Sample records for obtain exact expressions

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

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  3. Metal-cluster ionization energy: A profile-insensitive exact expression for the size effect

    NASA Astrophysics Data System (ADS)

    Seidl, Michael; Perdew, John P.; Brajczewska, Marta; Fiolhais, Carlos

    1997-05-01

    The ionization energy of a large spherical metal cluster of radius R is I(R)=W+(+c)/R, where W is the bulk work function and c~-0.1 is a material-dependent quantum correction to the electrostatic size effect. We present 'Koopmans' and 'displaced-profile change-in-self-consistent-field' expressions for W and c within the ordinary and stabilized-jellium models. These expressions are shown to be exact and equivalent when the exact density profile of a large neutral cluster is employed; these equivalences generalize the Budd-Vannimenus theorem. With an approximate profile obtained from a restricted variational calculation, the 'displaced-profile' expressions are the more accurate ones. This profile insensitivity is important, because it is not practical to extract c from solutions of the Kohn-Sham equations for small metal clusters.

  4. Formal expressions and corresponding expansions for the exact Kohn-Sham exchange potential

    NASA Astrophysics Data System (ADS)

    Bulat, Felipe A.; Levy, Mel

    2009-11-01

    Formal expressions and their corresponding expansions in terms of Kohn-Sham (KS) orbitals are deduced for the exchange potential vx(r) . After an alternative derivation of the basic optimized effective potential integrodifferential equations is given through a Hartree-Fock adiabatic connection perturbation theory, we present an exact infinite expansion for vx(r) that is particularly simple in structure. It contains the very same occupied-virtual quantities that appear in the well-known optimized effective potential integral equation, but in this new expression vx(r) is isolated on one side of the equation. An orbital-energy modified Slater potential is its leading term which gives encouraging numerical results. Along different lines, while the earlier Krieger-Li-Iafrate approximation truncates completely the necessary first-order perturbation orbitals, we observe that the improved localized Hartree-Fock (LHF) potential, or common energy denominator potential (CEDA), or effective local potential (ELP), incorporates the part of each first-order orbital that consists of the occupied KS orbitals. With this in mind, the exact correction to the LHF, CEDA, or ELP potential (they are all equivalent) is deduced and displayed in terms of the virtual portions of the first-order orbitals. We close by observing that the newly derived exact formal expressions and corresponding expansions apply as well for obtaining the correlation potential from an orbital-dependent correlation energy functional.

  5. The exact thermal rotational spectrum of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

    NASA Technical Reports Server (NTRS)

    Reimers, J. R.; Heller, E. J.

    1985-01-01

    The exact thermal rotational spectrum of a two-dimensional rigid rotor is obtained using Gaussian wave packet dynamics. The spectrum is obtained by propagating, without approximation, infinite sets of Gaussian wave packets. These sets are constructed so that collectively they have the correct periodicity, and indeed, are coherent states appropriate to this problem. Also, simple, almost classical, approximations to full wave packet dynamics are shown to give results which are either exact or very nearly exact. Advantages of the use of Gaussian wave packet dynamics over conventional linear response theory are discussed.

  6. Microscopic derivation of particle-based coarse-grained dynamics: Exact expression for memory function

    NASA Astrophysics Data System (ADS)

    Izvekov, Sergei

    2017-03-01

    We consider the generalized Langevin equations of motion describing exactly the particle-based coarse-grained dynamics in the classical microscopic ensemble that were derived recently within the Mori-Zwanzig formalism based on new projection operators [S. Izvekov, J. Chem. Phys. 138(13), 134106 (2013)]. The fundamental difference between the new family of projection operators and the standard Zwanzig projection operator used in the past to derive the coarse-grained equations of motion is that the new operators average out the explicit irrelevant trajectories leading to the possibility of solving the projected dynamics exactly. We clarify the definition of the projection operators and revisit the formalism to compute the projected dynamics exactly for the microscopic system in equilibrium. The resulting expression for the projected force is in the form of a "generalized additive fluctuating force" describing the departure of the generalized microscopic force associated with the coarse-grained coordinate from its projection. Starting with this key expression, we formulate a new exact formula for the memory function in terms of microscopic and coarse-grained conservative forces. We conclude by studying two independent limiting cases of practical importance: the Markov limit (vanishing correlations of projected force) and the limit of weak dependence of the memory function on the particle momenta. We present computationally affordable expressions which can be efficiently evaluated from standard molecular dynamics simulations.

  7. The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

    NASA Technical Reports Server (NTRS)

    Reimers, J. R.; Heller, E. J.

    1985-01-01

    Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

  8. Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution

    NASA Astrophysics Data System (ADS)

    Beléndez, Augusto; Francés, Jorge; Beléndez, Tarsicio; Bleda, Sergio; Pascual, Carolina; Arribas, Enrique

    2015-05-01

    A family of conservative, truly nonlinear, oscillators with integer or non-integer order nonlinearity is considered. These oscillators have only one odd power-form elastic-term and exact expressions for their period and solution were found in terms of Gamma functions and a cosine-Ateb function, respectively. Only for a few values of the order of nonlinearity, is it possible to obtain the periodic solution in terms of more common functions. However, for this family of conservative truly nonlinear oscillators we show in this paper that it is possible to obtain the Fourier series expansion of the exact solution, even though this exact solution is unknown. The coefficients of the Fourier series expansion of the exact solution are obtained as an integral expression in which a regularized incomplete Beta function appears. These coefficients are a function of the order of nonlinearity only and are computed numerically. One application of this technique is to compare the amplitudes for the different harmonics of the solution obtained using approximate methods with the exact ones computed numerically as shown in this paper. As an example, the approximate amplitudes obtained via a modified Ritz method are compared with the exact ones computed numerically.

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

    NASA Astrophysics Data System (ADS)

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

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

  10. Linearly exact parallel closures for slab geometry

    NASA Astrophysics Data System (ADS)

    Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun

    2013-08-01

    Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).

  11. Exact combinatorial approach to finite coagulating systems

    NASA Astrophysics Data System (ADS)

    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.

  12. Exact and approximate solutions to the oblique shock equations for real-time applications

    NASA Technical Reports Server (NTRS)

    Hartley, T. T.; Brandis, R.; Mossayebi, F.

    1991-01-01

    The derivation of exact solutions for determining the characteristics of an oblique shock wave in a supersonic flow is investigated. Specifically, an explicit expression for the oblique shock angle in terms of the free stream Mach number, the centerbody deflection angle, and the ratio of the specific heats, is derived. A simpler approximate solution is obtained and compared to the exact solution. The primary objectives of obtaining these solutions is to provide a fast algorithm that can run in a real time environment.

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

    NASA Astrophysics Data System (ADS)

    Vitanov, Nikolay K.

    2011-03-01

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

  14. Exact relativistic expressions for wave refraction in a generally moving fluid.

    PubMed

    Cavalleri, G; Tonni, E; Barbero, F

    2013-04-01

    The law for the refraction of a wave when the two fluids and the interface are moving with relativistic velocities is given in an exact form, at the same time correcting a first order error in a previous paper [Cavalleri and Tonni, Phys. Rev. E 57, 3478 (1998)]. The treatment is then extended to a generally moving fluid with variable refractive index, ready to be applied to the refraction of acoustic, electromagnetic, or magnetohydrodynamic waves in the atmosphere of rapidly rotating stars. In the particular case of a gas cloud receding because of the universe expansion, our result can be applied to predict observable micro- and mesolensings. The first order approximation of our exact result for the deviation due to refraction of the light coming from a further quasar has a relativistic dependence equal to the one obtained by Einsteins' linearized theory of gravitation.

  15. Exact analytical thermodynamic expressions for a Brownian heat engine

    NASA Astrophysics Data System (ADS)

    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.

  16. Exact analytical thermodynamic expressions for a Brownian heat engine.

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  18. General exact solution to the problem of the probability density for sums of random variables.

    PubMed

    Tribelsky, Michael I

    2002-08-12

    The exact explicit expression for the probability density p(N)(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 p(N)(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.

  19. Exact sum rules for inhomogeneous drums

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Amore, Paolo, E-mail: paolo.amore@gmail.com

    2013-09-15

    We derive general expressions for the sum rules of the eigenvalues of drums of arbitrary shape and arbitrary density, obeying different boundary conditions. The formulas that we present are a generalization of the analogous formulas for one dimensional inhomogeneous systems that we have obtained in a previous paper. We also discuss the extension of these formulas to higher dimensions. We show that in the special case of a density depending only on one variable the sum rules of any integer order can be expressed in terms of a single series. As an application of our result we derive exact summore » rules for the homogeneous circular annulus with different boundary conditions, for a homogeneous circular sector and for a radially inhomogeneous circular annulus with Dirichlet boundary conditions. -- Highlights: •We derive an explicit expression for the sum rules of inhomogeneous drums. •We discuss the extension to higher dimensions. •We discuss the special case of an inhomogeneity only along one direction.« less

  20. The difference between two random mixed quantum states: exact and asymptotic spectral analysis

    NASA Astrophysics Data System (ADS)

    Mejía, José; Zapata, Camilo; Botero, Alonso

    2017-01-01

    We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact joint eigenvalue probability density function for arbitrary dimensions can be obtained from the joint probability density function of the diagonal elements of the difference matrix, which is straightforward to compute. Subsequently, we use standard results from free probability theory to derive a relatively simple analytic expression for the asymptotic eigenvalue density (AED) of the difference matrix ensemble, and using Carlson’s theorem, we obtain an expression for its absolute moments. These results allow us to quantify the typical asymptotic distance between the two random mixed states using various distance measures; in particular, we obtain the almost sure asymptotic behavior of the operator norm distance and the trace distance.

  1. Deriving the exact nonadiabatic quantum propagator in the mapping variable representation.

    PubMed

    Hele, Timothy J H; Ananth, Nandini

    2016-12-22

    We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting Liouvillian is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact Liouvillian lead to existing approximate semiclassical and mixed quantum-classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact Liouvillian, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction rates in complex quantized systems.

  2. Exact milestoning

    PubMed Central

    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. PMID:25747056

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

    PubMed

    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.

  4. Entanglement dynamics in a non-Markovian environment: An exactly solvable model

    NASA Astrophysics Data System (ADS)

    Wilson, Justin H.; Fregoso, Benjamin M.; Galitski, Victor M.

    2012-05-01

    We study the non-Markovian effects on the dynamics of entanglement in an exactly solvable model that involves two independent oscillators, each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time correlations, we see nonmonotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of “sudden death” and “rebirth” of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

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

    ERIC Educational Resources Information Center

    Mei, W. N.; Holloway, A.

    2005-01-01

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

  6. An exact analysis of a rectangular plate piezoelectric generator.

    PubMed

    Yang, Jiashi; Chen, Ziguang; Hu, Yuantai

    2007-01-01

    We study thickness-twist vibration of a finite, piezoelectric plate of polarized ceramics or 6-mm crystals driven by surface mechanical loads. An exact solution from the three-dimensional equations of piezoelectricity is obtained. The plate is properly electroded and connected to a circuit such that an electric output is generated. The structure analyzed represents a piezoelectric generator for converting mechanical energy to electrical energy. Analytical expressions for the output voltage, current, power, efficiency, and power density are given. The basic behaviors of the generator are shown by numerical results.

  7. Exact solution of the hidden Markov processes.

    PubMed

    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.

  8. Exact solution of the hidden Markov processes

    NASA Astrophysics Data System (ADS)

    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 .

  9. Exact formulas for multipole moments using Slater-type molecular orbitals

    NASA Technical Reports Server (NTRS)

    Jones, H. W.

    1986-01-01

    A triple infinite sum of formulas expressed as an expansion in Legendre polynomials is generated by use of computer algebra to represent the potential from the midpoint of two Slater-type orbitals; the charge density that determines the potential is given as the product of the two orbitals. An example using 1s orbitals shows that only a few terms are needed to obtain four-figure accuracy. Exact formulas are obtained for multipole moments by means of a careful study of expanded formulas, allowing an 'extrapolation to infinity'. This Loewdin alpha-function approach augmented by using a C matrix to characterize Slater-type orbitals can be readily generalized to all cases.

  10. Exact Closed-form Solutions for Lamb's Problem

    NASA Astrophysics Data System (ADS)

    Feng, Xi; Zhang, Haiming

    2018-04-01

    In this article, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem, for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's (1974) integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson (1974), which strongly confirms the correctness of our explicit formulas. It is hoped that in due time, these formulas may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.

  11. Exact closed-form solutions for Lamb's problem

    NASA Astrophysics Data System (ADS)

    Feng, Xi; Zhang, Haiming

    2018-07-01

    In this paper, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson, which strongly confirms the correctness of our explicit formulae. It is hoped that in due time, these formulae may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.

  12. Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

    NASA Astrophysics Data System (ADS)

    Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

    2018-05-01

    A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

  13. Exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral harmonics

    NASA Astrophysics Data System (ADS)

    Mahajan, Bharat; Vadali, Srinivas R.; Alfriend, Kyle T.

    2018-03-01

    A novel approach for the exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral and sectorial spherical harmonics is presented in this work. It is shown that the exact solution for the Delaunay normalization can be reduced to quadratures by the application of Deprit's Lie-transform-based perturbation method. Two different series representations of the quadratures, one in powers of the eccentricity and the other in powers of the ratio of the Earth's angular velocity to the satellite's mean motion, are derived. The latter series representation produces expressions for the short-period variations that are similar to those obtained from the conventional method of relegation. Alternatively, the quadratures can be evaluated numerically, resulting in more compact expressions for the short-period variations that are valid for an elliptic orbit with an arbitrary value of the eccentricity. Using the proposed methodology for the Delaunay normalization, generalized expressions for the short-period variations of the equinoctial orbital elements, valid for an arbitrary tesseral or sectorial harmonic, are derived. The result is a compact unified artificial satellite theory for the sub-synchronous and super-synchronous orbit regimes, which is nonsingular for the resonant orbits, and is closed-form in the eccentricity as well. The accuracy of the proposed theory is validated by comparison with numerical orbit propagations.

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

    NASA Astrophysics Data System (ADS)

    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. Some Exact Solutions of a Nonintegrable Toda-type Equation

    NASA Astrophysics Data System (ADS)

    Kim, Chanju

    2018-05-01

    We study a Toda-type equation with two scalar fields which is not integrable and construct two families of exact solutions which are expressed in terms of rational functions. The equation appears in U(1) Chern-Simons theories coupled to two nonrelativistic matter fields with opposite charges. One family of solutions is a trivial embedding of Liouville-type solutions. The other family is obtained by transforming the equation into the Taubes vortex equation on the hyperbolic space. Though the Taubes equation is not integrable, a trivial vacuum solution provides nontrivial solutions to the original Toda-type equation.

  16. Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

    PubMed

    Demidenko, Eugene

    2017-09-01

    The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

  17. Classical heat transport in anharmonic molecular junctions: exact solutions.

    PubMed

    Liu, Sha; Agarwalla, Bijay Kumar; Wang, Jian-Sheng; Li, Baowen

    2013-02-01

    We study full counting statistics for classical heat transport through anharmonic or nonlinear molecular junctions formed by interacting oscillators. An analytical result of the steady-state heat flux for an overdamped anharmonic junction with arbitrary temperature bias is obtained. It is found that the thermal conductance can be expressed in terms of a temperature-dependent effective force constant. The role of anharmonicity is identified. We also give the general formula for the second cumulant of heat in steady state, as well as the average geometric heat flux when two system parameters are modulated adiabatically. We present an anharmonic example for which all cumulants for heat can be obtained exactly. For a bounded single oscillator model with mass we found that the cumulants are independent of the nonlinear potential.

  18. Analysis of multiplex gene expression maps obtained by voxelation.

    PubMed

    An, Li; Xie, Hongbo; Chin, Mark H; Obradovic, Zoran; Smith, Desmond J; Megalooikonomou, Vasileios

    2009-04-29

    Gene expression signatures in the mammalian brain hold the key to understanding neural development and neurological disease. Researchers have previously used voxelation in combination with microarrays for acquisition of genome-wide atlases of expression patterns in the mouse brain. On the other hand, some work has been performed on studying gene functions, without taking into account the location information of a gene's expression in a mouse brain. In this paper, we present an approach for identifying the relation between gene expression maps obtained by voxelation and gene functions. To analyze the dataset, we chose typical genes as queries and aimed at discovering similar gene groups. Gene similarity was determined by using the wavelet features extracted from the left and right hemispheres averaged gene expression maps, and by the Euclidean distance between each pair of feature vectors. We also performed a multiple clustering approach on the gene expression maps, combined with hierarchical clustering. Among each group of similar genes and clusters, the gene function similarity was measured by calculating the average gene function distances in the gene ontology structure. By applying our methodology to find similar genes to certain target genes we were able to improve our understanding of gene expression patterns and gene functions. By applying the clustering analysis method, we obtained significant clusters, which have both very similar gene expression maps and very similar gene functions respectively to their corresponding gene ontologies. The cellular component ontology resulted in prominent clusters expressed in cortex and corpus callosum. The molecular function ontology gave prominent clusters in cortex, corpus callosum and hypothalamus. The biological process ontology resulted in clusters in cortex, hypothalamus and choroid plexus. Clusters from all three ontologies combined were most prominently expressed in cortex and corpus callosum. The experimental

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

    NASA Astrophysics Data System (ADS)

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

    2010-06-01

    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.

  20. Exact expression of the t-J model in terms of local spin and fermionic holon operators

    NASA Astrophysics Data System (ADS)

    Wang, Y. R.; Rice, M. J.

    1994-02-01

    An exact expression for the Hamiltonian H of the t-J model in terms of local spin (Si) and fermionic holon (ei) operators is derived which requires no constraint between these operators. The result for the Hamiltonian H is H=-t tsumijeie°j(1/2+2Si.Sj)+(J/2)t smij(1-e°iei)(Si.Sj-1/4)(1-e°je The number of electrons at site i is given by ni=1-e°iei, and the true spin operator S~i, is related to the local spin operator by S~i=(1-e°iei)Si. The expression correctly produces the Nagaoka theorem in the limit J-->0, and preserves the time-reversal symmetry of the original model. For a bipartite lattice, H describes a competition between ferromagnetism, favored by the hopping term, and antiferromagnetism, favored by the Heisenberg term.

  1. Approximations to the exact exchange potential: KLI versus semilocal

    NASA Astrophysics Data System (ADS)

    Tran, Fabien; Blaha, Peter; Betzinger, Markus; Blügel, Stefan

    2016-10-01

    In the search for an accurate and computationally efficient approximation to the exact exchange potential of Kohn-Sham density functional theory, we recently compared various semilocal exchange potentials to the exact one [F. Tran et al., Phys. Rev. B 91, 165121 (2015), 10.1103/PhysRevB.91.165121]. It was concluded that the Becke-Johnson (BJ) potential is a very good starting point, but requires the use of empirical parameters to obtain good agreement with the exact exchange potential. In this work, we extend the comparison by considering the Krieger-Li-Iafrate (KLI) approximation, which is a beyond-semilocal approximation. It is shown that overall the KLI- and BJ-based potentials are the most reliable approximations to the exact exchange potential, however, sizable differences, especially for the antiferromagnetic transition-metal oxides, can be obtained.

  2. EXACT2: the semantics of biomedical protocols

    PubMed Central

    2014-01-01

    Background The reliability and reproducibility of experimental procedures is a cornerstone of scientific practice. There is a pressing technological need for the better representation of biomedical protocols to enable other agents (human or machine) to better reproduce results. A framework that ensures that all information required for the replication of experimental protocols is essential to achieve reproducibility. Methods We have developed the ontology EXACT2 (EXperimental ACTions) that is designed to capture the full semantics of biomedical protocols required for their reproducibility. To construct EXACT2 we manually inspected hundreds of published and commercial biomedical protocols from several areas of biomedicine. After establishing a clear pattern for extracting the required information we utilized text-mining tools to translate the protocols into a machine amenable format. We have verified the utility of EXACT2 through the successful processing of previously 'unseen' (not used for the construction of EXACT2) protocols. Results The paper reports on a fundamentally new version EXACT2 that supports the semantically-defined representation of biomedical protocols. The ability of EXACT2 to capture the semantics of biomedical procedures was verified through a text mining use case. In this EXACT2 is used as a reference model for text mining tools to identify terms pertinent to experimental actions, and their properties, in biomedical protocols expressed in natural language. An EXACT2-based framework for the translation of biomedical protocols to a machine amenable format is proposed. Conclusions The EXACT2 ontology is sufficient to record, in a machine processable form, the essential information about biomedical protocols. EXACT2 defines explicit semantics of experimental actions, and can be used by various computer applications. It can serve as a reference model for for the translation of biomedical protocols in natural language into a semantically

  3. A new exact method for line radiative transfer

    NASA Astrophysics Data System (ADS)

    Elitzur, Moshe; Asensio Ramos, Andrés

    2006-01-01

    We present a new method, the coupled escape probability (CEP), for exact calculation of line emission from multi-level systems, solving only algebraic equations for the level populations. The CEP formulation of the classical two-level problem is a set of linear equations, and we uncover an exact analytic expression for the emission from two-level optically thick sources that holds as long as they are in the `effectively thin' regime. In a comparative study of a number of standard problems, the CEP method outperformed the leading line transfer methods by substantial margins. The algebraic equations employed by our new method are already incorporated in numerous codes based on the escape probability approximation. All that is required for an exact solution with these existing codes is to augment the expression for the escape probability with simple zone-coupling terms. As an application, we find that standard escape probability calculations generally produce the correct cooling emission by the CII 158-μm line but not by the 3P lines of OI.

  4. Exact infinite-time statistics of the Loschmidt echo for a quantum quench.

    PubMed

    Campos Venuti, Lorenzo; Jacobson, N Tobias; Santra, Siddhartha; Zanardi, Paolo

    2011-07-01

    The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this Letter we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasicritical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.

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

    NASA Astrophysics Data System (ADS)

    Rivera, R.; Villarroel, D.

    2002-10-01

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

  6. Comparison of two leading uniform theories of edge diffraction with the exact uniform asymptotic solution

    NASA Technical Reports Server (NTRS)

    Boersma, J.; Rahmat-Samii, Y.

    1980-01-01

    The diffraction of an arbitrary cylindrical wave by a half-plane has been treated by Rahmat-Samii and Mittra who used a spectral domain approach. In this paper, their exact solution for the total field is expressed in terms of a new integral representation. For large wave number k, two rigorous procedures are described for the exact uniform asymptotic expansion of the total field solution. The uniform expansions obtained are valid in the entire space, including transition regions around the shadow boundaries. The final results are compared with the formulations of two leading uniform theories of edge diffraction, namely, the uniform asymptotic theory and the uniform theory of diffraction. Some unique observations and conclusions are made in relating the two theories.

  7. Landscape of an exact energy functional

    NASA Astrophysics Data System (ADS)

    Cohen, Aron J.; Mori-Sánchez, Paula

    2016-04-01

    One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to conceptualize. In this paper the asymmetric two-site Hubbard model is studied, which has a two-dimensional universe of density matrices. The exact functional becomes a simple function of two variables whose three-dimensional energy landscape can be visualized and explored. A walk on this unique landscape, tilted to an angle defined by the one-electron Hamiltonian, gives a valley whose minimum is the exact total energy. This is contrasted with the landscape of some approximate functionals, explaining their failure for electron transfer in the strongly correlated limit. We show concrete examples of pure-state density matrices that are not v representable due to the underlying nonconvex nature of the energy landscape. The exact functional is calculated for all numbers of electrons, including fractional, allowing the derivative discontinuity to be visualized and understood. The fundamental gap for all possible systems is obtained solely from the derivatives of the exact functional.

  8. Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

    NASA Astrophysics Data System (ADS)

    Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

    2018-04-01

    Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

  9. Exact image theory for the problem of dielectric/magnetic slab

    NASA Technical Reports Server (NTRS)

    Lindell, I. V.

    1987-01-01

    Exact image method, recently introduced for the exact solution of electromagnetic field problems involving homogeneous half spaces and microstrip-like geometries, is developed for the problem of homogeneous slab of dielectric and/or magnetic material in free space. Expressions for image sources, creating the exact reflected and transmitted fields, are given and their numerical evaluation is demonstrated. Nonradiating modes, guided by the slab and responsible for the loss of convergence of the image functions, are considered and extracted. The theory allows, for example, an analysis of finite ground planes in microstrip antenna structures.

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

    PubMed

    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.

  11. Exact solutions to model surface and volume charge distributions

    NASA Astrophysics Data System (ADS)

    Mukhopadhyay, S.; Majumdar, N.; Bhattacharya, P.; Jash, A.; Bhattacharya, D. S.

    2016-10-01

    Many important problems in several branches of science and technology deal with charges distributed along a line, over a surface and within a volume. Recently, we have made use of new exact analytic solutions of surface charge distributions to develop the nearly exact Boundary Element Method (neBEM) toolkit. This 3D solver has been successful in removing some of the major drawbacks of the otherwise elegant Green's function approach and has been found to be very accurate throughout the computational domain, including near- and far-field regions. Use of truly distributed singularities (in contrast to nodally concentrated ones) on rectangular and right-triangular elements used for discretizing any three-dimensional geometry has essentially removed many of the numerical and physical singularities associated with the conventional BEM. In this work, we will present this toolkit and the development of several numerical models of space charge based on exact closed-form expressions. In one of the models, Particles on Surface (ParSur), the space charge inside a small elemental volume of any arbitrary shape is represented as being smeared on several surfaces representing the volume. From the studies, it can be concluded that the ParSur model is successful in getting the estimates close to those obtained using the first-principles, especially close to and within the cell. In the paper, we will show initial applications of ParSur and other models in problems related to high energy physics.

  12. Exact folded-band chaotic oscillator.

    PubMed

    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.

  13. Exact Theory of Compressible Fluid Turbulence

    NASA Astrophysics Data System (ADS)

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Verde, Licia; Jimenez, Raul; Alvarez-Gaume, Luis

    2013-06-01

    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 more than 7σ for f{sub NL} values (both true and sampled) not ruledmore » 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.« less

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

    PubMed

    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.

  16. Exact-Output Tracking Theory for Systems with Parameter Jumps

    NASA Technical Reports Server (NTRS)

    Devasia, Santosh; Paden, Brad; Rossi, Carlo

    1996-01-01

    In this paper we consider the exact output tracking problem for systems with parameter jumps. Necessary and sufficient conditions are derived for the elimination of switching-introduced output transient. Previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches). Such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is applicable to nonminimum-phase systems and obtains bounded but possibly non-causal solutions. If the reference trajectories are generated by an exo-system, then we develop an exact-tracking controller in a feedback form. As in standard regulator theory, we obtain a linear map from the states of the exo-system to the desired system state which is defined via a matrix differential equation. The constant solution of this differential equation provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible manipulator with jumps in the pay-load mass.

  17. Exact-Output Tracking Theory for Systems with Parameter Jumps

    NASA Technical Reports Server (NTRS)

    Devasia, Santosh; Paden, Brad; Rossi, Carlo

    1997-01-01

    We consider the exact output tracking problem for systems with parameter jumps. Necessary and sufficient conditions are derived for the elimination of switching-introduced output transient. Previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches). Such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is applicable to non-minimum-phase systems and it obtains bounded but possibly non-causal solutions. If the reference trajectories are generated by an exosystem, then we develop an exact-tracking controller in a feed-back form. As in standard regulator theory, we obtain a linear map from the states of the exosystem to the desired system state which is defined via a matrix differential equation. The constant solution of this differential equation provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible manipulator with jumps in the pay-load mass.

  18. Exact solutions for postbuckling of a graded porous beam

    NASA Astrophysics Data System (ADS)

    Ma, L. S.; Ou, Z. Y.

    2018-06-01

    An exact, closed-form solution for the postbuckling responses of graded porous beams subjected to axially loading is obtained. It was assumed that the properties of the graded porous materials vary continuously through thickness of the beams, the equations governing the axial and transverse deformations are derived based on the classical beam theory and the physical neutral surface concept. The two equations are reduced to a single nonlinear fourth-order integral-differential equation governing the transverse deformations. The nonlinear equation is directly solved without any use of approximation and a closed-form solution for postbuckled deformation is obtained as a function of the applied load. The exact solutions explicitly describe the nonlinear equilibrium paths of the buckled beam and thus are able to provide insight into deformation problems. Based on the exact solutions obtained herein, the effects of various factors such as porosity distribution pattern, porosity coefficient and boundary conditions on postbuckling behavior of graded porous beams have been investigated.

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

    NASA Astrophysics Data System (ADS)

    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.

  20. Exact density functional theory for ideal polymer fluids with nearest neighbor bonding constraints.

    PubMed

    Woodward, Clifford E; Forsman, Jan

    2008-08-07

    We present a new density functional theory of ideal polymer fluids, assuming nearest-neighbor bonding constraints. The free energy functional is expressed in terms of end site densities of chain segments and thus has a simpler mathematical structure than previously used expressions using multipoint distributions. This work is based on a formalism proposed by Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005)]. Those authors obtain an approximate free energy functional for ideal polymers in terms of monomer site densities. Calculations on both repulsive and attractive surfaces show that their theory is reasonably accurate in some cases, but does differ significantly from the exact result for longer polymers with attractive surfaces. We suggest that segment end site densities, rather than monomer site densities, are the preferred choice of "site functions" for expressing the free energy functional of polymer fluids. We illustrate the application of our theory to derive an expression for the free energy of an ideal fluid of infinitely long polymers.

  1. Integrable flows between exact CFTs

    NASA Astrophysics Data System (ADS)

    Georgiou, George; Sfetsos, Konstantinos

    2017-11-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2018-05-01

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

  3. Exact Cosmological Models with Yang–Mills Fields on Lyra Manifold

    NASA Astrophysics Data System (ADS)

    Shchigolev, V. K.; Bezbatko, D. N.

    2018-04-01

    The present study deals with the Friedmann-Robertson-Walker cosmological models with Yang-Mills (YM) fields in Lyra geometry. The energy-momentum tensor of the YM fields for our models is obtained with the help of an exact solution to the YM equations with minimal coupling to gravity. Two specific exact solutions of the model are obtained regarding the effective equation of state and the exponential law of expansion. The physical and geometric behavior of the model is also discussed.

  4. Exactly solvable Schrödinger equation with double-well potential for hydrogen bond

    NASA Astrophysics Data System (ADS)

    Sitnitsky, A. E.

    2017-05-01

    We construct a double-well potential for which the Schrödinger equation can be exactly solved via reducing to the confluent Heun's one. Thus the wave function is expressed via the confluent Heun's function. The latter is tabulated in Maple so that the obtained solution is easily treated. The potential is infinite at the boundaries of the final interval that makes it to be highly suitable for modeling hydrogen bonds (both ordinary and low-barrier ones). We exemplify theoretical results by detailed treating the hydrogen bond in KHCO3 and show their good agreement with literature experimental data.

  5. Constructing exact symmetric informationally complete measurements from numerical solutions

    NASA Astrophysics Data System (ADS)

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  7. Exact BPS domain walls at finite gauge coupling

    NASA Astrophysics Data System (ADS)

    Blaschke, Filip

    2017-01-01

    Bogomol'nyi-Prasad-Sommerfield solitons in models with spontaneously broken gauge symmetry have been intensively studied at the infinite gauge coupling limit, where the governing equation-the so-called master equation-is exactly solvable. Except for a handful of special solutions, the standing impression is that analytic results at finite coupling are generally unavailable. The aim of this paper is to demonstrate, using domain walls in Abelian-Higgs models as the simplest example, that exact solitons at finite gauge coupling can be readily obtained if the number of Higgs fields (NF ) is large enough. In particular, we present a family of exact solutions, describing N domain walls at arbitrary positions in models with at least NF≥2 N +1 . We have also found that adding together any pair of solutions can produce a new exact solution if the combined tension is below a certain limit.

  8. Kinetic field theory: exact free evolution of Gaussian phase-space correlations

    NASA Astrophysics Data System (ADS)

    Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias

    2018-04-01

    In recent work we developed a description of cosmic large-scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial correlations between particles sampled from random Gaussian density and velocity fields have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correlations between all phase-space coordinates exactly by adopting a diagrammatic language for the different forms of correlations, directly inspired by the Mayer cluster expansion. We will demonstrate that explicit expressions for phase-space density cumulants of arbitrary n-point order, which fully capture the non-linear coupling of free streaming kinematics due to initial correlations, can be obtained from a simple set of Feynman rules. These cumulants will be the foundation for future investigations of perturbation theory in particle interactions.

  9. Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation

    NASA Astrophysics Data System (ADS)

    Denicol, Gabriel; Heinz, Ulrich; Martinez, Mauricio; Noronha, Jorge; Strickland, Michael

    2014-12-01

    We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructed by considering the conformal map between Minkowski space and the direct product of three-dimensional de Sitter space with a line. The resulting solution respects S O (3 )q⊗S O (1 ,1 )⊗Z2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations. The macroscopic solutions are obtained in de Sitter space and are subject to the same symmetries used to obtain the exact kinetic solution.

  10. Exact relations between homoclinic and periodic orbit actions in chaotic systems

    NASA Astrophysics Data System (ADS)

    Li, Jizhou; Tomsovic, Steven

    2018-02-01

    Homoclinic and unstable periodic orbits in chaotic systems play central roles in various semiclassical sum rules. The interferences between terms are governed by the action functions and Maslov indices. In this article, we identify geometric relations between homoclinic and unstable periodic orbits, and derive exact formulas expressing the periodic orbit classical actions in terms of corresponding homoclinic orbit actions plus certain phase space areas. The exact relations provide a basis for approximations of the periodic orbit actions as action differences between homoclinic orbits with well-estimated errors. This enables an explicit study of relations between periodic orbits, which results in an analytic expression for the action differences between long periodic orbits and their shadowing decomposed orbits in the cycle expansion.

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

    PubMed

    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.

  12. Near-exact distributions for the block equicorrelation and equivariance likelihood ratio test statistic

    NASA Astrophysics Data System (ADS)

    Coelho, Carlos A.; Marques, Filipe J.

    2013-09-01

    In this paper the authors combine the equicorrelation and equivariance test introduced by Wilks [13] with the likelihood ratio test (l.r.t.) for independence of groups of variables to obtain the l.r.t. of block equicorrelation and equivariance. This test or its single block version may find applications in many areas as in psychology, education, medicine, genetics and they are important "in many tests of multivariate analysis, e.g. in MANOVA, Profile Analysis, Growth Curve analysis, etc" [12, 9]. By decomposing the overall hypothesis into the hypotheses of independence of groups of variables and the hypothesis of equicorrelation and equivariance we are able to obtain the expressions for the overall l.r.t. statistic and its moments. From these we obtain a suitable factorization of the characteristic function (c.f.) of the logarithm of the l.r.t. statistic, which enables us to develop highly manageable and precise near-exact distributions for the test statistic.

  13. Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chin, Alex W.; Rivas, Angel; Huelga, Susana F.

    2010-09-15

    By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a one-dimensional chain with only nearest-neighbor interactions. This analytical transformation predicts a simple set of relations between the parameters of the chain and the recurrence coefficients of the orthogonal polynomials used in the transformation and allows the chain parameters to be computed using numerically stable algorithms that have been developed to compute recurrence coefficients. We then prove some general properties of this chain systemmore » for a wide range of spectral functions and give examples drawn from physical systems where exact analytic expressions for the chain properties can be obtained. Crucially, the short-range interactions of the effective chain system permit these open-quantum systems to be efficiently simulated by the density matrix renormalization group methods.« less

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

    PubMed Central

    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

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

    NASA Astrophysics Data System (ADS)

    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.

  16. Quantifying risks with exact analytical solutions of derivative pricing distribution

    NASA Astrophysics Data System (ADS)

    Zhang, Kun; Liu, Jing; Wang, Erkang; Wang, Jin

    2017-04-01

    Derivative (i.e. option) pricing is essential for modern financial instrumentations. Despite of the previous efforts, the exact analytical forms of the derivative pricing distributions are still challenging to obtain. In this study, we established a quantitative framework using path integrals to obtain the exact analytical solutions of the statistical distribution for bond and bond option pricing for the Vasicek model. We discuss the importance of statistical fluctuations away from the expected option pricing characterized by the distribution tail and their associations to value at risk (VaR). The framework established here is general and can be applied to other financial derivatives for quantifying the underlying statistical distributions.

  17. Exact results for the finite time thermodynamic uncertainty relation

    NASA Astrophysics Data System (ADS)

    Manikandan, Sreekanth K.; Krishnamurthy, Supriya

    2018-03-01

    We obtain exact results for the recently discovered finite-time thermodynamic uncertainty relation, for the dissipated work W d , in a stochastically driven system with non-Gaussian work statistics, both in the steady state and transient regimes, by obtaining exact expressions for any moment of W d at arbitrary times. The uncertainty function (the Fano factor of W d ) is bounded from below by 2k_BT as expected, for all times τ, in both steady state and transient regimes. The lower bound is reached at τ=0 as well as when certain system parameters vanish (corresponding to an equilibrium state). Surprisingly, we find that the uncertainty function also reaches a constant value at large τ for all the cases we have looked at. For a system starting and remaining in steady state, the uncertainty function increases monotonically, as a function of τ as well as other system parameters, implying that the large τ value is also an upper bound. For the same system in the transient regime, however, we find that the uncertainty function can have a local minimum at an accessible time τm , for a range of parameter values. The large τ value for the uncertainty function is hence not a bound in this case. The non-monotonicity suggests, rather counter-intuitively, that there might be an optimal time for the working of microscopic machines, as well as an optimal configuration in the phase space of parameter values. Our solutions show that the ratios of higher moments of the dissipated work are also bounded from below by 2k_BT . For another model, also solvable by our methods, which never reaches a steady state, the uncertainty function, is in some cases, bounded from below by a value less than 2k_BT .

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

    NASA Astrophysics Data System (ADS)

    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.

  19. FAST TRACK COMMUNICATION Time-dependent exact solutions of the nonlinear Kompaneets equation

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. H.

    2010-12-01

    Time-dependent exact solutions of the Kompaneets photon diffusion equation are obtained for several approximations of this equation. One of the approximations describes the case when the induced scattering is dominant. In this case, the Kompaneets equation has an additional symmetry which is used for constructing some exact solutions as group invariant solutions.

  20. Exact finite volume expectation values of local operators in excited states

    NASA Astrophysics Data System (ADS)

    Pozsgay, B.; Szécsényi, I. M.; Takács, G.

    2015-04-01

    We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

  1. Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases.

    PubMed

    D'Amico, María Belén; Calandrini, Guillermo L

    2015-11-01

    Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

  2. Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases

    NASA Astrophysics Data System (ADS)

    D'Amico, María Belén; Calandrini, Guillermo L.

    2015-11-01

    Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

  3. Exact solution of the relativistic quantum Toda chain

    NASA Astrophysics Data System (ADS)

    Zhang, Xin; Cao, Junpeng; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng

    2017-03-01

    The relativistic quantum Toda chain model is studied with the generalized algebraic Bethe Ansatz method. By employing a set of local gauge transformations, proper local vacuum states can be obtained for this model. The exact spectrum and eigenstates of the model are thus constructed simultaneously.

  4. Exact simulation of max-stable processes.

    PubMed

    Dombry, Clément; Engelke, Sebastian; Oesting, Marco

    2016-06-01

    Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown-Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed.

  5. Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application

    NASA Astrophysics Data System (ADS)

    Kundu, Anjan

    2016-08-01

    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.

  6. Exact collisional moments for plasma fluid theories

    NASA Astrophysics Data System (ADS)

    Pfefferlé, D.; Hirvijoki, E.; Lingam, M.

    2017-04-01

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

  7. Exact collisional moments for plasma fluid theories

    NASA Astrophysics Data System (ADS)

    Pfefferle, David; Hirvijoki, Eero; Lingam, Manasvi

    2017-10-01

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

  8. Exact collisional moments for plasma fluid theories

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Pfefferlé, D.; Hirvijoki, E.; Lingam, M.

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

  9. Exact collisional moments for plasma fluid theories

    DOE PAGES

    Pfefferlé, D.; Hirvijoki, E.; Lingam, M.

    2017-04-01

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

  10. Exact Baker-Campbell-Hausdorff formula for the contact Heisenberg algebra

    NASA Astrophysics Data System (ADS)

    Bravetti, Alessandro; Garcia-Chung, Angel; Tapias, Diego

    2017-03-01

    In this work we introduce the contact Heisenberg algebra which is the restriction of the Jacobi algebra on contact manifolds to the linear and constant functions. We give the exact expression of its corresponding Baker-Campbell-Hausdorff formula. We argue that this result is relevant to the quantization of contact systems.

  11. Exact finite difference schemes for the non-linear unidirectional wave equation

    NASA Technical Reports Server (NTRS)

    Mickens, R. E.

    1985-01-01

    Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

  12. Exact results for models of multichannel quantum nonadiabatic transitions

    DOE PAGES

    Sinitsyn, N. A.

    2014-12-11

    We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicitmore » expressions for scattering probabilities in such systems.« less

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

    NASA Astrophysics Data System (ADS)

    Gould, Tim; Kronik, Leeor; Pittalis, Stefano

    2018-05-01

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

  14. Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

    NASA Astrophysics Data System (ADS)

    Cinal, M.; Holas, A.

    2011-06-01

    The reported algorithm determines the exact exchange potential vx in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to vx and the latter for increments of ES and OS due to subsequent changes of vx. Thus, the need for solution of the differential equations for OSs, used by Kümmel and Perdew [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.90.043004 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms of ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact vx so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10-6 after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10-4 hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of vx iteration, while the accuracy limit of 10-6 to 10-7 hartree is reached after 20 density iterations.

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

    PubMed

    Grimson, R C

    1993-10-01

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

  16. Exact synchronization bound for coupled time-delay systems.

    PubMed

    Senthilkumar, D V; Pesquera, Luis; Banerjee, Santo; Ortín, Silvia; Kurths, J

    2013-04-01

    We obtain an exact bound for synchronization in coupled time-delay systems using the generalized Halanay inequality for the general case of time-dependent delay, coupling, and coefficients. Furthermore, we show that the same analysis is applicable to both uni- and bidirectionally coupled time-delay systems with an appropriate evolution equation for their synchronization manifold, which can also be defined for different types of synchronization. The exact synchronization bound assures an exponential stabilization of the synchronization manifold which is crucial for applications. The analytical synchronization bound is independent of the nature of the modulation and can be applied to any time-delay system satisfying a Lipschitz condition. The analytical results are corroborated numerically using the Ikeda system.

  17. On the Model-Based Bootstrap with Missing Data: Obtaining a "P"-Value for a Test of Exact Fit

    ERIC Educational Resources Information Center

    Savalei, Victoria; Yuan, Ke-Hai

    2009-01-01

    Evaluating the fit of a structural equation model via bootstrap requires a transformation of the data so that the null hypothesis holds exactly in the sample. For complete data, such a transformation was proposed by Beran and Srivastava (1985) for general covariance structure models and applied to structural equation modeling by Bollen and Stine…

  18. Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium.

    PubMed

    Netz, Roland R

    2018-05-14

    An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non

  19. Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium

    NASA Astrophysics Data System (ADS)

    Netz, Roland R.

    2018-05-01

    An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non

  20. Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering

    NASA Astrophysics Data System (ADS)

    Dorier, V.; Gevorgyan, M.; Ishkhanyan, A.; Leroy, C.; Jauslin, H. R.; Guérin, S.

    2017-12-01

    We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.

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

    NASA Astrophysics Data System (ADS)

    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.

  2. Exact quasinormal modes for a special class of black holes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Oliva, Julio; Troncoso, Ricardo; Centro de Ingenieria de la Innovacion del CECS

    2010-07-15

    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.

  3. Interaction and charge transfer between dielectric spheres: Exact and approximate analytical solutions.

    PubMed

    Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning

    2016-11-21

    We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.

  4. Efficient exact motif discovery.

    PubMed

    Marschall, Tobias; Rahmann, Sven

    2009-06-15

    The motif discovery problem consists of finding over-represented patterns in a collection of biosequences. It is one of the classical sequence analysis problems, but still has not been satisfactorily solved in an exact and efficient manner. This is partly due to the large number of possibilities of defining the motif search space and the notion of over-representation. Even for well-defined formalizations, the problem is frequently solved in an ad hoc manner with heuristics that do not guarantee to find the best motif. We show how to solve the motif discovery problem (almost) exactly on a practically relevant space of IUPAC generalized string patterns, using the p-value with respect to an i.i.d. model or a Markov model as the measure of over-representation. In particular, (i) we use a highly accurate compound Poisson approximation for the null distribution of the number of motif occurrences. We show how to compute the exact clump size distribution using a recently introduced device called probabilistic arithmetic automaton (PAA). (ii) We define two p-value scores for over-representation, the first one based on the total number of motif occurrences, the second one based on the number of sequences in a collection with at least one occurrence. (iii) We describe an algorithm to discover the optimal pattern with respect to either of the scores. The method exploits monotonicity properties of the compound Poisson approximation and is by orders of magnitude faster than exhaustive enumeration of IUPAC strings (11.8 h compared with an extrapolated runtime of 4.8 years). (iv) We justify the use of the proposed scores for motif discovery by showing our method to outperform other motif discovery algorithms (e.g. MEME, Weeder) on benchmark datasets. We also propose new motifs on Mycobacterium tuberculosis. The method has been implemented in Java. It can be obtained from http://ls11-www.cs.tu-dortmund.de/people/marschal/paa_md/.

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

    PubMed

    Iafrate, G J; Krieger, J B

    2013-03-07

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

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

    NASA Astrophysics Data System (ADS)

    Iafrate, G. J.; Krieger, J. B.

    2013-03-01

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

  7. Exact simulation of integrate-and-fire models with exponential currents.

    PubMed

    Brette, Romain

    2007-10-01

    Neural networks can be simulated exactly using event-driven strategies, in which the algorithm advances directly from one spike to the next spike. It applies to neuron models for which we have (1) an explicit expression for the evolution of the state variables between spikes and (2) an explicit test on the state variables that predicts whether and when a spike will be emitted. In a previous work, we proposed a method that allows exact simulation of an integrate-and-fire model with exponential conductances, with the constraint of a single synaptic time constant. In this note, we propose a method, based on polynomial root finding, that applies to integrate-and-fire models with exponential currents, with possibly many different synaptic time constants. Models can include biexponential synaptic currents and spike-triggered adaptation currents.

  8. Interior radiances in optically deep absorbing media. 1: Exact solutions for one-dimensional model

    NASA Technical Reports Server (NTRS)

    Kattawar, G. W.; Plass, G. N.

    1973-01-01

    The exact solutions are obtained for a one dimensional model of a scattering and absorbing medium. The results are given for both the reflected and transmitted radiance for any arbitrary surface albedo as well as for the interior radiance. These same quantities are calculated by the matrix operator method. The relative error of the solutions is obtained by comparison with the exact solutions as well as by an error analysis of the equations. The importance of an accurate starting value for the reflection and transmission operators is shown. A fourth order Runge-Kutta method can be used to solve the differential equations satisfied by these operators in order to obtain such accurate starting values.

  9. Knotted optical vortices in exact solutions to Maxwell's equations

    NASA Astrophysics Data System (ADS)

    de Klerk, Albertus J. J. M.; van der Veen, Roland I.; Dalhuisen, Jan Willem; Bouwmeester, Dirk

    2017-05-01

    We construct a family of exact solutions to Maxwell's equations in which the points of zero intensity form knotted lines topologically equivalent to a given but arbitrary algebraic link. These lines of zero intensity, more commonly referred to as optical vortices, and their topology are preserved as time evolves and the fields have finite energy. To derive explicit expressions for these new electromagnetic fields that satisfy the nullness property, we make use of the Bateman variables for the Hopf field as well as complex polynomials in two variables whose zero sets give rise to algebraic links. The class of algebraic links includes not only all torus knots and links thereof, but also more intricate cable knots. While the unknot has been considered before, the solutions presented here show that more general knotted structures can also arise as optical vortices in exact solutions to Maxwell's equations.

  10. Higher moments of multiplicity fluctuations in a hadron-resonance gas with exact conservation laws

    NASA Astrophysics Data System (ADS)

    Fu, Jing-Hua

    2017-09-01

    Higher moments of multiplicity fluctuations of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the canonical ensemble. Exact conservation of three charges, baryon number, electric charge, and strangeness is enforced in the large volume limit. Moments up to the fourth order of various particles are calculated at CERN Super Proton Synchrotron, BNL Relativistic Heavy Ion Collider (RHIC), and CERN Large Hadron Collider energies. The asymptotic fluctuations within a simplified model with only one conserved charge in the canonical ensemble are discussed where simple analytical expressions for moments of multiplicity distributions can be obtained. Moments products of net-proton, net-kaon, and net-charge distributions in Au + Au collisions at RHIC energies are calculated. The pseudorapidity coverage dependence of net-charge fluctuation is discussed.

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

    NASA Astrophysics Data System (ADS)

    Holme, Petter

    2017-12-01

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

  12. What exactly do numbers mean?

    PubMed Central

    Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse

    2014-01-01

    Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics (two means EXACTLY TWO), many linguistic accounts propose that numbers have lower-bounded semantics (AT LEAST TWO), and that speakers restrict their reference through a pragmatic inference (scalar implicature). We address this debate through studies of children who are in the process of acquiring the meanings of numbers. Adults and 2- and 3-year-olds were tested in a novel paradigm that teases apart semantic and pragmatic aspects of interpretation (the covered box task). Our findings establish that when scalar implicatures are cancelled in the critical trials of this task, both adults and children consistently give exact interpretations for number words. These results, in concert with recent work on real-time processing, provide the first unambiguous evidence that number words have exact semantics. PMID:25285053

  13. Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cinal, M.; Holas, A.

    2011-06-15

    The reported algorithm determines the exact exchange potential v{sub x} in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v{sub x} and the latter for increments of ES and OS due to subsequent changes of v{sub x}. Thus, the need for solution of the differential equations for OSs, used by Kuemmel and Perdew [Phys. Rev. Lett. 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms ofmore » ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v{sub x} so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10{sup -6} after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10{sup -4} hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of v{sub x} iteration, while the accuracy limit of 10{sup -6} to 10{sup -7} hartree is reached after 20 density iterations.« less

  14. A genome-scale map of expression for a mouse brain section obtained using voxelation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chin, Mark H.; Geng, Alex B.; Khan, Arshad H.

    Gene expression signatures in the mammalian brain hold the key to understanding neural development and neurological diseases. We have reconstructed 2- dimensional images of gene expression for 20,000 genes in a coronal slice of the mouse brain at the level of the striatum by using microarrays in combination with voxelation at a resolution of 1 mm3. Good reliability of the microarray results were confirmed using multiple replicates, subsequent quantitative RT-PCR voxelation, mass spectrometry voxelation and publicly available in situ hybridization data. Known and novel genes were identified with expression patterns localized to defined substructures within the brain. In addition, genesmore » with unexpected patterns were identified and cluster analysis identified a set of genes with a gradient of dorsal/ventral expression not restricted to known anatomical boundaries. The genome-scale maps of gene expression obtained using voxelation will be a valuable tool for the neuroscience community.« less

  15. Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal

    NASA Astrophysics Data System (ADS)

    Zhou, Y.-B.; Li, X.-F.

    2018-07-01

    The electroelastic problem related to two collinear cracks of equal length and normal to the boundaries of a one-dimensional hexagonal piezoelectric quasicrystal layer is analysed. By using the finite Fourier transform, a mixed boundary value problem is solved when antiplane mechanical loading and inplane electric loading are applied. The problem is reduce to triple series equations, which are then transformed to a singular integral equation. For uniform remote loading, an exact solution is obtained in closed form, and explicit expressions for the electroelastic field are determined. The intensity factors of the electroelastic field and the energy release rate at the inner and outer crack tips are given and presented graphically.

  16. Exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium.

    PubMed

    Petrov, E Yu; Kudrin, A V

    2010-05-14

    The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of special importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion and give examples of the obtained solutions that describe propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium and free electromagnetic oscillations in a cylindrical cavity resonator filled with such a medium.

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

    NASA Astrophysics Data System (ADS)

    Baradaran, M.; Panahi, H.

    2018-05-01

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

  18. BRST Exactness of Stress-Energy Tensors

    NASA Astrophysics Data System (ADS)

    Miyata, Hideo; Sugimoto, Hiroshi

    BRST commutators in the topological conformal field theories obtained by twisting N=2 theories are evaluated explicitly. By our systematic calculations of the multiple integrals which contain screening operators, the BRST exactness of the twisted stress-energy tensors is deduced for classical simple Lie algebras and general level k. We can see that the paths of integrations do not affect the result, and further, the N=2 coset theories are obtained by deleting two simple roots with Kac-label 1 from the extended Dynkin diagram; in other words, by not performing the integrations over the variables corresponding to the two simple roots of Kac-Moody algebras. It is also shown that a series of N=1 theories are generated in the same way by deleting one simple root with Kac-label 2.

  19. Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

    NASA Astrophysics Data System (ADS)

    Zhi, Longxiao; Gu, Hanming

    2018-03-01

    The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.

  20. AESS: Accelerated Exact Stochastic Simulation

    NASA Astrophysics Data System (ADS)

    Jenkins, David D.; Peterson, Gregory D.

    2011-12-01

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

  1. Representation of the exact relativistic electronic Hamiltonian within the regular approximation

    NASA Astrophysics Data System (ADS)

    Filatov, Michael; Cremer, Dieter

    2003-12-01

    The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c-20. Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations.

  2. Exact nonparametric confidence bands for the survivor function.

    PubMed

    Matthews, David

    2013-10-12

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

  3. The method of generating functions in exact scalar field inflationary cosmology

    NASA Astrophysics Data System (ADS)

    Chervon, Sergey V.; Fomin, Igor V.; Beesham, Aroonkumar

    2018-04-01

    The construction of exact solutions in scalar field inflationary cosmology is of growing interest. In this work, we review the results which have been obtained with the help of one of the most effective methods, viz., the method of generating functions for the construction of exact solutions in scalar field cosmology. We also include in the debate the superpotential method, which may be considered as the bridge to the slow roll approximation equations. Based on the review, we suggest a classification for the generating functions, and find a connection for all of them with the superpotential.

  4. Exact traveling soliton solutions for the generalized Benjamin-Bona-Mahony equation

    NASA Astrophysics Data System (ADS)

    Boudoue Hubert, Malwe; Kudryashov, Nikolai A.; Justin, Mibaile; Abbagari, Souleymanou; Betchewe, Gambo; Doka, Serge Y.

    2018-03-01

    In this paper, we investigate the generalized Benjamin-Bona-Mahony equation which better describes long waves with arbitrary power-law nonlinearity. As a result, we obtain exact travelling wave soliton solutions, such as anti-kink soliton solution, bright soliton solution, dark soliton solution and periodic solution. These solutions have many free parameters such that they may be used to simulate many experimental situations. The main contribution, in this work, is to not apply the computer codes for construction of exact solutions and not consider the integration constants as zero, because they give all variants for solutions.

  5. Unitary-matrix models as exactly solvable string theories

    NASA Technical Reports Server (NTRS)

    Periwal, Vipul; Shevitz, Danny

    1990-01-01

    Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.

  6. Exact posterior computation in non-conjugate Gaussian location-scale parameters models

    NASA Astrophysics Data System (ADS)

    Andrade, J. A. A.; Rathie, P. N.

    2017-12-01

    In Bayesian analysis the class of conjugate models allows to obtain exact posterior distributions, however this class quite restrictive in the sense that it involves only a few distributions. In fact, most of the practical applications involves non-conjugate models, thus approximate methods, such as the MCMC algorithms, are required. Although these methods can deal with quite complex structures, some practical problems can make their applications quite time demanding, for example, when we use heavy-tailed distributions, convergence may be difficult, also the Metropolis-Hastings algorithm can become very slow, in addition to the extra work inevitably required on choosing efficient candidate generator distributions. In this work, we draw attention to the special functions as a tools for Bayesian computation, we propose an alternative method for obtaining the posterior distribution in Gaussian non-conjugate models in an exact form. We use complex integration methods based on the H-function in order to obtain the posterior distribution and some of its posterior quantities in an explicit computable form. Two examples are provided in order to illustrate the theory.

  7. A class of exact classical solutions to string theory.

    PubMed

    Coley, A A

    2002-12-31

    We show that the recently obtained class of spacetimes for which all of the scalar curvature invariants vanish (which can be regarded as generalizations of pp-wave spacetimes) are exact solutions in string theory to all perturbative orders in the string tension scale. As a result the spectrum of the theory can be explicitly obtained, and these spacetimes are expected to provide some hints for the study of superstrings on more general backgrounds. Since these Lorentzian spacetimes suffer no quantum corrections to all loop orders they may also offer insights into quantum gravity.

  8. Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange.

    PubMed

    Kümmel, Stephan; Perdew, John P

    2003-01-31

    For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential V(xcsigma)(r) must be obtained as the solution of the optimized effective potential (OEP) integral equation. This is very demanding and has limited the use of orbital functionals. We demonstrate that instead the OEP can be obtained iteratively by solving the partial differential equations for the orbital shifts that exactify the Krieger-Li-Iafrate approximation. Unoccupied orbitals do not need to be calculated. Accuracy and efficiency of the method are shown for atoms and clusters using the exact-exchange energy. Counterintuitive asymptotic limits of the exact OEP are presented.

  9. Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ita III, Eyo Eyo, E-mail: ita@usna.edu; Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw

    Exact solutions of the Wheeler–DeWitt equation of the full theory of four dimensional gravity of Lorentzian signature are obtained. They are characterized by Schrödinger wavefunctionals having support on 3-metrics of constant spatial scalar curvature, and thus contain two full physical field degrees of freedom in accordance with the Yamabe construction. These solutions are moreover Gaussians of minimum uncertainty and they are naturally associated with a rigged Hilbert space. In addition, in the limit the regulator is removed, exact 3-dimensional diffeomorphism and local gauge invariance of the solutions are recovered.

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

    NASA Astrophysics Data System (ADS)

    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.

  11. Exact diffusion constant in a lattice-gas wind-tree model on a Bethe lattice

    NASA Astrophysics Data System (ADS)

    Zhang, Guihua; Percus, J. K.

    1992-02-01

    Kong and Cohen [Phys. Rev. B 40, 4838 (1989)] obtained the diffusion constant of a lattice-gas wind-tree model in the Boltzmann approximation. The result is consistent with computer simulations for low tree concentration. In this Brief Report we find the exact diffusion constant of the model on a Bethe lattice, which turns out to be identical with the Kong-Cohen and Gunn-Ortuño results. Our interpretation is that the Boltzmann approximation is exact for this type of diffusion on a Bethe lattice in the same sense that the Bethe-Peierls approximation is exact for the Ising model on a Bethe lattice.

  12. Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

    NASA Astrophysics Data System (ADS)

    Akram, Ghazala; Mahak, Nadia

    2018-06-01

    The nonlinear Schrödinger equation (NLSE) with the aid of three order dispersion terms is investigated to find the exact solutions via the extended (G'/G2)-expansion method and the first integral method. Many exact traveling wave solutions, such as trigonometric, hyperbolic, rational, soliton and complex function solutions, are characterized with some free parameters of the problem studied. It is corroborated that the proposed techniques are manageable, straightforward and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Some figures are plotted to describe the propagation of traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions.

  13. Calculation of the second term of the exact Green's function of the diffusion equation for diffusion-controlled chemical reactions

    NASA Astrophysics Data System (ADS)

    Plante, Ianik

    2016-01-01

    The exact Green's function of the diffusion equation (GFDE) is often considered to be the gold standard for the simulation of partially diffusion-controlled reactions. As the GFDE with angular dependency is quite complex, the radial GFDE is more often used. Indeed, the exact GFDE is expressed as a Legendre expansion, the coefficients of which are given in terms of an integral comprising Bessel functions. This integral does not seem to have been evaluated analytically in existing literature. While the integral can be evaluated numerically, the Bessel functions make the integral oscillate and convergence is difficult to obtain. Therefore it would be of great interest to evaluate the integral analytically. The first term was evaluated previously, and was found to be equal to the radial GFDE. In this work, the second term of this expansion was evaluated. As this work has shown that the first two terms of the Legendre polynomial expansion can be calculated analytically, it raises the question of the possibility that an analytical solution exists for the other terms.

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

    NASA Astrophysics Data System (ADS)

    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.

  15. Exact Path Integral for 3D Quantum Gravity.

    PubMed

    Iizuka, Norihiro; Tanaka, Akinori; Terashima, Seiji

    2015-10-16

    Three-dimensional Euclidean pure gravity with a negative cosmological constant can be formulated in terms of the Chern-Simons theory, classically. This theory can be written in a supersymmetric way by introducing auxiliary gauginos and scalars. We calculate the exact partition function of this Chern-Simons theory by using the localization technique. Thus, we obtain the quantum gravity partition function, assuming that it can be obtained nonperturbatively by summing over partition functions of the Chern-Simons theory on topologically different manifolds. The resultant partition function is modular invariant, and, in the case in which the central charge is expected to be 24, it is the J function, predicted by Witten.

  16. Exact time-dependent solutions for a self-regulating gene.

    PubMed

    Ramos, A F; Innocentini, G C P; Hornos, J E M

    2011-06-01

    The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

  17. Tensor spherical harmonics theories on the exact nature of the elastic fields of a spherically anisotropic multi-inhomogeneous inclusion

    NASA Astrophysics Data System (ADS)

    Shodja, H. M.; Khorshidi, A.

    2013-04-01

    Eshelby's theories on the nature of the disturbance strains due to polynomial eigenstrains inside an isotropic ellipsoidal inclusion, and the form of homogenizing eigenstrains corresponding to remote polynomial loadings in the equivalent inclusion method (EIM) are not valid for spherically anisotropic inclusions and inhomogeneities. Materials with spherically anisotropic behavior are frequently encountered in nature, for example, some graphite particles or polyethylene spherulites. Moreover, multi-inclusions/inhomogeneities/inhomogeneous inclusions have abundant engineering and scientific applications and their exact theoretical treatment would be of great value. The present work is devoted to the development of a mathematical framework for the exact treatment of a spherical multi-inhomogeneous inclusion with spherically anisotropic constituents embedded in an unbounded isotropic matrix. The formulations herein are based on tensor spherical harmonics having orthogonality and completeness properties. For polynomial eigenstrain field and remote applied loading, several theorems on the exact closed-form expressions of the elastic fields associated with the matrix and all the phases of the inhomogeneous inclusion are stated and proved. Several classes of impotent eigenstrain fields associated to a generally anisotropic inclusion as well as isotropic and spherically anisotropic multi-inclusions are also introduced. The presented theories are useful for obtaining highly accurate solutions of desired accuracy when the constituent phases of the multi-inhomogeneous inclusion are made of functionally graded materials (FGMs).

  18. Exact solutions for the entropy production rate of several irreversible processes.

    PubMed

    Ross, John; Vlad, Marcel O

    2005-11-24

    We investigate thermal conduction described by Newton's law of cooling and by Fourier's transport equation and chemical reactions based on mass action kinetics where we detail a simple example of a reaction mechanism with one intermediate. In these cases we derive exact expressions for the entropy production rate and its differential. We show that at a stationary state the entropy production rate is an extremum if and only if the stationary state is a state of thermodynamic equilibrium. These results are exact and independent of any expansions of the entropy production rate. In the case of thermal conduction we compare our exact approach with the conventional approach based on the expansion of the entropy production rate near equilibrium. If we expand the entropy production rate in a series and keep terms up to the third order in the deviation variables and then differentiate, we find out that the entropy production rate is not an extremum at a nonequilibrium steady state. If there is a strict proportionality between fluxes and forces, then the entropy production rate is an extremum at the stationary state even if the stationary state is far away from equilibrium.

  19. Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

    NASA Astrophysics Data System (ADS)

    Zhi, L.; Gu, H.

    2017-12-01

    The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion has a better applicability. It doesn't need some assumptions and can estimate more parameters simultaneously. Meanwhile, by using the generalized linear method, the inversion is easily realized and its calculation amount is small. We use the Marmousi model to generate synthetic seismic records to test and analyze the influence of random noise. Without noise, all estimation results are relatively accurate. With the increase of noise, P-wave velocity change and oil saturation change are stable and less affected by noise. S-wave velocity change is most affected by noise. Finally we use the actual field data of time-lapse seismic prospecting to process and the results can prove the availability and feasibility of our method in actual situation.

  20. Can quantum transition state theory be defined as an exact t = 0+ limit?

    NASA Astrophysics Data System (ADS)

    Jang, Seogjoo; Voth, Gregory A.

    2016-02-01

    The definition of the classical transition state theory (TST) as a t → 0+ limit of the flux-side time correlation function relies on the assumption that simultaneous measurement of population and flux is a well defined physical process. However, the noncommutativity of the two measurements in quantum mechanics makes the extension of such a concept to the quantum regime impossible. For this reason, quantum TST (QTST) has been generally accepted as any kind of quantum rate theory reproducing the TST in the classical limit, and there has been a broad consensus that no unique QTST retaining all the properties of TST can be defined. Contrary to this widely held view, Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)] recently suggested that a true QTST can be defined as the exact t → 0+ limit of a certain kind of quantum flux-side time correlation function and that it is equivalent to the ring polymer molecular dynamics (RPMD) TST. This work seeks to question and clarify certain assumptions underlying these suggestions and their implications. First, the time correlation function used by HA as a starting expression is not related to the kinetic rate constant by virtue of linear response theory, which is the first important step in relating a t = 0+ limit to a physically measurable rate. Second, a theoretical analysis calls into question a key step in HA's proof which appears not to rely on an exact quantum mechanical identity. The correction of this makes the true t = 0+ limit of HA's QTST different from the RPMD-TST rate expression, but rather equal to the well-known path integral quantum transition state theory rate expression for the case of centroid dividing surface. An alternative quantum rate expression is then formulated starting from the linear response theory and by applying a recently developed formalism of real time dynamics of imaginary time path integrals [S. Jang, A. V. Sinitskiy, and G. A. Voth, J. Chem. Phys. 140, 154103 (2014)]. It is shown

  1. Agent-based model for the h-index - exact solution

    NASA Astrophysics Data System (ADS)

    Żogała-Siudem, Barbara; Siudem, Grzegorz; Cena, Anna; Gagolewski, Marek

    2016-01-01

    Hirsch's h-index is perhaps the most popular citation-based measure of scientific excellence. In 2013, Ionescu and Chopard proposed an agent-based model describing a process for generating publications and citations in an abstract scientific community [G. Ionescu, B. Chopard, Eur. Phys. J. B 86, 426 (2013)]. Within such a framework, one may simulate a scientist's activity, and - by extension - investigate the whole community of researchers. Even though the Ionescu and Chopard model predicts the h-index quite well, the authors provided a solution based solely on simulations. In this paper, we complete their results with exact, analytic formulas. What is more, by considering a simplified version of the Ionescu-Chopard model, we obtained a compact, easy to compute formula for the h-index. The derived approximate and exact solutions are investigated on a simulated and real-world data sets.

  2. Exact finite elements for conduction and convection

    NASA Technical Reports Server (NTRS)

    Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.

    1981-01-01

    An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.

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

    NASA Astrophysics Data System (ADS)

    Guner, Ozkan; Bekir, Ahmet

    2018-01-01

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

  4. Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory

    NASA Astrophysics Data System (ADS)

    Sciarappa, Antonio

    2017-10-01

    We provide a proposal, motivated by Separation of Variables and gauge theory arguments, for constructing exact solutions to the quantum Baxter equation associated to the N-particle relativistic Toda chain and test our proposal against numerical results. Quantum Mechanical non-perturbative corrections, essential in order to obtain a sensible solution, are taken into account in our gauge theory approach by considering codimension two defects on curved backgrounds (squashed S 5 and degenerate limits) rather than flat space; this setting also naturally incorporates exact quantization conditions and energy spectrum of the relativistic Toda chain as well as its modular dual structure.

  5. Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion

    ERIC Educational Resources Information Center

    Belendez, Augusto; Arribas, Enrique; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi

    2011-01-01

    An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the…

  6. Exact mode volume and Purcell factor of open optical systems

    NASA Astrophysics Data System (ADS)

    Muljarov, E. A.; Langbein, W.

    2016-12-01

    The Purcell factor quantifies the change of the radiative decay of a dipole in an electromagnetic environment relative to free space. Designing this factor is at the heart of photonics technology, striving to develop ever smaller or less lossy optical resonators. The Purcell factor can be expressed using the electromagnetic eigenmodes of the resonators, introducing the notion of a mode volume for each mode. This approach allows an analytic treatment, reducing the Purcell factor and other observables to sums over eigenmode resonances. Calculating the mode volumes requires a correct normalization of the modes. We introduce an exact normalization of modes, not relying on perfectly matched layers. We present an analytic theory of the Purcell effect based on this exact mode normalization and the resulting effective mode volume. We use a homogeneous dielectric sphere in vacuum, which is analytically solvable, to exemplify these findings. We furthermore verify the applicability of the normalization to numerically determined modes of a finite dielectric cylinder.

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

    NASA Astrophysics Data System (ADS)

    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.

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

    PubMed

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

    2018-02-28

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

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

    NASA Astrophysics Data System (ADS)

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

    2018-02-01

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

  10. Exact solutions to force-free electrodynamics in black hole backgrounds

    NASA Astrophysics Data System (ADS)

    Brennan, T. Daniel; Gralla, Samuel E.; Jacobson, Ted

    2013-10-01

    A shared property of several of the known exact solutions to the equations of force-free electrodynamics is that their charge-current four-vector is null. We examine the general properties of null-current solutions and then focus on the principal congruences of the Kerr black hole spacetime. We obtain a large class of exact solutions, which are in general time-dependent and non-axisymmetric. These solutions include waves that, surprisingly, propagate without scattering on the curvature of the black hole’s background. They may be understood as generalizations to Robinson’s solutions to vacuum electrodynamics associated with a shear-free congruence of null geodesics. When stationary and axisymmetric, our solutions reduce to those of Menon and Dermer, the only previously known solutions in Kerr. In Kerr, all of our solutions have null electromagnetic fields (\\vec{E} \\cdot \\vec{B} = 0 and E2 = B2). However, in Schwarzschild or flat spacetime there is freedom to add a magnetic monopole field, making the solutions magnetically dominated (B2 > E2). This freedom may be used to reproduce the various flat-spacetime and Schwarzschild-spacetime (split) monopole solutions available in the literature (due to Michel and later authors), and to obtain a large class of time-dependent, non-axisymmetric generalizations. These generalizations may be used to model the magnetosphere of a conducting star that rotates with arbitrary prescribed time-dependent rotation axis and speed. We thus significantly enlarge the class of known exact solutions, while organizing and unifying previously discovered solutions in terms of their null structure.

  11. Exact finite elements for conduction and convection

    NASA Technical Reports Server (NTRS)

    Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.

    1981-01-01

    An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507

  12. Exact-Differential Large-Scale Traffic Simulation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hanai, Masatoshi; Suzumura, Toyotaro; Theodoropoulos, Georgios

    2015-01-01

    Analyzing large-scale traffics by simulation needs repeating execution many times with various patterns of scenarios or parameters. Such repeating execution brings about big redundancy because the change from a prior scenario to a later scenario is very minor in most cases, for example, blocking only one of roads or changing the speed limit of several roads. In this paper, we propose a new redundancy reduction technique, called exact-differential simulation, which enables to simulate only changing scenarios in later execution while keeping exactly same results as in the case of whole simulation. The paper consists of two main efforts: (i) amore » key idea and algorithm of the exact-differential simulation, (ii) a method to build large-scale traffic simulation on the top of the exact-differential simulation. In experiments of Tokyo traffic simulation, the exact-differential simulation shows 7.26 times as much elapsed time improvement in average and 2.26 times improvement even in the worst case as the whole simulation.« less

  13. Exact periodic solutions of the sixth-order generalized Boussinesq equation

    NASA Astrophysics Data System (ADS)

    Kamenov, O. Y.

    2009-09-01

    This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): utt = uxx + 3(u2)xx + uxxxx + αuxxxxxx, α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

  14. Volume of milk obtained in relation to location and circumstances of expression in mothers of very low birth weight infants.

    PubMed

    Acuña-Muga, Juliana; Ureta-Velasco, Noelia; de la Cruz-Bértolo, Javier; Ballesteros-López, Rosa; Sánchez-Martínez, Rocío; Miranda-Casabona, Eugenia; Miguel-Trigoso, Almudena; García-San José, Lidia; Pallás-Alonso, Carmen

    2014-02-01

    Given the importance of mother's milk for very low birth weight (VLBW) infants, it would be helpful to know which circumstances are most favorable for milk expression. This study aimed to estimate the volume of milk obtained by mothers of VLBW infants as a function of proximity to the infant and use of the kangaroo position during the actual expression. In this prospective cohort study, when the infant was stable and the mother had established a breastfeeding routine, she was given a notebook in which to record the location of expression and the amount of milk expressed for 10 consecutive days. Breast milk expression volumes were recorded and analyzed. Data were collected on 26 mother-VLBW infant dyads and 1642 milk expressions. The first early morning expressions (n = 276, 17%) were conducted at home. Thereafter, 743 (45%) expressions were conducted far from the infant, either in a different room within the hospital or at home, and 623 (38%) were performed in proximity to the infant (beside the incubator, during kangaroo mother care [KMC], after KMC, or during kangaroo father care). The mean milk volume was significantly higher when expression was conducted in proximity to the infant. When only milk expressions conducted in proximity to the infant were considered, volumes obtained during KMC (107.7 mL, 91.8-123.5) and after KMC (117.7 mL, 99.0-136.5) were significantly higher than those obtained beside the incubator (96.9 mL, 79.9-113.9), respectively, P = .0030 and P = .0024. Milk expression conducted in proximity to the infant, particularly during and immediately after KMC, is associated with higher milk volume.

  15. On symmetries, conservation laws and exact solutions of the nonlinear Schrödinger-Hirota equation

    NASA Astrophysics Data System (ADS)

    Akbulut, Arzu; Taşcan, Filiz

    2018-04-01

    In this paper, conservation laws and exact solution are found for nonlinear Schrödinger-Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger-Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.

  16. Correlation energy functional within the GW -RPA: Exact forms, approximate forms, and challenges

    NASA Astrophysics Data System (ADS)

    Ismail-Beigi, Sohrab

    2010-05-01

    In principle, the Luttinger-Ward Green’s-function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW -random-phase approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green’s functions) is necessary. Finally, we present some relevant numerical results for atomic systems.

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

    PubMed

    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.

  18. Efficient Calculation of Exact Exchange Within the Quantum Espresso Software Package

    NASA Astrophysics Data System (ADS)

    Barnes, Taylor; Kurth, Thorsten; Carrier, Pierre; Wichmann, Nathan; Prendergast, David; Kent, Paul; Deslippe, Jack

    Accurate simulation of condensed matter at the nanoscale requires careful treatment of the exchange interaction between electrons. In the context of plane-wave DFT, these interactions are typically represented through the use of approximate functionals. Greater accuracy can often be obtained through the use of functionals that incorporate some fraction of exact exchange; however, evaluation of the exact exchange potential is often prohibitively expensive. We present an improved algorithm for the parallel computation of exact exchange in Quantum Espresso, an open-source software package for plane-wave DFT simulation. Through the use of aggressive load balancing and on-the-fly transformation of internal data structures, our code exhibits speedups of approximately an order of magnitude for practical calculations. Additional optimizations are presented targeting the many-core Intel Xeon-Phi ``Knights Landing'' architecture, which largely powers NERSC's new Cori system. We demonstrate the successful application of the code to difficult problems, including simulation of water at a platinum interface and computation of the X-ray absorption spectra of transition metal oxides.

  19. Ferrofluid patterns in a radial magnetic field: linear stability, nonlinear dynamics, and exact solutions.

    PubMed

    Oliveira, Rafael M; Miranda, José A; Leandro, Eduardo S G

    2008-01-01

    The response of a ferrofluid droplet to a radial magnetic field is investigated, when the droplet is confined in a Hele-Shaw cell. We study how the stability properties of the interface and the shape of the emerging patterns react to the action of the magnetic field. At early linear stages, it is found that the radial field is destabilizing and determines the growth of fingering structures at the interface. In the weakly nonlinear regime, we have verified that the magnetic field favors the formation of peaked patterned structures that tend to become sharper and sharper as the magnitude of the magnetic effects is increased. A more detailed account of the pattern morphology is provided by the determination of nontrivial exact stationary solutions for the problem with finite surface tension. These solutions are obtained analytically and reveal the development of interesting polygon-shaped and starfishlike patterns. For sufficiently large applied fields or magnetic susceptibilities, pinch-off phenomena are detected, tending to occur near the fingertips. We have found that the morphological features obtained from the exact solutions are consistent with our linear and weakly nonlinear predictions. By contrasting the exact solutions for ferrofluids under radial field with those obtained for rotating Hele-Shaw flows with ordinary nonmagnetic fluids, we deduce that they coincide in the limit of very small susceptibilities.

  20. Exact partition functions for gauge theories on Rλ3

    NASA Astrophysics Data System (ADS)

    Wallet, Jean-Christophe

    2016-11-01

    The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sharma, Pankaj, E-mail: psharma@rtu.ac.in; Parashar, Sandeep Kumar, E-mail: parashar2@yahoo.com

    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 thicknessmore » 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.« less

  2. Lensing in the geodesic light-cone coordinates and its (exact) illustration to an off-center observer in Lemaȋtre-Tolman-Bondi models

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Fanizza, G.; Nugier, F., E-mail: giuseppe.fanizza@ba.infn.it, E-mail: fabienjean.nugier@unibo.it

    We present in this paper a new application of the geodesic light-cone (GLC) gauge for weak lensing calculations. Using interesting properties of this gauge, we derive an exact expression of the amplification matrix—involving convergence, magnification and shear—and of the deformation matrix—involving the optical scalars. These expressions are simple and non-perturbative as long as no caustics are created on the past light-cone and are, by construction, free from the thin lens approximation. We apply these general expressions on the example of an Lemaȋtre-Tolman-Bondi (LTB) model with an off-center observer and obtain explicit forms for the lensing quantities as a direct consequencemore » of the non-perturbative transformation between GLC and LTB coordinates. We show their evolution in redshift after a numerical integration, for underdense and overdense LTB models, and interpret their respective variations in the simple non-curvature case.« less

  3. An improved exact inversion formula for solenoidal fields in cone beam vector tomography

    NASA Astrophysics Data System (ADS)

    Katsevich, Alexander; Rothermel, Dimitri; Schuster, Thomas

    2017-06-01

    In this paper we present an improved inversion formula for the 3D cone beam transform of vector fields supported in the unit ball which is exact for solenoidal fields. It is well known that only the solenoidal part of a vector field can be determined from the longitudinal ray transform of a vector field in cone beam geometry. The inversion formula, as it was developed in Katsevich and Schuster (2013 An exact inversion formula for cone beam vector tomography Inverse Problems 29 065013), consists of two parts. The first part is of the filtered backprojection type, whereas the second part is a costly 4D integration and very inefficient. In this article we tackle this second term and obtain an improved formula, which is easy to implement and saves one order of integration. We also show that the first part contains all information about the curl of the field, whereas the second part has information about the boundary values. More precisely, the second part vanishes if the solenoidal part of the original field is tangential at the boundary. A number of numerical tests presented in the paper confirm the theoretical results and the exactness of the formula. Also, we obtain an inversion algorithm that works for general convex domains.

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

    NASA Astrophysics Data System (ADS)

    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.

  5. New exact solutions of the Dirac and Klein-Gordon equations of a charged particle propagating in a strong laser field in an underdense plasma

    NASA Astrophysics Data System (ADS)

    Varró, Sándor

    2014-03-01

    Exact solutions are presented of the Dirac and Klein-Gordon equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave in a medium of index of refraction nm<1. In the Dirac case the solutions are expressed in terms of new complex polynomials, and in the Klein-Gordon case the found solutions are expressed in terms of Ince polynomials. In each case they form a doubly infinite set, labeled by two integer quantum numbers. These integer numbers represent quantized momentum components of the charged particle along the polarization vector and along the propagation direction of the electromagnetic radiation. Since this radiation may represent a plasmon wave of arbitrary high amplitude, propagating in an underdense plasma, the solutions obtained may have relevance in describing possible quantum features of novel acceleration mechanisms.

  6. Exact Analytical Solution of the Peristaltic Nanofluids Flow in an Asymmetric Channel with Flexible Walls and Slip Condition: Application to the Cancer Treatment

    PubMed Central

    Ebaid, Abdelhalim; Aly, Emad H.

    2013-01-01

    In the cancer treatment, magnetic nanoparticles are injected into the blood vessel nearest to the cancer's tissues. The dynamic of these nanoparticles occurs under the action of the peristaltic waves generated on the flexible walls of the blood vessel. Studying such nanofluid flow under this action is therefore useful in treating tissues of the cancer. In this paper, the mathematical model describing the slip peristaltic flow of nanofluid was analytically investigated. Exact expressions were deduced for the temperature distribution and nano-particle concentration. In addition, the effects of the slip, thermophoresis, and Brownian motion parameters on the temperature and nano-particle concentration profiles were discussed and further compared with other approximate results in the literatures. In particular, these results have been obtained at the same values of the physical examined parameters that was considered in Akbar et al., “Peristaltic flow of a nanofluid with slip effects,” 2012. The results reveal that remarkable differences are detected between the exact current results and those approximately obtained in the literatures for behaviour of the temperature profile and nano-particles concentration. Accordingly, the current analysis and results are considered as optimal and therefore may be taken as a base for any future comparisons. PMID:24151526

  7. Computing exact bundle compliance control charts via probability generating functions.

    PubMed

    Chen, Binchao; Matis, Timothy; Benneyan, James

    2016-06-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2018-06-01

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

  9. Exact sum rules for inhomogeneous strings

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Amore, Paolo, E-mail: paolo.amore@gmail.com

    2013-11-15

    We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order N may be obtained in terms of a diagrammatic expansion, with (N−1)!/2 independent diagrams. These sum rules are used to derive upper and lower bounds to the energy of the fundamental mode of an inhomogeneous string; we also show that it is possible to improve these approximations taking into account the asymptotic behavior of the spectrum and applying the Shanks transformation to the sequence of approximations obtained to the differentmore » orders. We discuss three applications of these results. -- Highlights: •We derive an explicit expression for the sum rules of an inhomogeneous string. •We obtain a diagrammatic representation for the sum rules of a given order. •We obtain precise bounds on the lowest eigenvalue of the string.« less

  10. Exact mapping between different dynamics of isotropically trapped quantum gases

    NASA Astrophysics Data System (ADS)

    Wamba, Etienne; Pelster, Axel; Anglin, James R.

    2016-05-01

    Experiments on trapped quantum gases can probe challenging regimes of quantum many-body dynamics, where strong interactions or non-equilibrium states prevent exact theoretical treatment. In this talk, we present a class of exact mappings between all the observables of different experiments, under the experimentally attainable conditions that the gas particles interact via a homogeneously scaling two-body potential which is in general time-dependent, and are confined in an isotropic harmonic trap. We express our result through an identity relating second-quantized field operators in the Heisenberg picture of quantum mechanics which makes it general. It applies to arbitrary measurements on possibly multi-component Bose or Fermi gases in arbitrary initial quantum states, no matter how highly excited or far from equilibrium. We use an example to show how the results of two different and currently feasible experiments can be mapped onto each other by our spacetime transformation. DAMOP sorting category: 6.11 Nonlinear dynamics and out-of-equilibrium trapped gases EW acknowledge the financial support from the Alexander von Humboldt foundation.

  11. On the exact solvability of the anisotropic central spin model: An operator approach

    NASA Astrophysics Data System (ADS)

    Wu, Ning

    2018-07-01

    Using an operator approach based on a commutator scheme that has been previously applied to Richardson's reduced BCS model and the inhomogeneous Dicke model, we obtain general exact solvability requirements for an anisotropic central spin model with XXZ-type hyperfine coupling between the central spin and the spin bath, without any prior knowledge of integrability of the model. We outline basic steps of the usage of the operators approach, and pedagogically summarize them into two Lemmas and two Constraints. Through a step-by-step construction of the eigen-problem, we show that the condition gj‧2 - gj2 = c naturally arises for the model to be exactly solvable, where c is a constant independent of the bath-spin index j, and {gj } and { gj‧ } are the longitudinal and transverse hyperfine interactions, respectively. The obtained conditions and the resulting Bethe ansatz equations are consistent with that in previous literature.

  12. Does really Born Oppenheimer approximation break down in charge transfer processes? An exactly solvable model

    NASA Astrophysics Data System (ADS)

    Kuznetsov, Alexander M.; Medvedev, Igor G.

    2006-05-01

    Effects of deviation from the Born-Oppenheimer approximation (BOA) on the non-adiabatic transition probability for the transfer of a quantum particle in condensed media are studied within an exactly solvable model. The particle and the medium are modeled by a set of harmonic oscillators. The dynamic interaction of the particle with a single local mode is treated explicitly without the use of BOA. Two particular situations (symmetric and non-symmetric systems) are considered. It is shown that the difference between the exact solution and the true BOA is negligibly small at realistic parameters of the model. However, the exact results differ considerably from those of the crude Condon approximation (CCA) which is usually considered in the literature as a reference point for BOA (Marcus-Hush-Dogonadze formula). It is shown that the exact rate constant can be smaller (symmetric system) or larger (non-symmetric one) than that obtained in CCA. The non-Condon effects are also studied.

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

    NASA Astrophysics Data System (ADS)

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

    2017-05-01

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

  14. Nodal-line dynamics via exact polynomial solutions for coherent waves traversing aberrated imaging systems.

    PubMed

    Paganin, David M; Beltran, Mario A; Petersen, Timothy C

    2018-03-01

    We obtain exact polynomial solutions for two-dimensional coherent complex scalar fields propagating through arbitrary aberrated shift-invariant linear imaging systems. These solutions are used to model nodal-line dynamics of coherent fields output by such systems.

  15. Exact solutions to Brans-Dicke cosmologies in flat Friedmann universes.

    NASA Technical Reports Server (NTRS)

    Morganstern, R. E.

    1971-01-01

    The Brans-Dicke cosmological equations for flat Friedmann-type expanding universes are solved parametrically for time, density, expansion parameter, and scalar field. These results reduce to a previously obtained exact solution to the radiation cosmology. Although the scalar field may be undetectable at the present epoch, it is felt that, if it exists, it must play an important role as one approaches the initial singularity of the cosmology.

  16. New conditions for obtaining the exact solutions of the general Riccati equation.

    PubMed

    Bougoffa, Lazhar

    2014-01-01

    We propose a direct method for solving the general Riccati equation y' = f(x) + g(x)y + h(x)y(2). We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functions f(x), g(x), and h(x) of the equation to obtain an equivalent separable equation from which the previous equation can be solved in closed form. Several examples are presented to demonstrate the efficiency of this method.

  17. An Exact Solution to the Draining Reservoir Problem of the Incompressible and Non-Viscous Liquid

    ERIC Educational Resources Information Center

    Hong, Seok-In

    2009-01-01

    The exact expressions for the drain time and the height, velocity and acceleration of the free surface are found for the draining reservoir problem of the incompressible and non-viscous liquid. Contrary to the conventional approximate results, they correctly describe the initial time dependence of the liquid velocity and acceleration. Torricelli's…

  18. Explicitly broken supersymmetry with exactly massless moduli

    NASA Astrophysics Data System (ADS)

    Dong, Xi; Freedman, Daniel Z.; Zhao, Yue

    2016-06-01

    The AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a super-gravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents.

  19. Hidden algebra method (quasi-exact-solvability in quantum mechanics)

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Turbiner, Alexander; Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F.

    1996-02-20

    A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.

  20. Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation.

    PubMed

    Mohamad, Ahmad Qushairi; Khan, Ilyas; Ismail, Zulkhibri; Shafie, Sharidan

    2016-01-01

    Non-coaxial rotation has wide applications in engineering devices, e.g. in food processing such as mixer machines and stirrers with a two-axis kneader, in cooling turbine blades, jet engines, pumps and vacuum cleaners, in designing thermal syphon tubes, and in geophysical flows. Therefore, this study aims to investigate unsteady free convection flow of viscous fluid due to non-coaxial rotation and fluid at infinity over an oscillating vertical plate with constant wall temperature. The governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time ( t ), the Grashof number ( Gr ), the Prandtl number ([Formula: see text]), and the phase angle ([Formula: see text]). Skin friction and the Nusselt number are also evaluated. The exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver-Stehfest algorithm. The interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time ( t ), the Grashof number ( Gr ), the Prandtl number ([Formula: see text]), and the phase angle ([Formula: see text]).

  1. Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

    NASA Astrophysics Data System (ADS)

    Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

    2016-12-01

    Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

  2. An exact solution for R2,eff in CPMG experiments in the case of two site chemical exchange

    PubMed Central

    Baldwin, Andrew J.

    2014-01-01

    The Carr–Purcell–Meiboom–Gill (CPMG) experiment is widely used to quantitatively analyse the effects of chemical exchange on NMR spectra. In a CPMG experiment, the effective transverse relaxation rate, R2,eff, is typically measured as a function of the pulse frequency, νCPMG. Here, an exact expression for how R2,eff varies with νCPMG is derived for the commonly encountered scenario of two-site chemical exchange of in-phase magnetisation. This result, summarised in Appendix A, generalises a frequently used equation derived by Carver and Richards, published in 1972. The expression enables more rapid analysis of CPMG data by both speeding up calculation of R2,eff over numerical methods by a factor of ca. 130, and yields exact derivatives for use in data analysis. Moreover, the derivation provides insight into the physical principles behind the experiment. PMID:24852115

  3. Exact Riemann solutions of the Ripa model for flat and non-flat bottom topographies

    NASA Astrophysics Data System (ADS)

    Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

    2018-03-01

    This article is concerned with the derivation of exact Riemann solutions for Ripa model considering flat and non-flat bottom topographies. The Ripa model is a system of shallow water equations accounting for horizontal temperature gradients. In the case of non-flat bottom topography, the mass, momentum and energy conservation principles are utilized to relate the left and right states across the step-type bottom topography. The resulting system of algebraic equations is solved iteratively. Different numerical case studies of physical interest are considered. The solutions obtained from developed exact Riemann solvers are compared with the approximate solutions of central upwind scheme.

  4. Exact controllability for a Thermodiffusion System with locally distributed controls

    NASA Astrophysics Data System (ADS)

    de Moraes, F. G.; Schulz, R. A.; Soriano, J. A.

    2018-03-01

    In this work we establish a exact controllability result for a thermodiffusion system, modeled by Cattaneo's law, posed in a one-dimensional domain. In the present model the control mechanisms are effective in a small subinterval of the domain. To obtain the desired results, we prove an observability inequality for the adjoint system which, together with the multiplier methods and the Hilbert Uniqueness Method (HUM) developed by J.L. Lions, gives the controllability.

  5. Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions

    NASA Astrophysics Data System (ADS)

    Merzon, A.; Zhevandrov, P.; Romero Rodríguez, M. I.; De la Paz Méndez, J. E.

    2018-06-01

    Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.

  6. Exact and approximate solutions for transient squeezing flow

    NASA Astrophysics Data System (ADS)

    Lang, Ji; Santhanam, Sridhar; Wu, Qianhong

    2017-10-01

    In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity of the analytical approaches. The study presented herein fills the gap in the literature and will have a broad impact on industrial and biomedical applications.

  7. Some new traveling wave exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli equations.

    PubMed

    Qi, Jian-ming; Zhang, Fu; Yuan, Wen-jun; Huang, Zi-feng

    2014-01-01

    We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions ur,2 (z) and simply periodic solutions us,2-6(z) which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.

  8. Electron-cyclotron absorption in high-temperature plasmas: quasi-exact analytical evaluation and comparative numerical analysis

    NASA Astrophysics Data System (ADS)

    Albajar, F.; Bertelli, N.; Bornatici, M.; Engelmann, F.

    2007-01-01

    On the basis of the electromagnetic energy balance equation, a quasi-exact analytical evaluation of the electron-cyclotron (EC) absorption coefficient is performed for arbitrary propagation (with respect to the magnetic field) in a (Maxwellian) magneto-plasma for the temperature range of interest for fusion reactors (in which EC radiation losses tend to be important in the plasma power balance). The calculation makes use of Bateman's expansion for the product of two Bessel functions, retaining the lowest-order contribution. The integration over electron momentum can then be carried out analytically, fully accounting for finite Larmor radius effects in this approximation. On the basis of the analytical expressions for the EC absorption coefficients of both the extraordinary and ordinary modes thus obtained, (i) for the case of perpendicular propagation simple formulae are derived for both modes and (ii) a numerical analysis of the angular distribution of EC absorption is carried out. An assessment of the accuracy of asymptotic expressions that have been given earlier is also performed, showing that these approximations can be usefully applied for calculating EC power losses from reactor-grade plasmas. Presented in part at the 14th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating, Santorini, Greece, 9-12 May 2006.

  9. Hidden algebra method (quasi-exact-solvability in quantum mechanics)

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Turbiner, A.

    1996-02-01

    A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}

  10. Exact and approximate stochastic simulation of intracellular calcium dynamics.

    PubMed

    Wieder, Nicolas; Fink, Rainer H A; Wegner, Frederic von

    2011-01-01

    In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.

  11. Classes of exact Einstein Maxwell solutions

    NASA Astrophysics Data System (ADS)

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  13. Exact solutions for oscillatory shear sweep behaviors of complex fluids from the Oldroyd 8-constant framework

    NASA Astrophysics Data System (ADS)

    Saengow, Chaimongkol; Giacomin, A. Jeffrey

    2018-03-01

    In this paper, we provide a new exact framework for analyzing the most commonly measured behaviors in large-amplitude oscillatory shear flow (LAOS), a popular flow for studying the nonlinear physics of complex fluids. Specifically, the strain rate sweep (also called the strain sweep) is used routinely to identify the onset of nonlinearity. By the strain rate sweep, we mean a sequence of LAOS experiments conducted at the same frequency, performed one after another, with increasing shear rate amplitude. In this paper, we give exact expressions for the nonlinear complex viscosity and the corresponding nonlinear complex normal stress coefficients, for the Oldroyd 8-constant framework for oscillatory shear sweeps. We choose the Oldroyd 8-constant framework for its rich diversity of popular special cases (we list 18 of these). We evaluate the Fourier integrals of our previous exact solution to get exact expressions for the real and imaginary parts of the complex viscosity, and for the complex normal stress coefficients, as functions of both test frequency and shear rate amplitude. We explore the role of infinite shear rate viscosity on strain rate sweep responses for the special case of the corotational Jeffreys fluid. We find that raising η∞ raises the real part of the complex viscosity and lowers the imaginary. In our worked examples, we thus first use the corotational Jeffreys fluid, and then, for greater accuracy, we use the Johnson-Segalman fluid, to describe the strain rate sweep response of molten atactic polystyrene. For our comparisons with data, we use the Spriggs relations to generalize the Oldroyd 8-constant framework to multimode. Our generalization yields unequivocally, a longest fluid relaxation time, used to assign Weissenberg and Deborah numbers to each oscillatory shear flow experiment. We then locate each experiment in the Pipkin space.

  14. Towards an exact factorization of the molecular wave function

    NASA Astrophysics Data System (ADS)

    Parashar, Shubham; Sajeev, Y.; Ghosh, Swapan K.

    2015-10-01

    An exact single-product factorisation of the molecular wave function for the timedependent Schrödinger equation is investigated by using an ansatz involving a phase factor. By using the Frenkel variational method, we obtain the Schrödinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter ω in the phase factor is chosen such that the equations of motion retain the physically appealing Born- Oppenheimer-like form, and is therefore unique.

  15. Exact vacuum solution to conformal Weyl gravity and galactic rotation curves

    NASA Technical Reports Server (NTRS)

    Mannheim, Philip D.; Kazanas, Demosthenes

    1989-01-01

    The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.

  16. Exact solution of conductive heat transfer in cylindrical composite laminate

    NASA Astrophysics Data System (ADS)

    Kayhani, M. H.; Shariati, M.; Nourozi, M.; Karimi Demneh, M.

    2009-11-01

    This paper presents an exact solution for steady-state conduction heat transfer in cylindrical composite laminates. This laminate is cylindrical shape and in each lamina, fibers have been wound around the cylinder. In this article heat transfer in composite laminates is being investigated, by using separation of variables method and an analytical relation for temperature distribution in these laminates has been obtained under specific boundary conditions. Also Fourier coefficients in each layer obtain by solving set of equations that related to thermal boundary layer conditions at inside and outside of the cylinder also thermal continuity and heat flux continuity between each layer is considered. In this research LU factorization method has been used to solve the set of equations.

  17. An exact sum-rule for the Hubbard model: an historical/pedagogical approach

    NASA Astrophysics Data System (ADS)

    Di Matteo, S.; Claveau, Y.

    2017-07-01

    The aim of the present article is to derive an exact integral equation for the Green function of the Hubbard model through an equation-of-motion procedure, like in the original Hubbard papers. Though our exact integral equation does not allow to solve the Hubbard model, it represents a strong constraint on its approximate solutions. An analogous sum rule has been already obtained in the literature, through the use of a spectral moment technique. We think however that our equation-of-motion procedure can be more easily related to the historical procedure of the original Hubbard papers. We also discuss examples of possible applications of the sum rule and propose and analyse a solution, fulfilling it, that can be used for a pedagogical introduction to the Mott-Hubbard metal-insulator transition.

  18. An exact solution on unsteady MHD free convection chemically reacting silver nanofluid flow past an exponentially accelerated vertical plate through porous medium

    NASA Astrophysics Data System (ADS)

    Kumaresan, E.; Vijaya Kumar, A. G.; Rushi Kumar, B.

    2017-11-01

    This article studies, an exact solution of unsteady MHD free convection boundary-layer flow of a silver nanofluid past an exponentially accelerated moving vertical plate through aporous medium in the presence of thermal radiation, transverse applied amagnetic field, radiation absorption and Heat generation or absorption with chemical reaction are investigated theoretically. We consider nanofluids contain spherical shaped nanoparticle of silverwith a nanoparticle volume concentration range smaller than or equal to 0.04. This phenomenon is modeled in the form of partial differential equations with initial boundary conditions. Some suitable dimensional variables are introduced. The corresponding dimensionless equations with boundary conditions are solved by using Laplace transform technique. The exact solutions for velocity, energy, and species are obtained, also the corresponding numerical values of nanofluid velocity, temperature and concentration profiles are represented graphically. The expressions for skin friction coefficient, the rate of heat transfer and mass transfer are derived. The present study finds applications involving heat transfer, enhancement of thermal conductivity and other applications like transportation, industrial cooling applications, heating buildings and reducing pollution, energy applications and solar absorption. The effect of heat transfer is found to be more pronounced in a silver-water nanofluid than in the other nanofluids.

  19. Class of cooperative stochastic models: Exact and approximate solutions, simulations, and experiments using ionic self-assembly of nanoparticles.

    PubMed

    Mazilu, I; Mazilu, D A; Melkerson, R E; Hall-Mejia, E; Beck, G J; Nshimyumukiza, S; da Fonseca, Carlos M

    2016-03-01

    We present exact and approximate results for a class of cooperative sequential adsorption models using matrix theory, mean-field theory, and computer simulations. We validate our models with two customized experiments using ionically self-assembled nanoparticles on glass slides. We also address the limitations of our models and their range of applicability. The exact results obtained using matrix theory can be applied to a variety of two-state systems with cooperative effects.

  20. Exact analytic solution for the spin-up maneuver of an axially symmetric spacecraft

    NASA Astrophysics Data System (ADS)

    Ventura, Jacopo; Romano, Marcello

    2014-11-01

    The problem of spinning-up an axially symmetric spacecraft subjected to an external torque constant in magnitude and parallel to the symmetry axis is considered. The existing exact analytic solution for an axially symmetric body is applied for the first time to this problem. The proposed solution is valid for any initial conditions of attitude and angular velocity and for any length of time and rotation amplitude. Furthermore, the proposed solution can be numerically evaluated up to any desired level of accuracy. Numerical experiments and comparison with an existing approximated solution and with the integration of the equations of motion are reported in the paper. Finally, a new approximated solution obtained from the exact one is introduced in this paper.

  1. Comment on "Exact solution of resonant modes in a rectangular resonator".

    PubMed

    Gutiérrez-Vega, Julio C; Bandres, Miguel A

    2006-08-15

    We comment on the recent Letter by J. Wu and A. Liu [Opt. Lett. 31, 1720 (2006)] in which an exact scalar solution to the resonant modes and the resonant frequencies in a two-dimensional rectangular microcavity were presented. The analysis is incorrect because (a) the field solutions were imposed to satisfy simultaneously both Dirichlet and Neumann boundary conditions at the four sides of the rectangle, leading to an overdetermined problem, and (b) the modes in the cavity were expanded using an incorrect series ansatz, leading to an expression for the mode fields that does not satisfy the Helmholtz equation.

  2. The exact analysis of contingency tables in medical research.

    PubMed

    Mehta, C R

    1994-01-01

    A unified view of exact nonparametric inference, with special emphasis on data in the form of contingency tables, is presented. While the concept of exact tests has been in existence since the early work of RA Fisher, the computational complexity involved in actually executing such tests precluded their use until fairly recently. Modern algorithmic advances, combined with the easy availability of inexpensive computing power, has renewed interest in exact methods of inference, especially because they remain valid in the face of small, sparse, imbalanced, or heavily tied data. After defining exact p-values in terms of the permutation principle, we reference algorithms for computing them. Several data sets are then analysed by both exact and asymptotic methods. We end with a discussion of the available software.

  3. Exact finite element method analysis of viscoelastic tapered structures to transient loads

    NASA Technical Reports Server (NTRS)

    Spyrakos, Constantine Chris

    1987-01-01

    A general method is presented for determining the dynamic torsional/axial response of linear structures composed of either tapered bars or shafts to transient excitations. The method consists of formulating and solving the dynamic problem in the Laplace transform domain by the finite element method and obtaining the response by a numerical inversion of the transformed solution. The derivation of the torsional and axial stiffness matrices is based on the exact solution of the transformed governing equation of motion, and it consequently leads to the exact solution of the problem. The solution permits treatment of the most practical cases of linear tapered bars and shafts, and employs modeling of structures with only one element per member which reduces the number of degrees of freedom involved. The effects of external viscous or internal viscoelastic damping are also taken into account.

  4. Exact Rayleigh scattering calculations for use with the Nimbus-7 Coastal Zone Color Scanner

    NASA Technical Reports Server (NTRS)

    Gordon, Howard R.; Brown, James W.; Evans, Robert H.

    1988-01-01

    The radiance reflected from a plane-parallel atmosphere and flat sea surface in the absence of aerosols has been determined with an exact multiple scattering code to improve the analysis of Nimbus-7 CZCS imagery. It is shown that the single scattering approximation normally used to compute this radiance can result in errors of up to 5 percent for small and moderate solar zenith angles. A scheme to include the effect of variations in the surface pressure in the exact computation of the Rayleigh radiance is discussed. The results of an application of these computations to CZCS imagery suggest that accurate atmospheric corrections can be obtained for solar zenith angles at least as large as 65 deg.

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

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    Ghanbari, Behzad; Inc, Mustafa

    2018-04-01

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

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

    NASA Technical Reports Server (NTRS)

    Liu, Li; Mishchenko, Michael I.

    2016-01-01

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

  8. An exact solution for the Hawking effect in a dispersive fluid

    NASA Astrophysics Data System (ADS)

    Philbin, T. G.

    2016-09-01

    We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the group velocity of low-frequency waves. We find the exact solution for wave propagation in the flow. The scattering shows amplification of classical waves, leading to spontaneous emission when the waves are quantized. In the dispersionless limit the system corresponds to a 1 +1 -dimensional black-hole or white-hole binary and there is a thermal spectrum of Hawking radiation from each horizon. Dispersion changes the scattering coefficients so that the quantum emission is no longer thermal. The scattering coefficients were previously obtained by Busch and Parentani in a study of dispersive fields in de Sitter space [Phys. Rev. D 86, 104033 (2012)]. Our results give further details of the wave propagation in this exactly solvable case, where our focus is on laboratory systems.

  9. Exact-solution for cone-plate viscometry

    NASA Astrophysics Data System (ADS)

    Giacomin, A. J.; Gilbert, P. H.

    2017-11-01

    The viscosity of a Newtonian fluid is often measured by confining the fluid to the gap between a rotating cone that is perpendicular to a fixed disk. We call this experiment cone-plate viscometry. When the cone angle approaches π/2 , the viscometer gap is called narrow. The shear stress in the fluid, throughout a narrow gap, hardly departs from the shear stress exerted on the plate, and we thus call cone-plate flow nearly homogeneous. In this paper, we derive an exact solution for this slight heterogeneity, and from this, we derive the correction factors for the shear rate on the cone and plate, for the torque, and thus, for the measured Newtonian viscosity. These factors thus allow the cone-plate viscometer to be used more accurately, and with cone-angles well below π/2 . We find cone-plate flow field heterogeneity to be far slighter than previously thought. We next use our exact solution for the velocity to arrive at the exact solution for the temperature rise, due to viscous dissipation, in cone-plate flow subject to isothermal boundaries. Since Newtonian viscosity is a strong function of temperature, we expect our new exact solution for the temperature rise be useful to those measuring Newtonian viscosity, and especially so, to those using wide gaps. We include two worked examples to teach practitioners how to use our main results.

  10. Asymptotic behavior of exact exchange potential of slabs

    NASA Astrophysics Data System (ADS)

    Engel, E.

    2014-06-01

    In this contribution the exact exchange potential vx of density functional theory is examined for slabs such as graphene, for which one has a Bravais lattice in the x-y directions, while the electrons are confined to the finite region -L≤z≤L in the z direction. It is demonstrated analytically that the exact vx behaves as -e2/z for z ≫L. This result extends the corresponding statement of Horowitz, Proetto, and Rigamonti [Phys. Rev. Lett. 97, 026802 (2006), 10.1103/PhysRevLett.97.026802] for jellium slabs to slabs with arbitrary periodic density distributions. Application of the exact exchange to a Si(111) slab (within the Krieger-Li-Iafrate approximation) indicates that the corrugation of the exact vx is more pronounced than that of the local density approximation for vx.

  11. Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

    NASA Astrophysics Data System (ADS)

    Mandrà, Salvatore; Giacomo Guerreschi, Gian; Aspuru-Guzik, Alán

    2016-07-01

    We present an exact quantum algorithm for solving the Exact Satisfiability problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: the first step consists in the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the Exact Satisfiability; while the second part performs a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query complexities for the worst-case are respectively bounded by O(\\sqrt{{2}n-{M\\prime }}) and O({2}n-{M\\prime }), where n is the number of variables and {M}\\prime the number of linearly independent clauses. Remarkably, the proposed quantum algorithm results to be faster than any known exact classical algorithm to solve dense formulas of Exact Satisfiability. As a concrete application, we provide the worst-case complexity for the Hamiltonian cycle problem obtained after mapping it to a suitable Occupation problem. Specifically, we show that the time complexity for the proposed quantum algorithm is bounded by O({2}n/4) for 3-regular undirected graphs, where n is the number of nodes. The same worst-case complexity holds for (3,3)-regular bipartite graphs. As a reference, the current best classical algorithm has a (worst-case) running time bounded by O({2}31n/96). Finally, when compared to heuristic techniques for Exact Satisfiability problems, the proposed quantum algorithm is faster than the classical WalkSAT and Adiabatic Quantum Optimization for random instances with a density of constraints close to the satisfiability threshold, the regime in which instances are typically the hardest to solve. The proposed quantum algorithm can be straightforwardly extended to the generalized version of the Exact Satisfiability known as Occupation

  12. Resolvent analysis of exact coherent solutions

    NASA Astrophysics Data System (ADS)

    Rosenberg, Kevin; McKeon, Beverley

    2017-11-01

    Exact coherent solutions have been hypothesized to constitute the state-space skeleton of turbulent trajectories and thus are of interest as a means to better understand the underlying dynamics of turbulent flows. An asymptotic description of how these types of solutions self-sustain was provided by Hall & Sherwin. Here we offer a fully-nonlinear perspective on the self-sustainment of these solutions in terms of triadic scale interactions and use the resolvent framework of McKeon & Sharma to interpret these results from an input/output point of view. We analyze traveling wave solutions and periodic orbits in channel flow, and demonstrate how resolvent analysis can be used to obtain low-dimensional representations of these flows. We gratefully acknowledge funding from the AFOSR (FA9550-16-1-0361) and J.S. Park, M.D. Graham, and J.F. Gibson for providing data for the ECS solutions.

  13. Exact moments of the Sachdev-Ye-Kitaev model up to order 1 /N 2

    NASA Astrophysics Data System (ADS)

    García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

    2018-04-01

    We analytically evaluate the moments of the spectral density of the q-body Sachdev-Ye-Kitaev (SYK) model, and obtain order 1 /N 2 corrections for all moments, where N is the total number of Majorana fermions. To order 1 /N, moments are given by those of the weight function of the Q-Hermite polynomials. Representing Wick contractions by rooted chord diagrams, we show that the 1 /N 2 correction for each chord diagram is proportional to the number of triangular loops of the corresponding intersection graph, with an extra grading factor when q is odd. Therefore the problem of finding 1 /N 2 corrections is mapped to a triangle counting problem. Since the total number of triangles is a purely graph-theoretic property, we can compute them for the q = 1 and q = 2 SYK models, where the exact moments can be obtained analytically using other methods, and therefore we have solved the moment problem for any q to 1 /N 2 accuracy. The moments are then used to obtain the spectral density of the SYK model to order 1 /N 2. We also obtain an exact analytical result for all contraction diagrams contributing to the moments, which can be evaluated up to eighth order. This shows that the Q-Hermite approximation is accurate even for small values of N.

  14. A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

    PubMed Central

    Güner, Özkan; Cevikel, Adem C.

    2014-01-01

    We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

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

    PubMed

    Güner, Özkan; Cevikel, Adem C

    2014-01-01

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

  16. Obtaining natural-like flow releases in diverted river reaches from simple riparian benefit economic models.

    PubMed

    Perona, Paolo; Dürrenmatt, David J; Characklis, Gregory W

    2013-03-30

    We propose a theoretical river modeling framework for generating variable flow patterns in diverted-streams (i.e., no reservoir). Using a simple economic model and the principle of equal marginal utility in an inverse fashion we first quantify the benefit of the water that goes to the environment in relation to that of the anthropic activity. Then, we obtain exact expressions for optimal water allocation rules between the two competing uses, as well as the related statistical distributions. These rules are applied using both synthetic and observed streamflow data, to demonstrate that this approach may be useful in 1) generating more natural flow patterns in the river reach downstream of the diversion, thus reducing the ecodeficit; 2) obtaining a more enlightened economic interpretation of Minimum Flow Release (MFR) strategies, and; 3) comparing the long-term costs and benefits of variable versus MFR policies and showing the greater ecological sustainability of this new approach. Copyright © 2013 Elsevier Ltd. All rights reserved.

  17. Exact ghost-free bigravitational waves

    NASA Astrophysics Data System (ADS)

    Ayón-Beato, Eloy; Higuita-Borja, Daniel; Méndez-Zavaleta, Julio A.; Velázquez-Rodríguez, Gerardo

    2018-04-01

    We study the propagation of exact gravitational waves in the ghost-free bimetric theory. Our focus is on type-N spacetimes compatible with the cosmological constants provided by the bigravity interaction potential, and particularly in the single class known by allowing at least a Killing symmetry: the AdS waves. They have the advantage of being represented by a generalized Kerr-Schild transformation from AdS spacetime. This entails a notorious simplification in bigravity by allowing to straightforwardly compute any power of its interaction square root matrix, opening the door to explore physically meaningful exact configurations. For these exact gravitational waves the complex dynamical structure of bigravity decomposes into elementary exact massless or massive excitations propagating on AdS. We use a complexified formulation of the Euler-Darboux equations to provide for the first time the general solutions to the massive version of the Siklos equation which rules the resulting AdS-wave dynamics, using an integral representation originally due to Poisson. Inspired by this progress, we tackle the subtle problem of how matter couples to bigravity and, more concretely, if this occurs through a composite metric, which is hard to handle in a general setting. Surprisingly, the Kerr-Schild ansatz brings again a huge simplification in how the related energy-momentum tensors are calculated. This allows us to explicitly characterize AdS waves supported by either a massless free scalar field or a wavefront-homogeneous Maxwell field. Considering the most general allowed Maxwell source instead is a highly nontrivial task, which we accomplish by again exploiting the complexified Euler-Darboux description and taking advantage of the classical Riemann method. In fact, this eventually allows us to find the most general configurations for any matter source.

  18. A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    1997-12-01

    The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic volatility is reviewed starting from the first principles of finance. The equation of Merton and Garman is then recast using the path integration technique of theoretical physics. The price of the stock option is shown to be the analogue of the Schrödinger wavefunction of quantum mechanics and the exact Hamiltonian and Lagrangian of the system is obtained. The results of Hull and White are generalized to the case when stock price and volatility have non-zero correlation. Some exact results for pricing stock options for the general correlated case are derived.

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

    PubMed

    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.

  20. Exact theory of freeze-out

    NASA Astrophysics Data System (ADS)

    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.

  1. Exact and Approximate Solutions for Transient Squeezing Flow

    NASA Astrophysics Data System (ADS)

    Lang, Ji; Santhanam, Sridhar; Wu, Qianhong

    2017-11-01

    In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration is negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear, and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process, and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity of the analytical approaches. The study presented herein fills the gap in the literature, and will have a broad impact in industrial and biomedical applications. This work is supported by National Science Foundation CBET Fluid Dynamics Program under Award #1511096, and supported by the Seed Grant from The Villanova Center for the Advancement of Sustainability in Engineering (VCASE).

  2. Exact analytic solutions of Maxwell's equations describing propagating nonparaxial electromagnetic beams.

    PubMed

    Garay-Avendaño, Roger L; Zamboni-Rached, Michel

    2014-07-10

    In this paper, we propose a method that is capable of describing in exact and analytic form the propagation of nonparaxial scalar and electromagnetic beams. The main features of the method presented here are its mathematical simplicity and the fast convergence in the cases of highly nonparaxial electromagnetic beams, enabling us to obtain high-precision results without the necessity of lengthy numerical simulations or other more complex analytical calculations. The method can be used in electromagnetism (optics, microwaves) as well as in acoustics.

  3. An exact solution for ideal dam-break floods on steep slopes

    USGS Publications Warehouse

    Ancey, C.; Iverson, R.M.; Rentschler, M.; Denlinger, R.P.

    2008-01-01

    The shallow-water equations are used to model the flow resulting from the sudden release of a finite volume of frictionless, incompressible fluid down a uniform slope of arbitrary inclination. The hodograph transformation and Riemann's method make it possible to transform the governing equations into a linear system and then deduce an exact analytical solution expressed in terms of readily evaluated integrals. Although the solution treats an idealized case never strictly realized in nature, it is uniquely well-suited for testing the robustness and accuracy of numerical models used to model shallow-water flows on steep slopes. Copyright 2008 by the American Geophysical Union.

  4. Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations.

    PubMed

    Gu, Yongyi; Qi, Jianming

    2017-01-01

    In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the [Formula: see text]-expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

  5. Exact transition probabilities in a 6-state Landau–Zener system with path interference

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sinitsyn, Nikolai A.

    2015-04-23

    In this paper, we identify a nontrivial multistate Landau–Zener (LZ) model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model features the possibility of interference of different trajectories that connect the same initial and final states. Hence, transition probabilities are generally not described by the incoherent successive application of the LZ formula. Finally, we discuss reasons for integrability of this system and provide numerical tests of the suggested expression for the transition probability matrix.

  6. Optimum three-dimensional atmospheric entry from the analytical solution of Chapman's exact equations

    NASA Technical Reports Server (NTRS)

    Busemann, A.; Vinh, N. X.; Culp, R. D.

    1974-01-01

    The general solution for the optimum three-dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere is developed. A set of dimensionless variables, modified Chapman variables, is introduced. The resulting exact equations of motion, referred to as Chapman's exact equations, have the advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a completely general lift-drag relationship is used in the derivation. The results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary drag polar, and entering any planetary atmosphere. The aerodynamic controls chosen are the lift coefficient and the bank angle. General optimum control laws for these controls are developed. Several earlier particular solutions are shown to be special cases of this general result. Results are valid for both free and constrained terminal position.

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

    NASA Technical Reports Server (NTRS)

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

    1977-01-01

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

  8. Exact extraction method for road rutting laser lines

    NASA Astrophysics Data System (ADS)

    Hong, Zhiming

    2018-02-01

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

  9. The {sech}( {\\hat{ξ }} ) -Type Profiles: A Swiss-Army Knife for Exact Analytical Modeling of Thermal Diffusion and Wave Propagation in Graded Media

    NASA Astrophysics Data System (ADS)

    Krapez, J.-C.

    2018-07-01

    This work deals with the exact analytical modeling of transfer phenomena in heterogeneous materials exhibiting one-dimensional continuous variations of their properties. Regarding heat transfer, it has recently been shown that by applying a Liouville transformation and multiple Darboux transformations, infinite sequences of solvable profiles of thermal effusivity can be constructed together with the associated temperature (exact) solutions, all in closed-form expressions (vs. the diffusion-time variable and with a growing number of parameters). In addition, a particular class of profiles, the so-called {sech}( {\\hat{ξ }} ) -type profiles, exhibit high agility and at the same time parsimony. In this paper we delve further into the description of these solvable profiles and their properties. Most importantly, their quadrupole formulation is provided, enabling smooth synthetic profiles of effusivity of arbitrary complexity to be built, and allowing the corresponding temperature dynamic response to be obtained very easily thereafter. Examples are given with increasing variability of the effusivity and an increasing number of elementary profiles. These highly flexible profiles are equally relevant to providing an exact analytical solution to wave propagation problems in 1D graded media (i.e., Maxwell's equations, the acoustic equation, the telegraph equation, etc.). From now on, whether it be for diffusion-like or wave-like problems, when the leading properties present (possibly piecewise-) continuously heterogeneous profiles, the classical staircase model can be advantageously replaced by a "high-level" quadrupole model consisting of one or more {sech}( {\\hat{ξ }} ) -type profiles, which makes the latter a true Swiss-Army knife for analytical modeling.

  10. Exact and quasi-classical density matrix and Wigner functions for a particle in the box and half space

    NASA Technical Reports Server (NTRS)

    Akhundova, E. A.; Dodonov, V. V.; Manko, V. I.

    1993-01-01

    The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).

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

    NASA Astrophysics Data System (ADS)

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

    2018-06-01

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

  12. How hairpin vortices emerge from exact invariant solutions

    NASA Astrophysics Data System (ADS)

    Schneider, Tobias M.; Farano, Mirko; de Palma, Pietro; Robinet, Jean-Christoph; Cherubini, Stefania

    2017-11-01

    Hairpin vortices are among the most commonly observed flow structures in wall-bounded shear flows. However, within the dynamical system approach to turbulence, those structures have not yet been described. They are not captured by known exact invariant solutions of the Navier-Stokes equations nor have other state-space structures supporting hairpins been identified. We show that hairpin structures are observed along an optimally growing trajectory leaving a well known exact traveling wave solution of plane Poiseuille flow. The perturbation triggering hairpins does not correspond to an unstable mode of the exact traveling wave but lies in the stable manifold where non-normality causes strong transient amplification.

  13. Laplace-Beltrami operator and exact solutions for branes

    NASA Astrophysics Data System (ADS)

    Zheltukhin, A. A.

    2013-02-01

    Proposed is a new approach to finding exact solutions of nonlinear p-brane equations in D-dimensional Minkowski space based on the use of various initial value constraints. It is shown that the constraints Δx→=0 and Δx→=-Λ(t,σr)x→ give two sets of exact solutions.

  14. Exact models for isotropic matter

    NASA Astrophysics Data System (ADS)

    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.

  15. Exact traveling-wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional Schrödinger equation with polynomial nonlinearity of arbitrary order.

    PubMed

    Petrović, Nikola Z; Belić, Milivoj; Zhong, Wei-Ping

    2011-02-01

    We obtain exact traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients and polynomial Kerr nonlinearity of an arbitrarily high order. Exact solutions, given in terms of Jacobi elliptic functions, are presented for the special cases of cubic-quintic and septic models. We demonstrate that the widely used method for finding exact solutions in terms of Jacobi elliptic functions is not applicable to the nonlinear Schrödinger equation with saturable nonlinearity. ©2011 American Physical Society

  16. Spatial correlations and exact solution of the problem of the boson peak profile in amorphous media

    NASA Astrophysics Data System (ADS)

    Kirillov, Sviatoslav A.; A. Voyiatzis, George; Kolomiyets, Tatiana M.; H. Anastasiadis, Spiros

    1999-11-01

    Based on a model correlation function which covers spatial correlations from Gaussian to exponential, we have arrived at an exact analytic solution of the problem of the Boson peak profile in amorphous media. Probe fits made for polyisoprene and triacetin prove the working ability of the formulae obtained.

  17. Interior radiances in optically deep absorbing media. I - Exact solutions for one-dimensional model.

    NASA Technical Reports Server (NTRS)

    Kattawar, G. W.; Plass, G. N.

    1973-01-01

    An exact analytic solution to the one-dimensional scattering problem with arbitrary single scattering albedo and arbitrary surface albedo is presented. Expressions are given for the emergent flux from a homogeneous layer, the internal flux within the layer, and the radiative heating. A comparison of these results with the values calculated from the matrix operator theory indicates an exceedingly high accuracy. A detailed study is made of the error in the matrix operator results and its dependence on the accuracy of the starting value.

  18. An Exact Form of Lilley's Equation with a Velocity Quadrupole/Temperature Dipole Source Term

    NASA Technical Reports Server (NTRS)

    Goldstein, Marvin E.

    2001-01-01

    There have been several attempts to introduce approximations into the exact form of Lilley's equation in order to express the source term as the sum of a quadrupole whose strength is quadratic in the fluctuating velocities and a dipole whose strength is proportional to the temperature fluctuations. The purpose of this note is to show that it is possible to choose the dependent (i.e., the pressure) variable so that this type of result can be derived directly from the Euler equations without introducing any additional approximations.

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

    NASA Astrophysics Data System (ADS)

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

    2018-03-01

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

  20. Exact Schwarzschild-like solution in a bumblebee gravity model

    NASA Astrophysics Data System (ADS)

    Casana, R.; Cavalcante, A.; Poulis, F. P.; Santos, E. B.

    2018-05-01

    We obtain an exact vacuum solution from the gravity sector contained in the minimal standard-model extension. The theoretical model assumes a Riemann spacetime coupled to the bumblebee field which is responsible for the spontaneous Lorentz symmetry breaking. The solution achieved in a static and spherically symmetric scenario establishes a Schwarzschild-like black hole. In order to study the effects of the spontaneous Lorentz symmetry breaking we investigate some classic tests, including the advance of perihelion, the bending of light, and Shapiro's time delay. Furthermore, we compute some upper bounds, among which the most stringent associated with existing experimental data provides a sensitivity at the 10-15 level and that for future missions at the 10-19 level.

  1. Using exact solutions to develop an implicit scheme for the baroclinic primitive equations

    NASA Technical Reports Server (NTRS)

    Marchesin, D.

    1984-01-01

    The exact solutions presently obtained by means of a novel method for nonlinear initial value problems are used in the development of numerical schemes for the computer solution of these problems. The method is applied to a new, fully implicit scheme on a vertical slice of the isentropic baroclinic equations. It was not possible to find a global scale phenomenon that could be simulated by the baroclinic primitive equations on a vertical slice.

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

    NASA Astrophysics Data System (ADS)

    Yuan, Na

    2018-04-01

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

  3. Exact solutions of a hierarchy of mixing speeds models

    NASA Astrophysics Data System (ADS)

    Cornille, H.; Platkowski, T.

    1992-07-01

    This paper presents several new aspects of discrete kinetic theory (DKT). First a hierarchy of d-dimensional (d=1,2,3) models is proposed with (2d+3) velocities and three moduli speeds: 0, 2, and a third one that can be arbitrary. It is assumed that the particles at rest have an internal energy which, for microscopic collisions, supplies for the loss of the kinetic energy. In a more general way than usual, collisions are allowed that mix particles with different speeds. Second, for the (1+1)-dimensional restriction of the systems of PDE for these models which have two independent quadratic collision terms we construct different exact solutions. The usual types of exact solutions are studied: periodic solutions and shock wave solutions obtained from the standard linearization of the scalar Riccati equations called Riccatian shock waves. Then other types of solutions of the coupled Riccati equations are found called non-Riccatian shock waves and they are compared with the previous ones. The main new result is that, between the upstream and downstream states, these new solutions are not necessarily monotonous. Further, for the shock problem, a two-dimensional dynamical system of ODE is solved numerically with limit values corresponding to the upstream and downstream states. As a by-product of this study two new linearizations for the Riccati coupled equations with two functions are proposed.

  4. Some exact properties of the nonequilibrium response function for transient photoabsorption

    NASA Astrophysics Data System (ADS)

    Perfetto, E.; Stefanucci, G.

    2015-03-01

    The physical interpretation of time-resolved photoabsorption experiments is not as straightforward as for the more conventional photoabsorption experiments conducted on equilibrium systems. In fact, the relation between the transient photoabsorption spectrum and the properties of the examined sample can be rather intricate since the former is a complicated functional of both the driving pump and the feeble probe fields. In this work, we critically review the derivation of the time-resolved photoabsorption spectrum in terms of the nonequilibrium dipole response function χ and assess its domain of validity. We then analyze χ in detail and discuss a few exact properties useful to interpret the transient spectrum during (overlapping regime) and after (nonoverlapping regime) the action of the pump. The nonoverlapping regime is the simplest to address. The absorption energies are indeed independent of the delay between the pump and probe pulses and hence the transient spectrum can change only by a rearrangement of the spectral weights. We give a close expression of these spectral weights in two limiting cases (ultrashort and everlasting monochromatic probes) and highlight their strong dependence on coherence and probe envelope. In the overlapping regime, we obtain a Lehmann-type representation of χ in terms of light-dressed states and provide a unifying framework of various well-known effects in pump-driven systems. We also show the emergence of spectral substructures due to the finite duration of the pump pulse.

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

    NASA Astrophysics Data System (ADS)

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

    2018-04-01

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

  6. Exact solutions for laminated composite cylindrical shells in cylindrical bending

    NASA Technical Reports Server (NTRS)

    Yuan, F. G.

    1992-01-01

    Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.

  7. Aesthetic Responses to Exact Fractals Driven by Physical Complexity

    PubMed Central

    Bies, Alexander J.; Blanc-Goldhammer, Daryn R.; Boydston, Cooper R.; Taylor, Richard P.; Sereno, Margaret E.

    2016-01-01

    Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a

  8. Exact expressions and accurate approximations for the dependences of radius and index of refraction of solutions of inorganic solutes on relative humidity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Lewis, E.R.; Schwartz, S.

    2010-03-15

    Light scattering by aerosols plays an important role in Earth’s radiative balance, and quantification of this phenomenon is important in understanding and accounting for anthropogenic influences on Earth’s climate. Light scattering by an aerosol particle is determined by its radius and index of refraction, and for aerosol particles that are hygroscopic, both of these quantities vary with relative humidity RH. Here exact expressions are derived for the dependences of the radius ratio (relative to the volume-equivalent dry radius) and index of refraction on RH for aqueous solutions of single solutes. Both of these quantities depend on the apparent molal volumemore » of the solute in solution and on the practical osmotic coefficient of the solution, which in turn depend on concentration and thus implicitly on RH. Simple but accurate approximations are also presented for the RH dependences of both radius ratio and index of refraction for several atmospherically important inorganic solutes over the entire range of RH values for which these substances can exist as solution drops. For all substances considered, the radius ratio is accurate to within a few percent, and the index of refraction to within ~0.02, over this range of RH. Such parameterizations will be useful in radiation transfer models and climate models.« less

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

    NASA Astrophysics Data System (ADS)

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2018-06-01

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

  11. An exact elliptic superpotential for N=1 ∗ deformations of finite N=2 gauge theories

    NASA Astrophysics Data System (ADS)

    Dorey, Nick; Hollowood, Timothy J.; Kumar, S. Prem

    2002-03-01

    We study relevant deformations of the N=2 superconformal theory on the world-volume of N D3-branes at an Ak-1 singularity. In particular, we determine the vacuum structure of the mass-deformed theory with N=1 supersymmetry and show how the different vacua are permuted by an extended duality symmetry. We then obtain exact, modular covariant formulae (for all k, N and arbitrary gauge couplings) for the holomorphic observables in the massive vacua in two different ways: by lifting to M-theory, and by compactification to three dimensions and subsequent use of mirror symmetry. In the latter case, we find an exact superpotential for the model which coincides with a certain combination of the quadratic Hamiltonians of the spin generalization of the elliptic Calogero-Moser integrable system.

  12. Exact Analytic Solution for a Ballistic Orbiting Wind

    NASA Astrophysics Data System (ADS)

    Wilkin, Francis P.; Hausner, Harry

    2017-07-01

    Much theoretical and observational work has been done on stellar winds within binary systems. We present a new solution for a ballistic wind launched from a source in a circular orbit. The solution is that of a single wind—no second wind is included in the system and the shocks that arise are those due to the orbiting wind interacting with itself. Our method emphasizes the curved streamlines in the corotating frame, where the flow is steady-state, allowing us to obtain an exact solution for the mass density at all pre-shock locations. Assuming an initially isotropic wind, fluid elements launched from the interior hemisphere of the wind will be the first to cross other streamlines, resulting in a spiral structure bounded by two shock surfaces. Streamlines from the outer wind hemisphere later intersect these shocks as well. An analytic solution is obtained for the geometry of the two shock surfaces. Although the inner and outer shock surfaces asymptotically trace Archimedean spirals, our tail solution suggests many crossings where the shocks overlap, beyond which the analytic solution cannot be continued. Our solution can be readily extended to an initially anisotropic wind.

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

    PubMed

    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.

  14. Exact lower and upper bounds on stationary moments in stochastic biochemical systems

    NASA Astrophysics Data System (ADS)

    Ghusinga, Khem Raj; Vargas-Garcia, Cesar A.; Lamperski, Andrew; Singh, Abhyudai

    2017-08-01

    In the stochastic description of biochemical reaction systems, the time evolution of statistical moments for species population counts is described by a linear dynamical system. However, except for some ideal cases (such as zero- and first-order reaction kinetics), the moment dynamics is underdetermined as lower-order moments depend upon higher-order moments. Here, we propose a novel method to find exact lower and upper bounds on stationary moments for a given arbitrary system of biochemical reactions. The method exploits the fact that statistical moments of any positive-valued random variable must satisfy some constraints that are compactly represented through the positive semidefiniteness of moment matrices. Our analysis shows that solving moment equations at steady state in conjunction with constraints on moment matrices provides exact lower and upper bounds on the moments. These results are illustrated by three different examples—the commonly used logistic growth model, stochastic gene expression with auto-regulation and an activator-repressor gene network motif. Interestingly, in all cases the accuracy of the bounds is shown to improve as moment equations are expanded to include higher-order moments. Our results provide avenues for development of approximation methods that provide explicit bounds on moments for nonlinear stochastic systems that are otherwise analytically intractable.

  15. Exact Magnetic Diffusion Solutions for Magnetohydrodynamic Code Verification

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Miller, D S

    In this paper, the authors present several new exact analytic space and time dependent solutions to the problem of magnetic diffusion in R-Z geometry. These problems serve to verify several different elements of an MHD implementation: magnetic diffusion, external circuit time integration, current and voltage energy sources, spatially dependent conductivities, and ohmic heating. The exact solutions are shown in comparison with 2D simulation results from the Ares code.

  16. A hierarchical exact accelerated stochastic simulation algorithm

    NASA Astrophysics Data System (ADS)

    Orendorff, David; Mjolsness, Eric

    2012-12-01

    A new algorithm, "HiER-leap" (hierarchical exact reaction-leaping), is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or divide-and-conquer organization of reaction channels into tightly coupled "blocks" and is thereby able to speed up systems with many reaction channels. Like ER-leap, HiER-leap is based on the use of upper and lower bounds on the reaction propensities to define a rejection sampling algorithm with inexpensive early rejection and acceptance steps. But in HiER-leap, large portions of intra-block sampling may be done in parallel. An accept/reject step is used to synchronize across blocks. This method scales well when many reaction channels are present and has desirable asymptotic properties. The algorithm is exact, parallelizable and achieves a significant speedup over the stochastic simulation algorithm and ER-leap on certain problems. This algorithm offers a potentially important step towards efficient in silico modeling of entire organisms.

  17. Improved treatment of exact exchange in Quantum ESPRESSO

    DOE PAGES

    Barnes, Taylor A.; Kurth, Thorsten; Carrier, Pierre; ...

    2017-01-18

    Here, we present an algorithm and implementation for the parallel computation of exact exchange in Quantum ESPRESSO (QE) that exhibits greatly improved strong scaling. QE is an open-source software package for electronic structure calculations using plane wave density functional theory, and supports the use of local, semi-local, and hybrid DFT functionals. Wider application of hybrid functionals is desirable for the improved simulation of electronic band energy alignments and thermodynamic properties, but the computational complexity of evaluating the exact exchange potential limits the practical application of hybrid functionals to large systems and requires efficient implementations. We demonstrate that existing implementations ofmore » hybrid DFT that utilize a single data structure for both the local and exact exchange regions of the code are significantly limited in the degree of parallelization achievable. We present a band-pair parallelization approach, in which the calculation of exact exchange is parallelized and evaluated independently from the parallelization of the remainder of the calculation, with the wavefunction data being efficiently transformed on-the-fly into a form that is optimal for each part of the calculation. For a 64 water molecule supercell, our new algorithm reduces the overall time to solution by nearly an order of magnitude.« less

  18. Exact Synthesis of Reversible Circuits Using A* Algorithm

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

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

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

    NASA Astrophysics Data System (ADS)

    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].

  20. Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

    PubMed Central

    Simpson, Matthew J.; Sharp, Jesse A.; Morrow, Liam C.; Baker, Ruth E.

    2015-01-01

    Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit. PMID:26407013

  1. Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.

    PubMed

    Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E

    2015-01-01

    Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

  2. On exact solutions for disturbances to the asymptotic suction boundary layer: transformation of Barnes integrals to convolution integrals

    NASA Astrophysics Data System (ADS)

    Russell, John

    2000-11-01

    A modified Orr-Sommerfeld equation that applies to the asymptotic suction boundary layer was reported by Bussmann & Münz in a wartime report dated 1942 and by Hughes & Reid in J.F.M. ( 23, 1965, p715). Fundamental systems of exact solutions of the Orr-Sommerfeld equation for this mean velocity distribution were reported by D. Grohne in an unpublished typescript dated 1950. Exact solutions of the equation of Bussmann, Münz, Hughes, & Reid were reported by P. Baldwin in Mathematika ( 17, 1970, p206). Grohne and Baldwin noticed that these exact solutions may be expressed either as Barnes integrals or as convolution integrals. In a later paper (Phil. Trans. Roy. Soc. A, 399, 1985, p321), Baldwin applied the convolution integrals in the contruction of large-Reynolds number asymptotic approximations that hold uniformly. The present talk discusses the subtleties that arise in the construction of such convolution integrals, including several not reported by Grohne or Baldwin. The aim is to recover the full set of seven solutions (one well balanced, three balanced, and three dominant-recessive) postulated by W.H. Reid in various works on the uniformly valid solutions.

  3. When is quasi-linear theory exact. [particle acceleration

    NASA Technical Reports Server (NTRS)

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

    1975-01-01

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

  4. Exact simulation of polarized light reflectance by particle deposits

    NASA Astrophysics Data System (ADS)

    Ramezan Pour, B.; Mackowski, D. W.

    2015-12-01

    The use of polarimetric light reflection measurements as a means of identifying the physical and chemical characteristics of particulate materials obviously relies on an accurate model of predicting the effects of particle size, shape, concentration, and refractive index on polarized reflection. The research examines two methods for prediction of reflection from plane parallel layers of wavelength—sized particles. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a deposit of spherical particles that are exposed to a plane incident wave. We use a FORTRAN-90 implementation of this solution (the Multiple Sphere T Matrix (MSTM) code), coupled with parallel computational platforms, to directly simulate the reflection from particle layers. The second method examined is based upon the vector radiative transport equation (RTE). Mie theory is used in our RTE model to predict the extinction coefficient, albedo, and scattering phase function of the particles, and the solution of the RTE is obtained from adding—doubling method applied to a plane—parallel configuration. Our results show that the MSTM and RTE predictions of the Mueller matrix elements converge when particle volume fraction in the particle layer decreases below around five percent. At higher volume fractions the RTE can yield results that, depending on the particle size and refractive index, significantly depart from the exact predictions. The particle regimes which lead to dependent scattering effects, and the application of methods to correct the vector RTE for particle interaction, will be discussed.

  5. Exact Solution of Klein-Gordon and Dirac Equations with Snyder-de Sitter Algebra

    NASA Astrophysics Data System (ADS)

    Merad, M.; Hadj Moussa, M.

    2018-01-01

    In this paper, we present the exact solution of the (1+1)-dimensional relativistic Klein-Gordon and Dirac equations with linear vector and scalar potentials in the framework of deformed Snyder-de Sitter model. We introduce some changes of variables, we show that a one-dimensional linear potential for the relativistic system in a space deformed can be equivalent to the trigonometric Rosen-Morse potential in a regular space. In both cases, we determine explicitly the energy eigenvalues and their corresponding eigenfunctions expressed in terms of Romonovski polynomials. The limiting cases are analyzed for α 1 and α 2 → 0 and are compared with those of literature.

  6. Exact evaluation of the causal spectrum and localization properties of electronic states on a scale-free network

    NASA Astrophysics Data System (ADS)

    Xie, Pinchen; Yang, Bingjia; Zhang, Zhongzhi; Andrade, Roberto F. S.

    2018-07-01

    A deterministic network with tree structure is considered, for which the spectrum of its adjacency matrix can be exactly evaluated by a recursive renormalization approach. It amounts to successively increasing number of contributions at any finite step of construction of the tree, resulting in a causal chain. The resulting eigenvalues can be related the full energy spectrum of a nearest-neighbor tight-binding model defined on this structure. Given this association, it turns out that further properties of the eigenvectors can be evaluated, like the degree of quantum localization of the tight-binding eigenstates, expressed by the inverse participation ratio (IPR). It happens that, for the current model, the IPR's are also suitable to be analytically expressed in terms in corresponding eigenvalue chain. The resulting IPR scaling behavior is expressed by the tails of eigenvalue chains as well.

  7. Fast and Exact Continuous Collision Detection with Bernstein Sign Classification

    PubMed Central

    Tang, Min; Tong, Ruofeng; Wang, Zhendong; Manocha, Dinesh

    2014-01-01

    We present fast algorithms to perform accurate CCD queries between triangulated models. Our formulation uses properties of the Bernstein basis and Bézier curves and reduces the problem to evaluating signs of polynomials. We present a geometrically exact CCD algorithm based on the exact geometric computation paradigm to perform reliable Boolean collision queries. Our algorithm is more than an order of magnitude faster than prior exact algorithms. We evaluate its performance for cloth and FEM simulations on CPUs and GPUs, and highlight the benefits. PMID:25568589

  8. Exact traveling wave solutions for system of nonlinear evolution equations.

    PubMed

    Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

    2016-01-01

    In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

  9. Exact Relativistic `Antigravity' Propulsion

    NASA Astrophysics Data System (ADS)

    Felber, Franklin S.

    2006-01-01

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

  10. An exact solution for axial flow in cylindrically symmetric, steady-state detonation in polytropic explosive with an arbitrary rate of decomposition

    NASA Astrophysics Data System (ADS)

    Cowperthwaite, M.

    1994-03-01

    Methods of differential geometry and Bernoulli's equation, written as B=0, are used to develop a new approach for constructing an exact solution for axial flow in a classical, two-dimensional, ZND detonation wave in a polytropic explosive with an arbitrary rate of decomposition. This geometric approach is fundamentally different from the traditional approaches to this axial flow problem formulated by Wood and Kirkwood (WK) and Fickett and Davis (FD), and gives equations for the axial particle velocity (u), the sound speed (c), the pressure (p), and the density (ρ), that are expressed in terms of the detonation velocity (D), the extent of decomposition (λ), the polytropic index (K), and two nonideal parameters ɛ3 and ɛ1, and reduce to the equations for steady-state, one-dimensional detonation as ɛ3 and ɛ1 approach zero. In contrast to the FD approach, the equations for u and c are obtained from first integrals of a tangent vector à on (u,c,λ) space, and the invariant condition, ÃB=aB=0, bypasses the FD eigenvalue problem by defining ɛ3 in terms of the detonation velocity deficit D/D∞ and K. In contrast to the WK approach, the equations for p and ρ are obtained from equations expressing the conservation of axial momentum and energy. Because the equations for these flow variables are derived without using the conservation of mass, the axial radial particle velocity gradient (war) associated with the flow can be obtained from the continuity equation without making approximations. The relationship between ɛ1 and ɛ3 that closes the solution is obtained from equations expressing constraints imposed on the axial flow at the shock front by the axial and radial momentum equations, the curved shock and the decomposition rate law, and a particular solution is constructed from the ɛ1-ɛ3 relationship determined by a prescribed rate law and value of K. Properties of particular solutions are presented to provide a better understanding of two-dimensional detonation

  11. F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

    PubMed Central

    Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

    2014-01-01

    F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327

  12. F-expansion method and new exact solutions of the Schrödinger-KdV equation.

    PubMed

    Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

    2014-01-01

    F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

  13. Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice.

    PubMed

    Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

    2016-10-10

    In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

  14. Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

    PubMed Central

    Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

    2016-01-01

    In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435

  15. Exact ground states and topological order in interacting Kitaev/Majorana chains

    NASA Astrophysics Data System (ADS)

    Katsura, Hosho; Schuricht, Dirk; Takahashi, Masahiro

    2015-09-01

    We study a system of interacting spinless fermions in one dimension that, in the absence of interactions, reduces to the Kitaev chain [Kitaev, Phys. Usp. 44, 131 (2001), 10.1070/1063-7869/44/10S/S29]. In the noninteracting case, a signal of topological order appears as zero-energy modes localized near the edges. We show that the exact ground states can be obtained analytically even in the presence of nearest-neighbor repulsive interactions when the on-site (chemical) potential is tuned to a particular function of the other parameters. As with the noninteracting case, the obtained ground states are twofold degenerate and differ in fermionic parity. We prove the uniqueness of the obtained ground states and show that they can be continuously deformed to the ground states of the noninteracting Kitaev chain without gap closing. We also demonstrate explicitly that there exists a set of operators each of which maps one of the ground states to the other with opposite fermionic parity. These operators can be thought of as an interacting generalization of Majorana edge zero modes.

  16. Exact results of 1D traffic cellular automata: The low-density behavior of the Fukui-Ishibashi model

    NASA Astrophysics Data System (ADS)

    Salcido, Alejandro; Hernández-Zapata, Ernesto; Carreón-Sierra, Susana

    2018-03-01

    The maximum entropy states of the cellular automata models for traffic flow in a single-lane with no anticipation are presented and discussed. The exact analytical solutions for the low-density behavior of the stochastic Fukui-Ishibashi traffic model were obtained and compared with computer simulations of the model. An excellent agreement was found.

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

    NASA Astrophysics Data System (ADS)

    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.

  18. Exact solutions for the collaborative pickup and delivery problem.

    PubMed

    Gansterer, Margaretha; Hartl, Richard F; Salzmann, Philipp E H

    2018-01-01

    In this study we investigate the decision problem of a central authority in pickup and delivery carrier collaborations. Customer requests are to be redistributed among participants, such that the total cost is minimized. We formulate the problem as multi-depot traveling salesman problem with pickups and deliveries. We apply three well-established exact solution approaches and compare their performance in terms of computational time. To avoid unrealistic solutions with unevenly distributed workload, we extend the problem by introducing minimum workload constraints. Our computational results show that, while for the original problem Benders decomposition is the method of choice, for the newly formulated problem this method is clearly dominated by the proposed column generation approach. The obtained results can be used as benchmarks for decentralized mechanisms in collaborative pickup and delivery problems.

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

    NASA Astrophysics Data System (ADS)

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

    2018-03-01

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

  20. Exact one-sided confidence limits for the difference between two correlated proportions.

    PubMed

    Lloyd, Chris J; Moldovan, Max V

    2007-08-15

    We construct exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well-established optimality theory of Buehler. Starting with five different approximate lower and upper limits, we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size. Exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use.

  1. Familial Sinistrals Avoid Exact Numbers

    PubMed Central

    Sauerland, Uli; Gotzner, Nicole

    2013-01-01

    We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals – individuals who are left-handed themselves or have a left-handed close blood-relative – with those of pure familial dextrals – right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd’s (1988, Language in Society) index of the roundness of a number and report that familial sinistrals’ responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere. PMID:23544052

  2. Familial sinistrals avoid exact numbers.

    PubMed

    Sauerland, Uli; Gotzner, Nicole

    2013-01-01

    We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals--individuals who are left-handed themselves or have a left-handed close blood-relative--with those of pure familial dextrals--right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd's (1988, Language in Society) index of the roundness of a number and report that familial sinistrals' responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere.

  3. A new class of exact solutions of the Klein-Gordon equation of a charged particle interacting with an electromagnetic plane wave in a medium

    NASA Astrophysics Data System (ADS)

    Varró, Sándor

    2014-01-01

    Exact solutions are presented of the Klein-Gordon equation of a charged particle moving in a transverse monochromatic plasmon wave of arbitrary high amplitude, which propagates in an underdense plasma. These solutions are expressed in terms of Ince polynomials, forming a doubly infinite set, parametrized by discrete momentum components of the charged particle’s de Broglie wave along the polarization vector and along the propagation direction of the plasmon radiation. The envelope of the exact wavefunctions describes a high-contrast periodic structure of the particle density on the plasma length scale, which may have relevance in novel particle acceleration mechanisms.

  4. Bilinear, trilinear forms, and exact solution of certain fourth order integrable difference equations

    NASA Astrophysics Data System (ADS)

    Sahadevan, R.; Rajakumar, S.

    2008-03-01

    A systematic investigation of finding bilinear or trilinear representations of fourth order autonomous ordinary difference equation, x(n +4)=F(x(n),x(n+1),x(n+2),x(n+3)) or xn +4=F(xn,xn +1,xn +2,xn +3), is made. As an illustration, we consider fourth order symplectic integrable difference equations reported by [Capel and Sahadevan, Physica A 289, 86 (2001)] and derived their bilinear or trilinear forms. Also, it is shown that the obtained bilinear representations admit exact solution of rational form.

  5. Exact master equation and non-Markovian decoherence dynamics of Majorana zero modes under gate-induced charge fluctuations

    NASA Astrophysics Data System (ADS)

    Lai, Hon-Lam; Yang, Pei-Yun; Huang, Yu-Wei; Zhang, Wei-Min

    2018-02-01

    In this paper, we use the exact master equation approach to investigate the decoherence dynamics of Majorana zero modes in the Kitaev model, a 1D p -wave spinless topological superconducting chain (TSC) that is disturbed by gate-induced charge fluctuations. The exact master equation is derived by extending Feynman-Vernon influence functional technique to fermionic open systems involving pairing excitations. We obtain the exact master equation for the zero-energy Bogoliubov quasiparticle (bogoliubon) in the TSC, and then transfer it into the master equation for the Majorana zero modes. Within this exact master equation formalism, we can describe in detail the non-Markovian decoherence dynamics of the zero-energy bogoliubon as well as Majorana zero modes under local perturbations. We find that at zero temperature, local charge fluctuations induce level broadening to one of the Majorana zero modes but there is an isolated peak (localized bound state) located at zero energy that partially protects the Majorana zero mode from decoherence. At finite temperatures, the zero-energy localized bound state does not precisely exist, but the coherence of the Majorana zero mode can still be partially but weakly protected, due to the sharp dip of the spectral density near the zero frequency. The decoherence will be enhanced as one increases the charge fluctuations and/or the temperature of the gate.

  6. Accuracy of expressions for the fill factor of a solar cell in terms of open-circuit voltage and ideality factor

    NASA Astrophysics Data System (ADS)

    Leilaeioun, Mehdi; Holman, Zachary C.

    2016-09-01

    An approximate expression proposed by Green predicts the maximum obtainable fill factor (FF) of a solar cell from its open-circuit voltage (Voc). The expression was originally suggested for silicon solar cells that behave according to a single-diode model and, in addition to Voc, it requires an ideality factor as input. It is now commonly applied to silicon cells by assuming a unity ideality factor—even when the cells are not in low injection—as well as to non-silicon cells. Here, we evaluate the accuracy of the expression in several cases. In particular, we calculate the recombination-limited FF and Voc of hypothetical silicon solar cells from simulated lifetime curves, and compare the exact FF to that obtained with the approximate expression using assumed ideality factors. Considering cells with a variety of recombination mechanisms, wafer doping densities, and photogenerated current densities reveals the range of conditions under which the approximate expression can safely be used. We find that the expression is unable to predict FF generally: For a typical silicon solar cell under one-sun illumination, the error is approximately 6% absolute with an assumed ideality factor of 1. Use of the expression should thus be restricted to cells under very low or very high injection.

  7. Exact semiclassical expansions for one-dimensional quantum oscillators

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Delabaere, E.; Dillinger, H.; Pham, F.

    1997-12-01

    A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also the case when there are double turning points, are illustrated on various examples, and applied to the study of bound state or resonance spectra. In the case of simple oscillators, it is thus shown that the Rayleigh{endash}Schr{umlt o}dinger series is Borelmore » resummable, yielding the exact energy levels. In the case of the symmetrical anharmonic oscillator, one gets a simple and rigorous justification of the Zinn-Justin quantization condition, and of its solution in terms of {open_quotes}multi-instanton expansions.{close_quotes} {copyright} {ital 1997 American Institute of Physics.}« less

  8. Exact states in waveguides with periodically modulated nonlinearity

    NASA Astrophysics Data System (ADS)

    Ding, E.; Chan, H. N.; Chow, K. W.; Nakkeeran, K.; Malomed, B. A.

    2017-09-01

    We introduce a one-dimensional model based on the nonlinear Schrödinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi {dn} function, with three free parameters including the period, amplitude, and internal form-factor. An exact periodic solution is found for each set of parameters and, which is more important for physical realizations, we solve the inverse problem and predict the period and amplitude of the modulation that yields a particular exact spatially periodic state. A numerical stability analysis demonstrates that the periodic states become modulationally unstable for large periods, and regain stability in the limit of an infinite period, which corresponds to a bright soliton pinned to a localized nonlinearity-modulation pattern. The exact dark-bright soliton complex in a coupled system with a localized modulation structure is also briefly considered. The system can be realized in planar optical waveguides and cigar-shaped atomic Bose-Einstein condensates.

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

    NASA Astrophysics Data System (ADS)

    Adem, Abdullahi Rashid; Moawad, Salah M.

    2018-05-01

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

  10. Mixed Poisson distributions in exact solutions of stochastic autoregulation models.

    PubMed

    Iyer-Biswas, Srividya; Jayaprakash, C

    2014-11-01

    In this paper we study the interplay between stochastic gene expression and system design using simple stochastic models of autoactivation and autoinhibition. Using the Poisson representation, a technique whose particular usefulness in the context of nonlinear gene regulation models we elucidate, we find exact results for these feedback models in the steady state. Further, we exploit this representation to analyze the parameter spaces of each model, determine which dimensionless combinations of rates are the shape determinants for each distribution, and thus demarcate where in the parameter space qualitatively different behaviors arise. These behaviors include power-law-tailed distributions, bimodal distributions, and sub-Poisson distributions. We also show how these distribution shapes change when the strength of the feedback is tuned. Using our results, we reexamine how well the autoinhibition and autoactivation models serve their conventionally assumed roles as paradigms for noise suppression and noise exploitation, respectively.

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

    PubMed

    Tong, Liping; Thompson, Elizabeth

    2008-01-01

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

  12. Multilocus Lod Scores in Large Pedigrees: Combination of Exact and Approximate Calculations

    PubMed Central

    Tong, Liping; Thompson, Elizabeth

    2007-01-01

    To detect the positions of disease loci, lod scores are calculated at multiple chromosomal positions given trait and marker data on members of pedigrees. Exact lod score calculations are often impossible when the size of the pedigree and the number of markers are both large. In this case, a Markov Chain Monte Carlo (MCMC) approach provides an approximation. However, to provide accurate results, mixing performance is always a key issue in these MCMC methods. In this paper, we propose two methods to improve MCMC sampling and hence obtain more accurate lod score estimates in shorter computation time. The first improvement generalizes the block-Gibbs meiosis (M) sampler to multiple meiosis (MM) sampler in which multiple meioses are updated jointly, across all loci. The second one divides the computations on a large pedigree into several parts by conditioning on the haplotypes of some ‘key’ individuals. We perform exact calculations for the descendant parts where more data are often available, and combine this information with sampling of the hidden variables in the ancestral parts. Our approaches are expected to be most useful for data on a large pedigree with a lot of missing data. PMID:17934317

  13. Penetrable square-well fluids: exact results in one dimension.

    PubMed

    Santos, Andrés; Fantoni, Riccardo; Giacometti, Achille

    2008-05-01

    We introduce a model of attractive penetrable spheres by adding a short-range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point. The model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions. We derive the exact coefficients of a low-density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion. These exact results are used as a benchmark to test the reliability of approximate theories (Percus-Yevick and hypernetted chain). Notwithstanding the lack of an exact solution for arbitrary densities, our results are expected to be rather precise within a wide range of temperatures and densities. A detailed analysis of some limiting cases is carried out. In particular, we provide a complete solution of the sticky penetrable-sphere model in one dimension up to the same order in density. The issue of Ruelle's thermodynamics stability is analyzed and the region of a well-defined thermodynamic limit is identified.

  14. Dirac delta representation by exact parametric equations.. Application to impulsive vibration systems

    NASA Astrophysics Data System (ADS)

    Chicurel-Uziel, Enrique

    2007-08-01

    A pair of closed parametric equations are proposed to represent the Heaviside unit step function. Differentiating the step equations results in two additional parametric equations, that are also hereby proposed, to represent the Dirac delta function. These equations are expressed in algebraic terms and are handled by means of elementary algebra and elementary calculus. The proposed delta representation complies exactly with the values of the definition. It complies also with the sifting property and the requisite unit area and its Laplace transform coincides with the most general form given in the tables. Furthermore, it leads to a very simple method of solution of impulsive vibrating systems either linear or belonging to a large class of nonlinear problems. Two example solutions are presented.

  15. Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of nonlinear PDEs.

    PubMed

    Akbar, M Ali; Ali, Norhashidah Hj Mohd; Mohyud-Din, Syed Tauseef

    2013-01-01

    The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.

  16. COX-2 expression in papillary thyroid carcinoma (PTC) in cytological material obtained by fine needle aspiration biopsy (FNAB)

    PubMed Central

    2011-01-01

    Background COX-2 is an enzyme isoform that catalyses the formation of prostanoids from arachidonic acid. An increased COX-2 gene expression is believed to participate in carcinogenesis. Recent studies have shown that COX-2 up-regulation is associated with the development of numerous neoplasms, including skin, colorectal, breast, lung, stomach, pancreas and liver cancers. COX-2 products stimulate endothelial cell proliferation and their overexpression has been demonstrated to be involved in the mechanism of decreased resistance to apoptosis. Suppressed angiogenesis was found in experimental animal studies as a consequence of null mutation of COX-2 gene in mice. Despite the role of COX-2 expression remains a subject of numerous studies, its participation in carcinogenesis or the thyroid cancer progression remains unclear. Methods Twenty three (23) patients with cytological diagnosis of PTC were evaluated. After FNAB examination, the needle was washed out with a lysis buffer and the obtained material was used for COX-2 expression estimation. Total RNA was isolated (RNeasy Micro Kit), and RT reactions were performed. β-actin was used as endogenous control. Relative COX-2 expression was assessed in real-time PCR reactions by an ABI PRISM 7500 Sequence Detection System, using the ΔΔCT method. Results COX-2 gene expression was higher in patients with PTC, when compared to specimens from patients with non-toxic nodular goitre (NTG). Conclusions The preliminary results may indicate COX-2 role in thyroid cancer pathogenesis, however the observed variability in results among particular subjects requires additional clinical data and tumor progression analysis. PMID:21214962

  17. COX-2 expression in papillary thyroid carcinoma (PTC) in cytological material obtained by fine needle aspiration biopsy (FNAB).

    PubMed

    Krawczyk-Rusiecka, Kinga; Wojciechowska-Durczyńska, Katarzyna; Cyniak-Magierska, Anna; Adamczewski, Zbigniew; Gałecka, Elżbieta; Lewiński, Andrzej

    2011-01-10

    COX-2 is an enzyme isoform that catalyses the formation of prostanoids from arachidonic acid. An increased COX-2 gene expression is believed to participate in carcinogenesis. Recent studies have shown that COX-2 up-regulation is associated with the development of numerous neoplasms, including skin, colorectal, breast, lung, stomach, pancreas and liver cancers. COX-2 products stimulate endothelial cell proliferation and their overexpression has been demonstrated to be involved in the mechanism of decreased resistance to apoptosis. Suppressed angiogenesis was found in experimental animal studies as a consequence of null mutation of COX-2 gene in mice. Despite the role of COX-2 expression remains a subject of numerous studies, its participation in carcinogenesis or the thyroid cancer progression remains unclear. Twenty three (23) patients with cytological diagnosis of PTC were evaluated. After FNAB examination, the needle was washed out with a lysis buffer and the obtained material was used for COX-2 expression estimation. Total RNA was isolated (RNeasy Micro Kit), and RT reactions were performed. β-actin was used as endogenous control. Relative COX-2 expression was assessed in real-time PCR reactions by an ABI PRISM 7500 Sequence Detection System, using the ΔΔCT method. COX-2 gene expression was higher in patients with PTC, when compared to specimens from patients with non-toxic nodular goitre (NTG). The preliminary results may indicate COX-2 role in thyroid cancer pathogenesis, however the observed variability in results among particular subjects requires additional clinical data and tumor progression analysis.

  18. Computational tools for exact conditional logistic regression.

    PubMed

    Corcoran, C; Mehta, C; Patel, N; Senchaudhuri, P

    Logistic regression analyses are often challenged by the inability of unconditional likelihood-based approximations to yield consistent, valid estimates and p-values for model parameters. This can be due to sparseness or separability in the data. Conditional logistic regression, though useful in such situations, can also be computationally unfeasible when the sample size or number of explanatory covariates is large. We review recent developments that allow efficient approximate conditional inference, including Monte Carlo sampling and saddlepoint approximations. We demonstrate through real examples that these methods enable the analysis of significantly larger and more complex data sets. We find in this investigation that for these moderately large data sets Monte Carlo seems a better alternative, as it provides unbiased estimates of the exact results and can be executed in less CPU time than can the single saddlepoint approximation. Moreover, the double saddlepoint approximation, while computationally the easiest to obtain, offers little practical advantage. It produces unreliable results and cannot be computed when a maximum likelihood solution does not exist. Copyright 2001 John Wiley & Sons, Ltd.

  19. Pressure in an exactly solvable model of active fluid

    NASA Astrophysics Data System (ADS)

    Marini Bettolo Marconi, Umberto; Maggi, Claudio; Paoluzzi, Matteo

    2017-07-01

    We consider the pressure in the steady-state regime of three stochastic models characterized by self-propulsion and persistent motion and widely employed to describe the behavior of active particles, namely, the Active Brownian particle (ABP) model, the Gaussian colored noise (GCN) model, and the unified colored noise approximation (UCNA) model. Whereas in the limit of short but finite persistence time, the pressure in the UCNA model can be obtained by different methods which have an analog in equilibrium systems, in the remaining two models only the virial route is, in general, possible. According to this method, notwithstanding each model obeys its own specific microscopic law of evolution, the pressure displays a certain universal behavior. For generic interparticle and confining potentials, we derive a formula which establishes a correspondence between the GCN and the UCNA pressures. In order to provide explicit formulas and examples, we specialize the discussion to the case of an assembly of elastic dumbbells confined to a parabolic well. By employing the UCNA we find that, for this model, the pressure determined by the thermodynamic method coincides with the pressures obtained by the virial and mechanical methods. The three methods when applied to the GCN give a pressure identical to that obtained via the UCNA. Finally, we find that the ABP virial pressure exactly agrees with the UCNA and GCN results.

  20. Exact and heuristic algorithms for Space Information Flow.

    PubMed

    Uwitonze, Alfred; Huang, Jiaqing; Ye, Yuanqing; Cheng, Wenqing; Li, Zongpeng

    2018-01-01

    Space Information Flow (SIF) is a new promising research area that studies network coding in geometric space, such as Euclidean space. The design of algorithms that compute the optimal SIF solutions remains one of the key open problems in SIF. This work proposes the first exact SIF algorithm and a heuristic SIF algorithm that compute min-cost multicast network coding for N (N ≥ 3) given terminal nodes in 2-D Euclidean space. Furthermore, we find that the Butterfly network in Euclidean space is the second example besides the Pentagram network where SIF is strictly better than Euclidean Steiner minimal tree. The exact algorithm design is based on two key techniques: Delaunay triangulation and linear programming. Delaunay triangulation technique helps to find practically good candidate relay nodes, after which a min-cost multicast linear programming model is solved over the terminal nodes and the candidate relay nodes, to compute the optimal multicast network topology, including the optimal relay nodes selected by linear programming from all the candidate relay nodes and the flow rates on the connection links. The heuristic algorithm design is also based on Delaunay triangulation and linear programming techniques. The exact algorithm can achieve the optimal SIF solution with an exponential computational complexity, while the heuristic algorithm can achieve the sub-optimal SIF solution with a polynomial computational complexity. We prove the correctness of the exact SIF algorithm. The simulation results show the effectiveness of the heuristic SIF algorithm.

  1. Exactly energy conserving semi-implicit particle in cell formulation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-06-01

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

  3. The sagitta and lens thickness: the exact solution and a matrix approximation for lenses with toric, spherical, and cylindrical surfaces.

    PubMed

    Harris, W F

    1989-03-01

    The exact equation for sagitta of spherical surfaces is generalized to toric surfaces which include spherical and cylindrical surfaces as special cases. Lens thickness, therefore, can be calculated accurately anywhere on a lens even in cases of extreme spherical and cylindrical powers and large diameters. The sagittae of tire- and barrel-form toric surfaces differ off the principal meridians, as is shown by a numerical example. The same holds for pulley- and capstan-form toric surfaces. A general expression is given for thickness at an arbitrary point on a toric lens. Approximate expressions are derived and re-expressed in terms of matrices. The matrix provides an elegant means of generalizing equations for spherical surfaces and lenses to toric surfaces and lenses.

  4. Exact nonparaxial beams of the scalar Helmholtz equation.

    PubMed

    Rodríguez-Morales, Gustavo; Chávez-Cerda, Sabino

    2004-03-01

    It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For what is believed to be the first time, their beam behavior is investigated and their corresponding parameters are defined. Using the fact that the beam width of the family of paraxial Gaussian beams is described by a hyperbola, we formally establish the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams. These results are also helpful for investigating exact vector nonparaxial beams.

  5. Exact solutions and phenomenological constraints from massive scalars in a gravity's rainbow spacetime

    NASA Astrophysics Data System (ADS)

    Bezerra, V. B.; Christiansen, H. R.; Cunha, M. S.; Muniz, C. R.

    2017-07-01

    We obtain the exact (confluent Heun) solutions to the massive scalar field in a gravity's rainbow Schwarzschild metric. With these solutions at hand, we study the Hawking radiation resulting from the tunneling rate through the event horizon. We show that the emission spectrum obeys nonextensive statistics and is halted when a certain mass remnant is reached. Next, we infer constraints on the rainbow parameters from recent LHC particle physics experiments and Hubble STIS astrophysics measurements. Finally, we study the low frequency limit in order to find the modified energy spectrum around the source.

  6. Exact time-dependent nonlinear dispersive wave solutions in compressible magnetized plasmas exhibiting collapse.

    PubMed

    Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans

    2011-04-08

    Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.

  7. Analytical solution of the optimal three dimensional reentry problem using Chapman's exact equations

    NASA Technical Reports Server (NTRS)

    Vinh, N. X.; Busemann, A.; Culp, R. D.

    1974-01-01

    This paper presents the general solution for the optimal three dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere. A set of dimensionless variables is introduced, and the resulting exact equations of motion have the distinctive advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a general lift-drag polar is used to define the aerodynamic control. Hence, the results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary polar and entering any planetary atmosphere.

  8. Graph-associated entanglement cost of a multipartite state in exact and finite-block-length approximate constructions

    NASA Astrophysics Data System (ADS)

    Yamasaki, Hayata; Soeda, Akihito; Murao, Mio

    2017-09-01

    We introduce and analyze graph-associated entanglement cost, a generalization of the entanglement cost of quantum states to multipartite settings. We identify a necessary and sufficient condition for any multipartite entangled state to be constructible when quantum communication between the multiple parties is restricted to a quantum network represented by a tree. The condition for exact state construction is expressed in terms of the Schmidt ranks of the state defined with respect to edges of the tree. We also study approximate state construction and provide a second-order asymptotic analysis.

  9. Exact analytical solution of a classical Josephson tunnel junction problem

    NASA Astrophysics Data System (ADS)

    Kuplevakhsky, S. V.; Glukhov, A. M.

    2010-10-01

    We give an exact and complete analytical solution of the classical problem of a Josephson tunnel junction of arbitrary length W ɛ(0,∞) in the presence of external magnetic fields and transport currents. Contrary to a wide-spread belief, the exact analytical solution unambiguously proves that there is no qualitative difference between so-called "small" (W≪1) and "large" junctions (W≫1). Another unexpected physical implication of the exact analytical solution is the existence (in the current-carrying state) of unquantized Josephson vortices carrying fractional flux and located near one of the edges of the junction. We also refine the mathematical definition of critical transport current.

  10. Exact zeros of entanglement for arbitrary rank-two mixtures derived from a geometric view of the zero polytope

    NASA Astrophysics Data System (ADS)

    Osterloh, Andreas

    2016-12-01

    Here I present a method for how intersections of a certain density matrix of rank 2 with the zero polytope can be calculated exactly. This is a purely geometrical procedure which thereby is applicable to obtaining the zeros of SL- and SU-invariant entanglement measures of arbitrary polynomial degree. I explain this method in detail for a recently unsolved problem. In particular, I show how a three-dimensional view, namely, in terms of the Bloch-sphere analogy, solves this problem immediately. To this end, I determine the zero polytope of the three-tangle, which is an exact result up to computer accuracy, and calculate upper bounds to its convex roof which are below the linearized upper bound. The zeros of the three-tangle (in this case) induced by the zero polytope (zero simplex) are exact values. I apply this procedure to a superposition of the four-qubit Greenberger-Horne-Zeilinger and W state. It can, however, be applied to every case one has under consideration, including an arbitrary polynomial convex-roof measure of entanglement and for arbitrary local dimension.

  11. NEMA count-rate evaluation of the first and second generation of the Ecat Exact and Ecat Exact HR family of scanners

    NASA Astrophysics Data System (ADS)

    Eriksson, L.; Wienhard, K.; Eriksson, M.; Casey, M. E.; Knoess, C.; Bruckbauer, T.; Hamill, J.; Mulnix, T.; Vollmar, S.; Bendriem, B.; Heiss, W. D.; Nutt, R.

    2002-06-01

    The first and second generation of the Exact and Exact HR family of scanners has been evaluated in terms of noise equivalent count rate (NEC) and count-rate capabilities. The new National Electrical Manufacturers Association standard was used for the evaluation. In spite of improved electronics and improved count-rate capabilities, the peak NEC was found to be fairly constant between the generations. The results are discussed in terms of the different electronic solutions for the two generations and its implications on system dead time and NEC count-rate capability.

  12. Phase Transition to Exact Susy

    NASA Astrophysics Data System (ADS)

    Clavelli, L.

    2007-04-01

    The anthropic principle is based on the observation that, within narrow bounds, the laws of physics are such as to have allowed the evolution of life. The string theoretic approach to understanding this observation is based on the expectation that the effective potential has an enormous number of local minima with different particle masses and perhaps totally different fundamental couplings and space time topology. The vast majority of these alternative universes are totally inhospitable to life, having, for example, vacuum energies near the natural (Planck) scale. The statistics, however, are assumed to be such that a few of these local minima (and not more) have a low enough vacuum energy and suitable other properties to support life. In the inflationary era, the "multiverse" made successive transitions between the available minima until arriving at our current state of low vacuum energy. String theory, however, also suggests that the absolute minimum of the effective potential is exactly supersymmetric. Questions then arise as to why the inflationary era did not end by a transition to one of these, when will the universe make the phase transition to the exactly supersymmetric ground state, and what will be the properties of this final state.

  13. Exact axially symmetric galactic dynamos

    NASA Astrophysics Data System (ADS)

    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.

  14. Towards an exact correlated orbital theory for electrons

    NASA Astrophysics Data System (ADS)

    Bartlett, Rodney J.

    2009-12-01

    The formal and computational attraction of effective one-particle theories like Hartree-Fock and density functional theory raise the question of how far such approaches can be taken to offer exact results for selected properties of electrons in atoms, molecules, and solids. Some properties can be exactly described within an effective one-particle theory, like principal ionization potentials and electron affinities. This fact can be used to develop equations for a correlated orbital theory (COT) that guarantees a correct one-particle energy spectrum. They are built upon a coupled-cluster based frequency independent self-energy operator presented here, which distinguishes the approach from Dyson theory. The COT also offers an alternative to Kohn-Sham density functional theory (DFT), whose objective is to represent the electronic density exactly as a single determinant, while paying less attention to the energy spectrum. For any estimate of two-electron terms COT offers a litmus test of its accuracy for principal Ip's and Ea's. This feature for approximating the COT equations is illustrated numerically.

  15. Applying dynamic Bayesian networks to perturbed gene expression data.

    PubMed

    Dojer, Norbert; Gambin, Anna; Mizera, Andrzej; Wilczyński, Bartek; Tiuryn, Jerzy

    2006-05-08

    A central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayesian networks appear attractive in the field of inferring gene interactions structure from microarray experiments data. However, the basic formalism has some disadvantages, e.g. it is sometimes hard to distinguish between the origin and the target of an interaction. Two kinds of microarray experiments yield data particularly rich in information regarding the direction of interactions: time series and perturbation experiments. In order to correctly handle them, the basic formalism must be modified. For example, dynamic Bayesian networks (DBN) apply to time series microarray data. To our knowledge the DBN technique has not been applied in the context of perturbation experiments. We extend the framework of dynamic Bayesian networks in order to incorporate perturbations. Moreover, an exact algorithm for inferring an optimal network is proposed and a discretization method specialized for time series data from perturbation experiments is introduced. We apply our procedure to realistic simulations data. The results are compared with those obtained by standard DBN learning techniques. Moreover, the advantages of using exact learning algorithm instead of heuristic methods are analyzed. We show that the quality of inferred networks dramatically improves when using data from perturbation experiments. We also conclude that the exact algorithm should be used when it is possible, i.e. when considered set of genes is small enough.

  16. TVT-Exact and midurethral sling (SLING-IUFT) operative procedures: a randomized study.

    PubMed

    Aniuliene, Rosita; Aniulis, Povilas; Skaudickas, Darijus

    2015-01-01

    The aim of the study is to compare results, effectiveness and complications of TVT exact and midurethral sling (SLING-IUFT) operations in the treatment of female stress urinary incontinence (SUI). A single center nonblind, randomized study of women with SUI who were randomized to TVT-Exact and SLING-IUFT was performed by one surgeon from April 2009 to April 2011. SUI was diagnosed on coughing and Valsalva test and urodynamics (cystometry and uroflowmetry) were assessed before operation and 1 year after surgery. This was a prospective randomized study. The follow up period was 12 months. 76 patients were operated using the TVT-Exact operation and 78 patients - using the SLING-IUFT operation. There was no statistically significant differences between groups for BMI, parity, menopausal status and prolapsed stage (no patients had cystocele greater than stage II). Mean operative time was significantly shorter in the SLING-IUFT group (19 ± 5.6 min.) compared with the TVT-Exact group (27 ± 7.1 min.). There were statistically significant differences in the effectiveness of both procedures: TVT-Exact - at 94.5% and SLING-IUFT - at 61.2% after one year. Hospital stay was statistically significantly shorter in the SLING-IUFT group (1. 2 ± 0.5 days) compared with the TVT-Exact group (3.5 ± 1.5 days). Statistically significantly fewer complications occurred in the SLING-IUFT group. the TVT-Exact and SLING-IUFT operations are both effective for surgical treatment of female stress urinary incontinence. The SLING-IUFT involved a shorter operation time and lower complications rate., the TVT-Exact procedure had statistically significantly more complications than the SLING-IUFT operation, but a higher effectiveness.

  17. Explicit expressions of quantum mechanical rotation operators for spins 1 to 2

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kocakoç, Mehpeyker, E-mail: mkocakoc@cu.edu.tr; Tapramaz, Recep, E-mail: recept@omu.edu.tr

    2016-03-25

    Quantum mechanical rotation operators are the subject of quantum mechanics, mathematics and pulsed magnetic resonance spectroscopies, namely NMR, EPR and ENDOR. They are also necessary for spin based quantum information systems. The rotation operators of spin 1/2 are well known and can be found in related textbooks. But rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schrödinger equation, or by evaluating Wigner-d formula or by evaluating recently established expressions in polynomial forms discussed in the text. In this work, explicit symbolic expressions of x, y andmore » z components of rotation operators for spins 1 to 2 are worked out by evaluating series expansion of exponential operator for each element of operators and utilizing linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators. The operators of spins greater than 2 are under study and will be published in a separate paper.« less

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

    PubMed

    Hesselmann, Andreas; Görling, Andreas

    2011-01-21

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

  19. Exact geodesic distances in FLRW spacetimes

    NASA Astrophysics Data System (ADS)

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

    2017-11-01

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

  20. Climatology and archaeoastronomy - Environmental anthropology, a multidisciplinary exact science

    NASA Astrophysics Data System (ADS)

    Gregori, G. P.; Gregori, L. G.

    2003-04-01

    During the last few tens thousand years, a dominating unprecedented "virus" - the human kind - controlled climate. It widespread over the Earth's surface and implied both short- and long-range effects in space and time. Phenomena can be expressively investigated like cycles of climate and civilisation, by which the entire human history has to be reinterpreted in terms of environmental anthropology. This is just much like every classical and conventional exact science, based on experimental quantitative observations. Archaeoastronomy is the "instrumental" tool for exploiting such measurements (much like a particle accelerator is the instrument for high-energy subnuclear physics, or a telescope for astrophysics). Its comparative wealth of information is even much larger. The anthropic factor is one leader in climate control, and such understanding helps in facing present disquieting challenges of society. Deontologically, such multidisciplinary studies are a "must" for every savant in order to avoid (i) misunderstanding that can lead to false or non-sense concerns, and (ii) correct underestimating of the real severe challenges and hazards.

  1. Full self-consistency versus quasiparticle self-consistency in diagrammatic approaches: Exactly solvable two-site Hubbard model

    DOE PAGES

    Kutepov, A. L.

    2015-07-22

    Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ₁ from the first-order perturbation theory, and the exact vertex Γ E). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. Results obtained with the exact vertex are directly related to the present open question—which approximation is more advantageous for future implementations, GW + DMFT or QPGW +more » DMFT. It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on Perturbation Theory systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.« less

  2. The extended Einstein-Maxwell-aether-axion model: Exact solutions for axionically controlled pp-wave aether modes

    NASA Astrophysics Data System (ADS)

    Balakin, Alexander B.

    2018-03-01

    The extended Einstein-Maxwell-aether-axion model describes internal interactions inside the system, which contains gravitational, electromagnetic fields, the dynamic unit vector field describing the velocity of an aether, and the pseudoscalar field associated with the axionic dark matter. The specific feature of this model is that the axion field controls the dynamics of the aether through the guiding functions incorporated into Jacobson’s constitutive tensor. Depending on the state of the axion field, these guiding functions can control and switch on or switch off the influence of acceleration, shear, vorticity and expansion of the aether flow on the state of physical system as a whole. We obtain new exact solutions, which possess the pp-wave symmetry, and indicate them by the term pp-wave aether modes in contrast to the pure pp-waves, which cannot propagate in this field conglomerate. These exact solutions describe a specific dynamic state of the pseudoscalar field, which corresponds to one of the minima of the axion potential and switches off the influence of shear and expansion of the aether flow; the model does not impose restrictions on Jacobson’s coupling constants and on the axion mass. Properties of these new exact solutions are discussed.

  3. Full self-consistency versus quasiparticle self-consistency in diagrammatic approaches: exactly solvable two-site Hubbard model.

    PubMed

    Kutepov, A L

    2015-08-12

    Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ1 from the first-order perturbation theory, and the exact vertex Γ(E)). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. The results obtained with the exact vertex are directly related to the present open question-which approximation is more advantageous for future implementations, GW + DMFT or QPGW + DMFT. It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on perturbation theory (PT) systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.

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

    NASA Astrophysics Data System (ADS)

    Ristorcelli, J. R.

    2017-02-01

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

  5. Exact analytical solution to a transient conjugate heat-transfer problem

    NASA Technical Reports Server (NTRS)

    Sucec, J.

    1973-01-01

    An exact analytical solution is found for laminar, constant-property, slug flow over a thin plate which is also convectively cooled from below. The solution is found by means of two successive Laplace transformations when a transient in the plate and the fluid is initiated by a step change in the fluid inlet temperature. The exact solution yields the transient fluid temperature, surface heat flux, and surface temperature distributions. The results of the exact transient solution for the surface heat flux are compared to the quasi-steady values, and a criterion for the validity of the quasi-steady results is found. Also the effect of the plate coupling parameter on the surface heat flux are investigated.

  6. Myometrial contractility influences oxytocin receptor (OXTR) expression in term trophoblast cells obtained from the maternal surface of the human placenta.

    PubMed

    Szukiewicz, Dariusz; Bilska, Anna; Mittal, Tarun Kumar; Stangret, Aleksandra; Wejman, Jaroslaw; Szewczyk, Grzegorz; Pyzlak, Michal; Zamlynski, Jacek

    2015-09-16

    Oxytocin (OXT) acts through its specific receptor (OXTR) and increased density of OXTR and/or augmented sensitivity to OXT were postulated as prerequisites of normal onset of labor. Expression of OXTR in the placental term trophoblast cells has not yet been analyzed in the context of contractile activity of the uterus. Here we examine comparatively OXT contents in the placental tissue adjacent to the uterine wall and expressions of OXTR in this tissue and corresponding isolated placental trophoblast cells. Twenty eight placentae after normal labors at term (group I, N = 14) and after cesarean sections performed without uterine contractile activity (group II, N = 14) have been collected. Tissue excised from the maternal surface of examined placenta was used for OXT concentration measurement, cytotrophoblast cell cultures preparation and immunohistochemistry of OXTR. Concentration of OXT was estimated in the tissue homogenates by an enzyme immunoassay with colorimetric detection. Cytotrophoblast cells were isolated using Kliman's method based on trypsin, DNase, and a 5-70% Percoll gradient centrifugation. The cultures were incubated for 5 days in normoxia. Both placental specimens and terminated cytotrophoblast cultures were fixed and embedded in paraffin before being immunostained for OXTR. Using light microscopy with computed morphometry for quantitative analysis, OXTR expressions were estimated in calibrated areas of the paraffin sections. There were not significant differences between the groups in respect to the mean OXT concentration. However, in both groups the median value of OXT concentration was significantly (p < 0.05) higher in the tissue obtained from the peripheral regions of the maternal surface of the placenta, compared to the samples from the central region of this surface. In placental tissue the mean expression of OXTR in group I was significantly (p < 0.05) increased by approximately 3.2-fold and 3.45-fold (the samples collected

  7. Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel

    1997-01-01

    This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

  8. Generalized exact holographic mapping with wavelets

    NASA Astrophysics Data System (ADS)

    Lee, Ching Hua

    2017-12-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

    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.

  10. Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C-Metric

    NASA Astrophysics Data System (ADS)

    Kar, Priyasri; Singh, Ritesh K.; Dasgupta, Ananda; Panigrahi, Prasanta K.

    2018-03-01

    The equation of motion of a massless Dirac particle in the C-metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, is cast in terms of a new set of su(1, 1) generators involving differential operators of degrees ±1/2 and 0. Additional Heun polynomials are obtained using this new algebraic structure and are used to construct some exact solutions for the radial and the polar parts of the Dirac equation.

  11. TVT-Exact and midurethral sling (SLING-IUFT) operative procedures: a randomized study

    PubMed Central

    Aniulis, Povilas; Skaudickas, Darijus

    2015-01-01

    Objectives The aim of the study is to compare results, effectiveness and complications of TVT exact and midurethral sling (SLING-IUFT) operations in the treatment of female stress urinary incontinence (SUI). Methods A single center nonblind, randomized study of women with SUI who were randomized to TVT-Exact and SLING-IUFT was performed by one surgeon from April 2009 to April 2011. SUI was diagnosed on coughing and Valsalva test and urodynamics (cystometry and uroflowmetry) were assessed before operation and 1 year after surgery. This was a prospective randomized study. The follow up period was 12 months. 76 patients were operated using the TVT-Exact operation and 78 patients – using the SLING-IUFT operation. There was no statistically significant differences between groups for BMI, parity, menopausal status and prolapsed stage (no patients had cystocele greater than stage II). Results Mean operative time was significantly shorter in the SLING-IUFT group (19 ± 5.6 min.) compared with the TVT-Exact group (27 ± 7.1 min.). There were statistically significant differences in the effectiveness of both procedures: TVT-Exact – at 94.5% and SLING-IUFT – at 61.2% after one year. Hospital stay was statistically significantly shorter in the SLING-IUFT group (1. 2 ± 0.5 days) compared with the TVT-Exact group (3.5 ± 1.5 days). Statistically significantly fewer complications occurred in the SLING-IUFT group. Conclusion the TVT-Exact and SLING-IUFT operations are both effective for surgical treatment of female stress urinary incontinence. The SLING-IUFT involved a shorter operation time and lower complications rate., the TVT-Exact procedure had statistically significantly more complications than the SLING-IUFT operation, but a higher effectiveness. PMID:28352711

  12. Explicit least squares system parameter identification for exact differential input/output models

    NASA Technical Reports Server (NTRS)

    Pearson, A. E.

    1993-01-01

    The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.

  13. Bounding filter - A simple solution to lack of exact a priori statistics.

    NASA Technical Reports Server (NTRS)

    Nahi, N. E.; Weiss, I. M.

    1972-01-01

    Wiener and Kalman-Bucy estimation problems assume that models describing the signal and noise stochastic processes are exactly known. When this modeling information, i.e., the signal and noise spectral densities for Wiener filter and the signal and noise dynamic system and disturbing noise representations for Kalman-Bucy filtering, is inexactly known, then the filter's performance is suboptimal and may even exhibit apparent divergence. In this paper a system is designed whereby the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator obtains a bound on the actual error covariance which is not available, and also prevents its apparent divergence.

  14. Renormalization of the fragmentation equation: exact self-similar solutions and turbulent cascades.

    PubMed

    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. E 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.

  15. Localized light waves: Paraxial and exact solutions of the wave equation (a review)

    NASA Astrophysics Data System (ADS)

    Kiselev, A. P.

    2007-04-01

    Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “ X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.

  16. Density functional with full exact exchange, balanced nonlocality of correlations, and constraint satisfaction

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tao, Jianmin; Perdew, John P; Staroverov, Viktor N

    2008-01-01

    We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a 'normal' region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to -1. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly-varying density or because ofmore » error cancellation between exchange and correlation. 'Abnormal' regions, where non locality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a hybrid functional mixing exact and semi local exchange energy densities locally (i.e., with a mixing fraction that is a function of position r and a functional of the density). Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters (corresponding roughly to the four kinds of abnormal regions). Our local hybrid functional is perhaps the first accurate size-consistent density functional with full exact exchange. It satisfies other known exact

  17. Analysis of thin plates with holes by using exact geometrical representation within XFEM.

    PubMed

    Perumal, Logah; Tso, C P; Leng, Lim Thong

    2016-05-01

    This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.

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

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    Destounis, Kyriakos; Panotopoulos, Grigoris; Rincón, Ángel

    2018-02-01

    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-Nordström black hole is observed.

  20. Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

    NASA Astrophysics Data System (ADS)

    Ray, S. Saha

    2018-04-01

    In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.

  1. Hypothalamic AMPK-induced autophagy ameliorates hypercatabolism in septic rats by regulating POMC expression.

    PubMed

    Cao, Chun; Gao, Tao; Cheng, Yan; Cheng, Minhua; Su, Ting; Xi, Fengchan; Wu, Cuili; Yu, Wenkui

    2018-03-18

    Hypercatabolism plays a critical role in the pathogenesis of post-critical care debility in critical patients. Central nervous system may exerte a critical role in the regulation of hypercatabolism. However, little is known about the exact mechanisms of the central role. Here, we reported that actived hypothalamic AMP-activated protein kinase (AMPK)-induced autophagy modulated the expression of POMC to ameliorate hypercatabolism in septic rats. Firstly, rats were i.c.v. injected with the lentiviral vector containing shRNA against POMC. Two weeks after injections, rats were intraperitoneally injected with LPS or saline. Twenty-four hours later, blood, skeletal muscle and hypothalamus tissues were obtained. Hypercatabolism markers and neuropeptides expression were detected. Then, rats were injected with AICAR or saline into third ventricle and promptly intraperitoneally injected with LPS or saline. Twenty-four hours after infection, blood, skeletal muscle and hypothalamus tissues were obtained. Hypercatabolism, hypothalamic AMPK-induced autophagy markers and neuropeptides expression were also detected. Results showed that sepsis would decrease the level of hypothalamic autophagy accompany with the alterations of POMC expression and hypercatabolism. Knocking out hypothalamus POMC expression could significantly ameliorate hypercatabolism. Moreover, Central activation of AMPK-induced autophagy pathway via third ventricle injection of AICAR, an AMPK activator, could efficiently ameliorate hypercatabolism as well as attenuate the elevated POMC expression rather than other neuropeptides. Taken together, these results suggested that hypothalamic AMPK-autophagy pathway as a regulatory pathway for POMC expression was essential for hypercatabolism during sepsis. And hypothalamic AMPK-autophagy activation could attenuate the POMC expression to ameliorate hypercatabolism. Pharmaceuticals with the ability of activating hypothalamic AMPK-autophagy pathway may be a therapeutic

  2. Iterative direct inversion: An exact complementary solution for inverting fault-slip data to obtain palaeostresses

    NASA Astrophysics Data System (ADS)

    Mostafa, Mostafa E.

    2005-10-01

    The present study shows that reconstructing the reduced stress tensor (RST) from the measurable fault-slip data (FSD) and the immeasurable shear stress magnitudes (SSM) is a typical iteration problem. The result of direct inversion of FSD presented by Angelier [1990. Geophysical Journal International 103, 363-376] is considered as a starting point (zero step iteration) where all SSM are assigned constant value ( λ=√{3}/2). By iteration, the SSM and RST update each other until they converge to fixed values. Angelier [1990. Geophysical Journal International 103, 363-376] designed the function upsilon ( υ) and the two estimators: relative upsilon (RUP) and (ANG) to express the divergence between the measured and calculated shear stresses. Plotting individual faults' RUP at successive iteration steps shows that they tend to zero (simulated data) or to fixed values (real data) at a rate depending on the orientation and homogeneity of the data. FSD of related origin tend to aggregate in clusters. Plots of the estimators ANG versus RUP show that by iteration, labeled data points are disposed in clusters about a straight line. These two new plots form the basis of a technique for separating FSD into homogeneous clusters.

  3. 26 CFR 1.669(a)-3 - Tax computed by the exact throwback method.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... 26 Internal Revenue 8 2010-04-01 2010-04-01 false Tax computed by the exact throwback method. 1... Taxable Years Beginning Before January 1, 1969 § 1.669(a)-3 Tax computed by the exact throwback method. (a... compute the tax, on amounts deemed distributed under section 666, by the exact throwback method provided...

  4. On the exact solutions of high order wave equations of KdV type (I)

    NASA Astrophysics Data System (ADS)

    Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

    2014-12-01

    In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

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

    NASA Astrophysics Data System (ADS)

    Kucska, Nóra; Gulácsi, Zsolt

    2018-06-01

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

  6. Topological charge and the spectrum of exactly massless fermions on the lattice

    NASA Astrophysics Data System (ADS)

    Chiu, Ting-Wai

    1998-10-01

    The square root of the positive definite Hermitian operator D†wDw in Neuberger's proposal of exactly massless quarks on the lattice is implemented by the recursion formula Yk+1=12(Yk+D†wDwY-1k) with Y0=1, where Y2k converges to D†wDw quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investigated. For smooth background gauge fields with nonzero topological charge, the exact zero modes with definite chirality are reproduced to a very high precision on a finite lattice and the index theorem is satisfied exactly. The fermionic determinants are also computed and they are in good agreement with the continuum exact solution.

  7. Multi-analysis determination of tropane alkaloids in cereals and solanaceaes seeds by liquid chromatography coupled to single stage Exactive-Orbitrap.

    PubMed

    Marín-Sáez, Jesús; Romero-González, Roberto; Garrido Frenich, Antonia

    2017-10-06

    Tropane alkaloids are a wide group of substances that comprises more than 200 compounds occurring especially in the Solanaceae family. The main aim of this study is the development of a method for the analysis of the principal tropane alkaloids as atropine, scopolamine, anisodamine, tropane, tropine, littorine, homatropine, apoatropine, aposcopolamine, scopoline, tropinone, physoperuvine, pseudotropine and cuscohygrine in cereals and related matrices. For that, a simple solid-liquid extraction was optimized and a liquid chromatographic method coupled to a single stage Exactive-Orbitrap was developed. The method was validated obtaining recoveries in the range of 60-109% (except for some compounds in soy), precision values (expressed as relative standard deviation) lower than 20% and detection and quantification limits equal to or lower than 2 and 3μg/kg respectively. Finally, the method was applied to the analysis of different types of samples as buckwheat, linseed, soy and millet, obtaining positives for anisodamine, scopolamine, atropine, littorine and tropinone in a millet flour sample above the quantification limits, whereas atropine and scopolamine were detected in a buckwheat sample, below the quantification limit. Contaminated samples with Solanaceaes seeds (Datura Stramonium and Brugmansia Arborea) were also analysed, detecting concentrations up to 693μg/kg (scopolamine) for contaminated samples with Brugmansia seeds and 1847μg/kg (atropine) when samples were contaminated with Stramonium seeds. Copyright © 2017 Elsevier B.V. All rights reserved.

  8. Time-dependent flow model of a generalized Burgers' fluid with fractional derivatives through a cylindrical domain: An exact and numerical approach

    NASA Astrophysics Data System (ADS)

    Safdar, Rabia; Imran, M.; Khalique, Chaudry Masood

    2018-06-01

    Exact solutions for velocity field and tangential stress for rotational flow of a generalized Burgers' fluid within an infinite circular pipe are derived by using the methods of Laplace and finite Hankel transformations. Firstly we take the position of fluid at rest and then the fluid flow due to the rotation of the pipe around the axis of flow having time dependant angular velocity. The exact solutions are presented in terms of the generalized Ga,b,c (., t) -functions. The corresponding results can be freely specified for the same results of Burgers', Oldroyd B, Maxwell, second grade and Newtonian fluids (performing the same motion) as particular cases of the results obtained earlier. The impact of the different parameters, individually and in comparison, are represented by graphical demonstrations. Secondly the numerical solutions for velocity and stress are also obtained with the help of Laplace transformation, Gaver Stehfest's algorithm and MATHCAD. Finally a comparison of both methods for the same problem is done and shows the consistency of results.

  9. An exact solution of solute transport by one-dimensional random velocity fields

    USGS Publications Warehouse

    Cvetkovic, V.D.; Dagan, G.; Shapiro, A.M.

    1991-01-01

    The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity. ?? 1991 Springer-Verlag.

  10. Exact evaluation of the depletion force between nanospheres in a polydisperse polymer fluid under Θ conditions.

    PubMed

    Wang, Haiqiang; Woodward, Clifford E; Forsman, Jan

    2014-05-21

    We analyze a system consisting of two spherical particles immersed in a polydispersed polymer solution under theta conditions. An exact theory is developed to describe the potential of mean force between the spheres for the case where the polymer molecular weight dispersity is described by the Schulz-Flory distribution. Exact results can be derived for the protein regime, where the sphere radius (R(s)) is small compared to the average radius of gyration of the polymer (R(g)). Numerical results are relatively easily obtained in the cases where the sphere radius is increased. We find that even when q = R(g)/R(s) ⪆ 10, then the use of a monopole expansion for the polymer end-point distribution about the spheres is sufficient. For even larger spheres q ≈ 1, accuracy is maintained by including a dipolar correction. The implications of these findings on generating a full many-body effective interaction for a collection of N spheres imbedded in the polymer solution are discussed.

  11. Exact Solutions to Time-dependent Mdps

    NASA Technical Reports Server (NTRS)

    Boyan, Justin A.; Littman, Michael L.

    2000-01-01

    We describe an extension of the Markov decision process model in which a continuous time dimension is included in the state space. This allows for the representation and exact solution of a wide range of problems in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.

  12. Exact quantum numbers of collapsed and non-collapsed two-string solutions in the spin-1/2 Heisenberg spin chain

    NASA Astrophysics Data System (ADS)

    Deguchi, Tetsuo; Ranjan Giri, Pulak

    2016-04-01

    Every solution of the Bethe-ansatz equations (BAEs) is characterized by a set of quantum numbers, by which we can evaluate it numerically. However, no general rule is known how to give quantum numbers for the physical solutions of BAE. For the spin-1/2 XXX chain we rigorously derive all the quantum numbers for the complete set of the Bethe-ansatz eigenvectors in the two down-spin sector with any chain length N. Here we obtain them both for real and complex solutions. We also show that all the solutions associated with them are distinct. Consequently, we prove the completeness of the Bethe ansatz and give an exact expression for the number of real solutions which correspond to collapsed bound-state solutions (i.e., two-string solutions) in the sector: 2[(N-1)/2-(N/π ){{tan}}-1(\\sqrt{N-1})] in terms of Gauss’ symbol. Moreover, we prove in the sector the scheme conjectured by Takahashi for solving BAE systematically. We also suggest that by applying the present method we can derive the quantum numbers for the spin-1/2 XXZ chain.

  13. Exact Turbulence Law in Collisionless Plasmas: Hybrid Simulations

    NASA Astrophysics Data System (ADS)

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

    2017-12-01

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

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

    NASA Technical Reports Server (NTRS)

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  16. An Exactly Soluble Model for Hopping Particles Moving with Correlations Between States due to Exchange Sites

    NASA Astrophysics Data System (ADS)

    Zhao, Xian-Geng; Jia, Sue-Tang

    1992-09-01

    The motion of hopping particles on an infinite chain is investigated. The model is characterized by the correlations between states due to exchange sites. The analytic solutions for this system are discussed in general case. For some special cases, exact results are obtained with the help of explicit calculations of propagators and mean square displacement deviation. Both probability propagators for the creation and annihilation of two particles or for the deformation and formation of Frenkel excitons are indicated.

  17. Discovery of error-tolerant biclusters from noisy gene expression data.

    PubMed

    Gupta, Rohit; Rao, Navneet; Kumar, Vipin

    2011-11-24

    An important analysis performed on microarray gene-expression data is to discover biclusters, which denote groups of genes that are coherently expressed for a subset of conditions. Various biclustering algorithms have been proposed to find different types of biclusters from these real-valued gene-expression data sets. However, these algorithms suffer from several limitations such as inability to explicitly handle errors/noise in the data; difficulty in discovering small bicliusters due to their top-down approach; inability of some of the approaches to find overlapping biclusters, which is crucial as many genes participate in multiple biological processes. Association pattern mining also produce biclusters as their result and can naturally address some of these limitations. However, traditional association mining only finds exact biclusters, which limits its applicability in real-life data sets where the biclusters may be fragmented due to random noise/errors. Moreover, as they only work with binary or boolean attributes, their application on gene-expression data require transforming real-valued attributes to binary attributes, which often results in loss of information. Many past approaches have tried to address the issue of noise and handling real-valued attributes independently but there is no systematic approach that addresses both of these issues together. In this paper, we first propose a novel error-tolerant biclustering model, 'ET-bicluster', and then propose a bottom-up heuristic-based mining algorithm to sequentially discover error-tolerant biclusters directly from real-valued gene-expression data. The efficacy of our proposed approach is illustrated by comparing it with a recent approach RAP in the context of two biological problems: discovery of functional modules and discovery of biomarkers. For the first problem, two real-valued S.Cerevisiae microarray gene-expression data sets are used to demonstrate that the biclusters obtained from ET

  18. Exact reconstruction with directional wavelets on the sphere

    NASA Astrophysics Data System (ADS)

    Wiaux, Y.; McEwen, J. D.; Vandergheynst, P.; Blanc, O.

    2008-08-01

    A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et al. The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation are first identified. A scale-discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background data, such as the imprint of topological defects, in particular, cosmic strings, and for their reconstruction after separation from the other signal components.

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

    NASA Astrophysics Data System (ADS)

    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.

  20. Representing exact number visually using mental abacus.

    PubMed

    Frank, Michael C; Barner, David

    2012-02-01

    Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation.

  1. General relativity exactly described in terms of Newton's laws within curved geometries

    NASA Astrophysics Data System (ADS)

    Savickas, D.

    2014-07-01

    Many years ago Milne and McCrea showed in their well-known paper that the Hubble expansion occurring in general relativity could be exactly described by the use of Newtonian mechanics. It will be shown that a similar method can be extended to, and used within, curved geometries when Newton's second law is expressed within a four-dimensional curved spacetime. The second law will be shown to yield an equation that is exactly identical to the geodesic equation of motion of general relativity. This in itself yields no new information concerning relativity since the equation is mathematically identical to the relativistic equation. However, when the time in the second law is defined to have a constant direction as effectively occurs in Newtonian mechanics, and no longer acts as a fourth dimension as exists in relativity theory, it separates into a vector equation in a curved three-dimensional space and an additional second scalar equation that describes conservation of energy. It is shown that the curved Newtonian equations of motion define the metric coefficients which occur in the Schwarzschild solution and that they also define its equations of motion. Also, because the curved Newtonian equations developed here use masses as gravitational sources, as occurs in Newtonian mechanics, they make it possible to derive the solution for other kinds of mass distributions and are used here to find the metric equation for a thin mass-rod and the equation of motion for a mass particle orbiting it in its relativistic gravitational field.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Schulze-Halberg, Axel, E-mail: xbataxel@gmail.com; García-Ravelo, Jesús; Pacheco-García, Christian

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

  3. Exact Analytical Solutions for Elastodynamic Impact

    DTIC Science & Technology

    2015-11-30

    corroborated by derivation of exact discrete solutions from recursive equations for the impact problems. 15. SUBJECT TERMS One-dimensional impact; Elastic...wave propagation; Laplace transform; Floor function; Discrete solutions 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...impact Elastic wave propagation Laplace transform Floor function Discrete solutionsWe consider the one-dimensional impact problem in which a semi

  4. CTE Solvability, Exact Solutions and Nonlocal Symmetries of the Sharma-Tasso-Olver Equation

    NASA Astrophysics Data System (ADS)

    Pu, Huan; Jia, Man

    2015-12-01

    In this letter, we prove that the STO equation is CTE solvable and obtain the exact solutions of solitons fission and fusion. We also provide the nonlocal symmetries of the STO equation related to CTE. The nonlocal symmetries are localized by prolonging the related enlarged system. Supported by National Natural Science Foundation of China under Grant Nos. 11205092, 11175092 and 11435005, Ningbo Natural Science Foundation under Grant Nos. 2015A610159 and 2012A610178 and by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502. And the authors were sponsored by K. C. Wong Magna Fund in Ningbo University

  5. SW#db: GPU-Accelerated Exact Sequence Similarity Database Search.

    PubMed

    Korpar, Matija; Šošić, Martin; Blažeka, Dino; Šikić, Mile

    2015-01-01

    In recent years we have witnessed a growth in sequencing yield, the number of samples sequenced, and as a result-the growth of publicly maintained sequence databases. The increase of data present all around has put high requirements on protein similarity search algorithms with two ever-opposite goals: how to keep the running times acceptable while maintaining a high-enough level of sensitivity. The most time consuming step of similarity search are the local alignments between query and database sequences. This step is usually performed using exact local alignment algorithms such as Smith-Waterman. Due to its quadratic time complexity, alignments of a query to the whole database are usually too slow. Therefore, the majority of the protein similarity search methods prior to doing the exact local alignment apply heuristics to reduce the number of possible candidate sequences in the database. However, there is still a need for the alignment of a query sequence to a reduced database. In this paper we present the SW#db tool and a library for fast exact similarity search. Although its running times, as a standalone tool, are comparable to the running times of BLAST, it is primarily intended to be used for exact local alignment phase in which the database of sequences has already been reduced. It uses both GPU and CPU parallelization and was 4-5 times faster than SSEARCH, 6-25 times faster than CUDASW++ and more than 20 times faster than SSW at the time of writing, using multiple queries on Swiss-prot and Uniref90 databases.

  6. Effect of exact Coulomb-exchange calculations on band-head spectra of odd-proton nuclei

    NASA Astrophysics Data System (ADS)

    Koh, Meng-Hock; Nurhafiza, Mohamad Nor

    2017-10-01

    Previous calculations of band-head energy spectra of odd-mass heavy nuclei in the Hartree-Fock-plus-Bardeen-Cooper-Schrieffer (HF-BCS) framework showed that the agreement with data is better for odd-neutron as compared to odd-proton nuclei. The reason for a poorer agreement with data for the latter have been ascribed to the possible usage of the Slater approximation in calculating the Coulomb-exchange term. In this work, we report the effect of exact Coulomb-exchange calculations on band-head energy spectra of two odd-proton nuclei (namely 237Np and 241Am) as compared to the results obtained using the Slater approximation. We performed self-consistent blocking calculations while taking the breaking of time-reversal symmetry at the mean-field level into account due to the unpaired nucleon. The SkM* and SIII parametrizations of the Skyrme interaction have been employed to approximate the effective nucleon-nucleon interaction while a seniority force is used for the pairing channel. Contrary to what was expected, our preliminary results show no improvement on the band-head spectra as compared to data when the Coulomb-exchange term is calculated exactly.

  7. Quantum decay model with exact explicit analytical solution

    NASA Astrophysics Data System (ADS)

    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.

  8. Exact solution of matricial Φ23 quantum field theory

    NASA Astrophysics Data System (ADS)

    Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar

    2017-12-01

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

  9. Simple Analytic Expressions for the Magnetic Field of a Circular Current Loop

    NASA Technical Reports Server (NTRS)

    Simpson, James C.; Lane, John E.; Immer, Christopher D.; Youngquist, Robert C.

    2001-01-01

    Analytic expressions for the magnetic induction (magnetic flux density, B) of a simple planar circular current loop have been published in Cartesian and cylindrical coordinates [1,2], and are also known implicitly in spherical coordinates [3]. In this paper, we present explicit analytic expressions for B and its spatial derivatives in Cartesian, cylindrical, and spherical coordinates for a filamentary current loop. These results were obtained with extensive use of Mathematica "TM" and are exact throughout all space outside of the conductor. The field expressions reduce to the well-known limiting cases and satisfy V · B = 0 and V x B = 0 outside the conductor. These results are general and applicable to any model using filamentary circular current loops. Solenoids of arbitrary size may be easily modeled by approximating the total magnetic induction as the sum of those for the individual loops. The inclusion of the spatial derivatives expands their utility to magnetohydrodynamics where the derivatives are required. The equations can be coded into any high-level programming language. It is necessary to numerically evaluate complete elliptic integrals of the first and second kind, but this capability is now available with most programming packages.

  10. Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

    PubMed

    Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

    2002-04-01

    In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

  11. Exact Exchange calculations for periodic systems: a real space approach

    NASA Astrophysics Data System (ADS)

    Natan, Amir; Marom, Noa; Makmal, Adi; Kronik, Leeor; Kuemmel, Stephan

    2011-03-01

    We present a real-space method for exact-exchange Kohn-Sham calculations of periodic systems. The method is based on self-consistent solutions of the optimized effective potential (OEP) equation on a three-dimensional non-orthogonal grid, using norm conserving pseudopotentials. These solutions can be either exact, using the S-iteration approach, or approximate, using the Krieger, Li, and Iafrate (KLI) approach. We demonstrate, using a variety of systems, the importance of singularity corrections and use of appropriate pseudopotentials.

  12. Complexity of line-seru conversion for different scheduling rules and two improved exact algorithms for the multi-objective optimization.

    PubMed

    Yu, Yang; Wang, Sihan; Tang, Jiafu; Kaku, Ikou; Sun, Wei

    2016-01-01

    Productivity can be greatly improved by converting the traditional assembly line to a seru system, especially in the business environment with short product life cycles, uncertain product types and fluctuating production volumes. Line-seru conversion includes two decision processes, i.e., seru formation and seru load. For simplicity, however, previous studies focus on the seru formation with a given scheduling rule in seru load. We select ten scheduling rules usually used in seru load to investigate the influence of different scheduling rules on the performance of line-seru conversion. Moreover, we clarify the complexities of line-seru conversion for ten different scheduling rules from the theoretical perspective. In addition, multi-objective decisions are often used in line-seru conversion. To obtain Pareto-optimal solutions of multi-objective line-seru conversion, we develop two improved exact algorithms based on reducing time complexity and space complexity respectively. Compared with the enumeration based on non-dominated sorting to solve multi-objective problem, the two improved exact algorithms saves computation time greatly. Several numerical simulation experiments are performed to show the performance improvement brought by the two proposed exact algorithms.

  13. On Exact and Inexact Differentials and Applications

    ERIC Educational Resources Information Center

    Cortez, L. A. B.; de Oliveira, E. Capelas

    2017-01-01

    Considering the important role played by mathematical derivatives in the study of physical-chemical processes, this paper discusses the different possibilities and formulations of this concept and its application. In particular, in Chemical Thermodynamics, we study exact differentials associated with the so-called state functions and inexact…

  14. A new class of exact, nonlinear solutions to the Grad-Shafranov equation

    NASA Technical Reports Server (NTRS)

    Roumeliotis, George

    1993-01-01

    We have constructed a new class of exact, nonlinear solutions to the Grad-Shafranov equation, representing force-free magnetic fields with translational symmetry. These exact solutions are pertinent to the study of magnetic structures in the solar corona that are subjected to photospheric shearing motions.

  15. Pseudo 1-D Micro/Nanofluidic Device for Exact Electrokinetic Responses.

    PubMed

    Kim, Junsuk; Kim, Ho-Young; Lee, Hyomin; Kim, Sung Jae

    2016-06-28

    Conventionally, a 1-D micro/nanofluidic device, whose nanochannel bridged two microchannels, was widely chosen in the fundamental electrokinetic studies; however, the configuration had intrinsic limitations of the time-consuming and labor intensive tasks of filling and flushing the microchannel due to the high fluidic resistance of the nanochannel bridge. In this work, a pseudo 1-D micro/nanofluidic device incorporating air valves at each microchannel was proposed for mitigating these limitations. High Laplace pressure formed at liquid/air interface inside the microchannels played as a virtual valve only when the electrokinetic operations were conducted. The identical electrokinetic behaviors of the propagation of ion concentration polarization layer and current-voltage responses were obtained in comparison with the conventional 1-D micro/nanofluidic device by both experiments and numerical simulations. Therefore, the suggested pseudo 1-D micro/nanofluidic device owned not only experimental conveniences but also exact electrokinetic responses.

  16. Exact Solution of a Two-Species Quantum Dimer Model for Pseudogap Metals

    NASA Astrophysics Data System (ADS)

    Feldmeier, Johannes; Huber, Sebastian; Punk, Matthias

    2018-05-01

    We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015)., 10.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-Tc cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.

  17. Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension.

    PubMed

    Simpson, Matthew J; Baker, Ruth E

    2015-09-07

    Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard non-growing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

  18. EXACT S-MATRICES FOR AdS3/CFT2

    NASA Astrophysics Data System (ADS)

    Ahn, Changrim; Bombardelli, Diego

    2013-12-01

    We propose exact S-matrices for the AdS3/CFT2 duality between type IIB strings on AdS3×S3×M4 with M4 = S3×S1 or T4 and the corresponding two-dimensional conformal field theories. We fix the two-particle S-matrices on the basis of the symmetries su(1|1) and su(1|1)×su(1|1). A crucial justification comes from the derivation of the all-loop Bethe ansatz matching exactly the recent conjecture proposed by Babichenko et al. [J. High Energy Phys.1003, 058 (2010), arXiv:0912.1723 [hep-th

  19. A review of some exact solutions to the planar equations of motion of a thrusting spacecraft

    NASA Technical Reports Server (NTRS)

    Petropoulos, A. E.; Sims, J. A.

    2002-01-01

    With the complexities in computing optimal low thrust trajectories, easily-computed, good sub-optimal trajectories provide both a practical alternative for mission designers and a starting point for optimisation. The present paper collects in one place for easy reference and comparison several exact solutions that have been obtained in the literature over the last few decades: the logarithmic spiral, Pinkham's variant thereof, Forbes spiral, the exponential sinusoid, the case of constant radial thrust, Markopoulos's Keplerian thrust arcs, Lawden's spiral, and the analogous Bishop and Azimov spiral.

  20. Asymptotically Exact Solution of the Problem of Harmonic Vibrations of an Elastic Parallelepiped

    NASA Astrophysics Data System (ADS)

    Papkov, S. O.

    2017-11-01

    An asymptotically exact solution of the classical problem of elasticity about the steadystate forced vibrations of an elastic rectangular parallelepiped is constructed. The general solution of the vibration equations is constructed in the form of double Fourier series with undetermined coefficients, and an infinite system of linear algebraic equations is obtained for determining these coefficients. An analysis of the infinite system permits determining the asymptotics of the unknowns which are used to convolve the double series in both equations of the infinite systems and the displacement and stress components. The efficiency of this approach is illustrated by numerical examples and comparison with known solutions. The spectrum of the parallelepiped symmetric vibrations is studied for various ratios of its sides.

  1. More exact solutions of the constant astigmatism equation

    NASA Astrophysics Data System (ADS)

    Hlaváč, Adam

    2018-01-01

    By using Bäcklund transformation for the sine-Gordon equation, new periodic exact solutions of the constant astigmatism equation zyy +(1 / z) xx + 2 = 0 are generated from a seed which corresponds to Lipschitz surfaces of constant astigmatism.

  2. Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps

    NASA Astrophysics Data System (ADS)

    Goto, Shin-itiro; Umeno, Ken

    2018-03-01

    Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps, where it is defined on a subset of the real line and its probability distribution function is the Cauchy distribution with some parameters. With this reduction, some relations between the statistical picture and the orbital one are shown. From the viewpoint of information geometry, the parameter space can be identified with a statistical manifold, and then it is shown that the derived maps can be characterized. Also, with an induced symplectic structure from a statistical structure, symplectic and information geometric aspects of the derived maps are discussed.

  3. Exact Lyapunov exponent of the harmonic magnon modes of one-dimensional Heisenberg-Mattis spin glasses

    NASA Astrophysics Data System (ADS)

    Sepehrinia, Reza; Niry, M. D.; Bozorg, B.; Tabar, M. Reza Rahimi; Sahimi, Muhammad

    2008-03-01

    A mapping is developed between the linearized equation of motion for the dynamics of the transverse modes at T=0 of the Heisenberg-Mattis model of one-dimensional (1D) spin glasses and the (discretized) random wave equation. The mapping is used to derive an exact expression for the Lyapunov exponent (LE) of the magnon modes of spin glasses and to show that it follows anomalous scaling at low magnon frequencies. In addition, through numerical simulations, the differences between the LE and the density of states of the wave equation in a discrete 1D model of randomly disordered media (those with a finite correlation length) and that of continuous media (with a zero correlation length) are demonstrated and emphasized.

  4. Analytical study of exact solutions of the nonlinear Korteweg-de Vries equation with space-time fractional derivatives

    NASA Astrophysics Data System (ADS)

    Liu, Jiangen; Zhang, Yufeng

    2018-01-01

    This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg-de Vries equation with space-time local fractional derivatives. By using the improved (G‧ G )-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.

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

    NASA Astrophysics Data System (ADS)

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  7. Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: an exactly solvable nondissipative nonergodic model.

    PubMed

    Hasegawa, Hideo

    2011-07-01

    Responses of small open oscillator systems to applied external forces have been studied with the use of an exactly solvable classical Caldeira-Leggett model in which a harmonic oscillator (system) is coupled to finite N-body oscillators (bath) with an identical frequency (ω(n) = ω(o) for n = 1 to N). We have derived exact expressions for positions, momenta, and energy of the system in nonequilibrium states and for work performed by applied forces. A detailed study has been made on an analytical method for canonical averages of physical quantities over the initial equilibrium state, which is much superior to numerical averages commonly adopted in simulations of small systems. The calculated energy of the system which is strongly coupled to a finite bath is fluctuating but nondissipative. It has been shown that the Jarzynski equality is valid in nondissipative nonergodic open oscillator systems regardless of the rate of applied ramp force.

  8. Cloud level winds from UV and IR images obtained by VMC onboard Venus Express

    NASA Astrophysics Data System (ADS)

    Khatuntsev, Igor; Patsaeva, Marina; Titov, Dmitri; Ignatiev, Nikolay; Turin, Alexander; Bertaux, Jean-Loup

    2017-04-01

    During eight years Venus Monitoring Camera (VMC) [1] onboard the Venus Express orbiter has observed the upper cloud layer of Venus. The largest set of images was obtained in the UV (365 nm), visible (513 nm) and two infrared channels - 965 nm and 1010 nm. The UV dayside images were used to study the atmospheric circulation at the Venus cloud tops [2], [3]. Mean zonal and meridional profiles of winds and their variability were derived from cloud tracking of UV images. In low latitudes the mean retrograde zonal wind at the cloud top (67±2 km) is about 95 m/s with a maximum of about 102 m/s at 40-50°S. Poleward from 50°S the zonal wind quickly fades out with latitude. The mean poleward meridional wind slowly increases from zero value at the equator to about 10 m/s at 50°S. Poleward from this latitude, the absolute value of the meridional component monotonically decreases to zero at the pole. The VMC observations suggest clear diurnal signature in the wind field. They also indicate a long term trend for the zonal wind speed at low latitudes to increase from 85 m/s in the beginning of the mission to 110 m/s by the middle of 2012. The trend was explained by influence of the surface topography on the zonal flow [4]. Cloud features tracking in the IR images provided information about winds in the middle cloud deck (55±4 km). In the low and middle latitudes (5-65°S) the IR mean retrograde zonal velocity is about 68-70 m/s. In contrast to poleward flow at the cloud tops, equatorward motions dominate in the middle cloud with maximum speed of 5.8±1.2 m/s at latitude 15°S. The meridional speed slowly decreases to 0 at 65-70°S. At low latitudes the zonal and meridional speed demonstrate long term variations. Following [4] we explain the observed long term trend of zonal and meridional components by the influence of surface topography of highland region Aphrodite Terra on dynamic processes in the middle cloud deck through gravity waves. Acknowledgements: I.V. Khatuntsev

  9. Exact model reduction of combinatorial reaction networks

    PubMed Central

    Conzelmann, Holger; Fey, Dirk; Gilles, Ernst D

    2008-01-01

    Background Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. Results We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs. Conclusion The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks. PMID:18755034

  10. Exact and Heuristic Algorithms for Runway Scheduling

    NASA Technical Reports Server (NTRS)

    Malik, Waqar A.; Jung, Yoon C.

    2016-01-01

    This paper explores the Single Runway Scheduling (SRS) problem with arrivals, departures, and crossing aircraft on the airport surface. Constraints for wake vortex separations, departure area navigation separations and departure time window restrictions are explicitly considered. The main objective of this research is to develop exact and heuristic based algorithms that can be used in real-time decision support tools for Air Traffic Control Tower (ATCT) controllers. The paper provides a multi-objective dynamic programming (DP) based algorithm that finds the exact solution to the SRS problem, but may prove unusable for application in real-time environment due to large computation times for moderate sized problems. We next propose a second algorithm that uses heuristics to restrict the search space for the DP based algorithm. A third algorithm based on a combination of insertion and local search (ILS) heuristics is then presented. Simulation conducted for the east side of Dallas/Fort Worth International Airport allows comparison of the three proposed algorithms and indicates that the ILS algorithm performs favorably in its ability to find efficient solutions and its computation times.

  11. Functional determinants, index theorems, and exact quantum black hole entropy

    NASA Astrophysics Data System (ADS)

    Murthy, Sameer; Reys, Valentin

    2015-12-01

    The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the QV operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around Q-invariant off-shell configurations in four-dimensional N=2 supergravity with AdS 2 × S 2 boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in N=2 supergravity. We explain cancellations concerning 1/8 -BPS black holes in N=8 supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.

  12. Partition resampling and extrapolation averaging: approximation methods for quantifying gene expression in large numbers of short oligonucleotide arrays.

    PubMed

    Goldstein, Darlene R

    2006-10-01

    Studies of gene expression using high-density short oligonucleotide arrays have become a standard in a variety of biological contexts. Of the expression measures that have been proposed to quantify expression in these arrays, multi-chip-based measures have been shown to perform well. As gene expression studies increase in size, however, utilizing multi-chip expression measures is more challenging in terms of computing memory requirements and time. A strategic alternative to exact multi-chip quantification on a full large chip set is to approximate expression values based on subsets of chips. This paper introduces an extrapolation method, Extrapolation Averaging (EA), and a resampling method, Partition Resampling (PR), to approximate expression in large studies. An examination of properties indicates that subset-based methods can perform well compared with exact expression quantification. The focus is on short oligonucleotide chips, but the same ideas apply equally well to any array type for which expression is quantified using an entire set of arrays, rather than for only a single array at a time. Software implementing Partition Resampling and Extrapolation Averaging is under development as an R package for the BioConductor project.

  13. An Exact Model-Based Method for Near-Field Sources Localization with Bistatic MIMO System.

    PubMed

    Singh, Parth Raj; Wang, Yide; Chargé, Pascal

    2017-03-30

    In this paper, we propose an exact model-based method for near-field sources localization with a bistatic multiple input, multiple output (MIMO) radar system, and compare it with an approximated model-based method. The aim of this paper is to propose an efficient way to use the exact model of the received signals of near-field sources in order to eliminate the systematic error introduced by the use of approximated model in most existing near-field sources localization techniques. The proposed method uses parallel factor (PARAFAC) decomposition to deal with the exact model. Thanks to the exact model, the proposed method has better precision and resolution than the compared approximated model-based method. The simulation results show the performance of the proposed method.

  14. Faster computation of exact RNA shape probabilities.

    PubMed

    Janssen, Stefan; Giegerich, Robert

    2010-03-01

    Abstract shape analysis allows efficient computation of a representative sample of low-energy foldings of an RNA molecule. More comprehensive information is obtained by computing shape probabilities, accumulating the Boltzmann probabilities of all structures within each abstract shape. Such information is superior to free energies because it is independent of sequence length and base composition. However, up to this point, computation of shape probabilities evaluates all shapes simultaneously and comes with a computation cost which is exponential in the length of the sequence. We device an approach called RapidShapes that computes the shapes above a specified probability threshold T by generating a list of promising shapes and constructing specialized folding programs for each shape to compute its share of Boltzmann probability. This aims at a heuristic improvement of runtime, while still computing exact probability values. Evaluating this approach and several substrategies, we find that only a small proportion of shapes have to be actually computed. For an RNA sequence of length 400, this leads, depending on the threshold, to a 10-138 fold speed-up compared with the previous complete method. Thus, probabilistic shape analysis has become feasible in medium-scale applications, such as the screening of RNA transcripts in a bacterial genome. RapidShapes is available via http://bibiserv.cebitec.uni-bielefeld.de/rnashapes

  15. Expression of proteins in serum, synovial fluid, synovial membrane, and articular cartilage samples obtained from dogs with stifle joint osteoarthritis secondary to cranial cruciate ligament disease and dogs without stifle joint arthritis.

    PubMed

    Garner, Bridget C; Kuroki, Keiichi; Stoker, Aaron M; Cook, Cristi R; Cook, James L

    2013-03-01

    To identify proteins with differential expression between healthy dogs and dogs with stifle joint osteoarthritis secondary to cranial cruciate ligament (CCL) disease. Serum and synovial fluid samples obtained from dogs with stifle joint osteoarthritis before (n = 10) and after (8) surgery and control dogs without osteoarthritis (9) and archived synovial membrane and articular cartilage samples obtained from dogs with stifle joint osteoarthritis (5) and dogs without arthritis (5). Serum and synovial fluid samples were analyzed via liquid chromatography-tandem mass spectrometry; results were compared against a nonredundant protein database. Expression of complement component 3 in archived tissue samples was determined via immunohistochemical methods. No proteins had significantly different expression between serum samples of control dogs versus those of dogs with stifle joint osteoarthritis. Eleven proteins (complement component 3 precursor, complement factor I precursor, apolipoprotein B-100 precursor, serum paraoxonase and arylesterase 1, zinc-alpha-2-glycoprotein precursor, serum amyloid A, transthyretin precursor, retinol-binding protein 4 precursor, alpha-2-macroglobulin precursor, angiotensinogen precursor, and fibronectin 1 isoform 1 preproprotein) had significantly different expression (> 2.0-fold) between synovial fluid samples obtained before surgery from dogs with stifle joint osteoarthritis versus those obtained from control dogs. Complement component 3 was strongly expressed in all (5/5) synovial membrane samples of dogs with stifle joint osteoarthritis and weakly expressed in 3 of 5 synovial membrane samples of dogs without stifle joint arthritis. Findings suggested that the complement system and proteins involved in lipid and cholesterol metabolism may have a role in stifle joint osteoarthritis, CCL disease, or both.

  16. Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

    NASA Astrophysics Data System (ADS)

    Terasaki, J.; Smetana, A.; Šimkovic, F.; Krivoruchenko, M. I.

    2017-10-01

    It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number N = 2 and numerically for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation.

  17. Accuracy of electron densities obtained via Koopmans-compliant hybrid functionals

    NASA Astrophysics Data System (ADS)

    Elmaslmane, A. R.; Wetherell, J.; Hodgson, M. J. P.; McKenna, K. P.; Godby, R. W.

    2018-04-01

    We evaluate the accuracy of electron densities and quasiparticle energy gaps given by hybrid functionals by directly comparing these to the exact quantities obtained from solving the many-electron Schrödinger equation. We determine the admixture of Hartree-Fock exchange to approximate exchange-correlation in our hybrid functional via one of several physically justified constraints, including the generalized Koopmans' theorem. We find that hybrid functionals yield strikingly accurate electron densities and gaps in both exchange-dominated and correlated systems. We also discuss the role of the screened Fock operator in the success of hybrid functionals.

  18. The Poisson-Boltzmann theory for the two-plates problem: some exact results.

    PubMed

    Xing, Xiang-Jun

    2011-12-01

    The general solution to the nonlinear Poisson-Boltzmann equation for two parallel charged plates, either inside a symmetric electrolyte, or inside a 2q:-q asymmetric electrolyte, is found in terms of Weierstrass elliptic functions. From this we derive some exact asymptotic results for the interaction between charged plates, as well as the exact form of the renormalized surface charge density.

  19. Study of the exact analytical solution of the equation of longitudinal waves in a liquid with account of its relaxation properties

    NASA Astrophysics Data System (ADS)

    Kudinov, I. V.; Kudinov, V. A.

    2013-09-01

    A mathematical model of elastic vibrations of an incompressible liquid has been developed based on the hypothesis on the finite velocity of propagation of field potentials in this liquid. A hyperbolic equation of vibrations of such a liquid with account of its relaxation properties has been obtained. An exact analytical solution of this equation has been found and investigated in detail.

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

    NASA Astrophysics Data System (ADS)

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

    2018-04-01

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

  1. An exact stiffness theory for unidirectional xFRP composites

    NASA Astrophysics Data System (ADS)

    Klasztorny, M.; Konderla, P.; Piekarski, R.

    2009-01-01

    UD xFRP composites, i.e., isotropic plastics reinforced with long transversely isotropic fibres packed unidirectionally according to the hexagonal scheme are considered. The constituent materials are geometrically and physically linear. The previous formulations of the exact stiffness theory of such composites are revised, and the theory is developed further based on selected boundary-value problems of elasticity theory. The numerical examples presented are focussed on testing the theory with account of previous variants of this theory and experimental values of the effective elastic constants. The authors have pointed out that the exact stiffness theory of UD xFRP composites, with the modifications proposed in our study, will be useful in the engineering practice and in solving the current problems of the mechanics of composite materials.

  2. Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.

    PubMed

    Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali

    2015-01-01

    In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.

  3. A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers

    NASA Astrophysics Data System (ADS)

    Bartlett, M. S.; Porporato, A.

    2018-02-01

    The nonlinear equation of Boussinesq (1877) is a foundational approach for studying groundwater flow through an unconfined aquifer, but solving the full nonlinear version of the Boussinesq equation remains a challenge. Here, we present an exact solution to the full nonlinear Boussinesq equation that not only applies to sloping aquifers but also accounts for source and sink terms such as bedrock seepage, an often significant flux in headwater catchments. This new solution captures the hysteretic relationship (a loop rating curve) between the groundwater flow rate and the water table height, which may be used to provide a more realistic representation of streamflow and groundwater dynamics in hillslopes. In addition, the solution provides an expression where the flow recession varies based on hillslope parameters such as bedrock slope, bedrock seepage, aquifer recharge, plant transpiration, and other factors that vary across landscape types.

  4. Exact p-values for pairwise comparison of Friedman rank sums, with application to comparing classifiers.

    PubMed

    Eisinga, Rob; Heskes, Tom; Pelzer, Ben; Te Grotenhuis, Manfred

    2017-01-25

    The Friedman rank sum test is a widely-used nonparametric method in computational biology. In addition to examining the overall null hypothesis of no significant difference among any of the rank sums, it is typically of interest to conduct pairwise comparison tests. Current approaches to such tests rely on large-sample approximations, due to the numerical complexity of computing the exact distribution. These approximate methods lead to inaccurate estimates in the tail of the distribution, which is most relevant for p-value calculation. We propose an efficient, combinatorial exact approach for calculating the probability mass distribution of the rank sum difference statistic for pairwise comparison of Friedman rank sums, and compare exact results with recommended asymptotic approximations. Whereas the chi-squared approximation performs inferiorly to exact computation overall, others, particularly the normal, perform well, except for the extreme tail. Hence exact calculation offers an improvement when small p-values occur following multiple testing correction. Exact inference also enhances the identification of significant differences whenever the observed values are close to the approximate critical value. We illustrate the proposed method in the context of biological machine learning, were Friedman rank sum difference tests are commonly used for the comparison of classifiers over multiple datasets. We provide a computationally fast method to determine the exact p-value of the absolute rank sum difference of a pair of Friedman rank sums, making asymptotic tests obsolete. Calculation of exact p-values is easy to implement in statistical software and the implementation in R is provided in one of the Additional files and is also available at http://www.ru.nl/publish/pages/726696/friedmanrsd.zip .

  5. Approach to first-order exact solutions of the Ablowitz-Ladik equation.

    PubMed

    Ankiewicz, Adrian; Akhmediev, Nail; Lederer, Falk

    2011-05-01

    We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solutions of the nonlinear Schrödinger equation (NLSE). © 2011 American Physical Society

  6. Exact solution for spin precession in the radiationless relativistic Kepler problem

    NASA Astrophysics Data System (ADS)

    Mane, S. R.

    2014-11-01

    There is interest in circulating beams of polarized particles in all-electric storage rings to search for nonzero permanent electric dipole moments of subatomic particles. To this end, it is helpful to derive exact analytical solutions of the spin precession in idealized models, both for pedagogical reasons and to serve as benchmark tests for analysis and design of experiments. This paper derives exact solutions for the spin precession in the relativistic Kepler problem. Some counterintuitive properties of the solutions are pointed out.

  7. Virtual photon impact factors with exact gluon kinematics

    NASA Astrophysics Data System (ADS)

    Bialas, A.; Navelet, H.; Peschanski, R.

    2001-06-01

    An explicit analytic formula for the transverse and longitudinal impact factors ST, L( N, γ) of the photon using kT factorization with exact gluon kinematics is given. Applications to the QCD dipole model and the extraction of the unintegrated gluon structure function from data are proposed.

  8. Combined Exact-Repeat and Geodetic Mission Altimetry for High-Resolution Empirical Tide Mapping

    NASA Astrophysics Data System (ADS)

    Zaron, E. D.

    2014-12-01

    The configuration of present and historical exact-repeat mission (ERM) altimeter ground tracks determines the maximum resolution of empirical tidal maps obtained with ERM data. Although the mode-1 baroclinic tide is resolvable at mid-latitudes in the open ocean, the ability to detect baroclinic and barotropic tides near islands and complex coastlines is limited, in part, by ERM track density. In order to obtain higher resolution maps, the possibility of combining ERM and geodetic mission (GM) altimetry is considered, using a combination of spatial thin-plate splines and temporal harmonic analysis. Given the present spatial and temporal distribution of GM missions, it is found that GM data can contribute to resolving tidal features smaller than 75 km, provided the signal amplitude is greater than about 1 cm. Uncertainties in the mean sea surface and environmental corrections are significant components of the GM error budget, and methods to optimize data selection and along-track filtering are still being optimized. Application to two regions, Monterey Bay and Luzon Strait, finds evidence for complex tidal fields in agreement with independent observations and modeling studies.

  9. Exact cancellation of emittance growth due to coupled transverse dynamics in solenoids and rf couplers

    NASA Astrophysics Data System (ADS)

    Dowell, David H.; Zhou, Feng; Schmerge, John

    2018-01-01

    Weak, rotated magnetic and radio frequency quadrupole fields in electron guns and injectors can couple the beam's horizontal with vertical motion, introduce correlations between otherwise orthogonal transverse momenta, and reduce the beam brightness. This paper discusses two important sources of coupled transverse dynamics common to most electron injectors. The first is quadrupole focusing followed by beam rotation in a solenoid, and the second coupling comes from a skewed high-power rf coupler or cavity port which has a rotated rf quadrupole field. It is shown that a dc quadrupole field can correct for both types of couplings and exactly cancel their emittance growths. The degree of cancellation of the rf skew quadrupole emittance is limited by the electron bunch length. Analytic expressions are derived and compared with emittance simulations and measurements.

  10. Given a one-step numerical scheme, on which ordinary differential equations is it exact?

    NASA Astrophysics Data System (ADS)

    Villatoro, Francisco R.

    2009-01-01

    A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

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

    PubMed

    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.

  12. Perpendicular susceptibility and geometrical frustration in two-dimensional Ising antiferromagnets: Exact solutions

    NASA Astrophysics Data System (ADS)

    Muttalib, K. A.; Khatun, M.; Barry, J. H.

    2017-11-01

    Discovery of new materials and improved experimental as well as numerical techniques have led to a renewed interest in geometrically frustrated spin systems. However, there are very few exact results available that can provide a benchmark for comparison. In this work, we calculate exactly the perpendicular susceptibility χ⊥ for an Ising antiferromagnet with (i) nearest-neighbor pair interaction on a kagome lattice where strong frustration prevents long-range ordering and (ii) elementary triplet interactions on a kagome lattice which has no frustration but the system remains disordered down to zero temperature. By comparing with other known exact results with and without frustration, we propose that an appropriately temperature-scaled χ⊥ can be used as a quantitative measure of the degree of frustration in Ising spin systems.

  13. Delving Into Dissipative Quantum Dynamics: From Approximate to Numerically Exact Approaches

    NASA Astrophysics Data System (ADS)

    Chen, Hsing-Ta

    In this thesis, I explore dissipative quantum dynamics of several prototypical model systems via various approaches, ranging from approximate to numerically exact schemes. In particular, in the realm of the approximate I explore the accuracy of Pade-resummed master equations and the fewest switches surface hopping (FSSH) algorithm for the spin-boson model, and non-crossing approximations (NCA) for the Anderson-Holstein model. Next, I develop new and exact Monte Carlo approaches and test them on the spin-boson model. I propose well-defined criteria for assessing the accuracy of Pade-resummed quantum master equations, which correctly demarcate the regions of parameter space where the Pade approximation is reliable. I continue the investigation of spin-boson dynamics by benchmark comparisons of the semiclassical FSSH algorithm to exact dynamics over a wide range of parameters. Despite small deviations from golden-rule scaling in the Marcus regime, standard surface hopping algorithm is found to be accurate over a large portion of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic for the cases I consider. Next, I introduce new methods for numerically exact real-time simulation based on real-time diagrammatic Quantum Monte Carlo (dQMC) and the inchworm algorithm. These methods optimally recycle Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. In the context of the spin-boson model, I formulate the inchworm expansion in two distinct ways: the first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. In addition, a cumulant version of the inchworm Monte Carlo method is motivated by the latter expansion, which allows for further suppression of the growth of the sign error. I provide a comprehensive comparison of the

  14. Exact closed-form solution of the hyperbolic equation of string vibrations with material relaxation properties taken into account

    NASA Astrophysics Data System (ADS)

    Kudinov, I. V.; Kudinov, V. A.

    2014-09-01

    The differential equation of damped string vibrations was obtained with the finite speed of extension and strain propagation in the Hooke's law formula taken into account. In contrast to the well-known equations, the obtained equation contains the first and third time derivatives of the displacement and the mixed derivative with respect to the space and time variables. Separation of variables was used to obtain its exact closed-form solution, whose analysis showed that, for large values of the relaxation coefficient, the string return to the initial state after its escape from equilibrium is accompanied by high-frequency low-amplitude damped vibrations, which occur on the initial time interval only in the region of positive displacements. And in the limit, for some large values of the relaxation coefficient, the string return to the initial state occurs practically without any oscillatory process.

  15. Thoracic paravertebral ganglioneuroma with high immunohistochemical expression of TrkA.

    PubMed

    Nishio, S; Hamada, Y; Nakagawara, A; Haga, S; Suzuki, S; Fukui, M

    1999-01-01

    A 21-year-old man, who had previously undergone a total resection for a retroperitoneal ganglioneuroblastoma at 7 months of age, was revealed to have a thoracic paravertebral ganglioneuroma, in which immunohistochemical expression of neuron-specific enolase and neurofilament was noted. Furthermore, immunohistochemical expression of TrkA, which is a high-affinity receptor for nerve growth factor, was evident. Although the exact histogenesis remains uncertain, TrkA was considered to be involved in the development of this thoracic paravertebral tumor.

  16. Exact diagonalization library for quantum electron models

    NASA Astrophysics Data System (ADS)

    Iskakov, Sergei; Danilov, Michael

    2018-04-01

    We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. The observables that can be computed using EDLib are single particle Green's functions and spin-spin correlation functions. This code provides three different types of Hamiltonian matrix storage that can be chosen based on the model.

  17. Changes in myometrial expression of progesterone receptor membrane components 1 and 2 are associated with human parturition at term.

    PubMed

    Wang, Ray; Sheehan, Penelope M; Brennecke, Shaun P

    2016-04-01

    While the exact mechanism of human parturition remains unknown, functional progesterone withdrawal is believed to play a key regulatory role. Progesterone receptor membrane components 1 and 2 (PGRMC1, PGRMC2) are putative progesterone receptors and the aim of this project was to investigate their expression in human myometrium. Human term myometrium was obtained from the lower uterine segment incision in women undergoing elective (not-in-labour, NIL; n=11) and emergency Caesarean sections (in-labour, IL; n=10), following written consent. PGRMC1 and 2 expression was quantified using real-time reverse transcription polymerase chain reaction and western blot. Subcellular localisation was performed by immunohistochemistry and immunofluorescence. There was a significant decrease in PGRMC1 mRNA (P=0.0317) and protein expression (P=0.0151) in IL myometrium, compared with NIL myometrium. PGRMC2 mRNA expression (P=0.0151) was also decreased in IL myometrium, compared with NIL myometrium. Immunostaining studies confirmed the presence of PGRMC1 and 2 in smooth-muscle cells. Expression was perinuclear in NIL myometrium and more generalised and cytoplasmic in IL myometrium. The decrease in PGRMC1 expression and the translocation away from a perinuclear location for both PGRMC1 and 2 could contribute to a functional progesterone withdrawal that may ultimately initiate parturition.

  18. Exact Algorithms for Output Encoding, State Assignment and Four-Level Boolean Minimization

    DTIC Science & Technology

    1989-10-01

    APPROVED FOR PUBLIC DISTRIBUTION • DTIC MASSACHUSETTS INTITUTE OF TECHNOLOGY M VLSI PUBLICATIONSJAN 17 1990 VLSI Memo No. 89-569 JN. 9October 1989...nunijize large funclions exacly within reasonable amocunt. of CPt targeting twro-level logic imnplemientations involve finding ap- time. However, thle ,, m ...0(NV!) m ~iimizations . n5 10 The inptut encoding problemt can be exactly solved using mrultiple-valued Boolean nimuization. We present an exact (a) (b

  19. Study of analytical method to seek for exact solutions of variant Boussinesq equations.

    PubMed

    Khan, Kamruzzaman; Akbar, M Ali

    2014-01-01

    In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. Primarily, we have used the enhanced (G'/G)-expansion method to find exact solutions of Variant Boussinesq equations. Then, we attain some exact solutions including soliton solutions, hyperbolic and trigonometric function solutions of this equation. 35 K99; 35P05; 35P99.

  20. On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.

    PubMed

    Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo

    2016-08-01

    This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.

  1. Exact solutions and low-frequency instability of the adiabatic auroral arc model

    NASA Technical Reports Server (NTRS)

    Cornwall, John M.

    1988-01-01

    The adiabatic auroral arc model couples a kinetic theory parallel current driven by mirror forces to horizontal ionospheric currents; the resulting equations are nonlinear. Some exact stationary solutions to these equations, some of them based on the Liouville equation, are developed, with both latitudinal and longitudinal spatial variations. These Liouville equation exact solutions are related to stability boundaries of low-frequency instabilities such as Kelvin-Helmholtz, as shown by a study of a simplified model.

  2. Laser Radiation in Active Amplifying Media Treated as a Transport Problem - Transfer Equation Derived and Exactly Solved

    NASA Astrophysics Data System (ADS)

    Das Gupta, Santanu; Das Gupta, S. R.

    1991-10-01

    The flow of laser radiation in a plane-parallel cylindrical slab of active amplifying medium with axial symmetry is treated as a problem in radiative transfer. The appropriate one-dimensional transfer equation describing the transfer of laser radiation has been derived by an appeal to Einstein'sA, B coefficients (describing the processes of stimulated line absorption, spontaneous line emission, and stimulated line emission sustained by population inversion in the medium) and considering the ‘rate equations’ to completely establish the rational of the transfer equation obtained. The equation is then exactly solved and the angular distribution of the emergent laser beam intensity is obtained; its numerically computed values are given in tables and plotted in graphs showing the nature of peaks of the emerging laser beam intensity about the axis of the laser cylinder.

  3. Laser radiation in active amplifying media treated as a transport problem - Transfer equation derived and exactly solved

    NASA Astrophysics Data System (ADS)

    Gupta, S. R. D.; Gupta, Santanu D.

    1991-10-01

    The flow of laser radiation in a plane-parallel cylindrical slab of active amplifying medium with axial symmetry is treated as a problem in radiative transfer. The appropriate one-dimensional transfer equation describing the transfer of laser radiation has been derived by an appeal to Einstein's A, B coefficients (describing the processes of stimulated line absorption, spontaneous line emission, and stimulated line emission sustained by population inversion in the medium) and considering the 'rate equations' to completely establish the rational of the transfer equation obtained. The equation is then exactly solved and the angular distribution of the emergent laser beam intensity is obtained; its numerically computed values are given in tables and plotted in graphs showing the nature of peaks of the emerging laser beam intensity about the axis of the laser cylinder.

  4. Exact solutions for discrete breathers in a forced-damped chain.

    PubMed

    Gendelman, O V

    2013-06-01

    Exact solutions for symmetric on-site discrete breathers (DBs) are obtained in a forced-damped linear chain with on-site vibro-impact constraints. The damping in the system is caused by inelastic impacts; the forcing functions should satisfy conditions of periodicity and antisymmetry. Global conditions for existence and stability of the DBs are established by a combination of analytic and numeric methods. The DB can lose its stability through either pitchfork, or Neimark-Sacker bifurcations. The pitchfork bifurcation is related to the internal dynamics of each individual oscillator. It is revealed that the coupling can suppress this type of instability. To the contrary, the Neimark-Sacker bifurcation occurs for relatively large values of the coupling, presumably due to closeness of the excitation frequency to a boundary of the propagation zone of the chain. Both bifurcation mechanisms seem to be generic for the considered type of forced-damped lattices. Some unusual phenomena, like nonmonotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the initial system and illustrated numerically for small periodic lattices.

  5. Exact solutions for network rewiring models

    NASA Astrophysics Data System (ADS)

    Evans, T. S.

    2007-03-01

    Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree distribution is found and its exact solution and generating solution are given.

  6. New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

    NASA Astrophysics Data System (ADS)

    Csörgő, Tamás; Kasza, Gábor; Csanád, Máté; Jiang, Zefang

    2018-06-01

    We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision data at RHIC and LHC. In the longitudinally boost-invariant limit, these new solutions approach the Hwa-Bjorken solution and the corresponding rapidity distributions approach a rapidity plateaux.

  7. Expression of COX-2 and bcl-2 in oral lichen planus lesions and lichenoid reactions

    PubMed Central

    Arreaza, Alven J; Rivera, Helen; Correnti, María

    2014-01-01

    Oral lichen planus and lichenoid reactions are autoimmune type inflammatory conditions of the oral mucosa with similar clinical and histological characteristics. Recent data suggest that oral lichenoid reactions (OLR) present a greater percentage of malignant transformation than oral lichen planus (OLP). Objective To compare the expression of bcl-2 and COX-2 in OLP and OLR. Methods The study population consisted of 65 cases; 34 cases diagnosed as OLR and 31 as OLP. A retrospective study was done, and bcl-2 and COX-2 expression was semiquantitatively analysed. Results Fifty-three per cent (18/34) of the ORL samples tested positive for COX-2, whereas in the OLP group, 81% of the samples (25/31) immunostained positive for COX-2. The Fisher’s exact test for the expression of COX-2 revealed that there are significant differences between the two groups, P = 0.035. With respect to the expression of the bcl-2 protein, 76% (26/34) of the samples were positive in OLR, while 97% (30/31) were positive in the group with OLP. The Fisher’s exact test for the expression of bcl-2 revealed that there are significant statistical differences between the two groups, P = 0.028. Conclusions The expression of bcl-2 and COX-2 was more commonly expressed in OLP when compared with OLR. PMID:24834112

  8. Transverse vibration of Bernoulli Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution

    NASA Astrophysics Data System (ADS)

    Maiz, Santiago; Bambill, Diana V.; Rossit, Carlos A.; Laura, P. A. A.

    2007-06-01

    The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of the machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. An exact solution for the title problem is obtained in closed-form fashion, considering general boundary conditions by means of translational and rotatory springs at both ends. The model allows to analyze the influence of the masses and their rotatory inertia on the dynamic behavior of beams with all the classic boundary conditions, and also, as particular cases, to determine the frequencies of continuous beams.

  9. Spherical solid model system: Exact evaluation of the van der Waals interaction between a microscopic or submacroscopic spherical solid and a deformable fluid interface

    NASA Astrophysics Data System (ADS)

    Wang, Y. Z.; Wang, B.; Xiong, X. M.; Zhang, J. X.

    2011-03-01

    In many previous research work associated with studying the deformation of the fluid interface interacting with a solid, the theoretical calculation of the surface energy density on the deformed fluid interface (or its interaction surface pressure) is often approximately obtained by using the expression for the interaction energy per unit area (or pressure) between two parallel macroscopic plates, e.g. σ(D) = - A / 12 πD2or π(D) = - A / 6 πD3for the van der Waals (vdW) interaction, through invoking the Derjaguin approximation (DA). This approximation however would result in over- or even inaccurate-prediction of the interaction force and the corresponding deformation of the fluid interface due to the invalidation of Derjaguin approximation in cases of microscopic or submacroscopic solids. To circumvent the above limitations existing in the previous DA-based theoretical work, a more accurate and quantitative theoretical model, available for exactly calculating the vdW-induced deformation of a planar fluid interface interacting with a sphere, and the interaction forces taking into account its change, is presented in this paper. The validity and advantage of the new mathematical and physical technique is rigorously verified by comparison with the numerical results on basis of the previous Paraboloid solid (PS) model and the Hamaker's sphere-flat expression (viz. F = - 2 Aa3 / (3 D2( D + 2 a) 2)), as well as its well-known DA-based general form of F / a = - A / 6z p02.

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

    PubMed

    Alam, Md Nur; Akbar, M Ali

    2013-01-01

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

  11. [Transciptome among Mexicans: a large scale methodology to analyze the genetics expression profile of simultaneous samples in muscle, adipose tissue and lymphocytes obtained from the same individual].

    PubMed

    Bastarrachea, Raúl A; López-Alvarenga, Juan Carlos; Kent, Jack W; Laviada-Molina, Hugo A; Cerda-Flores, Ricardo M; Calderón-Garcidueñas, Ana Laura; Torres-Salazar, Amada; Torres-Salazar, Amanda; Nava-González, Edna J; Solis-Pérez, Elizabeth; Gallegos-Cabrales, Esther C; Cole, Shelley A; Comuzzie, Anthony G

    2008-01-01

    We describe the methodology used to analyze multiple transcripts using microarray techniques in simultaneous biopsies of muscle, adipose tissue and lymphocytes obtained from the same individual as part of the standard protocol of the Genetics of Metabolic Diseases in Mexico: GEMM Family Study. We recruited 4 healthy male subjects with BM1 20-41, who signed an informed consent letter. Subjects participated in a clinical examination that included anthropometric and body composition measurements, muscle biopsies (vastus lateralis) subcutaneous fat biopsies anda blood draw. All samples provided sufficient amplified RNA for microarray analysis. Total RNA was extracted from the biopsy samples and amplified for analysis. Of the 48,687 transcript targets queried, 39.4% were detectable in a least one of the studied tissues. Leptin was not detectable in lymphocytes, weakly expressed in muscle, but overexpressed and highly correlated with BMI in subcutaneous fat. Another example was GLUT4, which was detectable only in muscle and not correlated with BMI. Expression level concordance was 0.7 (p< 0.001) for the three tissues studied. We demonstrated the feasibility of carrying out simultaneous analysis of gene expression in multiple tissues, concordance of genetic expression in different tissues, and obtained confidence that this method corroborates the expected biological relationships among LEPand GLUT4. TheGEMM study will provide a broad and valuable overview on metabolic diseases, including obesity and type 2 diabetes.

  12. Exact renormalization group in Batalin-Vilkovisky theory

    NASA Astrophysics Data System (ADS)

    Zucchini, Roberto

    2018-03-01

    In this paper, inspired by the Costello's seminal work [11], we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In the spirit of effective field theory, the BV bracket and Laplacian structure as well as the BV effective action (EA) depend on an effective energy scale. The BV EA at a certain scale satisfies the BV quantum master equation at that scale. The RG flow of the EA is implemented by BV canonical maps intertwining the BV structures at different scales. Infinitesimally, this generates the BV exact renormalization group equation (RGE). We show that BV RG theory can be extended by augmenting the scale parameter space R to its shifted tangent bundle T [1]ℝ. The extra odd direction in scale space allows for a BV RG supersymmetry that constrains the structure of the BV RGE bringing it to Polchinski's form [6]. We investigate the implications of BV RG supersymmetry in perturbation theory. Finally, we illustrate our findings by constructing free models of BV RG flow and EA exhibiting RG supersymmetry in the degree -1 symplectic framework and studying the perturbation theory thereof. We find in particular that the odd partner of effective action describes perturbatively the deviation of the interacting RG flow from its free counterpart.

  13. Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

    NASA Astrophysics Data System (ADS)

    Saakian, David B.

    2017-08-01

    We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

  14. Exact cancellation of emittance growth due to coupled transverse dynamics in solenoids and rf couplers

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dowell, David H.; Zhou, Feng; Schmerge, John

    Weak, rotated magnetic and radio frequency quadrupole fields in electron guns and injectors can couple the beam’s horizontal with vertical motion, introduce correlations between otherwise orthogonal transverse momenta, and reduce the beam brightness. This paper discusses two important sources of coupled transverse dynamics common to most electron injectors. The first is quadrupole focusing followed by beam rotation in a solenoid, and the second coupling comes from a skewed high-power rf coupler or cavity port which has a rotated rf quadrupole field. It is shown that a dc quadrupole field can correct for both types of couplings and exactly cancel theirmore » emittance growths. The degree of cancellation of the rf skew quadrupole emittance is limited by the electron bunch length. Analytic expressions are derived and compared with emittance simulations and measurements.« less

  15. Exact cancellation of emittance growth due to coupled transverse dynamics in solenoids and rf couplers

    DOE PAGES

    Dowell, David H.; Zhou, Feng; Schmerge, John

    2018-01-17

    Weak, rotated magnetic and radio frequency quadrupole fields in electron guns and injectors can couple the beam’s horizontal with vertical motion, introduce correlations between otherwise orthogonal transverse momenta, and reduce the beam brightness. This paper discusses two important sources of coupled transverse dynamics common to most electron injectors. The first is quadrupole focusing followed by beam rotation in a solenoid, and the second coupling comes from a skewed high-power rf coupler or cavity port which has a rotated rf quadrupole field. It is shown that a dc quadrupole field can correct for both types of couplings and exactly cancel theirmore » emittance growths. The degree of cancellation of the rf skew quadrupole emittance is limited by the electron bunch length. Analytic expressions are derived and compared with emittance simulations and measurements.« less

  16. [Evaluation of mimetic expression of schizophrenic and depressed patients by the psychiatrist].

    PubMed

    Schneider, F; Mattes, R; Adam, B; Heimann, H

    1992-01-01

    Facial videos of schizophrenic and depressive patients and of healthy controls when watching both funny and horror films and during emotionally positive or negative interviews were rated by psychiatrists (experts) and students (novices). The observers' task was to rate joy, fear, sadness, and expressivity on a 7-point unipolar intensity scale. The soundless facial videos were presented to each observer for exactly 2.5 min. The observer groups did not differ significantly in their ratings except for sadness. Psychiatrists consistently rated expressed sadness as less intense than students. Facial expressivity and joy were rated as less intense in both patient groups in comparison with healthy controls. Depressives expressed significantly more sadness.

  17. Thermodynamic Bethe ansatz for non-equilibrium steady states: exact energy current and fluctuations in integrable QFT

    NASA Astrophysics Data System (ADS)

    Castro-Alvaredo, Olalla; Chen, Yixiong; Doyon, Benjamin; Hoogeveen, Marianne

    2014-03-01

    We evaluate the exact energy current and scaled cumulant generating function (related to the large-deviation function) in non-equilibrium steady states with energy flow, in any integrable model of relativistic quantum field theory (IQFT) with diagonal scattering. Our derivations are based on various recent results of Bernard and Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures Tl, Tr, and waiting for a long time. We evaluate the current J(Tl, Tr) using the exact QFT density matrix describing these non-equilibrium steady states and using Zamolodchikov’s method of the thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is obtained from the extended fluctuation relations which hold in integrable models. We verify our formula in particular by showing that the conformal field theory (CFT) result is obtained in the high-temperature limit. We analyze numerically our non-equilibrium steady-state TBA equations for three models: the sinh-Gordon model, the roaming trajectories model, and the sine-Gordon model at a particular reflectionless point. Based on the numerics, we conjecture that an infinite family of non-equilibrium c-functions, associated with the scaled cumulants, can be defined, which we interpret physically. We study the full scaled distribution function and find that it can be described by a set of independent Poisson processes. Finally, we show that the ‘additivity’ property of the current, which is known to hold in CFT and was proposed to hold more generally, does not hold in general IQFT—that is, J(Tl, Tr) is not of the form f(Tl) - f(Tr).

  18. An Exactly Solvable Model for the Spread of Disease

    ERIC Educational Resources Information Center

    Mickens, Ronald E.

    2012-01-01

    We present a new SIR epidemiological model whose exact analytical solution can be calculated. In this model, unlike previous models, the infective population becomes zero at a finite time. Remarkably, these results can be derived from only an elementary knowledge of differential equations.

  19. Outstanding performance of configuration interaction singles and doubles using exact exchange Kohn-Sham orbitals in real-space numerical grid method

    NASA Astrophysics Data System (ADS)

    Lim, Jaechang; Choi, Sunghwan; Kim, Jaewook; Kim, Woo Youn

    2016-12-01

    To assess the performance of multi-configuration methods using exact exchange Kohn-Sham (KS) orbitals, we implemented configuration interaction singles and doubles (CISD) in a real-space numerical grid code. We obtained KS orbitals with the exchange-only optimized effective potential under the Krieger-Li-Iafrate (KLI) approximation. Thanks to the distinctive features of KLI orbitals against Hartree-Fock (HF), such as bound virtual orbitals with compact shapes and orbital energy gaps similar to excitation energies; KLI-CISD for small molecules shows much faster convergence as a function of simulation box size and active space (i.e., the number of virtual orbitals) than HF-CISD. The former also gives more accurate excitation energies with a few dominant configurations than the latter, even with many more configurations. The systematic control of basis set errors is straightforward in grid bases. Therefore, grid-based multi-configuration methods using exact exchange KS orbitals provide a promising new way to make accurate electronic structure calculations.

  20. Kohn-Sham approach to quantum electrodynamical density-functional theory: Exact time-dependent effective potentials in real space.

    PubMed

    Flick, Johannes; Ruggenthaler, Michael; Appel, Heiko; Rubio, Angel

    2015-12-15

    The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account.

  1. High Resolution Thermometry for EXACT

    NASA Technical Reports Server (NTRS)

    Panek, J. S.; Nash, A. E.; Larson, M.; Mulders, N.

    2000-01-01

    High Resolution Thermometers (HRTs) based on SQUID detection of the magnetization of a paramagnetic salt or a metal alloy has been commonly used for sub-nano Kelvin temperature resolution in low temperature physics experiments. The main applications to date have been for temperature ranges near the lambda point of He-4 (2.177 K). These thermometers made use of materials such as Cu(NH4)2Br4 *2H2O, GdCl3, or PdFe. None of these materials are suitable for EXACT, which will explore the region of the He-3/He-4 tricritical point at 0.87 K. The experiment requirements and properties of several candidate paramagnetic materials will be presented, as well as preliminary test results.

  2. Frames for exact inversion of the rank order coder.

    PubMed

    Masmoudi, Khaled; Antonini, Marc; Kornprobst, Pierre

    2012-02-01

    Our goal is to revisit rank order coding by proposing an original exact decoding procedure for it. Rank order coding was proposed by Thorpe et al. who stated that the order in which the retina cells are activated encodes for the visual stimulus. Based on this idea, the authors proposed in [1] a rank order coder/decoder associated to a retinal model. Though, it appeared that the decoding procedure employed yields reconstruction errors that limit the model bit-cost/quality performances when used as an image codec. The attempts made in the literature to overcome this issue are time consuming and alter the coding procedure, or are lacking mathematical support and feasibility for standard size images. Here we solve this problem in an original fashion by using the frames theory, where a frame of a vector space designates an extension for the notion of basis. Our contribution is twofold. First, we prove that the analyzing filter bank considered is a frame, and then we define the corresponding dual frame that is necessary for the exact image reconstruction. Second, to deal with the problem of memory overhead, we design a recursive out-of-core blockwise algorithm for the computation of this dual frame. Our work provides a mathematical formalism for the retinal model under study and defines a simple and exact reverse transform for it with over than 265 dB of increase in the peak signal-to-noise ratio quality compared to [1]. Furthermore, the framework presented here can be extended to several models of the visual cortical areas using redundant representations.

  3. Exact goodness-of-fit tests for Markov chains.

    PubMed

    Besag, J; Mondal, D

    2013-06-01

    Goodness-of-fit tests are useful in assessing whether a statistical model is consistent with available data. However, the usual χ² asymptotics often fail, either because of the paucity of the data or because a nonstandard test statistic is of interest. In this article, we describe exact goodness-of-fit tests for first- and higher order Markov chains, with particular attention given to time-reversible ones. The tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple Monte Carlo sampling or by Markov chain Monte Carlo. They apply both to single and to multiple sequences and allow a free choice of test statistic. Three examples are given. The first concerns multiple sequences of dry and wet January days for the years 1948-1983 at Snoqualmie Falls, Washington State, and suggests that standard analysis may be misleading. The second one is for a four-state DNA sequence and lends support to the original conclusion that a second-order Markov chain provides an adequate fit to the data. The last one is six-state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first-order reversible Markov chain at 6 picosecond time steps. © 2013, The International Biometric Society.

  4. Comment on ‘Information hidden in the velocity distribution of ions and the exact kinetic Bohm criterion’

    NASA Astrophysics Data System (ADS)

    Mustafaev, A. S.; Sukhomlinov, V. S.; Timofeev, N. A.

    2018-03-01

    This Comment is devoted to some mathematical inaccuracies made by the authors of the paper ‘Information hidden in the velocity distribution of ions and the exact kinetic Bohm criterion’ (Plasma Sources Science and Technology 26 055003). In the Comment, we show that the diapason of plasma parameters for the validity of the theoretical results obtained by the authors was defined incorrectly; we made a more accurate definition of this diapason. As a result, we show that it is impossible to confirm or refute the feasibility of the Bohm kinetic criterion on the basis of the data of the cited paper.

  5. Large-amplitude hydromagnetic waves in collisionless relativistic plasma - Exact solution for the fast-mode magnetoacoustic wave

    NASA Technical Reports Server (NTRS)

    Barnes, A.

    1983-01-01

    An exact nonlinear solution is found to the relativistic kinetic and electrodynamic equations (in their hydromagnetic limit) that describes the large-amplitude fast-mode magnetoacoustic wave propagating normal to the magnetic field in a collisionless, previously uniform plasma. It is pointed out that a wave of this kind will be generated by transverse compression of any collisionless plasma. The solution is in essence independent of the detailed form of the particle momentum distribution functions. The solution is obtained, in part, through the method of characteristics; the wave exhibits the familiar properties of steepening and shock formation. A detailed analysis is given of the ultrarelativistic limit of this wave.

  6. Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.

    PubMed

    Yan, Zhenya; Konotop, V V

    2009-09-01

    It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the (1+3) space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.

  7. Pharmer: efficient and exact pharmacophore search.

    PubMed

    Koes, David Ryan; Camacho, Carlos J

    2011-06-27

    Pharmacophore search is a key component of many drug discovery efforts. Pharmer is a new computational approach to pharmacophore search that scales with the breadth and complexity of the query, not the size of the compound library being screened. Two novel methods for organizing pharmacophore data, the Pharmer KDB-tree and Bloom fingerprints, enable Pharmer to perform an exact pharmacophore search of almost two million structures in less than a minute. In general, Pharmer is more than an order of magnitude faster than existing technologies. The complete source code is available under an open-source license at http://pharmer.sourceforge.net .

  8. Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan-Porsezian-Daniel model

    NASA Astrophysics Data System (ADS)

    Manafian, Jalil; Foroutan, Mohammadreza; Guzali, Aref

    2017-11-01

    This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.

  9. Stability: Conservation laws, Painlevé analysis and exact solutions for S-KP equation in coupled dusty plasma

    NASA Astrophysics Data System (ADS)

    EL-Kalaawy, O. H.; Moawad, S. M.; Wael, Shrouk

    The propagation of nonlinear waves in unmagnetized strongly coupled dusty plasma with Boltzmann distributed electrons, iso-nonthermal distributed ions and negatively charged dust grains is considered. The basic set of fluid equations is reduced to the Schamel Kadomtsev-Petviashvili (S-KP) equation by using the reductive perturbation method. The variational principle and conservation laws of S-KP equation are obtained. It is shown that the S-KP equation is non-integrable using Painlevé analysis. A set of new exact solutions are obtained by auto-Bäcklund transformations. The stability analysis is discussed for the existence of dust acoustic solitary waves (DASWs) and it is found that the physical parameters have strong effects on the stability criterion. In additional to, the electric field and the true Mach number of this solution are investigated. Finally, we will study the physical meanings of solutions.

  10. From quantum affine groups to the exact dynamical correlation function of the Heisenberg model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bougourzi, A.H.; Couture, M.; Kacir, M.

    1997-01-20

    The exact form factors of the Heisenberg models XXX and XXZ have been recently computed through the quantum affine symmetry of XXZ model in the thermodynamic limit. The authors use them to derive an exact formula for the contribution of two spinons to the dynamical correlation function of XXX model at zero temperature.

  11. DFT treatment of transport through Anderson junction: exact results and approximations

    NASA Astrophysics Data System (ADS)

    Burke, Kieron

    2012-02-01

    Since the pioneering break-junction experiments of Reed and Tour measuring the conductance of dithiolated benzene between gold leads, many researchers in physics and chemistry have been calculating conductance for such systems using density functional theory (DFT). Off resonance, the predicted current is often 10-100 times larger than that measured. This error is often ascribed to the application of ground-state DFT to a non-equilibrium problem. I will argue that, in fact, this is largely due to errors in the density functional approximations in popular use, rather than necessarily errors in the methodology. A stark illustration of this principle is the ability of DFT to reproduce the exact transmission through an Anderson junction at zero-temperature and weak bias, including the Kondo plateau, but only if the exact ground-state density functional is used. In fact, this case can be used to reverse-engineer the exact functional for this problem. Popular approximations can also be tested, including both smooth and discontinuous functionals of the density, as well as symmetry-broken approaches. [4pt] [1] Kondo effect given exactly by density functional theory, J. P. Bergfield, Z. Liu, K. Burke, and C. A. Stafford, arXiv:1106.3104; [0pt] [2] Broadening of the Derivative Discontinuity in Density Functional Theory, F. Evers, and P. Schmitteckert, arXiv:1106.3658; [0pt] [3] DFT-based transport calculations, Friedel's sum rule and the Kondo effect, P. Tr"oster, P. Schmitteckert, and F. Evers, arXiv:1106.3669; [0pt] [4] Towards a description of the Kondo effect using time-dependent density functional theory, G. Stefanucci, and S. Kurth, arXiv:1106.3728.

  12. Exact solutions for species tree inference from discordant gene trees.

    PubMed

    Chang, Wen-Chieh; Górecki, Paweł; Eulenstein, Oliver

    2013-10-01

    Phylogenetic analysis has to overcome the grant challenge of inferring accurate species trees from evolutionary histories of gene families (gene trees) that are discordant with the species tree along whose branches they have evolved. Two well studied approaches to cope with this challenge are to solve either biologically informed gene tree parsimony (GTP) problems under gene duplication, gene loss, and deep coalescence, or the classic RF supertree problem that does not rely on any biological model. Despite the potential of these problems to infer credible species trees, they are NP-hard. Therefore, these problems are addressed by heuristics that typically lack any provable accuracy and precision. We describe fast dynamic programming algorithms that solve the GTP problems and the RF supertree problem exactly, and demonstrate that our algorithms can solve instances with data sets consisting of as many as 22 taxa. Extensions of our algorithms can also report the number of all optimal species trees, as well as the trees themselves. To better asses the quality of the resulting species trees that best fit the given gene trees, we also compute the worst case species trees, their numbers, and optimization score for each of the computational problems. Finally, we demonstrate the performance of our exact algorithms using empirical and simulated data sets, and analyze the quality of heuristic solutions for the studied problems by contrasting them with our exact solutions.

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

    NASA Astrophysics Data System (ADS)

    Banerjee, Supratik; Kritsuk, Alexei G.

    2017-11-01

    Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (S. Galtier and S. Banerjee, Phys. Rev. Lett. 107, 134501 (2011), 10.1103/PhysRevLett.107.134501; S. Banerjee and S. Galtier, Phys. Rev. E 87, 013019 (2013), 10.1103/PhysRevE.87.013019), the current exact relation shows that the pressure dilatation terms play practically no role in the energy cascade. Both the flux and source terms are written in terms of two-point differences. Sources enter the relation in a form of mixed second-order structure functions. Unlike the kinetic and thermodynamic potential energies, the gravitational contribution is absent from the flux term. An estimate shows that, for the isotropic case, the correlation between density and gravitational acceleration may play an important role in modifying the energy transfer in self-gravitating turbulence. The exact relation is also written in an alternative form in terms of two-point correlation functions, which is then used to describe scale-by-scale energy budget in spectral space.

  14. An exact solution for the steady state phase distribution in an array of oscillators coupled on a hexagonal lattice

    NASA Technical Reports Server (NTRS)

    Pogorzelski, Ronald J.

    2004-01-01

    When electronic oscillators are coupled to nearest neighbors to form an array on a hexagonal lattice, the planar phase distributions desired for excitation of a phased array antenna are not steady state solutions of the governing non-linear equations describing the system. Thus the steady state phase distribution deviates from planar. It is shown to be possible to obtain an exact solution for the steady state phase distribution and thus determine the deviation from the desired planar distribution as a function of beam steering angle.

  15. Stratified exact tests for the weak causal null hypothesis in randomized trials with a binary outcome.

    PubMed

    Chiba, Yasutaka

    2017-09-01

    Fisher's exact test is commonly used to compare two groups when the outcome is binary in randomized trials. In the context of causal inference, this test explores the sharp causal null hypothesis (i.e. the causal effect of treatment is the same for all subjects), but not the weak causal null hypothesis (i.e. the causal risks are the same in the two groups). Therefore, in general, rejection of the null hypothesis by Fisher's exact test does not mean that the causal risk difference is not zero. Recently, Chiba (Journal of Biometrics and Biostatistics 2015; 6: 244) developed a new exact test for the weak causal null hypothesis when the outcome is binary in randomized trials; the new test is not based on any large sample theory and does not require any assumption. In this paper, we extend the new test; we create a version of the test applicable to a stratified analysis. The stratified exact test that we propose is general in nature and can be used in several approaches toward the estimation of treatment effects after adjusting for stratification factors. The stratified Fisher's exact test of Jung (Biometrical Journal 2014; 56: 129-140) tests the sharp causal null hypothesis. This test applies a crude estimator of the treatment effect and can be regarded as a special case of our proposed exact test. Our proposed stratified exact test can be straightforwardly extended to analysis of noninferiority trials and to construct the associated confidence interval. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  16. Exact mean-energy expansion of Ginibre's gas for coupling constants Γ =2 ×(oddinteger)

    NASA Astrophysics Data System (ADS)

    Salazar, R.; Téllez, G.

    2017-12-01

    Using the approach of a Vandermonde determinant to the power Γ =Q2/kBT expansion on monomial functions, a way to find the excess energy Uexc of the two-dimensional one-component plasma (2DOCP) on hard and soft disks (or a Dyson gas) for odd values of Γ /2 is provided. At Γ =2 , the present study not only corroborates the result for the particle-particle energy contribution of the Dyson gas found by Shakirov [Shakirov, Phys. Lett. A 375, 984 (2011), 10.1016/j.physleta.2011.01.004] by using an alternative approach, but also provides the exact N -finite expansion of the excess energy of the 2DOCP on the hard disk. The excess energy is fitted to the ansatz of the form Uexc=K1N +K2√{N }+K3+K4/N +O (1 /N2) to study the finite-size correction, with Ki coefficients and N the number of particles. In particular, the bulk term of the excess energy is in agreement with the well known result of Jancovici for the hard disk in the thermodynamic limit [Jancovici, Phys. Rev. Lett. 46, 386 (1981), 10.1103/PhysRevLett.46.386]. Finally, an expression is found for the pair correlation function which still keeps a link with the random matrix theory via the kernel in the Ginibre ensemble [Ginibre, J. Math. Phys. 6, 440 (1965), 10.1063/1.1704292] for odd values of Γ /2 . A comparison between the analytical two-body density function and histograms obtained with Monte Carlo simulations for small systems and Γ =2 ,6 ,10 ,... shows that the approach described in this paper may be used to study analytically the crossover behavior from systems in the fluid phase to small crystals.

  17. Power-law tails and non-Markovian dynamics in open quantum systems: An exact solution from Keldysh field theory

    NASA Astrophysics Data System (ADS)

    Chakraborty, Ahana; Sensarma, Rajdeep

    2018-03-01

    The Born-Markov approximation is widely used to study the dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to a noninteracting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has nonanalyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power-law tails. The Green's functions show a short-time "quasi"-Markovian exponential decay before crossing over to a power-law tail governed by the nonanalyticity of the spectral function. We study a system of bosons (fermions) hopping on a one-dimensional lattice, where each site is coupled linearly to an independent bath of noninteracting bosons (fermions). We obtain exact expressions for the Green's functions of this system, which show power-law decay ˜|t - t'|-3 /2 . We use these to calculate the density and current profile, as well as unequal-time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long-time power-law tails |t - t'|-3 characteristic of non-Markovian dynamics. We show that the power-law decays survive in the presence of interparticle interaction in the system, but the crossover time scale is shifted to larger values with increasing interaction strength.

  18. CD4+ T-cell clones obtained from cattle chronically infected with Fasciola hepatica and specific for adult worm antigen express both unrestricted and Th2 cytokine profiles.

    PubMed Central

    Brown, W C; Davis, W C; Dobbelaere, D A; Rice-Ficht, A C

    1994-01-01

    The well-established importance of helper T (Th)-cell subsets in immunity and immunoregulation of many experimental helminth infections prompted a detailed study of the cellular immune response against Fasciola hepatica in the natural bovine host. T-cell lines established from two cattle infected with F. hepatica were characterized for the expression of T-cell surface markers and proliferative responses against F. hepatica adult worm antigen. Parasite-specific T-cell lines contained a mixture of CD4+, CD8+, and gamma/delta T-cell-receptor-bearing T cells. However, cell lines containing either fewer than 10% CD8+ T cells or depleted of gamma/delta T cells proliferated vigorously against F. hepatica antigen, indicating that these T-cell subsets are not required for proliferative responses in vitro. Seventeen F. hepatica-specific CD4+ Th-cell clones were examined for cytokine expression following concanavalin A stimulation. Biological assays to measure interleukin-2 (IL-2) or IL-4, gamma interferon (IFN-gamma), and tumor necrosis factor and Northern (RNA) blot analysis to verify the expression of IL-2, IL-4, and IFN-gamma revealed that the Th-cell clones expressed a spectrum of cytokine profiles. Several Th-cell clones were identified as Th2 cells by the strong expression of IL-4 but little or no IL-2 or IFN-gamma mRNA. The majority of Th-cell clones were classified as Th0 cells by the expression of either all three cytokines or combinations of IL-2 and IL-4 or IL-4 and IFN-gamma. No Th1-cell clones were obtained. All of the Th-cell clones expressed a typical memory cell surface phenotype, characterized as CD45Rlow, and all expressed the lymph node homing receptor (L selectin). These results are the first to describe cytokine responses of F. hepatica-specific T cells obtained from infected cattle and extend our previous analysis of Th0 and Th1 cells from cattle immune to Babesia bovis (W. C. Brown, V. M. Woods, D. A. E. Dobbelaere, and K. S. Logan, Infect. Immun. 61

  19. Exact and approximate aspects of the boson expansion theories

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tamura, T.; Weeks, K.J.; Pedrocchi, V.G.

    1981-03-01

    It is shown that a boson expansion theory of the Kishimoto-Tamura type not only maps the operators exactly but also the space, and, consequently, the matrix elements of the fermion system onto those of the bosons. Significance of approximations made in calculations is also discussed.

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

    NASA Astrophysics Data System (ADS)

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

    2017-10-01

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

  1. Facial expressions recognition with an emotion expressive robotic head

    NASA Astrophysics Data System (ADS)

    Doroftei, I.; Adascalitei, F.; Lefeber, D.; Vanderborght, B.; Doroftei, I. A.

    2016-08-01

    The purpose of this study is to present the preliminary steps in facial expressions recognition with a new version of an expressive social robotic head. So, in a first phase, our main goal was to reach a minimum level of emotional expressiveness in order to obtain nonverbal communication between the robot and human by building six basic facial expressions. To evaluate the facial expressions, the robot was used in some preliminary user studies, among children and adults.

  2. Classical Control System Design: A non-Graphical Method for Finding the Exact System Parameters

    NASA Astrophysics Data System (ADS)

    Hussein, Mohammed Tawfik

    2008-06-01

    The Root Locus method of control system design was developed in the 1940's. It is a set of rules that helps in sketching the path traced by the roots of the closed loop characteristic equation of the system, as a parameter such as a controller gain, k, is varied. The procedure provides approximate sketching guidelines. Designs on control systems using the method are therefore not exact. This paper aims at a non-graphical method for finding the exact system parameters to place a pair of complex conjugate poles on a specified damping ratio line. The overall procedure is based on the exact solution of complex equations on the PC using numerical methods.

  3. Algebraic Construction of Exact Difference Equations from Symmetry of Equations

    NASA Astrophysics Data System (ADS)

    Itoh, Toshiaki

    2009-09-01

    Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

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

    NASA Astrophysics Data System (ADS)

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

    2017-05-01

    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.

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

    PubMed

    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.

  6. Obtaining highly excited eigenstates of the localized XX chain via DMRG-X

    NASA Astrophysics Data System (ADS)

    Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A.; Sondhi, S. L.

    2017-10-01

    We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

  7. An exact noniterative linear method for locating sources based on measuring receiver arrival times.

    PubMed

    Militello, C; Buenafuente, S R

    2007-06-01

    In this paper an exact, linear solution to the source localization problem based on the time of arrival at the receivers is presented. The method is unique in that the source's position can be obtained by solving a system of linear equations, three for a plane and four for a volume. This simplification means adding an additional receiver to the minimum mathematically required (3+1 in two dimensions and 4+1 in three dimensions). The equations are easily worked out for any receiver configuration and their geometrical interpretation is straightforward. Unlike other methods, the system of reference used to describe the receivers' positions is completely arbitrary. The relationship between this method and previously published ones is discussed, showing how the present, more general, method overcomes nonlinearity and unknown dependency issues.

  8. Clinical Significance of SASH1 Expression in Glioma

    PubMed Central

    Yang, Liu; Zhang, Haitao; Yao, Qi; Yan, Yingying; Wu, Ronghua; Liu, Mei

    2015-01-01

    Objective. SAM and SH3 domain containing 1 (SASH1) is a recently discovered tumor suppressor gene. The role of SASH1 in glioma has not yet been described. We investigated SASH1 expression in glioma cases to determine its clinical significance on glioma pathogenesis and prognosis. Methods. We produced tissue microarrays using 121 patient-derived glioma samples and 30 patient-derived nontumor cerebral samples. Immunohistochemistry and Western blotting were used to evaluate SASH1 expression. We used Fisher's exact tests to determine relationships between SASH1 expression and clinicopathological characteristics; Cox regression analysis to evaluate the independency of different SASH1 expression; Kaplan-Meier analysis to determine any correlation of SASH1 expression with survival rate. Results. SASH1 expression was closely correlated with the WHO glioma grade. Of the 121 cases, 66.9% with low SASH1 expression were mostly grade III-IV cases, whereas 33.1% with high SASH1 expression were mostly grades I-II. Kaplan-Meier analysis revealed a significant positive correlation between SASH1 expression and postoperative survival. Conclusions. SASH1 was widely expressed in normal and low-grade glioma tissues. SASH1 expression strongly correlated with glioma grades, showing higher expression at a lower grade, which decreased significantly as grade increased. Furthermore, SASH1 expression was positively correlated with better postoperative survival in patients with glioma. PMID:26424902

  9. Clinical Significance of SASH1 Expression in Glioma.

    PubMed

    Yang, Liu; Zhang, Haitao; Yao, Qi; Yan, Yingying; Wu, Ronghua; Liu, Mei

    2015-01-01

    SAM and SH3 domain containing 1 (SASH1) is a recently discovered tumor suppressor gene. The role of SASH1 in glioma has not yet been described. We investigated SASH1 expression in glioma cases to determine its clinical significance on glioma pathogenesis and prognosis. We produced tissue microarrays using 121 patient-derived glioma samples and 30 patient-derived nontumor cerebral samples. Immunohistochemistry and Western blotting were used to evaluate SASH1 expression. We used Fisher's exact tests to determine relationships between SASH1 expression and clinicopathological characteristics; Cox regression analysis to evaluate the independency of different SASH1 expression; Kaplan-Meier analysis to determine any correlation of SASH1 expression with survival rate. SASH1 expression was closely correlated with the WHO glioma grade. Of the 121 cases, 66.9% with low SASH1 expression were mostly grade III-IV cases, whereas 33.1% with high SASH1 expression were mostly grades I-II. Kaplan-Meier analysis revealed a significant positive correlation between SASH1 expression and postoperative survival. SASH1 was widely expressed in normal and low-grade glioma tissues. SASH1 expression strongly correlated with glioma grades, showing higher expression at a lower grade, which decreased significantly as grade increased. Furthermore, SASH1 expression was positively correlated with better postoperative survival in patients with glioma.

  10. Exact harmonic solutions to Guyer-Krumhansl-type equation and application to heat transport in thin films

    NASA Astrophysics Data System (ADS)

    Zhukovsky, K.; Oskolkov, D.

    2018-03-01

    A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer-Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.

  11. Mapping Antiretroviral Drugs in Tissue by IR-MALDESI MSI Coupled to the Q Exactive and Comparison with LC-MS/MS SRM Assay

    NASA Astrophysics Data System (ADS)

    Barry, Jeremy A.; Robichaud, Guillaume; Bokhart, Mark T.; Thompson, Corbin; Sykes, Craig; Kashuba, Angela D. M.; Muddiman, David C.

    2014-12-01

    This work describes the coupling of the IR-MALDESI imaging source with the Q Exactive mass spectrometer. IR-MALDESI MSI was used to elucidate the spatial distribution of several HIV drugs in cervical tissues that had been incubated in either a low or high concentration. Serial sections of those analyzed by IR-MALDESI MSI were homogenized and analyzed by LC-MS/MS to quantify the amount of each drug present in the tissue. By comparing the two techniques, an agreement between the average intensities from the imaging experiment and the absolute quantities for each drug was observed. This correlation between these two techniques serves as a prerequisite to quantitative IR-MALDESI MSI. In addition, a targeted MS2 imaging experiment was also conducted to demonstrate the capabilities of the Q Exactive and to highlight the added selectivity that can be obtained with SRM or MRM imaging experiments.

  12. Monte Carlo Simulations Comparing Fisher Exact Test and Unequal Variances t Test for Analysis of Differences Between Groups in Brief Hospital Lengths of Stay.

    PubMed

    Dexter, Franklin; Bayman, Emine O; Dexter, Elisabeth U

    2017-12-01

    We examined type I and II error rates for analysis of (1) mean hospital length of stay (LOS) versus (2) percentage of hospital LOS that are overnight. These 2 end points are suitable for when LOS is treated as a secondary economic end point. We repeatedly resampled LOS for 5052 discharges of thoracoscopic wedge resections and lung lobectomy at 26 hospitals. Unequal variances t test (Welch method) and Fisher exact test both were conservative (ie, type I error rate less than nominal level). The Wilcoxon rank sum test was included as a comparator; the type I error rates did not differ from the nominal level of 0.05 or 0.01. Fisher exact test was more powerful than the unequal variances t test at detecting differences among hospitals; estimated odds ratio for obtaining P < .05 with Fisher exact test versus unequal variances t test = 1.94, with 95% confidence interval, 1.31-3.01. Fisher exact test and Wilcoxon-Mann-Whitney had comparable statistical power in terms of differentiating LOS between hospitals. For studies with LOS to be used as a secondary end point of economic interest, there is currently considerable interest in the planned analysis being for the percentage of patients suitable for ambulatory surgery (ie, hospital LOS equals 0 or 1 midnight). Our results show that there need not be a loss of statistical power when groups are compared using this binary end point, as compared with either Welch method or Wilcoxon rank sum test.

  13. The escape of high explosive products: An exact-solution problem for verification of hydrodynamics codes

    DOE PAGES

    Doebling, Scott William

    2016-10-22

    This paper documents the escape of high explosive (HE) products problem. The problem, first presented by Fickett & Rivard, tests the implementation and numerical behavior of a high explosive detonation and energy release model and its interaction with an associated compressible hydrodynamics simulation code. The problem simulates the detonation of a finite-length, one-dimensional piece of HE that is driven by a piston from one end and adjacent to a void at the other end. The HE equation of state is modeled as a polytropic ideal gas. The HE detonation is assumed to be instantaneous with an infinitesimal reaction zone. Viamore » judicious selection of the material specific heat ratio, the problem has an exact solution with linear characteristics, enabling a straightforward calculation of the physical variables as a function of time and space. Lastly, implementation of the exact solution in the Python code ExactPack is discussed, as are verification cases for the exact solution code.« less

  14. Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

    PubMed

    Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

    2014-04-08

    Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

  15. Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

    PubMed Central

    Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

    2014-01-01

    Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719

  16. Exact exchange and Wilson-Levy correlation: a pragmatic device for studying complex weakly-bonded systems.

    PubMed

    Walsh, T R

    2005-02-07

    The Wilson-Levy (WL) correlation functional is used together with Hartree-Fock (HF) theory to evaluate interaction energies at intermediate separations (i.e. around equilibrium separation) for several weakly-bonded systems. The HF+WL approach reproduces binding trends for all complexes studied: selected rare-gas dimers, isomers of the methane dimer, benzene dimer and naphthalene dimer, and base-pair stacking structures for pyrimidine, cytosine, uracil and guanine dimers. These HF+WL data are contrasted against results obtained from some popular functionals (including B3LYP and PBE), as well as two newly-developed functionals, X3LYP and xPBE. The utility of HF+WL, with reference to exact-exchange (EXX) density-functional theory, is discussed in terms of a suggested EXXWL exchange-correlation functional.

  17. 76 FR 35259 - Samaritan Pharmaceuticals, Inc., Seaena, Inc., Seirios International, Inc. (f/k/a Exactly...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-06-16

    ...., Seirios International, Inc. (f/k/a Exactly Sportswear, Inc.), et al.; Order of Suspension of Trading June 14, 2011. Samaritan Pharmaceuticals, Inc., Seaena, Inc., Seirios International, Inc. (f/k/a Exactly Sportswear, Inc.), Sento Corp., Shoe Pavilion, Inc., Silver Eagle Resources Ltd. (n/k/a Mercator Minerals Ltd...

  18. Performance Evaluation of the Q Exactive HF-X for Shotgun Proteomics.

    PubMed

    Kelstrup, Christian D; Bekker-Jensen, Dorte B; Arrey, Tabiwang N; Hogrebe, Alexander; Harder, Alexander; Olsen, Jesper V

    2018-01-05

    Progress in proteomics is mainly driven by advances in mass spectrometric (MS) technologies. Here we benchmarked the performance of the latest MS instrument in the benchtop Orbitrap series, the Q Exactive HF-X, against its predecessor for proteomics applications. A new peak-picking algorithm, a brighter ion source, and optimized ion transfers enable productive MS/MS acquisition above 40 Hz at 7500 resolution. The hardware and software improvements collectively resulted in improved peptide and protein identifications across all comparable conditions, with an increase of up to 50 percent at short LC-MS gradients, yielding identification rates of more than 1000 unique peptides per minute. Alternatively, the Q Exactive HF-X is capable of achieving the same proteome coverage as its predecessor in approximately half the gradient time or at 10-fold lower sample loads. The Q Exactive HF-X also enables rapid phosphoproteomics with routine analysis of more than 5000 phosphopeptides with short single-shot 15 min LC-MS/MS measurements, or 16 700 phosphopeptides quantified across ten conditions in six gradient hours using TMT10-plex and offline peptide fractionation. Finally, exciting perspectives for data-independent acquisition are highlighted with reproducible identification of 55 000 unique peptides covering 5900 proteins in half an hour of MS analysis.

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

    NASA Astrophysics Data System (ADS)

    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.

  20. PLNoise: a package for exact numerical simulation of power-law noises

    NASA Astrophysics Data System (ADS)

    Milotti, Edoardo

    2006-08-01

    Many simulations of stochastic processes require colored noises: here I describe a small program library that generates samples with a tunable power-law spectral density: the algorithm can be modified to generate more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen in the case of astronomical data, see e.g. [N.R. Lomb, Astrophys. Space Sci. 39 (1976) 447]. The method is exact in the sense that it reproduces a process that is theoretically guaranteed to produce a range-limited power-law spectrum 1/f with -1<β⩽1. The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v1_0.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Programming language used: ANSI C Computer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler No. of lines in distributed program, including test data, etc.:6238 No. of bytes in distributed program, including test data, etc.:52 387 Distribution format:tar.gz RAM: The code of the test program is very compact (about 50 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run (like the one discussed in Section 4 in the long write-up) with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes. External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B

  1. Exact parallel algorithms for some members of the traveling salesman problem family

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Pekny, J.F.

    1989-01-01

    The traveling salesman problem and its many generalizations comprise one of the best known combinatorial optimization problem families. Most members of the family are NP-complete problems so that exact algorithms require an unpredictable and sometimes large computational effort. Parallel computers offer hope for providing the power required to meet these demands. A major barrier to applying parallel computers is the lack of parallel algorithms. The contributions presented in this thesis center around new exact parallel algorithms for the asymmetric traveling salesman problem (ATSP), prize collecting traveling salesman problem (PCTSP), and resource constrained traveling salesman problem (RCTSP). The RCTSP is amore » particularly difficult member of the family since finding a feasible solution is an NP-complete problem. An exact sequential algorithm is also presented for the directed hamiltonian cycle problem (DHCP). The DHCP algorithm is superior to current heuristic approaches and represents the first exact method applicable to large graphs. Computational results presented for each of the algorithms demonstrates the effectiveness of combining efficient algorithms with parallel computing methods. Performance statistics are reported for randomly generated ATSPs with 7,500 cities, PCTSPs with 200 cities, RCTSPs with 200 cities, DHCPs with 3,500 vertices, and assignment problems of size 10,000. Sequential results were collected on a Sun 4/260 engineering workstation, while parallel results were collected using a 14 and 100 processor BBN Butterfly Plus computer. The computational results represent the largest instances ever solved to optimality on any type of computer.« less

  2. Exact results in 3d N = 2 Spin(7) gauge theories with vector and spinor matters

    NASA Astrophysics Data System (ADS)

    Nii, Keita

    2018-05-01

    We study three-dimensional N = 2 Spin(7) gauge theories with N S spinorial matters and with N f vectorial matters. The quantum Coulomb branch on the moduli space of vacua is one- or two-dimensional depending on the matter contents. For particular values of ( N f , N S ), we find s-confinement phases and derive exact superpotentials. The 3d dynamics of Spin(7) is connected to the 4d dynamics via KK-monopoles. Along the Higgs branch of the Spin(7) theories, we obtain 3d N = 2 G 2 or SU(4) theories and some of them lead to new s-confinement phases. As a check of our analysis we compute superconformal indices for these theories.

  3. Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

    DOE PAGES

    Smith, J. C.; Pribram-Jones, A.; Burke, K.

    2016-06-14

    Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

  4. Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Smith, J. C.; Pribram-Jones, A.; Burke, K.

    Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

  5. EXACT DISTRIBUTIONS OF INTRACLASS CORRELATION AND CRONBACH'S ALPHA WITH GAUSSIAN DATA AND GENERAL COVARIANCE.

    PubMed

    Kistner, Emily O; Muller, Keith E

    2004-09-01

    Intraclass correlation and Cronbach's alpha are widely used to describe reliability of tests and measurements. Even with Gaussian data, exact distributions are known only for compound symmetric covariance (equal variances and equal correlations). Recently, large sample Gaussian approximations were derived for the distribution functions. New exact results allow calculating the exact distribution function and other properties of intraclass correlation and Cronbach's alpha, for Gaussian data with any covariance pattern, not just compound symmetry. Probabilities are computed in terms of the distribution function of a weighted sum of independent chi-square random variables. New F approximations for the distribution functions of intraclass correlation and Cronbach's alpha are much simpler and faster to compute than the exact forms. Assuming the covariance matrix is known, the approximations typically provide sufficient accuracy, even with as few as ten observations. Either the exact or approximate distributions may be used to create confidence intervals around an estimate of reliability. Monte Carlo simulations led to a number of conclusions. Correctly assuming that the covariance matrix is compound symmetric leads to accurate confidence intervals, as was expected from previously known results. However, assuming and estimating a general covariance matrix produces somewhat optimistically narrow confidence intervals with 10 observations. Increasing sample size to 100 gives essentially unbiased coverage. Incorrectly assuming compound symmetry leads to pessimistically large confidence intervals, with pessimism increasing with sample size. In contrast, incorrectly assuming general covariance introduces only a modest optimistic bias in small samples. Hence the new methods seem preferable for creating confidence intervals, except when compound symmetry definitely holds.

  6. Production of a sterile species via active-sterile mixing: An exactly solvable model

    NASA Astrophysics Data System (ADS)

    Boyanovsky, D.

    2007-11-01

    The production of a sterile species via active-sterile mixing in a thermal medium is studied in an exactly solvable model. The exact time evolution of the sterile distribution function is determined by the dispersion relations and damping rates Γ1,2 for the quasiparticle modes. These depend on γ˜=Γaa/2ΔE, with Γaa the interaction rate of the active species in absence of mixing and ΔE the oscillation frequency in the medium without damping. γ˜≪1, γ˜≫1 describe the weak and strong damping limits, respectively. For γ˜≪1, Γ1=Γaacos⁡2θm; Γ2=Γaasin⁡2θm where θm is the mixing angle in the medium and the sterile distribution function does not obey a simple rate equation. For γ˜≫1, Γ1=Γaa and Γ2=Γaasin⁡22θm/4γ˜2, is the sterile production rate. In this regime sterile production is suppressed and the oscillation frequency vanishes at an Mikheyev-Smirnov-Wolfenstein (MSW) resonance, with a breakdown of adiabaticity. These are consequences of quantum Zeno suppression. For active neutrinos with standard model interactions the strong damping limit is only available near an MSW resonance if sin⁡2θ≪αw with θ the vacuum mixing angle. The full set of quantum kinetic equations for sterile production for arbitrary γ˜ are obtained from the quantum master equation. Cosmological resonant sterile neutrino production is quantum Zeno suppressed relieving potential uncertainties associated with the QCD phase transition.

  7. The exact solution of shear-lag problems in flat panels and box beams assumed rigid in the transverse direction

    NASA Technical Reports Server (NTRS)

    Hildebrand, Francis B

    1943-01-01

    A mathematical procedure is herein developed for obtaining exact solutions of shear-lag problems in flat panels and box beams: the method is based on the assumption that the amount of stretching of the sheets in the direction perpendicular to the direction of essential normal stresses is negligible. Explicit solutions, including the treatment of cut-outs, are given for several cases and numerical results are presented in graphic and tabular form. The general theory is presented in a from which further solutions can be readily obtained. The extension of the theory to cover certain cases of non-uniform cross section is indicated. Although the solutions are obtained in terms of infinite series, the present developments differ from those previously given in that, in practical cases, the series usually converge so rapidly that sufficient accuracy is afforded by a small number of terms. Comparisons are made in several cases between the present results and the corresponding solutions obtained by approximate procedures devised by Reissner and by Kuhn and Chiarito.

  8. Bi-Exact Groups, Strongly Ergodic Actions and Group Measure Space Type III Factors with No Central Sequence

    NASA Astrophysics Data System (ADS)

    Houdayer, Cyril; Isono, Yusuke

    2016-12-01

    We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras {M = B rtimes Γ} arising from arbitrary actions {Γ \\curvearrowright B} of bi-exact discrete groups (e.g. free groups) on amenable von Neumann algebras. We prove a spectral gap rigidity result for the central sequence algebra {N' \\cap M^ω} of any nonamenable von Neumann subalgebra with normal expectation {N subset M}. We use this result to show that for any strongly ergodic essentially free nonsingular action {Γ \\curvearrowright (X, μ)} of any bi-exact countable discrete group on a standard probability space, the corresponding group measure space factor {L^∞(X) rtimes Γ} has no nontrivial central sequence. Using recent results of Boutonnet et al. (Local spectral gap in simple Lie groups and applications, 2015), we construct, for every {0 < λ ≤ 1}, a type {III_λ} strongly ergodic essentially free nonsingular action {F_∞ \\curvearrowright (X_λ, μ_λ)} of the free group {{F}_∞} on a standard probability space so that the corresponding group measure space type {III_λ} factor {L^∞(X_λ, μ_λ) rtimes F_∞} has no nontrivial central sequence by our main result. In particular, we obtain the first examples of group measure space type {III} factors with no nontrivial central sequence.

  9. Transport tensors in perfectly aligned low-density fluids: Self-diffusion and thermal conductivity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Singh, G. S.; Kumar, B.

    2001-06-01

    The modified Taxman equation for the kinetic theory of low-density fluids composed of rigid aspherical molecules possessing internal degrees of freedom is generalized to obtain the transport tensors in a fluid of aligned molecules. The theory takes care of the shape of the particles exactly but the solution has been obtained only for the case of perfectly aligned hard spheroids within the framework of the first Sonine polynomial approximation. The expressions for the thermal-conductivity components have been obtained for the first time whereas the self-diffusion components obtained here turn out to be exactly the same as those derived by Kumarmore » and Masters [Mol. Phys. >81, 491 (1994)] through the solution of the Lorentz-Boltzmann equation. All our expressions yield correct results in the hard-sphere limit.« less

  10. Exact solution of the PPP model for correlated electronic states of tetracene and substituted tetracene.

    PubMed

    Pati, Y Anusooya; Ramasesha, S

    2014-06-12

    Tetracene is an important conjugated molecule for device applications. We have used the diagrammatic valence bond method to obtain the desired states, in a Hilbert space of about 450 million singlets and 902 million triplets. We have also studied the donor/acceptor (D/A)-substituted tetracenes with D and A groups placed symmetrically about the long axis of the molecule. In these cases, by exploiting a new symmetry, which is a combination of C2 symmetry and electron-hole symmetry, we are able to obtain their low-lying states. In the case of substituted tetracene, we find that optically allowed one-photon excitation gaps reduce with increasing D/A strength, while the lowest singlet-triplet gap is only weakly affected. In all the systems we have studied, the excited singlet state, S1, is at more than twice the energy of the lowest triplet state and the second triplet is very close to the S1 state. Thus, donor-acceptor-substituted tetracene could be a good candidate in photovoltaic device application as it satisfies energy criteria for singlet fission. We have also obtained the model exact second harmonic generation (SHG) coefficients using the correction vector method, and we find that the SHG responses increase with the increase in D/A strength.

  11. Exact solutions for a type of electron pairing model with spin-orbit interactions and Zeeman coupling.

    PubMed

    Liu, Jia; Han, Qiang; Shao, L B; Wang, Z D

    2011-07-08

    A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of the Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing symmetry is of the p + ip wave and the ground state possesses time-reversal symmetry, regardless of the strength of the pairing interaction. Intriguingly, how Majorana fermions can emerge in the system is also elaborated. Exact results are illustrated for two systems, respectively, with spin-orbit interactions and Zeeman coupling.

  12. Identifying Blocks Formed by Curbed Fractures Using Exact Arithmetic

    NASA Astrophysics Data System (ADS)

    Zheng, Y.; Xia, L.; Yu, Q.; Zhang, X.

    2015-12-01

    Identifying blocks formed by fractures is important in rock engineering. Most studies assume the fractures to be perfect planar whereas curved fractures are rarely considered. However, large fractures observed in the field are often curved. This paper presents a new method for identifying rock blocks formed by both curved and planar fractures based on the element-block-assembling approach. The curved and planar fractures are represented as triangle meshes and planar discs, respectively. In the beginning of the identification method, the intersection segments between different triangle meshes are calculated and the intersected triangles are re-meshed to construct a piecewise linear complex (PLC). Then, the modeling domain is divided into tetrahedral subdomains under the constraint of the PLC and these subdomains are further decomposed into element blocks by extended planar fractures. Finally, the element blocks are combined and the subdomains are assembled to form complex blocks. The combination of two subdomains is skipped if and only if the common facet lies on a curved fracture. In this study, the exact arithmetic is used to handle the computational errors, which may threat the robustness of the block identification program when the degenerated cases are encountered. Specifically, a real number is represented as the ratio between two integers and the basic arithmetic such as addition, subtraction, multiplication and division between different real numbers can be performed exactly if an arbitrary precision integer package is used. In this way, the exact construction of blocks can be achieved without introducing computational errors. Several analytical examples are given in this paper and the results show effectiveness of this method in handling arbitrary shaped blocks. Moreover, there is no limitation on the number of blocks in a block system. The results also show (suggest) that the degenerated cases can be handled without affecting the robustness of the

  13. Self-Relevance Appraisal Influences Facial Reactions to Emotional Body Expressions

    PubMed Central

    Grèzes, Julie; Philip, Léonor; Chadwick, Michèle; Dezecache, Guillaume; Soussignan, Robert; Conty, Laurence

    2013-01-01

    People display facial reactions when exposed to others' emotional expressions, but exactly what mechanism mediates these facial reactions remains a debated issue. In this study, we manipulated two critical perceptual features that contribute to determining the significance of others' emotional expressions: the direction of attention (toward or away from the observer) and the intensity of the emotional display. Electromyographic activity over the corrugator muscle was recorded while participants observed videos of neutral to angry body expressions. Self-directed bodies induced greater corrugator activity than other-directed bodies; additionally corrugator activity was only influenced by the intensity of anger expresssed by self-directed bodies. These data support the hypothesis that rapid facial reactions are the outcome of self-relevant emotional processing. PMID:23405230

  14. Denjoy minimal sets and Birkhoff periodic orbits for non-exact monotone twist maps

    NASA Astrophysics Data System (ADS)

    Qin, Wen-Xin; Wang, Ya-Nan

    2018-06-01

    A non-exact monotone twist map φbarF is a composition of an exact monotone twist map φ bar with a generating function H and a vertical translation VF with VF ((x , y)) = (x , y - F). We show in this paper that for each ω ∈ R, there exists a critical value Fd (ω) ≥ 0 depending on H and ω such that for 0 ≤ F ≤Fd (ω), the non-exact twist map φbarF has an invariant Denjoy minimal set with irrational rotation number ω lying on a Lipschitz graph, or Birkhoff (p , q)-periodic orbits for rational ω = p / q. Like the Aubry-Mather theory, we also construct heteroclinic orbits connecting Birkhoff periodic orbits, and show that quasi-periodic orbits in these Denjoy minimal sets can be approximated by periodic orbits. In particular, we demonstrate that at the critical value F =Fd (ω), the Denjoy minimal set is not uniformly hyperbolic and can be approximated by smooth curves.

  15. Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians.

    PubMed

    Ghassemi Tabrizi, Shadan; Arbuznikov, Alexei V; Kaupp, Martin

    2018-03-26

    Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl] 4 ('Ni 4 ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp - is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni 4 , is attributed to a Stevens operator with eightfold rotational symmetry, marking

  16. Exact Correlation Functions in S U (2 ) N =2 Superconformal QCD

    NASA Astrophysics Data System (ADS)

    Baggio, Marco; Niarchos, Vasilis; Papadodimas, Kyriakos

    2014-12-01

    We report an exact solution of 2- and 3-point functions of chiral primary fields in S U (2 ) N =2 super-Yang-Mills theory coupled to four hypermultiplets. It is shown that these correlation functions are nontrivial functions of the gauge coupling, obeying differential equations which take the form of the semi-infinite Toda chain. We solve these equations recursively in terms of the Zamolodchikov metric that can be determined exactly from supersymmetric localization on the four-sphere. Our results are verified independently in perturbation theory with a Feynman diagram computation up to 2 loops. This is a short version of a companion paper that contains detailed technical remarks, additional material, and aspects of an extension to the S U (N ) gauge group.

  17. Ferrofluid patterns in Hele-Shaw cells: Exact, stable, stationary shape solutions.

    PubMed

    Lira, Sérgio A; Miranda, José A

    2016-01-01

    We investigate a quasi-two-dimensional system composed of an initially circular ferrofluid droplet surrounded by a nonmagnetic fluid of higher density. These immiscible fluids flow in a rotating Hele-Shaw cell, under the influence of an in-plane radial magnetic field. We focus on the situation in which destabilizing bulk magnetic field effects are balanced by stabilizing centrifugal forces. In this framing, we consider the interplay of capillary and magnetic normal traction effects in determining the fluid-fluid interface morphology. By employing a vortex-sheet formalism, we have been able to find a family of exact stationary N-fold polygonal shape solutions for the interface. A weakly nonlinear theory is then used to verify that such exact interfacial solutions are in fact stable.

  18. Modeling the heliolatitudinal gradient of the solar wind parameters with exact MHD solutions

    NASA Technical Reports Server (NTRS)

    Lima, J. J. G.; Tsinganos, K.

    1995-01-01

    The heliolatitudinal dependence of observations of the solar wind macroscopic quantities such as the averaged proton speed, density and the mass and momentum flux are modeled. The published observations covering the last two and a half solar cycles, are obtained either via the technique of interplanetary scintillations for the last 2 solar cycles (1970-1990), or, from the plasma experiment aboard the ULYSSES spacecraft for the recent period 1990-1994. Exact, two dimensional solutions of the full set of the steady MHD equations are used which are obtained through a nonlinear separation of the variables in the MHD equations. The three parameters emerging from the solutions are fixed from these observations, as well as from observations of the solar rotation. It is found that near solar maximum the solar wind speed is uniformly low, around the 400 km/s over a wide range of latitudes. On the other hand, during solar minimum and the declining phase of the solar activity cycle, there is a strong heliolatitudinal gradient in proton speed between 400-800 from equator to pole. This modeling also agrees with previous findings that the gradient in wind speed with the latitude is offset by a gradient in density such that the mass and momentum flux vary relatively little.

  19. Continual Lie algebras and noncommutative counterparts of exactly solvable models

    NASA Astrophysics Data System (ADS)

    Zuevsky, A.

    2004-01-01

    Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.

  20. Exact consideration of data redundancies for spiral cone-beam CT

    NASA Astrophysics Data System (ADS)

    Lauritsch, Guenter; Katsevich, Alexander; Hirsch, Michael

    2004-05-01

    In multi-slice spiral computed tomography (CT) there is an obvious trend in adding more and more detector rows. The goals are numerous: volume coverage, isotropic spatial resolution, and speed. Consequently, there will be a variety of scan protocols optimizing clinical applications. Flexibility in table feed requires consideration of data redundancies to ensure efficient detector usage. Until recently this was achieved by approximate reconstruction algorithms only. However, due to the increasing cone angles there is a need of exact treatment of the cone beam geometry. A new, exact and efficient 3-PI algorithm for considering three-fold data redundancies was derived from a general, theoretical framework based on 3D Radon inversion using Grangeat's formula. The 3-PI algorithm possesses a simple and efficient structure as the 1-PI method for non-redundant data previously proposed. Filtering is one-dimensional, performed along lines with variable tilt on the detector. This talk deals with a thorough evaluation of the performance of the 3-PI algorithm in comparison to the 1-PI method. Image quality of the 3-PI algorithm is superior. The prominent spiral artifacts and other discretization artifacts are significantly reduced due to averaging effects when taking into account redundant data. Certainly signal-to-noise ratio is increased. The computational expense is comparable even to that of approximate algorithms. The 3-PI algorithm proves its practicability for applications in medical imaging. Other exact n-PI methods for n-fold data redundancies (n odd) can be deduced from the general, theoretical framework.