculation of analytical vortex solutions in the context of generalized Maxwell-Higgs models whose overall dynamics is controlled by two positive functions of the scalar field, namely, f(|ϕ|) and w(|ϕ|). We have also determined a natural constraint between these functions and the Higgs potential U(|ϕ|), allowing the existence of axially symmetric Bogomol'nyi-Prasad-Sommerfield (BPS) solutions possessing finite energy. Furthermore, when the generalizing functions are chosen suitably, the nonstandard BPS equations can be solved exactly. We have studied some examples, comparing them with the usual Abrikosov-Nielsen-Olesen (ANO) solution. The overall conclusion is that the analytical self-dual vortices are well-behaved in all relevant sectors, strongly supporting the consistency of the respective generalized models. In particular, our results mimic well-known properties of the usual (numerical) configurations, as localized energy density, while contributing to the understanding of topological solitons and their description by means of analytical methods.

Exact piecewise flat gravitational waves

NARCIS (Netherlands)

van de Meent, M.

2011-01-01

We generalize our previous linear result (van de Meent 2011 Class. Quantum Grav 28 075005) in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to

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

Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

CERN Document Server

Verde, Licia; Heavens, Alan F; Jimenez, Raul; Matarrese, Sabino

2013-01-01

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7{\\sigma} for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.

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.

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.)

Exact Results for 't Hooft Loops in Gauge Theories on S^4

CERN Document Server

Gomis, Jaume; Pestun, Vasily

2012-01-01

The path integral of a general N=2 supersymmetric gauge theory on S^4 is exactly evaluated in the presence of a supersymmetric 't Hooft loop operator. The result we find - obtained using localization techniques - captures all perturbative quantum corrections as well as non-perturbative effects due to instantons and monopoles, which are supported at the north pole, south pole and equator of S^4. As a by-product, our gauge theory calculations successfully confirm the predictions made for 't Hooft loops obtained from the calculation of topological defect correlators in Liouville/Toda conformal field theory.

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.

Jet substructure with analytical methods

Energy Technology Data Exchange (ETDEWEB)

Dasgupta, Mrinal [University of Manchester, Consortium for Fundamental Physics, School of Physics and Astronomy, Manchester (United Kingdom); Fregoso, Alessandro; Powling, Alexander [University of Manchester, School of Physics and Astronomy, Manchester (United Kingdom); Marzani, Simone [Durham University, Institute for Particle Physics Phenomenology, Durham (United Kingdom)

2013-11-15

We consider the mass distribution of QCD jets after the application of jet-substructure methods, specifically the mass-drop tagger, pruning, trimming and their variants. In contrast to most current studies employing Monte Carlo methods, we carry out analytical calculations at the next-to-leading order level, which are sufficient to extract the dominant logarithmic behaviour for each technique, and compare our findings to exact fixed-order results. Our results should ultimately lead to a better understanding of these jet-substructure methods which in turn will influence the development of future substructure tools for LHC phenomenology. (orig.)

Spherical indentation of a freestanding circular membrane revisited: Analytical solutions and experiments

International Nuclear Information System (INIS)

Jin, Congrui; Davoodabadi, Ali; Li, Jianlin; Wang, Yanli; Singler, Timothy

2017-01-01

Because of the development of novel micro-fabrication techniques to produce ultra-thin materials and increasing interest in thin biological membranes, in recent years, the mechanical characterization of thin films has received a significant amount of attention. To provide a more accurate solution for the relationship among contact radius, load and deflection, the fundamental and widely applicable problem of spherical indentation of a freestanding circular membrane have been revisited. The work presented here significantly extends the previous contributions by providing an exact analytical solution to the governing equations of Föppl–Hecky membrane indented by a frictionless spherical indenter. In this study, experiments of spherical indentation has been performed, and the exact analytical solution presented in this article is compared against experimental data from existing literature as well as our own experimental results.

An exactly solvable model for multiphoton excitation of polyatomic molecules in the presence of collisions

International Nuclear Information System (INIS)

Strekalov, M L

2013-01-01

A theoretical study has been made on the non-stationary phenomena in the relaxation of highly vibrationally excited molecules under laser radiation giving rise to these molecules. An exact analytical solution to the master equation has been obtained in terms of Meixner polynomials with regard to VV and VT processes. The time-dependent vibrational distribution is used to obtain analytical expressions for the mean number of photons, stored on the vibrational degrees of freedom and transferred to a thermal bath. Using the latter result, an explicit expression is given for the average energy transfer as a function of time. Its dependence on the partial pressure of absorbing molecules has also been established. (paper)

Exact bright and dark spatial soliton solutions in saturable nonlinear media

International Nuclear Information System (INIS)

Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.

2009-01-01

We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.

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 to a nonlinear dispersive model with variable coefficients

International Nuclear Information System (INIS)

Yin Jun; Lai Shaoyong; Qing Yin

2009-01-01

A mathematical technique based on an auxiliary differential equation and the symbolic computation system Maple is employed to investigate a prototypical and nonlinear K(n, n) equation with variable coefficients. The exact solutions to the equation are constructed analytically under various circumstances. It is shown that the variable coefficients and the exponent appearing in the equation determine the quantitative change in the physical structures of the solutions.

Exact analytical solutions of continuity equation for electron beams precipitating in Coulomb collisions

Energy Technology Data Exchange (ETDEWEB)

Dobranskis, R. R.; Zharkova, V. V., E-mail: valentina.zharkova@northumbria.ac.uk [Department of Mathematics and Information Sciences, University of Northumbria, Newcastle upon Tyne NE1 2XP (United Kingdom)

2014-06-10

The original continuity equation (CE) used for the interpretation of the power law energy spectra of beam electrons in flares was written and solved for an electron beam flux while ignoring an additional free term with an electron density. In order to remedy this omission, the original CE for electron flux, considering beam's energy losses in Coulomb collisions, was first differentiated by the two independent variables: depth and energy leading to partial differential equation for an electron beam density instead of flux with the additional free term. The analytical solution of this partial differential continuity equation (PDCE) is obtained by using the method of characteristics. This solution is further used to derive analytical expressions for mean electron spectra for Coulomb collisions and to carry out numeric calculations of hard X-ray (HXR) photon spectra for beams with different parameters. The solutions revealed a significant departure of electron densities at lower energies from the original results derived from the CE for the flux obtained for Coulomb collisions. This departure is caused by the additional exponential term that appeared in the updated solutions for electron differential density leading to its faster decrease at lower energies (below 100 keV) with every precipitation depth similar to the results obtained with numerical Fokker-Planck solutions. The effects of these updated solutions for electron densities on mean electron spectra and HXR photon spectra are also discussed.

Analytical purpose electron backscattering system

International Nuclear Information System (INIS)

Desdin, L.; Padron, I.; Laria, J.

1996-01-01

In this work an analytical purposes electron backscattering system improved at the Center of Applied Studies for Nuclear Development is described. This system can be applied for fast, exact and nondestructive testing of binary and AL/Cu, AL/Ni in alloys and for other applications

Explicit analytical solution of the nonlinear Vlasov Poisson system

International Nuclear Information System (INIS)

Skarka, V.; Mahajan, S.M.; Fijalkow, E.

1993-10-01

In order to describe the time evolution of an inhomogeneous collisionless plasma the nonlinear Vlasov equation is solved perturbatively, using the subdynamics approach and the diagrammatic techniques. The solution is given in terms of a double perturbation series, one with respect to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be performed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to nonlinearities is computed. For a choice of initial perturbation the first order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with ab initio numerical simulations. Analytical computation gives a better insight into the problem and it has the advantage to be simpler, and also accessible in some range of parameters where it is difficult to find numerical solutions. (author). 27 refs, 12 figs

Exact results for corner contributions to the entanglement entropy and Rényi entropies of free bosons and fermions in 3d

Directory of Open Access Journals (Sweden)

Henriette Elvang

2015-10-01

Full Text Available In the presence of a sharp corner in the boundary of the entanglement region, the entanglement entropy (EE and Rényi entropies for 3d CFTs have a logarithmic term whose coefficient, the corner function, is scheme-independent. In the limit where the corner becomes smooth, the corner function vanishes quadratically with coefficient σ for the EE and σn for the Rényi entropies. For a free real scalar and a free Dirac fermion, we evaluate analytically the integral expressions of Casini, Huerta, and Leitao to derive exact results for σ and σn for all n=2,3,… . The results for σ agree with a recent universality conjecture of Bueno, Myers, and Witczak-Krempa that σ/CT=π2/24 in all 3d CFTs, where CT is the central charge. For the Rényi entropies, the ratios σn/CT do not indicate similar universality. However, in the limit n→∞, the asymptotic values satisfy a simple relationship and equal 1/(4π2 times the asymptotic values of the free energy of free scalars/fermions on the n-covered 3-sphere.

3D Analytical Calculation of Forces between Linear Halbach-Type Permanent Magnet Arrays

OpenAIRE

Allag , Hicham; Yonnet , Jean-Paul; Latreche , Mohamed E. H.

2009-01-01

International audience; Usely, in analytical calculation of magnetic and mechanical quantities of Halbach systems, the authors use the Fourier series approximation because the exact calculations are more difficult. In this work the interaction forces between linear Halbach arrays are analytically calculated thanks to our recent development 3D exact calculation of forces between two cuboïdal magnets with parallel and perpendicular magnetization. We essentially describe the way to separately ca...

Exact exchange potential for slabs: Asymptotic behavior of the Krieger-Li-Iafrate approximation

Science.gov (United States)

Engel, Eberhard

2018-02-01

The Krieger-Li-Iafrate (KLI) approximation for the exact exchange (EXX) potential of density functional theory is investigated far outside the surface of slabs. For large z the Slater component of the EXX/KLI potential falls off as -1 /z , where z is the distance to the surface of a slab parallel to the x y plane. The Slater potential thus reproduces the behavior of the exact EXX potential. Here it is demonstrated that the second component of the EXX/KLI potential, often called the orbital-shift term, is also proportional to 1 /z for large z , at least in general. This result is obtained by an analytical evaluation of the Brillouin zone integrals involved, relying on the exponential decay of the states into the vacuum. Several situations need to be distinguished in the Brillouin zone integration, depending on the band structure of the slab. In all standard situations, including such prominent cases as graphene and Si(111) slabs, however, a 1 /z dependence of the orbital-shift potential is obtained to leading order. The complete EXX/KLI potential therefore does not reproduce the asymptotic behavior of the exact EXX potential.

Analysis of environmental contamination resulting from catastrophic incidents: part 2. Building laboratory capability by selecting and developing analytical methodologies.

Science.gov (United States)

Magnuson, Matthew; Campisano, Romy; Griggs, John; Fitz-James, Schatzi; Hall, Kathy; Mapp, Latisha; Mullins, Marissa; Nichols, Tonya; Shah, Sanjiv; Silvestri, Erin; Smith, Terry; Willison, Stuart; Ernst, Hiba

2014-11-01

Catastrophic incidents can generate a large number of samples of analytically diverse types, including forensic, clinical, environmental, food, and others. Environmental samples include water, wastewater, soil, air, urban building and infrastructure materials, and surface residue. Such samples may arise not only from contamination from the incident but also from the multitude of activities surrounding the response to the incident, including decontamination. This document summarizes a range of activities to help build laboratory capability in preparation for sample analysis following a catastrophic incident, including selection and development of fit-for-purpose analytical methods for chemical, biological, and radiological contaminants. Fit-for-purpose methods are those which have been selected to meet project specific data quality objectives. For example, methods could be fit for screening contamination in the early phases of investigation of contamination incidents because they are rapid and easily implemented, but those same methods may not be fit for the purpose of remediating the environment to acceptable levels when a more sensitive method is required. While the exact data quality objectives defining fitness-for-purpose can vary with each incident, a governing principle of the method selection and development process for environmental remediation and recovery is based on achieving high throughput while maintaining high quality analytical results. This paper illustrates the result of applying this principle, in the form of a compendium of analytical methods for contaminants of interest. The compendium is based on experience with actual incidents, where appropriate and available. This paper also discusses efforts aimed at adaptation of existing methods to increase fitness-for-purpose and development of innovative methods when necessary. The contaminants of interest are primarily those potentially released through catastrophes resulting from malicious activity

Thermodynamics of atomic and ionized hydrogen: analytical results versus equation-of-state tables and Monte Carlo data.

Science.gov (United States)

Alastuey, A; Ballenegger, V

2012-12-01

We compute thermodynamical properties of a low-density hydrogen gas within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential. Our calculations are done using the exact scaled low-temperature (SLT) expansion, which provides a rigorous extension of the well-known virial expansion-valid in the fully ionized phase-into the Saha regime where the system is partially or fully recombined into hydrogen atoms. After recalling the SLT expansion of the pressure [A. Alastuey et al., J. Stat. Phys. 130, 1119 (2008)], we obtain the SLT expansions of the chemical potential and of the internal energy, up to order exp(-|E_{H}|/kT) included (E_{H}≃-13.6 eV). Those truncated expansions describe the first five nonideal corrections to the ideal Saha law. They account exactly, up to the considered order, for all effects of interactions and thermal excitations, including the formation of bound states (atom H, ions H^{-} and H_{2}^{+}, molecule H_{2},⋯) and atom-charge and atom-atom interactions. Among the five leading corrections, three are easy to evaluate, while the remaining ones involve well-defined internal partition functions for the molecule H_{2} and ions H^{-} and H_{2}^{+}, for which no closed-form analytical formula exist currently. We provide accurate low-temperature approximations for those partition functions by using known values of rotational and vibrational energies. We compare then the predictions of the SLT expansion, for the pressure and the internal energy, with, on the one hand, the equation-of-state tables obtained within the opacity program at Livermore (OPAL) and, on the other hand, data of path integral quantum Monte Carlo (PIMC) simulations. In general, a good agreement is found. At low densities, the simple analytical SLT formulas reproduce the values of the OPAL tables up to the last digit in a large range of temperatures, while at higher densities (ρ∼10^{-2} g/cm^{3}), some

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.

Exact results for emission from one and two atoms in an ideal cavity at multiphoton resonance

International Nuclear Information System (INIS)

Fam Le Kien; Shumovskij, A.S.; Tran Quang.

1987-01-01

The emission from the system of one or two two-level atoms in an ideal cavity with one mode at mutiphoton resonance is examined. Exact results for the two-time dipole correlation function and the time-dependent spectra of multiphoton-induced fluorescence are presented

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

Experimental verification and analytical calculation of unbalanced magnetic force in permanent magnet machines

Directory of Open Access Journals (Sweden)

Kyung-Hun Shin

2017-05-01

Full Text Available In this study, an exact analytical solution based on Fourier analysis is proposed to compute the unbalanced magnetic force in a permanent magnet machine. The magnetic field solutions are obtained by using a magnetic vector potential and by selecting the appropriate boundary conditions. Based on these field solutions, the force characteristics are also determined analytically. All analytical results were extensively validated with nonlinear two-dimensional finite element analysis and experimental results. Using proposed method, we investigated the influence on the UMF according to machine parameters. Therefore, the proposed method should be very useful in initial design and optimization process of PM machines for UMF analysis.

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.

The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions

DEFF Research Database (Denmark)

Johannessen, Kim

2014-01-01

The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...

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

A quasi-exactly solvable Lipkin-Meshkov-Glick model

International Nuclear Information System (INIS)

Pan Feng; Lin Jijie; Xue Xiaogang; Draayer, J P

2010-01-01

We prove that a special Lipkin-Meshkov-Glick model is quasi-exactly solvable with solutions that can be expressed in the SU(2) coherent state form. Ground-state properties of the model are studied analytically. We also show that the model reduces to the standard two-site Bose-Hubbard model in the large-N limit for finite U/t or large (N - 1)|U|/t cases with finite N, which proves that in these cases the ground state of the standard two-site Bose-Hubbard model is an SU(2) coherent state.

A conditionally exactly solvable generalization of the inverse square root potential

Energy Technology Data Exchange (ETDEWEB)

Ishkhanyan, A.M., E-mail: aishkhanyan@gmail.com [Institute for Physical Research, NAS of Armenia, Ashtarak 0203 (Armenia); Armenian State Pedagogical University, Yerevan 0010 (Armenia); Institute of Physics and Technology, National Research Tomsk Polytechnic University, Tomsk 634050 (Russian Federation)

2016-11-25

We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum. - Highlights: • We present a conditionally exactly solvable singular potential for 1D Schrödinger equation. • Each of the two fundamental solutions is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. • The exact equation for the energy spectrum is written using two Hermite functions that do not reduce to polynomials.

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.

Exact partial solution to the steady-state, compressible fluid flow problems of jet formation and jet penetration

International Nuclear Information System (INIS)

Karpp, R.R.

1980-10-01

This report treats analytically the problem of the symmetric impact of two compressible fluid streams. The flow is assumed to be steady, plane, inviscid, and subsonic and that the compressible fluid is of the Chaplygin (tangent gas) type. In the analysis, the governing equations are first transformed to the hodograph plane where an exact, closed-form solution is obtained by standard techniques. The distributions of fluid properties along the plane of symmetry as well as the shapes of the boundary streamlines are exactly determined by transforming the solution back to the physical plane. The problem of a compressible fluid jet penetrating into an infinite target of similar material is also exactly solved by considering a limiting case of this solution. This new compressible flow solution reduces to the classical result of incompressible flow theory when the sound speed of the fluid is allowed to approach infinity. Several illustrations of the differences between compressible and incompressible flows of the type considered are presented

Analytical quality control in environmental analysis - Recent results and future trends of the IAEA's analytical quality control programme

Energy Technology Data Exchange (ETDEWEB)

Suschny, O; Heinonen, J

1973-12-01

The significance of analytical results depends critically on the degree of their reliability, an assessment of this reliability is indispensable if the results are to have any meaning at all. Environmental radionuclide analysis is a relatively new analytical field in which new methods are continuously being developed and into which many new laboratories have entered during the last ten to fifteen years. The scarcity of routine methods and the lack of experience of the new laboratories have made the need for the assessment of the reliability of results particularly urgent in this field. The IAEA, since 1962, has provided assistance to its member states by making available to their laboratories analytical quality control services in the form of standard samples, reference materials and the organization of analytical intercomparisons. The scope of this programme has increased over the years and now includes, in addition to environmental radionuclides, non-radioactive environmental contaminants which may be analysed by nuclear methods, materials for forensic neutron activation analysis, bioassay materials and nuclear fuel. The results obtained in recent intercomparisons demonstrate the continued need for these services. (author)

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)

Dynamics of an Imperfect Microbeam Considering its Exact Shape

KAUST Repository

Bataineh, Ahmad M.

2014-08-17

We study the static and dynamic behavior of electrically actuated micromachined arches. First, we conduct experiments on micromachined polysilicon beams by driving them electrically and varying their amplitude and frequency of voltage loads. The results reveal several interesting nonlinear phenomena of jumps, hysteresis, and softening behaviors. Next, we conduct analytical and theoretical investigation to understand the experiments. First, we solve the Eigen value problem analytically. We study the effect of the initial rise on the natural frequency and mode shapes, and use a Galerkin-based procedure to derive a reduced order model, which is then used to solve both the static and dynamic responses. We use two symmetric modes in the reduced order model to have accurate and converged results. We use long time integration to solve the nonlinear ordinary differential equations, and then modify our model using effective length to match experimental results. To further improve the matching with the experimental data, we curve-fit the exact profile of the microbeam to match the experimentally measured profile and use it in the reduced-order model to generate frequency-response curves. Finally, we use another numerical technique, the shooting technique, to solve the nonlinear ordinary differential equations. By using shooting and the curve fitted function, we found that we get good agreement with the experimental data.

Exactly solvable models: the way towards a rigorous treatment of phase transitions in finite systems

International Nuclear Information System (INIS)

Bugaev, K.A.

2007-01-01

The exact analytical solutions of a variety of statistical models recently obtained for finite systems are thoroughly discussed. Among them are a constrained version of the statistical multifragmentation model, the Bag Model of Gases and the Hills and Dales Model of surface partition. The finite volume analytical solutions of these models were obtained by a novel powerful mathematical method - the Laplace-Fourier transform. The Laplace-Fourier transform allows one to study the nuclear matter equation of state, the equation of state of hadronic and quark-gluon plasma and the surface entropy of large clusters on the same footing. A complete analysis of the isobaric partition singularities of these models is done for finite systems. The developed formalism allows one to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics [ru

Median of patient results as a tool for assessment of analytical stability.

Science.gov (United States)

Jørgensen, Lars Mønster; Hansen, Steen Ingemann; Petersen, Per Hyltoft; Sölétormos, György

2015-06-15

In spite of the well-established external quality assessment and proficiency testing surveys of analytical quality performance in laboratory medicine, a simple tool to monitor the long-term analytical stability as a supplement to the internal control procedures is often needed. Patient data from daily internal control schemes was used for monthly appraisal of the analytical stability. This was accomplished by using the monthly medians of patient results to disclose deviations from analytical stability, and by comparing divergences with the quality specifications for allowable analytical bias based on biological variation. Seventy five percent of the twenty analytes achieved on two COBASs INTEGRA 800 instruments performed in accordance with the optimum and with the desirable specifications for bias. Patient results applied in analytical quality performance control procedures are the most reliable sources of material as they represent the genuine substance of the measurements and therefore circumvent the problems associated with non-commutable materials in external assessment. Patient medians in the monthly monitoring of analytical stability in laboratory medicine are an inexpensive, simple and reliable tool to monitor the steadiness of the analytical practice. Copyright © 2015 Elsevier B.V. All rights reserved.

Exact solution of the nucleons diffusion equation with increase inelastic cross section

International Nuclear Information System (INIS)

Portella, H.M.

1985-01-01

The successive aproximations method is applied to obtain an exact and compact analytical solution of the differential equation wich describes the diffusion of nucleonic component in the atmosphere, when the inelastic cross section of the air interaction nucleon-nucleus increases with the energy. The result is compared with the experimental data wich have been obtained in Chacaltaya (x=540g/cm 2 ) by the Brazil - Japan cooperation using emulsion chambers. The value of the constant a measurement of the variation of the cross section with the energy, that makes the best adjustment of the result found out with the experimental data is between 0.05 and 0.06. (M.C.K.) [pt

Aging and coarsening in isolated quantum systems after a quench: Exact results for the quantum O(N) model with N → ∞.

Science.gov (United States)

Maraga, Anna; Chiocchetta, Alessio; Mitra, Aditi; Gambassi, Andrea

2015-10-01

The nonequilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

International Nuclear Information System (INIS)

Lo, C.F.

2009-01-01

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schroedinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well. (general)

Current fluctuations and statistics during a large deviation event in an exactly solvable transport model

International Nuclear Information System (INIS)

Hurtado, Pablo I; Garrido, Pedro L

2009-01-01

We study the distribution of the time-integrated current in an exactly solvable toy model of heat conduction, both analytically and numerically. The simplicity of the model allows us to derive the full current large deviation function and the system statistics during a large deviation event. In this way we unveil a relation between system statistics at the end of a large deviation event and for intermediate times. The mid-time statistics is independent of the sign of the current, a reflection of the time-reversal symmetry of microscopic dynamics, while the end-time statistics does depend on the current sign, and also on its microscopic definition. We compare our exact results with simulations based on the direct evaluation of large deviation functions, analyzing the finite-size corrections of this simulation method and deriving detailed bounds for its applicability. We also show how the Gallavotti–Cohen fluctuation theorem can be used to determine the range of validity of simulation results

The analytical and numerical study of the fluorination of uranium dioxide particles

International Nuclear Information System (INIS)

Sazhin, S.S.

1997-01-01

A detailed analytical study of the equations describing the fluorination of UO 2 particles is presented for some limiting cases assuming that the mass flowrate of these particles is so small that they do not affect the state of the gas. The analytical solutions obtained can be used for approximate estimates of the effect of fluorination on particle diameter and temperature but their major application, however, is probably in the verification of self-consistent numerical solutions. Computational results are presented and discussed for a self-consistent problem in which both the effects of gas on particles and particles on gas are accounted for. It has been shown that in the limiting cases for which analytical solutions have been obtained, the coincidence between numerical and analytical results is almost exact. This can be considered as a verification of both the analytical and numerical solutions. (orig.)

Some exact results for the two-point function of an integrable quantum field theory

International Nuclear Information System (INIS)

Creamer, D.B.; Thacker, H.B.; Wilkinson, D.

1981-01-01

The two-point correlation function for the quantum nonlinear Schroedinger (one-dimensional delta-function gas) model is studied. An infinite-series representation for this function is derived using the quantum inverse-scattering formalism. For the case of zero temperature, the infinite-coupling (c→infinity) result of Jimbo, Miwa, Mori, and Sato is extended to give an exact expression for the order-1/c correction to the two-point function in terms of a Painleve transcendent of the fifth kind

Some exact results for the two-point function of an integrable quantum field theory

International Nuclear Information System (INIS)

Creamer, D.B.; Thacker, H.B.; Wilkinson, D.

1981-02-01

The two point correlation function for the quantum nonlinear Schroedinger (delta-function gas) model is studied. An infinite series representation for this function is derived using the quantum inverse scattering formalism. For the case of zero temperature, the infinite coupling (c → infinity) result of Jimbo, Miwa, Mori and Sato is extended to give an exact expression for the order 1/c correction to the two point function in terms of a Painleve transcendent of the fifth kind

Exact solution of the three-boson problem at vanishing energy

International Nuclear Information System (INIS)

Mora, Ch.; Gogolin, A.O.; Egger, R.

2011-01-01

A zero-range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parameterizes the three-body boundary condition while the scattering length enters the Bethe-Peierls boundary condition. The model is solved exactly at zero energy for any value of the scattering length, positive or negative. From this solution, an analytical expression for the rate of three-body recombination to the universal shallow dimer is extracted. (authors)

The analytic renormalization group

Directory of Open Access Journals (Sweden)

Frank Ferrari

2016-08-01

Full Text Available Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k∈Z, associated with the Matsubara frequencies νk=2πk/β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct “Analytic Renormalization Group” linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk|<μ (with the possible exception of the zero mode G0, together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk|≥μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.

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

Directory of Open Access Journals (Sweden)

Olaniyi Samuel Iyiola

2014-09-01

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

A Semi-Analytical Approach for the Response of Nonlinear Conservative Systems

DEFF Research Database (Denmark)

Kimiaeifar, Amin; Barari, Amin; Fooladi, M

2011-01-01

This work applies Parameter expanding method (PEM) as a powerful analytical technique in order to obtain the exact solution of nonlinear problems in the classical dynamics. Lagrange method is employed to derive the governing equations. The nonlinear governing equations are solved analytically by ...

Exact covariant results related to the redshift, aberration and luminosity distance for arbitrary spacetime and instantaneous observers

Energy Technology Data Exchange (ETDEWEB)

Calvao, Maurcio O.; Lago, Bruno L.; Reis, Ribamar R.R. [Universidade Federal do Rio de Janeiro (IF/UFRJ), RJ (Brazil). Inst. de Fisica

2011-07-01

Full text: We start by emphasizing the importance of formalizing the the concepts of a (classical) relativistic instantaneous observer, observer, frame of reference (as distinct from a coordinate system or tetrad) and a local Lorentz boost. Then, as a first result, we apply their concrete definitions to obtain exact covariant expressions for the redshift and aberration, as well as for the redshift transformation under local Lorentz boosts. Afterwards we revisit the notion of luminosity distance, providing some clarifications which render its definition manifestly valid in a completely general setting (not only for comoving observers in the Robertson-Walker spacetime); therefrom we see clearly that (not unexpectedly) the luminosity distance is dependent on the instantaneous observers and we derive its corresponding exact, covariant transformation law. By Etherington's reciprocity theorem, analogous transformation laws can be obtained for other relativistic distances, e.g. the angular size one. The exact covariant transformation law for the luminosity distance has a particularly relevant application for the determination of the impact of peculiar motions on type Ia supernovae observations and data analysis, which is supposed to be one of the main systematic effects plaguing that probe. The redshift and aberration results, on the other hand, might be of interest for precise redshift drift and astrometric (e.g. Gaia) measurements, respectively. We conclude by listing some open avenues for generalizations. (author)

Exact calculation of three-body contact interaction to second order

International Nuclear Information System (INIS)

Kaiser, N.

2012-01-01

For a system of fermions with a three-body contact interaction the second-order contributions to the energy per particle anti E(k f ) are calculated exactly. The three-particle scattering amplitude in the medium is derived in closed analytical form from the corresponding two-loop rescattering diagram. We compare the (genuine) second-order three-body contribution to anti E(k f )∝k f 10 with the second-order term due to the density-dependent effective two-body interaction, and find that the latter term dominates. The results of the present study are of interest for nuclear many-body calculations where chiral three-nucleon forces are treated beyond leading order via a density-dependent effective two-body interaction. (orig.)

Search Analytics for Your Site

CERN Document Server

Rosenfeld, Louis

2011-01-01

Any organization that has a searchable web site or intranet is sitting on top of hugely valuable and usually under-exploited data: logs that capture what users are searching for, how often each query was searched, and how many results each query retrieved. Search queries are gold: they are real data that show us exactly what users are searching for in their own words. This book shows you how to use search analytics to carry on a conversation with your customers: listen to and understand their needs, and improve your content, navigation and search performance to meet those needs.

Eigenvalue ratio detection based on exact moments of smallest and largest eigenvalues

KAUST Repository

Shakir, Muhammad; Tang, Wuchen; Rao, Anlei; Imran, Muhammad Ali; Alouini, Mohamed-Slim

2011-01-01

Detection based on eigenvalues of received signal covariance matrix is currently one of the most effective solution for spectrum sensing problem in cognitive radios. However, the results of these schemes always depend on asymptotic assumptions since the close-formed expression of exact eigenvalues ratio distribution is exceptionally complex to compute in practice. In this paper, non-asymptotic spectrum sensing approach to approximate the extreme eigenvalues is introduced. In this context, the Gaussian approximation approach based on exact analytical moments of extreme eigenvalues is presented. In this approach, the extreme eigenvalues are considered as dependent Gaussian random variables such that the joint probability density function (PDF) is approximated by bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. In this context, the definition of Copula is cited to analyze the extent of the dependency between the extreme eigenvalues. Later, the decision threshold based on the ratio of dependent Gaussian extreme eigenvalues is derived. The performance analysis of our newly proposed approach is compared with the already published asymptotic Tracy-Widom approximation approach. © 2011 ICST.

Exact solution of planar and nonplanar weak shock wave problem in gasdynamics

International Nuclear Information System (INIS)

Singh, L.P.; Ram, S.D.; Singh, D.B.

2011-01-01

Highlights: → An exact solution is derived for a problem of weak shock wave in adiabatic gas dynamics. → The density ahead of the shock is taken as a power of the position from the origin of the shock wave. → For a planar and non-planar motion, the total energy carried by the wave varies with respect to time. → The solution obtained for the planer, and cylindrically symmetric flow is new one. → The results obtained are also presented graphically for different Mach numbers. - Abstract: In the present paper, an analytical approach is used to determine a new exact solution of the problem of one dimensional unsteady adiabatic flow of planer and non-planer weak shock waves in an inviscid ideal fluid. Here it is assumed that the density ahead of the shock front varies according to the power law of the distance from the source of disturbance. The solution of the problem is presented in the form of a power in the distance and the time.

Exactly solvable model of phase transition between hadron and quark-gluon-matter

International Nuclear Information System (INIS)

Gorenstein, M.I.; Petrov, V.K.; Shelest, V.P.; Zinovjev, G.M.

1982-01-01

An exactly solvable model of phase transition between hadron and quark-gluon matter is proposed. The hadron phase of this model is considered as a gas of bags filled by point massless constituents. The mass and volume spectrum of the bag is found. The thermodynamical characteristics of a bag gas in the neighbourhood of a phase transition point are ascertained in analytical form

On the analytic continuation of functions defined by Legendre series

International Nuclear Information System (INIS)

Grinstein, F.F.

1981-07-01

An infinite diagonal sequence of Punctual Pade Approximants is considered for the approximate analytical continuation of a function defined by a formal Legendre series. The technique is tested in the case of two series with exactly known analytical sum: the generating function for Legendre polynomials and the Coulombian scattering amplitude. (author)

Analytical energy spectrum for hybrid mechanical systems

International Nuclear Information System (INIS)

Zhong, Honghua; Xie, Qiongtao; Lee, Chaohong; Guan, Xiwen; Gao, Kelin; Batchelor, Murray T

2014-01-01

We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum is obtained. The analytical energy spectrum includes regular and exceptional parts, which are both confirmed by direct numerical simulation. The regular part is determined by the zeros of the Wronskian for a pair of analytical solutions. The exceptional part is relevant to the isolated exact solutions and its energy eigenvalues are obtained by analyzing the truncation conditions for the confluent Heun functions. By analyzing the energy eigenvalues for exceptional points, we obtain the analytical conditions for the energy-level crossings, which correspond to two-fold energy degeneracy. (paper)

Exact wave packet decoherence dynamics in a discrete spectrum environment

International Nuclear Information System (INIS)

Tu, Matisse W Y; Zhang Weimin

2008-01-01

We find an exact analytical solution of the reduced density matrix from the Feynman-Vernon influence functional theory for a wave packet in an environment containing a few discrete modes. We obtain two intrinsic energy scales relating to the time scales of the system and the environment. The different relationship between these two scales alters the overall form of the solution of the system. We also introduce a decoherence measure for a single wave packet which is defined as the ratio of Schroedinger uncertainty over the delocalization extension of the wave packet and characterizes the time-evolution behaviour of the off-diagonal reduced density matrix element. We utilize the exact solution and the decoherence measure to study the wave packet decoherence dynamics. We further demonstrate how the dynamical diffusion of the wave packet leads to non-Markovian decoherence in such a microscopic environment.

Pressure of a partially ionized hydrogen gas: numerical results from exact low temperature expansions

Energy Technology Data Exchange (ETDEWEB)

Alastuey, A. [Laboratoire de Physique, ENS Lyon, CNRS, Lyon (France); Ballenegger, V. [Institut UTINAM, Universite de Franche-Comte, CNRS, Besancon (France)

2010-01-15

We consider a partially ionized hydrogen gas at low densities, where it reduces almost to an ideal mixture made with hydrogen atoms in their ground-state, ionized protons and ionized electrons. By performing systematic low-temperature expansions within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential, exact formulae for the first.ve leading corrections to the ideal Saha equation of state have been derived[A. Alastuey, V. Ballenegger et al., J. Stat. Phys. 130, 1119 (2008)]. Those corrections account for all effects of interactions and thermal excitations up to order exp(E{sub H} /kT) included, where E{sub H} {approx_equal} -13.6 eV is the ground state energy of the hydrogen atom. Among the.ve leading corrections, three are easy to evaluate, while the remaining ones involve suitably truncated internal partition functions of H{sub 2} molecules and H{sup -} and H{sub 2}{sup +} ions, for which no analytical formulae are available in closed form. We estimate those partitions functions at.nite temperature via a simple phenomenology based on known values of rotational and vibrational energies. This allows us to compute numerically the leading deviations to the Saha pressure along several isotherms and isochores. Our values are compared with those of the OPAL tables (for pure hydrogen) calculated within the ACTEX method (copyright 2010 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

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

Determination of the exact range of the value of the parameter corresponding to chaos based on the Silnikov criterion

International Nuclear Information System (INIS)

Wei-Yi, Li; Qi-Chang, Zhang; Wei, Wang

2010-01-01

Based on the Silnikov criterion, this paper studies a chaotic system of cubic polynomial ordinary differential equations in three dimensions. Using the Cardano formula, it obtains the exact range of the value of the parameter corresponding to chaos by means of the centre manifold theory and the method of multiple scales combined with Floque theory. By calculating the manifold near the equilibrium point, the series expression of the homoclinic orbit is also obtained. The space trajectory and Lyapunov exponent are investigated via numerical simulation, which shows that there is a route to chaos through period-doubling bifurcation and that chaotic attractors exist in the system. The results obtained here mean that chaos occurred in the exact range given in this paper. Numerical simulations also verify the analytical results. (general)

Exact self-similar solutions for the magnetized Noh Z pinch problem

International Nuclear Information System (INIS)

Velikovich, A. L.; Giuliani, J. L.; Thornhill, J. W.; Zalesak, S. T.; Gardiner, T. A.

2012-01-01

A self-similar solution is derived for a radially imploding cylindrical plasma with an embedded, azimuthal magnetic field. The plasma stagnates through a strong, outward propagating shock wave of constant velocity. This analysis is an extension of the classic Noh gasdynamics problem to its ideal magnetohydrodynamics (MHD) counterpart. The present exact solution is especially suitable as a test for MHD codes designed to simulate linear Z pinches. To demonstrate the application of the new solution to code verification, simulation results from the cylindrical R-Z version of Mach2 and the 3D Cartesian code Athena are compared against the analytic solution. Alternative routines from the default ones in Athena lead to significant improvement of the results, thereby demonstrating the utility of the self-similar solution for verification.

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.

Exact spinor-scalar bound states in a quantum field theory with scalar interactions

International Nuclear Information System (INIS)

Shpytko, Volodymyr; Darewych, Jurij

2001-01-01

We study two-particle systems in a model quantum field theory in which scalar particles and spinor particles interact via a mediating scalar field. The Lagrangian of the model is reformulated by using covariant Green's functions to solve for the mediating field in terms of the particle fields. This results in a Hamiltonian in which the mediating-field propagator appears directly in the interaction term. It is shown that exact two-particle eigenstates of the Hamiltonian can be determined. The resulting relativistic fermion-boson equation is shown to have Dirac and Klein-Gordon one-particle limits. Analytical solutions for the bound state energy spectrum are obtained for the case of massless mediating fields

An analytical method for neutron thermalization calculations in heterogenous reactors

Energy Technology Data Exchange (ETDEWEB)

Pop-Jordanov, J [Boris Kidric Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1965-07-01

It is well known that the use of the diffusion approximation for sturesult in considerable errors. On the other hand, more exact numerical methods are rather laborious and require the use of large digital computers. In this paper, the use of the diffusion approximation in absorbing media has been avoided, but the treatment remained analytical, thus simplifying practical calculations.

An analytical method for neutron thermalization calculations in heterogenous reactors

International Nuclear Information System (INIS)

Pop-Jordanov, J.

1965-01-01

It is well known that the use of the diffusion approximation for studying neutron thermalization in heterogeneous reactors may result in considerable errors. On the other hand, more exact numerical methods are rather laborious and require the use of large digital computers. In this paper, the use of the diffusion approximation in absorbing media has been avoided, but the treatment remained analytical, thus simplifying practical calculations

Semi-analytical solution to arbitrarily shaped beam scattering

Science.gov (United States)

Wang, Wenjie; Zhang, Huayong; Sun, Yufa

2017-07-01

Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.

Jurin's law revisited: Exact meniscus shape and column height.

Science.gov (United States)

Liu, Sai; Li, Shanpeng; Liu, Jianlin

2018-03-30

Capillary rise of a liquid column is a historical problem, which has normally been formulated by Jurin's law. In the present study, we investigate the exact solutions of the column height, considering the real shape of the meniscus according to the Young-Laplace equation. The analytical solution in the planar model and the numerical solution in the axisymmetric model on the meniscus shape are both given, which are compared with the results from Jurin's law, modified Jurin's law and Surface Evolver simulation. The results quantitatively show that when the distance between the two plates or the diameter of the tube becomes bigger, Jurin's law and modified Jurin's law would cause serious errors, and the profile morphology of the meniscus must be calculated according to the Young-Laplace equation. These findings are beneficial for us to better understand the mechanism of capillarity and wetting, which are promising for such areas as oil displacement, ore floatation, building materials, fabrics, etc.

Analytic solutions of a class of nonlinearly dynamic systems

International Nuclear Information System (INIS)

Wang, M-C; Zhao, X-S; Liu, X

2008-01-01

In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently

Analytically derived weighting factors for transmission tomography cone beam projections

International Nuclear Information System (INIS)

Yao Weiguang; Leszczynski, Konrad

2009-01-01

Weighting factors, which define the contributions of individual voxels of a 3D object to individual projection elements (pixels) on the detector, are the basic elements required in iterative tomographic reconstructions from transmission projections. Exact or as accurate as possible values for weighting factors are required in high-resolution reconstructions. Geometric complexity of the problem, however, makes it difficult to obtain exact weighting factor values. In this work, we derive an analytical expression for the weighting factors in cone beam projection geometry. The resulting formula is validated and applied to reconstruction from mega and kilovoltage x-ray cone beam projections. The reconstruction speed and accuracy are significantly improved by using the weighting factor values.

Exact solutions for helical magnetohydrodynamic equilibria. II. Nonstatic and nonbarotropic solutions

International Nuclear Information System (INIS)

Villata, M.; Ferrari, A.

1994-01-01

In the framework of the analytical study of magnetohydrodynamic (MHD) equilibria with flow and nonuniform density, a general family of well-behaved exact solutions of the generalized Grad--Shafranov equation and of the whole set of time-independent MHD equations completed by the nonbarotropic ideal gas equation of state is obtained, both in helical and axial symmetry. The helical equilibrium solutions are suggested to be relevant to describe the helical morphology of some astrophysical jets

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

Analytic regularization of uniform cubic B-spline deformation fields.

Science.gov (United States)

Shackleford, James A; Yang, Qi; Lourenço, Ana M; Shusharina, Nadya; Kandasamy, Nagarajan; Sharp, Gregory C

2012-01-01

Image registration is inherently ill-posed, and lacks a unique solution. In the context of medical applications, it is desirable to avoid solutions that describe physically unsound deformations within the patient anatomy. Among the accepted methods of regularizing non-rigid image registration to provide solutions applicable to medical practice is the penalty of thin-plate bending energy. In this paper, we develop an exact, analytic method for computing the bending energy of a three-dimensional B-spline deformation field as a quadratic matrix operation on the spline coefficient values. Results presented on ten thoracic case studies indicate the analytic solution is between 61-1371x faster than a numerical central differencing solution.

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.

Exact solution for the Poisson field in a semi-infinite strip.

Science.gov (United States)

Cohen, Yossi; Rothman, Daniel H

2017-04-01

The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.

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

International Nuclear Information System (INIS)

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

2002-01-01

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

On analytical solutions to the problem of the Coulomb and confining potentials

International Nuclear Information System (INIS)

Dineykhan, M.; Nazmitdinov, R.G.

1997-01-01

The oscillator representation method is presented and applied to calculate the energy spectrum of the superposition of the Coulomb and the power-law potentials, the Coulomb and the Yukawa potentials. The method provides an efficient way to obtain analytical results for arbitrary set of parameters of the considered potentials. The energies of ground and excited states of a quantum system are in good agreement with the exact results

Preliminary results of testing bioassay analytical performance standards

International Nuclear Information System (INIS)

Fisher, D.R.; Robinson, A.V.; Hadley, R.T.

1983-08-01

The analytical performance of both in vivo and in vitro bioassay laboratories is being studied to determine the capability of these laboratories to meet the minimum criteria for accuracy and precision specified in the draft ANSI Standard N13.30, Performance Criteria for Radiobioassay. This paper presents preliminary results of the first round of testing

New Exact and Asymptotic Results of Dual-Branch MRC over Correlated Nakagami-m Fading Channels

KAUST Repository

Al-Quwaiee, Hessa

2015-05-01

We present in this paper a new performance analysis results of dual-branch maximal-ratio combining over correlated Nakagami-m fading channels with arbitrary fading parameter. In particular, we derive exact closed-form expressions of the outage probability, the average bit error rate, and the ergodic capacity in terms of the extended generalized bivariate Meijer G- function. Moreover, we also provide simple closed- form asymptotic expressions in the high signal-to- noise ratio regime of these three fundamental performance measures. © 2015 IEEE.

New Exact and Asymptotic Results of Dual-Branch MRC over Correlated Nakagami-m Fading Channels

KAUST Repository

Al-Quwaiee, Hessa; Alouini, Mohamed-Slim

2015-01-01

We present in this paper a new performance analysis results of dual-branch maximal-ratio combining over correlated Nakagami-m fading channels with arbitrary fading parameter. In particular, we derive exact closed-form expressions of the outage probability, the average bit error rate, and the ergodic capacity in terms of the extended generalized bivariate Meijer G- function. Moreover, we also provide simple closed- form asymptotic expressions in the high signal-to- noise ratio regime of these three fundamental performance measures. © 2015 IEEE.

Exact mean-field theory of ionic solutions: non-Debye screening

International Nuclear Information System (INIS)

Varela, L.M.; Garcia, Manuel; Mosquera, Victor

2003-01-01

The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Hueckel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory

Exact Reconstruction From Uniformly Attenuated Helical Cone-Beam Projections in SPECT

International Nuclear Information System (INIS)

Gullberg, Grant T.; Huang, Qiu; You, Jiangsheng; Zeng, Gengsheng L.

2008-01-01

In recent years the development of cone-beam reconstruction algorithms has been an active research area in x-ray computed tomography (CT), and significant progress has been made in the advancement of algorithms. Theoretically exact and computationally efficient analytical algorithms can be found in the literature. However, in single photon emission computed tomography (SPECT), published cone-beam reconstruction algorithms are either approximate or involve iterative methods. The SPECT reconstruction problem is more complicated due to degradations in the imaging detection process, one of which is the effect of attenuation of gamma ray photons. Attenuation should be compensated for to obtain quantitative results. In this paper, an analytical reconstruction algorithm for uniformly attenuated cone-beam projection data is presented for SPECT imaging. The algorithm adopts the DBH method, a procedure consisting of differentiation and backprojection followed by a finite inverse cosh-weighted Hilbert transform. The significance of the proposed approach is that a selected region of interest can be reconstructed even with a detector with a reduced field of view. The algorithm is designed for a general trajectory. However, to validate the algorithm, a numerical study was performed using a helical trajectory. The implementation is efficient and the simulation result is promising

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

Statistical mechanics of few-particle systems: exact results for two useful models

Science.gov (United States)

Miranda, Enrique N.

2017-11-01

The statistical mechanics of small clusters (n ˜ 10-50 elements) of harmonic oscillators and two-level systems is studied exactly, following the microcanonical, canonical and grand canonical formalisms. For clusters with several hundred particles, the results from the three formalisms coincide with those found in the thermodynamic limit. However, for clusters formed by a few tens of elements, the three ensembles yield different results. For a cluster with a few tens of harmonic oscillators, when the heat capacity per oscillator is evaluated within the canonical formalism, it reaches a limit value equal to k B , as in the thermodynamic case, while within the microcanonical formalism the limit value is k B (1-1/n). This difference could be measured experimentally. For a cluster with a few tens of two-level systems, the heat capacity evaluated within the canonical and microcanonical ensembles also presents differences that could be detected experimentally. Both the microcanonical and grand canonical formalism show that the entropy is non-additive for systems this small, while the canonical ensemble reaches the opposite conclusion. These results suggest that the microcanonical ensemble is the most appropriate for dealing with systems with tens of particles.

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.)

An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders

DEFF Research Database (Denmark)

Larsen, Niels Vesterdal; Breinbjerg, Olav

2004-01-01

Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...

Adaptive cyclically dominating game on co-evolving networks: numerical and analytic results

Science.gov (United States)

Choi, Chi Wun; Xu, Chen; Hui, Pak Ming

2017-10-01

A co-evolving and adaptive Rock (R)-Paper (P)-Scissors (S) game (ARPS) in which an agent uses one of three cyclically dominating strategies is proposed and studied numerically and analytically. An agent takes adaptive actions to achieve a neighborhood to his advantage by rewiring a dissatisfying link with a probability p or switching strategy with a probability 1 - p. Numerical results revealed two phases in the steady state. An active phase for p pc has three separate clusters of agents using only R, P, and S, respectively with terminated adaptive actions. A mean-field theory based on the link densities in co-evolving network is formulated and the trinomial closure scheme is applied to obtain analytical solutions. The analytic results agree with simulation results on ARPS well. In addition, the different probabilities of winning, losing, and drawing a game among the agents are identified as the origin of the small discrepancy between analytic and simulation results. As a result of the adaptive actions, agents of higher degrees are often those being taken advantage of. Agents with a smaller (larger) degree than the mean degree have a higher (smaller) probability of winning than losing. The results are informative for future attempts on formulating more accurate theories.

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

Science.gov (United States)

Iafrate, G J; Krieger, J B

2013-03-07

determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Interacting Brownian Swarms: Some Analytical Results

Directory of Open Access Journals (Sweden)

Guillaume Sartoretti

2016-01-01

Full Text Available We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. Implicitly, the implementation of rank-based mutual interactions, requires that agents have infinite interaction ranges. Using the probabilistic size of the swarm’s support, we analytically estimate the critical interaction range below that flocked swarms cannot survive. In the second part of the paper, we consider the interactions between two flocked swarms of Brownian agents with finite interaction ranges. Both swarms travel with different barycentric velocities, and agents from both swarms indifferently interact with each other. For appropriate initial configurations, both swarms eventually collide (i.e., all agents interact. Depending on the values of the control parameters, one of the following patterns emerges after collision: (i Both swarms remain essentially flocked, or (ii the swarms become ultimately quasi-free and recover their nominal barycentric speeds. We derive a set of analytical flocking conditions based on the generalized rank-based Brownian motion. An extensive set of numerical simulations corroborates our analytical findings.

Analytical solution of the thermo-mechanical stresses in a multilayered composite pressure vessel considering the influence of the closed ends

International Nuclear Information System (INIS)

Zhang, Q.; Wang, Z.W.; Tang, C.Y.; Hu, D.P.; Liu, P.Q.; Xia, L.Z.

2012-01-01

Limited work has been reported on determining the thermo-mechanical stresses in a multilayered composite pressure vessel when the influence of its closed ends is considered. In this study, an analytical solution was derived for determining the stress distribution of a multilayered composite pressure vessel subjected to an internal fluid pressure and a thermal load, based on thermo-elasticity theory. In the solution, a pseudo extrusion pressure was proposed to emulate the effect of the closed ends of the pressure vessel. To validate the analytical solution, the stress distribution of the pressure vessel was also computed using finite element (FE) method. It was found that the analytical results were in good agreement with the computational ones, and the effect of thermal load on the stress distribution was discussed in detail. The proposed analytical solution provides an exact means to design multilayered composite pressure vessels. Highlights: ► The thermal-mechanical stress was derived for a multilayered pressure vessel. ► A new pseudo extrusion pressure was proposed to emulate the effect of closed ends. ► The analytical results are in good agreement with the computational ones using FEM. ► The solution provides an exact way to design the multilayered pressure vessel.

Tank 48H Waste Composition and Results of Investigation of Analytical Methods

Energy Technology Data Exchange (ETDEWEB)

Walker , D.D. [Westinghouse Savannah River Company, AIKEN, SC (United States)

1997-04-02

This report serves two purposes. First, it documents the analytical results of Tank 48H samples taken between April and August 1996. Second, it describes investigations of the precision of the sampling and analytical methods used on the Tank 48H samples.

Vertex function for the coupling of an electron with intramolecular phonons: Exact results in the antiadiabatic limit

International Nuclear Information System (INIS)

Takada, Y.; Higuchi, T.

1995-01-01

The Green's-function techniques, especially the one developed in the preceding paper [Takada, Phys. Rev. B 52, 12 708 (1995)], are employed to calculate the electron-phonon vertex part as well as the electronic self-energy exactly on both real- and imaginary-frequency axes in the electron-phonon Holstein model with the on-site Coulomb repulsion in the limit in which the intramolecular phonon energy ω 0 is much larger than the electronic bandwidth. The rigorous vertex part is found to diverge at the frequencies at which an electron is locked by such local phonons with an infinitely strong effective coupling. Characteristic frequencies of this divergence, which are not equal to multiples of ω 0 , are calculated as a function of the electron-phonon bare coupling constant. Our results for the self-energy are checked successfully with the exact ones obtained by the Lang-Firsov canonical transformation

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.

Quantifying the measurement uncertainty of results from environmental analytical methods.

Science.gov (United States)

Moser, J; Wegscheider, W; Sperka-Gottlieb, C

2001-07-01

The Eurachem-CITAC Guide Quantifying Uncertainty in Analytical Measurement was put into practice in a public laboratory devoted to environmental analytical measurements. In doing so due regard was given to the provisions of ISO 17025 and an attempt was made to base the entire estimation of measurement uncertainty on available data from the literature or from previously performed validation studies. Most environmental analytical procedures laid down in national or international standards are the result of cooperative efforts and put into effect as part of a compromise between all parties involved, public and private, that also encompasses environmental standards and statutory limits. Central to many procedures is the focus on the measurement of environmental effects rather than on individual chemical species. In this situation it is particularly important to understand the measurement process well enough to produce a realistic uncertainty statement. Environmental analytical methods will be examined as far as necessary, but reference will also be made to analytical methods in general and to physical measurement methods where appropriate. This paper describes ways and means of quantifying uncertainty for frequently practised methods of environmental analysis. It will be shown that operationally defined measurands are no obstacle to the estimation process as described in the Eurachem/CITAC Guide if it is accepted that the dominating component of uncertainty comes from the actual practice of the method as a reproducibility standard deviation.

Analytic structure of the wave function for a hydrogen atom in an analytic potential

International Nuclear Information System (INIS)

Hill, R.N.

1984-01-01

The rate of convergence of an approximate method for solving Schroedinger's equation depends on the ability of the approximating sequence to mimic the analytic structure of the unknown exact wave function. Thus a knowledge of the analytic structure of the wave function can be of great value when approximation schemes are designed. Consider the Schroedinger equation [- 1/2 del 2 -r -1 +V(r)]Psi(r) = EPsi(r) for a hydrogen atom in a potential V(r). The general theory of elliptic partial differential equations implies that Psi is analytic at regular points, but no general theory is available at singular points. The present paper investigates the Coulomb singular point at r = 0 and shows that, if V(r) = V 1 (x, y, z)+rV 2 (x, y, z) where V 1 and V 2 are analytic functions of x, y, z at x = y = z = 0, then the wave function has the form Psi(r) = Psi 1 (x, y, z)+rPsi 2 (x, y, z) where Psi 1 and Psi 2 are analytic functions of x, y, z at x = y = z = 0

Analytical approaches for the approximate solution of a nonlinear fractional ordinary differential equation

International Nuclear Information System (INIS)

Basak, K C; Ray, P C; Bera, R K

2009-01-01

The aim of the present analysis is to apply the Adomian decomposition method and He's variational method for the approximate analytical solution of a nonlinear ordinary fractional differential equation. The solutions obtained by the above two methods have been numerically evaluated and presented in the form of tables and also compared with the exact solution. It was found that the results obtained by the above two methods are in excellent agreement with the exact solution. Finally, a surface plot of the approximate solutions of the fractional differential equation by the above two methods is drawn for 0≤t≤2 and 1<α≤2.

Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material

OpenAIRE

Dalarsson, Mariana; Tassin, Philippe

2012-01-01

We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results o...

Exact solution of corner-modified banded block-Toeplitz eigensystems

International Nuclear Information System (INIS)

Cobanera, Emilio; Alase, Abhijeet; Viola, Lorenza; Ortiz, Gerardo

2017-01-01

Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified . Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz , independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix , whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev. (paper)

Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis

Directory of Open Access Journals (Sweden)

Roman Cherniha

2016-06-01

Full Text Available The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration for a wide range of values of the model parameters.

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

Stability under scalar perturbations and quasinormal modes of 4D Einstein-Born-Infeld dilaton spacetime. Exact spectrum

International Nuclear Information System (INIS)

Destounis, Kyriakos; Panotopoulos, Grigoris; Rincon, Angel

2018-01-01

We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1 + 3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an exact analytical expression for the spectrum. We find that the frequencies are purely imaginary, and we confirm our results by computing them numerically. Although the scalar field that perturbs the black hole is electrically neutral, an instability similar to that seen in charged scalar perturbations of the Reissner-Nordstroem black hole is observed. (orig.)

Stability under scalar perturbations and quasinormal modes of 4D Einstein-Born-Infeld dilaton spacetime. Exact spectrum

Energy Technology Data Exchange (ETDEWEB)

Destounis, Kyriakos; Panotopoulos, Grigoris [Universidade de Lisboa, Centro Multidisciplinar de Astrofisica, Instituto Superior Tecnico, Lisbon (Portugal); Rincon, Angel [Pontificia Universidad Catolica de Chile, Instituto de Fisica, Santiago (Chile)

2018-02-15

We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1 + 3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an exact analytical expression for the spectrum. We find that the frequencies are purely imaginary, and we confirm our results by computing them numerically. Although the scalar field that perturbs the black hole is electrically neutral, an instability similar to that seen in charged scalar perturbations of the Reissner-Nordstroem black hole is observed. (orig.)

Black holes by analytic continuation

CERN Document Server

Amati, Daniele

1997-01-01

In the context of a two-dimensional exactly solvable model, the dynamics of quantum black holes is obtained by analytically continuing the description of the regime where no black hole is formed. The resulting spectrum of outgoing radiation departs from the one predicted by the Hawking model in the region where the outgoing modes arise from the horizon with Planck-order frequencies. This occurs early in the evaporation process, and the resulting physical picture is unconventional. The theory predicts that black holes will only radiate out an energy of Planck mass order, stabilizing after a transitory period. The continuation from a regime without black hole formation --accessible in the 1+1 gravity theory considered-- is implicit in an S matrix approach and provides in this way a possible solution to the problem of information loss.

Circular orbits of corotating binary black holes: Comparison between analytical and numerical results

International Nuclear Information System (INIS)

Damour, Thibault; Gourgoulhon, Eric; Grandclement, Philippe

2002-01-01

We compare recent numerical results, obtained within a 'helical Killing vector' approach, on circular orbits of corotating binary black holes to the analytical predictions made by the effective one-body (EOB) method (which has been recently extended to the case of spinning bodies). On the scale of the differences between the results obtained by different numerical methods, we find good agreement between numerical data and analytical predictions for several invariant functions describing the dynamical properties of circular orbits. This agreement is robust against the post-Newtonian accuracy used for the analytical estimates, as well as under choices of the resummation method for the EOB 'effective potential', and gets better as one uses a higher post-Newtonian accuracy. These findings open the way to a significant 'merging' of analytical and numerical methods, i.e. to matching an EOB-based analytical description of the (early and late) inspiral, up to the beginning of the plunge, to a numerical description of the plunge and merger. We illustrate also the 'flexibility' of the EOB approach, i.e. the possibility of determining some 'best fit' values for the analytical parameters by comparison with numerical data

Exact solution for four-order acousto-optic Bragg diffraction with arbitrary initial conditions.

Science.gov (United States)

Pieper, Ron; Koslover, Deborah; Poon, Ting-Chung

2009-03-01

An exact solution to the four-order acousto-optic (AO) Bragg diffraction problem with arbitrary initial conditions compatible with exact Bragg angle incident light is developed. The solution, obtained by solving a 4th-order differential equation, is formalized into a transition matrix operator predicting diffracted light orders at the exit of the AO cell in terms of the same diffracted light orders at the entrance. It is shown that the transition matrix is unitary and that this unitary matrix condition is sufficient to guarantee energy conservation. A comparison of analytical solutions with numerical predictions validates the formalism. Although not directly related to the approach used to obtain the solution, it was discovered that all four generated eigenvalues from the four-order AO differential matrix operator are expressed simply in terms of Euclid's Divine Proportion.

Homoclinic orbits around spinning black holes. I. Exact solution for the Kerr separatrix

International Nuclear Information System (INIS)

Levin, Janna; Perez-Giz, Gabe

2009-01-01

For equatorial Kerr orbits, we show that each separatrix between bound and plunging geodesics is a homoclinic orbit--an orbit that asymptotes to an energetically-bound, unstable circular orbit. We derive exact expressions for these trajectories in terms of elementary functions. We also clarify the formal connection between the separatrix and zoom-whirl orbits and show that, contrary to popular belief, zoom-whirl behavior is not intrinsically a near-separatrix phenomenon. This paper focuses on homoclinic behavior in physical space, while in a companion paper we paint the complementary phase space portrait. Although they refer to geodesic motion, the exact solutions for the Kerr separatrix could be useful for analytic or numerical studies of eccentric transitions from orbital to plunging motion under the dissipative effects of gravitational radiation.

Quantum quenches to the attractive one-dimensional Bose gas: exact results

Directory of Open Access Journals (Sweden)

Lorenzo Piroli, Pasquale Calabrese, Fabian H. L. Essler

2016-09-01

Full Text Available We study quantum quenches to the one-dimensional Bose gas with attractive interactions in the case when the initial state is an ideal one-dimensional Bose condensate. We focus on properties of the stationary state reached at late times after the quench. This displays a finite density of multi-particle bound states, whose rapidity distribution is determined exactly by means of the quench action method. We discuss the relevance of the multi-particle bound states for the physical properties of the system, computing in particular the stationary value of the local pair correlation function $g_2$.

Analytic formulation of neutrino oscillation probability in constant matter

International Nuclear Information System (INIS)

Kimura, Keiichi; Takamura, Akira; Yokomakura, Hidekazu

2003-01-01

In this paper, based on the work (Kimura K et al 2002 Phys. Lett. B 537 86) we present the simple derivation of an exact and analytic formula for neutrino oscillation probability. We consider three flavour neutrino oscillations in matter with constant density

3-D discrete analytical ridgelet transform.

Science.gov (United States)

Helbert, David; Carré, Philippe; Andres, Eric

2006-12-01

In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.

Exact two-point resistance, and the simple random walk on the complete graph minus N edges

International Nuclear Information System (INIS)

Chair, Noureddine

2012-01-01

An analytical approach is developed to obtain the exact expressions for the two-point resistance and the total effective resistance of the complete graph minus N edges of the opposite vertices. These expressions are written in terms of certain numbers that we introduce, which we call the Bejaia and the Pisa numbers; these numbers are the natural generalizations of the bisected Fibonacci and Lucas numbers. The correspondence between random walks and the resistor networks is then used to obtain the exact expressions for the first passage and mean first passage times on this graph. - Highlights: ► We obtain exact formulas for the two-point resistance of the complete graph minus N edges. ► We obtain also the total effective resistance of this graph. ► We modified Schwatt’s formula on trigonometrical power sum to suit our computations. ► We introduced the generalized bisected Fibonacci and Lucas numbers: the Bejaia and the Pisa numbers. ► The first passage and mean first passage times of the random walks have exact expressions.

Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport

International Nuclear Information System (INIS)

Litvinenko, Yuri E.; Effenberger, Frederic

2014-01-01

Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

Planck scale physics and topology change through an exactly solvable model

Energy Technology Data Exchange (ETDEWEB)

Lobo, Francisco S.N., E-mail: flobo@cii.fc.ul.pt [Centro de Astronomia e Astrofísica da Universidade de Lisboa, Campo Grande, Ed. C8, 1749-016 Lisboa (Portugal); Martinez-Asencio, Jesus, E-mail: jesusmartinez@ua.es [Departamento de Física Aplicada, Facultad de Ciencias, Fase II, Universidad de Alicante, Alicante E-03690 (Spain); Olmo, Gonzalo J., E-mail: gonzalo.olmo@csic.es [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia – CSIC, Universidad de Valencia, Burjassot, 46100, Valencia (Spain); Departamento de Física, Universidade Federal da Paraíba, 58051-900 João Pessoa, Paraíba (Brazil); Rubiera-Garcia, D., E-mail: drubiera@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, 58051-900 João Pessoa, Paraíba (Brazil)

2014-04-04

We consider the collapse of a charged radiation fluid in a Planck-suppressed quadratic extension of General Relativity (GR) formulated à la Palatini. We obtain exact analytical solutions that extend the charged Vaidya-type solution of GR, which allows to explore in detail new physics at the Planck scale. Starting from Minkowski space, we find that the collapsing fluid generates wormholes supported by the electric field. We discuss the relevance of our findings in relation to the quantum foam structure of space–time and the meaning of curvature divergences in this theory.

Planck scale physics and topology change through an exactly solvable model

International Nuclear Information System (INIS)

Lobo, Francisco S.N.; Martinez-Asencio, Jesus; Olmo, Gonzalo J.; Rubiera-Garcia, D.

2014-01-01

We consider the collapse of a charged radiation fluid in a Planck-suppressed quadratic extension of General Relativity (GR) formulated à la Palatini. We obtain exact analytical solutions that extend the charged Vaidya-type solution of GR, which allows to explore in detail new physics at the Planck scale. Starting from Minkowski space, we find that the collapsing fluid generates wormholes supported by the electric field. We discuss the relevance of our findings in relation to the quantum foam structure of space–time and the meaning of curvature divergences in this theory.

An exact formula to describe the amplification process in a photomultiplier tube

International Nuclear Information System (INIS)

Rademacker, Jonas

2002-01-01

An analytical function is derived that exactly describes the amplification process due to a series of discrete, Poisson-like amplifications like those in a photo multiplier tube (PMT). A numerical recipe is provided that implements this function as a computer program. It is shown how the program can be used as the core element of a faster, simplified routine to fit PMT spectra with high efficiency. The functionality of the method is demonstrated by fitting both, Monte Carlo generated and measured PMT spectra

Improving the trust in results of numerical simulations and scientific data analytics

Energy Technology Data Exchange (ETDEWEB)

Cappello, Franck [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil [Argonne National Lab. (ANL), Argonne, IL (United States); Hovland, Paul [Argonne National Lab. (ANL), Argonne, IL (United States); Peterka, Tom [Argonne National Lab. (ANL), Argonne, IL (United States); Phillips, Carolyn [Argonne National Lab. (ANL), Argonne, IL (United States); Snir, Marc [Argonne National Lab. (ANL), Argonne, IL (United States); Wild, Stefan [Argonne National Lab. (ANL), Argonne, IL (United States)

2015-04-30

This white paper investigates several key aspects of the trust that a user can give to the results of numerical simulations and scientific data analytics. In this document, the notion of trust is related to the integrity of numerical simulations and data analytics applications. This white paper complements the DOE ASCR report on Cybersecurity for Scientific Computing Integrity by (1) exploring the sources of trust loss; (2) reviewing the definitions of trust in several areas; (3) providing numerous cases of result alteration, some of them leading to catastrophic failures; (4) examining the current notion of trust in numerical simulation and scientific data analytics; (5) providing a gap analysis; and (6) suggesting two important research directions and their respective research topics. To simplify the presentation without loss of generality, we consider that trust in results can be lost (or the results’ integrity impaired) because of any form of corruption happening during the execution of the numerical simulation or the data analytics application. In general, the sources of such corruption are threefold: errors, bugs, and attacks. Current applications are already using techniques to deal with different types of corruption. However, not all potential corruptions are covered by these techniques. We firmly believe that the current level of trust that a user has in the results is at least partially founded on ignorance of this issue or the hope that no undetected corruptions will occur during the execution. This white paper explores the notion of trust and suggests recommendations for developing a more scientifically grounded notion of trust in numerical simulation and scientific data analytics. We first formulate the problem and show that it goes beyond previous questions regarding the quality of results such as V&V, uncertainly quantification, and data assimilation. We then explore the complexity of this difficult problem, and we sketch complementary general

Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength

Energy Technology Data Exchange (ETDEWEB)

Hoang-Do, Ngoc-Tram [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam); Pham, Dang-Lan [Institute for Computational Science and Technology, Quang Trung Software Town, District 12, Ho Chi Minh City (Viet Nam); Le, Van-Hoang, E-mail: hoanglv@hcmup.edu.vn [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)

2013-08-15

Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity.

Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength

International Nuclear Information System (INIS)

Hoang-Do, Ngoc-Tram; Pham, Dang-Lan; Le, Van-Hoang

2013-01-01

Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity

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.

Theory of a spherical electrostatic probe in a continuum plasma: Analytical models

International Nuclear Information System (INIS)

Brailsford, A.D.

1977-01-01

A simple physical model of the charge distribution surrounding a biased spherical probe in a quiescent plasma, suggested by the theory of Su and Lam, is used to rederive the probe current-voltage characteristic. The result is compared with that of a slightly different version due to Kiel and with the exact numerical results of Baum and Chapkis. It is shown that if the ratio of the probe radius to the Debye length of the plasma is greater than or of the order of unity, the model calculation is in excellent agreement with the exact results when the dimensionless probe voltage phi/sup asterisk//sub p/,=vertical-barephi/sub p//kTvertical-bar in standard notation, is greater than 10, for both thick and thin sheaths. The comparison also provides an assessment of the importance of various additional validity criteria encountered in analytical treatments of the problem

Discrete dynamics versus analytic dynamics

DEFF Research Database (Denmark)

Toxværd, Søren

2014-01-01

For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...... of such an analytic analogy, exists an exact hidden energy invariance E * for VA dynamics. The fact that the discrete VA dynamics has the same invariances as Newtonian dynamics raises the question, which of the formulations that are correct, or alternatively, the most appropriate formulation of classical dynamics....... In this context the relation between the discrete VA dynamics and the (general) discrete dynamics investigated by Lee [Phys. Lett. B122, 217 (1983)] is presented and discussed....

A model of modulated diffusion. I. Analytical results

International Nuclear Information System (INIS)

Bazzani, A.; Turcchetti, G.; Vaienti, S.

1994-01-01

We introduce an integrable isochronous system and perturb its frequency by an external-deterministic or purely random-noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion

Exact combinatorial reliability analysis of dynamic systems with sequence-dependent failures

International Nuclear Information System (INIS)

Xing Liudong; Shrestha, Akhilesh; Dai Yuanshun

2011-01-01

Many real-life fault-tolerant systems are subjected to sequence-dependent failure behavior, in which the order in which the fault events occur is important to the system reliability. Such systems can be modeled by dynamic fault trees (DFT) with priority-AND (pAND) gates. Existing approaches for the reliability analysis of systems subjected to sequence-dependent failures are typically state-space-based, simulation-based or inclusion-exclusion-based methods. Those methods either suffer from the state-space explosion problem or require long computation time especially when results with high degree of accuracy are desired. In this paper, an analytical method based on sequential binary decision diagrams is proposed. The proposed approach can analyze the exact reliability of non-repairable dynamic systems subjected to the sequence-dependent failure behavior. Also, the proposed approach is combinatorial and is applicable for analyzing systems with any arbitrary component time-to-failure distributions. The application and advantages of the proposed approach are illustrated through analysis of several examples. - Highlights: → We analyze the sequence-dependent failure behavior using combinatorial models. → The method has no limitation on the type of time-to-failure distributions. → The method is analytical and based on sequential binary decision diagrams (SBDD). → The method is computationally more efficient than existing methods.

Hole subbands in quantum wells: exact solution for six-dimensional Luttinger–Kohn Hamiltonian

International Nuclear Information System (INIS)

Belykh, V G; Tulupenko, V N

2009-01-01

The exact solution for wavefunctions of six-dimensional Luttinger–Kohn Hamiltonian, describing the valence band of cubic semiconductors in the effective mass approximation, is derived. The problem of space quantization for a rectangular quantum well with finite depth is solved. The wavefunctions of carriers in the quantum well are built up of a complete set of exact wavefunctions for the bulk materials constituting the heterojunction. Obtained formulae for wavefunctions permit one to derive the analytical expression for a determinant, which nulls give the allowed energy values. Comparison of the energy spectra for the Si/Si 0.88 Ge 0.12 quantum well obtained in the framework of the developed technique, and using four-dimensional Luttinger–Kohn Hamiltonian allows us to trace clearly the impact of the spin–orbit interaction on the formation of the energy spectrum for the quantum well

Application of Statistical Methods to Activation Analytical Results near the Limit of Detection

DEFF Research Database (Denmark)

Heydorn, Kaj; Wanscher, B.

1978-01-01

Reporting actual numbers instead of upper limits for analytical results at or below the detection limit may produce reliable data when these numbers are subjected to appropriate statistical processing. Particularly in radiometric methods, such as activation analysis, where individual standard...... deviations of analytical results may be estimated, improved discrimination may be based on the Analysis of Precision. Actual experimental results from a study of the concentrations of arsenic in human skin demonstrate the power of this principle....

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.

Analytical solution for the convectively-mixed atmospheric boundary layer

NARCIS (Netherlands)

Ouwersloot, H.G.; Vilà-Guerau de Arellano, J.

2013-01-01

Based on the prognostic equations of mixed-layer theory assuming a zeroth order jump at the entrainment zone, analytical solutions for the boundary-layer height evolution are derived with different degrees of accuracy. First, an exact implicit expression for the boundary-layer height for a situation

$W^+ W^-$ + Jet: Compact Analytic Results

Energy Technology Data Exchange (ETDEWEB)

Campbell, John [Fermilab; Miller, David [Glasgow U.; Robens, Tania [Dresden, Tech. U.

2016-01-14

In the second run of the LHC, which started in April 2015, an accurate understanding of Standard Model processes is more crucial than ever. Processes including electroweak gauge bosons serve as standard candles for SM measurements, and equally constitute important background for BSM searches. We here present the NLO QCD virtual contributions to W+W- + jet in an analytic format obtained through unitarity methods and show results for the full process using an implementation into the Monte Carlo event generator MCFM. Phenomenologically, we investigate total as well as differential cross sections for the LHC with 14 TeV center-of-mass energy, as well as a future 100 TeV proton-proton machine. In the format presented here, the one-loop virtual contributions also serve as important ingredients in the calculation of W+W- pair production at NNLO.

Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

OpenAIRE

Cui, Shuai; Cao, Jun-Peng; Fan, Heng; Amico, Luigi

2015-01-01

We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters along with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of the Braak method based on Bogolubov rotation of the underlying $su(1,1)$ Lie algebra. Accordingly, the spectrum is provided by the analytical properties of a suitable meromorphic function. Our formalism applies to the two-modes Rabi model as well, sharing the s...

Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes

DEFF Research Database (Denmark)

Häggström, Olle; Lieshout, Marie-Colette van; Møller, Jesper

1999-01-01

The area-interaction process and the continuum random-cluster model are characterized in terms of certain functional forms of their respective conditional intensities. In certain cases, these two point process models can be derived from a bivariate point process model which in many respects...... is simpler to analyse and simulate. Using this correspondence we devise a two-component Gibbs sampler, which can be used for fast and exact simulation by extending the recent ideas of Propp and Wilson. We further introduce a Swendsen-Wang type algorithm. The relevance of the results within spatial statistics...

Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

International Nuclear Information System (INIS)

Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T.; Santos, Marcio G.

2015-01-01

This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

Energy Technology Data Exchange (ETDEWEB)

Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte

2015-07-01

This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

Preliminary Results on Uncertainty Quantification for Pattern Analytics

Energy Technology Data Exchange (ETDEWEB)

Stracuzzi, David John [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Brost, Randolph [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Chen, Maximillian Gene [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Malinas, Rebecca [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Peterson, Matthew Gregor [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Phillips, Cynthia A. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Robinson, David G. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Woodbridge, Diane [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

2015-09-01

This report summarizes preliminary research into uncertainty quantification for pattern ana- lytics within the context of the Pattern Analytics to Support High-Performance Exploitation and Reasoning (PANTHER) project. The primary focus of PANTHER was to make large quantities of remote sensing data searchable by analysts. The work described in this re- port adds nuance to both the initial data preparation steps and the search process. Search queries are transformed from does the specified pattern exist in the data? to how certain is the system that the returned results match the query? We show example results for both data processing and search, and discuss a number of possible improvements for each.

Exact results and open questions in first principle functional RG

International Nuclear Information System (INIS)

Le Doussal, Pierre

2010-01-01

Some aspects of the functional RG (FRG) approach to pinned elastic manifolds (of internal dimension d) at finite temperature T > 0 are reviewed and reexamined in this much expanded version of Le Doussal (2006) . The particle limit d = 0 provides a test for the theory: there the FRG is equivalent to the decaying Burgers equation, with viscosity ν ∼ T-both being formally irrelevant. An outstanding question in FRG, i.e. how temperature regularizes the otherwise singular flow of T = 0 FRG, maps to the viscous layer regularization of inertial range Burgers turbulence (i.e. to the construction of the inviscid limit). Analogy between Kolmogorov scaling and FRG cumulant scaling is discussed. First, multi-loop FRG corrections are examined and the direct loop expansion at T > 0 is shown to fail already in d = 0, a hierarchy of ERG equations being then required (introduced in Balents and Le Doussal (2005) ). Next we prove that the FRG function R(u) and higher cumulants defined from the field theory can be obtained for any d from moments of a renormalized potential defined in an sliding harmonic well. This allows to measure the fixed point function R(u) in numerics and experiments. In d = 0 the beta function (of the inviscid limit) is obtained from first principles to four loop. For Sinai model (uncorrelated Burgers initial velocities) the ERG hierarchy can be solved and the exact function R(u) is obtained. Connections to exact solutions for the statistics of shocks in Burgers and to ballistic aggregation are detailed. A relation is established between the size distribution of shocks and the one for droplets. A droplet solution to the ERG functional hierarchy is found for any d, and the form of R(u) in the thermal boundary layer is related to droplet probabilities. These being known for the d = 0 Sinai model the function R(u) is obtained there at any T. Consistency of the ε=4-d expansion in one and two loop FRG is studied from first principles, and connected to shock and

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...

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.

New approach to the exact solution of viscous flow due to stretching (shrinking and porous sheet

Directory of Open Access Journals (Sweden)

Azhar Ali

Full Text Available Exact analytical solutions for the generalized stretching (shrinking of a porous surface, for the variable suction (injection velocity, is presented in this paper. The solution is generalized in the sense that the existing solutions that correspond to various stretching velocities are recovered as a special case of this study. A suitable similarity transformation is introduced to find self-similar solution of the non-linear governing equations. The flow is characterized by a few non-dimensional parameters signifying the problem completely. These parameters are such that the whole range of stretching (shrinking problems discussed earlier can be recovered by assigning appropriate values to these parameters. A key point of the whole narrative is that a number of earlier works can be abridged into one generalized problem through the introduction of a new similarity transformation and finding its exact solution encompassing all the earlier solutions. Keywords: Exact solutions, New similarities, Permeable and moving sheet

Exact two-point resistance, and the simple random walk on the complete graph minus N edges

Energy Technology Data Exchange (ETDEWEB)

Chair, Noureddine, E-mail: n.chair@ju.edu.jo

2012-12-15

An analytical approach is developed to obtain the exact expressions for the two-point resistance and the total effective resistance of the complete graph minus N edges of the opposite vertices. These expressions are written in terms of certain numbers that we introduce, which we call the Bejaia and the Pisa numbers; these numbers are the natural generalizations of the bisected Fibonacci and Lucas numbers. The correspondence between random walks and the resistor networks is then used to obtain the exact expressions for the first passage and mean first passage times on this graph. - Highlights: Black-Right-Pointing-Pointer We obtain exact formulas for the two-point resistance of the complete graph minus N edges. Black-Right-Pointing-Pointer We obtain also the total effective resistance of this graph. Black-Right-Pointing-Pointer We modified Schwatt's formula on trigonometrical power sum to suit our computations. Black-Right-Pointing-Pointer We introduced the generalized bisected Fibonacci and Lucas numbers: the Bejaia and the Pisa numbers. Black-Right-Pointing-Pointer The first passage and mean first passage times of the random walks have exact expressions.

New family of exact solutions for colliding plane gravitational waves

International Nuclear Information System (INIS)

Yurtsever, U.

1988-01-01

We construct an infinite-parameter family of exact solutions to the vacuum Einstein field equations describing colliding gravitational plane waves with parallel polarizations. The interaction regions of the solutions in this family are locally isometric to the interiors of those static axisymmetric (Weyl) black-hole solutions which admit both a nonsingular horizon, and an analytic extension of the exterior metric to the interior of the horizon. As a member of this family of solutions we also obtain, for the first time, a colliding plane-wave solution where both of the two incoming plane waves are purely anastigmatic, i.e., where both incoming waves have equal focal lengths

Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model

KAUST Repository

Mazaré , Pierre Emmanuel; Dehwah, Ahmad H.; Claudel, Christian G.; Bayen, Alexandre M.

2011-01-01

In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver. © 2011 Elsevier Ltd.

Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model

KAUST Repository

Mazaré, Pierre Emmanuel

2011-12-01

In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver. © 2011 Elsevier Ltd.

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.)

On Analytic Solution of resonant Mixing for Solar Neutrino Oscillations

OpenAIRE

Masatoshi, ITO; Takao, KANEKO; Masami, NAKAGAWA; Department of Physics, Meijo University; Department of Physics, Meijo University; Department of Physics, Meijo University

1988-01-01

Behavior of resonant mixing in matter-enhancing region for solar neutrino oscillation, the Mikheyev-Smirnov-Wolfenstein mechanism, is reanalyzed by means of an analytic treatment recently proposed. We give solutions in terms of confluent hypergeometric functions, which agree with "exact" solutions of coupled differential equations.

From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

Science.gov (United States)

Bodin, Jacques

2015-03-01

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

International Nuclear Information System (INIS)

Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A

2009-01-01

A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.

Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material.

Science.gov (United States)

Dalarsson, Mariana; Tassin, Philippe

2009-04-13

We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results obtained by accurate numerical simulations. Our model straightforwardly allows for arbitrary spectral dispersion.

Construction of exact solutions for the Stern-Gerlach effect

International Nuclear Information System (INIS)

Diaz Bulnes, J.; Oliveira, I.S.

2001-01-01

We obtain exact solutions for the Schroedinger-Pauli matrix equation for a neutral particle of spin 1/2 in a magnetic field with a field gradient. The analytical wave functions are written on the symmetry plane Y = 0, which contains the incident and splitted beams, in terms of the Airy functions. The time-evolution of the probability, |Ψ+| 2 and |Ψ-| 2 , and the eigenenergies are calculated. The include a small contribution from the field gradient, α, proportional to (α ℎ) 2/3 , which amount to equal energy displacements on both magnetic levels. The results are generalized for spin S = 3/2, and in this case we found that the m = ±1/2 and m = ±3/2 magnetic sublevels are unequally splitted by the field gradient, being the difference in energy of the order 0.4 MHz. Replacing real experimental parameters we obtained a spatial splitting of the spin up and spin down states of the order Δz ≅4 mm, in accordance to a real Stern-Gerlach experiment. (author)

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

Comment on 'Exact analytical solution for the generalized Lyapunov exponent of the two-dimensional Anderson localization'

International Nuclear Information System (INIS)

Markos, P; Schweitzer, L; Weyrauch, M

2004-01-01

In a recent publication, Kuzovkov et al (2002 J. Phys.: Condens. Matter. 14 13777) announced an analytical solution of the two-dimensional Anderson localization problem via the calculation of a generalized Lyapunov exponent using signal theory. Surprisingly, for certain energies and small disorder strength they observed delocalized states. We study the transmission properties of the same model using well-known transfer matrix methods. Our results disagree with the findings obtained using signal theory. We point to the possible origin of this discrepancy and comment on the general strategy of using a generalized Lyapunov exponent for studying Anderson localization. (comment)

Analytic theory of the gyrotron

International Nuclear Information System (INIS)

Lentini, P.J.

1989-06-01

An analytic theory is derived for a gyrotron operating in the linear gain regime. The gyrotron is a coherent source of microwave and millimeter wave radiation based on an electron beam emitting at cyclotron resonance Ω in a strong, uniform magnetic field. Relativistic equations of motion and first order perturbation theory are used. Results are obtained in both laboratory and normalized variables. An expression for cavity threshold gain is derived in the linear regime. An analytic expression for the electron phase angle in momentum space shows that the effect of the RF field is to form bunches that are equal to the unperturbed transit phase plus a correction term which varies as the sine of the input phase angle. The expression for the phase angle is plotted and bunching effects in and out of phase (0 and -π) with respect to the RF field are evident for detunings leading to gain and absorption, respectively. For exact resonance, field frequency ω = Ω, a bunch also forms at a phase of -π/2. This beam yields the same energy exchange with the RF field as an unbunched, (nonrelativistic) beam. 6 refs., 10 figs

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.

Analytical approach to phonons and electron-phonon interactions in single-walled zigzag carbon nanotubes

Energy Technology Data Exchange (ETDEWEB)

Kandemir, B S; Keskin, M [Department of Physics, Faculty of Sciences, Ankara University, 06100 Tandogan, Ankara (Turkey)

2008-08-13

In this paper, exact analytical expressions for the entire phonon spectra in single-walled carbon nanotubes with zigzag geometry are presented by using a new approach, originally developed by Kandemir and Altanhan. This approach is based on the concept of construction of a classical lattice Hamiltonian of single-walled carbon nanotubes, wherein the nearest and next nearest neighbor and bond bending interactions are all included, then its quantization and finally diagonalization of the resulting second quantized Hamiltonian. Furthermore, within this context, explicit analytical expressions for the relevant electron-phonon interaction coefficients are also investigated for single-walled carbon nanotubes having this geometry, by the phonon modulation of the hopping interaction.

Analytical approach to phonons and electron-phonon interactions in single-walled zigzag carbon nanotubes

International Nuclear Information System (INIS)

Kandemir, B S; Keskin, M

2008-01-01

In this paper, exact analytical expressions for the entire phonon spectra in single-walled carbon nanotubes with zigzag geometry are presented by using a new approach, originally developed by Kandemir and Altanhan. This approach is based on the concept of construction of a classical lattice Hamiltonian of single-walled carbon nanotubes, wherein the nearest and next nearest neighbor and bond bending interactions are all included, then its quantization and finally diagonalization of the resulting second quantized Hamiltonian. Furthermore, within this context, explicit analytical expressions for the relevant electron-phonon interaction coefficients are also investigated for single-walled carbon nanotubes having this geometry, by the phonon modulation of the hopping interaction

Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy's law

International Nuclear Information System (INIS)

Khan, M.; Hayat, T.; Asghar, S.

2005-12-01

This paper deals with an exact solution for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid in a circular pipe. For the description of such a fluid, the fractional calculus approach has been used throughout the analysis. Based on modified Darcy's law for generalized Oldroyd-B fluid, the velocity field is calculated analytically. Several known solutions can be recovered as the limiting cases of our solution. (author)

Exact fan-beam and 4π-acquisition cone-beam SPECT algorithms with uniform attenuation correction

International Nuclear Information System (INIS)

Tang Qiulin; Zeng, Gengsheng L.; Wu Jiansheng; Gullberg, Grant T.

2005-01-01

This paper presents analytical fan-beam and cone-beam reconstruction algorithms that compensate for uniform attenuation in single photon emission computed tomography. First, a fan-beam algorithm is developed by obtaining a relationship between the two-dimensional (2D) Fourier transform of parallel-beam projections and fan-beam projections. Using this relationship, 2D Fourier transforms of equivalent parallel-beam projection data are obtained from the fan-beam projection data. Then a quasioptimal analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan, is used to reconstruct the image. A cone-beam algorithm is developed by extending the fan-beam algorithm to 4π solid angle geometry. The cone-beam algorithm is also an exact algorithm

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.

Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels

Directory of Open Access Journals (Sweden)

Salvatore Brischetto

2014-01-01

equilibrium written in orthogonal curvilinear coordinates for the free vibrations of simply supported structures. These equations consider an exact geometry for shells without simplifications. The main novelty is the possibility of a general formulation for different geometries. The equations written in general orthogonal curvilinear coordinates allow the analysis of spherical shell panels and they automatically degenerate into cylindrical shell panel, cylindrical closed shell, and plate cases. Results are proposed for isotropic and orthotropic structures. An exhaustive overview is given of the vibration modes for a number of thickness ratios, imposed wave numbers, geometries, embedded materials, and angles of orthotropy. These results can also be used as reference solutions to validate two-dimensional models for plates and shells in both analytical and numerical form (e.g., closed solutions, finite element method, differential quadrature method, and global collocation method.

Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

International Nuclear Information System (INIS)

Liu Chunliang; Xie Xi; Chen Yinbao

1991-01-01

The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

Analytical solution of spatial kinetics of the diffusion model for subcritical homogeneous systems driven by external source

International Nuclear Information System (INIS)

Oliveira, Fernando Luiz de

2008-01-01

This work describes an analytical solution obtained by the expansion method for the spatial kinetics using the diffusion model with delayed emission for source transients in homogeneous media. In particular, starting from simple models, and increasing the complexity, numerical results were obtained for different types of source transients. An analytical solution of the one group without precursors was solved, followed by considering one precursors family. The general case of G-groups with R families of precursor although having a closed form solution, cannot be solved analytically, since there are no explicit formulae for the eigenvalues, and numerical methods must be used to solve such problem. To illustrate the general solution, the multi-group (three groups) time-dependent problem without precursors was solved and the numerical results of a finite difference code were compared with the exact results for different transients. (author)

(U) An Analytic Study of Piezoelectric Ejecta Mass Measurements

Energy Technology Data Exchange (ETDEWEB)

Tregillis, Ian Lee [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-02-16

We consider the piezoelectric measurement of the areal mass of an ejecta cloud, for the specific case where ejecta are created by a single shock at the free surface and fly ballistically through vacuum to the sensor. To do so, we define time- and velocity-dependent ejecta “areal mass functions” at the source and sensor in terms of typically unknown distribution functions for the ejecta particles. Next, we derive an equation governing the relationship between the areal mass function at the source (which resides in the rest frame of the free surface) and at the sensor (which resides in the laboratory frame). We also derive expressions for the analytic (“true”) accumulated ejecta mass at the sensor and the measured (“inferred”) value obtained via the standard method for analyzing piezoelectric voltage traces. This approach enables us to derive an exact expression for the error imposed upon a piezoelectric ejecta mass measurement (in a perfect system) by the assumption of instantaneous creation. We verify that when the ejecta are created instantaneously (i.e., when the time dependence is a delta function), the piezoelectric inference method exactly reproduces the correct result. When creation is not instantaneous, the standard piezo analysis will always overestimate the true mass. However, the error is generally quite small (less than several percent) for most reasonable velocity and time dependences. In some cases, errors exceeding 10-15% may require velocity distributions or ejecta production timescales inconsistent with experimental observations. These results are demonstrated rigorously with numerous analytic test problems.

Complete analytic results for radiative-recoil corrections to ground-state muonium hyperfine splitting

International Nuclear Information System (INIS)

Karshenboim, S.G.; Shelyuto, V.A.; Eides, M.E.

1988-01-01

Analytic expressions are obtained for radiative corrections to the hyperfine splitting related to the muon line. The corresponding contribution amounts to (Z 2 a) (Za) (m/M) (9/2 ζ(3) - 3π 2 ln 2 + 39/8) in units of the Fermi hyperfine splitting energy. A complete analytic result for all radiative-recoil corrections is also presented

Analytical Study on Propagation Dynamics of Optical Beam in Parity-Time Symmetric Optical Couplers

International Nuclear Information System (INIS)

Zhou Zheng; Zhang Li-Juan; Zhu Bo

2015-01-01

We present exact analytical solutions to parity-time (PT) symmetric optical system describing light transport in PT-symmetric optical couplers. We show that light intensity oscillates periodically between two waveguides for unbroken PT-symmetric phase, whereas light always leaves the system from the waveguide experiencing gain when light is initially input at either waveguide experiencing gain or waveguide experiencing loss for broken PT-symmetric phase. These analytical results agree with the recent experimental observation reported by Rüter et al. [Nat. Phys. 6 (2010) 192]. Besides, we present a scheme for manipulating PT symmetry by applying a periodic modulation. Our results provide an efficient way to control light propagation in periodically modulated PT-symmetric system by tuning the modulation amplitude and frequency. (paper)

Advances in classical and analytical mechanics: A reviews of author’s results

Directory of Open Access Journals (Sweden)

Hedrih-Stevanović Katica R.

2013-01-01

Full Text Available A review, in subjective choice, of author’s scientific results in area of: classical mechanics, analytical mechanics of discrete hereditary systems, analytical mechanics of discrete fractional order system vibrations, elastodynamics, nonlinear dynamics and hybrid system dynamics is presented. Main original author’s results were presented through the mathematical methods of mechanics with examples of applications for solving problems of mechanical real system dynamics abstracted to the theoretical models of mechanical discrete or continuum systems, as well as hybrid systems. Paper, also, presents serries of methods and scientific results authored by professors Mitropolyski, Andjelić and Rašković, as well as author’s of this paper original scientific research results obtained by methods of her professors. Vector method based on mass inertia moment vectors and corresponding deviational vector components for pole and oriented axis, defined in 1991 by K. Hedrih, is presented. Results in construction of analytical dynamics of hereditary discrete system obtained in collaboration with O. A. Gorosho are presented. Also, some selections of results author’s postgraduate students and doctorantes in area of nonlinear dynamics are presented. A list of scientific projects headed by author of this paper is presented with a list of doctoral dissertation and magister of sciences thesis which contain scientific research results obtained under the supervision by author of this paper or their fist doctoral candidates. [Projekat Ministarstva nauke Republike Srbije, br. ON174001: Dynamics of hybrid systems with complex structures

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.

Optimum shape design of incompressible hyperelastic structures with analytical sensitivity analysis

International Nuclear Information System (INIS)

Jarraya, A.; Wali, M.; Dammark, F.

2014-01-01

This paper is focused on the structural shape optimization of incompressible hyperelastic structures. An analytical sensitivity is developed for the rubber like materials. The whole shape optimization process is carried out by coupling a closed geometric shape in R 2 with boundaries, defined by B-splines curves, exact sensitivity analysis and mathematical programming method (S.Q.P: sequential quadratic programming). Design variables are the control points coordinate. The objective function is to minimize Von-Mises stress, constrained to the total material volume of the structure remains constant. In order to validate the exact Jacobian method, the sensitivity calculation is performed: numerically by an efficient finite difference scheme and by the exact Jacobian method. Numerical optimization examples are presented for elastic and hyperelastic materials using the proposed method.

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

Analytic model of the radiation-dominated decay of a compact toroid

International Nuclear Information System (INIS)

Auerbach, S.P.

1981-01-01

The coaxial-gun, compact-torus experiments at LLNL and LASNL are believed to be radiation-dominated, in the sense that most or all of the input energy is lost by impurity radiation. This paper presents a simple analytic model of the radiation-dominated decay of a compact torus, and demonstrates that several striking features of the experiment (finite lifetime, linear current decay, insensitivity of the lifetime to density or stored magnetic energy) may also be explained by the hypothesis that impurity radiation dominates the energy loss. The model incorporates the essential features of the more elaborate 1 1/2-D simulations of Shumaker et al., yet is simple enough to be solved exactly. Based on the analytic results, a simple criterion is given for the maximum tolerable impurity density

Non-dissipative kinetic simulation and analytical solution of three-mode equations of ion temperature gradient instability

International Nuclear Information System (INIS)

Watanabe, T.-H.; Sugama, H.; Sato, T.

1999-12-01

A non-dissipative drift kinetic simulation scheme, which rigorously satisfies the time-reversibility, is applied to the three-mode coupling problem of the ion temperature gradient (ITG) instability. It is found from the simulation that the three-mode ITG system repeats growth and decay with a period which shows a logarithmic divergence for infinitesimal initial perturbations. Accordingly, time average of the mode amplitude vanishes, as the initial amplitude approaches to zero. An exact solution is analytically given for a class of initial conditions. An excellent agreement is confirmed between the analytical solution and numerical results. The results obtained here provide a useful reference for basic benchmarking of theories and simulation of the ITG modes. (author)

Analytical results for a hole in an antiferromagnet

International Nuclear Information System (INIS)

Li, Y.M.; d'Ambrumenil, N.; Su, Z.B.

1996-04-01

The Green's function for a hole moving in an antiferromagnet is derived analytically in the long-wavelength limit. We find that the infrared divergence is eliminated in two and higher dimensions so that the quasiparticle weight is finite. Our results also suggest that the hole motion is polaronic in nature with a bandwidth proportional to t 2 /J exp[-c(t/J) 2 ] (c is a constant) for J/t >or approx 0.5. The connection of the long-wavelength approximation to the first-order approximation in the cumulant expansion is also clarified. (author). 23 refs, 2 figs

Analytical performances of food microbiology laboratories - critical analysis of 7 years of proficiency testing results.

Science.gov (United States)

Abdel Massih, M; Planchon, V; Polet, M; Dierick, K; Mahillon, J

2016-02-01

Based on the results of 19 food microbiology proficiency testing (PT) schemes, this study aimed to assess the laboratory performances, to highlight the main sources of unsatisfactory analytical results and to suggest areas of improvement. The 2009-2015 results of REQUASUD and IPH PT, involving a total of 48 laboratories, were analysed. On average, the laboratories failed to detect or enumerate foodborne pathogens in 3·0% of the tests. Thanks to a close collaboration with the PT participants, the causes of outliers could be identified in 74% of the cases. The main causes of erroneous PT results were either pre-analytical (handling of the samples, timing of analysis), analytical (unsuitable methods, confusion of samples, errors in colony counting or confirmation) or postanalytical mistakes (calculation and encoding of results). PT schemes are a privileged observation post to highlight analytical problems, which would otherwise remain unnoticed. In this perspective, this comprehensive study of PT results provides insight into the sources of systematic errors encountered during the analyses. This study draws the attention of the laboratories to the main causes of analytical errors and suggests practical solutions to avoid them, in an educational purpose. The observations support the hypothesis that regular participation to PT, when followed by feed-back and appropriate corrective actions, can play a key role in quality improvement and provide more confidence in the laboratory testing results. © 2015 The Society for Applied Microbiology.

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.

Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium

Science.gov (United States)

Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying

2015-01-01

A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066

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.

Analytical solution of point kinetics equations for linear reactivity variation during the start-up of a nuclear reactor

International Nuclear Information System (INIS)

Palma, Daniel A.P.; Martinez, Aquilino S.; Goncalves, Alessandro C.

2009-01-01

The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.

Analytical solution of point kinetics equations for linear reactivity variation during the start-up of a nuclear reactor

Energy Technology Data Exchange (ETDEWEB)

Palma, Daniel A.P. [CEFET QUIMICA de Nilopolis/RJ, 21941-914 Rio de Janeiro (Brazil)], E-mail: agoncalves@con.ufrj.br; Martinez, Aquilino S.; Goncalves, Alessandro C. [COPPE/UFRJ - Programa de Engenharia Nuclear, Rio de Janeiro (Brazil)

2009-09-15

The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.

On truncations of the exact renormalization group

CERN Document Server

Morris, T R

1994-01-01

We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.

Exact results for the O( N ) model with quenched disorder

Science.gov (United States)

Delfino, Gesualdo; Lamsen, Noel

2018-04-01

We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points for O( N )-symmetric models with quenched disorder in two dimensions. Random fixed points are characterized by two disorder parameters: a modulus that vanishes when approaching the pure case, and a phase angle. The critical lines fall into three classes depending on the values of the disorder modulus. Besides the class corresponding to the pure case, a second class has maximal value of the disorder modulus and includes Nishimori-like multicritical points as well as zero temperature fixed points. The third class contains critical lines that interpolate, as N varies, between the first two classes. For positive N , it contains a single line of infrared fixed points spanning the values of N from √{2}-1 to 1. The symmetry sector of the energy density operator is superuniversal (i.e. N -independent) along this line. For N = 2 a line of fixed points exists only in the pure case, but accounts also for the Berezinskii-Kosterlitz-Thouless phase observed in presence of disorder.

On Central Branch/Reinsurance Risk Networks: Exact Results and Heuristics

Directory of Open Access Journals (Sweden)

Florin Avram

2018-04-01

Full Text Available Modeling the interactions between a reinsurer and several insurers, or between a central management branch (CB and several subsidiary business branches, or between a coalition and its members, are fascinating problems, which suggest many interesting questions. Beyond two dimensions, one cannot expect exact answers. Occasionally, reductions to one dimension or heuristic simplifications yield explicit approximations, which may be useful for getting qualitative insights. In this paper, we study two such problems: the ruin problem for a two-dimensional CB network under a new mathematical model, and the problem of valuation of two-dimensional CB networks by optimal dividends. A common thread between these two problems is that the one dimensional reduction exploits the concept of invariant cones. Perhaps the most important contribution of the paper is the questions it raises; for that reason, we have found it useful to complement the particular examples solved by providing one possible formalization of the concept of a multi-dimensional risk network, which seems to us an appropriate umbrella for the kind of questions raised here.

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

Analytical method and result of radiation exposure for depressurization accident of HTTR

International Nuclear Information System (INIS)

Sawa, K.; Shiozawa, S.; Mikami, H.

1990-01-01

The Japan Atomic Energy Research Institute (JAERI) is now proceeding with the construction design of the High Temperature Engineering Test Reactor (HTTR). Since the HTTR has some characteristics different from LWRs, analytical method of radiation exposure in accidents provided for LWRs can not be applied directly. This paper describes the analytical method of radiation exposure developed by JAERI for the depressurization accident, which is the severest accident in respect to radiation exposure among the design basis accidents of the HTTR. The result is also described in this paper

Tank 241-S-102, Core 232 analytical results for the final report

Energy Technology Data Exchange (ETDEWEB)

STEEN, F.H.

1998-11-04

This document is the analytical laboratory report for tank 241-S-102 push mode core segments collected between March 5, 1998 and April 2, 1998. The segments were subsampled and analyzed in accordance with the Tank 241-S-102 Retained Gas Sampler System Sampling and Analysis Plan (TSAP) (McCain, 1998), Letter of Instruction for Compatibility Analysis of Samples from Tank 241-S-102 (LOI) (Thompson, 1998) and the Data Quality Objectives for Tank Farms Waste Compatibility Program (DQO) (Mulkey and Miller, 1998). The analytical results are included in the data summary table (Table 1).

An exact solution for orbit view-periods from a station on a tri-axial ellipsoidal planet

Science.gov (United States)

Tang, C. C. H.

1986-01-01

This paper presents the concise exact solution for predicting view-periods to be observed from a masked or unmasked tracking station on a tri-axial ellipsoidal surface. The new exact approach expresses the azimuth and elevation angles of a spacecraft in terms of the station-centered geodetic topocentric coordinates in an elegantly concise manner. A simple and efficient algorithm is developed to avoid costly repetitive computations in searching for neighborhoods near the rise and set times of each satellite orbit for each station. Only one search for each orbit is necessary for each station. Sample results indicate that the use of an assumed spherical earth instead of an 'actual' tri-axial ellipsoidal earth could introduce an error up to a few minutes in a view-period prediction for circular orbits of low or medium altitude. For an elliptical orbit of high eccentricity and long period, the maximum error could be even larger. The analytic treatment and the efficient algorithm are designed for geocentric orbits, but they should be applicable to interplanetary trajectories by an appropriate coordinates transformation at each view-period calculation. This analysis can be accomplished only by not using the classical orbital elements.

An exact solution for orbit view-periods from a station on a tri-axial ellipsoidal planet

Science.gov (United States)

Tang, C. C. H.

1986-08-01

This paper presents the concise exact solution for predicting view-periods to be observed from a masked or unmasked tracking station on a tri-axial ellipsoidal surface. The new exact approach expresses the azimuth and elevation angles of a spacecraft in terms of the station-centered geodetic topocentric coordinates in an elegantly concise manner. A simple and efficient algorithm is developed to avoid costly repetitive computations in searching for neighborhoods near the rise and set times of each satellite orbit for each station. Only one search for each orbit is necessary for each station. Sample results indicate that the use of an assumed spherical earth instead of an 'actual' tri-axial ellipsoidal earth could introduce an error up to a few minutes in a view-period prediction for circular orbits of low or medium altitude. For an elliptical orbit of high eccentricity and long period, the maximum error could be even larger. The analytic treatment and the efficient algorithm are designed for geocentric orbits, but they should be applicable to interplanetary trajectories by an appropriate coordinates transformation at each view-period calculation. This analysis can be accomplished only by not using the classical orbital elements.

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.

Entanglement dynamics following a sudden quench: An exact solution

Science.gov (United States)

Ghosh, Supriyo; Gupta, Kumar S.; Srivastava, Shashi C. L.

2017-12-01

We present an exact and fully analytical treatment of the entanglement dynamics for an isolated system of N coupled oscillators following a sudden quench of the system parameters. The system is analyzed using the solutions of the time-dependent Schrodinger's equation, which are obtained by solving the corresponding nonlinear Ermakov equations. The entanglement entropies exhibit a multi-oscillatory behaviour, where the number of dynamically generated time scales increases with N. The harmonic chains exhibit entanglement revival and for larger values of N (> 10), we find near-critical logarithmic scaling for the entanglement entropy, which is modulated by a time-dependent factor. The N = 2 case is equivalent to the two-site Bose-Hubbard model in the tunneling regime, which is amenable to empirical realization in cold-atom systems.

Review of analytical results from the proposed agent disposal facility site, Aberdeen Proving Ground

Energy Technology Data Exchange (ETDEWEB)

Brubaker, K.L.; Reed, L.L.; Myers, S.W.; Shepard, L.T.; Sydelko, T.G.

1997-09-01

Argonne National Laboratory reviewed the analytical results from 57 composite soil samples collected in the Bush River area of Aberdeen Proving Ground, Maryland. A suite of 16 analytical tests involving 11 different SW-846 methods was used to detect a wide range of organic and inorganic contaminants. One method (BTEX) was considered redundant, and two {open_quotes}single-number{close_quotes} methods (TPH and TOX) were found to lack the required specificity to yield unambiguous results, especially in a preliminary investigation. Volatile analytes detected at the site include 1, 1,2,2-tetrachloroethane, trichloroethylene, and tetrachloroethylene, all of which probably represent residual site contamination from past activities. Other volatile analytes detected include toluene, tridecane, methylene chloride, and trichlorofluoromethane. These compounds are probably not associated with site contamination but likely represent cross-contamination or, in the case of tridecane, a naturally occurring material. Semivolatile analytes detected include three different phthalates and low part-per-billion amounts of the pesticide DDT and its degradation product DDE. The pesticide could represent residual site contamination from past activities, and the phthalates are likely due, in part, to cross-contamination during sample handling. A number of high-molecular-weight hydrocarbons and hydrocarbon derivatives were detected and were probably naturally occurring compounds. 4 refs., 1 fig., 8 tabs.

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

Analytical study of dissipative solitary waves

Energy Technology Data Exchange (ETDEWEB)

Dini, Fatemeh [Department of Physics, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Emamzadeh, Mehdi Molaie [Department of Physics, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Khorasani, Sina [School of Electrical Engineering, Sharif University of Technology, PO Box 11365-363, Tehran (Iran, Islamic Republic of); Bobin, Jean Louis [Universite Pierre et Marie Curie, Paris (France); Amrollahi, Reza [Department of Physics, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Sodagar, Majid [School of Electrical Engineering, Sharif University of Technology, PO Box 11365-363, Tehran (Iran, Islamic Republic of); Khoshnegar, Milad [School of Electrical Engineering, Sharif University of Technology, PO Box 11365-363, Tehran (Iran, Islamic Republic of)

2008-02-15

In this paper, the analytical solution to a new class of nonlinear solitons is presented with cubic nonlinearity, subject to a dissipation term arising as a result of a first-order derivative with respect to time, in the weakly nonlinear regime. Exact solutions are found using the combination of the perturbation and Green's function methods up to the third order. We present an example and discuss the asymptotic behavior of the Green's function. The dissipative solitary equation is also studied in the phase space in the non-dissipative and dissipative forms. Bounded and unbounded solutions of this equation are characterized, yielding an energy conversation law for non-dissipative waves. Applications of the model include weakly nonlinear solutions of terahertz Josephson plasma waves in layered superconductors and ablative Rayleigh-Taylor instability.

An exactly solvable three-dimensional nonlinear quantum oscillator

International Nuclear Information System (INIS)

Schulze-Halberg, A.; Morris, J. R.

2013-01-01

Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states

An exactly solvable three-dimensional nonlinear quantum oscillator

Energy Technology Data Exchange (ETDEWEB)

Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Morris, J. R. [Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

2013-11-15

Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.

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.

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.

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.

Computationally simple, analytic, closed form solution of the Coulomb self-interaction problem in Kohn Sham density functional theory

International Nuclear Information System (INIS)

Gonis, Antonios; Daene, Markus W.; Nicholson, Don M.; Stocks, George Malcolm

2012-01-01

We have developed and tested in terms of atomic calculations an exact, analytic and computationally simple procedure for determining the functional derivative of the exchange energy with respect to the density in the implementation of the Kohn Sham formulation of density functional theory (KS-DFT), providing an analytic, closed-form solution of the self-interaction problem in KS-DFT. We demonstrate the efficacy of our method through ground-state calculations of the exchange potential and energy for atomic He and Be atoms, and comparisons with experiment and the results obtained within the optimized effective potential (OEP) method.

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 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)

Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models

Science.gov (United States)

Ghosh, Pijush K.; Sinha, Debdeep

2018-01-01

A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occurs in a pairwise fashion. It is also shown that with the choice of a suitable co-ordinate, the Hamiltonian can always be reformulated in the background of a pseudo-Euclidean metric. If the equations of motion of some of the well-known many-body systems like Calogero models are generalized to include balanced loss and gain, it appears that the same may not be amenable to a Hamiltonian formulation. A few exactly solvable systems with balanced loss and gain, along with a set of integrals of motion are constructed. The examples include a coupled chain of nonlinear oscillators and a many-particle Calogero-type model with four-body inverse square plus two-body pair-wise harmonic interactions. For the case of nonlinear oscillators, stable solution exists even if the loss and gain parameter has unbounded upper range. Further, the range of the parameter for which the stable solutions are obtained is independent of the total number of the oscillators. The set of coupled nonlinear equations are solved exactly for the case when the values of all the constants of motions except the Hamiltonian are equal to zero. Exact, analytical classical solutions are presented for all the examples considered.

Pressure of a partially ionized hydrogen gas : numerical results from exact low temperature expansions

OpenAIRE

Alastuey , Angel; Ballenegger , Vincent

2010-01-01

8 pages; International audience; We consider a partially ionized hydrogen gas at low densities, where it reduces almost to an ideal mixture made with hydrogen atoms in their ground-state, ionized protons and ionized electrons. By performing systematic low-temperature expansions within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential, exact formulae for the first five leading corrections to the ideal Saha equation ...

Analytic expressions for the construction of a fire event PSA model

International Nuclear Information System (INIS)

Kang, Dae Il; Kim, Kil Yoo; Kim, Dong San; Hwang, Mee Jeong; Yang, Joon Eon

2016-01-01

In this study, the changing process of an internal event PSA model to a fire event PSA model is analytically presented and discussed. Many fire PSA models have fire induced initiating event fault trees not shown in an internal event PSA model. Fire-induced initiating fault tree models are developed for addressing multiple initiating event issues. A single fire event within a fire compartment or fire scenario can cause multiple initiating events. As an example, a fire in a turbine building area can cause a loss of the main feed-water and loss of off-site power initiating events. Up to now, there has been no analytic study on the construction of a fire event PSA model using an internal event PSA model with fault trees of initiating events. In this paper, the changing process of an internal event PSA model to a fire event PSA model was analytically presented and discussed. This study results show that additional cutsets can be obtained if the fault trees of initiating events for a fire event PSA model are not exactly developed.

Analytic expressions for the construction of a fire event PSA model

Energy Technology Data Exchange (ETDEWEB)

Kang, Dae Il; Kim, Kil Yoo; Kim, Dong San; Hwang, Mee Jeong; Yang, Joon Eon [KAERI, Daejeon (Korea, Republic of)

2016-05-15

In this study, the changing process of an internal event PSA model to a fire event PSA model is analytically presented and discussed. Many fire PSA models have fire induced initiating event fault trees not shown in an internal event PSA model. Fire-induced initiating fault tree models are developed for addressing multiple initiating event issues. A single fire event within a fire compartment or fire scenario can cause multiple initiating events. As an example, a fire in a turbine building area can cause a loss of the main feed-water and loss of off-site power initiating events. Up to now, there has been no analytic study on the construction of a fire event PSA model using an internal event PSA model with fault trees of initiating events. In this paper, the changing process of an internal event PSA model to a fire event PSA model was analytically presented and discussed. This study results show that additional cutsets can be obtained if the fault trees of initiating events for a fire event PSA model are not exactly developed.

Analytical Model and Optimized Design of Power Transmitting Coil for Inductively Coupled Endoscope Robot.

Science.gov (United States)

Ke, Quan; Luo, Weijie; Yan, Guozheng; Yang, Kai

2016-04-01

A wireless power transfer system based on the weakly inductive coupling makes it possible to provide the endoscope microrobot (EMR) with infinite power. To facilitate the patients' inspection with the EMR system, the diameter of the transmitting coil is enlarged to 69 cm. Due to the large transmitting range, a high quality factor of the Litz-wire transmitting coil is a necessity to ensure the intensity of magnetic field generated efficiently. Thus, this paper builds an analytical model of the transmitting coil, and then, optimizes the parameters of the coil by enlarging the quality factor. The lumped model of the transmitting coil includes three parameters: ac resistance, self-inductance, and stray capacitance. Based on the exact two-dimension solution, the accurate analytical expression of ac resistance is derived. Several transmitting coils of different specifications are utilized to verify this analytical expression, being in good agreements with the measured results except the coils with a large number of strands. Then, the quality factor of transmitting coils can be well predicted with the available analytical expressions of self- inductance and stray capacitance. Owing to the exact estimation of quality factor, the appropriate coil turns of the transmitting coil is set to 18-40 within the restrictions of transmitting circuit and human tissue issues. To supply enough energy for the next generation of the EMR equipped with a Ø9.5×10.1 mm receiving coil, the coil turns of the transmitting coil is optimally set to 28, which can transfer a maximum power of 750 mW with the remarkable delivering efficiency of 3.55%.

Exact Symbol Error Probability of Cross-QAM in AWGN and Fading Channels

Directory of Open Access Journals (Sweden)

Zhang Xi-chun

2010-01-01

Full Text Available The exact symbol error probability (SEP performance of -ary cross quadrature amplitude modulation (QAM in additive white Gaussian noise (AWGN channel and fading channels, including Rayleigh, Nakagami-m, Rice, and Nakagami-q (Hoyt channels, is analyzed. The obtained closed-form SEP expressions contain a finite (in proportion to sum of single integrals with finite limits and an integrand composed of elementary (exponential, trigonometric, and/or power functions, thus readily enabling numerical evaluation. Particularly, Gaussian -function is a special case of these integrals and is included in the SEP expressions. Simple and very precise approximations, which contain only Gaussian -function for AWGN channel and contain three terms of the single integrals mentioned above for fading channels, respectively, are also given. The analytical expressions show excellent agreement with the simulation results, and numerical evaluation with the proposed expressions reveals that cross QAM can obtain at least 1.1 dB gain compared to rectangular QAM when SEP < 0.3 in all the considered channels.

Analytic study of nonperturbative solutions in open string field theory

International Nuclear Information System (INIS)

Bars, I.; Kishimoto, I.; Matsuo, Y.

2003-01-01

We propose an analytic framework to study the nonperturbative solutions of Witten's open string field theory. The method is based on the Moyal star formulation where the kinetic term can be split into two parts. The first one describes the spectrum of two identical half strings which are independent from each other. The second one, which we call midpoint correction, shifts the half string spectrum to that of the standard open string. We show that the nonlinear equation of motion of string field theory is exactly solvable at zeroth order in the midpoint correction. An infinite number of solutions are classified in terms of projection operators. Among them, there exists only one stable solution which is identical to the standard butterfly state. We include the effect of the midpoint correction around each exact zeroth order solution as a perturbation expansion which can be formally summed to the complete exact solution

Bistability in a self-assembling system confined by elastic walls: Exact results in a one-dimensional lattice model

Energy Technology Data Exchange (ETDEWEB)

Pȩkalski, J.; Ciach, A. [Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa (Poland); Almarza, N. G. [Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid (Spain)

2015-01-07

The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk. Exact and asymptotic expressions for the local density and for the effective potential between the confining surfaces are obtained for a one-dimensional lattice model introduced by J. Pȩkalski et al. [J. Chem. Phys. 138, 144903 (2013)]. The simple asymptotic formulas are shown to be in good quantitative agreement with exact results for slits containing at least 5 layers. We observe that the incommensurability of the system size and the average distance between the clusters or layers in the bulk leads to structural deformations that are different for different values of the chemical potential μ. The change of the type of defects is reflected in the dependence of density on μ that has a shape characteristic for phase transitions. Our results may help to avoid misinterpretation of the change of the type of defects as a phase transition in simulations of inhomogeneous systems. Finally, we show that a system confined by soft elastic walls may exhibit bistability such that two system sizes that differ approximately by the average distance between the clusters or layers are almost equally probable. This may happen when the equilibrium separation between the soft boundaries of an empty slit corresponds to the largest stress in the confined self-assembling system.

Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results

Directory of Open Access Journals (Sweden)

V. Ilyin

2010-01-01

Full Text Available We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the probability distribution function obtained within the continuous random walk approach but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial.

The Similarity Hypothesis and New Analytical Support on the Estimation of Horizontal Infiltration into Sand

International Nuclear Information System (INIS)

Prevedello, C.L.; Loyola, J.M.T.

2010-01-01

A method based on a specific power-law relationship between the hydraulic head and the Boltzmann variable, presented using a similarity hypothesis, was recently generalized to a range of powers to satisfy the Bruce and Klute equation exactly. Here, considerations are presented on the proposed similarity assumption, and new analytical support is given to estimate the water density flux into and inside the soil, based on the concept of sorptivity and on Buckingham-Darcy's law. Results show that the new analytical solution satisfies both theories in the calculation of water density fluxes and is in agreement with experimental results of water infiltrating horizontally into sand. However, the utility of this analysis still needs to be verified for a variety of different textured soils having a diverse range of initial soil water contents.

Exact asymptotic expansion for the resistance between the center node and a node on the cobweb network boundary

Directory of Open Access Journals (Sweden)

R. Kenna

2014-09-01

Full Text Available We analyze the resistance between two nodes in a cobweb network of resistors. Based on an exact expression, we derive the asymptotic expansions for the resistance between the center node and a node on the boundary of the M x N cobweb network with resistors r and s in the two spatial directions. All coefficients in this expansion are expressed through analytical functions.

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 solution of unsteady flow generated by sinusoidal pressure gradient in a capillary tube

Directory of Open Access Journals (Sweden)

M. Abdulhameed

2015-12-01

Full Text Available In this paper, the mathematical modeling of unsteady second grade fluid in a capillary tube with sinusoidal pressure gradient is developed with non-homogenous boundary conditions. Exact analytical solutions for the velocity profiles have been obtained in explicit forms. These solutions are written as the sum of the steady and transient solutions for small and large times. For growing times, the starting solution reduces to the well-known periodic solution that coincides with the corresponding solution of a Newtonian fluid. Graphs representing the solutions are discussed.

Analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation

International Nuclear Information System (INIS)

Durand, B.; Durand, L.

1983-01-01

We construct an analytic solution to the spinless S-wave Salpeter equation for two quarks interacting via a Coulomb potential, [2(-del 2 +m 2 )/sup 1/2/-M-α/r] psi(r) = 0, by transforming the momentum-space form of the equation into a mapping or boundary-value problem for analytic functions. The principal part of the three-dimensional wave function is identical to the solution of a one-dimensional Salpeter equation found by one of us and discussed here. The remainder of the wave function can be constructed by the iterative solution of an inhomogeneous singular integral equation. We show that the exact bound-state eigenvalues for the Coulomb problem are M/sub n/ = 2m/(1+α 2 /4n 2 )/sup 1/2/, n = 1,2,..., and that the wave function for the static interaction diverges for r→0 as C(mr)/sup -nu/, where #betta# = (α/π)(1+α/π+...) is known exactly

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

Science.gov (United States)

Gould, Tim; Kronik, Leeor; Pittalis, Stefano

2018-05-01

By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.

Quasi-integrable non-linear Schrödinger models, infinite towers of exactly conserved charges and bright solitons

Science.gov (United States)

Blas, H.; do Bonfim, A. C. R.; Vilela, A. M.

2017-05-01

Deformations of the focusing non-linear Schrödinger model (NLS) are considered in the context of the quasi-integrability concept. We strengthen the results of JHEP 09 (2012) 103 10.1007/JHEP06(2015)177" TargetType="URL"/> for bright soliton collisions. We addressed the focusing NLS as a complement to the one in JHEP 03 (2016) 005 10.1007/JHEP06(2015)177" TargetType="URL"/> , in which the modified defocusing NLS models with dark solitons were shown to exhibit an infinite tower of exactly conserved charges. We show, by means of analytical and numerical methods, that for certain two-bright-soliton solutions, in which the modulus and phase of the complex modified NLS field exhibit even parities under a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved during the scattering process of the solitons. We perform extensive numerical simulations and consider the bright solitons with deformed potential V=2η /2+\\upepsilon{({|ψ |}^2)}^{2+\\upepsilon},\\upepsilon \\in \\mathbb{R},η <0 . However, for two-soliton field components without definite parity we also show numerically the vanishing of the first non-trivial anomaly and the exact conservation of the relevant charge. So, the parity symmetry seems to be a sufficient but not a necessary condition for the existence of the infinite tower of conserved charges. The model supports elastic scattering of solitons for a wide range of values of the amplitudes and velocities and the set { η, ɛ}. Since the NLS equation is ubiquitous, our results may find potential applications in several areas of non-linear science.

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 Solution of the Two-Dimensional Problem on an Impact Ideal-Liquid Jet

Science.gov (United States)

Belik, V. D.

2018-05-01

The two-dimensional problem on the collision of a potential ideal-liquid jet, outflowing from a reservoir through a nozzle, with an infinite plane obstacle was considered for the case where the distance between the nozzle exit section and the obstacle is finite. An exact solution of this problem has been found using methods of the complex-variable function theory. Simple analytical expressions for the complex velocity of the liquid, its flow rate, and the force of action of the jet on the obstacle have been obtained. The velocity distributions of the liquid at the nozzle exit section, in the region of spreading of the jet, and at the obstacle have been constructed for different distances between the nozzle exit section and the obstacle. Analytical expressions for the thickness of the boundary layer and the Nusselt number at the point of stagnation of the jet have been obtained. A number of distributions of the local friction coefficient and the Nusselt number of the indicated jet are presented.

Analytical solution for beam with time-dependent boundary conditions versus response spectrum

International Nuclear Information System (INIS)

Gou, P.F.; Panahi, K.K.

2001-01-01

This paper studies the responses of a uniform simple beam for which the supports are subjected to time-dependent conditions. Analytical solution in terms of series was presented for two cases: (1) Two supports of a simple beam are subjected to a harmonic motion, and (2) One of the two supports is stationary while the other is subjected to a harmonic motion. The results of the analytical solution were investigated and compared with the results of conventional response spectrum method using the beam finite element model. One of the applications of the results presented in this paper can be used to assess the adequacy and accuracy of the engineering approaches such as response spectra methods. It has been found that, when the excitation frequency equals the fundamental frequency of the beam, the results from response spectrum method are in good agreement with the exact calculation. The effects of initial conditions on the responses are also examined. It seems that the non-zero initial velocity has pronounced effects on the displacement time histories but it has no effect on the maximum accelerations. (author)

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

Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach

International Nuclear Information System (INIS)

Darmani, G.; Setayeshi, S.; Ramezanpour, H.

2012-01-01

In this paper an efficient computational method based on extending the sensitivity approach (SA) is proposed to find an analytic exact solution of nonlinear differential difference equations. In this manner we avoid solving the nonlinear problem directly. By extension of sensitivity approach for differential difference equations (DDEs), the nonlinear original problem is transformed into infinite linear differential difference equations, which should be solved in a recursive manner. Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained. Numerical examples are employed to show the effectiveness of the proposed approach. (general)

Analytical Solution of Nonlinear Problems in Classical Dynamics by Means of Lagrange-Ham

DEFF Research Database (Denmark)

Kimiaeifar, Amin; Mahdavi, S. H; Rabbani, A.

2011-01-01

In this work, a powerful analytical method, called Homotopy Analysis Methods (HAM) is coupled with Lagrange method to obtain the exact solution for nonlinear problems in classic dynamics. In this work, the governing equations are obtained by using Lagrange method, and then the nonlinear governing...

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

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

Exploring ECD on a Benchtop Q Exactive Orbitrap Mass Spectrometer

DEFF Research Database (Denmark)

Fort, Kyle L; Cramer, Christian N; Voinov, Valery G

2018-01-01

As the application of mass spectrometry intensifies in scope and diversity, the need for advanced instrumentation addressing a wide variety of analytical needs also increases. To this end, many modern, top-end mass spectrometers are designed or modified to include a wider range of fragmentation...... applications including middle-down proteomics, top-down proteomics, glycoproteomics, and disulfide bond mapping. We describe the modification of the popular Q Exactive Orbitrap mass spectrometer to extend its fragmentation capabilities to include ECD. We show that this modification allows ≥85% matched ion...... intensity to originate from ECD fragment ion types as well as provides high sequence coverage (≥60%) of intact proteins and high fragment identification rates with ∼70% of ion signals matched. Finally, the ECD implementation promotes selective disulfide bond dissociation, facilitating the identification...

Assessment of effectiveness of geologic isolation systems. Analytic modeling of flow in a permeable fissured medium

International Nuclear Information System (INIS)

Strack, O.D.L.

1982-02-01

An analytic model has been developed for two dimensional steady flow through infinite fissured porous media, and is implemented in a computer program. The model is the first, and major, step toward the development of a model with finite boundaries, intended for use as a tool for numerical experiments. These experiments may serve to verify some of the simplifying assumptions made in continuum models and to gain insight in the mechanics of the flow. The model is formulated in terms of complex variables and the analytic functions presented are closed-form expressions obtained from singular Cauchy integrals. An exact solution is given for the case of a single crack in an infinite porous medium. The exact solution is compared with the result obtained by the use of an independent method, which assumes Darcian flow in the crack and models the crack as an inhomogeneity in the permeability, in order to verify the simplifying assumptions. The approximate model is compared with solutions obtained from the above independent method for some cases of intersecting cracks. The agreement is good, provided that a sufficient number of elements are used to model the cracks

Surface-state mediated three-adsorbate interaction: exact and numerical results and simple asymptotic expression

International Nuclear Information System (INIS)

Hyldgaard, Per; Einstein, T.L.

2003-01-01

The interaction energy of three adsorbates on a surface consists of the sum of the three-pair interactions plus a trio contribution produced primarily by interference of electrons which traverse the entire perimeter, d 123 , of the three-adsorbate cluster. Here, we investigate this three-adatom interaction when mediated by the isotropic Shockley surface-state band found on noble-metal (1 1 1) surfaces, extending work on pair interactions. Our experimentally testable result depends on the s-wave phase-shift, characterizing the standing-wave patterns seen in scanning-tunneling microscopy (STM) images. Compared with the adsorbate-pair interactions, and in contrast to bulk-mediated interactions, the trio contribution exhibits a slightly weaker amplitude and a slightly faster asymptotic envelope decay, d 123 -5/2 . It also has a different but well-defined oscillation period dependent on d 123 and little dependence on the shape of the cluster. We finally compare the asymptotic description with exact model calculations assuming short-range interactions, which are viable even in the non-asymptotic range (when not outweighed by bulk-mediated interactions)

Delay in a tandem queueing model with mobile queues: An analytical approximation

NARCIS (Netherlands)

Al Hanbali, Ahmad; de Haan, Roland; Boucherie, Richardus J.; van Ommeren, Jan C.W.

In this paper, we analyze the end-to-end delay performance of a tandem queueing system with mobile queues. Due to state-space explosion, there is no hope for a numerical exact analysis for the joint-queue-length distribution. For this reason, we present an analytical approximation that is based on

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 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 results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants

International Nuclear Information System (INIS)

Bershtein, Mikhail; Bonelli, Giulio; Ronzani, Massimiliano; Tanzini, Alessandro

2016-01-01

We provide a contour integral formula for the exact partition function of N=2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N=2"∗ theory on ℙ"2 for all instanton numbers. In the zero mass case, corresponding to the N=4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a long-standing conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

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 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

Analytic results for planar three-loop integrals for massive form factors

Energy Technology Data Exchange (ETDEWEB)

Henn, Johannes M. [PRISMA Cluster of Excellence, Johannes Gutenberg Universität Mainz,55099 Mainz (Germany); Kavli Institute for Theoretical Physics, UC Santa Barbara,Santa Barbara (United States); Smirnov, Alexander V. [Research Computing Center, Moscow State University,119992 Moscow (Russian Federation); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics of Moscow State University,119992 Moscow (Russian Federation); Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT),76128 Karlsruhe (Germany)

2016-12-28

We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general q{sup 2} are expressed in terms of multiple polylogarithms, and results for fiftyone master integrals at the threshold q{sup 2}=4m{sup 2} are expressed in terms of multiple polylogarithms of argument one, with indices equal to zero or to a sixth root of unity.

Opportunity and Challenges for Migrating Big Data Analytics in Cloud

Science.gov (United States)

Amitkumar Manekar, S.; Pradeepini, G., Dr.

2017-08-01

Big Data Analytics is a big word now days. As per demanding and more scalable process data generation capabilities, data acquisition and storage become a crucial issue. Cloud storage is a majorly usable platform; the technology will become crucial to executives handling data powered by analytics. Now a day’s trend towards “big data-as-a-service” is talked everywhere. On one hand, cloud-based big data analytics exactly tackle in progress issues of scale, speed, and cost. But researchers working to solve security and other real-time problem of big data migration on cloud based platform. This article specially focused on finding possible ways to migrate big data to cloud. Technology which support coherent data migration and possibility of doing big data analytics on cloud platform is demanding in natute for new era of growth. This article also gives information about available technology and techniques for migration of big data in cloud.

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

On application of asymmetric Kan-like exact equilibria to the Earth magnetotail modeling

Science.gov (United States)

Korovinskiy, Daniil B.; Kubyshkina, Darya I.; Semenov, Vladimir S.; Kubyshkina, Marina V.; Erkaev, Nikolai V.; Kiehas, Stefan A.

2018-04-01

A specific class of solutions of the Vlasov-Maxwell equations, developed by means of generalization of the well-known Harris-Fadeev-Kan-Manankova family of exact two-dimensional equilibria, is studied. The examined model reproduces the current sheet bending and shifting in the vertical plane, arising from the Earth dipole tilting and the solar wind nonradial propagation. The generalized model allows magnetic configurations with equatorial magnetic fields decreasing in a tailward direction as slow as 1/x, contrary to the original Kan model (1/x3); magnetic configurations with a single X point are also available. The analytical solution is compared with the empirical T96 model in terms of the magnetic flux tube volume. It is found that parameters of the analytical model may be adjusted to fit a wide range of averaged magnetotail configurations. The best agreement between analytical and empirical models is obtained for the midtail at distances beyond 10-15 RE at high levels of magnetospheric activity. The essential model parameters (current sheet scale, current density) are compared to Cluster data of magnetotail crossings. The best match of parameters is found for single-peaked current sheets with medium values of number density, proton temperature and drift velocity.

How animals move along? Exactly solvable model of superdiffusive spread resulting from animal's decision making.

Science.gov (United States)

Tilles, Paulo F C; Petrovskii, Sergei V

2016-07-01

Patterns of individual animal movement have been a focus of considerable attention recently. Of particular interest is a question how different macroscopic properties of animal dispersal result from the stochastic processes occurring on the microscale of the individual behavior. In this paper, we perform a comprehensive analytical study of a model where the animal changes the movement velocity as a result of its behavioral response to environmental stochasticity. The stochasticity is assumed to manifest itself through certain signals, and the animal modifies its velocity as a response to the signals. We consider two different cases, i.e. where the change in the velocity is or is not correlated to its current value. We show that in both cases the early, transient stage of the animal movement is super-diffusive, i.e. ballistic. The large-time asymptotic behavior appears to be diffusive in the uncorrelated case but super-ballistic in the correlated case. We also calculate analytically the dispersal kernel of the movement and show that, whilst it converge to a normal distribution in the large-time limit, it possesses a fatter tail during the transient stage, i.e. at early and intermediate time. Since the transients are known to be highly relevant in ecology, our findings may indicate that the fat tails and superdiffusive spread that are sometimes observed in the movement data may be a feature of the transitional dynamics rather than an inherent property of the animal movement.

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.

Asymptotically exact expression for the energies of the 3Se Rydberg series in a two-electron system

International Nuclear Information System (INIS)

Ivanov, I.A.; Bromley, M.W.J.; Mitroy, J.

2002-01-01

The 1sns 3 S e Rydberg series in a two-electron system with the charge of the nucleus, Z≅1, is treated by means of the quantum-defect theory. Comparison with configuration interaction calculations suggests that the quantum-defect expression for the energy levels becomes asymptotically exact as Z→1. This provides an analytic description of the disappearance of the 1sns 3 S e bound states when Z approaches the critical value of 1

Tank 241-T-203, core 190 analytical results for the final report

International Nuclear Information System (INIS)

Steen, F.H.

1997-01-01

This document is the analytical laboratory report for tank 241-T-203 push mode core segments collected on April 17, 1997 and April 18, 1997. The segments were subsainpled and analyzed in accordance with the Tank 241-T-203 Push Mode Core Sampling andanalysis Plan (TSAP) (Schreiber, 1997a), the Safety Screening Data Quality Objective (DQO)(Dukelow, et al., 1995) and Leffer oflnstructionfor Core Sample Analysis of Tanks 241-T-201, 241-T-202, 241-T-203, and 241-T-204 (LOI)(Hall, 1997). The analytical results are included in the data summary report (Table 1). None of the samples submitted for Differential Scanning Calorimetry (DSC), Total Alpha Activity (AT) and Total Organic Carbon (TOC) exceeded notification limits as stated in the TSAP (Schreiber, 1997a). The statistical results of the 95% confidence interval on the mean calculations are provided by the Tank Waste Remediation Systems (TWRS) Technical Basis Group in accordance with the Memorandum of Understanding (Schreiber, 1997b) and not considered in this report

The big bang and inflation united by an analytic solution

International Nuclear Information System (INIS)

Bars, Itzhak; Chen, Shih-Hung

2011-01-01

Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index, and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data. The model simultaneously describes the big bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Friedmann equations, we have utilized an essential Weyl symmetry of our theory in 3+1 dimensions which is a predicted remaining symmetry of 2T-physics field theory in 4+2 dimensions. This led to a new method of obtaining analytic solutions in the 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow-roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time; rather, it oscillates around the potential minimum while settling down, unlike the slow-roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations.

Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

International Nuclear Information System (INIS)

Cui, Shuai; Cao, Jun-Peng; Fan, Heng; Amico, Luigi

2017-01-01

We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters the Hamiltonian with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of the Braak method based on Bogolubov rotation of the underlying su (1, 1) Lie algebra. Accordingly, the spectrum is provided by the analytical properties of a suitable meromorphic function. Our formalism applies to the two-modes Rabi model as well, sharing the same algebraic structure of the two-photon model. Through the analysis of the spectrum, we discover that the model displays close analogies to many-body systems undergoing quantum phase transitions. (paper)

Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

Science.gov (United States)

Cui, Shuai; Cao, Jun-Peng; Fan, Heng; Amico, Luigi

2017-05-01

We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters the Hamiltonian with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of the Braak method based on Bogolubov rotation of the underlying su(1, 1) Lie algebra. Accordingly, the spectrum is provided by the analytical properties of a suitable meromorphic function. Our formalism applies to the two-modes Rabi model as well, sharing the same algebraic structure of the two-photon model. Through the analysis of the spectrum, we discover that the model displays close analogies to many-body systems undergoing quantum phase transitions.

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)

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 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.

Analytical recursive method to ascertain multisite entanglement in doped quantum spin ladders

Science.gov (United States)

Roy, Sudipto Singha; Dhar, Himadri Shekhar; Rakshit, Debraj; SenDe, Aditi; Sen, Ujjwal

2017-08-01

We formulate an analytical recursive method to generate the wave function of doped short-range resonating valence bond (RVB) states as a tool to efficiently estimate multisite entanglement as well as other physical quantities in doped quantum spin ladders. We prove that doped RVB ladder states are always genuine multipartite entangled. Importantly, our results show that within specific doping concentration and model parameter regimes, the doped RVB state essentially characterizes the trends of genuine multiparty entanglement in the exact ground states of the Hubbard model with large on-site interactions, in the limit that yields the t -J Hamiltonian.

Analytic continuation by duality estimation of the S parameter

International Nuclear Information System (INIS)

Ignjatovic, S. R.; Wijewardhana, L. C. R.; Takeuchi, T.

2000-01-01

We investigate the reliability of the analytic continuation by duality (ACD) technique in estimating the electroweak S parameter for technicolor theories. The ACD technique, which is an application of finite energy sum rules, relates the S parameter for theories with unknown particle spectra to known OPE coefficients. We identify the sources of error inherent in the technique and evaluate them for several toy models to see if they can be controlled. The evaluation of errors is done analytically and all relevant formulas are provided in appendixes including analytical formulas for approximating the function 1/s with a polynomial in s. The use of analytical formulas protects us from introducing additional errors due to numerical integration. We find that it is very difficult to control the errors even when the momentum dependence of the OPE coefficients is known exactly. In realistic cases in which the momentum dependence of the OPE coefficients is only known perturbatively, it is impossible to obtain a reliable estimate. (c) 2000 The American Physical Society

Dynamics of entanglement and uncertainty relation in coupled harmonic oscillator system: exact results

Science.gov (United States)

Park, DaeKil

2018-06-01

The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schrödinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily time dependent. We derive the spectral and Schmidt decompositions for vacuum solution. Using the decompositions, we derive the analytical expressions for von Neumann and Rényi entropies. Making use of Wigner distribution function defined in phase space, we derive the time dependence of position-momentum uncertainty relations. To show the dynamics of entanglement and uncertainty relation graphically, we introduce two toy models and one realistic quenched model. While the dynamics can be conjectured by simple consideration in the toy models, the dynamics in the realistic quenched model is somewhat different from that in the toy models. In particular, the dynamics of entanglement exhibits similar pattern to dynamics of uncertainty parameter in the realistic quenched model.

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.

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.

An Analytic Approach to Developing Transport Threshold Models of Neoclassical Tearing Modes in Tokamaks

International Nuclear Information System (INIS)

Mikhailovskii, A.B.; Shirokov, M.S.; Konovalov, S.V.; Tsypin, V.S.

2005-01-01

Transport threshold models of neoclassical tearing modes in tokamaks are investigated analytically. An analysis is made of the competition between strong transverse heat transport, on the one hand, and longitudinal heat transport, longitudinal heat convection, longitudinal inertial transport, and rotational transport, on the other hand, which leads to the establishment of the perturbed temperature profile in magnetic islands. It is shown that, in all these cases, the temperature profile can be found analytically by using rigorous solutions to the heat conduction equation in the near and far regions of a chain of magnetic islands and then by matching these solutions. Analytic expressions for the temperature profile are used to calculate the contribution of the bootstrap current to the generalized Rutherford equation for the island width evolution with the aim of constructing particular transport threshold models of neoclassical tearing modes. Four transport threshold models, differing in the underlying competing mechanisms, are analyzed: collisional, convective, inertial, and rotational models. The collisional model constructed analytically is shown to coincide exactly with that calculated numerically; the reason is that the analytical temperature profile turns out to be the same as the numerical profile. The results obtained can be useful in developing the next generation of general threshold models. The first steps toward such models have already been made

Analytical Solution of Multicompartment Solute Kinetics for Hemodialysis

Directory of Open Access Journals (Sweden)

Przemysław Korohoda

2013-01-01

Full Text Available Objective. To provide an exact solution for variable-volume multicompartment kinetic models with linear volume change, and to apply this solution to a 4-compartment diffusion-adjusted regional blood flow model for both urea and creatinine kinetics in hemodialysis. Methods. A matrix-based approach applicable to linear models encompassing any number of compartments is presented. The procedure requires the inversion of a square matrix and the computation of its eigenvalues λ, assuming they are all distinct. This novel approach bypasses the evaluation of the definite integral to solve the inhomogeneous ordinary differential equation. Results. For urea two out of four eigenvalues describing the changes of concentrations in time are about 105 times larger than the other eigenvalues indicating that the 4-compartment model essentially reduces to the 2-compartment regional blood flow model. In case of creatinine, however, the distribution of eigenvalues is more balanced (a factor of 102 between the largest and the smallest eigenvalue indicating that all four compartments contribute to creatinine kinetics in hemodialysis. Interpretation. Apart from providing an exact analytic solution for practical applications such as the identification of relevant model and treatment parameters, the matrix-based approach reveals characteristic details on model symmetry and complexity for different solutes.

Exact Solution of the Gyration Radius of an Individual's Trajectory for a Simplified Human Regular Mobility Model

Science.gov (United States)

Yan, Xiao-Yong; Han, Xiao-Pu; Zhou, Tao; Wang, Bing-Hong

2011-12-01

We propose a simplified human regular mobility model to simulate an individual's daily travel with three sequential activities: commuting to workplace, going to do leisure activities and returning home. With the assumption that the individual has a constant travel speed and inferior limit of time at home and in work, we prove that the daily moving area of an individual is an ellipse, and finally obtain an exact solution of the gyration radius. The analytical solution captures the empirical observation well.

Tank 214-AW-105, grab samples, analytical results for the final report

International Nuclear Information System (INIS)

Esch, R.A.

1997-01-01

This document is the final report for tank 241-AW-105 grab samples. Twenty grabs samples were collected from risers 10A and 15A on August 20 and 21, 1996, of which eight were designated for the K Basin sludge compatibility and mixing studies. This document presents the analytical results for the remaining twelve samples. Analyses were performed in accordance with the Compatibility Grab Sampling and Analysis Plan (TSAP) and the Data Quality Objectives for Tank Farms Waste Compatibility Program (DO). The results for the previous sampling of this tank were reported in WHC-SD-WM-DP-149, Rev. 0, 60-Day Waste Compatibility Safety Issue and Final Results for Tank 241-A W-105, Grab Samples 5A W-95-1, 5A W-95-2 and 5A W-95-3. Three supernate samples exceeded the TOC notification limit (30,000 microg C/g dry weight). Appropriate notifications were made. No immediate notifications were required for any other analyte. The TSAP requested analyses for polychlorinated biphenyls (PCB) for all liquids and centrifuged solid subsamples. The PCB analysis of the liquid samples has been delayed and will be presented in a revision to this document

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...

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison.

Science.gov (United States)

Kumar, Santosh; Dietz, Barbara; Guhr, Thomas; Richter, Achim

2017-12-15

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

Exact solution of thermal energy storage system using PCM flat slabs configuration

International Nuclear Information System (INIS)

Bechiri, Mohammed; Mansouri, Kacem

2013-01-01

Highlights: • An exact solution of a latent heat storage unit (LHSU) consisting of several flat slabs was obtained. • The working fluid (HTF) circulating by forced convection between the slabs charges and discharges the storage unit. • The charging/discharging process is investigated for various HTF working conditions and different design parameters. - Abstract: An analytical investigation of thermal energy storage system (TESS) consisting of several flat slabs of phase change material (PCM) is presented. The working fluid (HTF) circulating on laminar forced convection between the slabs charges and discharges the storage unit. The melting and solidification of the PCM was treated as a radial one dimensional conduction problem. The forced convective heat transfer inside the channels is analyzed by solving the energy equation, which is coupled with the heat conduction equation in the PCM container. The comparison between the present exact solution with the numerical predictions and experimental data available in literature shows good agreement. The charging/discharging process is investigated in terms of liquid–solid interface position, liquid fraction, total heat transmitted to the PCM and thermal storage efficiency for various HTF working conditions and different design parameters such as PCM slab length, fluid passage gap and thickness of PCM duct container

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

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)

Dynamic Programming Approach for Exact Decision Rule Optimization

KAUST Repository

Amin, Talha M.; Chikalov, Igor; Moshkov, Mikhail; Zielosko, Beata

2013-01-01

This chapter is devoted to the study of an extension of dynamic programming approach that allows sequential optimization of exact decision rules relative to the length and coverage. It contains also results of experiments with decision tables from

Recent results for random networks of automata

International Nuclear Information System (INIS)

Flyvbjerg, H.

1987-05-01

After a very brief historical and contextual introduction to random networks of automata we review recent numerical and analytical results. Open questions and unsolved problems are pointed out and discussed. One such question is also answered: it is shown that the size of the stable core can be used as order parameter for a transition between phases of frozen and chaotic network behavior. A mean-field-like but exact selfconsistency equation for the size of the stable core is given. A new derivation of critical parameter values follows from it. (orig.)

Analytical results for entanglement in the five-qubit anisotropic Heisenberg model

International Nuclear Information System (INIS)

Wang Xiaoguang

2004-01-01

We solve the eigenvalue problem of the five-qubit anisotropic Heisenberg model, without use of Bethe's ansatz, and give analytical results for entanglement and mixedness of two nearest-neighbor qubits. The entanglement takes its maximum at Δ=1 (Δ>1) for the case of zero (finite) temperature with Δ being the anisotropic parameter. In contrast, the mixedness takes its minimum at Δ=1 (Δ>1) for the case of zero (finite) temperature

Exact Tests for Two-Way Contingency Tables with Structural Zeros

Directory of Open Access Journals (Sweden)

Luke J. West

2008-11-01

Full Text Available Fisher's exact test, named for Sir Ronald Aylmer Fisher, tests contingency tables for homogeneity of proportion. This paper discusses a generalization of Fisher's exact test for the case where some of the table entries are constrained to be zero. The resulting test is useful for assessing cases where the null hypothesis of conditional multinomial distribution is suspected to be false. The test is implemented in the form of a new R package, aylmer.

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.

On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid

Science.gov (United States)

Khan, M.; Anjum, Asia; Qi, Haitao; Fetecau, C.

2010-02-01

This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms in terms of the Mittag-Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary Oldroyd-B fluids is shown by means of graphical illustrations.

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

Science.gov (United States)

Romero, G.; Alvarez, L.; Alanís, E.; Nallim, L.; Grossi, R.

2003-07-01

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh-Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram-Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.

Hawking Radiation from a (4+n)-dimensional Black Hole Exact Results for the Schwarzschild Phase

CERN Document Server

Harris, C M; Harris, Chris M.; Kanti, Panagiota

2003-01-01

We start our analysis by deriving a master equation that describes the motion of a field with arbitrary spin $s$ on a 3-brane embedded in a non-rotating, uncharged (4+n)-dimensional black hole background. By numerical analysis, we derive exact results for the greybody factors and emission rates for scalars, fermions and gauge bosons emitted directly on the brane, for all energy regimes and for an arbitrary number $n$ of extra dimensions. The relative emissivities on the brane for different types of particles are computed and their dependence on the dimensionality of spacetime is demonstrated -- we therefore conclude that both the amount and the type of radiation emitted can be used for the determination of $n$ if the Hawking radiation from these black holes is observed. The emission of scalar modes in the bulk from the same black holes is also studied and the relative bulk-to-brane energy emissivity is accurately computed. We demonstrate that this quantity varies considerably with $n$ but always remains small...

Exact periodic and solitonic states of the spinor condensates in a uniform external potential

Energy Technology Data Exchange (ETDEWEB)

Zhang, Zhi-Hai [School of Physics and Electronics, Yancheng Teachers University, Yancheng 224051 (China); Yang, Shi-Jie, E-mail: yangshijie@tsinghua.org.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)

2016-08-15

We propose a method to analytically solve the one-dimensional coupled nonlinear Gross–Pitaevskii equations which govern the motion of the spinor Bose–Einstein condensates. In a uniform external potential, several classes of exact periodic and solitonic solutions, either in real or in complex forms, are obtained for both the F=1 and F=2 condensates for the Hamiltonian comprising the kinetic energy, the linear and the quadratic Zeeman energies. Real solutions take the form of composite soliton trains. Complex solutions correspond to the mass counter-flows as well as spin currents. These solutions are general that contains neither approximations nor constraints on the system parameters.

Practical approach to a procedure for judging the results of analytical verification measurements

International Nuclear Information System (INIS)

Beyrich, W.; Spannagel, G.

1979-01-01

For practical safeguards a particularly transparent procedure is described to judge analytical differences between declared and verified values based on experimental data relevant to the actual status of the measurement technique concerned. Essentially it consists of two parts: Derivation of distribution curves for the occurrence of interlaboratory differences from the results of analytical intercomparison programmes; and judging of observed differences using criteria established on the basis of these probability curves. By courtesy of the Euratom Safeguards Directorate, Luxembourg, the applicability of this judging procedure has been checked in practical data verification for safeguarding; the experience gained was encouraging and implementation of the method is intended. Its reliability might be improved further by evaluation of additional experimental data. (author)

An approximate and an analytical solution to the carousel-pendulum problem

Energy Technology Data Exchange (ETDEWEB)

Vial, Alexandre [Pole Physique, Mecanique, Materiaux et Nanotechnologies, Universite de technologie de Troyes, 12, rue Marie Curie BP-2060, F-10010 Troyes Cedex (France)], E-mail: alexandre.vial@utt.fr

2009-09-15

We show that an improved solution to the carousel-pendulum problem can be easily obtained through a first-order Taylor expansion, and its accuracy is determined after the obtention of an unusable analytical exact solution, advantageously replaced by a numerical one. It is shown that the accuracy is unexpectedly high, even when the ratio length of the pendulum to carousel radius approaches unity. (letters and comments)

Exact Turbulence Law in Collisionless Plasmas: Hybrid Simulations

Science.gov (United States)

Hellinger, P.; Verdini, A.; Landi, S.; Franci, L.; Matteini, L.

2017-12-01

An exact vectorial law for turbulence in homogeneous incompressible Hall-MHD is derived and tested in two-dimensional hybrid simulations of plasma turbulence. The simulations confirm the validity of the MHD exact law in the kinetic regime, the simulated turbulence exhibits a clear inertial range on large scales where the MHD cascade flux dominates. The simulation results also indicate that in the sub-ion range the cascade continues via the Hall term and that the total cascade rate tends to decrease at around the ion scales, especially in high-beta plasmas. This decrease is like owing to formation of non-thermal features, such as collisionless ion energization, that can not be retained in the Hall MHD approximation.

Analytical approximations to the Hotelling trace for digital x-ray detectors

Science.gov (United States)

Clarkson, Eric; Pineda, Angel R.; Barrett, Harrison H.

2001-06-01

The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

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 with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.

An analytical model for backscattered luminance in fog: comparisons with Monte Carlo computations and experimental results

International Nuclear Information System (INIS)

Taillade, Frédéric; Dumont, Eric; Belin, Etienne

2008-01-01

We propose an analytical model for backscattered luminance in fog and derive an expression for the visibility signal-to-noise ratio as a function of meteorological visibility distance. The model uses single scattering processes. It is based on the Mie theory and the geometry of the optical device (emitter and receiver). In particular, we present an overlap function and take the phase function of fog into account. The results of the backscattered luminance obtained with our analytical model are compared to simulations made using the Monte Carlo method based on multiple scattering processes. An excellent agreement is found in that the discrepancy between the results is smaller than the Monte Carlo standard uncertainties. If we take no account of the geometry of the optical device, the results of the model-estimated backscattered luminance differ from the simulations by a factor 20. We also conclude that the signal-to-noise ratio computed with the Monte Carlo method and our analytical model is in good agreement with experimental results since the mean difference between the calculations and experimental measurements is smaller than the experimental uncertainty

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.

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.

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.

Rigorous results of low-energy models of the analytic S-matrix theory

International Nuclear Information System (INIS)

Meshcheryakov, V.A.

1974-01-01

Results of analytic S-matrix theory, mainly dealing with the static limit of dispersion relations, are applied to pion-nucleon scattering in the low-energy region. Various approaches to solving equations of the chew-Low type are discussed. It is concluded that interesting results are obtained by reducing the equations to a system of nonlinear difference equations; the crucial element of this approach being the study of functions on the whole Riemann surface. Boundary and crossing symmetry conditions are studied. (HFdV)

26Al(n,p)26Mg reaction: Comparison between the Hauser-Feshbach formula and the exact random-matrix result for the cross section

International Nuclear Information System (INIS)

Thomas, J.; Zirnbauer, M.R.; Langanke, K.

1986-01-01

We have calculated the 26 Al(n,p) 26 Mg reaction rate using an exact expression for the compound-nucleus cross section derived recently by Verbaarschot et al. This reaction is astrophysically important, and it happens to fall in a kinematic regime where the exact expression is expected to yield large deviations from the standard Hauser-Feshbach formula. We find that the exact statistical cross section is 20% lower at energies greater than 300 keV, and drops to 40% lower at 0 energy but still does not describe the available data. These deviations are quite similar to those predicted by the formula of Tepel et al

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

Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

CERN Document Server

Dixon, Lance J.; Henn, Johannes M.

2012-01-01

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two function...

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order

International Nuclear Information System (INIS)

Reiher, Markus; Wolf, Alexander

2004-01-01

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order.

Science.gov (United States)

Reiher, Markus; Wolf, Alexander

2004-12-08

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented. (c) 2004 American Institute of Physics.

Exact Performance Analysis of Dual-Hop Semi-Blind AF Relaying over Arbitrary Nakagami-m Fading Channels

KAUST Repository

Xia, Minghua

2011-10-01

Relay transmission is promising for future wireless systems due to its significant cooperative diversity gain. The performance of dual-hop semi-blind amplify-and-forward (AF) relaying systems was extensively investigated, for transmissions over Rayleigh fading channels or Nakagami- fading channels with integer fading parameter. For the general Nakagami- fading with arbitrary values, the exact closed-form system performance analysis is more challenging. In this paper, we explicitly derive the moment generation function (MGF), probability density function (PDF) and moments of the end-to-end signal-to-noise ratio (SNR) over arbitrary Nakagami- fading channels with semi-blind AF relay. With these results, the system performance evaluation in terms of outage probability, average symbol error probability, ergodic capacity and diversity order, is conducted. The analysis developed in this paper applies to any semi-blind AF relaying systems with fixed relay gain, and two major strategies for computing the relay gain are compared in terms of system performance. All analytical results are corroborated by simulation results and they are shown to be efficient tools to evaluate system performance.

Exact Performance Analysis of Dual-Hop Semi-Blind AF Relaying over Arbitrary Nakagami-m Fading Channels

KAUST Repository

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

2011-01-01

Relay transmission is promising for future wireless systems due to its significant cooperative diversity gain. The performance of dual-hop semi-blind amplify-and-forward (AF) relaying systems was extensively investigated, for transmissions over Rayleigh fading channels or Nakagami-𝑚 fading channels with integer fading parameter. For the general Nakagami-𝑚 fading with arbitrary 𝑚 values, the exact closed-form system performance analysis is more challenging. In this paper, we explicitly derive the moment generation function (MGF), probability density function (PDF) and moments of the end-to-end signal-to-noise ratio (SNR) over arbitrary Nakagami-𝑚 fading channels with semi-blind AF relay. With these results, the system performance evaluation in terms of outage probability, average symbol error probability, ergodic capacity and diversity order, is conducted. The analysis developed in this paper applies to any semi-blind AF relaying systems with fixed relay gain, and two major strategies for computing the relay gain are compared in terms of system performance. All analytical results are corroborated by simulation results and they are shown to be efficient tools to evaluate system performance.

Three faces of node importance in network epidemiology: Exact results for small graphs

Science.gov (United States)

Holme, Petter

2017-12-01

We investigate three aspects of the importance of nodes with respect to susceptible-infectious-removed (SIR) disease dynamics: influence maximization (the expected outbreak size given a set of seed nodes), the effect of vaccination (how much deleting nodes would reduce the expected outbreak size), and sentinel surveillance (how early an outbreak could be detected with sensors at a set of nodes). We calculate the exact expressions of these quantities, as functions of the SIR parameters, for all connected graphs of three to seven nodes. We obtain the smallest graphs where the optimal node sets are not overlapping. We find that (i) node separation is more important than centrality for more than one active node, (ii) vaccination and influence maximization are the most different aspects of importance, and (iii) the three aspects are more similar when the infection rate is low.

Exact and approximate formulas for neutrino mixing and oscillations with non-standard interactions

International Nuclear Information System (INIS)

Meloni, Davide; Ohlsson, Tommy; Zhang, He

2009-01-01

We present, both exactly and approximately, a complete set of mappings between the vacuum (or fundamental) leptonic mixing parameters and the effective ones in matter with non-standard neutrino interaction (NSI) effects included. Within the three-flavor neutrino framework and a constant matter density profile, a full set of sum rules is established, which enables us to reconstruct the moduli of the effective leptonic mixing matrix elements, in terms of the vacuum mixing parameters in order to reproduce the neutrino oscillation probabilities for future long-baseline experiments. Very compact, but quite accurate, approximate mappings are obtained based on series expansions in the neutrino mass hierarchy parameter η ≡ Δm 2 21 /Δm 2 31 , the vacuum leptonic mixing parameter s 13 ≡ sin θ 13 , and the NSI parameters ε αβ . A detailed numerical analysis about how the NSIs affect the smallest leptonic mixing angle θ 13 , the deviation of the leptonic mixing angle θ 23 from its maximal mixing value, and the transition probabilities useful for future experiments are performed using our analytical results.

Analytical models of optical response in one-dimensional semiconductors

International Nuclear Information System (INIS)

Pedersen, Thomas Garm

2015-01-01

The quantum mechanical description of the optical properties of crystalline materials typically requires extensive numerical computation. Including excitonic and non-perturbative field effects adds to the complexity. In one dimension, however, the analysis simplifies and optical spectra can be computed exactly. In this paper, we apply the Wannier exciton formalism to derive analytical expressions for the optical response in four cases of increasing complexity. Thus, we start from free carriers and, in turn, switch on electrostatic fields and electron–hole attraction and, finally, analyze the combined influence of these effects. In addition, the optical response of impurity-localized excitons is discussed. - Highlights: • Optical response of one-dimensional semiconductors including excitons. • Analytical model of excitonic Franz–Keldysh effect. • Computation of optical response of impurity-localized excitons

Analytic evidence for the Gubser-Mitra conjecture

International Nuclear Information System (INIS)

Miyamoto, Umpei

2008-01-01

A simple master equation for the static perturbation of charged black strings is derived with employing the gauge proposed by Kol. The sign changes of the potential in the master equation and specific heat of the background exactly coincide. That is, for the black strings with positive specific heat, the potential becomes positive definite to forbid the bound state implying the onset of Gregory-Laflamme instability. It can safely be said that this is the first analytic and explicit evidence for the Gubser-Mitra conjecture, correlating the classical and thermodynamic instabilities of black branes. Possible generalizations of the analysis are also discussed

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.

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 the Lienard equation and its applications

International Nuclear Information System (INIS)

Feng Zhaosheng

2004-01-01

In this paper, a kind of explicit exact solutions to the Lienard equation is obtained, and the applications of the result in seeking traveling solitary wave solution of the nonlinear Schroedinger equation are presented

Possibilities of Utilizing the Method of Analytical Hierarchy Process Within the Strategy of Corporate Social Business

Science.gov (United States)

Drieniková, Katarína; Hrdinová, Gabriela; Naňo, Tomáš; Sakál, Peter

2010-01-01

The paper deals with the analysis of the theory of corporate social responsibility, risk management and the exact method of analytic hierarchic process that is used in the decision-making processes. The Chapters 2 and 3 focus on presentation of the experience with the application of the method in formulating the stakeholders' strategic goals within the Corporate Social Responsibility (CSR) and simultaneously its utilization in minimizing the environmental risks. The major benefit of this paper is the application of Analytical Hierarchy Process (AHP).

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

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

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.

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 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)

In-core LOCA-s: analytical solution for the delayed mixing model for moderator poison concentration

International Nuclear Information System (INIS)

Firla, A.P.

1995-01-01

Solutions to dynamic moderator poison concentration model with delayed mixing under single pressure tube / calandria tube rupture scenario are discussed. Such a model is described by a delay differential equation, and for such equations the standard ways of solution are not directly applicable. In the paper an exact, direct time-domain analytical solution to the delayed mixing model is presented and discussed. The obtained solution has a 'marching' form and is easy to calculate numerically. Results of the numerical calculations based on the analytical solution indicate that for the expected range of mixing times the existing uniform mixing model is a good representation of the moderator poison mixing process for single PT/CT breaks. However, for postulated multi-pipe breaks ( which is very unlikely to occur ) the uniform mixing model is not adequate any more; at the same time an 'approximate' solution based on Laplace transform significantly overpredicts the rate of poison concentration decrease, resulting in excessive increase in the moderator dilution factor. In this situation the true, analytical solution must be used. The analytical solution presented in the paper may also serve as a bench-mark test for the accuracy of the existing poison mixing models. Moreover, because of the existing oscillatory tendency of the solution, special care must be taken in using delay differential models in other applications. (author). 3 refs., 3 tabs., 8 figs

Auto-Baecklund Transformation and Analytic Solutions of (2+1)-Dimensional Boussinesq Equation

International Nuclear Information System (INIS)

Liu Guanting

2008-01-01

Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of (2+1)-dimensional Boussinesq equation. An auto-Baecklund transformation and a number of exact solutions of this equation have been found. The set of solutions include solitary wave solutions, solitoff solutions, and periodic solutions in terms of elliptic Jacobi functions and Weierstrass wp function. Some of them are novel.

Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

Institute of Scientific and Technical Information of China (English)

XU Xiu-Wei; REN Ting-Qi; LIU Shu-Yan; MA Qiu-Ming; LIU Sheng-Dian

2007-01-01

Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators (BEQPO's), we present the analytic expression of arbitrary matrix elements for BEQPO's. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO's.

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

Path integral analysis of Jarzynski's equality: Analytical results

Science.gov (United States)

Minh, David D. L.; Adib, Artur B.

2009-02-01

We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propagators, and validate Jarzynski’s equality.

Exact ground-state correlation functions of an atomic-molecular Bose–Einstein condensate model

Science.gov (United States)

Links, Jon; Shen, Yibing

2018-05-01

We study the ground-state properties of an atomic-molecular Bose–Einstein condensate model through an exact Bethe Ansatz solution. For a certain range of parameter choices, we prove that the ground-state Bethe roots lie on the positive real-axis. We then use a continuum limit approach to obtain a singular integral equation characterising the distribution of these Bethe roots. Solving this equation leads to an analytic expression for the ground-state energy. The form of the expression is consistent with the existence of a line of quantum phase transitions, which has been identified in earlier studies. This line demarcates a molecular phase from a mixed phase. Certain correlation functions, which characterise these phases, are then obtained through the Hellmann–Feynman theorem.

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.

Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

Directory of Open Access Journals (Sweden)

U. Filobello-Nino

2015-01-01

Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.

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 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.

Exact quantification of the complexity of spacewise pattern growth in cellular automata

International Nuclear Information System (INIS)

Freire, Joana G; Gallas, Jason A C; Brison, Owen J

2009-01-01

We analyze the two possible ways of simulating complex systems with cellular automata: by using the familiar timewise updating or by using the complementary spacewise updating. Both updating algorithms operate on identical sets of initial conditions defining the state of the automaton. While timewise growth generally probes just vanishingly small sets of initial conditions producing statistical samples of the asymptotic attractors, spacewise growth operates with much restricted sets which allow one to simulate them all, exhaustively. Our main result is the derivation of an exact analytical formula to quantify precisely one of the two sources of algorithmic complexity of spacewise detection of the complete set of attractors for elementary 1D cellular automata with generic non-periodic architectures of any arbitrary size. The formula gives the total number of initial conditions that need to be investigated to locate rigorously all possible patterns for any given rule. As simple applications, we illustrate how this knowledge may be used (i) to uncover missing patterns in previous classifications in the literature and (ii) to obtain surprisingly novel patterns that are totally unreachable with the time-honored technique of artificially imposing spatially periodic boundary conditions.

Dynamic Programming Approach for Exact Decision Rule Optimization

KAUST Repository

Amin, Talha

2013-01-01

This chapter is devoted to the study of an extension of dynamic programming approach that allows sequential optimization of exact decision rules relative to the length and coverage. It contains also results of experiments with decision tables from UCI Machine Learning Repository. © Springer-Verlag Berlin Heidelberg 2013.

Analytic theory of the energy and time independent particle transport in the plane geometry

International Nuclear Information System (INIS)

Simovic, R.D.

2001-01-01

An analytic investigation of the energy and time independent particle transport in the plane geometry described by a common anisotropic scattering function is carried out. Regarding the particles with specific diffusion histories in the infinite or the semi-infinite medium, new exact solutions of the corresponding transport equations are analytically derived by means of the Fourier inversion technique. Two particular groups of particles scattered after each successive collision into the directions μ 0, were considered. Its Fourier transformed transport equations have solutions without logarithmic singular points, in the upper part or the lower part of the complex k-plane. The Fourier inversion of solutions are carried out analytically and the obtained formulae represents valid generalization of the expressions for the flux of once scattered particles. (author)

New analytical results in the electromagnetic response of composite superconducting wire in parallel fields

NARCIS (Netherlands)

Niessen, E.M.J.; Niessen, E.M.J.; Zandbergen, P.J.

1993-01-01

Analytical results are presented concerning the electromagnetic response of a composite superconducting wire in fields parallel to the wire axis, using the Maxwell equations supplemented with constitutive equations. The problem is nonlinear due to the nonlinearity in the constitutive equation

Exact Jacobians of Roe-type flux difference splitting of the equations of radiation hydrodynamics (and Euler equations) for use in time-implicit higher-order Godunov schemes

International Nuclear Information System (INIS)

Balsara, D.S.

1999-01-01

In this paper we analyze some of the numerical issues that are involved in making time-implicit higher-order Godunov schemes for the equations of radiation hydrodynamics (and the Euler or Navier-Stokes equations). This is done primarily with the intent of incorporating such methods in the author's RIEMANN code. After examining the issues it is shown that the construction of a time-implicit higher-order Godunov scheme for radiation hydrodynamics would be benefited by our ability to evaluate exact Jacobians of the numerical flux that is based on Roe-type flux difference splitting. In this paper we show that this can be done analytically in a form that is suitable for efficient computational implementation. It is also shown that when multiple fluid species are used or when multiple radiation frequencies are used the computational cost in the evaluation of the exact Jacobians scales linearly with the number of fluid species or the number of radiation frequencies. Connections are made to other types of numerical fluxes, especially those based on flux difference splittings. It is shown that the evaluation of the exact Jacobian for such numerical fluxes is also benefited by the present strategy and the results given here. It is, however, pointed out that time-implicit schemes that are based on the evaluation of the exact Jacobians for flux difference splittings using the methods developed here are both computationally more efficient and numerically more stable than corresponding time-implicit schemes that are based on the evaluation of the exact or approximate Jacobians for flux vector splittings. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

A semi-analytical study on helical springs made of shape memory polymer

International Nuclear Information System (INIS)

Baghani, M; Naghdabadi, R; Arghavani, J

2012-01-01

In this paper, the responses of shape memory polymer (SMP) helical springs under axial force are studied both analytically and numerically. In the analytical solution, we first derive the response of a cylindrical tube under torsional loadings. This solution can be used for helical springs in which both the curvature and pitch effects are negligible. This is the case for helical springs with large ratios of the mean coil radius to the cross sectional radius (spring index) and also small pitch angles. Making use of this solution simplifies the analysis of the helical springs to that of the torsion of a straight bar with circular cross section. The 3D phenomenological constitutive model recently proposed for SMPs is also reduced to the 1D shear case. Thus, an analytical solution for the torsional response of SMP tubes in a full cycle of stress-free strain recovery is derived. In addition, the curvature effect is added to the formulation and the SMP helical spring is analyzed using the exact solution presented for torsion of curved SMP tubes. In this modified solution, the effect of the direct shear force is also considered. In the numerical analysis, the 3D constitutive equations are implemented in a finite element program and a full cycle of stress-free strain recovery of an SMP (extension or compression) helical spring is simulated. Analytical and numerical results are compared and it is shown that the analytical solution gives accurate stress distributions in the cross section of the helical SMP spring besides the global load–deflection response. Some case studies are presented to show the validity of the presented analytical method. (paper)

Kawerau fluid chemistry : analytical results

International Nuclear Information System (INIS)

Mroczek, E.K.; Christenson, B.W.; Mountain, B.; Stewart, M.K.

2001-01-01

This report summarises the water and gas analytical data collected from Kawerau geothermal field 1998-2000 under the Sustainable Management of Geothermal and Mineral Resources (GMR) Project, Objective 2 'Understanding New Zealand Geothermal Systems'. The work is part of the continuing effort to characterise the chemical, thermal and isotopic signatures of the deep magmatic heat sources which drive our geothermal systems. At Kawerau there is clear indication that the present-day heat source relates to young volcanism within the field. However, being at the margins of the explored reservoir, little is presently known of the characteristics of that heat source. The Kawerau study follows on directly from the recently completed work characterising the geochemical signatures of the Ohaaki hydrothermal system. In the latter study the interpretation of the radiogenic noble gas isotope systematics was of fundamental importance in characterising the magmatic heat source. Unfortunately the collaboration with LLNL, which analysed the isotopes, could not be extended to include the Kawerau data. The gas samples have been archived and will be analysed once a new collaborator is found to continue the work. The purpose of the present compilation is to facilitate the final completion of the study by ensuring the data is accessible in one report. (author). 5 refs., 2 figs., 9 tabs

Analytic results for the one loop NMHV H anti qqgg amplitude

International Nuclear Information System (INIS)

Badger, Simon; Campbell, John M.; Williams, Ciaran

2009-01-01

We compute the one-loop amplitude for a Higgs boson, a quark-antiquark pair and a pair of gluons of negative helicity, i.e. for the next-to-maximally helicity violating (NMHV) case, A(H, 1 - anti q , 2 + q , 3 - g , 4 - g ). The calculation is performed using an effective Lagrangian which is valid in the limit of very large top quark mass. As a result of this paper all amplitudes for the transition of a Higgs boson into 4 partons are now known analytically at one-loop order. (orig.)

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

Evaluation of analytical results on DOE Quality Assessment Program Samples