Exact analytical thermodynamic expressions for a Brownian heat engine
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.
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
Analytic progress on exact lattice chiral symmetry
International Nuclear Information System (INIS)
Kikukawa, Y.
2002-01-01
Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional)
Exact analytical solutions for nonlinear reaction-diffusion equations
International Nuclear Information System (INIS)
Liu Chunping
2003-01-01
By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way
Quantum decay model with exact explicit analytical solution
Marchewka, Avi; Granot, Er'El
2009-01-01
A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.
Exact 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
An Exact Analytical Solution to Exponentially Tapered Piezoelectric Energy Harvester
Directory of Open Access Journals (Sweden)
H. Salmani
2015-01-01
Full Text Available It has been proven that tapering the piezoelectric beam through its length optimizes the power extracted from vibration based energy harvesting. This phenomenon has been investigated by some researchers using semianalytical, finite element and experimental methods. In this paper, an exact analytical solution is presented to calculate the power generated from vibration of exponentially tapered unimorph and bimorph with series and parallel connections. The mass normalized mode shapes of the exponentially tapered piezoelectric beam with tip mass are implemented to transfer the proposed electromechanical coupled equations into modal coordinates. The steady states harmonic solution results are verified both numerically and experimentally. Results show that there exist values for tapering parameter and electric resistance in a way that the output power per mass of the energy harvester will be maximized. Moreover it is concluded that the electric resistance must be higher than a specified value for gaining more power by tapering the beam.
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...
Corollary from the Exact Expression for Enthalpy of Vaporization
A. A. Sobko
2011-01-01
A problem on determining effective volumes for atoms and molecules becomes actual due to rapidly developing nanotechnologies. In the present study an exact expression for enthalpy of vaporization is obtained, from which an exact expression is derived for effective volumes of atoms and molecules, and under certain assumptions on the form of an atom (molecule) it is possible to find their linear dimensions. The accuracy is only determined by the accuracy of measurements of thermodynamic paramet...
The laser second threshold: Its exact analytical dependence on detuning and relaxation rates
International Nuclear Information System (INIS)
Bakasov, A.A.; Abraham, N.B.
1992-11-01
An exact analysis has been carried out for general analytical expressions for the second threshold of a single-mode homogeneously broadened laser and for the initial pulsation frequency at the second threshold for arbitrary physical values of the relaxation rates, and at arbitrary detuning between the cavity frequency and the atomic resonance frequency. These expressions also give correspondingly exact forms for asymptotic cases that have previously studied with some approximations. Earlier approximate results are partly confirmed and partly improved by these more general expressions. The physical status of various expressions and approximations is re-considered and specified more clearly, including an analysis of which reasonably can be attained in lasers or masers. A general analytical proof is given that for larger detuning of the laser cavity from resonance a higher value of the laser excitation is required to destabilize the steady state solution (the second threshold). We also present results for the minimum value of the second threshold at fixed detuning as a function of the other parameters of the system and on the dependence of the ratio of the second threshold to the first threshold as a function of detuning. Minima of the second threshold and of the threshold ratio occur only if the population relaxation rate is equal to zero. The minima of the threshold ratio are shown to be bounded from above as well as from below (as functions of the relaxation rates, so long as the second threshold exists). The upper bound on the threshold ratio is equal to 17. The variation of the second threshold in the semi-infinite parameter space of the decay rates is shown at various detunings in plots with a finite domain by normalizing the material relaxation rates to the cavity decay rate. (author). 53 refs, 22 figs, 3 tabs
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.
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.
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)
Saengow, C.; Giacomin, A. J.
2017-12-01
The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η∞ affects the normal stress differences in LAOS.
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.
2018-04-01
We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.
International Nuclear Information System (INIS)
Baxter, Mathew; Van Gorder, Robert A
2013-01-01
We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions. (paper)
Resonant amplification of neutrino transitions in the Sun: exact analytical results
International Nuclear Information System (INIS)
Toshev, S.; Petkov, P.
1988-01-01
We investigate in detail the Mikheyev-Smirnov-Wolfenstein explanation of the solar neutrino puzzle using analytical expressions for the neutrino transition probabilities in matter with exponentially varying electron number density
New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods
S Saha, Ray
2016-04-01
In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.
New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods
International Nuclear Information System (INIS)
Saha Ray, S
2016-01-01
In this paper, new exact solutions of the time fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov (KdV–KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann–Liouville derivative is used to convert the nonlinear time fractional KdV–KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV–KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV–KZK equation. (paper)
Energy Technology Data Exchange (ETDEWEB)
Sharma, Pankaj, E-mail: psharma@rtu.ac.in; Parashar, Sandeep Kumar, E-mail: parashar2@yahoo.com [Mechanical Engineering Department, Rajasthan Technical University, Kota (India)
2016-05-06
The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.
Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator
Directory of Open Access Journals (Sweden)
Takibayev N.Zh.
2010-04-01
Full Text Available Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two ﬁxed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two ﬁxed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei ﬁxed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.
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
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
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.
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.
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
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.
Analytical expressions for the electron backscattering coefficient
International Nuclear Information System (INIS)
August, H.J.; Wernisch, J.
1989-01-01
Several analytical expressions for the electron backscattering coefficient for massive homogeneous samples are compared with experimental data, directing special attention to the dependence of this quantity on the electron acceleration energy. It is shown that this dependence generally cannot be neglected. The expression proposed by Hunger and Kuechler turns out to be better than that of Love and Scott, although even the better formula can be slightly improved by a small modification. (author)
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.
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.
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.
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
Study of coupled nonlinear partial differential equations for finding exact analytical solutions.
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.
Study of coupled nonlinear partial differential equations for finding exact analytical solutions
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
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.
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.
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
Nonlinear differential equations with exact solutions expressed via the Weierstrass function
Kudryashov, NA
2004-01-01
A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear
Manual of a suite of computer codes, EXPRESS (EXact PREparedness Supporting System)
International Nuclear Information System (INIS)
Chino, Masamichi
1992-06-01
The emergency response supporting system EXPRESS (EXact PREparedness Supporting System) is constructed in JAERI for low cost engineering work stations under the UNIX operation. The purpose of this system is real-time predictions of affected areas due to radioactivities discharged into atmosphere from nuclear facilities. The computational models in EXPRESS are the mass-consistent wind field model EXPRESS-I and the particle dispersion model EXPRESS-II for atmospheric dispersions. In order to attain the quick response even when the codes are used in a small-scale computer, a high-speed iteration method MILUCR (Modified Incomplete Linear Unitary Conjugate Residual) is applied to EXPRESS-I and kernel density method is to EXPRESS-II. This manual describes the model configurations, code structures, related files, namelists and sample outputs of EXPRESS-I and -II. (author)
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.
Lou, Ping; Lee, Jin Yong
2009-04-14
For a simple modified Poisson-Boltzmann (SMPB) theory, taking into account the finite ionic size, we have derived the exact analytic expression for the contact values of the difference profile of the counterion and co-ion, as well as of the sum (density) and product profiles, near a charged planar electrode that is immersed in a binary symmetric electrolyte. In the zero ionic size or dilute limit, these contact values reduce to the contact values of the Poisson-Boltzmann (PB) theory. The analytic results of the SMPB theory, for the difference, sum, and product profiles were compared with the results of the Monte-Carlo (MC) simulations [ Bhuiyan, L. B.; Outhwaite, C. W.; Henderson, D. J. Electroanal. Chem. 2007, 607, 54 ; Bhuiyan, L. B.; Henderson, D. J. Chem. Phys. 2008, 128, 117101 ], as well as of the PB theory. In general, the analytic expression of the SMPB theory gives better agreement with the MC data than the PB theory does. For the difference profile, as the electrode charge increases, the result of the PB theory departs from the MC data, but the SMPB theory still reproduces the MC data quite well, which indicates the importance of including steric effects in modeling diffuse layer properties. As for the product profile, (i) it drops to zero as the electrode charge approaches infinity; (ii) the speed of the drop increases with the ionic size, and these behaviors are in contrast with the predictions of the PB theory, where the product is identically 1.
Analytical and exact solutions of the spherical and cylindrical diodes of Langmuir-Blodgett law
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.
Sarma, Rajkumar; Deka, Nabajit; Sarma, Kuldeep; Mondal, Pranab Kumar
2018-06-01
We present a mathematical model to study the electroosmotic flow of a viscoelastic fluid in a parallel plate microchannel with a high zeta potential, taking hydrodynamic slippage at the walls into account in the underlying analysis. We use the simplified Phan-Thien-Tanner (s-PTT) constitutive relationships to describe the rheological behavior of the viscoelastic fluid, while Navier's slip law is employed to model the interfacial hydrodynamic slip. Here, we derive analytical solutions for the potential distribution, flow velocity, and volumetric flow rate based on the complete Poisson-Boltzmann equation (without considering the frequently used Debye-Hückel linear approximation). For the underlying electrokinetic transport, this investigation primarily reveals the influence of fluid rheology, wall zeta potential as modulated by the interfacial electrochemistry and interfacial slip on the velocity distribution, volumetric flow rate, and fluid stress, as well as the apparent viscosity. We show that combined with the viscoelasticity of the fluid, a higher wall zeta potential and slip coefficient lead to a phenomenal enhancement in the volumetric flow rate. We believe that this analysis, besides providing a deep theoretical insight to interpret the transport process, will also serve as a fundamental design tool for microfluidic devices/systems under electrokinetic influence.
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)
Nam, Sungsik; Hasna, Mazen Omar; Alouini, Mohamed-Slim
2010-01-01
in mind, we capitalize in this paper on some new order statistics results to derive exact closed-form expressions for outage probability of GSC RAKE receivers subject to self-interference over independent and identically distributed Rayleigh fading
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.
Quasi exact solution of the Rabi Hamiltonian
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.
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
Mayday - integrative analytics for expression data
Directory of Open Access Journals (Sweden)
Nieselt Kay
2010-03-01
Full Text Available Abstract Background DNA Microarrays have become the standard method for large scale analyses of gene expression and epigenomics. The increasing complexity and inherent noisiness of the generated data makes visual data exploration ever more important. Fast deployment of new methods as well as a combination of predefined, easy to apply methods with programmer's access to the data are important requirements for any analysis framework. Mayday is an open source platform with emphasis on visual data exploration and analysis. Many built-in methods for clustering, machine learning and classification are provided for dissecting complex datasets. Plugins can easily be written to extend Mayday's functionality in a large number of ways. As Java program, Mayday is platform-independent and can be used as Java WebStart application without any installation. Mayday can import data from several file formats, database connectivity is included for efficient data organization. Numerous interactive visualization tools, including box plots, profile plots, principal component plots and a heatmap are available, can be enhanced with metadata and exported as publication quality vector files. Results We have rewritten large parts of Mayday's core to make it more efficient and ready for future developments. Among the large number of new plugins are an automated processing framework, dynamic filtering, new and efficient clustering methods, a machine learning module and database connectivity. Extensive manual data analysis can be done using an inbuilt R terminal and an integrated SQL querying interface. Our visualization framework has become more powerful, new plot types have been added and existing plots improved. Conclusions We present a major extension of Mayday, a very versatile open-source framework for efficient micro array data analysis designed for biologists and bioinformaticians. Most everyday tasks are already covered. The large number of available plugins as well
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'
Ball Bearing Stiffnesses- A New Approach Offering Analytical Expressions
Guay, Pascal; Frikha, Ahmed
2015-09-01
Space mechanisms use preloaded ball bearings in order to withstand the severe vibrations during launch.The launch strength requires the calculation of the bearing stiffness, but this calculation is complex. Nowadays, there is no analytical expression that gives the stiffness of a bearing. Stiffness is computed using an iterative algorithm such as Newton-Raphson, to solve the nonlinear system of equations.This paper aims at offering a simplified analytical approach, based on the assumption that the contact angle is constant. This approach gives analytical formulas of the stiffness of preloaded ball bearing.
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.
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.
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.)
Formulating analytic expressions for atomic collision cross sections
International Nuclear Information System (INIS)
Tabata, Tatsuo; Kubo, Hirotaka; Sataka, Masao
2003-08-01
Methods to formulate analytic expression for atomic collision cross sections as a function of projectile energy are described on the basis of the experiences of the data compilation work for more than 20 years. Topics considered are the choice of appropriate functional forms for the expressions and optimization of adjustable parameters. To make extrapolation possible, functions to be used should have the form with reasonable asymptotic behavior. In this respect, modified Green-McNeal formulas have been found useful for various atomic collision cross sections. For ionization processes, a modified Lotz formula has often given a good fit. The ALESQ code for least-squares fits has been convenient to optimize adjustable parameters in analytic expressions. (author)
International Nuclear Information System (INIS)
Accorsi, R; Metzler, S D
2006-01-01
The expressions for the sensitivity of converging collimators found in the literature diverge at points near the focal locus of the collimator. In this paper, an analytical formula that does not diverge is derived and compared to that available in the literature. An analysis is provided to predict the cases in which use of the new formula is advisable. Since the first expression derived is rather complex, approximations were made to reach simpler formulae. The formulae derived can be used to define and extend the realm of applicability of the literature expression in the cases identified in their derivation
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.
Analytical Expressions for Thermo-Osmotic Permeability of Clays
Gonçalvès, J.; Ji Yu, C.; Matray, J.-M.; Tremosa, J.
2018-01-01
In this study, a new formulation for the thermo-osmotic permeability of natural pore solutions containing monovalent and divalent cations is proposed. The mathematical formulation proposed here is based on the theoretical framework supporting thermo-osmosis which relies on water structure alteration in the pore space of surface-charged materials caused by solid-fluid electrochemical interactions. The ionic content balancing the surface charge of clay minerals causes a disruption in the hydrogen bond network when more structured water is present at the clay surface. Analytical expressions based on our heuristic model are proposed and compared to the available data for NaCl solutions. It is shown that the introduction of divalent cations reduces the thermo-osmotic permeability by one third compared to the monovalent case. The analytical expressions provided here can be used to advantage for safety calculations in deep underground nuclear waste repositories.
An Analytical Time–Domain Expression for the Net Ripple Produced by Parallel Interleaved Converters
Energy Technology Data Exchange (ETDEWEB)
Johnson, Brian B.; Krein, Philip T.
2017-03-01
We apply modular arithmetic and Fourier series to analyze the superposition of N interleaved triangular waveforms with identical amplitudes and duty-ratios. Here, interleaving refers to the condition when a collection of periodic waveforms with identical periods are each uniformly phase-shifted across one period. The main result is a time-domain expression which provides an exact representation of the summed and interleaved triangular waveforms, where the peak amplitude and parameters of the time-periodic component are all specified in closed-form. Analysis is general and can be used to study various applications in multi-converter systems. This model is unique not only in that it reveals a simple and intuitive expression for the net ripple, but its derivation via modular arithmetic and Fourier series is distinct from prior approaches. The analytical framework is experimentally validated with a system of three parallel converters under time-varying operating conditions.
Nam, Sungsik
2010-11-01
Previous work on performance analyses of generalized selection combining (GSC) RAKE receivers based on the signal to noise ratio focused on the development of methodologies to derive exact closed-form expressions for various performance measures. However, some open problems related to the performance evaluation of GSC RAKE receivers still remain to be solved such that an assessment of the impact of self-interference on the performance of GSC RAKE receivers. To have a full and exact understanding of the performance of GSC RAKE receivers, the outage probability of GSC RAKE receivers needs to be analyzed as closed-form expressions. The major difficulty in this problem is to derive some joint statistics of ordered exponential variates. With this motivation in mind, we capitalize in this paper on some new order statistics results to derive exact closed-form expressions for outage probability of GSC RAKE receivers subject to self-interference over independent and identically distributed Rayleigh fading channels. © 2010 IEEE.
Analytical results for a stochastic model of gene expression with arbitrary partitioning of proteins
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.
De Nardis, J.; Caux, J.-S.
2014-01-01
We apply the logic of the quench action to give an exact analytical expression for the time evolution of the one-body density matrix after an interaction quench in the Lieb-Liniger model from the ground state of the free theory (BEC state) to the infinitely repulsive regime. In this limit there
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)
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)
Exact closed-form expression for the inverse moments of one-sided correlated Gram matrices
Elkhalil, Khalil
2016-08-15
In this paper, we derive a closed-form expression for the inverse moments of one sided-correlated random Gram matrices. Such a question is mainly motivated by applications in signal processing and wireless communications for which evaluating this quantity is a question of major interest. This is for instance the case of the best linear unbiased estimator, in which the average estimation error corresponds to the first inverse moment of a random Gram matrix.
Exact closed-form expression for the inverse moments of one-sided correlated Gram matrices
Elkhalil, Khalil; Kammoun, Abla; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2016-01-01
In this paper, we derive a closed-form expression for the inverse moments of one sided-correlated random Gram matrices. Such a question is mainly motivated by applications in signal processing and wireless communications for which evaluating this quantity is a question of major interest. This is for instance the case of the best linear unbiased estimator, in which the average estimation error corresponds to the first inverse moment of a random Gram matrix.
International Nuclear Information System (INIS)
Zypman, F R
2006-01-01
We begin by deriving a general useful theoretical relationship between the plane-particle interaction forces in solution, and the corresponding plane-plane interaction energies. This is the main result of the paper. It provides a simple tool to obtain closed-form particle-plane forces from knowledge of plane-plane interaction energies. To illustrate the simplicity of use of this general formalism, we apply it to find particle-plane interactions within the Derjaguin-Landau-Verwey-Overbeek (DLVO) framework. Specifically, we obtain analytical expressions for forces and interaction energies in the van der Waals and the electrical double layer cases. The van der Waals expression is calculated here for benchmarking purposes and is compared with well-established expressions from Hamaker theory. The interactions for the electric double layer situation are computed in two cases: the linear superposition approximation and the constant surface potential. In both cases, our closed-form expressions were compared with existent numerical results. We also use the main result of this paper to generate an analytical force-separation expression based on atomic force microscope experiments for a tip and surface immersed in an aqueous solution, and compare it with the corresponding numerical results. Finally, based on our main result, we generalize the Derjaguin approximation by calculating the next order of approximation, thus obtaining a formula valuable for colloidal interaction estimations
Analytical expression for sheath edge around corner cathodes
International Nuclear Information System (INIS)
Sheridan, T E
2009-01-01
A simple analytical expression for the position of the sheath edge around a two-dimensional corner cathode with included angle θ c has been discovered. This expression is valid for weakly collisional sheaths in the Child-Langmuir regime φ c >> kT e /e, where -φ c e is the electron temperature. In polar coordinates (r, θ), the sheath edge is given by (r/s 0 )sin[πθ/(2π - θ c )] = [π/(2π - θ c )] where s 0 is the planar sheath width far from the vertex of the corner. This result is verified by comparison with previous numerical solutions (Watterson P A 1989 J. Phys. D: Appl. Phys. 22 1300) for the knife edge (θ c = 0) and convex square corner (θ c = π/2). The observed agreement suggests that this expression gives the sheath edge for all corner angles, both concave and convex. The utility of this result is demonstrated by computing the full sheath solution for a knife-edge cathode with φ c = 100kT e /e.
International Nuclear Information System (INIS)
Antonov, A.N.; Christov, Chr.V.; Nikolov, E.N.
1989-01-01
Differential cross-section of the 1.04 GeV - proton elastic scattering from 40 Ca is calculated within the Glauber-Sitenko theoretical scheme using the coherent density fluctuation model (CDFM). It is shown that the use of exact noneikonal expression for the two-body scattering amplitude (which describes the p-p data) leads to a satisfactory agreement with the experimental data. The influence of the flucton correlations on the differential cross-sections is considerable as the use of a realistic charge density distribution leads to a better agreement with the experimental data of the CDFM which is not for the case of the independent-particle model. 20 refs.; 4 figs
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
A Unified Channel Charges Expression for Analytic MOSFET Modeling
Directory of Open Access Journals (Sweden)
Hugues Murray
2012-01-01
Full Text Available Based on a 1D Poissons equation resolution, we present an analytic model of inversion charges allowing calculation of the drain current and transconductance in the Metal Oxide Semiconductor Field Effect Transistor. The drain current and transconductance are described by analytical functions including mobility corrections and short channel effects (CLM, DIBL. The comparison with the Pao-Sah integral shows excellent accuracy of the model in all inversion modes from strong to weak inversion in submicronics MOSFET. All calculations are encoded with a simple C program and give instantaneous results that provide an efficient tool for microelectronics users.
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
Analytic expressions for polarimetry in plasma with large Cotton endash Mouton or Faraday effects
International Nuclear Information System (INIS)
Segre, S.E.
1996-01-01
Analytic expressions for plasma polarimetry are derived for the case when either the Cotton endash Mouton effect or the Faraday effect is large while the other effect is small. copyright 1996 American Institute of Physics
The derivation of the analytic expressions of the dynamical ...
African Journals Online (AJOL)
... expressions of the dynamical susceptibility of the spin system, by setting up the equation of motion and solving it in a generalized HFA of the susceptibility tensor, Χ-+, and quoting the result for the first derivative of the Green's function. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 579-582 ...
Analytical expressions for transition edge sensor excess noise models
International Nuclear Information System (INIS)
Brandt, Daniel; Fraser, George W.
2010-01-01
Transition edge sensors (TESs) are high-sensitivity thermometers used in cryogenic microcalorimeters which exploit the steep gradient in resistivity with temperature during the superconducting phase transition. Practical TES devices tend to exhibit a white noise of uncertain origin, arising inside the device. We discuss two candidate models for this excess noise, phase slip shot noise (PSSN) and percolation noise. We extend the existing PSSN model to include a magnetic field dependence and derive a basic analytical model for percolation noise. We compare the predicted functional forms of the noise current vs. resistivity curves of both models with experimental data and provide a set of equations for both models to facilitate future experimental efforts to clearly identify the source of excess noise.
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.
International Nuclear Information System (INIS)
Lublinsky, Michael
2004-01-01
A simple analytic expression for the nonsinglet structure function f NS is given. The expression is derived from the result of Ermolaev, Manaenkov, and Ryskin obtained by low x resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD
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.
DEFF Research Database (Denmark)
Ye, Feihong; Tu, Jiajing; Saitoh, Kunimasa
2014-01-01
An analytical expression for the mode coupling coe cient in homogeneous trench-assisted multi-core fibers is derived, which has a sim- ple relationship with the one in normal step-index structures. The amount of inter-core crosstalk reduction (in dB) with trench-assisted structures compared...... to the one with normal step-index structures can then be written by a simple expression. Comparison with numerical simulations confirms that the obtained analytical expression has very good accuracy for crosstalk estimation. The crosstalk properties in trench-assisted multi-core fibers, such as crosstalk...... dependence on core pitch and wavelength-dependent crosstalk, can be obtained by this simple analytical expression....
Analytical expression for initial magnetization curve of Fe-based soft magnetic composite material
Energy Technology Data Exchange (ETDEWEB)
Birčáková, Zuzana, E-mail: zuzana.bircakova@upjs.sk [Institute of Physics, Faculty of Science, Pavol Jozef Šafárik University, Park Angelinum 9, 04154 Košice (Slovakia); Kollár, Peter; Füzer, Ján [Institute of Physics, Faculty of Science, Pavol Jozef Šafárik University, Park Angelinum 9, 04154 Košice (Slovakia); Bureš, Radovan; Fáberová, Mária [Institute of Materials Research, Slovak Academy of Sciences, Watsonova 47, 04001 Košice (Slovakia)
2017-02-01
The analytical expression for the initial magnetization curve for Fe-phenolphormaldehyde resin composite material was derived based on the already proposed ideas of the magnetization vector deviation function and the domain wall annihilation function, characterizing the reversible magnetization processes through the extent of deviation of magnetization vectors from magnetic field direction and the irreversible processes through the effective numbers of movable domain walls, respectively. As for composite materials the specific dependences of these functions were observed, the ideas were extended meeting the composites special features, which are principally the much higher inner demagnetizing fields produced by magnetic poles on ferromagnetic particle surfaces. The proposed analytical expression enables us to find the relative extent of each type of magnetization processes when magnetizing a specimen along the initial curve. - Highlights: • Analytical expression of the initial curve derived for SMC. • Initial curve described by elementary magnetization processes. • Influence of inner demagnetizing fields on magnetization process in SMC.
International Nuclear Information System (INIS)
Wang Qi; Chen Yong
2007-01-01
With the aid of symbolic computation, some algorithms are presented for the rational expansion methods, which lead to closed-form solutions of nonlinear partial differential equations (PDEs). The new algorithms are given to find exact rational formal polynomial solutions of PDEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symbolic computation system Maple. As applications of the methods, we choose some nonlinear PDEs to illustrate the methods. As a result, we not only can successfully obtain the solutions found by most existing Jacobi elliptic function methods and Tanh-methods, but also find other new and more general solutions at the same time
Analytical expression for the bit error rate of cascaded all-optical regenerators
DEFF Research Database (Denmark)
Mørk, Jesper; Öhman, Filip; Bischoff, S.
2003-01-01
We derive an approximate analytical expression for the bit error rate of cascaded fiber links containing all-optical 2R-regenerators. A general analysis of the interplay between noise due to amplification and the degree of reshaping (nonlinearity) of the regenerator is performed.......We derive an approximate analytical expression for the bit error rate of cascaded fiber links containing all-optical 2R-regenerators. A general analysis of the interplay between noise due to amplification and the degree of reshaping (nonlinearity) of the regenerator is performed....
Directory of Open Access Journals (Sweden)
Qian Yang
2017-01-01
Full Text Available The near fields of electric dipole are commonly used in wide-band analysis of complex electromagnetic problems. In this paper, we propose new near field time-domain expressions for electric dipole. The analytical expressions for the frequency-domain of arbitrarily oriented electric dipole are given at first; next we give the time-domain expressions by time-frequency transformation. The proposed expressions are used in hybrid TDIE/DGTD method for analysis of circular antenna with radome. The accuracy of the proposed algorithm is verified by numerical examples.
Analytical expressions for time-resolved optically stimulated luminescence experiments in quartz
International Nuclear Information System (INIS)
Pagonis, V.; Lawless, J.; Chen, R.; Chithambo, M.L.
2011-01-01
Optically stimulated luminescence (OSL) signals can be obtained using a time-resolved optical stimulation (TR-OSL) method, also known as pulsed OSL. During TR-OSL measurements, the stimulation and emission of luminescence are experimentally separated in time using short light pulses. This paper presents analytical expressions for the TR-OSL intensity observed during and after such a pulse in quartz experiments. The analytical expressions are derived using a recently published kinetic model which describes thermal quenching phenomena in quartz samples. In addition, analytical expressions are derived for the concentration of electrons in the conduction band during and after the TR-OSL pulse, and for the maximum signals attained during optical stimulation of the samples. The relevance of the model for dosimetric applications is examined, by studying the dependence of the maximum TR-OSL signals on the degree of initial trap filling, and also on the probability of electron retrapping into the dosimetric trap. Analytical expressions are derived for two characteristic times of the TR-OSL mechanism; these times are the relaxation time for electrons in the conduction band, and the corresponding relaxation time for the radiative transition within the luminescence center. The former relaxation time is found to depend on several experimental parameters, while the latter relaxation time depends only on internal parameters characteristic of the recombination center. These differences between the two relaxation times can be explained by the presence of localized and delocalized transitions in the quartz sample. The analytical expressions in this paper are shown to be equivalent to previous analytical expressions derived using a different mathematical approach. A description of thermal quenching processes in quartz based on AlO 4 - /AlO 4 defects is presented, which illustrates the connection between the different descriptions of the luminescence process found in the literature
International Nuclear Information System (INIS)
Sorcini, B.B.; Hyoedynmaa, S; Brahme, A.
1995-01-01
Qualification of the bremsstrahlung photon background generated by an electron beam in a phantom is important for accurate high energy electron beam dosimetry in radiation therapy. An analytical expression has been derived for the background of phantom generated bremsstrahlung photons in plane parallel electron beams normally incident on phantoms of any atomic number between 4 and 92 (Be, C, H 2 O, Al, Cu, Ag, Pb and U). The expression can be used with fairly good accuracy in the energy range between 1 and 50 MeV. The expression is globally based on known scattering power and radiation and collision stopping power data for the phantom material at the mean energy of the incident electrons. The depth dose distribution due to the bremsstrahlung generated in the phantom is derived by folding the bremsstrahlung energy fluence with a simple analytical one-dimensional photon energy deposition kernel. The energy loss of the primary electrons and the generation, attenuation and absorption of bremsstrahlung photons are taken into account in the analytical formula. The photon energy deposition kernel is used to account for the bremsstrahlung produced at one depth that will contribute to the down stream dose. A simple analytical expression for photon energy deposition kernel is consistent with the classical analytical relation describing the photon depth dose distribution. From the surface to the practical range the photon dose increases almost linearly due to accumulation and buildup of the photon produced at different phantom layers. At depths beyond the practical range a simple exponential function can be use to describe the bremsstrahlung attenuation in the phantom. For comparison Monte Carlo calculated distributions using ITS3 Monte Carlo Code were used. Good agreement is found between the analytical expression and Monte Carlo calculation. Deviations of 5% from Monte Carlo calculated bremmstrahlung background are observed for high atomic number materials. The method can
Analytical expressions for two-nucleon transfer spectroscopic factors in sdg interacting boson model
International Nuclear Information System (INIS)
Devi, Y.D.; Kota, V.K.B.
1991-01-01
Analytical expressions for two-nucleon (l = 0,2 and 4) transfer spectroscopic factors are derived in the SU sdg (3) limit of the sdg interacting boson model. In addition, large N (boson number) limit expressions for the ratio of summed l = 0 transfer strength to excited 0 + states to that of ground state are derived in all the symmetry limits of the sdg model. Some comparisons with data are made. (author)
Analytical expressions for two-nucleon transfer spectroscopic factors in sdg interacting boson model
Energy Technology Data Exchange (ETDEWEB)
Devi, Y.D.; Kota, V.K.B. (Physical Research Lab., Ahmedabad (India))
1991-11-01
Analytical expressions for two-nucleon (l = 0,2 and 4) transfer spectroscopic factors are derived in the SU{sub sdg}(3) limit of the sdg interacting boson model. In addition, large N (boson number) limit expressions for the ratio of summed l = 0 transfer strength to excited 0{sup +} states to that of ground state are derived in all the symmetry limits of the sdg model. Some comparisons with data are made. (author).
Analytical Expressions of Matrix Elements of Physical Quantities for Dirac Oscillator
Institute of Scientific and Technical Information of China (English)
LI Ning; JU Guo-Xing; REN Zhong-Zhou
2004-01-01
The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case of operator's square is discussed in details. The twodimensional Dirac oscillator has similar behavior to that for three-dimensional one.
DEFF Research Database (Denmark)
Bruun, Erik
1999-01-01
One of the origins of harmonic distortion in current mirrors is the inevitable mismatch between the mirror transistors. In this brief we examine both single current mirrors and complementary class AB current mirrors and develop analytical expressions for the mismatch induced harmonic distortion. ...
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.
Chen, Jingchao; Huang, Zhaofeng; Huang, Hongjuan; Wei, Shouhui; Liu, Yan; Jiang, Cuilan; Zhang, Jie; Zhang, Chaoxian
2017-04-21
Goosegrass (Eleusine indica) is one of the most serious annual grassy weeds worldwide, and its evolved herbicide-resistant populations are more difficult to control. Quantitative real-time PCR (qPCR) is a common technique for investigating the resistance mechanism; however, there is as yet no report on the systematic selection of stable reference genes for goosegrass. This study proposed to test the expression stability of 9 candidate reference genes in goosegrass in different tissues and developmental stages and under stress from three types of herbicide. The results show that for different developmental stages and organs (control), eukaryotic initiation factor 4 A (eIF-4) is the most stable reference gene. Chloroplast acetolactate synthase (ALS) is the most stable reference gene under glyphosate stress. Under glufosinate stress, eIF-4 is the best reference gene. Ubiquitin-conjugating enzyme (UCE) is the most stable reference gene under quizalofop-p-ethyl stress. The gene eIF-4 is the recommended reference gene for goosegrass under the stress of all three herbicides. Moreover, pairwise analysis showed that seven reference genes were sufficient to normalize the gene expression data under three herbicides treatment. This study provides a list of reliable reference genes for transcript normalization in goosegrass, which will facilitate resistance mechanism studies in this weed species.
International Nuclear Information System (INIS)
Minguez, E.
1983-01-01
A review of the analytical expressions between α-parameter and reactivity (rho) has been done in this article. Finally, several lineal approximations have been obtained for two important points of values. The analytical expansion has been made using only one family of precursors from delayed neutrons; diffusion equation in one energy groups; neutron flux separability with known spatial function. Numerical results have been obtained using typical data from fast and thermal reactors; considering and homogeneous media of Pu 239 in the first case, and U-235 in the second one. (author)
Explicit analytical expression for the condition number of polynomials in power form
Rack, Heinz-Joachim
2017-07-01
In his influential papers [1-3] W. Gautschi has defined and reshaped the condition number κ∞ of polynomials Pn of degree ≤ n which are represented in power form on a zero-symmetric interval [-ω, ω]. Basically, κ∞ is expressed as the product of two operator norms: an explicit factor times an implicit one (the l∞-norm of the coefficient vector of the n-th Chebyshev polynomial of the first kind relative to [-ω, ω]). We provide a new proof, economize the second factor and express it by an explicit analytical formula.
Analytical expressions for the correlation function of a hard sphere dimer fluid
Kim, Soonho; Chang, Jaeeon; Kim, Hwayong
A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.
Analytical expression for the correlation function of a hard sphere chain fluid
Chang, Jaeeon; Kim, Hwayong
A closed form expression is given for the correlation function of flexible hard sphere chain fluid. A set of integral equations obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with the polymer Percus-Yevick ideal chain approximation is considered. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of individual correlation functions are obtained. By inverse Laplace transformation the inter- and intramolecular radial distribution functions (RDFs) are obtained in closed forms up to 3D(D is segment diameter). These analytical expressions for the RDFs would be useful in developing the perturbation theory of chain fluids.
Meaux, Emilie; Vuilleumier, Patrik
2016-11-01
The ability to decode facial emotions is of primary importance for human social interactions; yet, it is still debated how we analyze faces to determine their expression. Here we compared the processing of emotional face expressions through holistic integration and/or local analysis of visual features, and determined which brain systems mediate these distinct processes. Behavioral, physiological, and brain responses to happy and angry faces were assessed by presenting congruent global configurations of expressions (e.g., happy top+happy bottom), incongruent composite configurations (e.g., angry top+happy bottom), and isolated features (e.g. happy top only). Top and bottom parts were always from the same individual. Twenty-six healthy volunteers were scanned using fMRI while they classified the expression in either the top or the bottom face part but ignored information in the other non-target part. Results indicate that the recognition of happy and anger expressions is neither strictly holistic nor analytic Both routes were involved, but with a different role for analytic and holistic information depending on the emotion type, and different weights of local features between happy and anger expressions. Dissociable neural pathways were engaged depending on emotional face configurations. In particular, regions within the face processing network differed in their sensitivity to holistic expression information, which predominantly activated fusiform, inferior occipital areas and amygdala when internal features were congruent (i.e. template matching), whereas more local analysis of independent features preferentially engaged STS and prefrontal areas (IFG/OFC) in the context of full face configurations, but early visual areas and pulvinar when seen in isolated parts. Collectively, these findings suggest that facial emotion recognition recruits separate, but interactive dorsal and ventral routes within the face processing networks, whose engagement may be shaped by
Directory of Open Access Journals (Sweden)
Alkharouf Nadim W.
2005-01-01
Full Text Available Gene expression databases contain a wealth of information, but current data mining tools are limited in their speed and effectiveness in extracting meaningful biological knowledge from them. Online analytical processing (OLAP can be used as a supplement to cluster analysis for fast and effective data mining of gene expression databases. We used Analysis Services 2000, a product that ships with SQLServer2000, to construct an OLAP cube that was used to mine a time series experiment designed to identify genes associated with resistance of soybean to the soybean cyst nematode, a devastating pest of soybean. The data for these experiments is stored in the soybean genomics and microarray database (SGMD. A number of candidate resistance genes and pathways were found. Compared to traditional cluster analysis of gene expression data, OLAP was more effective and faster in finding biologically meaningful information. OLAP is available from a number of vendors and can work with any relational database management system through OLE DB.
Alkharouf, Nadim W; Jamison, D Curtis; Matthews, Benjamin F
2005-06-30
Gene expression databases contain a wealth of information, but current data mining tools are limited in their speed and effectiveness in extracting meaningful biological knowledge from them. Online analytical processing (OLAP) can be used as a supplement to cluster analysis for fast and effective data mining of gene expression databases. We used Analysis Services 2000, a product that ships with SQLServer2000, to construct an OLAP cube that was used to mine a time series experiment designed to identify genes associated with resistance of soybean to the soybean cyst nematode, a devastating pest of soybean. The data for these experiments is stored in the soybean genomics and microarray database (SGMD). A number of candidate resistance genes and pathways were found. Compared to traditional cluster analysis of gene expression data, OLAP was more effective and faster in finding biologically meaningful information. OLAP is available from a number of vendors and can work with any relational database management system through OLE DB.
International Nuclear Information System (INIS)
Kusba, J.; Sipp, B.
1985-01-01
We present a discussion about the range of validity of the usual approximate transfer rate expressions used in the description of the kinetics of diffusion-modulated excitation transfer, for a reactive interaction of exponential functional form. We simulate the features of energy transfer by a numerical inversion of the exact Laplace transform of the transfer rate. It is shown that for high diffusion coefficients of the order of 10 -5 cm 2 s -1 , the kinetics may be well reproduced, even at short times, by the asymptotic form of the transfer rate. For slow molecular displacements, the short time static regime is brought to direct observation, but the transfer rate approaches is asymptotic value at a much later time
Analytic expression for the giant fieldlike spin torque in spin-filter magnetic tunnel junctions
Tang, Y.-H.; Huang, Z.-W.; Huang, B.-H.
2017-08-01
We propose analytic expressions for fieldlike, T⊥, and spin-transfer, T∥, spin torque components in the spin-filter-based magnetic tunnel junction (SFMTJ), by using the single-band tight-binding model with the nonequilibrium Keldysh formalism. In consideration of multireflection processes between noncollinear magnetization of the spin-filter (SF) barrier and the ferromagnetic (FM) electrode, the central spin-selective SF barrier plays an active role in the striking discovery T⊥≫T∥ , which can be further identified by the unusual barrier thickness dependence of giant T⊥. Our general expressions reveal the sinusoidal angular dependence of both spin torque components, even in the presence of the SF barrier.
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 Analytical Solutions for Elastodynamic Impact
2015-11-30
the displacement We consider one-dimensional deformations of a homogeneous, linear elastic solid, assuming small displacement gradients . Let ukðx; tÞ...residues for problems involving the sudden arrest of rods in motion. The use of residue calculus and the evaluation of the Bromwich integral (akin to the
Exact analytical density profiles and surface tension
Indian Academy of Sciences (India)
journal of. May 2005 physics pp. 785–801. Classical charged fluids at equilibrium near ... is provided by the excess surface tension for an air–water interface, which is determined ... the potential drop created by the electric layer which appears as soon as the fluid has ...... radii, by symmetry, the charge density profile is flat,.
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...
International Nuclear Information System (INIS)
Lublinsky, M.
2004-01-01
A simple analytic expression for the non-singlet structure function fns is given. The expression is derived from the result of B. I. Ermolaev et al. (1996) obtained by low x resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD. (orig.)
Exact combinatorial approach to finite coagulating systems
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.
International Nuclear Information System (INIS)
Hinkel-Lipsker, D.E.; Fried, B.D.; Morales, G.J.
1993-01-01
This study provides an analytic solution to the general problem of mode conversion in an unmagnetized plasma. Specifically, an electromagnetic wave of frequency ω propagating through a plasma with a parabolic density profile of scale length L p is examined. The mode conversion points are located a distance Δ 0 from the peak of the profile, where the electron plasma frequency ω p (z) matches the wave frequency ω. The corresponding reflection, transmission, and mode conversion coefficients are expressed analytically in terms of parabolic cylinder functions for all values of Δ 0 . The method of solution is based on a source approximation technique that is valid when the electromagnetic and electrostatic scale lengths are well separated. For large Δ 0 , i.e., (cL p /ω) 1/2 much-lt Δ 0 p , the appropriately scaled result [D. E. Hinkel-Lipsker et al., Phys. Fluids B 4, 559 (1992)] for a linear density profile is recovered as the parabolic cylinder functions asymptotically become Airy functions. When Δ 0 →0, the special case of conversion at the peak of the profile [D. E. Hinkel-Lipsker et al., Phys. Fluids B 4, 1772 (1992)] is obtained
Analytic expressions of amplitudes by the cross-ratio identity method
International Nuclear Information System (INIS)
Zhou, Kang
2017-01-01
In order to obtain the analytic expression of an amplitude from a generic CHY-integrand, a new algorithm based on the so-called cross-ratio identities has been proposed recently. In this paper, we apply this new approach to a variety of theories including the non-linear sigma model, special Galileon theory, pure Yang-Mills theory, pure gravity, Born-Infeld theory, Dirac-Born-Infeld theory and its extension, Yang-Mills-scalar theory, and Einstein-Maxwell and Einstein-Yang-Mills theory. CHY-integrands of these theories which contain higher-order poles can be calculated conveniently by using the cross-ratio identity method, and all results above have been verified numerically. (orig.)
Analytic expressions of amplitudes by the cross-ratio identity method
Energy Technology Data Exchange (ETDEWEB)
Zhou, Kang [Zhejiang University, Zhejiang Institute of Modern Physics, Hangzhou (China)
2017-06-15
In order to obtain the analytic expression of an amplitude from a generic CHY-integrand, a new algorithm based on the so-called cross-ratio identities has been proposed recently. In this paper, we apply this new approach to a variety of theories including the non-linear sigma model, special Galileon theory, pure Yang-Mills theory, pure gravity, Born-Infeld theory, Dirac-Born-Infeld theory and its extension, Yang-Mills-scalar theory, and Einstein-Maxwell and Einstein-Yang-Mills theory. CHY-integrands of these theories which contain higher-order poles can be calculated conveniently by using the cross-ratio identity method, and all results above have been verified numerically. (orig.)
Directory of Open Access Journals (Sweden)
P. Tolias
2017-12-01
Full Text Available The status of the literature is reviewed for several thermophysical properties of pure solid and liquid tungsten which constitute input for the modelling of intense plasma-surface interaction phenomena that are important for fusion applications. Reliable experimental data are analyzed for the latent heat of fusion, the electrical resistivity, the specific isobaric heat capacity, the thermal conductivity and the mass density from the room temperature up to the boiling point of tungsten as well as for the surface tension and the dynamic viscosity across the liquid state. Analytical expressions of high accuracy are recommended for these thermophysical properties that involved a minimum degree of extrapolations. In particular, extrapolations were only required for the surface tension and viscosity.
Gender Differences in Emotion Expression in Children: A Meta-Analytic Review
Chaplin, Tara M.; Aldao, Amelia
2012-01-01
Emotion expression is an important feature of healthy child development that has been found to show gender differences. However, there has been no empirical review of the literature on gender and facial, vocal, and behavioral expressions of different types of emotions in children. The present study constitutes a comprehensive meta-analytic review of gender differences, and moderators of differences, in emotion expression from infancy through adolescence. We analyzed 555 effect sizes from 166 studies with a total of 21,709 participants. Significant, but very small, gender differences were found overall, with girls showing more positive emotions (g = −.08) and internalizing emotions (e.g., sadness, anxiety, sympathy; g = −.10) than boys, and boys showing more externalizing emotions (e.g., anger; g = .09) than girls. Notably, gender differences were moderated by age, interpersonal context, and task valence, underscoring the importance of contextual factors in gender differences. Gender differences in positive emotions were more pronounced with increasing age, with girls showing more positive emotions than boys in middle childhood (g = −.20) and adolescence (g = −.28). Boys showed more externalizing emotions than girls at toddler/preschool age (g = .17) and middle childhood (g = .13) and fewer externalizing emotions than girls in adolescence (g = −.27). Gender differences were less pronounced with parents and were more pronounced with unfamiliar adults (for positive emotions) and with peers/when alone (for externalizing emotions). Our findings of gender differences in emotion expression in specific contexts have important implications for gender differences in children’s healthy and maladaptive development. PMID:23231534
Gender differences in emotion expression in children: a meta-analytic review.
Chaplin, Tara M; Aldao, Amelia
2013-07-01
Emotion expression is an important feature of healthy child development that has been found to show gender differences. However, there has been no empirical review of the literature on gender and facial, vocal, and behavioral expressions of different types of emotions in children. The present study constitutes a comprehensive meta-analytic review of gender differences and moderators of differences in emotion expression from infancy through adolescence. We analyzed 555 effect sizes from 166 studies with a total of 21,709 participants. Significant but very small gender differences were found overall, with girls showing more positive emotions (g = -.08) and internalizing emotions (e.g., sadness, anxiety, sympathy; g = -.10) than boys, and boys showing more externalizing emotions (e.g., anger; g = .09) than girls. Notably, gender differences were moderated by age, interpersonal context, and task valence, underscoring the importance of contextual factors in gender differences. Gender differences in positive emotions were more pronounced with increasing age, with girls showing more positive emotions than boys in middle childhood (g = -.20) and adolescence (g = -.28). Boys showed more externalizing emotions than girls at toddler/preschool age (g = .17) and middle childhood (g = .13) and fewer externalizing emotions than girls in adolescence (g = -.27). Gender differences were less pronounced with parents and were more pronounced with unfamiliar adults (for positive emotions) and with peers/when alone (for externalizing emotions). Our findings of gender differences in emotion expression in specific contexts have important implications for gender differences in children's healthy and maladaptive development. 2013 APA, all rights reserved
Directory of Open Access Journals (Sweden)
Kronenwett Ralf
2012-10-01
Full Text Available Abstract Background EndoPredict (EP is a clinically validated multianalyte gene expression test to predict distant metastasis in ER-positive, HER2-negative breast cancer treated with endocrine therapy alone. The test is based on the combined analysis of 12 genes in formalin-fixed, paraffin-embedded (FFPE tissue by reverse transcription-quantitative real-time PCR (RT-qPCR. Recently, it was shown that EP is feasible for reliable decentralized assessment of gene expression. The aim of this study was the analytical validation of the performance characteristics of the assay and its verification in a molecular-pathological routine laboratory. Methods Gene expression values to calculate the EP score were assayed by one-step RT-qPCR using RNA from FFPE tumor tissue. Limit of blank, limit of detection, linear range, and PCR efficiency were assessed for each of the 12 PCR assays using serial samples dilutions. Different breast cancer samples were used to evaluate RNA input range, precision and inter-laboratory variability. Results PCR assays were linear up to Cq values between 35.1 and 37.2. Amplification efficiencies ranged from 75% to 101%. The RNA input range without considerable change of the EP score was between 0.16 and 18.5 ng/μl. Analysis of precision (variation of day, day time, instrument, operator, reagent lots resulted in a total noise (standard deviation of 0.16 EP score units on a scale from 0 to 15. The major part of the total noise (SD 0.14 was caused by the replicate-to-replicate noise of the PCR assays (repeatability and was not associated with different operating conditions (reproducibility. Performance characteristics established in the manufacturer’s laboratory were verified in a routine molecular pathology laboratory. Comparison of 10 tumor samples analyzed in two different laboratories showed a Pearson coefficient of 0.995 and a mean deviation of 0.15 score units. Conclusions The EP test showed reproducible performance
International Nuclear Information System (INIS)
Kronenwett, Ralf; Brase, Jan C; Weber, Karsten E; Fisch, Karin; Müller, Berit M; Schmidt, Marcus; Filipits, Martin; Dubsky, Peter; Petry, Christoph; Dietel, Manfred; Denkert, Carsten; Bohmann, Kerstin; Prinzler, Judith; Sinn, Bruno V; Haufe, Franziska; Roth, Claudia; Averdick, Manuela; Ropers, Tanja; Windbergs, Claudia
2012-01-01
EndoPredict (EP) is a clinically validated multianalyte gene expression test to predict distant metastasis in ER-positive, HER2-negative breast cancer treated with endocrine therapy alone. The test is based on the combined analysis of 12 genes in formalin-fixed, paraffin-embedded (FFPE) tissue by reverse transcription-quantitative real-time PCR (RT-qPCR). Recently, it was shown that EP is feasible for reliable decentralized assessment of gene expression. The aim of this study was the analytical validation of the performance characteristics of the assay and its verification in a molecular-pathological routine laboratory. Gene expression values to calculate the EP score were assayed by one-step RT-qPCR using RNA from FFPE tumor tissue. Limit of blank, limit of detection, linear range, and PCR efficiency were assessed for each of the 12 PCR assays using serial samples dilutions. Different breast cancer samples were used to evaluate RNA input range, precision and inter-laboratory variability. PCR assays were linear up to C q values between 35.1 and 37.2. Amplification efficiencies ranged from 75% to 101%. The RNA input range without considerable change of the EP score was between 0.16 and 18.5 ng/μl. Analysis of precision (variation of day, day time, instrument, operator, reagent lots) resulted in a total noise (standard deviation) of 0.16 EP score units on a scale from 0 to 15. The major part of the total noise (SD 0.14) was caused by the replicate-to-replicate noise of the PCR assays (repeatability) and was not associated with different operating conditions (reproducibility). Performance characteristics established in the manufacturer’s laboratory were verified in a routine molecular pathology laboratory. Comparison of 10 tumor samples analyzed in two different laboratories showed a Pearson coefficient of 0.995 and a mean deviation of 0.15 score units. The EP test showed reproducible performance characteristics with good precision and negligible laboratory
Analytic expression for any pure rotational transition (ΔJ≥1) for a diatomic molecule
International Nuclear Information System (INIS)
Korek, M.; Hamdoun, B.; Fakhreddine, K.
1999-01-01
Full text.The problem of the pure rotational transitions vJ↔vJ' for any spectra |J-J'|≥1 for a diatomic molecule is considered. It is proved that, the wave functions ΨvJ and ΨvJ' are expanded in terms of the running number m=[J'(J'+1)-J(J+1)]/2 as ΨvJ=Σπ n m n (n=0) and ΨvJ'=Σπ n (-m) n (n=0) where π n are expressed in terms of the pure vibrational wave function φ 0 and its rotational corrections φ n (defined in the conventional perturbation theory). By using this m-representation of the wave functions the pure rotational matrix elements of the considered transitions are given by M vJ vJ' = =Σμ 2n m 2n (n=0) where μ 2n are simple combinations of simple integrals of the form i |γ|φ n >. This formulation is valid for any potential (either numerical or analytical), any vibrational level v and any operator γ. The numerical application to the Dunham potential of the molecule H 2 in the Raman transitions and to the Huffaker potential of the molecule CO in the infrared transitions shows the validity and the high accuracy of the present formulation
Energy Technology Data Exchange (ETDEWEB)
Kumar, Mukesh, E-mail: mukeshk@rrcat.gov.in [Beam Diagnostics Section, Indus Operations, Beam Dynamics & Diagnostics Division, Raja Ramanna Centre for Advanced Technology, Indore, 452013 MP (India); Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400 094 (India); Ojha, A.; Garg, A.D.; Puntambekar, T.A. [Beam Diagnostics Section, Indus Operations, Beam Dynamics & Diagnostics Division, Raja Ramanna Centre for Advanced Technology, Indore, 452013 MP (India); Senecha, V.K. [Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400 094 (India); Ion Source Lab., Proton Linac & Superconducting Cavities Division, Raja Ramanna Centre for Advanced Technology, Indore, 452013 MP (India)
2017-02-01
According to the quasi electrostatic model of linear response capacitive beam position monitor (BPM), the position sensitivity of the device depends only on the aperture of the device and it is independent of processing frequency and load impedance. In practice, however, due to the inter-electrode capacitive coupling (cross talk), the actual position sensitivity of the device decreases with increasing frequency and load impedance. We have taken into account the inter-electrode capacitance to derive and propose a new analytical expression for the position sensitivity as a function of frequency and load impedance. The sensitivity of a linear response shoe-box type BPM has been obtained through simulation using CST Studio Suite to verify and confirm the validity of the new analytical equation. Good agreement between the simulation results and the new analytical expression suggest that this method can be exploited for proper designing of BPM.
Directory of Open Access Journals (Sweden)
S. Ayadi
2015-07-01
Full Text Available The simplest model of the laser is that of a single mode system homogenously broadened. The dynamical behavior of this laser is described by three differential equations, called Haken-Lorenz equations[1], similar to the Lorenz model [1] already known to predict deterministic chaos. In previous recent work [5-7] we have proposed a simple harmonic expansion method to obtain a series of harmonics terms that yield analytical solutions to the laser equations. ¶This method allows us to derive an analytical expression of the laser field amplitude when this last undergoes a periodic oscillations around zero mean value. We also obtain an analytical expression of the pulsing frequency.
Danielsen, Per Lander
1981-01-01
A general and efficient model for optical fibers with a few modes and arbitrary index profiles is established. The model yields a solution of the vectorial wave equation and analytical expressions for the group delay and the far field. Convergence tests have shown that the dispersion can be calculated with an accuracy better than 0.2 ps/(km . nm).
DEFF Research Database (Denmark)
Danielsen, Per Lander
1981-01-01
A general and efficient model for optical fibers with a few modes and arbitrary index profiles is established. The model yields a solution of the vectorial wave equation and analytical expressions for the group delay and the far field. Convergence tests have shown that the dispersion can...
DEFF Research Database (Denmark)
Liu, Qing Zhong
1992-01-01
Unified analytical expressions have been derived for calculating the resonant frequencies, transimpedance and equivalent input noise current densities of the four most widely used tuned optical receiver front ends built with FETs and p-i-n diodes. A more accurate FET model has been used to improve...
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.
Exact capacity analysis of multihop transmission over amplify-and-forward relay fading channels
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
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.
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.
Exact performance analysis of decode-and-forward opportunistic relaying
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.
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
Expressing analytical performance from multi-sample evaluation in laboratory EQA.
Thelen, Marc H M; Jansen, Rob T P; Weykamp, Cas W; Steigstra, Herman; Meijer, Ron; Cobbaert, Christa M
2017-08-28
To provide its participants with an external quality assessment system (EQAS) that can be used to check trueness, the Dutch EQAS organizer, Organization for Quality Assessment of Laboratory Diagnostics (SKML), has innovated its general chemistry scheme over the last decade by introducing fresh frozen commutable samples whose values were assigned by Joint Committee for Traceability in Laboratory Medicine (JCTLM)-listed reference laboratories using reference methods where possible. Here we present some important innovations in our feedback reports that allow participants to judge whether their trueness and imprecision meet predefined analytical performance specifications. Sigma metrics are used to calculate performance indicators named 'sigma values'. Tolerance intervals are based on both Total Error allowable (TEa) according to biological variation data and state of the art (SA) in line with the European Federation of Clinical Chemistry and Laboratory Medicine (EFLM) Milan consensus. The existing SKML feedback reports that express trueness as the agreement between the regression line through the results of the last 12 months and the values obtained from reference laboratories and calculate imprecision from the residuals of the regression line are now enriched with sigma values calculated from the degree to which the combination of trueness and imprecision are within tolerance limits. The information and its conclusion to a simple two-point scoring system are also graphically represented in addition to the existing difference plot. By adding sigma metrics-based performance evaluation in relation to both TEa and SA tolerance intervals to its EQAS schemes, SKML provides its participants with a powerful and actionable check on accuracy.
Analytic Expressions for the Inner-rim Structure of Passively Heated Protoplanetary Disks
Energy Technology Data Exchange (ETDEWEB)
Ueda, Takahiro; Okuzumi, Satoshi [Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Meguro, Tokyo, 152-8551 (Japan); Flock, Mario, E-mail: t_ueda@geo.titech.ac.jp [Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 (United States)
2017-07-01
We analytically derive the expressions for the structure of the inner region of protoplanetary disks based on the results from the recent hydrodynamical simulations. The inner part of a disk can be divided into four regions: a dust-free region with a gas temperature in the optically thin limit, an optically thin dust halo, an optically thick condensation front, and the classical, optically thick region, in order from the innermost to the outermost. We derive the dust-to-gas mass ratio profile in the dust halo using the fact that partial dust condensation regulates the temperature relative to the dust evaporation temperature. Beyond the dust halo, there is an optically thick condensation front where all the available silicate gas condenses out. The curvature of the condensation surface is determined by the condition that the surface temperature must be nearly equal to the characteristic temperature ∼1200 K. We derive the midplane temperature in the outer two regions using the two-layer approximation, with the additional heating by the condensation front for the outermost region. As a result, the overall temperature profile is step-like, with steep gradients at the borders between the outer three regions. The borders might act as planet traps where the inward migration of planets due to gravitational interaction with the gas disk stops. The temperature at the border between the two outermost regions coincides with the temperature needed to activate magnetorotational instability, suggesting that the inner edge of the dead zone must lie at this border. The radius of the dead zone inner edge predicted from our solution is ∼2–3 times larger than that expected from the classical optically thick temperature.
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
Exact outage analysis of incremental decode-and-forward opportunistic relaying
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
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 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 solutions to nonlinear symmetron theory: One- and two-mirror systems
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.
Maghrabi, Mufeed; Al-Abdullah, Tariq; Khattari, Ziad
2018-03-24
The two heating rates method (originally developed for first-order glow peaks) was used for the first time to evaluate the activation energy (E) from glow peaks obeying mixed-order (MO) kinetics. The derived expression for E has an insignificant additional term (on the scale of a few meV) when compared with the first-order case. Hence, the original expression for E using the two heating rates method can be used with excellent accuracy in the case of MO glow peaks. In addition, we derived a simple analytical expression for the MO parameter. The present procedure has the advantage that the MO parameter can now be evaluated using analytical expression instead of using the graphical representation between the geometrical factor and the MO parameter as given by the existing peak shape methods. The applicability of the derived expressions for real samples was demonstrated for the glow curve of Li 2 B 4 O 7 :Mn single crystal. The obtained parameters compare very well with those obtained by glow curve fitting and with the available published data.
Ansari, Imran Shafique
2012-07-31
Error performance is one of the main performance measures and the derivation of its closed-form expression has proved to be quite involved for certain systems. In this paper, a unified closed-form expression, applicable to different binary modulation schemes, for the bit error rate of dual-branch selection diversity based systems undergoing independent but not necessarily identically distributed generalized-K fading is derived in terms of the extended generalized bivariate Meijer G-function.
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)
BAC-Dkk3-EGFP Transgenic Mouse: An In Vivo Analytical Tool for Dkk3 Expression
Directory of Open Access Journals (Sweden)
Yuki Muranishi
2012-01-01
Full Text Available Dickkopf (DKK family proteins are secreted modulators of the Wnt signaling pathway and are capable of regulating the development of many organs and tissues. We previously identified Dkk3 to be a molecule predominantly expressed in the mouse embryonic retina. However, which cell expresses Dkk3 in the developing and mature mouse retina remains to be elucidated. To examine the precise expression of the Dkk3 protein, we generated BAC-Dkk3-EGFP transgenic mice that express EGFP integrated into the Dkk3 gene in a BAC plasmid. Expression analysis using the BAC-Dkk3-EGFP transgenic mice revealed that Dkk3 is expressed in retinal progenitor cells (RPCs at embryonic stages and in Müller glial cells in the adult retina. Since Müller glial cells may play a potential role in retinal regeneration, BAC-Dkk3-EGFP mice could be useful for retinal regeneration studies.
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 axially symmetric galactic dynamos
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.
Spectral emissivity of tungsten: analytic expressions for the 340-nm to 2.6-μm spectral region
International Nuclear Information System (INIS)
Pon, R.M.; Hessler, J.P.
1984-01-01
To correct emission spectra a standard radiance source is often used to determine the spectral responsivity of the detection system. In the near-UV, visible, and near-IR spectral regions the most common radiance standard is a tungsten strip lamp calibrated by a standards laboratory. For day-to-day experiments where slightly less accuracy is acceptable, a less expensive uncalibrated lamp is useful. In this case, the radiant temperature T/sub r/ of the lamp is measured with an optical pyrometer, generally at a single wavelength such as 650 nm, and the source spectral radiance L(λ) is calculated from L(λ) = tau(λ)epsilon(λ,T)L/sub B/(λ,T). The transmittance of the source is tau(λ), the spectral emissivity is epsilon(λ,T), and L/sub B/(λ,T) is the spectral distribution of blackbody radiation, Planck's radiation law. To obtain the true temperature T, Wien's approximation is employed. To conveniently calibrate a system, especially one which utilizes a microcomputer, it is advantageous to have analytic expressions for the spectral emissivity of tungsten. Although Larrabee has published such expressions, they are limited to the 450-800-nm spectral region. To obtain analytic expressions from 340 nm to 2.6 μm they have used the measurements of DeVos. Although DeVos's results differ by 2% from those of Larrabee, this difference is assumed to be acceptable
Analytical solution for the convectively-mixed atmospheric boundary layer
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
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.
An analytical expression of electric potential and field of organic thin film transistors
International Nuclear Information System (INIS)
Pankalla, S; Glesner, M
2012-01-01
The two-dimensional electric potential and field of an organic thin-film transistor (OTFT) is derived by conformal mapping using the Schwarz-Christoffel-transformation of the Poisson equation. In this paper we compare this analytical closed-form solution to field simulation results from Silvaco TCAD. Inter alia the potential close to the surface is calculated and we found excellent accordance to the numerical simulations and thus proofed its usability for charge transport calculations. Thus, it is used for calculation of the drain-source-current in the channel.
International Nuclear Information System (INIS)
Raju Viswanathan, R.
1991-09-01
We study examples of one dimensional matrix models whose potentials possess an energy spectrum that can be explicitly determined. This allows for an exact solution in the continuum limit. Specifically, step-like potentials and the Morse potential are considered. The step-like potentials show no scaling behaviour and the Morse potential (which corresponds to a γ = -1 model) has the interesting feature that there are no quantum corrections to the scaling behaviour in the continuum limit. (author). 5 refs
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Exact approaches for scaffolding
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...
DR-Integrator: a new analytic tool for integrating DNA copy number and gene expression data.
Salari, Keyan; Tibshirani, Robert; Pollack, Jonathan R
2010-02-01
DNA copy number alterations (CNA) frequently underlie gene expression changes by increasing or decreasing gene dosage. However, only a subset of genes with altered dosage exhibit concordant changes in gene expression. This subset is likely to be enriched for oncogenes and tumor suppressor genes, and can be identified by integrating these two layers of genome-scale data. We introduce DNA/RNA-Integrator (DR-Integrator), a statistical software tool to perform integrative analyses on paired DNA copy number and gene expression data. DR-Integrator identifies genes with significant correlations between DNA copy number and gene expression, and implements a supervised analysis that captures genes with significant alterations in both DNA copy number and gene expression between two sample classes. DR-Integrator is freely available for non-commercial use from the Pollack Lab at http://pollacklab.stanford.edu/ and can be downloaded as a plug-in application to Microsoft Excel and as a package for the R statistical computing environment. The R package is available under the name 'DRI' at http://cran.r-project.org/. An example analysis using DR-Integrator is included as supplemental material. Supplementary data are available at Bioinformatics online.
How effective are expressive writing interventions for adolescents? A meta-analytic review.
Travagin, Gabriele; Margola, Davide; Revenson, Tracey A
2015-03-01
This meta-analysis evaluated the effects of the expressive writing intervention (EW; Pennebaker & Beall, 1986) among adolescents. Twenty-one independent studies that assessed the efficacy of expressive writing on youth samples aged 10-18 ears were collected and analyzed. Results indicated an overall mean g-effect size that was positive in direction but relatively small (0.127), as well as significant g-effect sizes ranging from 0.107 to 0.246 for the outcome domains of Emotional Distress, Problem Behavior, Social Adjustment, and School Participation. Few significant effects were found within specific outcome domains for putative moderator variables that included characteristics of the participants, intervention instructions, or research design. Studies involving adolescents with high levels of emotional problems at baseline reported larger effects on school performance. Studies that implemented a higher dosage intervention (i.e., greater number and, to some extent, greater spacing of sessions) reported larger effects on somatic complaints. Overall, the findings suggest that expressive writing tends to produce small yet significant improvements on adolescents' well-being. The findings highlight the importance of modifying the traditional expressive writing protocol to enhance its efficacy and reduce potential detrimental effects. At this stage of research the evidence on expressive writing as a viable intervention for adolescents is promising but not decisive. Copyright © 2015 Elsevier Ltd. All rights reserved.
Non-Fermi-liquid behavior: Exact results for ensembles of magnetic impurities
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...
International Nuclear Information System (INIS)
Shan, C.; Javandel, I.
1996-05-01
Analytical solutions are developed for modeling solute transport in a vertical section of a homogeneous aquifer. Part 1 of the series presents a simplified analytical solution for cases in which a constant-concentration source is located at the top (or the bottom) of the aquifer. The following transport mechanisms have been considered: advection (in the horizontal direction), transverse dispersion (in the vertical direction), adsorption, and biodegradation. In the simplified solution, however, longitudinal dispersion is assumed to be relatively insignificant with respect to advection, and has been neglected. Example calculations are given to show the movement of the contamination front, the development of concentration profiles, the mass transfer rate, and an application to determine the vertical dispersivity. The analytical solution developed in this study can be a useful tool in designing an appropriate monitoring system and an effective groundwater remediation method
Analytical expressions for radiatively corrected Higgs masses and couplings in the MSSM
International Nuclear Information System (INIS)
Carena, M.
1995-03-01
We propose, for the computation of the Higgs mass spectrum and couplings, a renormalization-group improved leading-log approximation, where the renormalization scale is fixed to the top-quark pole mass. For the case m A ∝M SUSY , our leading-log approximation differs by less than 2 GeV from previous results on the Higgs mass computed using a nearly scale independent renormalization-group improved effective potential up to next-to-leading order. Moreover, for the general case m A SUSY , we provide analytical formulae (including two-loop leading-log corrections) for all the masses and couplings in the Higgs sector. For M SUSY A , tan β and the stop mixing parameters, they reproduce the numerical renormalization-group improved leading-log result for the Higgs masses with an error of less than 3 GeV. For the Higgs couplings, our analytical formulae reproduce the numerical results equally well. Comparison with other methods is also performed. (orig.)
The areal reduction factor: A new analytical expression for the Lazio Region in central Italy
Mineo, C.; Ridolfi, E.; Napolitano, F.; Russo, F.
2018-05-01
For the study and modeling of hydrological phenomena, both in urban and rural areas, a proper estimation of the areal reduction factor (ARF) is crucial. In this paper, we estimated the ARF from observed rainfall data as the ratio between the average rainfall occurring in a specific area and the point rainfall. Then, we compared the obtained ARF values with some of the most widespread empirical approaches in literature which are used when rainfall observations are not available. Results highlight that the literature formulations can lead to a substantial over- or underestimation of the ARF estimated from observed data. These findings can have severe consequences, especially in the design of hydraulic structures where empirical formulations are extensively applied. The aim of this paper is to present a new analytical relationship with an explicit dependence on the rainfall duration and area that can better represent the ARF-area trend over the area case of study. The analytical curve presented here can find an important application to estimate the ARF values for design purposes. The test study area is the Lazio Region (central Italy).
International Nuclear Information System (INIS)
Marie, Stephane
2004-01-01
This article proposes an extension of the known analytical solution for the temperature and stresses in the event of a linear shock in a pipe containing a fluid. The intention is to propose a simple solution for any variation of the temperature in the fluid and to cover the influence of cladding on the inner surface. The approach consists of breaking down the fluid temperature variation into a succession of linear shocks. Using the linear shock resolution approach, it is possible to propose a simple analytical solution, using the same constant (Biot number B, etc.). The proposed solution is compared with finite element analysis: the solution is found to be reliable for any thermal shock or cyclic variation of fluid temperature, and can even replicate the transient regime. The following stage has made it possible to account for the effect of cladding on the inner surface of the piping on temperature distribution. The second part gives analytical expressions for the elastic stresses due to the temperature field alone
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
Some exact solutions for maximally symmetric topological defects in Anti de Sitter space
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.
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
Energy Technology Data Exchange (ETDEWEB)
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
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 analytic expression for the sheath criterion in magnetized plasmas with multi-charged ion species
International Nuclear Information System (INIS)
Hatami, M. M.
2015-01-01
The generalized Bohm criterion in magnetized multi-component plasmas consisting of multi-charged positive and negative ion species and electrons is analytically investigated by using the hydrodynamic model. It is assumed that the electrons and negative ion density distributions are the Boltzmann distribution with different temperatures and the positive ions enter into the sheath region obliquely. Our results show that the positive and negative ion temperatures, the orientation of the applied magnetic field and the charge number of positive and negative ions strongly affect the Bohm criterion in these multi-component plasmas. To determine the validity of our derived generalized Bohm criterion, it reduced to some familiar physical condition and it is shown that monotonically reduction of the positive ion density distribution leading to the sheath formation occurs only when entrance velocity of ion into the sheath satisfies the obtained Bohm criterion. Also, as a practical application of the obtained Bohm criterion, effects of the ionic temperature and concentration as well as magnetic field on the behavior of the charged particle density distributions and so the sheath thickness of a magnetized plasma consisting of electrons and singly charged positive and negative ion species are studied numerically
Analytical expressions for chatter analysis in milling operations with one dominant mode
Iglesias, A.; Munoa, J.; Ciurana, J.; Dombovari, Z.; Stepan, G.
2016-08-01
In milling, an accurate prediction of chatter is still one of the most complex problems in the field. The presence of these self-excited vibrations can spoil the surface of the part and can also cause a large reduction in tool life. The stability diagrams provide a practical selection of the optimum cutting conditions determined either by time domain or frequency domain based methods. Applying these methods parametric or parameter traced representations of the linear stability limits can be achieved by solving the corresponding eigenvalue problems. In this work, new analytical formulae are proposed related to the parameter domains of both Hopf and period doubling type stability boundaries emerging in the regenerative mechanical model of time periodical milling processes. These formulae are useful to enrich and speed up the currently used numerical methods. Also, the destabilization mechanism of double period chatter is explained, creating an analogy with the chatter related to the Hopf bifurcation, considering one dominant mode and using concepts established by the Pioneers of chatter research.
Deprit, A.
1975-01-01
A theory for generating segmented ephemerides is discussed as a means for fast generation and simple retrieval of nominal orbit data. Over a succession of finite intervals of time, the orbit is represented by a best approximation expressed by Chebyshev polynomials. Storage of coefficients tables for Chebyshev polynomials is seen as a method to reduce data and decrease transmission costs. A general algorithm was constructed and computer programs were designed. The possibility of storing an ephemeris for a few days in the on-board computer, or in microprocessors attached to the data collectors is suggested.
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
Exact solution of the hidden Markov processes
Saakian, David B.
2017-11-01
We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .
Jingree, Treena; Finlay, W M L
2013-06-01
This paper uses critical discursive psychology to examine expressions of dissatisfaction and complaint by people with learning disabilities. UK government policies stress that people with learning disabilities should have more control over their lives. Expressing dissatisfaction about services is an important aspect of this process. However, given that such individuals are often treated as incompetent, and given the delicate nature of complaining about services one might rely on for day-to-day support, this can be difficult to do. In building complaints, speakers drew on repertoires about competence and incompetence, the right to free choice as a principle, and tempered dissatisfaction to make contrasts between good and bad supporters and practice. While the complaints show many of the general features of complaints identified in previous work in the general population, they were crafted to the particular institutional context of social care, and attended both explicitly and implicitly to the particular issues of competence, power, and authority found in those services. Speakers positioned themselves as competent, and service workers as more or less competent in their roles. Issues of power in social care services were observed explicitly in the accounts, whereby people described staff as controlling and it being difficult to voice dissatisfaction. They were also implicit in the way speakers drew on the others with institutional authority for corroboration and comparison. © 2011 The British Psychological Society.
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.
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.
Analytical Expressions for the Hard-Scattering Production of Massive Partons
Energy Technology Data Exchange (ETDEWEB)
Wong, Cheuk-Yin [ORNL
2016-01-01
We obtain explicit expressions for the two-particle differential cross section $E_c E_\\kappa d\\sigma (AB \\to c\\kappa X) /d\\bb c d \\bb \\kappa$ and the two-particle angular correlation function \\break $d\\sigma(AB$$ \\to$$ c\\kappa X)/d\\Delta \\phi \\, d\\Delta y$ in the hard-scattering production of massive partons in order to exhibit the ``ridge" structure on the away side in the hard-scattering process. The single-particle production cross section $d\\sigma(AB \\to cX) /dy_c c_T dc_T $ is also obtained and compared with the ALICE experimental data for charm production in $pp$ collisions at 7 TeV at LHC.
Exactly solvable position dependent mass schroedinger equation
International Nuclear Information System (INIS)
Koc, R.; Tuetuencueler, H.; Koercuek, E.
2002-01-01
Exact solution of the Schrodinger equation with a variable mass is presented. We have derived general expressions for the eigenstates and eigenvalues of the position dependent mass systems. We provide supersymmetric and Lie algebraic methods to discuss the position dependent mass systems
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.
International Nuclear Information System (INIS)
Xie Chuan-Mei; Xing Hang; Zhang Zhan-Jun; Liu Yi-Min
2015-01-01
Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105 (2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed. (paper)
Analytical Expressions of the Efficiency of Standard and High Contact Ratio Involute Spur Gears
Directory of Open Access Journals (Sweden)
Miguel Pleguezuelos
2013-01-01
Full Text Available Simple, traditional methods for computation of the efficiency of spur gears are based on the hypotheses of constant friction coefficient and uniform load sharing along the path of contact. However, none of them is accurate. The friction coefficient is variable along the path of contact, though average values can be often considered for preliminary calculations. Nevertheless, the nonuniform load sharing produced by the changing rigidity of the pair of teeth has significant influence on the friction losses, due to the different relative sliding at any contact point. In previous works, the authors obtained a nonuniform model of load distribution based on the minimum elastic potential criterion, which was applied to compute the efficiency of standard gears. In this work, this model of load sharing is applied to study the efficiency of both standard and high contact ratio involute spur gears (with contact ratio between 1 and 2 and greater than 2, resp.. Approximate expressions for the friction power losses and for the efficiency are presented assuming the friction coefficient to be constant along the path of contact. A study of the influence of some transmission parameters (as the gear ratio, pressure angle, etc. on the efficiency is also presented.
Exactly solvable birth and death processes
International Nuclear Information System (INIS)
Sasaki, Ryu
2009-01-01
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q x (with x being the population) corresponding to the q-Racah polynomial.
Carah, Nicholas; Meurk, Carla; Angus, Daniel
2017-03-01
Hello Sunday Morning is an online health promotion organisation that began in 2009. Hello Sunday Morning asks participants to stop consuming alcohol for a period of time, set a goal and document their progress on a personal blog. Hello Sunday Morning is a unique health intervention for three interrelated reasons: (1) it was generated outside a clinical setting, (2) it uses new media technologies to create structured forms of participation in an iterative and open-ended way and (3) participants generate a written record of their progress along with demographic, behavioural and engagement data. This article presents a text analysis of the blog posts of Hello Sunday Morning participants using the software program Leximancer. Analysis of blogs illustrates how participants' expressions change over time. In the first month, participants tended to set goals, describe their current drinking practices in individual and cultural terms, express hopes and anxieties and report on early efforts to change. After month 1, participants continued to report on efforts to change and associated challenges and reflect on their place as individuals in a drinking culture. In addition to this, participants evaluated their efforts to change and presented their 'findings' and 'theorised' them to provide advice for others. We contextualise this text analysis with respect to Hello Sunday Morning's development of more structured forms of online participation. We offer a critical appraisal of the value of text analytics in the development of online health interventions.
Directory of Open Access Journals (Sweden)
K. Indira
2012-01-01
Full Text Available Theoretical analysis corresponding to the diffusion and kinetics of substrate and product in an amperometric biosensor is developed and reported in this paper. The nonlinear coupled system of diffusion equations was analytically solved by Homotopy perturbation method. Herein, we report the approximate analytical expressions pertaining to substrate concentration, product concentration, and current response for all possible values of diffusion and kinetic parameters. The numerical solution of this problem is also reported using Scilab/Matlab program. Also, we found excellent agreement between the analytical results and numerical results upon comparison.
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.)
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.
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.
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
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.
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)
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.
Energy Technology Data Exchange (ETDEWEB)
Kiefer, René; Schad, Ariane; Roth, Markus [Kiepenheuer-Institut für Sonnenphysik, Schöneckstraße 6, D-79104 Freiburg (Germany)
2017-09-10
Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global oscillations. The properties of solar and stellar acoustic modes are changing with the level of magnetic activity. However, until now, the inference on subsurface magnetic fields with seismic measures has been very limited. The aim of this paper is to develop a formalism to calculate the effect of large-scale toroidal magnetic fields on solar and stellar global oscillation eigenfunctions and eigenfrequencies. If the Lorentz force is added to the equilibrium equation of motion, stellar eigenmodes can couple. In quasi-degenerate perturbation theory, this coupling, also known as the direct effect, can be quantified by the general matrix element. We present the analytical expression of the matrix element for a superposition of subsurface zonal toroidal magnetic field configurations. The matrix element is important for forward calculations of perturbed solar and stellar eigenfunctions and frequency perturbations. The results presented here will help to ascertain solar and stellar large-scale subsurface magnetic fields, and their geometric configuration, strength, and change over the course of activity cycles.
Linear orbit parameters for the exact equations of motion
International Nuclear Information System (INIS)
Parzen, G.
1995-01-01
This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The β, α and ψ functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittance. The differential equations for η = x/β 1/2 is found. New relationships between α, β, ψ and ν are derived
Exact soliton-like solutions of perturbed phi4-equation
International Nuclear Information System (INIS)
Gonzalez, J.A.
1986-05-01
Exact soliton-like solutions of damped, driven phi 4 -equation are found. The exact expressions for the velocities of solitons are given. It is non-perturbatively proved that the perturbed phi 4 -equation has stable kink-like solutions of a new type. (author)
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.
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.
Exact piecewise flat gravitational waves
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
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.
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.
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.
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.
Exact solution for four-order acousto-optic Bragg diffraction with arbitrary initial conditions.
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.
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
Exact Outage Probability of Dual-Hop CSI-Assisted AF Relaying Over Nakagami-m Fading Channels
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.
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 scattering and diffraction of antiplane shear waves by a vertical edge crack
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.
Exact solutions to chaotic and stochastic systems
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.
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.
Exactly marginal deformations from exceptional generalised geometry
Energy Technology Data Exchange (ETDEWEB)
Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford,Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Gabella, Maxime [Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Graña, Mariana [Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHE,75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)
2017-01-27
We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS{sub 5} flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS{sub 5} flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.
Exact 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.)
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.)
Model checking exact cost for attack scenarios
DEFF Research Database (Denmark)
Aslanyan, Zaruhi; Nielson, Flemming
2017-01-01
Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support....... However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....
DEFF Research Database (Denmark)
Rios, P.R.; Godiksen, R.B.; Schmidt, Søren
2006-01-01
This paper shows that interfacial area density between transformed grains during nucleation and growth transformations and the contiguity are useful descriptors of microstructural evolution. These descriptors are evaluated analytically and compared with results from computer simulation. Usage...
Exact solution for the Poisson field in a semi-infinite strip.
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 Solution of a Strongly Coupled Gauge Theory in 0 +1 Dimensions
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].
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
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
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 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.)
Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
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.
Exact analysis of discrete data
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...
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 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
Some exact velocity profiles for granular flow in converging hoppers
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.
The exact mass-gaps of the principal chiral models
Hollowood, Timothy J
1994-01-01
An exact expression for the mass-gap, the ratio of the physical particle mass to the $\\Lambda$-parameter, is found for the principal chiral sigma models associated to all the classical Lie algebras. The calculation is based on a comparison of the free-energy in the presence of a source coupling to a conserved charge of the theory computed in two ways: via the thermodynamic Bethe Ansatz from the exact scattering matrix and directly in perturbation theory. The calculation provides a non-trivial test of the form of the exact scattering matrix.
Exact ground-state correlation functions of an atomic-molecular Bose–Einstein condensate model
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.
On truncations of the exact renormalization group
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.
Efficient analytical expressions for dynamic structure of liquid binary alloys: K–Cs as a case study
International Nuclear Information System (INIS)
Wax, Jean-François; Bryk, Taras; Johnson, Mark R
2016-01-01
A fitting scheme for analysis of collective dynamics in liquid binary alloys is proposed. It is based on explicit treatment of contributions from three relaxing modes and two types of propagating modes to the partial density–density time correlation functions and corresponding partial dynamic structure factors. Exact sum rules for each partial dynamic structure factor were taken into account. The proposed fitting scheme was applied to the liquid equimolar K–Cs alloy. Analysis of simulation-derived partial time correlation functions as well as of their corresponding Bhatia–Thornton ‘number-concentration’ combinations allowed dispersion and damping of the two branches of collective excitations and the behaviour of relaxing modes in a wide range of wave numbers to be obtained. A comparison with the inelastic neutron-scattering intensities for the liquid K–Cs alloy was performed. (paper)
Directory of Open Access Journals (Sweden)
Y. A. Dyachenko
2016-01-01
Full Text Available During the last decades becoming more sharply there is a problem of chemical and environmental monitoring and industrial inspection the content of toxic elements in food raw materials and foodstuff. At the same time there is a need to develop rapid methods, informative, integral, reflecting not only the safety but also the ecological purity of food raw materials. The method of determination of content of toxic elements on activity of its own lipase of in situ (AОL-method in seeds of oil-bearing crops, on the example of sunflower is offered. The system of mathematical assessment of analytical criteria of laboratory test used in clinical laboratory diagnostics was for this purpose adapted. Sunflower seeds in which established the maintenance of toxiferous elements served as an object of a research: Cd, Pb, As, Hg, by atomic absorption method on the KVANT-Z.ETA device. Further tests divided on clear, including high-quality and pollution-free, and polluted - naturally containing toxiferous elements and which are artificially contaminated. Definition of activity of a lipase of seeds was carried out by the standard titrimetric method. Decrease of the activity of enzyme was connected with the maintenance of toxiferous elements. Proceeding from the received results counted an analytical significance (sensitivity, specificity, and predictive value of descriptiveness the positive and negative results of determination of level of maintenance of toxiferous elements in sunflower seeds by the AОL-method. The set values of analytical specificity of a method and predictive value of a positive take at the level of 77.3% and 71.4% respectively, do not allow to use the offered method for the quantitative analysis, however, analytical sensitivity at the level of 86.2% and the predictive value of the negative result at the level of 89.5%, allow to recommend the AOL-method for screening programs of chemical environmental monitoring and technological monitoring of a
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
International Nuclear Information System (INIS)
Dimitrijević, J; Arsenović, D
2012-01-01
We study a double-Λ atomic scheme that interacts with four laser light beams so that a closed loop of radiation-induced transitions is formed. When specific relations for field phases, frequencies and amplitudes are satisfied, coherent superpositions (the so-called ‘dark states’) can be formed in a double-Λ, which leads to the well-known effect of electromagnetically induced transparency (EIT). If the interaction scheme in a double-Λ system is such that a closed loop is formed, the relative phase of the laser light fields becomes very important. We analyze here the effect of the lasers' relative phase on the EIT in double-Λ configuration of levels. The theoretical study of interactions of lasers with a double-Λ atomic scheme is commonly conducted by solving the optical Bloch equations (OBEs). We use here a perturbative method for solving OBEs, where the interaction of lasers with double-Λ is considered a perturbation. An advantage of the perturbative method is that it generally produces simpler solutions, and analytical expressions can be obtained. We present analytical expressions for the lower-order corrections of the EIT signal. Our results show that the EIT by the perturbative method can be approximated by the sum of products of complex Lorentzians. Through these expressions, we see in what way the relative phase affects the overall EIT profile. (paper)
Exact solution for a non-Markovian dissipative quantum dynamics.
Ferialdi, Luca; Bassi, Angelo
2012-04-27
We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.
Exact models for isotropic matter
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.
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.)
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.)
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025
Alishahi, Fatemeh; Mehrany, Khashayar
2010-06-01
We analytically relate the giant Goos-Hänchen shift, observed at the interface of a high refractive index prism and a waveguide structure with an arbitrary refractive index profile, to the spatial resonance phenomenon. The proximity effect of the high refractive index prism on modal properties of the waveguide is discussed, and the observed shift is expressed in terms of proper and improper electromagnetic modes supported by the waveguide with no prism. The transversely increasing improper modes are shown playing an increasingly important role as the high refractive index prism comes closer to the waveguide.
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
Stajdohar, Miha; Rosengarten, Rafael D; Kokosar, Janez; Jeran, Luka; Blenkus, Domen; Shaulsky, Gad; Zupan, Blaz
2017-06-02
Dictyostelium discoideum, a soil-dwelling social amoeba, is a model for the study of numerous biological processes. Research in the field has benefited mightily from the adoption of next-generation sequencing for genomics and transcriptomics. Dictyostelium biologists now face the widespread challenges of analyzing and exploring high dimensional data sets to generate hypotheses and discovering novel insights. We present dictyExpress (2.0), a web application designed for exploratory analysis of gene expression data, as well as data from related experiments such as Chromatin Immunoprecipitation sequencing (ChIP-Seq). The application features visualization modules that include time course expression profiles, clustering, gene ontology enrichment analysis, differential expression analysis and comparison of experiments. All visualizations are interactive and interconnected, such that the selection of genes in one module propagates instantly to visualizations in other modules. dictyExpress currently stores the data from over 800 Dictyostelium experiments and is embedded within a general-purpose software framework for management of next-generation sequencing data. dictyExpress allows users to explore their data in a broader context by reciprocal linking with dictyBase-a repository of Dictyostelium genomic data. In addition, we introduce a companion application called GenBoard, an intuitive graphic user interface for data management and bioinformatics analysis. dictyExpress and GenBoard enable broad adoption of next generation sequencing based inquiries by the Dictyostelium research community. Labs without the means to undertake deep sequencing projects can mine the data available to the public. The entire information flow, from raw sequence data to hypothesis testing, can be accomplished in an efficient workspace. The software framework is generalizable and represents a useful approach for any research community. To encourage more wide usage, the backend is open
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)
Polygons of differential equations for finding exact solutions
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.; Demina, Maria V.
2007-01-01
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given
Liang, Jun; Cui, Fang; Wang, Ru; Huang, Wei; Cui, Zhifeng
2013-04-01
Calculations of Franck-Condon factors are crucial for interpreting vibronic spectra of molecules and studying nonradiative processes. We have derived straightforwardly a more general analytical expression for the calculation of the three-dimensional Franck-Condon overlap integrals on the basis of harmonic oscillator approximation under the influence of mode mixing effects. This new analytical expression was applied to study the photoelectron spectra of PO2-. The theoretical spectrum obtained by employing CCSD(T) values is in excellent agreement with the observed one. An 'irregular spacing' observed in the experimental photoelectron spectrum of PO2- is interpreted as contributing from a hot-band sequence of the bending vibration ω2 and combination bands of the stretching vibration ω1 and the bending vibration ω2. In addition, the equilibrium geometry parameters, r(O-P) = 1.495 ± 0.005 Å and ∠(O-P-O) = 119.5 ± 0.5°, of theXA1 state of PO2-, are derived by employing an iterative Franck-Condon analysis procedure in the spectral simulation.
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.
Exact constants in approximation theory
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 simulation of max-stable processes.
Dombry, Clément; Engelke, Sebastian; Oesting, Marco
2016-06-01
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown-Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed.
Exact collisional moments for plasma fluid theories
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 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)
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
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 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.)
Some exact Bradlow vortex solutions
Energy Technology Data Exchange (ETDEWEB)
Gudnason, Sven Bjarke [Institute of Modern Physics, Chinese Academy of Sciences,Lanzhou 730000 (China); Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)
2017-05-08
We consider the Bradlow equation for vortices which was recently found by Manton and find a two-parameter class of analytic solutions in closed form on nontrivial geometries with non-constant curvature. The general solution to our class of metrics is given by a hypergeometric function and the area of the vortex domain by the Gaussian hypergeometric function.
An Exact Solution of the Binary Singular Problem
Directory of Open Access Journals (Sweden)
Baiqing Sun
2014-01-01
Full Text Available Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method.
Directory of Open Access Journals (Sweden)
Javier Cubas
2014-06-01
Full Text Available Due to the high dependence of photovoltaic energy efficiency on environmental conditions (temperature, irradiation..., it is quite important to perform some analysis focusing on the characteristics of photovoltaic devices in order to optimize energy production, even for small-scale users. The use of equivalent circuits is the preferred option to analyze solar cells/panels performance. However, the aforementioned small-scale users rarely have the equipment or expertise to perform large testing/calculation campaigns, the only information available for them being the manufacturer datasheet. The solution to this problem is the development of new and simple methods to define equivalent circuits able to reproduce the behavior of the panel for any working condition, from a very small amount of information. In the present work a direct and completely explicit method to extract solar cell parameters from the manufacturer datasheet is presented and tested. This method is based on analytical formulation which includes the use of the Lambert W-function to turn the series resistor equation explicit. The presented method is used to analyze commercial solar panel performance (i.e., the current-voltage–I-V–curve at different levels of irradiation and temperature. The analysis performed is based only on the information included in the manufacturer’s datasheet.
AESS: Accelerated Exact Stochastic Simulation
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
Exact performance analysis of decode-and-forward opportunistic relaying
Tourki, Kamel; Alouini, Mohamed-Slim; Yang, Hongchuan
2010-01-01
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
On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid
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.
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)
Exact Bremsstrahlung and effective couplings
Energy Technology Data Exchange (ETDEWEB)
Mitev, Vladimir [Institut für Physik, WA THEP, Johannes Gutenberg-Universität Mainz,Staudingerweg 7, 55128 Mainz (Germany); Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,IRIS Haus, Zum Großen Windkanal 6, 12489 Berlin (Germany); Pomoni, Elli [DESY Hamburg, Theory Group, Notkestrasse 85, D-22607 Hamburg (Germany); Physics Division, National Technical University of Athens,15780 Zografou Campus, Athens (Greece)
2016-06-13
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of N=2 SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the N=4 SYM ones, we obtain interpolating functions f(g{sup 2}) such that a given N=2 SCFT observable is obtained by replacing in the corresponding N=4 SYM result the coupling constant by f(g{sup 2}). These “exact effective couplings” encode the finite, relative renormalization between the N=2 and the N=4 gluon propagator and they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
High Resolution Thermometry for EXACT
Panek, J. S.; Nash, A. E.; Larson, M.; Mulders, N.
2000-01-01
High Resolution Thermometers (HRTs) based on SQUID detection of the magnetization of a paramagnetic salt or a metal alloy has been commonly used for sub-nano Kelvin temperature resolution in low temperature physics experiments. The main applications to date have been for temperature ranges near the lambda point of He-4 (2.177 K). These thermometers made use of materials such as Cu(NH4)2Br4 *2H2O, GdCl3, or PdFe. None of these materials are suitable for EXACT, which will explore the region of the He-3/He-4 tricritical point at 0.87 K. The experiment requirements and properties of several candidate paramagnetic materials will be presented, as well as preliminary test results.
EPA’s Web Analytics Program collects, analyzes, and provides reports on traffic, quality assurance, and customer satisfaction metrics for EPA’s website. The program uses a variety of analytics tools, including Google Analytics and CrazyEgg.
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.
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...
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 Results on Quantum Interference and Magnetoconductance in Variable-Range Hopping
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 Solution of the Two-Dimensional Problem on an Impact Ideal-Liquid Jet
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.
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.
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)
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.
Eigenvalue ratio detection based on exact moments of smallest and largest eigenvalues
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.
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
Constructing exact symmetric informationally complete measurements from numerical solutions
Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne
2018-04-01
Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.
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.
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 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)
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.
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
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
Aymard, François; Gulminelli, Francesca; Margueron, Jérôme
2016-08-01
The problem of determination of nuclear surface energy is addressed within the framework of the extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. In this first paper, we consider the case of symmetric nuclei. In this situation, the ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed and it is shown that they cannot be deduced simply from the local part of the functional, as it was suggested in previous works.
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.)
Extremal black holes as exact string solutions
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in α' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five-dimensional background which is proved to be an exact string solution
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
On exact solutions of scattering problems
International Nuclear Information System (INIS)
Nikishov, P.Yu.; Plekhanov, E.B.; Zakhariev, B.N.
1982-01-01
Examples illustrating the quality of the reconstruction of potentials from single-channel scattering data by using exactly solvable models are given. Simple exact solutions for multi-channel systems with non-degenerated resonance singularities of the scattering matrix are derived
Exact, 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....
Transversal magnetotransport in Weyl semimetals: Exact numerical approach
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.
Intermittency inhibited by transport: An exactly solvable model
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.
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
New Exact Solutions for New Model Nonlinear Partial Differential Equation
Maher, A.; El-Hawary, H. M.; Al-Amry, M. S.
2013-01-01
In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.
Exact Outage Probability of Dual-Hop CSI-Assisted AF Relaying Over Nakagami-m Fading Channels
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.
Directory of Open Access Journals (Sweden)
Wang-Xia Wang
2014-02-01
Full Text Available The miR-15/107 family comprises a group of 10 paralogous microRNAs (miRNAs, sharing a 5′ AGCAGC sequence. These miRNAs have overlapping targets. In order to characterize the expression of miR-15/107 family miRNAs, we employed customized TaqMan Low-Density micro-fluid PCR-array to investigate the expression of miR-15/107 family members, and other selected miRNAs, in 11 human tissues obtained at autopsy including the cerebral cortex, frontal cortex, primary visual cortex, thalamus, heart, lung, liver, kidney, spleen, stomach and skeletal muscle. miR-103, miR-195 and miR-497 were expressed at similar levels across various tissues, whereas miR-107 is enriched in brain samples. We also examined the expression patterns of evolutionarily conserved miR-15/107 miRNAs in three distinct primary rat brain cell preparations (enriched for cortical neurons, astrocytes and microglia, respectively. In primary cultures of rat brain cells, several members of the miR-15/107 family are enriched in neurons compared to other cell types in the central nervous system (CNS. In addition to mature miRNAs, we also examined the expression of precursors (pri-miRNAs. Our data suggested a generally poor correlation between the expression of mature miRNAs and their precursors. In summary, we provide a detailed study of the tissue and cell type-specific expression profile of this highly expressed and phylogenetically conserved family of miRNA genes.
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.)
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.
Exact statistical results for binary mixing and reaction in variable density turbulence
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 optics - III. Schwarzschild's spectrograph camera revised
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.
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
Dynamical Response of Networks Under External Perturbations: Exact Results
Chinellato, David D.; Epstein, Irving R.; Braha, Dan; Bar-Yam, Yaneer; de Aguiar, Marcus A. M.
2015-04-01
We give exact statistical distributions for the dynamic response of influence networks subjected to external perturbations. We consider networks whose nodes have two internal states labeled 0 and 1. We let nodes be frozen in state 0, in state 1, and the remaining nodes change by adopting the state of a connected node with a fixed probability per time step. The frozen nodes can be interpreted as external perturbations to the subnetwork of free nodes. Analytically extending and to be smaller than 1 enables modeling the case of weak coupling. We solve the dynamical equations exactly for fully connected networks, obtaining the equilibrium distribution, transition probabilities between any two states and the characteristic time to equilibration. Our exact results are excellent approximations for other topologies, including random, regular lattice, scale-free and small world networks, when the numbers of fixed nodes are adjusted to take account of the effect of topology on coupling to the environment. This model can describe a variety of complex systems, from magnetic spins to social networks to population genetics, and was recently applied as a framework for early warning signals for real-world self-organized economic market crises.
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
Bruce, William J; Maxwell, E A; Sneddon, I N
1963-01-01
Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy. The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions
Federal Laboratory Consortium — The Analytical Labspecializes in Oil and Hydraulic Fluid Analysis, Identification of Unknown Materials, Engineering Investigations, Qualification Testing (to support...
An Exact Confidence Region in Multivariate Calibration
Mathew, Thomas; Kasala, Subramanyam
1994-01-01
In the multivariate calibration problem using a multivariate linear model, an exact confidence region is constructed. It is shown that the region is always nonempty and is invariant under nonsingular transformations.
Euclidean shortest paths exact or approximate algorithms
Li, Fajie
2014-01-01
This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.
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
Fast Exact Euclidean Distance (FEED) Transformation
Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.
2004-01-01
Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
2Department of Engineering Sciences, Faculty of Technology and Engineering,. University ... of nonlinear partial differential equations (NPDEs) in mathematical physics. Keywords. ... This method has been successfully applied to obtain exact.
Exact Algorithms for Solving Stochastic Games
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels
2012-01-01
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....
On exactly soluble model in quantum electrodynamics
International Nuclear Information System (INIS)
Bogolubov, N.N.; Shumovsky, A.S.; Fam Le Kien
1984-01-01
Equations of motion describing the dynamics of three-level atom of ladder type interacting with two modes of quantized radiation field are solved exactly. Evolution of level population and photon rumbers under different unitial conditions is irvestigated
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
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.
Bosse, J; Pathak, K N; Singh, G S
2011-10-01
The fluctuation-dissipation theorem together with the exact density response spectrum for ideal quantum gases has been utilized to yield a new expression for the static structure factor, which we use to derive exact analytical expressions for the temperature-dependent pair distribution function g(r) of the ideal gases. The plots of bosonic and fermionic g(r) display "Bose pile" and "Fermi hole" typically akin to bunching and antibunching as observed experimentally for ultracold atomic gases. The behavior of spin-scaled pair correlation for fermions is almost featureless, but bosons show a rich structure including long-range correlations near T(c). The coherent state at T=0 shows no correlation at all, just like single-mode lasers. The depicted decreasing trend in correlation with decrease in temperature for T
The exact equation of motion of a simple pendulum of arbitrary amplitude: a hypergeometric approach
International Nuclear Information System (INIS)
Qureshi, M I; Rafat, M; Azad, S Ismail
2010-01-01
The motion of a simple pendulum of arbitrary amplitude is usually treated by approximate methods. By using generalized hypergeometric functions, it is however possible to solve the problem exactly. In this paper, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. A new and exact expression for the time of swinging of a simple pendulum from the vertical position to an arbitrary angular position θ is given by equation (3.10). The time period of such a pendulum is also exactly expressible in terms of hypergeometric functions. The exact expressions thus obtained are used to plot the graphs that compare the exact time period T(θ 0 ) with the time period T(0) (based on simple harmonic approximation). We also compare the relative difference between T(0) and T(θ 0 ) found from the exact equation of motion with the usual perturbation theory estimate. The treatment is intended for graduate students, who have acquired some familiarity with the hypergeometric functions. This approach may also be profitably used by specialists who encounter during their investigations nonlinear differential equations similar in form to the pendulum equation. Such nonlinear differential equations could arise in diverse fields, such as acoustic vibrations, oscillations in small molecules, turbulence and electronic filters, among others.
DEFF Research Database (Denmark)
Michaelsen, Rasmus Schandorph; Johansen, Tom Keinicke; Krozer, Viktor
2013-01-01
Instead of using frequency multipliers before a fundamental mixer, subharmonic mixers can be used. In order to develop novel subharmonic mixer architectures it is necessary to know the exact signal phase at the nonlinear element. The purpose of this paper is to generalize the description of the s....... With an RF frequency of 640 GHz, this design achieves a conversion gain of −13.5 dB with a LO-power of only −2.5 dBm....
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
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 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 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)
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)
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
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.
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
International Nuclear Information System (INIS)
Ancelin, C.; Le, P.; DeSaint-Quentin, S.; Villatte, N.
1987-01-01
This paper presents EXPRESS, an expert system developed for the automation of reliability studies. The first part consists in the description of the method for static thermohydraulic systems. In this step, the authors define the knowledge representation based on the two inference engines - ALOUETTE and LCR developed by EDF. They explain all the process to construct a fault tree from a topological and functional description of the system. Numerous examples are exhibited in illustration of the method. This is followed by the lessons derived from the studies performed on some safety systems of the PALUEL nuclear plant. The development of the same approach for electric power systems is described, insisting on the difference resulting from the sequential nature of these systems. Finally, they show the main advantages identified during the studies
Energy Technology Data Exchange (ETDEWEB)
Chae, Myeong Hu; Lee, Hu Jun; Kim, Ha Seok
1989-02-15
This book give explanations on analytical chemistry with ten chapters, which deal with development of analytical chemistry, the theory of error with definition and classification, sample and treatment gravimetry on general process of gravimetry in aqueous solution and non-aqueous solution, precipitation titration about precipitation reaction and types, complexometry with summary and complex compound, oxidation-reduction equilibrium on electrode potential and potentiometric titration, solvent extraction and chromatograph and experiment with basic operation for chemical experiment.
International Nuclear Information System (INIS)
Chae, Myeong Hu; Lee, Hu Jun; Kim, Ha Seok
1989-02-01
This book give explanations on analytical chemistry with ten chapters, which deal with development of analytical chemistry, the theory of error with definition and classification, sample and treatment gravimetry on general process of gravimetry in aqueous solution and non-aqueous solution, precipitation titration about precipitation reaction and types, complexometry with summary and complex compound, oxidation-reduction equilibrium on electrode potential and potentiometric titration, solvent extraction and chromatograph and experiment with basic operation for chemical experiment.
Exact solutions in three-dimensional gravity
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...
Classes of exact Einstein Maxwell solutions
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 bidirectional X -wave solutions in fiber Bragg gratings
Efremidis, Nikolaos K.; Nye, Nicholas S.; Christodoulides, Demetrios N.
2017-10-01
We find exact solutions describing bidirectional pulses propagating in fiber Bragg gratings. They are derived by solving the coupled-mode theory equations and are expressed in terms of products of modified Bessel functions with algebraic functions. Depending on the values of the two free parameters, the general bidirectional X -wave solution can also take the form of a unidirectional pulse. We analyze the symmetries and the asymptotic properties of the solutions and also discuss additional waveforms that are obtained by interference of more than one solution. Depending on their parameters, such pulses can create a sharp focus with high contrast.
Exact partition functions for gauge theories on Rλ3
Directory of Open Access Journals (Sweden)
Jean-Christophe Wallet
2016-11-01
Full Text Available The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
Exact solutions and ladder operators for a new anharmonic oscillator
International Nuclear Information System (INIS)
Dong Shihai; Sun Guohua; Lozada-Cassou, M.
2005-01-01
In this Letter, we propose a new anharmonic oscillator and present the exact solutions of the Schrodinger equation with this oscillator. The ladder operators are established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions. Some comments are made on the general calculation formula and recurrence relation for off-diagonal matrix elements. Finally, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r->ir
An exact solution for orbit view-periods from a station on a tri-axial ellipsoidal planet
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
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.
Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution
International Nuclear Information System (INIS)
Baradaran, M.; Panahi, H.
2016-01-01
We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2). Then, we obtain the general exact solutions of the problem by employing the representation theory of sl(2) Lie algebra.
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
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)
Exactly solvable energy-dependent potentials
International Nuclear Information System (INIS)
Garcia-Martinez, J.; Garcia-Ravelo, J.; Pena, J.J.; Schulze-Halberg, A.
2009-01-01
We introduce a method for constructing exactly-solvable Schroedinger equations with energy-dependent potentials. Our method is based on converting a general linear differential equation of second order into a Schroedinger equation with energy-dependent potential. Particular examples presented here include harmonic oscillator, Coulomb and Morse potentials with various types of energy dependence.
Exact relativistic cylindrical solution of disordered radiation
International Nuclear Information System (INIS)
Fonseca Teixeira, A.F. da; Wolk, I.; Som, M.M.
1976-05-01
A source free disordered distribution of electromagnetic radiation is considered in Einstein' theory, and a time independent exact solution with cylindrical symmetry is obtained. The gravitation and pressure effects of the radiation alone are sufficient to give the distribution an equilibrium. A finite maximum concentration is found on the axis of symmetry, and decreases monotonically to zero outwards. Timelike and null geodesics are discussed
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 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.
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark
2006-01-01
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan
2004-01-01
We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...
Off-diagonal Bethe ansatz for exactly solvable models
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.
Entanglement dynamics following a sudden quench: An exact solution
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.
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 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.)
Jurin's law revisited: Exact meniscus shape and column height.
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.
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...
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
Lemos, Nivaldo A
2018-01-01
Analytical mechanics is the foundation of many areas of theoretical physics including quantum theory and statistical mechanics, and has wide-ranging applications in engineering and celestial mechanics. This introduction to the basic principles and methods of analytical mechanics covers Lagrangian and Hamiltonian dynamics, rigid bodies, small oscillations, canonical transformations and Hamilton–Jacobi theory. This fully up-to-date textbook includes detailed mathematical appendices and addresses a number of advanced topics, some of them of a geometric or topological character. These include Bertrand's theorem, proof that action is least, spontaneous symmetry breakdown, constrained Hamiltonian systems, non-integrability criteria, KAM theory, classical field theory, Lyapunov functions, geometric phases and Poisson manifolds. Providing worked examples, end-of-chapter problems, and discussion of ongoing research in the field, it is suitable for advanced undergraduate students and graduate students studying analyt...
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...
An Exact Method to Determine the Conductivity of Aqueous Solutions in Acid-Base Titrations
Directory of Open Access Journals (Sweden)
Norma Rodríguez-Laguna
2015-01-01
Full Text Available Several works in the literature show that it is possible to establish the analytic equations to estimate the volume V of a strong base or a strong acid (Vb and Va, resp. being added to a solution of a substance or a mix of substances during an acid-base titration, as well as the equations to estimate the first derivative of the titration plot dpH/dV, and algebraic expressions to determine the buffer β capacity with dilution βdil. This treatment allows establishing the conditions of thermodynamic equilibria for all species within a system containing a mix of species from one or from various polyacid systems. The present work shows that it is possible to determine exactly the electric conductivity of aqueous solutions for these Brønsted acid-base titrations, because the functional relation between this property and the composition of the system in equilibrium is well known; this is achieved using the equivalent conductivity λi values of each of the ions present in a given system. The model employed for the present work confirms the experimental outcomes with the H2SO4, B(OH3, CH3COOH, and H3PO4 aqueous solutions’ titration.
Spain, Barry; Ulam, S; Stark, M
1960-01-01
Analytical Quadrics focuses on the analytical geometry of three dimensions. The book first discusses the theory of the plane, sphere, cone, cylinder, straight line, and central quadrics in their standard forms. The idea of the plane at infinity is introduced through the homogenous Cartesian coordinates and applied to the nature of the intersection of three planes and to the circular sections of quadrics. The text also focuses on paraboloid, including polar properties, center of a section, axes of plane section, and generators of hyperbolic paraboloid. The book also touches on homogenous coordi
Exact mean-energy expansion of Ginibre's gas for coupling constants Γ =2 ×(oddinteger)
Salazar, R.; Téllez, G.
2017-12-01
Using the approach of a Vandermonde determinant to the power Γ =Q2/kBT expansion on monomial functions, a way to find the excess energy Uexc of the two-dimensional one-component plasma (2DOCP) on hard and soft disks (or a Dyson gas) for odd values of Γ /2 is provided. At Γ =2 , the present study not only corroborates the result for the particle-particle energy contribution of the Dyson gas found by Shakirov [Shakirov, Phys. Lett. A 375, 984 (2011), 10.1016/j.physleta.2011.01.004] by using an alternative approach, but also provides the exact N -finite expansion of the excess energy of the 2DOCP on the hard disk. The excess energy is fitted to the ansatz of the form Uexc=K1N +K2√{N }+K3+K4/N +O (1 /N2) to study the finite-size correction, with Ki coefficients and N the number of particles. In particular, the bulk term of the excess energy is in agreement with the well known result of Jancovici for the hard disk in the thermodynamic limit [Jancovici, Phys. Rev. Lett. 46, 386 (1981), 10.1103/PhysRevLett.46.386]. Finally, an expression is found for the pair correlation function which still keeps a link with the random matrix theory via the kernel in the Ginibre ensemble [Ginibre, J. Math. Phys. 6, 440 (1965), 10.1063/1.1704292] for odd values of Γ /2 . A comparison between the analytical two-body density function and histograms obtained with Monte Carlo simulations for small systems and Γ =2 ,6 ,10 ,... shows that the approach described in this paper may be used to study analytically the crossover behavior from systems in the fluid phase to small crystals.
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.
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 complexity: The spectral decomposition of intrinsic computation
International Nuclear Information System (INIS)
Crutchfield, James P.; Ellison, Christopher J.; Riechers, Paul M.
2016-01-01
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full eigenvalue spectrum of the mixed-state presentation of a process's ϵ-machine causal-state dynamic. Measures include correlation functions, power spectra, past-future mutual information, transient and synchronization informations, and many others. As a result, a direct and complete analysis of intrinsic computation is now available for the temporal organization of finitary hidden Markov models and nonlinear dynamical systems with generating partitions and for the spatial organization in one-dimensional systems, including spin systems, cellular automata, and complex materials via chaotic crystallography. - Highlights: • We provide exact, closed-form expressions for a hidden stationary process' intrinsic computation. • These include information measures such as the excess entropy, transient information, and synchronization information and the entropy-rate finite-length approximations. • The method uses an epsilon-machine's mixed-state presentation. • The spectral decomposition of the mixed-state presentation relies on the recent development of meromorphic functional calculus for nondiagonalizable operators.
2016-04-30
Warfare, Naval Sea Systems Command Acquisition Cycle Time : Defining the Problem David Tate, Institute for Defense Analyses Schedule Analytics Jennifer...research was comprised of the following high- level steps : Identify and review primary data sources 1...research. However, detailed reviews of the OMB IT Dashboard data revealed that schedule data is highly aggregated. Program start date and program end date
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.
Communication: An exact bound on the bridge function in integral equation theories.
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.
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
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.
International Nuclear Information System (INIS)
Abourabia, A.M.; El-Danaf, T.S.; Morad, A.M.
2008-01-01
The problem under consideration are related to wave propagation in micro structured materials, characterized by higher-order nonlinear and higher-order dispersive effects; particularly, the wave propagation in dilatant granular materials. In the present paper the model equation is solved analytically by exact method called Jacobi elliptic method. The types of solutions are defined and discussed over a wide range of material parameters (two dispersion parameters and one microstructure parameter). The dispersion properties and the relation between group and phase velocities of the model equation are studied. The diagrams are drawn to illustrate the physical properties of the exact solutions
Exact WKB analysis and cluster algebras
International Nuclear Information System (INIS)
Iwaki, Kohei; Nakanishi, Tomoki
2014-01-01
We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schrödinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes automorphisms associated with periods of cluster algebras. The paper also includes an extensive introduction of the exact WKB analysis and the surface realization of cluster algebras for nonexperts. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)
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.)
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 folded-band chaotic oscillator.
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.
Exact geodesic distances in FLRW spacetimes
Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri
2017-11-01
Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.
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.
New exact solutions of the Dirac equation
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Lavrov, P.M.; Shapovalov, V.N.
1980-01-01
Search for new exact solutions of the Dirac and Klein-Gordon equations are in progress. Considered are general properties of the Dirac equation solutions for an electron in a purely magnetic field, in combination with a longitudinal magnetic and transverse electric fields. New solutions for the equations of charge motion in an electromagnetic field of axial symmetry and in a nonstationary field of a special form have been found for potentials selected concretely
Exact solutions and singularities in string theory
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail
Exact diagonalization library for quantum electron models
Iskakov, Sergei; Danilov, Michael
2018-04-01
We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. The observables that can be computed using EDLib are single particle Green's functions and spin-spin correlation functions. This code provides three different types of Hamiltonian matrix storage that can be chosen based on the model.
Exactly and completely integrable nonlinear dynamical systems
International Nuclear Information System (INIS)
Leznov, A.N.; Savel'ev, M.V.
1987-01-01
The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions
Exact Theory of Compressible Fluid Turbulence
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.
International Nuclear Information System (INIS)
Nguyen Bich Ha; Nguyen Van Hop
2009-01-01
The Kondo and Fano resonances in the two-point Green's function of the single-level quantum dot were found and investigated in many previous works by means of different numerical calculation methods. In this work we present the derivation of the analytical expressions of resonance terms in the expression of the two-point Green's function. For that purpose the system of Dyson equations for the two-point nonequilibrium Green's functions in the complex-time Keldysh formalism was established in the second order with respect to the tunneling coupling constants and the mean field approximation. This system of Dyson equations was solved exactly and the analytical expressions of the resonance terms are derived. The conditions for the existence of Kondo or Fano resonances are found.
Dynamics of an Imperfect Microbeam Considering its Exact Shape
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.
Exact extreme-value statistics at mixed-order transitions.
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.
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.
Analytical studies on the Benney-Luke equation in mathematical physics
Islam, S. M. Rayhanul; Khan, Kamruzzaman; Woadud, K. M. Abdul Al
2018-04-01
The enhanced (G‧/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney-Luke equation by using the enhanced (G‧/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NLEEs). The traveling wave solutions have expressed in term of the hyperbolic and trigonometric functions. We also have plotted the 2D and 3D graphics of some analytical solutions obtained in this paper.
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.)
Energy Technology Data Exchange (ETDEWEB)
Choi, Jae Seong
1993-02-15
This book is comprised of nineteen chapters, which describes introduction of analytical chemistry, experimental error and statistics, chemistry equilibrium and solubility, gravimetric analysis with mechanism of precipitation, range and calculation of the result, volume analysis on general principle, sedimentation method on types and titration curve, acid base balance, acid base titration curve, complex and firing reaction, introduction of chemical electro analysis, acid-base titration curve, electrode and potentiometry, electrolysis and conductometry, voltammetry and polarographic spectrophotometry, atomic spectrometry, solvent extraction, chromatograph and experiments.
International Nuclear Information System (INIS)
Choi, Jae Seong
1993-02-01
This book is comprised of nineteen chapters, which describes introduction of analytical chemistry, experimental error and statistics, chemistry equilibrium and solubility, gravimetric analysis with mechanism of precipitation, range and calculation of the result, volume analysis on general principle, sedimentation method on types and titration curve, acid base balance, acid base titration curve, complex and firing reaction, introduction of chemical electro analysis, acid-base titration curve, electrode and potentiometry, electrolysis and conductometry, voltammetry and polarographic spectrophotometry, atomic spectrometry, solvent extraction, chromatograph and experiments.
International Nuclear Information System (INIS)
Anon.
1985-01-01
The division for Analytical Chemistry continued to try and develope an accurate method for the separation of trace amounts from mixtures which, contain various other elements. Ion exchange chromatography is of special importance in this regard. New separation techniques were tried on certain trace amounts in South African standard rock materials and special ceramics. Methods were also tested for the separation of carrier-free radioisotopes from irradiated cyclotron discs
Quasi-exact solutions of nonlinear differential equations
Kudryashov, Nikolay A.; Kochanov, Mark B.
2014-01-01
The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.
Exact partition functions for deformed N=2 theories with N{sub f}=4 flavours
Energy Technology Data Exchange (ETDEWEB)
Beccaria, Matteo; Fachechi, Alberto; Macorini, Guido; Martina, Luigi [Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento,Via Arnesano, 73100 Lecce (Italy); INFN, Via Arnesano, 73100 Lecce (Italy)
2016-12-07
We consider the Ω-deformed N=2SU(2) gauge theory in four dimensions with N{sub f}=4 massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters ε{sub 1},ε{sub 2}, the scalar field expectation value a, and the hypermultiplet masses m=(m{sub 1},m{sub 2},m{sub 3},m{sub 4}). Motivated by recent findings in the N=2{sup ∗} theory, we explore the theories that are characterized by special fixed ratios ε{sub 2}/ε{sub 1} and m/ε{sub 1} and propose a simple condition on the structure of the multi-instanton contributions to the prepotential determining the effective action. This condition determines a finite set Π{sub N} of special points such that the prepotential has N poles at fixed positions independent on the instanton number. In analogy with what happens in the N=2{sup ∗} gauge theory, the full prepotential of the Π{sub N} theories may be given in closed form as an explicit function of a and the modular parameter q appearing in special combinations of Eisenstein series and Jacobi theta functions with well defined modular properties. The resulting finite pole partition functions are related by AGT correspondence to special 4-point spherical conformal blocks of the Virasoro algebra. We examine in full details special cases where the closed expression of the block is known and confirms our Ansatz. We systematically study the special features of Zamolodchikov’s recursion for the Π{sub N} conformal blocks. As a result, we provide a novel effective recursion relation that can be exactly solved and allows to prove the conjectured closed expressions analytically in the case of the Π{sub 1} and Π{sub 2} conformal blocks.
Exact partition functions for deformed N=2 theories with N_f=4 flavours
International Nuclear Information System (INIS)
Beccaria, Matteo; Fachechi, Alberto; Macorini, Guido; Martina, Luigi
2016-01-01
We consider the Ω-deformed N=2SU(2) gauge theory in four dimensions with N_f=4 massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters ε_1,ε_2, the scalar field expectation value a, and the hypermultiplet masses m=(m_1,m_2,m_3,m_4). Motivated by recent findings in the N=2"∗ theory, we explore the theories that are characterized by special fixed ratios ε_2/ε_1 and m/ε_1 and propose a simple condition on the structure of the multi-instanton contributions to the prepotential determining the effective action. This condition determines a finite set Π_N of special points such that the prepotential has N poles at fixed positions independent on the instanton number. In analogy with what happens in the N=2"∗ gauge theory, the full prepotential of the Π_N theories may be given in closed form as an explicit function of a and the modular parameter q appearing in special combinations of Eisenstein series and Jacobi theta functions with well defined modular properties. The resulting finite pole partition functions are related by AGT correspondence to special 4-point spherical conformal blocks of the Virasoro algebra. We examine in full details special cases where the closed expression of the block is known and confirms our Ansatz. We systematically study the special features of Zamolodchikov’s recursion for the Π_N conformal blocks. As a result, we provide a novel effective recursion relation that can be exactly solved and allows to prove the conjectured closed expressions analytically in the case of the Π_1 and Π_2 conformal blocks.
Welti, Jonathan; Rodrigues, Daniel Nava; Sharp, Adam; Sun, Shihua; Lorente, David; Riisnaes, Ruth; Figueiredo, Ines; Zafeiriou, Zafeiris; Rescigno, Pasquale; de Bono, Johann S; Plymate, Stephen R
2016-10-01
The androgen receptor splice variant-7 (AR-V7) has been implicated in the development of castration-resistant prostate cancer (CRPC) and resistance to abiraterone and enzalutamide. To develop a validated assay for detection of AR-V7 protein in tumour tissue and determine its expression and clinical significance as patients progress from hormone-sensitive prostate cancer (HSPC) to CRPC. Following monoclonal antibody generation and validation, we retrospectively identified patients who had HSPC and CRPC tissue available for AR-V7 immunohistochemical (IHC) analysis. Nuclear AR-V7 expression was determined using IHC H score (HS) data. The change in nuclear AR-V7 expression from HSPC to CRPC and the association between nuclear AR-V7 expression and overall survival (OS) was determined. Nuclear AR-V7 expression was significantly lower in HSPC (median HS 50, interquartile range [IQR] 17.5-90) compared to CRPC (HS 135, IQR 80-157.5; pprostate cancer. A higher level of AR-V7 identifies a group of patients who respond less well to certain prostate cancer treatments and live for a shorter period of time. Copyright © 2016 European Association of Urology. Published by Elsevier B.V. All rights reserved.
Analytic Treatment of Deep Neural Networks Under Additive Gaussian Noise
Alfadly, Modar
2018-01-01
Despite the impressive performance of deep neural networks (DNNs) on numerous vision tasks, they still exhibit yet-to-understand uncouth behaviours. One puzzling behaviour is the reaction of DNNs to various noise attacks, where it has been shown that there exist small adversarial noise that can result in a severe degradation in the performance of DNNs. To rigorously treat this, we derive exact analytic expressions for the first and second moments (mean and variance) of a small piecewise linear (PL) network with a single rectified linear unit (ReLU) layer subject to general Gaussian input. We experimentally show that these expressions are tight under simple linearizations of deeper PL-DNNs, especially popular architectures in the literature (e.g. LeNet and AlexNet). Extensive experiments on image classification show that these expressions can be used to study the behaviour of the output mean of the logits for each class, the inter-class confusion and the pixel-level spatial noise sensitivity of the network. Moreover, we show how these expressions can be used to systematically construct targeted and non-targeted adversarial attacks. Then, we proposed a special estimator DNN, named mixture of linearizations (MoL), and derived the analytic expressions for its output mean and variance, as well. We employed these expressions to train the model to be particularly robust against Gaussian attacks without the need for data augmentation. Upon training this network on a loss that is consolidated with the derived output probabilistic moments, the network is not only robust under very high variance Gaussian attacks but is also as robust as networks that are trained with 20 fold data augmentation.
Analytic Treatment of Deep Neural Networks Under Additive Gaussian Noise
Alfadly, Modar M.
2018-04-12
Despite the impressive performance of deep neural networks (DNNs) on numerous vision tasks, they still exhibit yet-to-understand uncouth behaviours. One puzzling behaviour is the reaction of DNNs to various noise attacks, where it has been shown that there exist small adversarial noise that can result in a severe degradation in the performance of DNNs. To rigorously treat this, we derive exact analytic expressions for the first and second moments (mean and variance) of a small piecewise linear (PL) network with a single rectified linear unit (ReLU) layer subject to general Gaussian input. We experimentally show that these expressions are tight under simple linearizations of deeper PL-DNNs, especially popular architectures in the literature (e.g. LeNet and AlexNet). Extensive experiments on image classification show that these expressions can be used to study the behaviour of the output mean of the logits for each class, the inter-class confusion and the pixel-level spatial noise sensitivity of the network. Moreover, we show how these expressions can be used to systematically construct targeted and non-targeted adversarial attacks. Then, we proposed a special estimator DNN, named mixture of linearizations (MoL), and derived the analytic expressions for its output mean and variance, as well. We employed these expressions to train the model to be particularly robust against Gaussian attacks without the need for data augmentation. Upon training this network on a loss that is consolidated with the derived output probabilistic moments, the network is not only robust under very high variance Gaussian attacks but is also as robust as networks that are trained with 20 fold data augmentation.
Energy Technology Data Exchange (ETDEWEB)
Yalcin, S. [Education Faculty, Kastamonu University, 37200 Kastamonu (Turkey)]. E-mail: yalcin@gazi.edu.tr; Gurler, O. [Physics Department, Faculty of Arts and Sciences, Uludag University, Gorukle Campus, 16059 Bursa (Turkey); Gultekin, A. [Physics Department, Faculty of Arts and Sciences, Uludag University, Gorukle Campus, 16059 Bursa (Turkey); Gundogdu, O. [School of Engineering, University of Surrey, Guildford, GU2 7XH (United Kingdom)]. E-mail: o.gundogdu@surrey.ac.uk
2006-07-31
In this Letter, an expression is presented to calculate elastic scattering cross sections for incident electrons as a function of both energy and atomic number in the energy range between 1 keV and 1 MeV for materials with effective atomic number between 3 and 18. The expression we present has a rather simple analytical form which gives accurate results that are in very good agreement with the results calculated by a relativistic partial-wave expansion method. Hence, this equation can be employed accurately and efficiently in a continuous manner, without the need to go through rather large look-up tables, thus making the whole process quick, efficient and removing possible computational errors that may arise from the efforts of interpolation.
International Nuclear Information System (INIS)
Yalcin, S.; Gurler, O.; Gultekin, A.; Gundogdu, O.
2006-01-01
In this Letter, an expression is presented to calculate elastic scattering cross sections for incident electrons as a function of both energy and atomic number in the energy range between 1 keV and 1 MeV for materials with effective atomic number between 3 and 18. The expression we present has a rather simple analytical form which gives accurate results that are in very good agreement with the results calculated by a relativistic partial-wave expansion method. Hence, this equation can be employed accurately and efficiently in a continuous manner, without the need to go through rather large look-up tables, thus making the whole process quick, efficient and removing possible computational errors that may arise from the efforts of interpolation
Directory of Open Access Journals (Sweden)
Ho-Yong Jeong
2015-08-01
Full Text Available Voltage is an important variable that reflects system conditions in DC distribution systems and affects many characteristics of a system. In a DC distribution system, there is a close relationship between the real power and the voltage magnitude, and this is one of major differences from the characteristics of AC distribution systems. One such relationship is expressed as the voltage sensitivity, and an understanding of voltage sensitivity is very useful to describe DC distribution systems. In this paper, a formulation for a novel approximate expression for the voltage sensitivity in a radial DC distribution system is presented. The approximate expression is derived from the power flow equation with some additional assumptions. The results of approximate expression is compared with an exact calculation, and relations between the voltage sensitivity and electrical quantities are analyzed analytically using both the exact form and the approximate voltage sensitivity equation.
Mean field approximation versus exact treatment of collisions in few-body systems
International Nuclear Information System (INIS)
Lemm, J.; Weiguny, A.; Giraud, B.G.
1990-01-01
A variational principle for calculating matrix elements of the full resolvent operator for a many-body system is studied. Its mean field approximation results in non-linear equations of Hartree (-Fock) type, with initial and final channel wave functions as driving terms. The mean field equations will in general have many solutions whereas the exact problem being linear, has a unique solution. In a schematic model with separable forces the mean field equations are analytically soluble, and for the exact problem the resulting integral equations are solved numerically. Comparing exact and mean field results over a wide range of system parameters, the mean field approach proves to be a very reliable approximation, which is not plagued by the notorious problem of defining asymptotic channels in the time-dependent mean field method. (orig.)
Exact results for the spectra of bosons and fermions with contact interaction
Energy Technology Data Exchange (ETDEWEB)
Mashkevich, Stefan [Schroedinger, 120 West 45th St., New York, NY 10036 (United States)]. E-mail: mash@mashke.org; Matveenko, Sergey [Landau Institute for Theoretical Physics, Kosygina Str. 2, 119334 Moscow (Russian Federation)]. E-mail: matveen@landau.ac.ru; Ouvry, Stephane [Laboratoire de Physique Theorique et Modeles Statistiques, Unite de Recherche de l' Universite Paris 11 associee au CNRS, UMR 8626., Bat. 100, Universite Paris-Sud, 91405 Orsay (France)]. E-mail: ouvry@lptms.u-psud.fr
2007-02-19
An N-body bosonic model with delta-contact interactions projected on the lowest Landau level is considered. For a given number of particles in a given angular momentum sector, any energy level can be obtained exactly by means of diagonalizing a finite matrix: they are roots of algebraic equations. A complete solution of the three-body problem is presented, some general properties of the N-body spectrum are pointed out, and a number of novel exact analytic eigenstates are obtained. The FQHE N-fermion model with Laplacian-delta interactions is also considered along the same lines of analysis. New exact eigenstates are proposed, along with the Slater determinant, whose eigenvalues are shown to be related to Catalan numbers.
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)
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
An exact solution in Einstein-Cartan
International Nuclear Information System (INIS)
Roque, W.L.
1982-01-01
The exact solution of the field equations of the Einstein-Cartan theory is obtained for an artificial dust of radially polarized spins, with spherical symmetry and static. For a best estimation of the effect due the spin, the energy-momentum metric tensor is considered null. The gravitational field dynamics is studied for several torsion strengths, through the massive and spinless test-particle moviment, in particular for null torsion Schwarzschild solutions is again obtained. It is observed that the gravitational effects related to the torsin (spin) sometimes are attractives sometimes are repulsives, depending of the torsion values and of the test-particle position and velocity. (L.C.) [pt
Exact renormalization group equations: an introductory review
Bagnuls, C.; Bervillier, C.
2001-07-01
We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.
Exactly soluble problems in statistical mechanics
International Nuclear Information System (INIS)
Yang, C.N.
1983-01-01
In the last few years, a number of two-dimensional classical and one-dimensional quantum mechanical problems in statistical mechanics have been exactly solved. Although these problems range over models of diverse physical interest, their solutions were obtained using very similar mathematical methods. In these lectures, the main points of the methods are discussed. In this introductory lecture, an overall survey of all these problems without going into the detailed method of solution is given. In later lectures, they shall concentrate on one particular problem: the delta function interaction in one dimension, and go into the details of that problem
An exact approach for aggregated formulations
DEFF Research Database (Denmark)
Gamst, Mette; Spoorendonk, Simon; Røpke, Stefan
Aggregating formulations is a powerful approach for problems to take on tractable forms. Aggregation may lead to loss of information, i.e. the aggregated formulation may be an approximation of the original problem. In branch-and-bound context, aggregation can also complicate branching, e.g. when...... optimality cannot be guaranteed by branching on aggregated variables. We present a generic exact solution method to remedy the drawbacks of aggregation. It combines the original and aggregated formulations and applies Benders' decomposition. We apply the method to the Split Delivery Vehicle Routing Problem....
Resonant particle production during inflation: a full analytical study
Energy Technology Data Exchange (ETDEWEB)
Pearce, Lauren; Peloso, Marco [School of Physics and Astronomy, University of Minnesota, 116 Church Street S.E., Minneapolis, MN 55455 (United States); Sorbo, Lorenzo, E-mail: lpearce@physics.umn.edu, E-mail: peloso@physics.umn.edu, E-mail: sorbo@physics.umass.edu [Amherst Center for Fundamental Interactions, Department of Physics, University of Massachusetts, 1126 Lederle Graduate Research Tower (LGRT), Amherst, MA 01003 (United States)
2017-05-01
We revisit the study of the phenomenology associated to a burst of particle production of a field whose mass is controlled by the inflaton field and vanishes at one given instance during inflation. This generates a bump in the correlators of the primordial scalar curvature. We provide a unified formalism to compute various effects that have been obtained in the literature and confirm that the dominant effects are due to the rescattering of the produced particles on the inflaton condensate. We improve over existing results (based on numerical fits) by providing exact analytic expressions for the shape and height of the bump, both in the power spectrum and the equilateral bispectrum. We then study the regime of validity of the perturbative computations of this signature. Finally, we extend these computations to the case of a burst of particle production in a sector coupled only gravitationally to the inflaton.
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
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%.
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)
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 and Heuristic Algorithms for Runway Scheduling
Malik, Waqar A.; Jung, Yoon C.
2016-01-01
This paper explores the Single Runway Scheduling (SRS) problem with arrivals, departures, and crossing aircraft on the airport surface. Constraints for wake vortex separations, departure area navigation separations and departure time window restrictions are explicitly considered. The main objective of this research is to develop exact and heuristic based algorithms that can be used in real-time decision support tools for Air Traffic Control Tower (ATCT) controllers. The paper provides a multi-objective dynamic programming (DP) based algorithm that finds the exact solution to the SRS problem, but may prove unusable for application in real-time environment due to large computation times for moderate sized problems. We next propose a second algorithm that uses heuristics to restrict the search space for the DP based algorithm. A third algorithm based on a combination of insertion and local search (ILS) heuristics is then presented. Simulation conducted for the east side of Dallas/Fort Worth International Airport allows comparison of the three proposed algorithms and indicates that the ILS algorithm performs favorably in its ability to find efficient solutions and its computation times.
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.
Explicitly broken supersymmetry with exactly massless moduli
Energy Technology Data Exchange (ETDEWEB)
Dong, Xi [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Freedman, Daniel Z. [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Center for Theoretical Physics and Department of Mathematics,Massachusetts Institute of Technology,Cambridge, MA 02139 (United States); Zhao, Yue [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States)
2016-06-16
The AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a supergravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents.
Analytical calculation of magnet interactions in 3D
Yonnet , Jean-Paul; Allag , Hicham
2009-01-01
International audience; A synthesis of all the analytical expressions of the interaction energy, force components and torque components is presented. It allows the analytical calculation of all the interactions when the magnetizations are in any direction. The 3D analytical expressions are difficult to obtain, but the torque and force expressions are very simple to use.
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
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)
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
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)
Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model
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...
(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.
Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
Córdova, Clay; Heidenreich, Ben; Popolitov, Alexandr; Shakirov, Shamil
2018-02-01
We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully factorized into a product of terms linear in the rank of the matrix and the parameters of the model. We extend our formulas to include both logarithmic and finite-difference deformations, thereby generalizing the celebrated Selberg and Kadell integrals. We conjecture a formula for correlators of two Schur functions in these models, and explain how our results follow from a general orbifold-like procedure that can be applied to any one-matrix model with a single-trace potential.
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
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)
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.
Search Analytics for Your Site
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.
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.)
Helrich, Carl S
2017-01-01
This advanced undergraduate textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations, with constraints incorporated through Lagrange multipliers. Hamilton's Principle and the canonical equations remain the basis of the remainder of the text. Topics considered for applications include small oscillations, motion in electric and magnetic fields, and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally the text has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance. The text is enriched with an outline of the history of mechanics, which particularly outlines the importance of the work of Euler, Lagrange, Hamilton and Jacobi. Numerous exercises with solutions support the exceptionally clear and concise treatment...
A Simple Exact Error Rate Analysis for DS-CDMA with Arbitrary Pulse Shape in Flat Nakagami Fading
Rahman, Mohammad Azizur; Sasaki, Shigenobu; Kikuchi, Hisakazu; Harada, Hiroshi; Kato, Shuzo
A simple exact error rate analysis is presented for random binary direct sequence code division multiple access (DS-CDMA) considering a general pulse shape and flat Nakagami fading channel. First of all, a simple model is developed for the multiple access interference (MAI). Based on this, a simple exact expression of the characteristic function (CF) of MAI is developed in a straight forward manner. Finally, an exact expression of error rate is obtained following the CF method of error rate analysis. The exact error rate so obtained can be much easily evaluated as compared to the only reliable approximate error rate expression currently available, which is based on the Improved Gaussian Approximation (IGA).
Exact solutions of Feinberg–Horodecki equation for time-dependent ...
Indian Academy of Sciences (India)
proposed to find the exact solutions of the Feinberg–Horodecki equation for the .... is a polynomial of degree n and satisfies the Rodrigues relation [24] ... The discriminant of expression (15) under the square root has to be zero, so that the.
Exact evaluation of the mass gap in the O(N) non-linear sigma model
International Nuclear Information System (INIS)
Gliozzi, F.
1985-01-01
When the Luescher nonlocal quantum charges are transcribed in a lattice hamiltonian formalism, they become unusually manageable. Their conservation induces an exact expression for the mass of the low-lying vector multiplet of the theory. Its value in units Λsub(PV) (Pauli-Villars scale) reads simple m=exp[1/(N-2)]Λsub(PV). (orig.)
Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering
Dorier, V.; Gevorgyan, M.; Ishkhanyan, A.; Leroy, C.; Jauslin, H. R.; Guérin, S.
2017-12-01
We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.
Exact solutions of linearized Schwinger endash Dyson equation of fermion self-energy
International Nuclear Information System (INIS)
Zhou, B.
1997-01-01
The Schwinger endash Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the independent solutions, which, respectively, submit to irregular and regular ultraviolet boundary condition are derived and expounded. copyright 1997 American Institute of Physics
Two-dimensional nonlinear string-type equations and their exact integration
International Nuclear Information System (INIS)
Leznov, A.N.; Saveliev, M.V.
1982-01-01
On the base of group-theoretical formulation for exactly integrable two-dimensional non-linear dynamical systems associated with a local part of an arbitrary graded Lie algebra we study a string-type subclass of the equations. Explicit expressions have been obtained for their general solutions
Electrostatics of a Point Charge between Intersecting Planes: Exact Solutions and Method of Images
Mei, W. N.; Holloway, A.
2005-01-01
In this work, the authors present a commonly used example in electrostatics that could be solved exactly in a conventional manner, yet expressed in a compact form, and simultaneously work out special cases using the method of images. Then, by plotting the potentials and electric fields obtained from these two methods, the authors demonstrate that…
Exact asymptotic expansions for solutions of multi-dimensional renewal equations
International Nuclear Information System (INIS)
Sgibnev, M S
2006-01-01
We derive expansions with exact asymptotic expressions for the remainders for solutions of multi-dimensional renewal equations. The effect of the roots of the characteristic equation on the asymptotic representation of solutions is taken into account. The resulting formulae are used to investigate the asymptotic behaviour of the average number of particles in age-dependent branching processes having several types of particles
Painlevé analysis and exact solutions for the Belousov–Zhabotinskii reaction–diffusion system
International Nuclear Information System (INIS)
Kudryashov, Nikolay A.; Zakharchenko, Anastasia S.
2014-01-01
A system of equations for description of the Belousov–Zhabotinskii chemical reaction is considered. The Painlevé analysis of this reaction–diffusion system is studied. Exact traveling wave solutions of the system for the Belousov–Zhabotinskii reaction are found. Periodic solutions expressed in terms of the Weierstrass elliptic function are also given
Exact solutions for some discrete models of the Boltzmann equation
International Nuclear Information System (INIS)
Cabannes, H.; Hong Tiem, D.
1987-01-01
For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr
Exact Solution and Exotic Fluid in Cosmology
Directory of Open Access Journals (Sweden)
Phillial Oh
2012-09-01
Full Text Available We investigate cosmological consequences of nonlinear sigma model coupled with a cosmological fluid which satisfies the continuity equation. The target space action is of the de Sitter type and is composed of four scalar fields. The potential which is a function of only one of the scalar fields is also introduced. We perform a general analysis of the ensuing cosmological equations and give various critical points and their properties. Then, we show that the model exhibits an exact cosmological solution which yields a transition from matter domination into dark energy epoch and compare it with the Λ-CDM behavior. Especially, we calculate the age of the Universe and show that it is consistent with the observational value if the equation of the state ωf of the cosmological fluid is within the range of 0.13 < ωf < 0.22. Some implication of this result is also discussed.
A search for exact superstring vacua
Peterman, Andreas; Zichichi, Antonino
1994-01-01
We investigate $2d$ sigma-models with a $2+N$ dimensional Minkowski signature target space metric and Killing symmetry, specifically supersymmetrized, and see under which conditions they might lead to corresponding exact string vacua. It appears that the issue relies heavily on the properties of the vector $M_{\\mu}$, a reparametrization term, which needs to possess a definite form for the Weyl invariance to be satisfied. We give, in the $n = 1$ supersymmetric case, two non-renormalization theorems from which we can relate the $u$ component of $M_{\\mu}$ to the $\\beta^G_{uu}$ function. We work out this $(u,u)$ component of the $\\beta^G$ function and find a non-vanishing contribution at four loops. Therefore, it turns out that at order $\\alpha^{\\prime 4}$, there are in general non-vanishing contributions to $M_u$ that prevent us from deducing superstring vacua in closed form.
Interference-exact radiative transfer equation
DEFF Research Database (Denmark)
Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani
2017-01-01
Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... and scattering coefficients derived from the recently introduced quantized fluctuational electrodynamics (QFED) framework. In addition to describing the nonlocal optical interference processes as local directionally resolved effects, this allows reformulating the well known and widely used radiative transfer...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices....
Exact iterative reconstruction for the interior problem
International Nuclear Information System (INIS)
Zeng, Gengsheng L; Gullberg, Grant T
2009-01-01
There is a trend in single photon emission computed tomography (SPECT) that small and dedicated imaging systems are becoming popular. For example, many companies are developing small dedicated cardiac SPECT systems with different designs. These dedicated systems have a smaller field of view (FOV) than a full-size clinical system. Thus data truncation has become the norm rather than the exception in these systems. Therefore, it is important to develop region of interest (ROI) reconstruction algorithms using truncated data. This paper is a stepping stone toward this direction. This paper shows that the common generic iterative image reconstruction algorithms are able to exactly reconstruct the ROI under the conditions that the convex ROI is fully sampled and the image value in a sub-region within the ROI is known. If the ROI includes a sub-region that is outside the patient body, then the conditions can be easily satisfied.
Exact solutions to operator differential equations
International Nuclear Information System (INIS)
Bender, C.M.
1992-01-01
In this talk we consider the Heisenberg equations of motion q = -i(q, H), p = -i(p, H), for the quantum-mechanical Hamiltonian H(p, q) having one degree of freedom. It is a commonly held belief that such operator differential equations are intractable. However, a technique is presented here that allows one to obtain exact, closed-form solutions for huge classes of Hamiltonians. This technique, which is a generalization of the classical action-angle variable methods, allows us to solve, albeit formally and implicitly, the operator differential equations of two anharmonic oscillators whose Hamiltonians are H = p 2 /2 + q 4 /4 and H = p 4 /4 + q 4 /4
Exactly soluble QCD and confinement of quarks
International Nuclear Information System (INIS)
Rusakov, B.
1997-01-01
An exactly soluble non-perturbative model of the pure gauge QCD is derived as a weak coupling limit of the lattice theory in plaquette formulation [B. Rusakov, Phys. Lett. B 398 (1997) 331]. The model represents QCD as a theory of the weakly interacting field strength fluxes. The area law behavior of the Wilson loop average is a direct result of this representation: the total flux through macroscopic loop is the additive (due to the weakness of the interaction) function of the elementary fluxes. The compactness of the gauge group is shown to be the factor which prevents the elementary fluxes contributions from cancellation. There is no area law in the non-compact theory. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr [Department of Chemistry, Atatürk University, Erzurum 25240, Turkey and Department of Chemistry, Middle East Technical University, Ankara 06800 (Turkey)
2014-09-28
General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.
Exact classical scaling formalism for nonreactive processes
International Nuclear Information System (INIS)
DePristo, A.E.
1981-01-01
A general nonreactive collision system is considered with internal molecular variables (p, r) and/or (I, theta) of arbitrary dimensions and relative translational variables (P, R) of three or less dimensions. We derive an exact classical scaling formalism which relates the collisional change in any function of molecular variables directly to the initial values of these variables. The collision dynamics is then described by an explicit function of the initial point in the internal molecular phase space, for a fixed point in the relative translational phase space. In other words, the systematic variation of the internal molecular properties (e.g., actions and average internal kinetic energies) is given as a function of the initial internal action-angle variables. A simple three term approximation to the exact formalism is derived, the natural variables of which are the internal action I and internal linear momenta p. For the final average internal kinetic energies T, the result is T-T/sup( 0 ) = α+βp/sup( 0 )+γI/sup( 0 ), where the superscripted ''0'' indicates the initial value. The parameters α, β, and γ in this scaling theory are directly related to the moments of the change in average internal kinetic energy. Utilizing a very limited number of input moments generated from classical trajectory calculations, the scaling can be used to predict the entire distribution of final internal variables as a function of initial internal actions and linear momenta. Initial examples for atom--collinear harmonic oscillator collision systems are presented in detail, with the scaling predictions (e.g., moments and quasiclassical histogram transition probabilities) being generally very good to excellent quantitatively
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.
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)
Jargalsaikhan, Bolor
Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out
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 treatment of mode locking for a piecewise linear map
International Nuclear Information System (INIS)
Ding, E.J.; Hemmer, P.C.
1987-01-01
A piecewise linear map with one discontinuity is studied by analytic means in the two-dimensional parameter space. When the slope of the map is less than unity, periodic orbits are present, and they give the precise symbolic dynamic classification of these. The localization of the periodic domains in parameter space is given by closed expressions. The winding number forms a devil's terrace, a two-dimensional function whose cross sections are complete devil's staircases. In such a cross section the complementary set to the periodic intervals is a Cantor set with dimension D = 0
Exact solitary waves of the Korteveg - de Vries - Burgers equation
Kudryashov, N. A.
2004-01-01
New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.
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....
Exact solution to the moment problem for the XY chain
International Nuclear Information System (INIS)
Witte, N.S.
1996-01-01
We present the exact solution to the moment problem for the spin-1/2 isotropic antiferromagnetic XY chain with explicit forms for the moments with respect to the Neel state, the cumulant generating function, and the Resolvent Operator. We verify the correctness of the Horn-Weinstein Theorems, but the analytic structure of the generating function (e -tH ) in the complex t-plane is quite different from that assumed by the t-Expansion and the Connected Moments Expansion due to the vanishing gap. This function has a finite radius of convergence about t = 0, and for large 't' has a leading descending algebraic series E(t)-E o ∼ At -2 . The Resolvent has a branch cut and essential singularity near the ground state energy of the form G(s)/s∼B|s+1| -3/4 exp(C|s+1| 1/2 ). Consequently extrapolation strategies based on these assumptions are flawed and in practice we find that the CMX methods are pathological and cannot be applied, while numerical evidence for two of the t-expansion methods indicates a clear asymptotic convergence behaviour with truncation order. (author). 28 refs., 2 figs
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
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)
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.
Nonequilibrium Dynamics of Arbitrary-Range Ising Models with Decoherence: An Exact Analytic Solution
2013-04-03
C. Cross, Phys. Rev. Lett. 108, 023602 (2012). [4] B. Kraus, H. P. Büchler, S. Diehl, A. Kantian , A. Micheli, and P. Zoller, Phys. Rev. A 78...042307 (2008). 042101-7 FOSS-FEIG, HAZZARD, BOLLINGER, AND REY PHYSICAL REVIEW A 87, 042101 (2013) [5] S. Diehl, A. Micheli, A. Kantian , B. Kraus, H. P
Exact analytic solutions for a global equation of plant cell growth.
Pietruszka, Mariusz
2010-05-21
A generalization of the Lockhart equation for plant cell expansion in isotropic case is presented. The goal is to account for the temporal variation in the wall mechanical properties--in this case by making the wall extensibility a time dependent parameter. We introduce a time-differential equation describing the plant growth process with some key biophysical aspects considered. The aim of this work was to improve prior modeling efforts by taking into account the dynamic character of the plant cell wall with characteristics reminiscent of damped (aperiodic) motion. The equations selected to encapsulate the time evolution of the wall extensibility offer a new insight into the control of cell wall expansion. We find that the solutions to the time dependent second order differential equation reproduce much of the known experimental data for long- and short-time scales. Additionally, in order to support the biomechanical approach, a new growth equation based on the action of expansin proteins is proposed. Remarkably, both methods independently converge to the same kind, sigmoid-shaped, growth description functional V(t) proportional, exp(-exp(-t)), properly describing the volumetric growth and, consequently, growth rate as its time derivative. Copyright (c) 2010 Elsevier Ltd. All rights reserved.
Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium
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Jacopo De Nardis, Miłosz Panfil
2016-12-01
Full Text Available We study the density-density correlation function of the 1D Lieb-Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We achieve this by summing exactly over the relevant form factors of the density operator in the small momentum limit. The result is valid for any eigenstate, including thermal and non-thermal states. We also show that the small momentum limit of the dynamic structure factors obeys a generalized detailed balance relation valid for any equilibrium state.
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
Entanglement, decoherence and thermal relaxation in exactly solvable models
International Nuclear Information System (INIS)
Lychkovskiy, Oleg
2011-01-01
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression describing the evolution of the reduced density matrix. This expression proves to be tractable when the combined closed system (i.e. open system plus environment) is integrable. Then we focus on comparing decoherence and thermalization timescales in the XX chain. We find that for a single spin these timescales are comparable, in contrast to what should be expected for a macroscopic body. This indicates that the process of quantum relaxation of a system with few accessible states can not be separated in two distinct stages - decoherence and thermalization. Finally, we turn to finite-size effects in the time evolution of a single spin in the XY chain. We observe three consecutive stages of the evolution: regular evolution, partial revivals, irregular (apparently chaotic) evolution. The duration of the regular stage is proportional to the number of spins in the chain. We observe a 'quiet and cold period' in the end of the regular stage, which breaks up abruptly at some threshold time.
International Nuclear Information System (INIS)
Lazarides, N
2004-01-01
An analytical expression for the magnetic-field-dependent critical current I c (H) of Josephson junctions with periodically alternating critical current density J c (x) is derived within the uniform field approximation. Comparison with numerically calculated I c (H) patterns for junctions with identical, thick, periodically arranged defects with the corresponding analytical expression reveals fair agreement for a wide range of parameters, due to increased characteristic length. Based on qualitative arguments, we give the dependence of the new characteristic length on the geometrical parameters of the junction, which is in agreement with self-consistent calculations with the static sine-Gordon equation. The analytical expression captures the observed qualitative features of the I c (H) patterns, while it is practically exact for short junctions or high fields. It also produces the shift of the major peak from the zero-field position of the standard Fraunhofer pattern to another position related to the periodicity of the critical current density in φ-junctions
Duality invariant class of exact string backgrounds
Klimcík, C
1994-01-01
We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.
Exact-exchange-based quasiparticle calculations
International Nuclear Information System (INIS)
Aulbur, Wilfried G.; Staedele, Martin; Goerling, Andreas
2000-01-01
One-particle wave functions and energies from Kohn-Sham calculations with the exact local Kohn-Sham exchange and the local density approximation (LDA) correlation potential [EXX(c)] are used as input for quasiparticle calculations in the GW approximation (GWA) for eight semiconductors. Quasiparticle corrections to EXX(c) band gaps are small when EXX(c) band gaps are close to experiment. In the case of diamond, quasiparticle calculations are essential to remedy a 0.7 eV underestimate of the experimental band gap within EXX(c). The accuracy of EXX(c)-based GWA calculations for the determination of band gaps is as good as the accuracy of LDA-based GWA calculations. For the lowest valence band width a qualitatively different behavior is observed for medium- and wide-gap materials. The valence band width of medium- (wide-) gap materials is reduced (increased) in EXX(c) compared to the LDA. Quasiparticle corrections lead to a further reduction (increase). As a consequence, EXX(c)-based quasiparticle calculations give valence band widths that are generally 1-2 eV smaller (larger) than experiment for medium- (wide-) gap materials. (c) 2000 The American Physical Society
Generalized exact holographic mapping with wavelets
Lee, Ching Hua
2017-12-01
The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic N -dimensional lattice system to a (N +1 )-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high-pass wavelet filter is revealed to be proportional to the radius of the dual anti-de Sitter space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.
STELLAR: fast and exact local alignments
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Weese David
2011-10-01
Full Text Available Abstract Background Large-scale comparison of genomic sequences requires reliable tools for the search of local alignments. Practical local aligners are in general fast, but heuristic, and hence sometimes miss significant matches. Results We present here the local pairwise aligner STELLAR that has full sensitivity for ε-alignments, i.e. guarantees to report all local alignments of a given minimal length and maximal error rate. The aligner is composed of two steps, filtering and verification. We apply the SWIFT algorithm for lossless filtering, and have developed a new verification strategy that we prove to be exact. Our results on simulated and real genomic data confirm and quantify the conjecture that heuristic tools like BLAST or BLAT miss a large percentage of significant local alignments. Conclusions STELLAR is very practical and fast on very long sequences which makes it a suitable new tool for finding local alignments between genomic sequences under the edit distance model. Binaries are freely available for Linux, Windows, and Mac OS X at http://www.seqan.de/projects/stellar. The source code is freely distributed with the SeqAn C++ library version 1.3 and later at http://www.seqan.de.
Exact renormalization group for gauge theories
International Nuclear Information System (INIS)
Balaban, T.; Imbrie, J.; Jaffe, A.
1984-01-01
Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study
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.
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)
Nguyen, Tien Long; Sansour, Carlo; Hjiaj, Mohammed
2017-05-01
In this paper, an energy-momentum method for geometrically exact Timoshenko-type beam is proposed. The classical time integration schemes in dynamics are known to exhibit instability in the non-linear regime. The so-called Timoshenko-type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known Bernoulli-type model. The treatment of the Bernoulli-model has been recently addressed by the authors. In this present work, we extend our approach of using the strain rates to define the strain fields to in-plane geometrically exact Timoshenko-type beams. The large rotational degrees of freedom are exactly computed. The well-known enhanced strain method is used to avoid locking phenomena. Conservation of energy, momentum and angular momentum is proved formally and numerically. The excellent performance of the formulation will be demonstrated through a range of examples.
A new exact quantum mechanical propagator
Wiegel, F.W.; van Andel, P.W.
1987-01-01
The authors derive a closed-form expression for the time-dependent propagator for a quantum mechanical particle which is subject to an external force which is the sum of (i) a reflecting half-plane barrier with a straight edge, and (ii) a harmonic force pointing towards a point of the edge. This new
Toward an exact formulation of special relativity
International Nuclear Information System (INIS)
Kajfosz, J.
1982-01-01
In order to clear up some controversial problems of special relativity new terms for the expression of inertial motion are introduced and it is showed that although the descriptions of two identical physical systems moving with respect to one another can be equal, their physical states differ. Some epistemological consequences of this fact are briefly discussed. (author)
Dilatonic imprints on exact gravitational wave signatures
McCarthy, Fiona; KubizÅák, David; Mann, Robert B.
2018-05-01
By employing the moduli space approximation, we analytically calculate the gravitational wave signatures emitted upon the merger of two extremally charged dilatonic black holes. We probe several values of the dilatonic coupling constant a , and find significant departures from the Einstein-Maxwell (a =0 ) counterpart studied in [Phys. Rev. D 96, 061501 (2017), 10.1103/PhysRevD.96.061501]. For (low-energy) string theory black holes (a =1 ) there are no coalescence orbits and only a memory effect is observed, whereas for an intermediate value of the coupling (a =1 /√{3 } ) the late-time merger signature becomes exponentially suppressed, compared to the polynomial decay in the a =0 case without a dilaton. Such an imprint shows a clear difference between the case with and without a scalar field (as, for example, predicted by string theory) in black hole mergers.
Exact Identification of a Quantum Change Point
Sentís, Gael; Calsamiglia, John; Muñoz-Tapia, Ramon
2017-10-01
The detection of change points is a pivotal task in statistical analysis. In the quantum realm, it is a new primitive where one aims at identifying the point where a source that supposedly prepares a sequence of particles in identical quantum states starts preparing a mutated one. We obtain the optimal procedure to identify the change point with certainty—naturally at the price of having a certain probability of getting an inconclusive answer. We obtain the analytical form of the optimal probability of successful identification for any length of the particle sequence. We show that the conditional success probabilities of identifying each possible change point show an unexpected oscillatory behavior. We also discuss local (online) protocols and compare them with the optimal procedure.
So what exactly is nursing knowledge?
Clarke, L
2011-06-01
This paper aims to present a discussion about intrinsic nursing knowledge. The paper stems from the author's study of knowledge claims enshrined in nursing journal articles, books and conference speeches. It is argued that claims by academic nurses have largely depended on principles drawn from continental and not Analytic (British-American) philosophy. Thus, claims are credible only insofar as they defer propositional logic. This is problematic inasmuch as nursing is a practice-based activity usually carried out in medical settings. Transpersonal nursing models are particularly criticizable in respect of their unworldly character as are also concepts based on shallow usages of physics or mathematics. I argue that sensible measurements of the 'real world' are possible--without endorsing positivism--and that nursing requires little recourse to logically unsustainable claims. The paper concludes with an analysis of a recent review of nursing knowledge, which analysis indicates the circularity that attends many discussions on the topic. © 2011 Blackwell Publishing.
Exact sampling hardness of Ising spin models
Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.
2017-09-01
We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.
Topological mass mechanism and exact fields mapping
International Nuclear Information System (INIS)
Amaral, R L P G; Ventura, O S; Buffon, L O; Costa, J V
2006-01-01
We present a class of mappings between models with topological mass mechanism and purely topological models in arbitrary dimensions. These mappings are established by directly mapping the fields of one model in terms of the fields of the other model in closed expressions. These expressions provide the mappings of their actions as well as the mappings of their propagators. For a general class of models in which the topological model becomes the BF model the mappings present arbitrary functions which otherwise are absent for Chern-Simons like actions. This work generalizes the results of (Ventura O S, Amaral R L P G, Costa J V, Buffon L O and Lemes V E R 2004 J. Phys. A: Math. Gen. 37 11711-23) for arbitrary dimensions
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
Berk, Alexander
2013-03-01
Exact expansions for Voigt line-shape total, line-tail and spectral bin equivalent widths and for Voigt finite spectral bin single-line transmittances have been derived in terms of optical depth dependent exponentially-scaled modified Bessel functions of integer order and optical depth independent Fourier integral coefficients. The series are convergent for the full range of Voigt line-shapes, from pure Doppler to pure Lorentzian. In the Lorentz limit, the expansion reduces to the Ladenburg and Reiche function for the total equivalent width. Analytic expressions are derived for the first 8 Fourier coefficients for pure Lorentzian lines, for pure Doppler lines and for Voigt lines with at most moderate Doppler dependence. A strong-line limit sum rule on the Fourier coefficients is enforced to define an additional Fourier coefficient and to optimize convergence of the truncated expansion. The moderate Doppler dependence scenario is applicable to and has been implemented in the MODTRAN5 atmospheric band model radiative transfer software. Finite-bin transmittances computed with the truncated expansions reduce transmittance residuals compared to the former Rodgers-Williams equivalent width based approach by ∼2 orders of magnitude.
International Nuclear Information System (INIS)
Sokolow, Adam; Sen, Surajit
2007-01-01
An energy pulse refers to a spatially compact energy bundle. In nonlinear pulse propagation, the nonlinearity of the relevant dynamical equations could lead to pulse propagation that is nondispersive or weakly dispersive in space and time. Nonlinear pulse propagation through layered media with widely varying pulse transmission properties is not wave-like and a problem of broad interest in many areas such as optics, geophysics, atmospheric physics and ocean sciences. We study nonlinear pulse propagation through a semi-infinite sequence of layers where the layers can have arbitrary energy transmission properties. By assuming that the layers are rigid, we are able to develop exact expressions for the backscattered energy received at the surface layer. The present study is likely to be relevant in the context of energy transport through soil and similar complex media. Our study reveals a surprising connection between the problem of pulse propagation and the number patterns in the well known Pascal's and Catalan's triangles and hence provides an analytic benchmark in a challenging problem of broad interest. We close with comments on the relationship between this study and the vast body of literature on the problem of wave localization in disordered systems
Upper bounds on minimum cardinality of exact and approximate reducts
Chikalov, Igor
2010-01-01
In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.
A class of exact solutions to the Einstein field equations
International Nuclear Information System (INIS)
Goyal, Nisha; Gupta, R K
2012-01-01
The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)
Dynamically triangulated surfaces - some analytical results
International Nuclear Information System (INIS)
Kostov, I.K.
1987-01-01
We give a brief review of the analytical results concerning the model of dynamically triangulated surfaces. We will discuss the possible types of critical behaviour (depending on the dimension D of the embedding space) and the exact solutions obtained for D=0 and D=-2. The latter are important as a check of the Monte Carlo simulations applyed to study the model in more physical dimensions. They give also some general insight of its critical properties
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.)
An Exact Solution to the Central Core Model of the Renal Medulla
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.
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.
Analytic Models of Brown Dwarfs and the Substellar Mass Limit
Directory of Open Access Journals (Sweden)
Sayantan Auddy
2016-01-01
Full Text Available We present the analytic theory of brown dwarf evolution and the lower mass limit of the hydrogen burning main-sequence stars and introduce some modifications to the existing models. We give an exact expression for the pressure of an ideal nonrelativistic Fermi gas at a finite temperature, therefore allowing for nonzero values of the degeneracy parameter. We review the derivation of surface luminosity using an entropy matching condition and the first-order phase transition between the molecular hydrogen in the outer envelope and the partially ionized hydrogen in the inner region. We also discuss the results of modern simulations of the plasma phase transition, which illustrate the uncertainties in determining its critical temperature. Based on the existing models and with some simple modification, we find the maximum mass for a brown dwarf to be in the range 0.064M⊙–0.087M⊙. An analytic formula for the luminosity evolution allows us to estimate the time period of the nonsteady state (i.e., non-main-sequence nuclear burning for substellar objects. We also calculate the evolution of very low mass stars. We estimate that ≃11% of stars take longer than 107 yr to reach the main sequence, and ≃5% of stars take longer than 108 yr.
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.
The exact wavefunction factorization of a vibronic coupling system
International Nuclear Information System (INIS)
Chiang, Ying-Chih; Klaiman, Shachar; Otto, Frank; Cederbaum, Lorenz S.
2014-01-01
We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation
EXACT SOLUTION TO FINITE TEMPERATURE SFDM: NATURAL CORES WITHOUT FEEDBACK
International Nuclear Information System (INIS)
Robles, Victor H.; Matos, T.
2013-01-01
Recent high-quality observations of low surface brightness (LSB) galaxies have shown that their dark matter (DM) halos prefer flat central density profiles. However, the standard cold dark matter model simulations predict a more cuspy behavior. One mechanism used to reconcile the simulations with the observed data is the feedback from star formation. While this mechanism may be successful in isolated dwarf galaxies, its success in LSB galaxies remains unclear. Additionally, the inclusion of too much feedback in the simulations is a double-edged sword—in order to obtain a cored DM distribution from an initially cuspy one, the feedback recipes usually require one to remove a large quantity of baryons from the center of the galaxies; however, some feedback recipes produce twice the number of satellite galaxies of a given luminosity and with much smaller mass-to-light ratios from those that are observed. Therefore, one DM profile that produces cores naturally and that does not require large amounts of feedback would be preferable. We find both requirements to be satisfied in the scalar field dark matter model. Here, we consider that DM is an auto-interacting real scalar field in a thermal bath at temperature T with an initial Z 2 symmetric potential. As the universe expands, the temperature drops so that the Z 2 symmetry is spontaneously broken and the field rolls down to a new minimum. We give an exact analytic solution to the Newtonian limit of this system, showing that it can satisfy the two desired requirements and that the rotation curve profile is no longer universal.
Exact tensor network ansatz for strongly interacting systems
Zaletel, Michael P.
It appears that the tensor network ansatz, while not quite complete, is an efficient coordinate system for the tiny subset of a many-body Hilbert space which can be realized as a low energy state of a local Hamiltonian. However, we don't fully understand precisely which phases are captured by the tensor network ansatz, how to compute their physical observables (even numerically), or how to compute a tensor network representation for a ground state given a microscopic Hamiltonian. These questions are algorithmic in nature, but their resolution is intimately related to understanding the nature of quantum entanglement in many-body systems. For this reason it is useful to compute the tensor network representation of various `model' wavefunctions representative of different phases of matter; this allows us to understand how the entanglement properties of each phase are expressed in the tensor network ansatz, and can serve as test cases for algorithm development. Condensed matter physics has many illuminating model wavefunctions, such as Laughlin's celebrated wave function for the fractional quantum Hall effect, the Bardeen-Cooper-Schrieffer wave function for superconductivity, and Anderson's resonating valence bond ansatz for spin liquids. This thesis presents some results on exact tensor network representations of these model wavefunctions. In addition, a tensor network representation is given for the time evolution operator of a long-range one-dimensional Hamiltonian, which allows one to numerically simulate the time evolution of power-law interacting spin chains as well as two-dimensional strips and cylinders.
General Exact Solution to the Problem of the Probability Density for Sums of Random Variables
Tribelsky, Michael I.
2002-07-01
The exact explicit expression for the probability density pN(x) for a sum of N random, arbitrary correlated summands is obtained. The expression is valid for any number N and any distribution of the random summands. Most attention is paid to application of the developed approach to the case of independent and identically distributed summands. The obtained results reproduce all known exact solutions valid for the, so called, stable distributions of the summands. It is also shown that if the distribution is not stable, the profile of pN(x) may be divided into three parts, namely a core (small x), a tail (large x), and a crossover from the core to the tail (moderate x). The quantitative description of all three parts as well as that for the entire profile is obtained. A number of particular examples are considered in detail.
Analytic approximations for inside-outside interferometry
Energy Technology Data Exchange (ETDEWEB)
Padula, S.S.; Gyulassy, M. (Lawrence Berkeley Lab., CA (USA). Nuclear Science Div.)
1990-07-30
Analytical expressions for pion interferometry are derived illustrating the competing effects of various non-ideal aspects of inside-outside cascade dynamics at energies {proportional to}200 AGeV. (orig.).
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
Analytical maximum-likelihood method to detect patterns in real networks
International Nuclear Information System (INIS)
Squartini, Tiziano; Garlaschelli, Diego
2011-01-01
In order to detect patterns in real networks, randomized graph ensembles that preserve only part of the topology of an observed network are systematically used as fundamental null models. However, the generation of them is still problematic. Existing approaches are either computationally demanding and beyond analytic control or analytically accessible but highly approximate. Here, we propose a solution to this long-standing problem by introducing a fast method that allows one to obtain expectation values and standard deviations of any topological property analytically, for any binary, weighted, directed or undirected network. Remarkably, the time required to obtain the expectation value of any property analytically across the entire graph ensemble is as short as that required to compute the same property using the adjacency matrix of the single original network. Our method reveals that the null behavior of various correlation properties is different from what was believed previously, and is highly sensitive to the particular network considered. Moreover, our approach shows that important structural properties (such as the modularity used in community detection problems) are currently based on incorrect expressions, and provides the exact quantities that should replace them.
Exact Boundary Controllability of Electromagnetic Fields in a General Region
International Nuclear Information System (INIS)
Eller, M. M.; Masters, J. E.
2002-01-01
We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which reduces the proof of exact controllability to the proof of continuous observability for the homogeneous adjoint system. There is no geometric restriction imposed on the domain
Exact solution for the generalized Telegraph Fisher's equation
International Nuclear Information System (INIS)
Abdusalam, H.A.; Fahmy, E.S.
2009-01-01
In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.
Exact solutions of some nonlinear partial differential equations using ...
Indian Academy of Sciences (India)
The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...
Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions
Directory of Open Access Journals (Sweden)
Armando Martínez-Pérez
2017-10-01
Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.
Exact Cover Problem in Milton Babbitt's All-partition Array
DEFF Research Database (Denmark)
Bemman, Brian; Meredith, David
2015-01-01
One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set...
New exact solutions of the Dirac equation. 11
International Nuclear Information System (INIS)
Bagrov, V.G.; Noskov, M.D.
1984-01-01
Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found
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
Energy vs. density on paths toward exact density functionals
DEFF Research Database (Denmark)
Kepp, Kasper Planeta
2018-01-01
Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness...
Exact traveling wave solutions of the Boussinesq equation
International Nuclear Information System (INIS)
Ding Shuangshuang; Zhao Xiqiang
2006-01-01
The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained
Exact results for the Kuramoto model with a bimodal frequency distribution
DEFF Research Database (Denmark)
Martens, Erik Andreas; Barreto, E.; Strogatz, S. H.
2009-01-01
weighted Lorentzians. Using an ansatz recently discov- ered by Ott and Antonsen, we show that in this case the infinite-dimensional problem reduces exactly to a flow in four dimensions. Depending on the parameters and initial conditions, the long-term dynamics evolves to one of three states: incoherence......, where all the oscillators are desynchronized; partial synchrony, where a macro- scopic group of phase-locked oscillators coexists with a sea of desynchronized ones; and a standing wave state, where two counter-rotating groups of phase-locked oscillators emerge. Analytical results are presented...
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.
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
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.
Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model
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.
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
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.
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.
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.
Exactly integrable two-dimensional dynamical systems related with supersymmetric algebras
International Nuclear Information System (INIS)
Leznov, A.N.
1983-01-01
A wide class of exactly integrable dynamical systems in two-dimensional space related with superalgebras, which generalize supersymmetric Liouville equation, is constructed. The equations can be interpretated as nonlinearly interacting Bose and Fermi fields belonging within classical limit to even and odd parts of the Grassman space. Explicit expressions for the solutions of the constructed systems are obtained on the basis of standard perturbation theory
Directory of Open Access Journals (Sweden)
Wei Li
2014-01-01
Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.
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