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Sample records for exact analytic description

  1. 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.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2014-06-15

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

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

    Science.gov (United States)

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

    2014-06-01

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

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

    International Nuclear Information System (INIS)

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

    2014-01-01

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

  5. Quantum decay model with exact explicit analytical solution

    Science.gov (United States)

    Marchewka, Avi; Granot, Er'El

    2009-01-01

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

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

    DEFF Research Database (Denmark)

    Nørrelykke, Simon F; Flyvbjerg, Henrik

    2011-01-01

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

  7. 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

  8. A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

    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.

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

    International Nuclear Information System (INIS)

    Lode, Axel U.J.

    2013-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

    Lode, Axel U.J.

    2013-06-03

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

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

    International Nuclear Information System (INIS)

    Baxter, Mathew; Van Gorder, Robert A

    2013-01-01

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

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

    Science.gov (United States)

    Saengow, C.; Giacomin, A. J.

    2017-12-01

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

  13. Exact coherent structures in an asymptotically reduced description of parallel shear flows

    Science.gov (United States)

    Beaume, Cédric; Knobloch, Edgar; Chini, Gregory P.; Julien, Keith

    2015-02-01

    A reduced description of shear flows motivated by the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow (Wang J, Gibson J and Waleffe F 2007 Phys. Rev. Lett. 98 204501) is constructed. Exact time-independent nonlinear solutions of the reduced equations corresponding to both lower and upper branch states are found for a sinusoidal, body-forced shear flow. The lower branch solution is characterized by fluctuations that vary slowly along the critical layer while the upper branch solutions display a bimodal structure and are more strongly focused on the critical layer. The reduced equations provide a rational framework for investigations of subcritical spatiotemporal patterns in parallel shear flows.

  14. Exact coherent structures in an asymptotically reduced description of parallel shear flows

    International Nuclear Information System (INIS)

    Beaume, Cédric; Knobloch, Edgar; Chini, Gregory P; Julien, Keith

    2015-01-01

    A reduced description of shear flows motivated by the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow (Wang J, Gibson J and Waleffe F 2007 Phys. Rev. Lett. 98 204501) is constructed. Exact time-independent nonlinear solutions of the reduced equations corresponding to both lower and upper branch states are found for a sinusoidal, body-forced shear flow. The lower branch solution is characterized by fluctuations that vary slowly along the critical layer while the upper branch solutions display a bimodal structure and are more strongly focused on the critical layer. The reduced equations provide a rational framework for investigations of subcritical spatiotemporal patterns in parallel shear flows. (paper)

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

    CERN Document Server

    Meleshko, Sergey V

    2005-01-01

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

  16. Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

    Energy Technology Data Exchange (ETDEWEB)

    Sharma, Pankaj, E-mail: psharma@rtu.ac.in; Parashar, Sandeep Kumar, E-mail: parashar2@yahoo.com [Mechanical Engineering Department, Rajasthan Technical University, Kota (India)

    2016-05-06

    The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.

  17. The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

    Science.gov (United States)

    Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.

    2018-04-01

    We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

  18. New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

    Science.gov (United States)

    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.

  19. 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)

  20. Descriptive and analytic epidemiology. Bridges to cancer control

    International Nuclear Information System (INIS)

    Mettlin, C.

    1988-01-01

    Epidemiology serves as a bridge between basic science and cancer control. The two major orientations of epidemiology are descriptive and analytic. The former is useful in assessing the scope and dimensions of the cancer problem and the latter is used to assess environmental and lifestyle sources of cancer risk. A recent development in descriptive epidemiology is the use of functional measures of disease such as lost life expectancy. In analytical epidemiology, there is new or renewed interest in several lifestyle factors including diet and exercise as well as environmental factors such as involuntary tobacco exposure and radon in dwellings. Review of the evidence should consider the strengths and weaknesses of different research procedures. Each method is inconclusive by itself but, the different research designs of epidemiology collectively may represent a hierarchy of proof. Although the roles of many factors remain to be defined, the aggregate epidemiologic data continue to demonstrate the special importance of personal behavior and lifestyle in affecting cancer risk

  1. 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)

  2. 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)

  3. 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.

  4. 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.

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

    Science.gov (United States)

    Gai, Litao; Bilige, Sudao; Jie, Yingmo

    2016-01-01

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

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

    International Nuclear Information System (INIS)

    Segre, S. E.

    2001-01-01

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

  7. 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

  8. IBM Watson Analytics: Automating Visualization, Descriptive, and Predictive Statistics.

    Science.gov (United States)

    Hoyt, Robert Eugene; Snider, Dallas; Thompson, Carla; Mantravadi, Sarita

    2016-10-11

    . IBMWA is a new alternative for data analytics software that automates descriptive, predictive, and visual analytics. This program is very user-friendly but requires data preprocessing, statistical conceptual understanding, and domain expertise.

  9. 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)

  10. 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)

  11. Description of JNC's analytical method and its performance for FBR cores

    International Nuclear Information System (INIS)

    Ishikawa, M.

    2000-01-01

    The description of JNC's analytical method and its performance for FBR cores includes: an outline of JNC's Analytical System Compared with ERANOS; a standard data base for FBR Nuclear Design in JNC; JUPITER Critical Experiment; details of Analytical Method and Its Effects on JUPITER; performance of JNC Analytical System (effective multiplication factor k eff , control rod worth, and sodium void reactivity); design accuracy of a 600 MWe-class FBR Core. JNC developed a consistent analytical system for FBR core evaluation, based on JENDL library, f-table method, and three dimensional diffusion/transport theory, which includes comprehensive sensitivity tools to improve the prediction accuracy of core parameters. JNC system was verified by analysis of JUPITER critical experiment, and other facilities. Its performance can be judged quite satisfactory for FBR-core design work, though there is room for further improvement, such as more detailed treatment of cross-section resonance regions

  12. Analytical Description of the H/D Exchange Kinetic of Macromolecule.

    Science.gov (United States)

    Kostyukevich, Yury; Kononikhin, Alexey; Popov, Igor; Nikolaev, Eugene

    2018-04-17

    We present the accurate analytical solution obtained for the system of rate equations describing the isotope exchange process for molecules containing an arbitrary number of equivalent labile atoms. The exact solution was obtained using Mathematica 7.0 software, and this solution has the form of the time-dependent Gaussian distribution. For the case when forward exchange considerably overlaps the back exchange, it is possible to estimate the activation energy of the reaction by obtaining a temperature dependence of the reaction degree. Using a previously developed approach for performing H/D exchange directly in the ESI source, we have estimated the activation energies for ions with different functional groups and they were found to be in a range 0.04-0.3 eV. Since the value of the activation energy depends on the type of functional group, the developed approach can have potential analytical applications for determining types of functional groups in complex mixtures, such as petroleum, humic substances, bio-oil, and so on.

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

    Directory of Open Access Journals (Sweden)

    Md. Nur Alam

    2017-11-01

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

  14. Analytical methodology and facility description spent fuel policy

    Energy Technology Data Exchange (ETDEWEB)

    1978-08-01

    Three generic environmental impact statements (GEISs) on domestic fuels, foreign fuels, and storage charges are being prepared to provide environmental input into decisions on whether, and if so how the 1977 Presidential policy on spent fuel storage should be implmented. This report provides background information for two of these environmental impact statements: Storage of U.S. Spent Power Reactor Fuel and Storage of Foreign Spent Power Reactor Fuel. It includes the analytical methodology used in GEISs to assess the environmental effects and a description of the facilities used in the two GEISs.

  15. Analytical methodology and facility description spent fuel policy

    International Nuclear Information System (INIS)

    1978-08-01

    Three generic environmental impact statements (GEISs) on domestic fuels, foreign fuels, and storage charges are being prepared to provide environmental input into decisions on whether, and if so how the 1977 Presidential policy on spent fuel storage should be implmented. This report provides background information for two of these environmental impact statements: Storage of U.S. Spent Power Reactor Fuel and Storage of Foreign Spent Power Reactor Fuel. It includes the analytical methodology used in GEISs to assess the environmental effects and a description of the facilities used in the two GEISs

  16. Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium

    Science.gov (United States)

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

    2015-01-01

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

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

    Science.gov (United States)

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

    2014-01-01

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

  18. Exact work

    International Nuclear Information System (INIS)

    Zeger, J.

    1993-01-01

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

  19. 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

  20. Exact Slater integrals

    International Nuclear Information System (INIS)

    Golden, L.B.

    1968-01-01

    In atomic structure calculations, one has to evaluate the Slater integrals. In the present program, the authors evaluate exactly the Slater integral when hydrogenic wave functions are used for the bound-state orbitals. When hydrogenic wave functions are used, the Slater integrals involve integrands which can be written in the form of a product of an exponential, exp(ax) and a known analytic polynomial function, f(x). By repeated partial integration such an integral can be expressed in terms of a finite series involving the exponential, the polynomial function and its derivatives. PL/1-FORMAC has a built-in subroutine that will analytically find the derivatives of any multinomial. Thus, the finite series and hence the Slater integral can be evaluated analytically. (Auth.)

  1. 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.

  2. 40 CFR 90.421 - Dilute gaseous exhaust sampling and analytical system description.

    Science.gov (United States)

    2010-07-01

    ... gas mixture temperature, measured at a point immediately ahead of the critical flow venturi, must be... analytical system description. (a) General. The exhaust gas sampling system described in this section is... requirements are as follows: (1) This sampling system requires the use of a Positive Displacement Pump—Constant...

  3. Exact milestoning

    International Nuclear Information System (INIS)

    Bello-Rivas, Juan M.; Elber, Ron

    2015-01-01

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

  4. 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

  5. Analytical BPS Maxwell-Higgs Vortices

    International Nuclear Information System (INIS)

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

    2014-01-01

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

  6. Analytic description of the chemical erosion of graphite by hydrogen ions

    International Nuclear Information System (INIS)

    Roth, J.; Garcia-Rosales, C.

    1996-01-01

    One main concern about the use of graphite as a plasma facing material is the enhanced erosion, under hydrogen bombardment due to hydrocarbon formation. In view of the lifetime evaluation of plasma exposed carbon components and of impurity production in present and future machines such as ITER, an analytical expression for the erosion yield by chemical sputtering for the relevant energies, temperatures and incident fluxes is of special importance. An extrapolation to fluxes and energies relevant for high density divertor plasmas has not been possible up to now on the basis of semiempirical fits to laboratory data. Starting from a short review of the existing empirical formulas, recent detailed investigations of the atomistic processes for the thermally activated hydrocarbon emission are described, which enable the formulation of an improved analytical description including the ion flux as a parameter. The chemical erosion of graphite by hydrogen bombardment results from two processes: the thermally activated hydrocarbon emission, Y therm , and a surface process at low energies and low temperatures resulting from the kinetic ejection of surface hydrocarbon complexes from collisional energy transfer, Y surf . The new analytic description can be fitted well to the existing data for ion beam erosion, and extrapolation to divertor relevant fluxes is possible. At high ion fluxes the maximum of chemical erosion is shifted to higher temperatures, where annealing of damaged structures leads to a stronger reduction of Y therm than previously estimated. There are no data on a possible flux dependence of Y surf , leaving still some uncertainty in extrapolation. (author). 46 refs, 10 figs, 1 tab

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

    Science.gov (United States)

    Jabbari, Ali

    2018-01-01

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

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

    Science.gov (United States)

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

    2015-07-01

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

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

    Science.gov (United States)

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

    2015-01-01

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

  10. Quasi exact solution of the Rabi Hamiltonian

    CERN Document Server

    Koç, R; Tuetuencueler, H

    2002-01-01

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

  11. 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

  12. 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

  13. Exact theory of freeze-out

    Science.gov (United States)

    Cannoni, Mirco

    2015-03-01

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

  14. On truncations of the exact renormalization group

    CERN Document Server

    Morris, T R

    1994-01-01

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

  15. Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps

    International Nuclear Information System (INIS)

    Méndez-Bermúdez, J.A.; Oliveira, Juliano A. de; Leonel, Edson D.

    2016-01-01

    The critical dynamics near the transition from unlimited to limited action diffusion for two families of well known dissipative nonlinear maps, namely the dissipative standard and dissipative discontinuous maps, is characterized by the use of an analytical approach. The approach is applied to explicitly obtain the average squared action as a function of the (discrete) time and the parameters controlling nonlinearity and dissipation. This allows to obtain a set of critical exponents so far obtained numerically in the literature. The theoretical predictions are verified by extensive numerical simulations. We conclude that all possible dynamical cases, independently on the map parameter values and initial conditions, collapse into the universal exponential decay of the properly normalized average squared action as a function of a normalized time. The formalism developed here can be extended to many other different types of mappings therefore making the methodology generic and robust. - Highlights: • We analytically approach scaling properties of a family of two-dimensional dissipative nonlinear maps. • We derive universal scaling functions that were obtained before only approximately. • We predict the unexpected condition where diffusion and dissipation compensate each other exactly. • We find a new universal scaling function that embraces all possible dissipative behaviors.

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

    Czech Academy of Sciences Publication Activity Database

    Sasaki, R.; Znojil, Miloslav

    2016-01-01

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

  17. An analytical description of the low temperature behaviour of a weakly interacting Bose gas

    International Nuclear Information System (INIS)

    Su Guozhen; Chen Lixuan; Chen Jincan

    2004-01-01

    An analytical description of the low temperature behaviour of a trapped interacting Bose gas is presented by using a simple approach that is based on the principle of the constancy of chemical potentials in equilibrium and the local-density approximation. Several thermodynamic quantities, which include the ground-state fraction, chemical potential, total energy, entropy and heat capacity, are derived analytically. It is shown that the results obtained here are in excellent agreement with the experimental data and the theoretical predictions based on the numerical calculation. Meanwhile, by selecting a suitable variable, the divergent problem existing in some papers is solved

  18. Exact theory of freeze-out

    International Nuclear Information System (INIS)

    Cannoni, Mirco

    2015-01-01

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

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

    International Nuclear Information System (INIS)

    Mikata, Y.

    2014-01-01

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

  20. 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

  1. 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.

  2. Some exact velocity profiles for granular flow in converging hoppers

    Science.gov (United States)

    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.

  3. Exact theory of freeze-out

    Energy Technology Data Exchange (ETDEWEB)

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

    2015-03-01

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

  4. 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.

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

    Science.gov (United States)

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

    2018-03-01

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

  6. An accurate analytic description of neutrino oscillations in matter

    Science.gov (United States)

    Akhmedov, E. Kh.; Niro, Viviana

    2008-12-01

    A simple closed-form analytic expression for the probability of two-flavour neutrino oscillations in a matter with an arbitrary density profile is derived. Our formula is based on a perturbative expansion and allows an easy calculation of higher order corrections. The expansion parameter is small when the density changes relatively slowly along the neutrino path and/or neutrino energy is not very close to the Mikheyev-Smirnov-Wolfenstein (MSW) resonance energy. Our approximation is not equivalent to the adiabatic approximation and actually goes beyond it. We demonstrate the validity of our results using a few model density profiles, including the PREM density profile of the Earth. It is shown that by combining the results obtained from the expansions valid below and above the MSW resonance one can obtain a very good description of neutrino oscillations in matter in the entire energy range, including the resonance region.

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

    International Nuclear Information System (INIS)

    Garcia-Vicente, F.; Rodriguez, C.

    2000-01-01

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

  8. 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

  9. Black holes by analytic continuation

    CERN Document Server

    Amati, Daniele

    1997-01-01

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

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

    KAUST Repository

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

    2010-01-01

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

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

    KAUST Repository

    Yilmaz, Ferkan

    2010-09-01

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

  12. 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

  13. Exact solution for a non-Markovian dissipative quantum dynamics.

    Science.gov (United States)

    Ferialdi, Luca; Bassi, Angelo

    2012-04-27

    We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

  14. Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms

    International Nuclear Information System (INIS)

    Kharchenko, V.F.

    2015-01-01

    The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno–Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determine the polarizability of the atom in excited bound states. - Highlights: • A new description for electric polarization of hydrogen-like atoms. • Expression for multipole polarizabilities in terms of off-shell scattering functions. • Derivation of integral equation determining the off-shell scattering function. • Rigorous analytic solving the integral equations both for ground and excited states. • Study of contributions of virtual multiple scattering to electric polarizabilities

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

    Science.gov (United States)

    Alvarez, Orlando; Haddad, Matthew

    2018-03-01

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

  16. Developing an Emergency Physician Productivity Index Using Descriptive Health Analytics.

    Science.gov (United States)

    Khalifa, Mohamed

    2015-01-01

    Emergency department (ED) crowding became a major barrier to receiving timely emergency care. At King Faisal Specialist Hospital and Research Center, Saudi Arabia, we identified variables and factors affecting crowding and performance to develop indicators to help evaluation and improvement. Measuring efficiency of work and activity of throughput processes; it was important to develop an ED physician productivity index. Data on all ED patients' encounters over the last six months of 2014 were retrieved and descriptive health analytics methods were used. Three variables were identified for their influence on productivity and performance; Number of Treated Patients per Physician, Patient Acuity Level and Treatment Time. The study suggested a formula to calculate the productivity index of each physician through dividing the Number of Treated Patients by Patient Acuity Level squared and Treatment Time to identify physicians with low productivity index and investigate causes and factors.

  17. 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

  18. 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.

  19. Exact braneworld cosmology induced from bulk black holes

    International Nuclear Information System (INIS)

    Gregory, James P; Padilla, Antonio

    2002-01-01

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

  20. A Descriptive and Analytic Look at Marxs Own Explanations for the Falling Rate of Profit

    OpenAIRE

    Howard Petith

    2001-01-01

    Abstract: Marxs conclusions about the falling rate of profit have been analysed exhaustively. Usually this has been done by building models which broadly conform to Marxs views and then showing that his conclusions are either correct or, more frequently, that they can not be sustained. By contrast, this paper examines, both descriptively and analytically, Marxs arguments from the Hodgskin section of Theories of Surplus Value, the General Law section of the recently published Volume 33 of the ...

  1. A Descriptive and Analytic Look at Marx's Own Explanations for the Falling Rate of Profit

    OpenAIRE

    Petith, Howard

    2001-01-01

    Marx's conclusions about the falling rate of profit have been analysed exhaustively. Usually this has been done by building models which broadly conform to Marx's views and then showing that his conclusions are either correct or, more frequently, that they can not be sustained. By contrast, this paper examines, both descriptively and analytically, Marx's arguments from the Hodgskin section of Theories of Surplus Value, the General Law section of the recently published Volume 33 of the Collect...

  2. From continuum analytical description to discrete numerical modelling of localized fluidization in granular media

    Directory of Open Access Journals (Sweden)

    Puig i Montellà Eduard

    2017-01-01

    Full Text Available We present analytical and numerical results on localized fluidization within a granular layer subjected to a local injection of fluid. As the injection rate increases the three different regimes previously reported in the literature are recovered: homogeneous expansion of the bed, fluidized cavity in which fluidization starts developing above the injection area, and finally the chimney of fluidized grains when the fluidization zone reaches the free surface. The analytical approach is at the continuum scale, based on Darcy’s law and Therzaghi’s effective stress principle. It provides a good description of the phenomenon as long as the porosity of the granular assembly remains relatively homogeneous. The numerical approach is at the particle scale based on the coupled DEM-PFV method. It tackles the more heterogeneous situations which occur at larger injection rates. A direct link is evidenced between the occurrence of the different regimes of fluidization and the injection aperture. Finally, the merging of chimneys in case of two injection points is investigated.

  3. Exact Analytic Result of Contact Value for the Density in a Modified Poisson-Boltzmann Theory of an Electrical Double Layer.

    Science.gov (United States)

    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.

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

    Science.gov (United States)

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

    2013-04-01

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

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

    Science.gov (United States)

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

    2013-04-01

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

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

    KAUST Repository

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

    2010-01-01

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

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

    KAUST Repository

    Tourki, Kamel

    2010-11-01

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

  8. 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)

  9. Analytic descriptions of ion cyclotron absorption

    International Nuclear Information System (INIS)

    Bers, A.; Francis, G.; Fuchs, V.; Lashmore-Davies, C.N.; Ram, A.K.

    1987-05-01

    Analysis of energy propagation and absorption in ion-cyclotron heating of tokamak plasmas has relied on numerical solutions of fourth (and sixth) order differential equations for slab models of the plasma (poloidal) cross section. Realistic two-dimensional and fully toroidal geometry analyses would become quite unwieldy. It is shown here that the analysis of the slab model can be simplified considerably. A first-order differential equation is shown to describe the transmission coefficient for the fast wave, and it is solved analytically. A second order differential equation is shown to adequately describe both transmission and reflection. Conditions for ion absorption or mode conversion are derived. Including toroidal effects in propagation, conditions for electron absorption on the mode-converted ion-Bernstein waves are also described analytically

  10. Assessment the Relationship Between Parents' Literacy Level with Children Growth in Mashhad: An Analytic Descriptive Study

    Directory of Open Access Journals (Sweden)

    Masumeh Saeidi

    2013-12-01

    Full Text Available Introduction: Present children are the investments of community in the future. Preparing children health which leads to the stability of community health, provided to accurate implementation of educational and health programs in the community and especially in mothers. So it is necessary to determine the relationship between parents' literacy  with growth rate in children. Materials and Methods: This cross-sectional descriptive-analytic study was conducted on 300 mothers referring to 10 selected Mashhad health-care centers for monitoring their 6-24-month year old infants. They completed questionnaire. Participants were selected by cluster and simple random sampling. Data were analyzed by descriptive- analytic statistics and using SPSS 16. Results: Presentfindings showed a significant relationship between literacy  level of parents with child growth status, breast feeding rate, junk food consumption, referring to health care center for growth monitoring, the age of initiating supplementary nutrition, the use of oil and butter in baby food and rate of attending in educational classes. So that higher literacy  level of parents was associated with using more formula, less junk food, oil and butter in baby's food and more referring times to health care center for monitoring child growth, desirable growth, and  also initiating supplementary food more at the assigned time (p

  11. Assessment the Relationship between Parents' Literacy Level with Children Growth in Mashhad: An Analytic Descriptive Study

    Directory of Open Access Journals (Sweden)

    Bibi Leila Hoseini

    2014-04-01

    Full Text Available Introduction: Present children are the investments of community in the future. Preparing children health which leads to the stability of community health, provided to accurate implementation of educational and health programs in the community and especially in mothers. So it is necessary to determine the relationship between parents' literacy with growth rate in children.   Materials and Methods: This cross-sectional descriptive-analytic study was conducted on 300 mothers referring to 10 selected Mashhad health-care centers for monitoring their 6-24-month year old infants. They completed questionnaire. Participants were selected by cluster and simple random sampling. Data were analyzed by descriptive- analytic statistics and using SPSS 16.   Results: Presentfindings showed a significant relationship between literacy  level of parents with child growth status, breast feeding rate, junk food consumption, referring to health care center for growth monitoring, the age of initiating supplementary nutrition, the use of oil and butter in baby food and rate of attending in educational classes. So that higher literacy  level of parents was associated with using more formula, less junk food, oil and butter in baby's food and more referring times to health care center for monitoring child growth, desirable growth, and  also initiating supplementary food more at the assigned time (P

  12. 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.

  13. Exact analytical thermodynamic expressions for a Brownian heat engine

    Science.gov (United States)

    Taye, Mesfin Asfaw

    2015-09-01

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

  14. Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries

    Science.gov (United States)

    Savickas, David

    2015-04-01

    General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).

  15. 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

  16. Exact time-dependent exchange-correlation potentials for strong-field electron dynamics

    International Nuclear Information System (INIS)

    Lein, Manfred; Kuemmel, Stephan

    2005-01-01

    By solving the time-dependent Schroedinger equation and inverting the time-dependent Kohn-Sham scheme we obtain the exact time-dependent exchange-correlation potential of density-functional theory for the strong-field dynamics of a correlated system. We demonstrate that essential features of the exact exchange-correlation potential can be related to derivative discontinuities in stationary density-functional theory. Incorporating the discontinuity in a time-dependent density-functional calculation greatly improves the description of the ionization process

  17. Multi-scale modelling of ions in solution: from atomistic descriptions to chemical engineering

    International Nuclear Information System (INIS)

    Molina, J.J.

    2011-01-01

    Ions in solution play a fundamental role in many physical, chemical, and biological processes. The PUREX process used in the nuclear industry to the treatment of spent nuclear fuels is considered as an example. For industrial applications these systems are usually described using simple analytical models which are fitted to reproduce the available experimental data. In this work, we propose a multi-scale coarse graining procedure to derive such models from atomistic descriptions. First, parameters for classical force-fields of ions in solution are extracted from ab-initio calculations. Effective (McMillan-Mayer) ion-ion potentials are then derived from radial distribution functions measured in classical molecular dynamics simulations, allowing us to define an implicit solvent model of electrolytes. Finally, perturbation calculations are performed to define the best possible representation for these systems, in terms of charged hard-sphere models. Our final model is analytical and contains no free 'fitting' parameters. It shows good agreement with the exact results obtained from Monte-Carlo simulations for the thermodynamic and structural properties. Development of a similar model for the electrolyte viscosity, from information derived from atomistic descriptions, is also introduced. (author)

  18. 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)

  19. 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.)

  20. 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.

  1. 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.

  2. 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

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

    Science.gov (United States)

    Tsaur, Deng-How

    2010-06-01

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

  4. 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)

  5. 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

  6. 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.

  7. 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

  8. 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.)

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

    Science.gov (United States)

    Sasaki, Ryu

    2011-03-28

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

  10. Exact axially symmetric galactic dynamos

    Science.gov (United States)

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

    2018-05-01

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

  11. 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)

  12. A Descriptive and Analytic Look at Marxs Own Explanations for the Falling Rate of Profit (Long Version)

    OpenAIRE

    Petith, Howard

    2001-01-01

    Abstract: Marxs conclusions about the falling rate of profit have been analysed exhaustively. Usually this has been done by building models which broadly conform to Marxs views and then showing that his conclusions are either correct or, more frequently, that they can not be sustained. By contrast, this paper examines, both descriptively and analytically, Marxs arguments from the Hodgskin section of Theories of Surplus Value, the General Law section of the recently published Volume 33 of the ...

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

    KAUST Repository

    Xia, Minghua

    2012-10-01

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

  14. 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

  15. Exact Mass-Coupling Relation for the Homogeneous Sine-Gordon Model.

    Science.gov (United States)

    Bajnok, Zoltán; Balog, János; Ito, Katsushi; Satoh, Yuji; Tóth, Gábor Zsolt

    2016-05-06

    We derive the exact mass-coupling relation of the simplest multiscale quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass scales. The relation is obtained by comparing the perturbed conformal field theory description of the model valid at short distances to the large distance bootstrap description based on the model's integrability. In particular, we find a differential equation for the relation by constructing conserved tensor currents, which satisfy a generalization of the Θ sum rule Ward identity. The mass-coupling relation is written in terms of hypergeometric functions.

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

    Science.gov (United States)

    Kast, Stefan M; Tomazic, Daniel

    2012-11-07

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

  17. 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

  18. The shadow of black holes an analytic description

    CERN Document Server

    Grenzebach, Arne

    2016-01-01

    This book introduces an analytic method to describe the shadow of black holes. As an introduction, it presents a survey of the attempts to observe the shadow of galactic black holes. Based on a detailed discussion of the Plebański–Demiański class of space-times, the book derives analytical formulas for the photon regions and for the boundary curve of the shadow as seen by an observer in the domain of outer communication. It also analyzes how the shadow depends on the motion of the observer. For all cases, the photon regions and shadows are visualized for various values of the parameters. Finally, it considers how the analytical formulas can be used for calculating the horizontal and vertical angular diameters of the shadow, and estimates values for the black holes at the centers of our Galaxy near Sgr A* and of the neighboring galaxy M87.

  19. 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.

  20. 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.

  1. 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.

  2. 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.)

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

    Science.gov (United States)

    Brax, Philippe; Pitschmann, Mario

    2018-03-01

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

  4. Quasi-exact solvability

    International Nuclear Information System (INIS)

    Ushveridze, A.G.

    1992-01-01

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

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

    International Nuclear Information System (INIS)

    Ikhdair, S.M.; Sever, R.

    2007-01-01

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

  6. 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)

  7. ExactPack Documentation

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-05-09

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

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

    CERN Document Server

    Zvyagin, A A

    2002-01-01

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

  9. Exact solutions to chaotic and stochastic systems

    Science.gov (United States)

    González, J. A.; Reyes, L. I.; Guerrero, L. E.

    2001-03-01

    We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.

  10. 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.

  11. 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.

  12. 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

  13. Explicit analytical solution of the nonlinear Vlasov Poisson system

    International Nuclear Information System (INIS)

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

    1993-10-01

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

  14. 3D Analytical Calculation of Forces between Linear Halbach-Type Permanent Magnet Arrays

    OpenAIRE

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

    2009-01-01

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

  15. Intermittency inhibited by transport: An exactly solvable model

    Science.gov (United States)

    Zanette, Damián H.

    1994-04-01

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

  16. Communication: Density functional theory model for multi-reference systems based on the exact-exchange hole normalization.

    Science.gov (United States)

    Laqua, Henryk; Kussmann, Jörg; Ochsenfeld, Christian

    2018-03-28

    The correct description of multi-reference electronic ground states within Kohn-Sham density functional theory (DFT) requires an ensemble-state representation, employing fractionally occupied orbitals. However, the use of fractional orbital occupation leads to non-normalized exact-exchange holes, resulting in large fractional-spin errors for conventional approximative density functionals. In this communication, we present a simple approach to directly include the exact-exchange-hole normalization into DFT. Compared to conventional functionals, our model strongly improves the description for multi-reference systems, while preserving the accuracy in the single-reference case. We analyze the performance of our proposed method at the example of spin-averaged atoms and spin-restricted bond dissociation energy surfaces.

  17. Communication: Density functional theory model for multi-reference systems based on the exact-exchange hole normalization

    Science.gov (United States)

    Laqua, Henryk; Kussmann, Jörg; Ochsenfeld, Christian

    2018-03-01

    The correct description of multi-reference electronic ground states within Kohn-Sham density functional theory (DFT) requires an ensemble-state representation, employing fractionally occupied orbitals. However, the use of fractional orbital occupation leads to non-normalized exact-exchange holes, resulting in large fractional-spin errors for conventional approximative density functionals. In this communication, we present a simple approach to directly include the exact-exchange-hole normalization into DFT. Compared to conventional functionals, our model strongly improves the description for multi-reference systems, while preserving the accuracy in the single-reference case. We analyze the performance of our proposed method at the example of spin-averaged atoms and spin-restricted bond dissociation energy surfaces.

  18. 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.

  19. Exact performance analysis of decode-and-forward opportunistic relaying

    KAUST Repository

    Tourki, Kamel

    2010-06-01

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

  20. Exact combinatorial approach to finite coagulating systems

    Science.gov (United States)

    Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr

    2018-02-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-11-15

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

  2. 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

  3. Analytic nuclear scattering theories

    International Nuclear Information System (INIS)

    Di Marzio, F.; University of Melbourne, Parkville, VIC

    1999-01-01

    A wide range of nuclear reactions are examined in an analytical version of the usual distorted wave Born approximation. This new approach provides either semi analytic or fully analytic descriptions of the nuclear scattering processes. The resulting computational simplifications, when used within the limits of validity, allow very detailed tests of both nuclear interaction models as well as large basis models of nuclear structure to be performed

  4. Dynamical Response of Networks Under External Perturbations: Exact Results

    Science.gov (United States)

    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.

  5. 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.

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

    DEFF Research Database (Denmark)

    Johannessen, Kim

    2014-01-01

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

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

    KAUST Repository

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

    2012-01-01

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

  8. 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.

  9. 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

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

    Directory of Open Access Journals (Sweden)

    Khaled S.M.

    2018-01-01

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

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

    International Nuclear Information System (INIS)

    Lo, C.F.

    2009-01-01

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

  12. General classical and quantum-mechanical description of magnetic resonance: an application to electric-dipole-moment experiments

    Energy Technology Data Exchange (ETDEWEB)

    Silenko, Alexander J. [Belarusian State University, Research Institute for Nuclear Problems, Minsk (Belarus); Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna (Russian Federation)

    2017-05-15

    A general theoretical description of a magnetic resonance is presented. This description is necessary for a detailed analysis of spin dynamics in electric-dipole-moment experiments in storage rings. General formulas describing a behavior of all components of the polarization vector at the magnetic resonance are obtained for an arbitrary initial polarization. These formulas are exact on condition that the nonresonance rotating field is neglected. The spin dynamics is also calculated at frequencies far from resonance with allowance for both rotating fields. A general quantum-mechanical analysis of the spin evolution at the magnetic resonance is fulfilled and the full agreement between the classical and quantum-mechanical approaches is shown. Quasimagnetic resonances for particles and nuclei moving in noncontinuous perturbing fields of accelerators and storage rings are considered. Distinguishing features of quasimagnetic resonances in storage ring electric-dipole-moment experiments are investigated in detail. The exact formulas for the effect caused by the electric dipole moment are derived. The difference between the resonance effects conditioned by the rf electric-field flipper and the rf Wien filter is found and is calculated for the first time. The existence of this difference is crucial for the establishment of a consent between analytical derivations and computer simulations and for checking spin tracking programs. The main systematical errors are considered. (orig.)

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

    Directory of Open Access Journals (Sweden)

    Asterios Pantokratoras

    2008-01-01

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

  14. 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)

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

    Directory of Open Access Journals (Sweden)

    Olaniyi Samuel Iyiola

    2014-09-01

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

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

    DEFF Research Database (Denmark)

    Kimiaeifar, Amin; Barari, Amin; Fooladi, M

    2011-01-01

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

  17. On the validity of collective variable description of Bose systems

    International Nuclear Information System (INIS)

    Takahashi, Minoru

    1975-01-01

    The validity of Sunakawa, Yamasaki and Kebukawa's Hamiltonian and that of Bogoliubov and Zubarev's Hamiltonian are examined. Perturbational expansion of the ground state energy by these Hamiltonians disagrees with the exact solution of Lieb and Liniger for one-dimensional Bose system with repulsive delta-function interaction. This fact suggests that these Hamiltonians are not microscopic descriptions of the many-Boson system. Mathematical inconsistency in Bogoliubov and Zubarev's theory is also pointed out. Moreover analytic expression of high density expansion for the ground state energy density e 0 is found out to be e 0 n -3 =γ-(4/3π)γsup(3/2)+(1/6-1/π 2 )γ 2 +O(γsup(5/2)), γ=c/n, for one-dimensional Bose system with delta function interaction (density n, strength 2c, h=2m=1) by the use of the correlated basis function method. (auth.)

  18. Distinguishing Features and Similarities Between Descriptive Phenomenological and Qualitative Description Research.

    Science.gov (United States)

    Willis, Danny G; Sullivan-Bolyai, Susan; Knafl, Kathleen; Cohen, Marlene Z

    2016-09-01

    Scholars who research phenomena of concern to the discipline of nursing are challenged with making wise choices about different qualitative research approaches. Ultimately, they want to choose an approach that is best suited to answer their research questions. Such choices are predicated on having made distinctions between qualitative methodology, methods, and analytic frames. In this article, we distinguish two qualitative research approaches widely used for descriptive studies: descriptive phenomenological and qualitative description. Providing a clear basis that highlights the distinguishing features and similarities between descriptive phenomenological and qualitative description research will help students and researchers make more informed choices in deciding upon the most appropriate methodology in qualitative research. We orient the reader to distinguishing features and similarities associated with each approach and the kinds of research questions descriptive phenomenological and qualitative description research address. © The Author(s) 2016.

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

    Directory of Open Access Journals (Sweden)

    Md. Nur Alam

    2016-06-01

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

  20. Activated aging dynamics and effective trap model description in the random energy model

    Science.gov (United States)

    Baity-Jesi, M.; Biroli, G.; Cammarota, C.

    2018-01-01

    We study the out-of-equilibrium aging dynamics of the random energy model (REM) ruled by a single spin-flip Metropolis dynamics. We focus on the dynamical evolution taking place on time-scales diverging with the system size. Our aim is to show to what extent the activated dynamics displayed by the REM can be described in terms of an effective trap model. We identify two time regimes: the first one corresponds to the process of escaping from a basin in the energy landscape and to the subsequent exploration of high energy configurations, whereas the second one corresponds to the evolution from a deep basin to the other. By combining numerical simulations with analytical arguments we show why the trap model description does not hold in the former but becomes exact in the second.

  1. 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

  2. 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)

  3. 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)

  4. 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.

  5. Patients' perception of noise in the operating room-a descriptive and analytic cross-sectional study

    DEFF Research Database (Denmark)

    Hasfeldt, Dorthe; Maindal, Helle Terkildsen; Toft, Palle

    2014-01-01

    in the OR before anesthesia, the correlation between the actual noise levels and the patient's perception of noise, and if there are particular patient subgroups that are especially vulnerable to noise. DESIGN: This cross-sectional study was performed within a mixed descriptive and analytical design, including 120...... patients (60 acute/60 elective) undergoing general anesthesia for orthopaedic surgery. METHODS: Data collection consisted of registration of demographic variables and measurements of noise levels in the OR combined with a questionnaire. FINDINGS: Results showed that 10% of the patients perceived noise...... levels in the OR as very high and experienced the noise as annoying, disruptive, and stressful. There was no correlation between the actual noise levels to which patients were exposed and their perception of noise. Acute patients perceived significantly more noise than elective patients (P

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

    Science.gov (United States)

    Panotopoulos, Grigoris

    2018-06-01

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

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

    International Nuclear Information System (INIS)

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

    2008-01-01

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

  8. Transversal magnetotransport in Weyl semimetals: Exact numerical approach

    Science.gov (United States)

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

    2018-02-01

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

  9. 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)

  10. Analytical Description of Ascending Motion of Rockets in the Atmosphere

    Science.gov (United States)

    Rodrigues, H.; de Pinho, M. O.; Portes, D., Jr.; Santiago, A.

    2009-01-01

    In continuation of a previous work, we present an analytic study of ascending vertical motion of a rocket subjected to a quadratic drag for the case where the mass-variation law is a linear function of time. We discuss the detailed analytical solution of the model differential equations in closed form. Examples of application are presented and…

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

    International Nuclear Information System (INIS)

    Gonis, A.; Garland, J.W.

    1977-01-01

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

  12. 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

  13. 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

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

    International Nuclear Information System (INIS)

    Villata, M.; Ferrari, A.

    1994-01-01

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

  15. Encyclopedia of analytical surfaces

    CERN Document Server

    Krivoshapko, S N

    2015-01-01

    This encyclopedia presents an all-embracing collection of analytical surface classes. It provides concise definitions  and description for more than 500 surfaces and categorizes them in 38 classes of analytical surfaces. All classes are cross references to the original literature in an excellent bibliography. The encyclopedia is of particular interest to structural and civil engineers and serves as valuable reference for mathematicians.

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

    International Nuclear Information System (INIS)

    Castejon, F.; Pavlov, S. S.

    2006-01-01

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

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

    Science.gov (United States)

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

    2017-12-01

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

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

    Science.gov (United States)

    Cohen, Yossi; Rothman, Daniel H

    2017-04-01

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

  19. The Impact of Business Analytics on Management Accounting

    DEFF Research Database (Denmark)

    Nielsen, Steen

    The concept of 'analytics' has gained great interest in the academic literature but mostly for practical management since its formal show in the beginning of 2000. Analytics provide an integrated environment for predictive and descriptive modeling, data mining, text analytics, forecasting...

  20. Analytical description of ascending motion of rockets in the atmosphere

    Energy Technology Data Exchange (ETDEWEB)

    Rodrigues, H; Pinho, M O de; Portes, D Jr [Centro Federal de Educacao Tecnologica do Rio de Janeiro, 20271-110, Rio de Janeiro, RJ (Brazil); Santiago, A [Instituto de Fisica, Universidade Estadual do Rio de Janeiro, 20559-900, Rio de Janeiro, RJ (Brazil)], E-mail: harg@cbpf.br, E-mail: ajsant@uerj.br

    2009-01-15

    In continuation of a previous work, we present an analytic study of ascending vertical motion of a rocket subjected to a quadratic drag for the case where the mass-variation law is a linear function of time. We discuss the detailed analytical solution of the model differential equations in closed form. Examples of application are presented and discussed. This paper is intended for undergraduate physics teachers and for graduate students.

  1. 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)

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

    Science.gov (United States)

    Krishnan, Chethan; Kumar, K. V. Pavan

    2018-05-01

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

  3. 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)

  4. Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries.

    Science.gov (United States)

    Sun, Qiming; Chan, Garnet Kin-Lic

    2014-09-09

    Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantum mechanical (QM) effects across arbitrary quantum mechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct "approximately" optimal link orbitals for practical QM/MM calculations.

  5. Analytical description of photon beam phase spaces in inverse Compton scattering sources

    Directory of Open Access Journals (Sweden)

    C. Curatolo

    2017-08-01

    Full Text Available We revisit the description of inverse Compton scattering sources and the photon beams generated therein, emphasizing the behavior of their phase space density distributions and how they depend upon those of the two colliding beams of electrons and photons. The main objective is to provide practical formulas for bandwidth, spectral density, brilliance, which are valid in general for any value of the recoil factor, i.e. both in the Thomson regime of negligible electron recoil, and in the deep Compton recoil dominated region, which is of interest for gamma-gamma colliders and Compton sources for the production of multi-GeV photon beams. We adopt a description based on the center of mass reference system of the electron-photon collision, in order to underline the role of the electron recoil and how it controls the relativistic Doppler/boost effect in various regimes. Using the center of mass reference frame greatly simplifies the treatment, allowing us to derive simple formulas expressed in terms of rms momenta of the two colliding beams (emittance, energy spread, etc. and the collimation angle in the laboratory system. Comparisons with Monte Carlo simulations of inverse Compton scattering in various scenarios are presented, showing very good agreement with the analytical formulas: in particular we find that the bandwidth dependence on the electron beam emittance, of paramount importance in Thomson regime, as it limits the amount of focusing imparted to the electron beam, becomes much less sensitive in deep Compton regime, allowing a stronger focusing of the electron beam to enhance luminosity without loss of mono-chromaticity. A similar effect occurs concerning the bandwidth dependence on the frequency spread of the incident photons: in deep recoil regime the bandwidth comes out to be much less dependent on the frequency spread. The set of formulas here derived are very helpful in designing inverse Compton sources in diverse regimes, giving a

  6. 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.)

  7. Finding an analytic description of the resolution function for n_TOF-EAR2 at CERN

    CERN Document Server

    Eriksson, John Benjamin

    2017-01-01

    At CERN's neutron time-of-flight facility n_TOF a high intensity pulsed neutron source is used to measure energy-dependent neutron-induced reaction cross sections of isotopes relevant to various fields of research such as nuclear astrophysics, -technology or -medicine. Neutron kinetic energies are determined using the time-of-flight (ToF) technique. A correct ToF to energy conversion is essential and is influenced by many factors, one of which is the so-called resolution function (RF). The RF is a characteristic unique to each experimental facility and can only be determined through simulations using Monte Carlo codes. The goal of this project is to find an analytic description of the RF for n_TOF-EAR2. Two functions for two different energy ranges were found, each a combination of linear, polynomial and exponential functions. Furthermore, the energy dependence of the function's parameters was investigated.

  8. 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)

  9. 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...

  10. Exact results for the Floquet coin toss for driven integrable models

    Science.gov (United States)

    Bhattacharya, Utso; Maity, Somnath; Banik, Uddipan; Dutta, Amit

    2018-05-01

    We study an integrable Hamiltonian reducible to free fermions, which is subjected to an imperfect periodic driving with the amplitude of driving (or kicking), randomly chosen from a binary distribution like a coin-toss problem. The randomness present in the driving protocol destabilizes the periodic steady state reached in the limit of perfectly periodic driving, leading to a monotonic rise of the stroboscopic residual energy with the number of periods (N ) for such Hamiltonians. We establish that a minimal deviation from the perfectly periodic driving in the present case using such protocols would always result in a bounded heating up of the system with N to an asymptotic finite value. Exploiting the completely uncorrelated nature of the randomness and the knowledge of the stroboscopic Floquet operator in the perfectly periodic situation, we provide an exact analytical formalism to derive the disorder averaged expectation value of the residual energy through a disorder operator. This formalism not only leads to an immense numerical simplification, but also enables us to derive an exact analytical form for the residual energy in the asymptotic limit which is universal, i.e., independent of the bias of coin-toss and the protocol chosen. Furthermore, this formalism clearly establishes the nature of the monotonic growth of the residual energy at intermediate N while clearly revealing the possible nonuniversal behavior of the same.

  11. Exact extreme-value statistics at mixed-order transitions.

    Science.gov (United States)

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

    2016-05-01

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

  12. Lecture Notes and Exercises for Course 21240 (Basic Analytical Chemistry)

    DEFF Research Database (Denmark)

    1999-01-01

    The publication contains notes dealing with difficult topics in analytical chemistry (cfr. Course Descriptions, DTU), relevant exercises as well as final examination problems from the last years.......The publication contains notes dealing with difficult topics in analytical chemistry (cfr. Course Descriptions, DTU), relevant exercises as well as final examination problems from the last years....

  13. Lecture Notes and Exercises for Course 21240 (Basic Analytical Chemistry)

    DEFF Research Database (Denmark)

    1998-01-01

    The publication contains notes dealing with difficult topics in analytical chemistry (cfr. Course Descriptions, DTU), relevant exercises as well as final examination problems from the last years.......The publication contains notes dealing with difficult topics in analytical chemistry (cfr. Course Descriptions, DTU), relevant exercises as well as final examination problems from the last years....

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

    International Nuclear Information System (INIS)

    Hill, R.N.

    1984-01-01

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

  15. Irreducible descriptive sets of attributes for information systems

    KAUST Repository

    Moshkov, Mikhail; Skowron, Andrzej; Suraj, Zbigniew

    2010-01-01

    . An irreducible descriptive set for the considered information system S is a minimal (relative to the inclusion) set B of attributes which defines exactly the set Ext(S) by means of true and realizable rules constructed over attributes from the considered set B

  16. Microscopic description of magnetized plasma: quasiparticle concept

    International Nuclear Information System (INIS)

    Sosenko, P.P.; Decyk, V.K.

    1993-01-01

    A quasiparticle concept is developed systematically, from first principles, within the context of microscopic description of magnetized plasma. It is argued that the zeroth velocity-gyroangle harmonic of the microscopic particle distribution function under the gyrokinetic change of variables can be taken as a microscopic quasi-particle density in a reduced phase space. The nature of quasiparticles is discussed and equations of their motion are derived within both exact and reduced microscopic descriptions. The reduced one employs explicitly the separation of interesting time scales. (orig.)

  17. 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

  18. 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.

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

    Science.gov (United States)

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

    2009-03-01

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

  20. 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.

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

    International Nuclear Information System (INIS)

    Yamanaka, Masanori; Honjo, Shinsuke; Kohmoto, Mahito

    1996-01-01

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

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

    International Nuclear Information System (INIS)

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

    2016-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-08-15

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

  4. Analytic formulation of neutrino oscillation probability in constant matter

    International Nuclear Information System (INIS)

    Kimura, Keiichi; Takamura, Akira; Yokomakura, Hidekazu

    2003-01-01

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

  5. 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.

  6. Analytical chemistry department. Annual report, 1977

    International Nuclear Information System (INIS)

    Knox, E.M.

    1978-09-01

    The annual report describes the analytical methods, analyses and equipment developed or adopted for use by the Analytical Chemistry Department during 1977. The individual articles range from a several page description of development and study programs to brief one paragraph descriptions of methods adopted for use with or without some modification. This year, we have included a list of the methods incorporated into our Analytical Chemistry Methods Manual. This report is organized into laboratory sections within the Department as well as major programs within General Atomic Company. Minor programs and studies are included under Miscellaneous. The analytical and technical support activities for GAC include gamma-ray spectroscopy, radiochemistry, activation analysis, gas chromatography, atomic absorption, spectrophotometry, emission spectroscopy, x-ray diffractometry, electron microprobe, titrimetry, gravimetry, and quality control. Services are provided to all organizations throughout General Atomic Company. The major effort, however, is in support of the research and development programs within HTGR Generic Technology Programs ranging from new fuel concepts, end-of-life studies, and irradiated capsules to fuel recycle studies

  7. 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.

  8. 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.

  9. 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...

  10. 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.

  11. 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

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

    Science.gov (United States)

    Mickens, Ronald E.

    1998-11-01

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

  13. Analytical performance specifications for external quality assessment - definitions and descriptions.

    Science.gov (United States)

    Jones, Graham R D; Albarede, Stephanie; Kesseler, Dagmar; MacKenzie, Finlay; Mammen, Joy; Pedersen, Morten; Stavelin, Anne; Thelen, Marc; Thomas, Annette; Twomey, Patrick J; Ventura, Emma; Panteghini, Mauro

    2017-06-27

    External Quality Assurance (EQA) is vital to ensure acceptable analytical quality in medical laboratories. A key component of an EQA scheme is an analytical performance specification (APS) for each measurand that a laboratory can use to assess the extent of deviation of the obtained results from the target value. A consensus conference held in Milan in 2014 has proposed three models to set APS and these can be applied to setting APS for EQA. A goal arising from this conference is the harmonisation of EQA APS between different schemes to deliver consistent quality messages to laboratories irrespective of location and the choice of EQA provider. At this time there are wide differences in the APS used in different EQA schemes for the same measurands. Contributing factors to this variation are that the APS in different schemes are established using different criteria, applied to different types of data (e.g. single data points, multiple data points), used for different goals (e.g. improvement of analytical quality; licensing), and with the aim of eliciting different responses from participants. This paper provides recommendations from the European Federation of Laboratory Medicine (EFLM) Task and Finish Group on Performance Specifications for External Quality Assurance Schemes (TFG-APSEQA) and on clear terminology for EQA APS. The recommended terminology covers six elements required to understand APS: 1) a statement on the EQA material matrix and its commutability; 2) the method used to assign the target value; 3) the data set to which APS are applied; 4) the applicable analytical property being assessed (i.e. total error, bias, imprecision, uncertainty); 5) the rationale for the selection of the APS; and 6) the type of the Milan model(s) used to set the APS. The terminology is required for EQA participants and other interested parties to understand the meaning of meeting or not meeting APS.

  14. 8. All Polish Conference on Analytical Chemistry: Analytical Chemistry for the Community of the 21. Century

    International Nuclear Information System (INIS)

    Koscielniak, P.; Wieczorek, M.; Kozak, J.

    2010-01-01

    Book of Abstracts contains short descriptions of lectures, communications and posters presented during 8 th All Polish Conference on Analytical Chemistry (Cracow, 4-9.07.2010). Scientific programme consisted of: basic analytical problems, preparation of the samples, chemometry and metrology, miniaturization of the analytical procedures, environmental analysis, medicinal analyses, industrial analyses, food analyses, biochemical analyses, analysis of relicts of the past. Several posters were devoted to the radiochemical separations, radiochemical analysis, environmental behaviour of the elements important for the nuclear science and the professional tests.

  15. A calibration method for fringe reflection technique based on the analytical phase-slope description

    Science.gov (United States)

    Wu, Yuxiang; Yue, Huimin; Pan, Zhipeng; Liu, Yong

    2018-05-01

    The fringe reflection technique (FRT) has been one of the most popular methods to measure the shape of specular surface these years. The existing system calibration methods of FRT usually contain two parts, which are camera calibration and geometric calibration. In geometric calibration, the liquid crystal display (LCD) screen position calibration is one of the most difficult steps among all the calibration procedures, and its accuracy is affected by the factors such as the imaging aberration, the plane mirror flatness, and LCD screen pixel size accuracy. In this paper, based on the deduction of FRT analytical phase-slope description, we present a novel calibration method with no requirement to calibrate the position of LCD screen. On the other hand, the system can be arbitrarily arranged, and the imaging system can either be telecentric or non-telecentric. In our experiment of measuring the 5000mm radius sphere mirror, the proposed calibration method achieves 2.5 times smaller measurement error than the geometric calibration method. In the wafer surface measuring experiment, the measurement result with the proposed calibration method is closer to the interferometer result than the geometric calibration method.

  16. 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....

  17. 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.)

  18. 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

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

    Science.gov (United States)

    Rao, T. R. Ramesh

    2018-04-01

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

  20. Analytical solution for the convectively-mixed atmospheric boundary layer

    NARCIS (Netherlands)

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

    2013-01-01

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

  1. Analytical Chemistry Division's sample transaction system

    International Nuclear Information System (INIS)

    Stanton, J.S.; Tilson, P.A.

    1980-10-01

    The Analytical Chemistry Division uses the DECsystem-10 computer for a wide range of tasks: sample management, timekeeping, quality assurance, and data calculation. This document describes the features and operating characteristics of many of the computer programs used by the Division. The descriptions are divided into chapters which cover all of the information about one aspect of the Analytical Chemistry Division's computer processing

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

    OpenAIRE

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

    2015-01-01

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

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

    International Nuclear Information System (INIS)

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

    1999-01-01

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

  4. Exact solution of the generalized time-dependent Jaynes-Cummings Hamiltonian

    International Nuclear Information System (INIS)

    Gruver, J.L.; Aliaga, J.; Cerdeira, H.A.; Proto, A.N.

    1993-04-01

    A time-dependent generalization of the Jaynes-Cummings Hamiltonian is studied using the maximum entropy formalism. The approach, related to a semi-Lie algebra, allows to find three different sets of physical relevant operators which describe the dynamics of the system for any temporal dependence. It is shown how the initial conditions of the operators are determined via the maximum entropy principle density operator, where the inclusion of the temperature turns the description of the problem into a thermodynamical one. The generalized time-independent Jaynes-Cummings Hamiltonian is exactly solved as a particular example. (author). 14 refs

  5. Exact Boson-Fermion Duality on a 3D Euclidean Lattice

    Science.gov (United States)

    Chen, Jing-Yuan; Son, Jun Ho; Wang, Chao; Raghu, S.

    2018-01-01

    The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless two-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly nontrivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a nonperturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.

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

    Science.gov (United States)

    Engel, Eberhard

    2018-02-01

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

  7. Self-consistent description of isobaric 0+ states taking the one-particle continuum into account exactly

    International Nuclear Information System (INIS)

    Pyatov, N.I.; Salamov, D.I.; Fayans, S.A.

    1981-01-01

    The properties of discrete and resonance isobaric 0 + states of nuclei are studied within the framework of a self-consistent approach. The equations for the charge-exchange effective field are solved in the coordinate representation taking the one-particle continuum into account exactly. Microscopic estimates of the analog-state energies and the matrix elements, transition densities, and strength functions of the isospin-allowed and forbidden Fermi transitions are obtained together with the values of the isospin admixtures in the ground states of the parent nuclei and their analogs. The escape widths of the isobaric resonances are also discussed

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

    International Nuclear Information System (INIS)

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

    2015-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2015-07-01

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

  10. Quo vadis, analytical chemistry?

    Science.gov (United States)

    Valcárcel, Miguel

    2016-01-01

    This paper presents an open, personal, fresh approach to the future of Analytical Chemistry in the context of the deep changes Science and Technology are anticipated to experience. Its main aim is to challenge young analytical chemists because the future of our scientific discipline is in their hands. A description of not completely accurate overall conceptions of our discipline, both past and present, to be avoided is followed by a flexible, integral definition of Analytical Chemistry and its cornerstones (viz., aims and objectives, quality trade-offs, the third basic analytical reference, the information hierarchy, social responsibility, independent research, transfer of knowledge and technology, interfaces to other scientific-technical disciplines, and well-oriented education). Obsolete paradigms, and more accurate general and specific that can be expected to provide the framework for our discipline in the coming years are described. Finally, the three possible responses of analytical chemists to the proposed changes in our discipline are discussed.

  11. Analytical methods used at model facility

    International Nuclear Information System (INIS)

    Wing, N.S.

    1984-01-01

    A description of analytical methods used at the model LEU Fuel Fabrication Facility is presented. The methods include gravimetric uranium analysis, isotopic analysis, fluorimetric analysis, and emission spectroscopy

  12. 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

  13. 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.

  14. 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

  15. 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

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

    KAUST Repository

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

    2011-01-01

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

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

    KAUST Repository

    Mazaré, Pierre Emmanuel

    2011-12-01

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

  18. Impedance description of coherent synchrotron radiation with account of bunch deformation

    Directory of Open Access Journals (Sweden)

    Robert Warnock

    2005-01-01

    Full Text Available We are concerned with coherent longitudinal motion in a storage ring, especially with situations in which coherent synchrotron radiation (CSR can influence stability of the beam. The collective force from CSR is usually described by an impedance or a wake function in such a way that the force depends only on the charge distribution at the present time. This description is exact only for a rigid bunch, since causality demands that the force depend on the prior history of the bunch. We show how to treat a deforming bunch by applying the “complete impedance” Z(n,ω, a function of wave number and frequency. We derive this impedance and study its analytic properties for a special model: radiation from circular orbits shielded by parallel plates representing the metallic vacuum chamber. We analyze the corresponding collective force, obtaining the usual formula as a first approximation, plus easily computed corrections that depend on present and prior values of the time derivative of the charge density. In related papers we have applied these results in numerical simulations of instabilities induced by CSR.

  19. 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.)

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

    International Nuclear Information System (INIS)

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

    2017-01-01

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

  1. On Analytic Solution of resonant Mixing for Solar Neutrino Oscillations

    OpenAIRE

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

    1988-01-01

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

  2. Boundary Value Problems for a Super-Sublinear Asymmetric Oscillator: The Exact Number of Solutions

    Directory of Open Access Journals (Sweden)

    Armands Gritsans

    2013-01-01

    Full Text Available Properties of asymmetric oscillator described by the equation (i, where and , are studied. A set of such that the problem (i, (ii, and (iii have a nontrivial solution, is called α-spectrum. We give full description of α-spectra in terms of solution sets and solution surfaces. The exact number of nontrivial solutions of the two-parameter Dirichlet boundary value problem (i, and (ii is given.

  3. Semi-Local DFT Functionals with Exact-Exchange-Like Features: Beyond the AK13

    Science.gov (United States)

    Armiento, Rickard

    The Armiento-Kümmel functional from 2013 (AK13) is a non-empirical semi-local exchange functional on generalized gradient approximation form (GGA) in Kohn-Sham (KS) density functional theory (DFT). Recent works have established that AK13 gives improved electronic-structure exchange features over other semi-local methods, with a qualitatively improved orbital description and band structure. For example, the Kohn-Sham band gap is greatly extended, as it is for exact exchange. This talk outlines recent efforts towards new exchange-correlation functionals based on, and extending, the AK13 design ideas. The aim is to improve the quantitative accuracy, the description of energetics, and to address other issues found with the original formulation. Swedish e-Science Research Centre (SeRC).

  4. Analytical relativistic self-consistent-field calculations for atoms

    International Nuclear Information System (INIS)

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

    1980-01-01

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

  5. Quasi-exact solutions of nonlinear differential equations

    OpenAIRE

    Kudryashov, Nikolay A.; Kochanov, Mark B.

    2014-01-01

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

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

    International Nuclear Information System (INIS)

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

    2005-01-01

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

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

    International Nuclear Information System (INIS)

    Strekalov, M L

    2013-01-01

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

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

    International Nuclear Information System (INIS)

    Liu Chunliang; Xie Xi; Chen Yinbao

    1991-01-01

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

  9. Analytic description of the frictionally engaged in-plane bending process incremental swivel bending (ISB)

    Science.gov (United States)

    Frohn, Peter; Engel, Bernd; Groth, Sebastian

    2018-05-01

    Kinematic forming processes shape geometries by the process parameters to achieve a more universal process utilizations regarding geometric configurations. The kinematic forming process Incremental Swivel Bending (ISB) bends sheet metal strips or profiles in plane. The sequence for bending an arc increment is composed of the steps clamping, bending, force release and feed. The bending moment is frictionally engaged by two clamping units in a laterally adjustable bending pivot. A minimum clamping force hindering the material from slipping through the clamping units is a crucial criterion to achieve a well-defined incremental arc. Therefore, an analytic description of a singular bent increment is developed in this paper. The bending moment is calculated by the uniaxial stress distribution over the profiles' width depending on the bending pivot's position. By a Coulomb' based friction model, necessary clamping force is described in dependence of friction, offset, dimensions of the clamping tools and strip thickness as well as material parameters. Boundaries for the uniaxial stress calculation are given in dependence of friction, tools' dimensions and strip thickness. The results indicate that changing the bending pivot to an eccentric position significantly affects the process' bending moment and, hence, clamping force, which is given in dependence of yield stress and hardening exponent. FE simulations validate the model with satisfactory accordance.

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

    International Nuclear Information System (INIS)

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

    2013-01-01

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

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

    Science.gov (United States)

    Palisoc, Arthur L.; Lee, Chin C.

    1988-12-01

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

  12. A novel analytical description of periodic volume coil geometries in MRI

    Science.gov (United States)

    Koh, D.; Felder, J.; Shah, N. J.

    2018-03-01

    MRI volume coils can be represented by equivalent lumped element circuits and for a variety of these circuit configurations analytical design equations have been presented. The unification of several volume coil topologies results in a two-dimensional gridded equivalent lumped element circuit which compromises the birdcage resonator, its multiple endring derivative but also novel structures like the capacitive coupled ring resonator. The theory section analyzes a general two-dimensional circuit by noting that its current distribution can be decomposed into a longitudinal and an azimuthal dependency. This can be exploited to compare the current distribution with a transfer function of filter circuits along one direction. The resonances of the transfer function coincide with the resonance of the volume resonator and the simple analytical solution can be used as a design equation. The proposed framework is verified experimentally against a novel capacitive coupled ring structure which was derived from the general circuit formulation and is proven to exhibit a dominant homogeneous mode. In conclusion, a unified analytical framework is presented that allows determining the resonance frequency of any volume resonator that can be represented by a two dimensional meshed equivalent circuit.

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

    International Nuclear Information System (INIS)

    Karpp, R.R.

    1980-10-01

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

  14. Optimum shape design of incompressible hyperelastic structures with analytical sensitivity analysis

    International Nuclear Information System (INIS)

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

    2014-01-01

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

  15. 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.

  16. 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

  17. Off-diagonal Bethe ansatz for exactly solvable models

    CERN Document Server

    Wang, Yupeng; Cao, Junpeng; Shi, Kangjie

    2015-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2014-06-10

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

  19. 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.

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

    Science.gov (United States)

    Bastianello, Alvise; Piroli, Lorenzo; Calabrese, Pasquale

    2018-05-01

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

  1. Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

    Directory of Open Access Journals (Sweden)

    Roman Cherniha

    2018-04-01

    Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

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

    KAUST Repository

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

    2010-01-01

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

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

    KAUST Repository

    Yilmaz, Ferkan

    2010-09-01

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

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

    KAUST Repository

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

    2011-01-01

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

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

    International Nuclear Information System (INIS)

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

    2011-01-01

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

  6. Exact piecewise flat gravitational waves

    NARCIS (Netherlands)

    van de Meent, M.

    2011-01-01

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

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

    CERN Document Server

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

    2013-01-01

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

  8. Exact exchange-correlation potentials of singlet two-electron systems

    Science.gov (United States)

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

    2017-10-01

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

  9. Entanglement dynamics following a sudden quench: An exact solution

    Science.gov (United States)

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

    2017-12-01

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

  10. 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

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

    International Nuclear Information System (INIS)

    Hopper, R.W.

    1984-01-01

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

  12. Exact solutions for a system of nonlinear plasma fluid equations

    International Nuclear Information System (INIS)

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

    1991-04-01

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

  13. 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

  14. 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.

  15. 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.

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

    Science.gov (United States)

    Torres-Cordoba, Rafael; Martinez-Garcia, Edgar

    2017-10-01

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

  17. Exact calculation of three-body contact interaction to second order

    International Nuclear Information System (INIS)

    Kaiser, N.

    2012-01-01

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

  18. 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.)

  19. 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)

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

    Science.gov (United States)

    Ghosh, Pijush K.; Sinha, Debdeep

    2018-01-01

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

  1. General Exact Solution to the Problem of the Probability Density for Sums of Random Variables

    Science.gov (United States)

    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.

  2. Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

    Science.gov (United States)

    Li, Haifeng; Shao, Jiushu; Wang, Shikuan

    2011-11-01

    A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

  3. Analytic study of nonperturbative solutions in open string field theory

    International Nuclear Information System (INIS)

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

    2003-01-01

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

  4. Intuitive versus analytical decision making modulates trust in e-commerce

    Directory of Open Access Journals (Sweden)

    Paola Iannello

    2014-11-01

    Full Text Available The hypothesis that intuition and analytical processes affect differently trust in e-commerce was tested. Participants were offered products by a series of sellers via Internet. In the intuitive condition pictures of the sellers were followed by neutral descriptions and participants had less time to decide whether to trust the seller. In the analytical condition participants were given an informative description of the seller and had a longer time to decide. Interactions among condition, price and trust emerged in behavioral and psychophysiological responses. EMG signals increased during analytical processing, suggesting a cognitive effort, whereas higher cardiovascular measures mirrored the emotional involvement when faced to untrustworthy sellers. The study supported the fruitful application of the intuitive vs. analytical approach to e-commerce and of the combination of different sources of information about the buyers while they have to choose to trust the seller in a financial transaction over the Internet.

  5. Heat illness surveillance in schoolboys participating in physical education class in tropical climate: an analytical prospective descriptive study.

    Science.gov (United States)

    Somboonwong, Juraiporn; Sanguanrungsirikul, Sompol; Pitayanon, Chatchatchai

    2012-01-01

    This study aimed to determine thermoregulatory and cardiovascular responses as well as the occurrence of heat illness in children exercising outdoors in physical education class under hot and humid climate. Little information regarding this issue under real-life situation is available, especially in the Southeast Asia. Analytical, prospective descriptive study. A primary school in Bangkok, Thailand. A total of 457 schoolboys (aged 5.5-12 years) were observed while exercising outdoors during their physical education classes throughout the academic year of 2009, including semester 1 (between July and September 2009) and semester 2 (between November 2009 and February 2010). Primary outcome measure was tympanic temperature. Secondary outcome measures included blood pressure, heart rate, hydration status and the occurrence of heat-related illness. Outdoor physical activity consisted of skill practice (duration 24.11±11.04 min, intensity risk for heat illness during outdoor activities in physical education class in primary school children, especially those who are overweight and have poor hydration status.

  6. Irreducible descriptive sets of attributes for information systems

    KAUST Repository

    Moshkov, Mikhail

    2010-01-01

    The maximal consistent extension Ext(S) of a given information system S consists of all objects corresponding to attribute values from S which are consistent with all true and realizable rules extracted from the original information system S. An irreducible descriptive set for the considered information system S is a minimal (relative to the inclusion) set B of attributes which defines exactly the set Ext(S) by means of true and realizable rules constructed over attributes from the considered set B. We show that there exists only one irreducible descriptive set of attributes. We present a polynomial algorithm for this set construction. We also study relationships between the cardinality of irreducible descriptive set of attributes and the number of attributes in S. The obtained results will be useful for the design of concurrent data models from experimental data. © 2010 Springer-Verlag.

  7. EDUCATION OF RELIGIOUS VALUES IN BUILDING HEALTHY PERSONALITY (Analytical Descriptive Study in Madrasah Aliyah Darul Arqam Garut

    Directory of Open Access Journals (Sweden)

    Dewi Sadiah

    2016-03-01

    Full Text Available Educational value as a teaching or counseling leads students to realize the values of truth, goodness, and beauty, through the process of the correct value judgments and habituation to act consistently. This study aims at identifying goals and assessment of religious values education in building healthy characters, and adopts an analytical descriptive method and qualitative approach. People with healthy personalities are those who are judged to be well adjusted. They are so judged because they are able to function efficiently in the word of people. They experience a kind of “inner harmony” in the sense that they are at peace with other as well as with themselves. The teacher expected goals is in line with the vision and mission of Darul Arqam Madrasah Aliyah equipped with extra-curricular activities and school discipline. Someone with a healthy personality can give happiness to her needs through behaviors (adjusted with the environmental norms and needs of his conscience, thus forming the character of the students become independent, accomplished, happy, sholeh, honest, faithful and pious to Allah SWT.

  8. Matrix-exponential description of radiative transfer

    International Nuclear Information System (INIS)

    Waterman, P.C.

    1981-01-01

    By appling the matrix-exponential operator technique to the radiative-transfer equation in discrete form, new analytical solutions are obtained for the transmission and reflection matrices in the limiting cases x >1, where x is the optical depth of the layer. Orthongonality of the eigenvectors of the matrix exponential apparently yields new conditions for determining. Chandrasekhar's characteristic roots. The exact law of reflection for the discrete eigenfunctions is also obtained. Finally, when used in conjuction with the doubling method, the matrix exponential should result in reduction in both computation time and loss of precision

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

    Directory of Open Access Journals (Sweden)

    R. Kenna

    2014-09-01

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

  10. 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.

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

    International Nuclear Information System (INIS)

    Durand, B.; Durand, L.

    1983-01-01

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

  12. Exact analytic solutions for a global equation of plant cell growth.

    Science.gov (United States)

    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.

  13. 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.)

  14. Search Analytics for Your Site

    CERN Document Server

    Rosenfeld, Louis

    2011-01-01

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

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

    Science.gov (United States)

    Belik, V. D.

    2018-05-01

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

  16. Introduction to the polymorphic tracking code Fibre bundles, polymorphic Taylor types and "Exact tracking"

    CERN Document Server

    Schmidt, F; McIntosh, E

    2002-01-01

    This is a description of the basic ideas behind the ``Polymorphic Tracking Code'' or PTC. PTC is truly a ``kick code'' or symplectic integrator in the tradition of TRACYII, SixTrack, and TEAPOT. However it separates correctly the mathematical atlas of charts and the magnets at a structural level by implementing a ``restricted fibre bundle.'' The resulting structures allow backward propagation and recirculation, something not possible in standard tracking codes. Also PTC is polymorphic in handling real (single, double and even quadruple precision) and Taylor series. Therefore it has all the tools associated to the TPSA packages: Lie methods, Normal Forms, Cosy-Infinity capabilities, beam envelopes for radiation, etc., as well as parameter dependence on-the-fly. However PTC is an integrator, and as such, one must, generally, adhere to the Talman ``exactness'' view of modelling. Incidentally, it supports exact sector and rectangular bends as well. Of course, one can certainly bypass its integrator and the user i...

  17. 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

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

    International Nuclear Information System (INIS)

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

    2012-01-01

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

  19. Analytic description of four-wave mixing in silicon-on-insulator waveguides

    DEFF Research Database (Denmark)

    Friis, Søren Michael Mørk; Koefoed, Jacob Gade; Guo, Kai

    2018-01-01

    and becomes a nonlinear differential equation that we solve analytically without further approximations. The signal and idler equations have no known solutions for arbitrary pump power evolution, but we calculate approximate field expressions based on a Magnus expansion, which has been used to study time...

  20. 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.

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

    DEFF Research Database (Denmark)

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

    2011-01-01

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

  2. A Modal Description of Multiport Antennas

    Directory of Open Access Journals (Sweden)

    Jonathan J. Lynch

    2011-01-01

    Full Text Available This paper presents a modal description of multiport antennas that leads directly to a rigorous network representation and simple quadratic expressions for gain, efficiency, and effective area. The analysis shows that the transmitting and receiving properties of an element antenna array are exactly described by a 2×2 element scattering matrix together with a set of orthonormal mode functions and accounts for effects such as mutual coupling, scattering, reflection, and losses. The approach is quite general, only requiring that the antenna be finite and reciprocal. The scattering network description simplifies accounting of power flow while retaining a close connection to the physical antenna characteristics. The orthonormal mode functions provide a complete basis for radiated and received fields, facilitating beamforming. The theory provides rigorous definitions of input-output signals and links them to the underlying electromagnetics in a straightforward manner.

  3. 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

  4. 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...

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

    International Nuclear Information System (INIS)

    Hurtado, Pablo I; Garrido, Pedro L

    2009-01-01

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

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

    NARCIS (Netherlands)

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

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

  7. Non-empirical exchange-correlation parameterizations based on exact conditions from correlated orbital theory.

    Science.gov (United States)

    Haiduke, Roberto Luiz A; Bartlett, Rodney J

    2018-05-14

    Some of the exact conditions provided by the correlated orbital theory are employed to propose new non-empirical parameterizations for exchange-correlation functionals from Density Functional Theory (DFT). This reparameterization process is based on range-separated functionals with 100% exact exchange for long-range interelectronic interactions. The functionals developed here, CAM-QTP-02 and LC-QTP, show mitigated self-interaction error, correctly predict vertical ionization potentials as the negative of eigenvalues for occupied orbitals, and provide nice excitation energies, even for challenging charge-transfer excited states. Moreover, some improvements are observed for reaction barrier heights with respect to the other functionals belonging to the quantum theory project (QTP) family. Finally, the most important achievement of these new functionals is an excellent description of vertical electron affinities (EAs) of atoms and molecules as the negative of appropriate virtual orbital eigenvalues. In this case, the mean absolute deviations for EAs in molecules are smaller than 0.10 eV, showing that physical interpretation can indeed be ascribed to some unoccupied orbitals from DFT.

  8. Non-empirical exchange-correlation parameterizations based on exact conditions from correlated orbital theory

    Science.gov (United States)

    Haiduke, Roberto Luiz A.; Bartlett, Rodney J.

    2018-05-01

    Some of the exact conditions provided by the correlated orbital theory are employed to propose new non-empirical parameterizations for exchange-correlation functionals from Density Functional Theory (DFT). This reparameterization process is based on range-separated functionals with 100% exact exchange for long-range interelectronic interactions. The functionals developed here, CAM-QTP-02 and LC-QTP, show mitigated self-interaction error, correctly predict vertical ionization potentials as the negative of eigenvalues for occupied orbitals, and provide nice excitation energies, even for challenging charge-transfer excited states. Moreover, some improvements are observed for reaction barrier heights with respect to the other functionals belonging to the quantum theory project (QTP) family. Finally, the most important achievement of these new functionals is an excellent description of vertical electron affinities (EAs) of atoms and molecules as the negative of appropriate virtual orbital eigenvalues. In this case, the mean absolute deviations for EAs in molecules are smaller than 0.10 eV, showing that physical interpretation can indeed be ascribed to some unoccupied orbitals from DFT.

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

    Directory of Open Access Journals (Sweden)

    Kyung-Hun Shin

    2017-05-01

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

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

    International Nuclear Information System (INIS)

    Sazhin, S.S.

    1997-01-01

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

  11. Dynamics of an Imperfect Microbeam Considering its Exact Shape

    KAUST Repository

    Bataineh, Ahmad M.

    2014-08-17

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

  12. Exact solution of corner-modified banded block-Toeplitz eigensystems

    International Nuclear Information System (INIS)

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

    2017-01-01

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

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

    Science.gov (United States)

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

    2018-02-01

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

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

    Science.gov (United States)

    Iafrate, G J; Krieger, J B

    2013-03-07

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

  15. Analytic regularization of uniform cubic B-spline deformation fields.

    Science.gov (United States)

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

    2012-01-01

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

  16. Opportunity and Challenges for Migrating Big Data Analytics in Cloud

    Science.gov (United States)

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

    2017-08-01

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

  17. 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

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

    Science.gov (United States)

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

    2018-04-01

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

  19. Semi-analytical solution to arbitrarily shaped beam scattering

    Science.gov (United States)

    Wang, Wenjie; Zhang, Huayong; Sun, Yufa

    2017-07-01

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

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

    International Nuclear Information System (INIS)

    Portella, H.M.

    1985-01-01

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

  1. The big bang and inflation united by an analytic solution

    International Nuclear Information System (INIS)

    Bars, Itzhak; Chen, Shih-Hung

    2011-01-01

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

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

    International Nuclear Information System (INIS)

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

    2017-01-01

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

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

    Science.gov (United States)

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

    2017-05-01

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

  4. 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)

  5. Exact discretization of Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-01-08

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

  6. Exact discretization of Schrödinger equation

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2016-01-01

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

  7. An analytical method for neutron thermalization calculations in heterogenous reactors

    Energy Technology Data Exchange (ETDEWEB)

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

    1965-07-01

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

  8. An analytical method for neutron thermalization calculations in heterogenous reactors

    International Nuclear Information System (INIS)

    Pop-Jordanov, J.

    1965-01-01

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

  9. Analytic continuation by duality estimation of the S parameter

    International Nuclear Information System (INIS)

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

    2000-01-01

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

  10. Descriptive and inferential statistical methods used in burns research.

    Science.gov (United States)

    Al-Benna, Sammy; Al-Ajam, Yazan; Way, Benjamin; Steinstraesser, Lars

    2010-05-01

    Burns research articles utilise a variety of descriptive and inferential methods to present and analyse data. The aim of this study was to determine the descriptive methods (e.g. mean, median, SD, range, etc.) and survey the use of inferential methods (statistical tests) used in articles in the journal Burns. This study defined its population as all original articles published in the journal Burns in 2007. Letters to the editor, brief reports, reviews, and case reports were excluded. Study characteristics, use of descriptive statistics and the number and types of statistical methods employed were evaluated. Of the 51 articles analysed, 11(22%) were randomised controlled trials, 18(35%) were cohort studies, 11(22%) were case control studies and 11(22%) were case series. The study design and objectives were defined in all articles. All articles made use of continuous and descriptive data. Inferential statistics were used in 49(96%) articles. Data dispersion was calculated by standard deviation in 30(59%). Standard error of the mean was quoted in 19(37%). The statistical software product was named in 33(65%). Of the 49 articles that used inferential statistics, the tests were named in 47(96%). The 6 most common tests used (Student's t-test (53%), analysis of variance/co-variance (33%), chi(2) test (27%), Wilcoxon & Mann-Whitney tests (22%), Fisher's exact test (12%)) accounted for the majority (72%) of statistical methods employed. A specified significance level was named in 43(88%) and the exact significance levels were reported in 28(57%). Descriptive analysis and basic statistical techniques account for most of the statistical tests reported. This information should prove useful in deciding which tests should be emphasised in educating burn care professionals. These results highlight the need for burn care professionals to have a sound understanding of basic statistics, which is crucial in interpreting and reporting data. Advice should be sought from professionals

  11. 3-D discrete analytical ridgelet transform.

    Science.gov (United States)

    Helbert, David; Carré, Philippe; Andres, Eric

    2006-12-01

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

  12. Some exact computations on the twisted butterfly state in string field theory

    International Nuclear Information System (INIS)

    Okawa, Yuji

    2004-01-01

    The twisted butterfly state solves the equation of motion of vacuum string field theory in the singular limit. The finiteness of the energy density of the solution is an important issue, but possible conformal anomaly resulting from the twisting has prevented us from addressing this problem. We present a description of the twisted regulated butterfly state in terms of a conformal field theory with a vanishing central charge which consists of the ordinary bc ghosts and a matter system with c=26. Various quantities relevant to vacuum string field theory are computed exactly using this description. We find that the energy density of the solution can be finite in the limit, but the finiteness depends on the sub leading structure of vacuum string field theory. We further argue, contrary to our previous expectation, that contributions from sub leading terms in the kinetic term to the energy density can be of the same order as the contribution from the leading term which consists of the midpoint ghost insertion. (author)

  13. Analytical Techniques and the Air Force Logistics Readiness Officer

    National Research Council Canada - National Science Library

    Main, Bryan D

    2008-01-01

    .... Over 500 LROs and supervisors provided inputs. Analysis of survey responses found that Forecasting, Graphical Statistics, and Descriptive Statistics are the analytical techniques valued most by both LROs and their supervisors...

  14. Analytical description of ballistic spin currents and torques in magnetic tunnel junctions

    KAUST Repository

    Chshiev, M.; Manchon, Aurelien; Kalitsov, A.; Ryzhanova, N.; Vedyayev, A.; Strelkov, N.; Butler, W. H.; Dieny, B.

    2015-01-01

    In this work we demonstrate explicit analytical expressions for both charge and spin currents which constitute the 2×2 spinor in magnetic tunnel junctions with noncollinear magnetizations under applied voltage. The calculations have been performed

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

    Directory of Open Access Journals (Sweden)

    Roman Cherniha

    2016-06-01

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

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

    Science.gov (United States)

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

    2011-12-01

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

  17. Analytical description of transfer of Pu-239 in undisturbed soil

    Energy Technology Data Exchange (ETDEWEB)

    Tianshan, Ren; Linsalata, P; Cohen, N

    1986-04-01

    The paper reports on an analytical model for describing the horizontal and down-ward transfer of /sup 239/Pu in undisturbed soil based on observed data. The model has been developed to predict how the depth distribution of /sup 239/Pu in soil would change with time. This information is essential for estimation of the quantities of /sup 239/Pu that have entered surface water body via erosion and runoff processes and for estimation of the long-term impact of /sup 239/Pu isice the commencement of nuclear fallout deposition.

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

    International Nuclear Information System (INIS)

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

    2010-01-01

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

  19. Exact analysis of discrete data

    CERN Document Server

    Hirji, Karim F

    2005-01-01

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

  20. Renormalization of the fragmentation equation: Exact self-similar solutions and turbulent cascades

    Science.gov (United States)

    Saveliev, V. L.; Gorokhovski, M. A.

    2012-12-01

    Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E1539-375510.1103/PhysRevE.65.051205 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

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

    International Nuclear Information System (INIS)

    Bechiri, Mohammed; Mansouri, Kacem

    2013-01-01

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

  2. 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....

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

    Science.gov (United States)

    Liu, Sai; Li, Shanpeng; Liu, Jianlin

    2018-03-30

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

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

    International Nuclear Information System (INIS)

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

    2012-01-01

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

  5. 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

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

    Science.gov (United States)

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

    2018-02-01

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

  7. 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)

  8. Entry format for representation of analytical relations on the ES computer

    International Nuclear Information System (INIS)

    Katan, I.B.; Sal'nikova, O.V.; Blokhin, A.I.

    1981-01-01

    Structure and description of an input format for representation of analytical relations on the ES compUter as well as dictionaries of key words and system identificators for thermal-physical and hydraulic data are presented. It is shown that the format considered can be the basis at the formation of library of analytical relations [ru

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

    DEFF Research Database (Denmark)

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

    2010-01-01

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

  10. Which energy mix for the UK (United Kingdom)? An evolutive descriptive mapping with the integrated GAIA (graphical analysis for interactive aid)–AHP (analytic hierarchy process) visualization tool

    International Nuclear Information System (INIS)

    Ishizaka, Alessio; Siraj, Sajid; Nemery, Philippe

    2016-01-01

    Although Multi-Criteria Decision Making methods have been extensively used in energy planning, their descriptive use has been rarely considered. In this paper, we add an evolutionary description phase as an extension to the AHP (analytic hierarchy process) method that helps policy makers to gain insights into their decision problems. The proposed extension has been implemented in an open-source software that allows the users to visualize the difference of opinions within a decision process, and also the evolution of preferences over time. The method was tested in a two-phase experiment to understand the evolution of opinions on energy sources. Participants were asked to provide their preferences for different energy sources for the next twenty years for the United Kingdom. They were first asked to compare the options intuitively without using any structured approach, and then were given three months to compare the same set of options after collecting detailed information on the technical, economic, environmental and social impacts created by each of the selected energy sources. The proposed visualization method allow us to quickly discover the preference directions, and also the changes in their preferences from first to second phase. The proposed tool can help policy makers in better understanding of the energy planning problems that will lead us towards better planning and decisions in the energy sector. - Highlights: • We introduce a descriptive visual analysis tool for the analytic hierarchy process. • The method has been implemented as an open-source preference elicitation tool. • We analyse user preferences in the energy sector using this method. • The tool also provides a way to visualize temporal preferences changes. • The main negative temporal shift in the ranking was found for the nuclear energy.

  11. Virtues and limitations of the truncated Holstein–Primakoff description of quantum rotors

    International Nuclear Information System (INIS)

    Hirsch, Jorge G; Castaños, Octavio; López-Peña, Ramón; Nahmad-Achar, Eduardo

    2013-01-01

    A Hamiltonian describing the collective behaviour of N interacting spins can be mapped to a bosonic one employing the Holstein–Primakoff realization, at the expense of having an infinite series in powers of the boson creation and annihilation operators. Truncating this series up to quadratic terms allows obtaining analytic solutions through a Bogoliubov transformation, which becomes exact in the limit N → ∞. The Hamiltonian exhibits a phase transition from single-spin excitations to a collective mode. In the vicinity of this phase transition, the truncated solutions predict the existence of singularities for a finite number of spins, which have no counterpart in the exact diagonalization. Renormalization allows to extract from these divergences the exact behaviour of relevant observables with the number of spins around the phase transition, and to relate it with the class of universality to which the model belongs. In this work a detailed analysis of these aspects is presented for the Lipkin model. (comment)

  12. Classes of exact Einstein Maxwell solutions

    Science.gov (United States)

    Komathiraj, K.; Maharaj, S. D.

    2007-12-01

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

  13. Exact optics - III. Schwarzschild's spectrograph camera revised

    Science.gov (United States)

    Willstrop, R. V.

    2004-03-01

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

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

    International Nuclear Information System (INIS)

    Shpytko, Volodymyr; Darewych, Jurij

    2001-01-01

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

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

    Science.gov (United States)

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

    2010-02-01

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

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

    Science.gov (United States)

    Lin, Yeong-Lieh; Nori, Franco

    1997-03-01

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

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

    International Nuclear Information System (INIS)

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

    2008-01-01

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

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

    International Nuclear Information System (INIS)

    Xing Liudong; Shrestha, Akhilesh; Dai Yuanshun

    2011-01-01

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

  19. 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.

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

    International Nuclear Information System (INIS)

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

    2009-01-01

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

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

    International Nuclear Information System (INIS)

    Damour, Thibault; Gourgoulhon, Eric; Grandclement, Philippe

    2002-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2009-09-15

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

  3. Analytic treatment of nuclear spin-lattice relaxation for diffusion in a cone model

    Science.gov (United States)

    Sitnitsky, A. E.

    2011-12-01

    We consider nuclear spin-lattice relaxation rate resulted from a diffusion equation for rotational wobbling in a cone. We show that the widespread point of view that there are no analytical expressions for correlation functions for wobbling in a cone model is invalid and prove that nuclear spin-lattice relaxation in this model is exactly tractable and amenable to full analytical description. The mechanism of relaxation is assumed to be due to dipole-dipole interaction of nuclear spins and is treated within the framework of the standard Bloemberger, Purcell, Pound-Solomon scheme. We consider the general case of arbitrary orientation of the cone axis relative the magnetic field. The BPP-Solomon scheme is shown to remain valid for systems with the distribution of the cone axes depending only on the tilt relative the magnetic field but otherwise being isotropic. We consider the case of random isotropic orientation of cone axes relative the magnetic field taking place in powders. Also we consider the cases of their predominant orientation along or opposite the magnetic field and that of their predominant orientation transverse to the magnetic field which may be relevant for, e.g., liquid crystals. Besides we treat in details the model case of the cone axis directed along the magnetic field. The latter provides direct comparison of the limiting case of our formulas with the textbook formulas for free isotropic rotational diffusion. The dependence of the spin-lattice relaxation rate on the cone half-width yields results similar to those predicted by the model-free approach.

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

    Science.gov (United States)

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

    2001-06-01

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

  5. Analytical shear and flexion of Einasto dark matter haloes

    OpenAIRE

    Retana-Montenegro, E.; Frutos-Alfaro, F.; Baes, M.

    2012-01-01

    N-body simulations predict that dark matter haloes are described by specific density profiles on both galactic- and cluster-sized scales. Weak gravitational lensing through the measurements of their first and second order properties, shear and flexion, is a powerful observational tool for investigating the true shape of these profiles. One of the three-parameter density profiles recently favoured in the description of dark matter haloes is the Einasto profile. We present exact expressions for...

  6. Descriptive Topology in Selected Topics of Functional Analysis

    CERN Document Server

    Kakol, J; Pellicer, Manuel Lopez

    2011-01-01

    "Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Frechet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical set

  7. 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

  8. Energies of the ground state and first excited 0 sup + state in an exactly solvable pairing model

    CERN Document Server

    Dinh Dang, N

    2003-01-01

    Several approximations are tested by calculating the ground-state energy and the energy of the first excited 0 sup + state using an exactly solvable model with two symmetric levels interacting via a pairing force. They are the BCS approximation (BCS), Lipkin-Nogami (LN) method, random-phase approximation (RPA), quasiparticle RPA (QRPA), the renormalized RPA (RRPA), and renormalized QRPA (RQRPA). It is shown that, in the strong-coupling regime, the QRPA which neglects the scattering term of the model Hamiltonian offers the best fit to the exact solutions. A recipe is proposed using the RRPA and RQRPA in combination with the pairing gap given by the LN method. Applying this recipe, it is shown that the superfluid-normal phase transition is avoided, and a reasonably good description for both of the ground-state energy and the energy of the first excited 0 sup + state is achieved. (orig.)

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

    Science.gov (United States)

    Bodin, Jacques

    2015-03-01

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

  10. Implementation of a Gauss convoluted Pandel PDF for track reconstruction in neutrino telescopes

    NARCIS (Netherlands)

    van Eijndhoven, N.J.A.M.; Fadiran, O.; Japaridze, G.

    2007-01-01

    A probability distribution function is presented which provides a realistic description of the detection of scattered photons. The resulting probabilities can be described analytically by means of a superposition of several special functions. These exact expressions can be evaluated numerically only

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

    International Nuclear Information System (INIS)

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

    2012-01-01

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

  12. Analytic description of tokamak equilibrium sustained by high fraction bootstrap current

    International Nuclear Information System (INIS)

    Shi Bingren

    2002-01-01

    Recently, to save the current drive power and to obtain more favorable confinement merit for tokamak reactor, large faction bootstrap current sustained equilibrium has attracted great interests both theoretically and experimentally. An powerful expanding technique and the tokamak ordering are used to expand the Grad-Shafranov equation to obtain a series of ordinary differential equations which allow for different sets of input parameters. The fully bootstrap current sustained tokamak equilibria are then solved analytically

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

    International Nuclear Information System (INIS)

    Reiher, Markus; Wolf, Alexander

    2004-01-01

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

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

    Science.gov (United States)

    Reiher, Markus; Wolf, Alexander

    2004-12-08

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

  15. Analytic evidence for the Gubser-Mitra conjecture

    International Nuclear Information System (INIS)

    Miyamoto, Umpei

    2008-01-01

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

  16. A meta-analytic review of two modes of learning and the description-experience gap.

    Science.gov (United States)

    Wulff, Dirk U; Mergenthaler-Canseco, Max; Hertwig, Ralph

    2018-02-01

    People can learn about the probabilistic consequences of their actions in two ways: One is by consulting descriptions of an action's consequences and probabilities (e.g., reading up on a medication's side effects). The other is by personally experiencing the probabilistic consequences of an action (e.g., beta testing software). In principle, people taking each route can reach analogous states of knowledge and consequently make analogous decisions. In the last dozen years, however, research has demonstrated systematic discrepancies between description- and experienced-based choices. This description-experience gap has been attributed to factors including reliance on a small set of experience, the impact of recency, and different weighting of probability information in the two decision types. In this meta-analysis focusing on studies using the sampling paradigm of decisions from experience, we evaluated these and other determinants of the decision-experience gap by reference to more than 70,000 choices made by more than 6,000 participants. We found, first, a robust description-experience gap but also a key moderator, namely, problem structure. Second, the largest determinant of the gap was reliance on small samples and the associated sampling error: free to terminate search, individuals explored too little to experience all possible outcomes. Third, the gap persisted when sampling error was basically eliminated, suggesting other determinants. Fourth, the occurrence of recency was contingent on decision makers' autonomy to terminate search, consistent with the notion of optional stopping. Finally, we found indications of different probability weighting in decisions from experience versus decisions from description when the problem structure involved a risky and a safe option. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

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

    International Nuclear Information System (INIS)

    Destounis, Kyriakos; Panotopoulos, Grigoris; Rincon, Angel

    2018-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2018-02-15

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

  19. Exact solutions in three-dimensional gravity

    CERN Document Server

    Garcia-Diaz, Alberto A

    2017-01-01

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

  20. An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State

    Energy Technology Data Exchange (ETDEWEB)

    Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-03-05

    This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.

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

    Science.gov (United States)

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

    2010-01-01

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

  2. Description and Recognition of the Concept of Social Capital in Higher Education System

    Science.gov (United States)

    Tonkaboni, Forouzan; Yousefy, Alireza; Keshtiaray, Narges

    2013-01-01

    The current research is intended to describe and recognize the concept of social capital in higher education based on theoretical method in a descriptive-analytical approach. Description and Recognition of the data, gathered from theoretical and experimental studies, indicated that social capital is one of the most important indices for…

  3. The PHMC algorithm for simulations of dynamical fermions; 1, description and properties

    CERN Document Server

    Frezzotti, R

    1999-01-01

    We give a detailed description of the so-called Polynomial Hybrid Monte Carlo (PHMC) algorithm. The effects of the correction factor, which is introduced to render the algorithm exact, are discussed, stressing their relevance for the statistical fluctuations and (almost) zero mode contributions to physical observables. We also investigate rounding-error effects and propose several ways to reduce memory requirements.

  4. Finding optimal exact reducts

    KAUST Repository

    AbouEisha, Hassan M.

    2014-01-01

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

  5. Analytic and heuristic processing influences on adolescent reasoning and decision-making.

    Science.gov (United States)

    Klaczynski, P A

    2001-01-01

    The normative/descriptive gap is the discrepancy between actual reasoning and traditional standards for reasoning. The relationship between age and the normative/descriptive gap was examined by presenting adolescents with a battery of reasoning and decision-making tasks. Middle adolescents (N = 76) performed closer to normative ideals than early adolescents (N = 66), although the normative/descriptive gap was large for both groups. Correlational analyses revealed that (1) normative responses correlated positively with each other, (2) nonnormative responses were positively interrelated, and (3) normative and nonnormative responses were largely independent. Factor analyses suggested that performance was based on two processing systems. The "analytic" system operates on "decontextualized" task representations and underlies conscious, computational reasoning. The "heuristic" system operates on "contextualized," content-laden representations and produces "cognitively cheap" responses that sometimes conflict with traditional norms. Analytic processing was more clearly linked to age and to intelligence than heuristic processing. Implications for cognitive development, the competence/performance issue, and rationality are discussed.

  6. 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.

  7. 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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2013-08-15

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

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

    International Nuclear Information System (INIS)

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

    2013-01-01

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

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

    OpenAIRE

    Dalarsson, Mariana; Tassin, Philippe

    2012-01-01

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

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

    International Nuclear Information System (INIS)

    Liu Guanting

    2008-01-01

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

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

    Institute of Scientific and Technical Information of China (English)

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

    2007-01-01

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

  13. 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

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

    Science.gov (United States)

    Links, Jon; Shen, Yibing

    2018-05-01

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

  15. Exact folded-band chaotic oscillator.

    Science.gov (United States)

    Corron, Ned J; Blakely, Jonathan N

    2012-06-01

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

  16. Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

    Directory of Open Access Journals (Sweden)

    U. Filobello-Nino

    2015-01-01

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

  17. Dissociation between exact and approximate addition in developmental dyslexia.

    Science.gov (United States)

    Yang, Xiujie; Meng, Xiangzhi

    2016-09-01

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

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

    Science.gov (United States)

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

    2017-11-01

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

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

    International Nuclear Information System (INIS)

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

    2003-01-01

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

  20. 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

  1. Parameter-free one-center model potential for an effective one-electron description of molecular hydrogen

    DEFF Research Database (Denmark)

    Lühr, Armin Christian; Vanne, Yulian; Saenz, Alejandro

    2008-01-01

    For the description of an H2 molecule, an effective one-electron model potential is proposed which is fully determined by the exact ionization potential of the H2 molecule. In order to test the model potential and examine its properties, it is employed to determine excitation energies, transition...

  2. Analytic mean-field hall crystal solution at ν=1/3: composite fermion like sub-bands and correlation effects

    International Nuclear Information System (INIS)

    Cabo, Alejandro; Claro, Francisco

    2003-07-01

    An analytic solution of the Hartree-Fock problem for a 2DEG at filling 1/3 and half an electron per unit cell is presented. The Coulomb interaction dynamically breaks the first Landau level in three narrow sub-bands, one of which is fully occupied and the other empty, as in the composite fermion model. The localized orbitals associated to the Bloch like single electron wavefunctions are nearly static, resembling the angular momentum eigenstates within a Landau level for non-interacting fermions. Strong correlations are expected owing to the large charge density overlap between neighboring plaquettes. A numerical evaluation brings the cohesive energy close to that of the best present day models. It is also found that correlations are long range, requiring over 50 particles spread over a finite sample to approach convergence. Since presently allowed exact calculations are far from this number, the question of how relevant the considered wave-function is for the description of the ground state of the 2DEG system remains open. (author)

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

    Science.gov (United States)

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

    2016-09-01

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

  4. 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)

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2018-02-15

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

  6. Analytical theory of intensity fluctuations in SASE

    Energy Technology Data Exchange (ETDEWEB)

    Yu, L.H.; Krinsky, S. [Brookhaven National Lab., Upton, NY (United States). National Synchrotron Light Source

    1997-07-01

    Recent advances in SASE experiments stimulate interest in quantitative comparison of measurements with theory. Extending the previous analysis of the SASE intensity in guided modes, the authors provide an analytical description of the intensity fluctuations by calculating intensity correlation functions in the frequency domain. Comparison of the results with experiment yields new insight into the SASE process.

  7. 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)

  8. Elastic stars in general relativity: III. Stiff ultrarigid exact solutions

    International Nuclear Information System (INIS)

    Karlovini, Max; Samuelsson, Lars

    2004-01-01

    We present an equation of state for elastic matter which allows for purely longitudinal elastic waves in all propagation directions, not just principal directions. The speed of these waves is equal to the speed of light whereas the transversal type speeds are also very high, comparable to but always strictly less than that of light. Clearly such an equation of state does not give a reasonable matter description for the crust of a neutron star, but it does provide a nice causal toy model for an extremely rigid phase in a neutron star core, should such a phase exist. Another reason for focusing on this particular equation of state is simply that it leads to a very simple recipe for finding stationary rigid motion exact solutions to the Einstein equations. In fact, we show that a very large class of stationary spacetimes with constant Ricci scalar can be interpreted as rigid motion solutions with this matter source. We use the recipe to derive a static spherically symmetric exact solution with constant energy density, regular centre and finite radius, having a nontrivial parameter that can be varied to yield a mass-radius curve from which stability can be read off. It turns out that the solution is stable down to a tenuity R/M slightly less than 3. The result of this static approach to stability is confirmed by a numerical determination of the fundamental radial oscillation mode frequency. We also present another solution with outwards decreasing energy density. Unfortunately, this solution only has a trivial scaling parameter and is found to be unstable

  9. 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

  10. 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.

  11. The BTWorld use case for big data analytics : Description, MapReduce logical workflow, and empirical evaluation

    NARCIS (Netherlands)

    Hegeman, T.; Ghit, B.; Capota, M.; Hidders, A.J.H.; Epema, D.H.J.; Iosup, A.

    2013-01-01

    The commoditization of big data analytics, that is, the deployment, tuning, and future development of big data processing platforms such as MapReduce, relies on a thorough understanding of relevant use cases and workloads. In this work we propose BTWorld, a use case for time-based big data analytics

  12. 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.

  13. Analytical treatment of the runaway-effect

    International Nuclear Information System (INIS)

    Kaeppeler, H.J.

    1980-09-01

    In the analytical treatment of the runaway-effect there appear the integrals Isub(m)(α). For m = 1, 2 and 3, series expansions for these integrals can be found in the literature. Furthermore, asymptotic solutions for Isub(m)(α) are known. It is shown here that the solutions for Isub(m)(α) can be approximated by the modified Bessel Function Ksub(n)(αsup(ν)) in such a way that for α → 0 the exact limiting value for Isub(m)(α) follows and that for α → infinite essentially the known asymptotic solutions for Isub(m)(α) follow. The maximum error for this approximation in the order of percent is considered justifiable for the application considered. (orig.)

  14. 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

  15. 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

  16. Quasitraces on exact C*-algebras are traces

    DEFF Research Database (Denmark)

    Haagerup, Uffe

    2014-01-01

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

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

    International Nuclear Information System (INIS)

    Dineykhan, M.; Nazmitdinov, R.G.

    1997-01-01

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

  18. 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

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

    OpenAIRE

    Kudryashov, N. A.

    2004-01-01

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

  20. Towards an analytical framework for tailoring supercontinuum generation.

    Science.gov (United States)

    Castelló-Lurbe, David; Vermeulen, Nathalie; Silvestre, Enrique

    2016-11-14

    A fully analytical toolbox for supercontinuum generation relying on scenarios without pulse splitting is presented. Furthermore, starting from the new insights provided by this formalism about the physical nature of direct and cascaded dispersive wave emission, a unified description of this radiation in both normal and anomalous dispersion regimes is derived. Previously unidentified physics of broadband spectra reported in earlier works is successfully explained on this basis. Finally, a foundry-compatible few-millimeters-long silicon waveguide allowing octave-spanning supercontinuum generation pumped at telecom wavelengths in the normal dispersion regime is designed, hence showcasing the potential of this new analytical approach.

  1. A nonquasiclassical description of inhomogeneous superconductors

    International Nuclear Information System (INIS)

    Zaikin, A.D.; Panyukov, S.V.

    1988-01-01

    Exact microscopic equations are derived that make it possible to describe inhomogeneous superconductors when the quasi-classical approach is not suitable. These equations are simpler than the Gorkov equations. The authors generalize the derived equations for describing the nonequilibrium states of inhomogeneous superconductors. It is demonstrated that the derived equations (including the case of a nonequilibrium quasi particle distribution function) may be written in the form of linear differential equations for the simultaneous wave function μ, ν. The quasi-classical limit of such equations is examined. Effective boundary conditions are derived for the μ, ν functions that allow description of superconductors with a sharp change in parameters within the scope of the quasi-classical approach

  2. Exact Analytical Solutions for Elastodynamic Impact

    Science.gov (United States)

    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

  3. 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

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

    International Nuclear Information System (INIS)

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

    2009-01-01

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

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

    NARCIS (Netherlands)

    Jargalsaikhan, Bolor

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

  6. Computing exact Fourier series coefficients of IC rectilinear polygons from low-resolution fast Fourier coefficients

    Science.gov (United States)

    Scheibler, Robin; Hurley, Paul

    2012-03-01

    We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.

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

    Science.gov (United States)

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

    2016-04-01

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

  8. Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems

    DEFF Research Database (Denmark)

    Bayat, M.; Shahidi, M.; Barari, Amin

    2011-01-01

    approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...

  9. 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.

  10. 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.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2008-08-13

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

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

    International Nuclear Information System (INIS)

    Kandemir, B S; Keskin, M

    2008-01-01

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

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

    International Nuclear Information System (INIS)

    Markos, P; Schweitzer, L; Weyrauch, M

    2004-01-01

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

  14. Faithful effective-one-body waveforms of small-mass-ratio coalescing black hole binaries

    International Nuclear Information System (INIS)

    Damour, Thibault; Nagar, Alessandro

    2007-01-01

    We address the problem of constructing high-accuracy, faithful analytic waveforms describing the gravitational wave signal emitted by inspiralling and coalescing binary black holes. We work within the effective-one-body (EOB) framework and propose a methodology for improving the current (waveform) implementations of this framework based on understanding, element by element, the physics behind each feature of the waveform and on systematically comparing various EOB-based waveforms with exact waveforms obtained by numerical relativity approaches. The present paper focuses on small-mass-ratio nonspinning binary systems, which can be conveniently studied by Regge-Wheeler-Zerilli-type methods. Our results include (i) a resummed, 3 PN-accurate description of the inspiral waveform, (ii) a better description of radiation reaction during the plunge, (iii) a refined analytic expression for the plunge waveform, (iv) an improved treatment of the matching between the plunge and ring-down waveforms. This improved implementation of the EOB approach allows us to construct complete analytic waveforms which exhibit a remarkable agreement with the exact ones in modulus, frequency, and phase. In particular, the analytic and numerical waveforms stay in phase, during the whole process, within ±1.1% of a cycle. We expect that the extension of our methodology to the comparable-mass case will be able to generate comparably accurate analytic waveforms of direct use for the ground-based network of interferometric detectors of gravitational waves

  15. Continuous Analytical Performances Monitoring at the On-Site Laboratory through Proficiency, Inter-Laboratory Testing and Inter-Comparison Analytical Methods

    International Nuclear Information System (INIS)

    Duhamel, G.; Decaillon, J.-G.; Dashdondog, S.; Kim, C.-K.; Toervenyi, A.; Hara, S.; Kato, S.; Kawaguchi, T.; Matsuzawa, K.

    2015-01-01

    Since 2008, as one measure to strengthen its quality management system, the On-Site Laboratory for nuclear safeguards at the Rokkasho Reprocessing Plant, has increased its participation in domestic and international proficiency and inter-laboratory testing for the purpose of determining analytical method accuracy, precision and robustness but also to support method development and improvement. This paper provides a description of the testing and its scheduling. It presents the way the testing was optimized to cover most of the analytical methods at the OSL. The paper presents the methodology used for the evaluation of the obtained results based on Analysis of variance (ANOVA). Results are discussed with respect to random, systematic and long term systematic error. (author)

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

    Science.gov (United States)

    Tang, C. C. H.

    1986-01-01

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

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

    Science.gov (United States)

    Tang, C. C. H.

    1986-08-01

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

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

    Science.gov (United States)

    Martirosyan, A; Saakian, David B

    2011-08-01

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

  19. 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

  20. Exact models for isotropic matter

    Science.gov (United States)

    Thirukkanesh, S.; Maharaj, S. D.

    2006-04-01

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

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

    International Nuclear Information System (INIS)

    Auerbach, S.P.

    1981-01-01

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

  2. Analytical details of the instability threshold of the laser-Lorenz model

    International Nuclear Information System (INIS)

    Bakasov, A.A.; Abraham, N.B.

    1992-11-01

    An exact analysis of the second threshold of a single-mode homogeneously broadened laser is given for the most general operating conditions. We provide a general analytical proof that increasing the detuning increases the second threshold is given. An analysis of the second threshold at a fixed detuning and of the ratio of the second threshold to the first threshold reveals that the smallest values occur when the population relaxation rate is minimized. (author). 13 refs, 4 figs, 2 tabs

  3. An analytic interface dynamo over a shear layer of finite depth

    OpenAIRE

    Petrovay, K.; Kerekes, A.; Erdélyi, R.

    2010-01-01

    Parker's analytic Cartesian interface dynamo is generalized to the case of a shear layer of finite thickness and low resistivity ("tachocline"), bounded by a perfect conductor ("radiative zone") on the one side, and by a highly diffusive medium ("convective zone") supporting an $\\alpha$-effect on the other side. In the limit of high diffusivity contrast between the shear layer and the diffusive medium, thought to be relevant for the Sun, a pair of exact dispersion relations for the growth rat...

  4. Micro-optics for microfluidic analytical applications.

    Science.gov (United States)

    Yang, Hui; Gijs, Martin A M

    2018-02-19

    This critical review summarizes the developments in the integration of micro-optical elements with microfluidic platforms for facilitating detection and automation of bio-analytical applications. Micro-optical elements, made by a variety of microfabrication techniques, advantageously contribute to the performance of an analytical system, especially when the latter has microfluidic features. Indeed the easy integration of optical control and detection modules with microfluidic technology helps to bridge the gap between the macroscopic world and chip-based analysis, paving the way for automated and high-throughput applications. In our review, we start the discussion with an introduction of microfluidic systems and micro-optical components, as well as aspects of their integration. We continue with a detailed description of different microfluidic and micro-optics technologies and their applications, with an emphasis on the realization of optical waveguides and microlenses. The review continues with specific sections highlighting the advantages of integrated micro-optical components in microfluidic systems for tackling a variety of analytical problems, like cytometry, nucleic acid and protein detection, cell biology, and chemical analysis applications.

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

    Science.gov (United States)

    Dalarsson, Mariana; Tassin, Philippe

    2009-04-13

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

  6. Symmetries and exact solutions of the nondiagonal Einstein-Rosen metrics

    International Nuclear Information System (INIS)

    Goyal, N; Gupta, R K

    2012-01-01

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

  7. (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.

  8. Multi-analytical Approaches Informing the Risk of Sepsis

    Science.gov (United States)

    Gwadry-Sridhar, Femida; Lewden, Benoit; Mequanint, Selam; Bauer, Michael

    Sepsis is a significant cause of mortality and morbidity and is often associated with increased hospital resource utilization, prolonged intensive care unit (ICU) and hospital stay. The economic burden associated with sepsis is huge. With advances in medicine, there are now aggressive goal oriented treatments that can be used to help these patients. If we were able to predict which patients may be at risk for sepsis we could start treatment early and potentially reduce the risk of mortality and morbidity. Analytic methods currently used in clinical research to determine the risk of a patient developing sepsis may be further enhanced by using multi-modal analytic methods that together could be used to provide greater precision. Researchers commonly use univariate and multivariate regressions to develop predictive models. We hypothesized that such models could be enhanced by using multiple analytic methods that together could be used to provide greater insight. In this paper, we analyze data about patients with and without sepsis using a decision tree approach and a cluster analysis approach. A comparison with a regression approach shows strong similarity among variables identified, though not an exact match. We compare the variables identified by the different approaches and draw conclusions about the respective predictive capabilities,while considering their clinical significance.

  9. 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.

  10. Exact solution of the hidden Markov processes

    Science.gov (United States)

    Saakian, David B.

    2017-11-01

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

  11. 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

  12. Exact phase boundaries and topological phase transitions of the X Y Z spin chain

    Science.gov (United States)

    Jafari, S. A.

    2017-07-01

    Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the X Y Z spin chain. First, we identify the Ising order along x ̂ or y ̂ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the X Y interaction and the coupling Δ of the Δ σzσz interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the X Y Z spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1 , depending on whether the Ising order parameter is along x ̂ or y ̂ directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the X Y Z model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the X Y Z model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

  13. Exact Theory of Compressible Fluid Turbulence

    Science.gov (United States)

    Drivas, Theodore; Eyink, Gregory

    2017-11-01

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

  14. Analytical pair correlations in ideal quantum gases: temperature-dependent bunching and antibunching.

    Science.gov (United States)

    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

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

    OpenAIRE

    Bemman, Brian; Meredith, David

    2015-01-01

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

  16. Analytical studies on the Benney-Luke equation in mathematical physics

    Science.gov (United States)

    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.

  17. Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid

    Science.gov (United States)

    Gupta, Sumeet; Poulikakos, Dimos; Kurtcuoglu, Vartan

    2008-09-01

    We present here the analytical solution of transient, laminar, viscous flow of an incompressible, Newtonian fluid driven by a harmonically oscillating pressure gradient in a straight elliptic annulus. The analytical formulation is based on the exact solution of the governing fluid flow equations known as Navier-Stokes equations. We validate the analytical solution using a finite-volume computational fluid dynamics approach. As the analytical solution includes Mathieu and modified Mathieu functions, we also present a stepwise procedure for their evaluation for large complex arguments typically associated with viscous flows. We further outline the procedure for evaluating the associated Fourier coefficients and their eigenvalues. We finally apply the analytical solution to investigate the cerebrospinal fluid flow in the human spinal cavity, which features a shape similar to an elliptic annulus.

  18. Charge transfer through single molecule contacts: How reliable are rate descriptions?

    Directory of Open Access Journals (Sweden)

    Denis Kast

    2011-08-01

    Full Text Available Background: The trend for the fabrication of electrical circuits with nanoscale dimensions has led to impressive progress in the field of molecular electronics in the last decade. However, a theoretical description of molecular contacts as the building blocks of future devices is challenging, as it has to combine the properties of Fermi liquids in the leads with charge and phonon degrees of freedom on the molecule. Outside of ab initio schemes for specific set-ups, generic models reveal the characteristics of transport processes. Particularly appealing are descriptions based on transfer rates successfully used in other contexts such as mesoscopic physics and intramolecular electron transfer. However, a detailed analysis of this scheme in comparison with numerically exact solutions is still elusive.Results: We show that a formulation in terms of transfer rates provides a quantitatively accurate description even in domains of parameter space where strictly it is expected to fail, e.g., at lower temperatures. Typically, intramolecular phonons are distributed according to a voltage driven steady state that can only roughly be captured by a thermal distribution with an effective elevated temperature (heating. An extension of a master equation for the charge–phonon complex, to effectively include the impact of off-diagonal elements of the reduced density matrix, provides very accurate solutions even for stronger electron–phonon coupling.Conclusion: Rate descriptions and master equations offer a versatile model to describe and understand charge transfer processes through molecular junctions. Such methods are computationally orders of magnitude less expensive than elaborate numerical simulations that, however, provide exact solutions as benchmarks. Adjustable parameters obtained, e.g., from ab initio calculations allow for the treatment of various realizations. Even though not as rigorously formulated as, e.g., nonequilibrium Green’s function

  19. Exact solution of nonsteady thermal boundary layer equation

    International Nuclear Information System (INIS)

    Dorfman, A.S.

    1995-01-01

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

  20. Constructing exact symmetric informationally complete measurements from numerical solutions

    Science.gov (United States)

    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.

  1. Analytic Theology as Sapiential Theology: A Response to Jordan Wessling

    Directory of Open Access Journals (Sweden)

    Vanhoozer Kevin J.

    2017-10-01

    Full Text Available This article responds to Jordan Wessling’s paper that engages a concern I expressed about analytic theology not doing justice to the sapiential requirements of theology. I examine Wessling’s summary of my paper, conclude that his description is accurate and fair, appreciate his proposed solution, then go on to restate why I think he may not have fully allayed my concern. I suggest that analytic theology is a vital tool in the theologian’s toolkit, but that ultimately more is needed in order to interpret Scripture theologically.

  2. An exact fermion-pair to boson mapping

    International Nuclear Information System (INIS)

    Johnson, C.W.

    1993-01-01

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

  3. The exact mass-gaps of the principal chiral models

    CERN Document Server

    Hollowood, Timothy J

    1994-01-01

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

  4. Analytical calculation of heavy quarkonia production processes in computer

    International Nuclear Information System (INIS)

    Braguta, V V; Likhoded, A K; Luchinsky, A V; Poslavsky, S V

    2014-01-01

    This report is devoted to the analytical calculation of heavy quarkonia production processes in modern experiments such as LHC, B-factories and superB-factories in computer. Theoretical description of heavy quarkonia is based on the factorization theorem. This theorem leads to special structure of the production amplitudes which can be used to develop computer algorithm which calculates these amplitudes automatically. This report is devoted to the description of this algorithm. As an example of its application we present the results of the calculation of double charmonia production in bottomonia decays and inclusive the χ cJ mesons production in pp-collisions

  5. Description and principles of use of an automatic control device usable, in particular, in analytical chemistry; Description et principes d'utilisation d'un dispositif de commande automatique utilisable, en particulier, en chimie analytique

    Energy Technology Data Exchange (ETDEWEB)

    Rigaudiere, Roger; Jeanmaire, Lucien [Commissariat a l' Energie Atomique - CEA, Centre d' Etudes Nucleaires de Fontenay-aux-Roses, Direction de la Protection et de la Surete Radiologiques, Departement de la Protection Sanitaire, Section de Controle Sanitaire (France)

    1969-07-01

    This note describes an automatic control device for the programming of about 20 different functions, chronologically and during a given time. Any voltage can be chosen at the output to perform the different functions. Three examples of utilisation taken in analytical chemistry are given to illustrate the possibilities offered by this device, but its domain of use is much more universal and independent of the type of functions [French] Description d'un dispositif de commande automatique destine a programmer une vingtaine de fonctions differentes dans l'ordre et pendant le temps desire. Aux bornes d'utilisation de ce dispositif, on peut choisir a volonte du 24 V continu, du 220 V alternatif ou un contact de court-circuit pour realiser les fonctions elles-memes. Afin d'illustrer concretement les possibilites de cet appareil, il est donne trois exemples d'utilisation empruntes a la chimie analytique pour laquelle il a ete prevu initialement. En realite, son domaine d'utilisation est beaucoup plus universel, car il est relativement independant de la nature des fonctions. (auteurs)

  6. Simple Parametric Model for Airfoil Shape Description

    Science.gov (United States)

    Ziemkiewicz, David

    2017-12-01

    We show a simple, analytic equation describing a class of two-dimensional shapes well suited for representation of aircraft airfoil profiles. Our goal was to create a description characterized by a small number of parameters with easily understandable meaning, providing a tool to alter the shape with optimization procedures as well as manual tweaks by the designer. The generated shapes are well suited for numerical analysis with 2D flow solving software such as XFOIL.

  7. Analytical mass formula and nuclear surface properties in the ETF approximation. Part I: symmetric nuclei

    Science.gov (United States)

    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.

  8. Analytical method validation for quality control and the study of the 50 mg Propylthiouracil stability

    International Nuclear Information System (INIS)

    Valdes Bendoyro, Maria Olga; Garcia Penna, Caridad Margarita; Fernandez, Juan Lugones; Garcia Borges, Lisandra; Martinez Espinosa, Vivian

    2010-01-01

    A high-performance liquid chromatography analytical method was developed and validated for the quality control and stability studies of 50 mg Propylthiouracil tablets. Method is based in active principle separation through a 100 RP-18 RP-18 (5 μm) (250 x 4 mm) Lichrospher chromatography with UV detection to 272 nm, using a mobile phase composed by a ungaseous mixture of a 0.025 M buffer solution-monobasic potassium phosphate to pH= 4,6 ad acetonitrile in a 80:20 ratio with a flux speed of 0,5 mL/min. Analytical method was linear, precise, specific and exact in the study concentrations interval

  9. 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.

  10. 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.

  11. 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.

  12. 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)

  13. Library improvement through data analytics

    CERN Document Server

    Farmer, Lesley S J

    2017-01-01

    This book shows how to act on and make sense of data in libraries. Using a range of techniques, tools and methodologies it explains how data can be used to help inform decision making at every level. Sound data analytics is the foundation for making an evidence-based case for libraries, in addition to guiding myriad organizational decisions, from optimizing operations for efficiency to responding to community needs. Designed to be useful for beginners as well as those with a background in data, this book introduces the basics of a six point framework that can be applied to a variety of library settings for effective system based, data-driven management. Library Improvement Through Data Analytics includes: - the basics of statistical concepts - recommended data sources for various library functions and processes, and guidance for using census, university, or - - government data in analysis - techniques for cleaning data - matching data to appropriate data analysis methods - how to make descriptive statistics m...

  14. A primer of analytical mechanics

    CERN Document Server

    Strocchi, Franco

    2018-01-01

    This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hami...

  15. 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.

  16. Analytical and numerical description of the PELE fragmentation upon impact with thin target plates

    NARCIS (Netherlands)

    Verreault, J.

    2015-01-01

    The PELE ammunition is characterized by a low-density filling material surrounded by a high-density brittle jacket material. An analytical model describing the fragmentation of this ammunition behind a target plate is presented. This model assumes uniaxial strain in the filling and uses the

  17. Analytical study of dissipative solitary waves

    Energy Technology Data Exchange (ETDEWEB)

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

    2008-02-15

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

  18. Mixed Initiative Visual Analytics Using Task-Driven Recommendations

    Energy Technology Data Exchange (ETDEWEB)

    Cook, Kristin A.; Cramer, Nicholas O.; Israel, David; Wolverton, Michael J.; Bruce, Joseph R.; Burtner, Edwin R.; Endert, Alexander

    2015-12-07

    Visual data analysis is composed of a collection of cognitive actions and tasks to decompose, internalize, and recombine data to produce knowledge and insight. Visual analytic tools provide interactive visual interfaces to data to support tasks involved in discovery and sensemaking, including forming hypotheses, asking questions, and evaluating and organizing evidence. Myriad analytic models can be incorporated into visual analytic systems, at the cost of increasing complexity in the analytic discourse between user and system. Techniques exist to increase the usability of interacting with such analytic models, such as inferring data models from user interactions to steer the underlying models of the system via semantic interaction, shielding users from having to do so explicitly. Such approaches are often also referred to as mixed-initiative systems. Researchers studying the sensemaking process have called for development of tools that facilitate analytic sensemaking through a combination of human and automated activities. However, design guidelines do not exist for mixed-initiative visual analytic systems to support iterative sensemaking. In this paper, we present a candidate set of design guidelines and introduce the Active Data Environment (ADE) prototype, a spatial workspace supporting the analytic process via task recommendations invoked by inferences on user interactions within the workspace. ADE recommends data and relationships based on a task model, enabling users to co-reason with the system about their data in a single, spatial workspace. This paper provides an illustrative use case, a technical description of ADE, and a discussion of the strengths and limitations of the approach.

  19. Exact solutions of nonlinear differential equations using continued fractions

    International Nuclear Information System (INIS)

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

    1990-01-01

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

  20. Exact Lattice Supersymmetry

    Energy Technology Data Exchange (ETDEWEB)

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

    2009-03-31

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

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

    International Nuclear Information System (INIS)

    Litvinenko, Yuri E.; Effenberger, Frederic

    2014-01-01

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

  2. 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.

  3. Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation

    International Nuclear Information System (INIS)

    Yomba, Emmanuel; Kofane, Timoleon Crepin

    2003-01-01

    The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modified Schroedinger limit

  4. New hybrid voxelized/analytical primitive in Monte Carlo simulations for medical applications

    International Nuclear Information System (INIS)

    Bert, Julien; Lemaréchal, Yannick; Visvikis, Dimitris

    2016-01-01

    Monte Carlo simulations (MCS) applied in particle physics play a key role in medical imaging and particle therapy. In such simulations, particles are transported through voxelized phantoms derived from predominantly patient CT images. However, such voxelized object representation limits the incorporation of fine elements, such as artificial implants from CAD modeling or anatomical and functional details extracted from other imaging modalities. In this work we propose a new hYbrid Voxelized/ANalytical primitive (YVAN) that combines both voxelized and analytical object descriptions within the same MCS, without the need to simultaneously run two parallel simulations, which is the current gold standard methodology. Given that YVAN is simply a new primitive object, it does not require any modifications on the underlying MC navigation code. The new proposed primitive was assessed through a first simple MCS. Results from the YVAN primitive were compared against an MCS using a pure analytical geometry and the layer mass geometry concept. A perfect agreement was found between these simulations, leading to the conclusion that the new hybrid primitive is able to accurately and efficiently handle phantoms defined by a mixture of voxelized and analytical objects. In addition, two application-based evaluation studies in coronary angiography and intra-operative radiotherapy showed that the use of YVAN was 6.5% and 12.2% faster than the layered mass geometry method, respectively, without any associated loss of accuracy. However, the simplification advantages and differences in computational time improvements obtained with YVAN depend on the relative proportion of the analytical and voxelized structures used in the simulation as well as the size and number of triangles used in the description of the analytical object meshes. (paper)

  5. New hybrid voxelized/analytical primitive in Monte Carlo simulations for medical applications.

    Science.gov (United States)

    Bert, Julien; Lemaréchal, Yannick; Visvikis, Dimitris

    2016-05-07

    Monte Carlo simulations (MCS) applied in particle physics play a key role in medical imaging and particle therapy. In such simulations, particles are transported through voxelized phantoms derived from predominantly patient CT images. However, such voxelized object representation limits the incorporation of fine elements, such as artificial implants from CAD modeling or anatomical and functional details extracted from other imaging modalities. In this work we propose a new hYbrid Voxelized/ANalytical primitive (YVAN) that combines both voxelized and analytical object descriptions within the same MCS, without the need to simultaneously run two parallel simulations, which is the current gold standard methodology. Given that YVAN is simply a new primitive object, it does not require any modifications on the underlying MC navigation code. The new proposed primitive was assessed through a first simple MCS. Results from the YVAN primitive were compared against an MCS using a pure analytical geometry and the layer mass geometry concept. A perfect agreement was found between these simulations, leading to the conclusion that the new hybrid primitive is able to accurately and efficiently handle phantoms defined by a mixture of voxelized and analytical objects. In addition, two application-based evaluation studies in coronary angiography and intra-operative radiotherapy showed that the use of YVAN was 6.5% and 12.2% faster than the layered mass geometry method, respectively, without any associated loss of accuracy. However, the simplification advantages and differences in computational time improvements obtained with YVAN depend on the relative proportion of the analytical and voxelized structures used in the simulation as well as the size and number of triangles used in the description of the analytical object meshes.

  6. Upper bounds on minimum cardinality of exact and approximate reducts

    KAUST Repository

    Chikalov, Igor

    2010-01-01

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

  7. Algebraic descriptions of nuclear and molecular rotation-vibration spectra

    International Nuclear Information System (INIS)

    Roosmalen, O.S. van.

    1982-01-01

    The application of algebraic models to the description of rotational and vibrational degrees of freedom of nuclei and molecules are discussed. Simple model Hamiltonians are shown to give good agreement with the energy spectra of diatomic molecules and nuclei. Some formal aspects of path integral methods for many-boson systems are treated. The two representations for the quantum mechanical propagator are compared and appear to be identical in leading order in 1/N (N is the number of bosons). Approximations for both are static and dynamic problems are discussed. Applications of mean field techniques are also treated. A description of tri- and tetra-atomic molecules in terms of a U(4)xU(4) and U(4)xU(4)xU(4) group structure is given. Linear molecules appear to correspond with symmetries of O(4) type. S-matrix elements are calculated to test mean field methods, and the results compared with exact calculations. (Auth.)

  8. Electron transfer dynamics: Zusman equation versus exact theory

    International Nuclear Information System (INIS)

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

    2009-01-01

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

  9. 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 ...

  10. An analytical model for the description of the full-polarimetric sea surface Doppler signature

    NARCIS (Netherlands)

    Fois, F.; Hoogeboom, P.; Le Chevalier, F.; Stoffelen, A.

    2015-01-01

    This paper describes an analytical model of the full-polarimetric sea surface scattering and Doppler signature. The model combines the small-slope-approximation theory (at the second order) with a weak nonlinear sea surface representation. Such a model is used to examine the variation of the Doppler

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

    International Nuclear Information System (INIS)

    Brailsford, A.D.

    1977-01-01

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

  12. 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...

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

    International Nuclear Information System (INIS)

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

    2010-01-01

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

  14. 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)

  15. 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

  16. 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

  17. Symmetry analysis of the high-order equations for the description of the Fermi – Pasta – Ulam problem

    International Nuclear Information System (INIS)

    Kudryashov, N A; Volkov, A K

    2017-01-01

    Recently some new nonlinear equations for the description of the Fermi – Pasta – Ulam problem have been derived. The main aim of this work is to use the symmetry test to investigate these equations. We consider equations for the description of the α and α + β Fermi – Pasta – Ulam model. We find the infinitesimal operators and Lie groups, admitted by the equations. Using the groups we find the self-similar variables as well as the reductions to the ordinary differential equations. Some exact solutions are also constructed. (paper)

  18. On the limits of the effective description of hyperbolic materials in the presence of surface waves

    International Nuclear Information System (INIS)

    Tschikin, Maria; Biehs, Svend-Age; Messina, Riccardo; Ben-Abdallah, Philippe

    2013-01-01

    Here, we address the question of the validity of an effective description for hyperbolic metamaterials in the near-field region. We show that the presence of localized modes such as surface waves drastically limits the validity of the effective description, and requires revisiting the concept of homogenization in the near-field. We demonstrate, from exact scattering matrix calculations for multilayer hyperbolic structures, that one can find surface modes in spectral regions where the effective approach predicts hyperbolic modes only. Hence, the presence of surface modes which are not accounted for in the effective description can lead to physical misinterpretations in the description of hyperbolic materials and their related properties. In particular, we discuss in detail how the choice of the topmost layer affects the validity of the effective medium approach for calculating the local density of states and the super-Planckian thermal radiation. (paper)

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

    International Nuclear Information System (INIS)

    Strack, O.D.L.

    1982-02-01

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

  20. 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...