Sample records for explicit analytical expression

  1. Explicit analytical expression for the condition number of polynomials in power form

    NASA Astrophysics Data System (ADS)

    Rack, Heinz-Joachim

    2017-07-01

    In his influential papers [1-3] W. Gautschi has defined and reshaped the condition number κ∞ of polynomials Pn of degree ≤ n which are represented in power form on a zero-symmetric interval [-ω, ω]. Basically, κ∞ is expressed as the product of two operator norms: an explicit factor times an implicit one (the l∞-norm of the coefficient vector of the n-th Chebyshev polynomial of the first kind relative to [-ω, ω]). We provide a new proof, economize the second factor and express it by an explicit analytical formula.

  2. Analytical drafting curves provide exact equations for plotted data

    NASA Technical Reports Server (NTRS)

    Stewart, R. B.

    1967-01-01

    Analytical drafting curves provide explicit mathematical expressions for any numerical data that appears in the form of graphical plots. The curves each have a reference coordinate axis system indicated on the curve as well as the mathematical equation from which the curve was generated.

  3. Revisiting the positive DC corona discharge theory: Beyond Peek's and Townsend's law

    NASA Astrophysics Data System (ADS)

    Monrolin, Nicolas; Praud, Olivier; Plouraboué, Franck

    2018-06-01

    The classical positive Corona Discharge theory in a cylindrical axisymmetric configuration is revisited in order to find analytically the influence of gas properties and thermodynamic conditions on the corona current. The matched asymptotic expansion of Durbin and Turyn [J. Phys. D: Appl. Phys. 20, 1490-1495 (1987)] of a simplified but self-consistent problem is performed and explicit analytical solutions are derived. The mathematical derivation enables us to express a new positive DC corona current-voltage characteristic, choosing either a dimensionless or dimensional formulation. In dimensional variables, the current voltage law and the corona inception voltage explicitly depend on the electrode size and physical gas properties such as ionization and photoionization parameters. The analytical predictions are successfully confronted with experiments and Peek's and Townsend's laws. An analytical expression of the corona inception voltage φ o n is proposed, which depends on the known values of physical parameters without adjustable parameters. As a proof of consistency, the classical Townsend current-voltage law I = C φ ( φ - φ o n ) is retrieved by linearizing the non-dimensional analytical solution. A brief parametric study showcases the interest in this analytical current model, especially for exploring small corona wires or considering various thermodynamic conditions.

  4. Explicit robust schemes for implementation of general principal value-based constitutive models

    NASA Technical Reports Server (NTRS)

    Arnold, S. M.; Saleeb, A. F.; Tan, H. Q.; Zhang, Y.

    1993-01-01

    The issue of developing effective and robust schemes to implement general hyperelastic constitutive models is addressed. To this end, special purpose functions are used to symbolically derive, evaluate, and automatically generate the associated FORTRAN code for the explicit forms of the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid for the entire deformation range. The analytical form of these explicit expressions is given here for the case in which the strain-energy potential is taken as a nonseparable polynomial function of the principle stretches.

  5. High-order tail in Schwarzschild spacetime

    NASA Astrophysics Data System (ADS)

    Casals, Marc; Ottewill, Adrian

    2015-12-01

    We present an analysis of the behavior at late times of linear field perturbations of a Schwarzschild black hole spacetime. In particular, we give explicit analytic expressions for the field perturbations (for a specific ℓ-multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order (˜t-2 ℓ-3), a new logarithmic behavior at third leading order (˜t-2 ℓ-5ln t ). We obtain these late-time results by developing an analytical formalism initially formulated by Mano, Suzuki and Takasugi (MST) [Prog. Theor. Phys. 95, 1079 (1996); 96, 549 (1996)] formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small frequency for the Fourier modes, for late time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a "perturbative regime."

  6. An explicit analytical solution for sound propagation in a three-dimensional penetrable wedge with small apex angle.

    PubMed

    Petrov, Pavel S; Sturm, Frédéric

    2016-03-01

    A problem of sound propagation in a shallow-water waveguide with a weakly sloping penetrable bottom is considered. The adiabatic mode parabolic equations are used to approximate the solution of the three-dimensional (3D) Helmholtz equation by modal decomposition of the acoustic pressure field. The mode amplitudes satisfy parabolic equations that admit analytical solutions in the special case of the 3D wedge. Using the analytical formula for modal amplitudes, an explicit and remarkably simple expression for the acoustic pressure in the wedge is obtained. The proposed solution is validated by the comparison with a solution of the 3D penetrable wedge problem obtained using a fully 3D parabolic equation that includes a leading-order cross term correction.

  7. Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

    NASA Astrophysics Data System (ADS)

    Bubin, Sergiy; Adamowicz, Ludwik

    2006-06-01

    In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

  8. Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

    PubMed

    Bubin, Sergiy; Adamowicz, Ludwik

    2006-06-14

    In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

  9. Band-to-band tunneling distance analysis in the heterogate electron–hole bilayer tunnel field-effect transistor

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

    Padilla, J. L., E-mail: jose.padilladelatorre@epfl.ch; Departamento de Electrónica y Tecnología de los Computadores, Universidad de Granada, Avda. Fuentenueva s/n, 18071 Granada; Palomares, A.

    In this work, we analyze the behavior of the band-to-band tunneling distance between electron and hole subbands resulting from field-induced quantum confinement in the heterogate electron–hole bilayer tunnel field-effect transistor. We show that, analogously to the explicit formula for the tunneling distance that can be easily obtained in the semiclassical framework where the conduction and valence band edges are allowed states, an equivalent analytical expression can be derived in the presence of field-induced quantum confinement for describing the dependence of the tunneling distance on the body thickness and material properties of the channel. This explicit expression accounting for quantum confinementmore » holds valid provided that the potential wells for electrons and holes at the top and bottom of the channel can be approximated by triangular profiles. Analytical predictions are compared to simulation results showing very accurate agreement.« less

  10. 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.

  11. Relativistic calculation of correlational energy for a helium-like atom

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

    Palchikov, V.G.

    This paper presents an analytical method for calculating the firstorder correlational energy from the electron interaction, taking account of lag effects. Explicit analytical expressions are obtained for radial matrix elements. The nonrelativistic limit is investigated. The given method may be used to calculate correlation effects in higher orders of perturbation theory (second and higher orders with respect to 1/z) using the Strum expansion for the Coulomb Green's functions.

  12. Approximate analytical relationships for linear optimal aeroelastic flight control laws

    NASA Astrophysics Data System (ADS)

    Kassem, Ayman Hamdy

    1998-09-01

    This dissertation introduces new methods to uncover functional relationships between design parameters of a contemporary control design technique and the resulting closed-loop properties. Three new methods are developed for generating such relationships through analytical expressions: the Direct Eigen-Based Technique, the Order of Magnitude Technique, and the Cost Function Imbedding Technique. Efforts concentrated on the linear-quadratic state-feedback control-design technique applied to an aeroelastic flight control task. For this specific application, simple and accurate analytical expressions for the closed-loop eigenvalues and zeros in terms of basic parameters such as stability and control derivatives, structural vibration damping and natural frequency, and cost function weights are generated. These expressions explicitly indicate how the weights augment the short period and aeroelastic modes, as well as the closed-loop zeros, and by what physical mechanism. The analytical expressions are used to address topics such as damping, nonminimum phase behavior, stability, and performance with robustness considerations, and design modifications. This type of knowledge is invaluable to the flight control designer and would be more difficult to formulate when obtained from numerical-based sensitivity analysis.

  13. Explicit formulas for effective piezoelectric coefficients of ferroelectric 0-3 composites based on effective medium theory

    NASA Astrophysics Data System (ADS)

    Wong, C. K.; Poon, Y. M.; Shin, F. G.

    2003-01-01

    Explicit formulas were derived for the effective piezoelectric stress coefficients of a 0-3 composite of ferroelectric spherical particles in a ferroelectric matrix which were then combined to give the more commonly used strain coefficients. Assuming that the elastic stiffness of the inclusion phase is sufficiently larger than that of the matrix phase, the previously derived explicit expressions for the case of a low volume concentration of inclusion particles [C. K. Wong, Y. M. Poon, and F. G. Shin, Ferroelectrics 264, 39 (2001); J. Appl. Phys. 90, 4690 (2001)] were "transformed" analytically by an effective medium theory (EMT) with appropriate approximations, to suit the case of a more concentrated suspension. Predictions of the EMT expressions were compared with the experimental values of composites of lead zirconate titanate ceramic particles dispersed in polyvinylidene fluoride and polyvinylidene fluoride-trifluoroethylene copolymer, reported by Furukawa [IEEE Trans. Electr. Insul. 24, 375 (1989)] and by Ng et al. [IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1308 (2000)] respectively. Fairly good agreement was obtained. Comparisons with other predictions, including the predictions given by numerically solving the EMT scheme, were also made. It was found that the analytic and numeric EMT schemes agreed with each other very well for an inclusion of volume fraction not exceeding 60%.

  14. On the effect of the degeneracy among dark energy parameters

    NASA Astrophysics Data System (ADS)

    Gong, Yungui; Gao, Qing

    2014-01-01

    The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter and the fractional energy density . Based on the approximation, for slowly rolling scalar fields, we derived the analytical expressions of which reduce to the popular Chevallier-Polarski-Linder parametrization with an explicit degeneracy relation between and . The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among , , and . With the explicit degeneracy relations, we test their effects on the constraints of the cosmological parameters. We find that: (1) The analytical relations between and for the two models are consistent with observational data. (2) The degeneracies have little effect on . (3) The error of was reduced about 30 % with the degeneracy relations.

  15. Longitudinal dielectric function and dispersion relation of electrostatic waves in relativistic plasmas

    NASA Astrophysics Data System (ADS)

    Touil, B.; Bendib, A.; Bendib-Kalache, K.

    2017-02-01

    The longitudinal dielectric function is derived analytically from the relativistic Vlasov equation for arbitrary values of the relevant parameters z = m c 2 / T , where m is the rest electron mass, c is the speed of light, and T is the electron temperature in energy units. A new analytical approach based on the Legendre polynomial expansion and continued fractions was used. Analytical expression of the electron distribution function was derived. The real part of the dispersion relation and the damping rate of electron plasma waves are calculated both analytically and numerically in the whole range of the parameter z . The results obtained improve significantly the previous results reported in the literature. For practical purposes, explicit expressions of the real part of the dispersion relation and the damping rate in the range z > 30 and strongly relativistic regime are also proposed.

  16. Analytic integration of real-virtual counterterms in NNLO jet cross sections II

    NASA Astrophysics Data System (ADS)

    Bolzoni, Paolo; Moch, Sven-Olaf; Somogyi, Gábor; Trócsányi, Zoltán

    2009-08-01

    We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in 4 - 2epsilon dimensions to obtain the coefficients of their Laurent expansions around epsilon = 0. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in epsilon both numerically and analytically by complex integration over the Mellin-Barnes contours.

  17. Pressure-coupled combustion response model for solid propellants based on Zeldovich-Novozhilov approach

    NASA Technical Reports Server (NTRS)

    Harstad, K. G.; Strand, L. D.

    1987-01-01

    An exact analytical solution is given to the problem of long-time propellant thermal response to a specified pressure oscillation. Coupling to the gas phase is made using the quasisteady Zeldovich-Novozhilov approximation. Explicit linear and lowest order (quadratic) nonlinear expressions for propellant response are obtained from the implicit nonlinear solutions. Using these expressions, response curves are presented for an ammonium perchlorate composite propellant and HMX monopropellant.

  18. Spiral trajectory design: a flexible numerical algorithm and base analytical equations.

    PubMed

    Pipe, James G; Zwart, Nicholas R

    2014-01-01

    Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories. Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results. Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement. A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories. Copyright © 2013 Wiley Periodicals, Inc.

  19. An Analytical State Transition Matrix for Orbits Perturbed by an Oblate Spheroid

    NASA Technical Reports Server (NTRS)

    Mueller, A. C.

    1977-01-01

    An analytical state transition matrix and its inverse, which include the short period and secular effects of the second zonal harmonic, were developed from the nonsingular PS satellite theory. The fact that the independent variable in the PS theory is not time is in no respect disadvantageous, since any explicit analytical solution must be expressed in the true or eccentric anomaly. This is shown to be the case for the simple conic matrix. The PS theory allows for a concise, accurate, and algorithmically simple state transition matrix. The improvement over the conic matrix ranges from 2 to 4 digits accuracy.

  20. Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Ahmed, H. M.

    2004-08-01

    A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed.

  1. Performance Analysis of Blind Subspace-Based Signature Estimation Algorithms for DS-CDMA Systems with Unknown Correlated Noise

    NASA Astrophysics Data System (ADS)

    Zarifi, Keyvan; Gershman, Alex B.

    2006-12-01

    We analyze the performance of two popular blind subspace-based signature waveform estimation techniques proposed by Wang and Poor and Buzzi and Poor for direct-sequence code division multiple-access (DS-CDMA) systems with unknown correlated noise. Using the first-order perturbation theory, analytical expressions for the mean-square error (MSE) of these algorithms are derived. We also obtain simple high SNR approximations of the MSE expressions which explicitly clarify how the performance of these techniques depends on the environmental parameters and how it is related to that of the conventional techniques that are based on the standard white noise assumption. Numerical examples further verify the consistency of the obtained analytical results with simulation results.

  2. Target annihilation by diffusing particles in inhomogeneous geometries

    NASA Astrophysics Data System (ADS)

    Cassi, Davide

    2009-09-01

    The survival probability of immobile targets annihilated by a population of random walkers on inhomogeneous discrete structures, such as disordered solids, glasses, fractals, polymer networks, and gels, is analytically investigated. It is shown that, while it cannot in general be related to the number of distinct visited points as in the case of homogeneous lattices, in the case of bounded coordination numbers its asymptotic behavior at large times can still be expressed in terms of the spectral dimension d˜ and its exact analytical expression is given. The results show that the asymptotic survival probability is site-independent of recurrent structures (d˜≤2) , while on transient structures (d˜>2) it can strongly depend on the target position, and such dependence is explicitly calculated.

  3. Stochastic modelling of the hydrologic operation of rainwater harvesting systems

    NASA Astrophysics Data System (ADS)

    Guo, Rui; Guo, Yiping

    2018-07-01

    Rainwater harvesting (RWH) systems are an effective low impact development practice that provides both water supply and runoff reduction benefits. A stochastic modelling approach is proposed in this paper to quantify the water supply reliability and stormwater capture efficiency of RWH systems. The input rainfall series is represented as a marked Poisson process and two typical water use patterns are analytically described. The stochastic mass balance equation is solved analytically, and based on this, explicit expressions relating system performance to system characteristics are derived. The performances of a wide variety of RWH systems located in five representative climatic regions of the United States are examined using the newly derived analytical equations. Close agreements between analytical and continuous simulation results are shown for all the compared cases. In addition, an analytical equation is obtained expressing the required storage size as a function of the desired water supply reliability, average water use rate, as well as rainfall and catchment characteristics. The equations developed herein constitute a convenient and effective tool for sizing RWH systems and evaluating their performances.

  4. Polarization effects in recoil-induced resonances

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

    Lazebnyi, D. B., E-mail: becks.ddf@gmail.com; Brazhnikov, D. V.; Taichenachev, A. V.

    2017-01-15

    The effect of the field polarization on the amplitude of recoil-induced resonances (RIRs) is considered for laser-cooled free atoms and for atoms in a working magneto-optical trap (MOT). For all closed dipole transitions, explicit analytical expressions are obtained for the polarization dependence of the resonance amplitudes within a perturbation theory. Optimal polarization conditions are found for the observation of resonances.

  5. Brillouin precursors in Debye media

    NASA Astrophysics Data System (ADS)

    Macke, Bruno; Ségard, Bernard

    2015-05-01

    We theoretically study the formation of Brillouin precursors in Debye media. We point out that the precursors are visible only at propagation distances such that the impulse response of the medium is essentially determined by the frequency dependence of its absorption and is practically Gaussian. By simple convolution, we then obtain explicit analytical expressions of the transmitted waves generated by reference incident waves, distinguishing precursor and main signal by a simple examination of the long-time behavior of the overall signal. These expressions are in good agreement with the signals obtained in numerical or real experiments performed on water in the radio-frequency domain and explain in particular some observed shapes of the precursor. Results are obtained for other remarkable incident waves. In addition, we show quite generally that the shape of the Brillouin precursor appearing alone at sufficiently large propagation distance and the law giving its amplitude as a function of this distance do not depend on the precise form of the incident wave but only on its integral properties. The incidence of a static conductivity of the medium is also examined and explicit analytical results are again given in the limit of weak and strong conductivities.

  6. Analytic continuation of quantum Monte Carlo data by stochastic analytical inference.

    PubMed

    Fuchs, Sebastian; Pruschke, Thomas; Jarrell, Mark

    2010-05-01

    We present an algorithm for the analytic continuation of imaginary-time quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for the calculation of a weighted average over possible energy spectra, which can be evaluated by standard Monte Carlo simulations, yielding as by-product also the distribution function as function of the regularization parameter. Our algorithm thus avoids the usual ad hoc assumptions introduced in similar algorithms to fix the regularization parameter. We apply the algorithm to imaginary-time quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum-entropy calculation.

  7. Shape anomaly detection under strong measurement noise: An analytical approach to adaptive thresholding

    NASA Astrophysics Data System (ADS)

    Krasichkov, Alexander S.; Grigoriev, Eugene B.; Bogachev, Mikhail I.; Nifontov, Eugene M.

    2015-10-01

    We suggest an analytical approach to the adaptive thresholding in a shape anomaly detection problem. We find an analytical expression for the distribution of the cosine similarity score between a reference shape and an observational shape hindered by strong measurement noise that depends solely on the noise level and is independent of the particular shape analyzed. The analytical treatment is also confirmed by computer simulations and shows nearly perfect agreement. Using this analytical solution, we suggest an improved shape anomaly detection approach based on adaptive thresholding. We validate the noise robustness of our approach using typical shapes of normal and pathological electrocardiogram cycles hindered by additive white noise. We show explicitly that under high noise levels our approach considerably outperforms the conventional tactic that does not take into account variations in the noise level.

  8. Dynamic imaging model and parameter optimization for a star tracker.

    PubMed

    Yan, Jinyun; Jiang, Jie; Zhang, Guangjun

    2016-03-21

    Under dynamic conditions, star spots move across the image plane of a star tracker and form a smeared star image. This smearing effect increases errors in star position estimation and degrades attitude accuracy. First, an analytical energy distribution model of a smeared star spot is established based on a line segment spread function because the dynamic imaging process of a star tracker is equivalent to the static imaging process of linear light sources. The proposed model, which has a clear physical meaning, explicitly reflects the key parameters of the imaging process, including incident flux, exposure time, velocity of a star spot in an image plane, and Gaussian radius. Furthermore, an analytical expression of the centroiding error of the smeared star spot is derived using the proposed model. An accurate and comprehensive evaluation of centroiding accuracy is obtained based on the expression. Moreover, analytical solutions of the optimal parameters are derived to achieve the best performance in centroid estimation. Finally, we perform numerical simulations and a night sky experiment to validate the correctness of the dynamic imaging model, the centroiding error expression, and the optimal parameters.

  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. Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

    NASA Astrophysics Data System (ADS)

    Przedborski, Michelle; Anco, Stephen C.

    2017-09-01

    A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

  11. Analytical inversions in remote sensing of particle size distributions. IV - Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation

    NASA Technical Reports Server (NTRS)

    Fymat, A. L.; Smith, C. B.

    1979-01-01

    It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.

  12. Shock-induced solitary waves in granular crystals.

    PubMed

    Hasan, M Arif; Nemat-Nasser, Sia

    2018-02-01

    Solitary waves (SWs) are generated in monoatomic (homogeneous) lightly contacting spherical granules by an applied input force of any time-variation and intensity. We consider finite duration shock loads on one-dimensional arrays of granules and focus on the transition regime that leads to the formation of SWs. Based on geometrical and material properties of the granules and the properties of the input shock, we provide explicit analytic expressions to calculate the peak value of the compressive contact force at each contact point in the transition regime that precedes the formation of a primary solitary wave. We also provide explicit expressions to estimate the number of granules involved in the transition regime and show its dependence on the characteristics of the input shock and material/geometrical properties of the interacting granules. Finally, we assess the accuracy of our theoretical results by comparing them with those obtained through numerical integration of the equations of motion.

  13. Analytical ground state for the Jaynes-Cummings model with ultrastrong coupling

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

    Zhang Yuanwei; Institute of Theoretical Physics, Shanxi University, Taiyuan 030006; Chen Gang

    2011-06-15

    We present a generalized variational method to analytically obtain the ground-state properties of the Jaynes-Cummings model with the ultrastrong coupling. An explicit expression for the ground-state energy, which agrees well with the numerical simulation in a wide range of the experimental parameters, is given. In particular, the introduced method can successfully solve this Jaynes-Cummings model with the positive detuning (the atomic resonant level is larger than the photon frequency), which cannot be treated in the adiabatical approximation and the generalized rotating-wave approximation. Finally, we also demonstrate analytically how to control the mean photon number by means of the current experimentalmore » parameters including the photon frequency, the coupling strength, and especially the atomic resonant level.« less

  14. Analytical model of ground-state lasing phenomenon in broadband semiconductor quantum dot lasers

    NASA Astrophysics Data System (ADS)

    Korenev, Vladimir V.; Savelyev, Artem V.; Zhukov, Alexey E.; Omelchenko, Alexander V.; Maximov, Mikhail V.

    2013-05-01

    We introduce an analytical approach to the description of broadband lasing spectra of semiconductor quantum dot lasers emitting via ground-state optical transitions of quantum dots. The explicit analytical expressions describing the shape and the width of lasing spectra as well as their temperature and injection current dependences are obtained in the case of low homogeneous broadening. It is shown that in this case these dependences are determined by only two dimensionless parameters, which are the dispersion of the distribution of QDs over the energy normalized to the temperature and loss-to-maximum gain ratio. The possibility of optimization of laser's active region size and structure by using the intentionally introduced disorder is also carefully considered.

  15. Temporal fluctuations after a quantum quench: Many-particle dephasing

    NASA Astrophysics Data System (ADS)

    Marquardt, Florian; Kiendl, Thomas

    After a quantum quench, the expectation values of observables continue to fluctuate in time. In the thermodynamic limit, one expects such fluctuations to decrease to zero, in order for standard statistical physics to hold. However, it is a challenge to determine analytically how the fluctuations decay as a function of system size. So far, there have been analytical predictions for integrable models (which are, naturally, somewhat special), analytical bounds for arbitrary systems, and numerical results for moderate-size systems. We have discovered a dynamical regime where the decrease of fluctuations is driven by many-particle dephasing, instead of a redistribution of occupation numbers. On the basis of this insight, we are able to provide exact analytical expressions for a model with weak integrability breaking (transverse Ising chain with additional terms). These predictions explicitly show how fluctuations are exponentially suppressed with system size.

  16. Fluctuations in time intervals of financial data from the view point of the Gini index

    NASA Astrophysics Data System (ADS)

    Sazuka, Naoya; Inoue, Jun-ichi

    2007-09-01

    We propose an approach to explain fluctuations in time intervals of financial markets data from the view-point of the Gini index. We show the explicit form of the Gini index for a Weibull distribution: A good candidate to describe the first passage time of foreign exchange rate. The analytical expression of the Gini index compares well with the value obtained from empirical data.

  17. Numerically stable formulas for a particle-based explicit exponential integrator

    NASA Astrophysics Data System (ADS)

    Nadukandi, Prashanth

    2015-05-01

    Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

  18. Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L =1

    NASA Astrophysics Data System (ADS)

    Bubin, Sergiy; Adamowicz, Ludwik

    2008-03-01

    In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L =1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

  19. Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L=1.

    PubMed

    Bubin, Sergiy; Adamowicz, Ludwik

    2008-03-21

    In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

  20. The Challenge of Understanding Process in Clinical Behavior Analysis: The Case of Functional Analytic Psychotherapy

    ERIC Educational Resources Information Center

    Follette, William C.; Bonow, Jordan T.

    2009-01-01

    Whether explicitly acknowledged or not, behavior-analytic principles are at the heart of most, if not all, empirically supported therapies. However, the change process in psychotherapy is only now being rigorously studied. Functional analytic psychotherapy (FAP; Kohlenberg & Tsai, 1991; Tsai et al., 2009) explicitly identifies behavioral-change…

  1. 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.

  2. Analytical description of the transverse Anderson localization of light

    NASA Astrophysics Data System (ADS)

    Schirmacher, Walter; Leonetti, Marco; Ruocco, Giancarlo

    2017-04-01

    We develop an analytical theory for describing the transverse localization properties of light beams in optical fibers with lateral disorder. This theory, which starts from the widely used paraxial approximation for the Helmholtz equation of the electric field, is a combination of an effective-medium theory for transverse disorder with the self-consistent localization theory of Vollhardt and Wölfle. We obtain explicit expressions for the dependence of the transverse localization length on the direction along the fiber. These results are in agreement with simulational data published recently by Karbasi et al. In particular we explain the focussing mechanism leading to the establishment of narrow transparent channels along the sample.

  3. Focal shift and the axial optical coordinate for high-aperture systems of finite Fresnel number.

    PubMed

    Sheppard, Colin J R; Török, Peter

    2003-11-01

    Analytic expressions are given for the on-axis intensity predicted by the Rayleigh-Sommerfeld and Kirchhoff diffraction integrals for a scalar optical system of high numerical aperture and finite value of Fresnel number. A definition of the axial optical coordinate is introduced that is valid for finite values of Fresnel number, for high-aperture systems, and for observation points distant from the focus. The focal shift effect is reexamined. For the case when the focal shift is small, explicit expressions are given for the focal shift and the axial peak in intensity.

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

    PubMed

    Theodorakis, Stavros

    2003-06-01

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

  5. Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

    NASA Astrophysics Data System (ADS)

    Wu, Baisheng; Liu, Weijia; Lim, C. W.

    2017-07-01

    A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

  6. Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave.

    PubMed

    Frisvad, Jeppe Revall

    2018-04-01

    In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation of the complex hypergeometric function F 1 2 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far-field scattering components, that is, the phase function. I include recurrence formulas for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity is not negligible for light entering an absorbing medium at an oblique angle. The presented theory could thus be useful for predicting scattering behavior in dye-based random lasing and in solar cell absorption enhancement.

  7. Nonlinear field equations for aligning self-propelled rods.

    PubMed

    Peshkov, Anton; Aranson, Igor S; Bertin, Eric; Chaté, Hugues; Ginelli, Francesco

    2012-12-28

    We derive a set of minimal and well-behaved nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.

  8. Closed form solution for a double quantum well using Gröbner basis

    NASA Astrophysics Data System (ADS)

    Acus, A.; Dargys, A.

    2011-07-01

    Analytical expressions for the spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and the effective masses are different. This was achieved by using a Gröbner basis algorithm that allowed us to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.

  9. Flux and Hall states in ABJM with dynamical flavors

    NASA Astrophysics Data System (ADS)

    Bea, Yago; Jokela, Niko; Lippert, Matthew; Ramallo, Alfonso V.; Zoakos, Dimitrios

    2015-03-01

    We study the physics of probe D6-branes with quantized internal worldvolume flux in the ABJM background with unquenched massless flavors. This flux breaks parity in the (2+1)-dimensional gauge theory and allows quantum Hall states. Parity breaking is also explicitly demonstrated via the helicity dependence of the meson spectrum. We obtain general expressions for the conductivities, both in the gapped Minkowski embeddings and in the compressible black hole ones. These conductivities depend on the flux and contain a contribution from the dynamical flavors which can be regarded as an effect of intrinsic disorder due to quantum fluctuations of the fundamentals. We present an explicit, analytic family of supersymmetric solutions with nonzero charge density, electric, and magnetic fields.

  10. Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

    NASA Astrophysics Data System (ADS)

    Kjeldsen, Tinne Hoff; Lützen, Jesper

    2015-07-01

    In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

  11. Exact linearized Coulomb collision operator in the moment expansion

    DOE PAGES

    Ji, Jeong -Young; Held, Eric D.

    2006-10-05

    In the moment expansion, the Rosenbluth potentials, the linearized Coulomb collision operators, and the moments of the collision operators are analytically calculated for any moment. The explicit calculation of Rosenbluth potentials converts the integro-differential form of the Coulomb collision operator into a differential operator, which enables one to express the collision operator in a simple closed form for any arbitrary mass and temperature ratios. In addition, it is shown that gyrophase averaging the collision operator acting on arbitrary distribution functions is the same as the collision operator acting on the corresponding gyrophase averaged distribution functions. The moments of the collisionmore » operator are linear combinations of the fluid moments with collision coefficients parametrized by mass and temperature ratios. Furthermore, useful forms involving the small mass-ratio approximation are easily found since the collision operators and their moments are expressed in terms of the mass ratio. As an application, the general moment equations are explicitly written and the higher order heat flux equation is derived.« less

  12. On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials

    NASA Astrophysics Data System (ADS)

    Doha, E. H.

    2003-05-01

    A formula expressing the Laguerre coefficients of a general-order derivative of an infinitely differentiable function in terms of its original coefficients is proved, and a formula expressing explicitly the derivatives of Laguerre polynomials of any degree and for any order as a linear combination of suitable Laguerre polynomials is deduced. A formula for the Laguerre coefficients of the moments of one single Laguerre polynomial of certain degree is given. Formulae for the Laguerre coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Laguerre coefficients are also obtained. A simple approach in order to build and solve recursively for the connection coefficients between Jacobi-Laguerre and Hermite-Laguerre polynomials is described. An explicit formula for these coefficients between Jacobi and Laguerre polynomials is given, of which the ultra-spherical polynomials of the first and second kinds and Legendre polynomials are important special cases. An analytical formula for the connection coefficients between Hermite and Laguerre polynomials is also obtained.

  13. DROMO formulation for planar motions: solution to the Tsien problem

    NASA Astrophysics Data System (ADS)

    Urrutxua, Hodei; Morante, David; Sanjurjo-Rivo, Manuel; Peláez, Jesús

    2015-06-01

    The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen's ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo-Stiefel methods.

  14. Pressure and wall shear stress in blood hammer - Analytical theory.

    PubMed

    Mei, Chiang C; Jing, Haixiao

    2016-10-01

    We describe an analytical theory of blood hammer in a long and stiffened artery due to sudden blockage. Based on the model of a viscous fluid in laminar flow, we derive explicit expressions of oscillatory pressure and wall shear stress. To examine the effects on local plaque formation we also allow the blood vessel radius to be slightly nonuniform. Without resorting to discrete computation, the asymptotic method of multiple scales is utilized to deal with the sharp contrast of time scales. The effects of plaque and blocking time on blood pressure and wall shear stress are studied. The theory is validated by comparison with existing water hammer experiments. Copyright © 2016. Published by Elsevier Inc.

  15. High-order moments of spin-orbit energy in a multielectron configuration

    NASA Astrophysics Data System (ADS)

    Na, Xieyu; Poirier, M.

    2016-07-01

    In order to analyze the energy-level distribution in complex ions such as those found in warm dense plasmas, this paper provides values for high-order moments of the spin-orbit energy in a multielectron configuration. Using second-quantization results and standard angular algebra or fully analytical expressions, explicit values are given for moments up to 10th order for the spin-orbit energy. Two analytical methods are proposed, using the uncoupled or coupled orbital and spin angular momenta. The case of multiple open subshells is considered with the help of cumulants. The proposed expressions for spin-orbit energy moments are compared to numerical computations from Cowan's code and agree with them. The convergence of the Gram-Charlier expansion involving these spin-orbit moments is analyzed. While a spectrum with infinitely thin components cannot be adequately represented by such an expansion, a suitable convolution procedure ensures the convergence of the Gram-Charlier series provided high-order terms are accounted for. A corrected analytical formula for the third-order moment involving both spin-orbit and electron-electron interactions turns out to be in fair agreement with Cowan's numerical computations.

  16. Towards a model of pion generalized parton distributions from Dyson-Schwinger equations

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

    Moutarde, H.

    2015-04-10

    We compute the pion quark Generalized Parton Distribution H{sup q} and Double Distributions F{sup q} and G{sup q} in a coupled Bethe-Salpeter and Dyson-Schwinger approach. We use simple algebraic expressions inspired by the numerical resolution of Dyson-Schwinger and Bethe-Salpeter equations. We explicitly check the support and polynomiality properties, and the behavior under charge conjugation or time invariance of our model. We derive analytic expressions for the pion Double Distributions and Generalized Parton Distribution at vanishing pion momentum transfer at a low scale. Our model compares very well to experimental pion form factor or parton distribution function data.

  17. A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization

    NASA Astrophysics Data System (ADS)

    Sulyok, G.

    2017-07-01

    Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the ultraviolet (UV-)divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast to existing recursion schemes, we are able to present a general analytic result in closed form that enables direct determination of the UV-divergent part of any one-loop tensor N-point coefficient independent from UV-divergent parts of other one-loop tensor N-point coefficients. Simplified formulas and explicit expressions are presented for A-, B-, C-, D-, E-, and F-functions.

  18. Control of the electromagnetic drag using fluctuating light fields

    NASA Astrophysics Data System (ADS)

    Pastor, Víctor J. López; Marqués, Manuel I.

    2018-05-01

    An expression for the electromagnetic drag force experienced by an electric dipole in a light field consisting of a monochromatic plane wave with polarization and phase randomly fluctuating is obtained. The expression explicitly considers the transformations of the field and frequency due to the Doppler shift and the change of the polarizability response of the electric dipole. The conditions to be fulfilled by the polarizability of the dipole in order to obtain a positive, a null, and a negative drag coefficient are analytically determined and checked against numerical simulations for the dynamics of a silver nanoparticle. The theoretically predicted diffusive, superdiffusive, and exponentially accelerated dynamical regimes are numerically confirmed.

  19. Fully Anisotropic Rotational Diffusion Tensor from Molecular Dynamics Simulations.

    PubMed

    Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

    2018-05-31

    We present a method to calculate the fully anisotropic rotational diffusion tensor from molecular dynamics simulations. Our approach is based on fitting the time-dependent covariance matrix of the quaternions that describe the rigid-body rotational dynamics. Explicit analytical expressions have been derived for the covariances by Favro, which are valid irrespective of the degree of anisotropy. We use these expressions to determine an optimal rotational diffusion tensor from trajectory data. The molecular structures are aligned against a reference by optimal rigid-body superposition. The quaternion covariances can then be obtained directly from the rotation matrices used in the alignment. The rotational diffusion tensor is determined by a fit to the time-dependent quaternion covariances, or directly by Laplace transformation and matrix diagonalization. To quantify uncertainties in the fit, we derive analytical expressions and compare them with the results of Brownian dynamics simulations of anisotropic rotational diffusion. We apply the method to microsecond long trajectories of the Dickerson-Drew B-DNA dodecamer and of horse heart myoglobin. The anisotropic rotational diffusion tensors calculated from simulations agree well with predictions from hydrodynamics.

  20. 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].

  1. Analytical Solutions, Moments, and Their Asymptotic Behaviors for the Time-Space Fractional Cable Equation

    NASA Astrophysics Data System (ADS)

    Li, Can; Deng, Wei-Hua

    2014-07-01

    Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L. Wearne, Phys. Rev. Lett. 100 (2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law; and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented.

  2. Exact solution of a linear molecular motor model driven by two-step fluctuations and subject to protein friction.

    PubMed

    Fogedby, Hans C; Metzler, Ralf; Svane, Axel

    2004-08-01

    We investigate by analytical means the stochastic equations of motion of a linear molecular motor model based on the concept of protein friction. Solving the coupled Langevin equations originally proposed by Mogilner et al. [Phys. Lett. A 237, 297 (1998)], and averaging over both the two-step internal conformational fluctuations and the thermal noise, we present explicit, analytical expressions for the average motion and the velocity-force relationship. Our results allow for a direct interpretation of details of this motor model which are not readily accessible from numerical solutions. In particular, we find that the model is able to predict physiologically reasonable values for the load-free motor velocity and the motor mobility.

  3. Molecular motion in cell membranes: Analytic study of fence-hindered random walks

    NASA Astrophysics Data System (ADS)

    Kenkre, V. M.; Giuggioli, L.; Kalay, Z.

    2008-05-01

    A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G -protein coupled μ -opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.

  4. Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in a conductor

    NASA Astrophysics Data System (ADS)

    Grants, Ilmārs; Bojarevičs, Andris; Gerbeth, Gunter

    2016-06-01

    Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.

  5. Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius.

    PubMed

    Guérin, T

    2017-08-01

    Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.

  6. High-temperature ratchets with sawtooth potentials

    NASA Astrophysics Data System (ADS)

    Rozenbaum, Viktor M.; Shapochkina, Irina V.; Sheu, Sheh-Yi; Yang, Dah-Yen; Lin, Sheng Hsien

    2016-11-01

    The concept of the effective potential is suggested as an efficient instrument to get a uniform analytical description of stochastic high-temperature on-off flashing and rocking ratchets. The analytical representation for the average particle velocity, obtained within this technique, allows description of ratchets with sharp potentials (and potentials with jumps in particular). For sawtooth potentials, the explicit analytical expressions for the average velocity of on-off flashing and rocking ratchets valid for arbitrary frequencies of potential energy fluctuations are derived; the difference in their high-frequency asymptotics is explored for the smooth and cusped profiles, and profiles with jumps. The origin of the difference as well as the appearance of the jump behavior in ratchet characteristics are interpreted in terms of self-similar universal solutions which give the continuous description of the effect. It is shown how the jump behavior in motor characteristics arises from the competition between the characteristic times of the system.

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

    NASA Astrophysics Data System (ADS)

    Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

    2016-08-01

    We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas-Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.

  8. Analytic theory of orbit contraction

    NASA Technical Reports Server (NTRS)

    Vinh, N. X.; Longuski, J. M.; Busemann, A.; Culp, R. D.

    1977-01-01

    The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.

  9. Potential profile near singularity point in kinetic Tonks-Langmuir discharges as a function of the ion sources temperature

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

    Kos, L.; Tskhakaya, D. D.; Jelic, N.

    2011-05-15

    A plasma-sheath transition analysis requires a reliable mathematical expression for the plasma potential profile {Phi}(x) near the sheath edge x{sub s} in the limit {epsilon}{identical_to}{lambda}{sub D}/l=0 (where {lambda}{sub D} is the Debye length and l is a proper characteristic length of the discharge). Such expressions have been explicitly calculated for the fluid model and the singular (cold ion source) kinetic model, where exact analytic solutions for plasma equation ({epsilon}=0) are known, but not for the regular (warm ion source) kinetic model, where no analytic solution of the plasma equation has ever been obtained. For the latter case, Riemann [J. Phys.more » D: Appl. Phys. 24, 493 (1991)] only predicted a general formula assuming relatively high ion-source temperatures, i.e., much higher than the plasma-sheath potential drop. Riemann's formula, however, according to him, never was confirmed in explicit solutions of particular models (e.g., that of Bissell and Johnson [Phys. Fluids 30, 779 (1987)] and Scheuer and Emmert [Phys. Fluids 31, 3645 (1988)]) since ''the accuracy of the classical solutions is not sufficient to analyze the sheath vicinity''[Riemann, in Proceedings of the 62nd Annual Gaseous Electronic Conference, APS Meeting Abstracts, Vol. 54 (APS, 2009)]. Therefore, for many years, there has been a need for explicit calculation that might confirm the Riemann's general formula regarding the potential profile at the sheath edge in the cases of regular very warm ion sources. Fortunately, now we are able to achieve a very high accuracy of results [see, e.g., Kos et al., Phys. Plasmas 16, 093503 (2009)]. We perform this task by using both the analytic and the numerical method with explicit Maxwellian and ''water-bag'' ion source velocity distributions. We find the potential profile near the plasma-sheath edge in the whole range of ion source temperatures of general interest to plasma physics, from zero to ''practical infinity.'' While within limits of ''very low'' and ''relatively high'' ion source temperatures, the potential is proportional to the space coordinate powered by rational numbers {alpha}=1/2 and {alpha}=2/3, with medium ion source temperatures. We found {alpha} between these values being a non-rational number strongly dependent on the ion source temperature. The range of the non-rational power-law turns out to be a very narrow one, at the expense of the extension of {alpha}=2/3 region towards unexpectedly low ion source temperatures.« less

  10. Is the Jeffreys' scale a reliable tool for Bayesian model comparison in cosmology?

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

    Nesseris, Savvas; García-Bellido, Juan, E-mail: savvas.nesseris@uam.es, E-mail: juan.garciabellido@uam.es

    2013-08-01

    We are entering an era where progress in cosmology is driven by data, and alternative models will have to be compared and ruled out according to some consistent criterium. The most conservative and widely used approach is Bayesian model comparison. In this paper we explicitly calculate the Bayes factors for all models that are linear with respect to their parameters. We do this in order to test the so called Jeffreys' scale and determine analytically how accurate its predictions are in a simple case where we fully understand and can calculate everything analytically. We also discuss the case of nestedmore » models, e.g. one with M{sub 1} and another with M{sub 2} superset of M{sub 1} parameters and we derive analytic expressions for both the Bayes factor and the figure of Merit, defined as the inverse area of the model parameter's confidence contours. With all this machinery and the use of an explicit example we demonstrate that the threshold nature of Jeffreys' scale is not a ''one size fits all'' reliable tool for model comparison and that it may lead to biased conclusions. Furthermore, we discuss the importance of choosing the right basis in the context of models that are linear with respect to their parameters and how that basis affects the parameter estimation and the derived constraints.« less

  11. Light-cone observables and gauge-invariance in the geodesic light-cone formalism

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

    Scaccabarozzi, Fulvio; Yoo, Jaiyul, E-mail: fulvio@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch

    The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and itmore » complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.« less

  12. Nonlinearity in bacterial population dynamics: Proposal for experiments for the observation of abrupt transitions in patches

    PubMed Central

    Kenkre, V. M.; Kumar, Niraj

    2008-01-01

    An explicit proposal for experiments leading to abrupt transitions in spatially extended bacterial populations in a Petri dish is presented on the basis of an exact formula obtained through an analytic theory. The theory provides accurately the transition expressions despite the fact that the actual solutions, which involve strong nonlinearity, are inaccessible to it. The analytic expressions are verified through numerical solutions of the relevant nonlinear equation. The experimental setup suggested uses opaque masks in a Petri dish bathed in ultraviolet radiation [Lin A-L, et al. (2004) Biophys J 87:75–80 and Perry N (2005) J R Soc Interface 2:379–387], but is based on the interplay of two distances the bacteria must traverse, one of them favorable and the other adverse. As a result of this interplay feature, the experiments proposed introduce highly enhanced reliability in interpretation of observations and in the potential for extraction of system parameters. PMID:19033185

  13. Two-dimensional dispersion of magnetostatic volume spin waves

    NASA Astrophysics Data System (ADS)

    Buijnsters, Frank J.; van Tilburg, Lennert J. A.; Fasolino, Annalisa; Katsnelson, Mikhail I.

    2018-06-01

    Owing to the dipolar (magnetostatic) interaction, long-wavelength spin waves in in-plane magnetized films show an unusual dispersion behavior, which can be mathematically described by the model of and and refinements thereof. However, solving the two-dimensional dispersion requires the evaluation of a set of coupled transcendental equations and one has to rely on numerics. In this work, we present a systematic perturbative analysis of the spin wave model. An expansion in the in-plane wavevector allows us to obtain explicit closed-form expressions for the dispersion relation and mode profiles in various asymptotic regimes. Moreover, we derive a very accurate semi-analytical expression for the dispersion relation of the lowest-frequency mode that is straightforward to evaluate.

  14. A study of density effects in plasmas using analytical approximations for the self-consistent potential

    NASA Astrophysics Data System (ADS)

    Poirier, M.

    2015-06-01

    Density effects in ionized matter require particular attention since they modify energies, wavefunctions and transition rates with respect to the isolated-ion situation. The approach chosen in this paper is based on the ion-sphere model involving a Thomas-Fermi-like description for free electrons, the bound electrons being described by a full quantum mechanical formalism. This permits to deal with plasmas out of thermal local equilibrium, assuming only a Maxwell distribution for free electrons. For H-like ions, such a theory provides simple and rather accurate analytical approximations for the potential created by free electrons. Emphasis is put on the plasma potential rather than on the electron density, since the energies and wavefunctions depend directly on this potential. Beyond the uniform electron gas model, temperature effects may be analyzed. In the case of H-like ions, this formalism provides analytical perturbative expressions for the energies, wavefunctions and transition rates. Explicit expressions are given in the case of maximum orbital quantum number, and compare satisfactorily with results from a direct integration of the radial Schrödinger equation. Some formulas for lower orbital quantum numbers are also proposed.

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

    Schäfer, Gerhard

    The current knowledge in the post-Newtonian (PN) dynamics and motion of non-spinning and spinning compact binaries will be presented based on the Arnowitt-Deser-Misner Hamiltonian approach to general relativity. The presentation will cover the binary dynamics with non-spinning components up to the 4PN order and for spinning binaries up to the next-to-next-to-leading order in the spin-orbit and spin-spin couplings. Radiation reaction will be treated for both non-spinning and spinning binaries. Explicit analytic expressions for the motion will be given, innermost stable circular orbits will be discussed.

  16. An alternative model for a partially coherent elliptical dark hollow beam

    NASA Astrophysics Data System (ADS)

    Li, Xu; Wang, Fei; Cai, Yangjian

    2011-04-01

    An alternative theoretical model named partially coherent hollow elliptical Gaussian beam (HEGB) is proposed to describe a partially coherent beam with an elliptical dark hollow profile. Explicit expression for the propagation factors of a partially coherent HEGB is derived. Based on the generalized Collins formula, analytical formulae for the cross-spectral density and mean-squared beam width of a partially coherent HEGB, propagating through a paraxial ABCD optical system, are derived. Propagation properties of a partially coherent HEGB in free space are studied as a numerical example.

  17. From non-trivial geometries to power spectra and vice versa

    NASA Astrophysics Data System (ADS)

    Brooker, D. J.; Tsamis, N. C.; Woodard, R. P.

    2018-04-01

    We review a recent formalism which derives the functional forms of the primordial—tensor and scalar—power spectra of scalar potential inflationary models. The formalism incorporates the case of geometries with non-constant first slow-roll parameter. Analytic expressions for the power spectra are given that explicitly display the dependence on the geometric properties of the background. Moreover, we present the full algorithm for using our formalism, to reconstruct the model from the observed power spectra. Our techniques are applied to models possessing "features" in their potential with excellent agreement.

  18. Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

    NASA Astrophysics Data System (ADS)

    Dutykh, Denys; Hoefer, Mark; Mitsotakis, Dimitrios

    2018-04-01

    Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order 4.

  19. Nonlinear vibration of an axially loaded beam carrying rigid bodies

    NASA Astrophysics Data System (ADS)

    Barry, O.

    2016-12-01

    This paper investigates the nonlinear vibration due to mid-plane stretching of an axially loaded simply supported beam carrying multiple rigid masses. Explicit expressions and closed form solutions of both linear and nonlinear analysis of the present vibration problem are presented for the first time. The validity of the analytical model is demonstrated using finite element analysis and via comparison with the result in the literature. Parametric studies are conducted to examine how the nonlinear frequency and frequency response curve are affected by tension, rotational inertia, and number of intermediate rigid bodies.

  20. Geometry of Thin Nematic Elastomer Sheets

    NASA Astrophysics Data System (ADS)

    Aharoni, Hillel; Sharon, Eran; Kupferman, Raz

    A thin sheet of nematic elastomer attains 3D configurations depending on the nematic director field upon heating. In this talk we describe the intrinsic geometry of such a sheet, and derive an expression for the metric induced by general smooth nematic director fields. Furthermore, we investigate the reverse problem of constructing a director field that induces a specified 2D geometry. We provide an explicit analytical recipe for constructing any surface of revolution using this method. We demonstrate how the design of an arbitrary 2D geometry is accessible using approximate numerical methods.

  1. Designing a Double-Pole Nanoscale Relay Based on a Carbon Nanotube: A Theoretical Study

    NASA Astrophysics Data System (ADS)

    Mu, Weihua; Ou-Yang, Zhong-can; Dresselhaus, Mildred S.

    2017-08-01

    We theoretically investigate a novel and powerful double-pole nanoscale relay based on a carbon nanotube, which is one of the nanoelectromechanical switches being able to work under the strong nuclear radiation, and analyze the physical mechanism of the operating stages in the operation, including "pull in," "connection," and "pull back," as well as the key factors influencing the efficiency of the devices. We explicitly provide the analytical expression of the two important operation voltages, Vpull in and Vpull back , therefore clearly showing the dependence of the material properties and geometry of the present devices by the analytical method from basic physics, avoiding complex numerical calculations. Our method is easy to use in preparing the design guide for fabricating the present device and other nanoelectromechanical devices.

  2. Tornado model for a magnetised plasma

    NASA Astrophysics Data System (ADS)

    Onishchenko, O. G.; Fedun, V.; Smolyakov, A.; Horton, W.; Pokhotelov, O. A.; Verth, G.

    2018-05-01

    A new analytical model of axially-symmetric magnetic vortices with both a twisted fluid flow and a magnetic field is proposed. The exact solution for the three-dimensional structure of the fluid velocity and the magnetic field is obtained within the framework of the ideal magnetohydrodynamic equations for an incompressible fluid in a gravitational field. A quasi-stationary localised vortex arises when the radial flow that tends to concentrate vorticity in a narrow column around the axis of symmetry is balanced by the vertical vortex advection in the axial direction. The explicit expressions for the velocity and magnetic field components are obtained. The proposed analytic model may be used to parameterise the observed solar tornadoes and can provide a new indirect way for estimating magnetic twist from the observed azimuthal velocity profiles.

  3. Non-collinear magnetism with analytic Bond-Order Potentials

    NASA Astrophysics Data System (ADS)

    Ford, Michael E.; Pettifor, D. G.; Drautz, Ralf

    2015-03-01

    The theory of analytic Bond-Order Potentials as applied to non-collinear magnetic structures of transition metals is extended to take into account explicit rotations of Hamiltonian and local moment matrix elements between locally and globally defined spin-coordinate systems. Expressions for the gradients of the energy with respect to the Hamiltonian matrix elements, the interatomic forces and the magnetic torques are derived. The method is applied to simulations of the rotation of magnetic moments in α iron, as well as α and β manganese, based on d-valent orthogonal tight-binding parametrizations of the electronic structure. A new weighted-average terminator is introduced to improve the convergence of the Bond-Order Potential energies and torques with respect to tight-binding reference values, although the general behavior is qualitatively correct for low-moment expansions.

  4. Towards a minimal stochastic model for a large class of diffusion-reactions on biological membranes.

    PubMed

    Chevalier, Michael W; El-Samad, Hana

    2012-08-28

    Diffusion of biological molecules on 2D biological membranes can play an important role in the behavior of stochastic biochemical reaction systems. Yet, we still lack a fundamental understanding of circumstances where explicit accounting of the diffusion and spatial coordinates of molecules is necessary. In this work, we illustrate how time-dependent, non-exponential reaction probabilities naturally arise when explicitly accounting for the diffusion of molecules. We use the analytical expression of these probabilities to derive a novel algorithm which, while ignoring the exact position of the molecules, can still accurately capture diffusion effects. We investigate the regions of validity of the algorithm and show that for most parameter regimes, it constitutes an accurate framework for studying these systems. We also document scenarios where large spatial fluctuation effects mandate explicit consideration of all the molecules and their positions. Taken together, our results derive a fundamental understanding of the role of diffusion and spatial fluctuations in these systems. Simultaneously, they provide a general computational methodology for analyzing a broad class of biological networks whose behavior is influenced by diffusion on membranes.

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

    NASA Astrophysics Data System (ADS)

    Tschirhart, Hugo; Platini, Thierry

    2018-05-01

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

  6. Nonlinear core deflection in injection molding

    NASA Astrophysics Data System (ADS)

    Poungthong, P.; Giacomin, A. J.; Saengow, C.; Kolitawong, C.; Liao, H.-C.; Tseng, S.-C.

    2018-05-01

    Injection molding of thin slender parts is often complicated by core deflection. This deflection is caused by molten plastics race tracking through the slit between the core and the rigid cavity wall. The pressure of this liquid exerts a lateral force of the slender core causing the core to bend, and this bending is governed by a nonlinear fifth order ordinary differential equation for the deflection that is not directly in the position along the core. Here we subject this differential equation to 6 sets of boundary conditions, corresponding to 6 commercial core constraints. For each such set of boundary conditions, we develop an explicit approximate analytical solution, including both a linear term and a nonlinear term. By comparison with finite difference solutions, we find our new analytical solutions to be accurate. We then use these solutions to derive explicit analytical approximations for maximum deflections and for the core position of these maximum deflections. Our experiments on the base-gated free-tip boundary condition agree closely with our new explicit approximate analytical solution.

  7. 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.

  8. Quantum thermal diode based on two interacting spinlike systems under different excitations.

    PubMed

    Ordonez-Miranda, Jose; Ezzahri, Younès; Joulain, Karl

    2017-02-01

    We demonstrate that two interacting spinlike systems characterized by different excitation frequencies and coupled to a thermal bath each, can be used as a quantum thermal diode capable of efficiently rectifying the heat current. This is done by deriving analytical expressions for both the heat current and rectification factor of the diode, based on the solution of a master equation for the density matrix. Higher rectification factors are obtained for lower heat currents, whose magnitude takes their maximum values for a given interaction coupling proportional to the temperature of the hotter thermal bath. It is shown that the rectification ability of the diode increases with the excitation frequencies difference, which drives the asymmetry of the heat current, when the temperatures of the thermal baths are inverted. Furthermore, explicit conditions for the optimization of the rectification factor and heat current are explicitly found.

  9. GPU-accelerated simulations of isolated black holes

    NASA Astrophysics Data System (ADS)

    Lewis, Adam G. M.; Pfeiffer, Harald P.

    2018-05-01

    We present a port of the numerical relativity code SpEC which is capable of running on NVIDIA GPUs. Since this code must be maintained in parallel with SpEC itself, a primary design consideration is to perform as few explicit code changes as possible. We therefore rely on a hierarchy of automated porting strategies. At the highest level we use TLoops, a C++ library of our design, to automatically emit CUDA code equivalent to tensorial expressions written into C++ source using a syntax similar to analytic calculation. Next, we trace out and cache explicit matrix representations of the numerous linear transformations in the SpEC code, which allows these to be performed on the GPU using pre-existing matrix-multiplication libraries. We port the few remaining important modules by hand. In this paper we detail the specifics of our port, and present benchmarks of it simulating isolated black hole spacetimes on several generations of NVIDIA GPU.

  10. Optimum design of structures subject to general periodic loads

    NASA Technical Reports Server (NTRS)

    Reiss, Robert; Qian, B.

    1989-01-01

    A simplified version of Icerman's problem regarding the design of structures subject to a single harmonic load is discussed. The nature of the restrictive conditions that must be placed on the design space in order to ensure an analytic optimum are discussed in detail. Icerman's problem is then extended to include multiple forcing functions with different driving frequencies. And the conditions that now must be placed upon the design space to ensure an analytic optimum are again discussed. An important finding is that all solutions to the optimality condition (analytic stationary design) are local optima, but the global optimum may well be non-analytic. The more general problem of distributing the fixed mass of a linear elastic structure subject to general periodic loads in order to minimize some measure of the steady state deflection is also considered. This response is explicitly expressed in terms of Green's functional and the abstract operators defining the structure. The optimality criterion is derived by differentiating the response with respect to the design parameters. The theory is applicable to finite element as well as distributed parameter models.

  11. A semi-analytical description of protein folding that incorporates detailed geometrical information

    PubMed Central

    Suzuki, Yoko; Noel, Jeffrey K.; Onuchic, José N.

    2011-01-01

    Much has been done to study the interplay between geometric and energetic effects on the protein folding energy landscape. Numerical techniques such as molecular dynamics simulations are able to maintain a precise geometrical representation of the protein. Analytical approaches, however, often focus on the energetic aspects of folding, including geometrical information only in an average way. Here, we investigate a semi-analytical expression of folding that explicitly includes geometrical effects. We consider a Hamiltonian corresponding to a Gaussian filament with structure-based interactions. The model captures local features of protein folding often averaged over by mean-field theories, for example, loop contact formation and excluded volume. We explore the thermodynamics and folding mechanisms of beta-hairpin and alpha-helical structures as functions of temperature and Q, the fraction of native contacts formed. Excluded volume is shown to be an important component of a protein Hamiltonian, since it both dominates the cooperativity of the folding transition and alters folding mechanisms. Understanding geometrical effects in analytical formulae will help illuminate the consequences of the approximations required for the study of larger proteins. PMID:21721664

  12. From the fundamental rule to the analysing situation.

    PubMed

    Donnet, J L

    2001-02-01

    The analytic method relies on the mental capacity to produce an associative sequence, and, afterwards, to discern its unconscious logic; within the social practice of the analytic cure, the method presents itself as the mastered enactment of the condition through which free association proves to be possible, interpretable and beneficial. There is a contradiction between the necessity of relying on a former theorisation and that of willingly suspending a knowledge that might serve the authenticity of the experience. The author reminds us of the structural links between the fundamental rule and the defined situations within which the analytic process of transformative investigation can take place. He raises the problems that it is suggested arise with the initial objectivation method by acknowledging the transference as the created-found object of interpretation. He shows how the transformation of the patient into analysand implies the functional introjection of the various elements contained by the analytic site. The meaning given to the expression 'analysing situation' is made explicit. The crucial value of the process of enunciation is illustrated by a brief example.

  13. Analytical steady-state solutions for water-limited cropping systems using saline irrigation water

    NASA Astrophysics Data System (ADS)

    Skaggs, T. H.; Anderson, R. G.; Corwin, D. L.; Suarez, D. L.

    2014-12-01

    Due to the diminishing availability of good quality water for irrigation, it is increasingly important that irrigation and salinity management tools be able to target submaximal crop yields and support the use of marginal quality waters. In this work, we present a steady-state irrigated systems modeling framework that accounts for reduced plant water uptake due to root zone salinity. Two explicit, closed-form analytical solutions for the root zone solute concentration profile are obtained, corresponding to two alternative functional forms of the uptake reduction function. The solutions express a general relationship between irrigation water salinity, irrigation rate, crop salt tolerance, crop transpiration, and (using standard approximations) crop yield. Example applications are illustrated, including the calculation of irrigation requirements for obtaining targeted submaximal yields, and the generation of crop-water production functions for varying irrigation waters, irrigation rates, and crops. Model predictions are shown to be mostly consistent with existing models and available experimental data. Yet the new solutions possess advantages over available alternatives, including: (i) the solutions were derived from a complete physical-mathematical description of the system, rather than based on an ad hoc formulation; (ii) the analytical solutions are explicit and can be evaluated without iterative techniques; (iii) the solutions permit consideration of two common functional forms of salinity induced reductions in crop water uptake, rather than being tied to one particular representation; and (iv) the utilized modeling framework is compatible with leading transient-state numerical models.

  14. Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics

    NASA Astrophysics Data System (ADS)

    Marrochio, Hugo; Noronha, Jorge; Denicol, Gabriel S.; Luzum, Matthew; Jeon, Sangyong; Gale, Charles

    2015-01-01

    We use symmetry arguments developed by Gubser to construct the first radially expanding explicit solutions of the Israel-Stewart formulation of hydrodynamics. Along with a general semi-analytical solution, an exact analytical solution is given which is valid in the cold plasma limit where viscous effects from shear viscosity and the relaxation time coefficient are important. The radially expanding solutions presented in this paper can be used as nontrivial checks of numerical algorithms employed in hydrodynamic simulations of the quark-gluon plasma formed in ultrarelativistic heavy ion collisions. We show this explicitly by comparing such analytic and semi-analytic solutions with the corresponding numerical solutions obtained using the music viscous hydrodynamics simulation code.

  15. Analytical approximations for spatial stochastic gene expression in single cells and tissues

    PubMed Central

    Smith, Stephen; Cianci, Claudia; Grima, Ramon

    2016-01-01

    Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686

  16. Highly accurate analytic formulae for projectile motion subjected to quadratic drag

    NASA Astrophysics Data System (ADS)

    Turkyilmazoglu, Mustafa

    2016-05-01

    The classical phenomenon of motion of a projectile fired (thrown) into the horizon through resistive air charging a quadratic drag onto the object is revisited in this paper. No exact solution is known that describes the full physical event under such an exerted resistance force. Finding elegant analytical approximations for the most interesting engineering features of dynamical behavior of the projectile is the principal target. Within this purpose, some analytical explicit expressions are derived that accurately predict the maximum height, its arrival time as well as the flight range of the projectile at the highest ascent. The most significant property of the proposed formulas is that they are not restricted to the initial speed and firing angle of the object, nor to the drag coefficient of the medium. In combination with the available approximations in the literature, it is possible to gain information about the flight and complete the picture of a trajectory with high precision, without having to numerically simulate the full governing equations of motion.

  17. Cross-section fluctuations in chaotic scattering systems.

    PubMed

    Ericson, Torleif E O; Dietz, Barbara; Richter, Achim

    2016-10-01

    Exact analytical expressions for the cross-section correlation functions of chaotic scattering systems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering (S)-matrix correlation functions accurately. Our results are given in the energy and in the time representations and apply in the whole range from isolated to overlapping resonances. The S-matrix contributions to the cross-section correlations are obtained in terms of explicit irreducible and reducible correlation functions. Consequently, the model can be used for a detailed exploration of the key features of the cross-section correlations and the underlying physical mechanisms. In the region of isolated resonances, the cross-section correlations contain a dominant contribution from the self-correlation term. For narrow states the self-correlations originate predominantly from widely spaced states with exceptionally large partial width. In the asymptotic region of well-overlapping resonances, the cross-section autocorrelation functions are given in terms of the S-matrix autocorrelation functions. For inelastic correlations, in particular, the Ericson fluctuations rapidly dominate in that region. Agreement with known analytical and experimental results is excellent.

  18. Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Kubenko, V. D.

    2016-11-01

    The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed

  19. Optimal control, optimization and asymptotic analysis of Purcell's microswimmer model

    NASA Astrophysics Data System (ADS)

    Wiezel, Oren; Or, Yizhar

    2016-11-01

    Purcell's swimmer (1977) is a classic model of a three-link microswimmer that moves by performing periodic shape changes. Becker et al. (2003) showed that the swimmer's direction of net motion is reversed upon increasing the stroke amplitude of joint angles. Tam and Hosoi (2007) used numerical optimization in order to find optimal gaits for maximizing either net displacement or Lighthill's energetic efficiency. In our work, we analytically derive leading-order expressions as well as next-order corrections for both net displacement and energetic efficiency of Purcell's microswimmer. Using these expressions enables us to explicitly show the reversal in direction of motion, as well as obtaining an estimate for the optimal stroke amplitude. We also find the optimal swimmer's geometry for maximizing either displacement or energetic efficiency. Additionally, the gait optimization problem is revisited and analytically formulated as an optimal control system with only two state variables, which can be solved using Pontryagin's maximum principle. It can be shown that the optimal solution must follow a "singular arc". Numerical solution of the boundary value problem is obtained, which exactly reproduces Tam and Hosoi's optimal gait.

  20. A theoretical framework for modeling dilution enhancement of non-reactive solutes in heterogeneous porous media.

    PubMed

    de Barros, F P J; Fiori, A; Boso, F; Bellin, A

    2015-01-01

    Spatial heterogeneity of the hydraulic properties of geological porous formations leads to erratically shaped solute clouds, thus increasing the edge area of the solute body and augmenting the dilution rate. In this study, we provide a theoretical framework to quantify dilution of a non-reactive solute within a steady state flow as affected by the spatial variability of the hydraulic conductivity. Embracing the Lagrangian concentration framework, we obtain explicit semi-analytical expressions for the dilution index as a function of the structural parameters of the random hydraulic conductivity field, under the assumptions of uniform-in-the-average flow, small injection source and weak-to-mild heterogeneity. Results show how the dilution enhancement of the solute cloud is strongly dependent on both the statistical anisotropy ratio and the heterogeneity level of the porous medium. The explicit semi-analytical solution also captures the temporal evolution of the dilution rate; for the early- and late-time limits, the proposed solution recovers previous results from the literature, while at intermediate times it reflects the increasing interplay between large-scale advection and local-scale dispersion. The performance of the theoretical framework is verified with high resolution numerical results and successfully tested against the Cape Cod field data. Copyright © 2015 Elsevier B.V. All rights reserved.

  1. Analytical results for the time-dependent current density distribution of expanding ultracold gases after a sudden change of the confining potential

    NASA Astrophysics Data System (ADS)

    Boumaza, R.; Bencheikh, K.

    2017-12-01

    Using the so-called operator product expansion to lowest order, we extend the work in Campbell et al (2015 Phys. Rev. Lett 114 125302) by deriving a simple analytical expression for the long-time asymptotic one-body reduced density matrix during free expansion for a one-dimensional system of bosons with large atom number interacting through a repulsive delta potential initially confined by a potential well. This density matrix allows direct access to the momentum distribution and also to the mass current density. For initially confining power-law potentials we give explicit expressions, in the limits of very weak and very strong interaction, for the current density distributions during the free expansion. In the second part of the work we consider the expansion of ultracold gas from a confining harmonic trap to another harmonic trap with a different frequency. For the case of a quantum impenetrable gas of bosons (a Tonks-Girardeau gas) with a given atom number, we present an exact analytical expression for the mass current distribution (mass transport) after release from one harmonic trap to another harmonic trap. It is shown that, for a harmonically quenched Tonks-Girardeau gas, the current distribution is a suitable collective observable and under the weak quench regime, it exhibits oscillations at the same frequencies as those recently predicted for the peak momentum distribution in the breathing mode. The analysis is extended to other possible quenched systems.

  2. Explicit role of ionic strength in retention behavior of polystyrene latex particles in sedimentation field-flow fractionation: Slip boundary model.

    PubMed

    Rah, Kyunil; Han, Sujeong; Choi, Jaeyeong; Eum, Chul Hun; Lee, Seungho

    2017-12-15

    We investigate an explicit role of the ionic strength in the retention behaviors of polystyrene (PS) latex particles in sedimentation field-flow fractionation (SdFFF) by hinging upon the retention theory recently developed [1] asR=(R o +v b * )/(1+v b * ). Here R is an experimental retention ratio, and R o is the analytical expression of the standard retention theory based on the parabolic flow velocity. The reduced boundary velocityv b * is expressed in terms of the ionic strength I of the carrier liquid as v b * =v b,o * /(1+εI), where v b,o * =0.070and ε=60 mM -1 for all the PS latex systems under investigation. We then apply this to study the explicit ionic strength effect on the retention behaviors of PS beads of 200, 300, 400, and 500nm, respectively. As a primary result, the strong dependence of the retention ratio on the ionic strength can be quantitatively accounted for in an excellent accuracy: The slip effect at the channel surface is significant, particularly when I≲0.5mM, without showing any distinguishable dependence on the specific additives to control I, such as FL-70, SDS, NaNO 3 , and NaN 3 . Based on the present study, we put forward an experimental means to estimate the ionic strength of an aqueous solution using an FFF technique. Copyright © 2017. Published by Elsevier B.V.

  3. Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

    NASA Technical Reports Server (NTRS)

    Madnia, C. K.; Frankel, S. H.; Givi, P.

    1992-01-01

    Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.

  4. Localized mRNA translation and protein association

    NASA Astrophysics Data System (ADS)

    Zhdanov, Vladimir P.

    2014-08-01

    Recent direct observations of localization of mRNAs and proteins both in prokaryotic and eukaryotic cells can be related to slowdown of diffusion of these species due to macromolecular crowding and their ability to aggregate and form immobile or slowly mobile complexes. Here, a generic kinetic model describing both these factors is presented and comprehensively analyzed. Although the model is non-linear, an accurate self-consistent analytical solution of the corresponding reaction-diffusion equation has been constructed, the types of localized protein distributions have been explicitly shown, and the predicted kinetic regimes of gene expression have been classified.

  5. The non-radiating component of the field generated by a finite monochromatic scalar source distribution

    NASA Astrophysics Data System (ADS)

    Hoenders, Bernhard J.; Ferwerda, Hedzer A.

    1998-09-01

    We separate the field generated by a spherically symmetric bounded scalar monochromatic source into a radiative and non-radiative part. The non-radiative part is obtained by projecting the total field on the space spanned by the non-radiating inhomogeneous modes, i.e. the modes which satisfy the inhomogeneous wave equation. Using residue techniques, introduced by Cauchy, we obtain an explicit analytical expression for the non-radiating component. We also identify the part of the source distribution which corresponds to this non-radiating part. The analysis is based on the scalar wave equation.

  6. Optimal behavior of viscoelastic flow at resonant frequencies.

    PubMed

    Lambert, A A; Ibáñez, G; Cuevas, S; del Río, J A

    2004-11-01

    The global entropy generation rate in the zero-mean oscillatory flow of a Maxwell fluid in a pipe is analyzed with the aim of determining its behavior at resonant flow conditions. This quantity is calculated explicitly using the analytic expression for the velocity field and assuming isothermal conditions. The global entropy generation rate shows well-defined peaks at the resonant frequencies where the flow displays maximum velocities. It was found that resonant frequencies can be considered optimal in the sense that they maximize the power transmitted to the pulsating flow at the expense of maximum dissipation.

  7. On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

    NASA Astrophysics Data System (ADS)

    Doha, E. H.

    2002-02-01

    An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

  8. How cosmic microwave background correlations at large angles relate to mass autocorrelations in space

    NASA Technical Reports Server (NTRS)

    Blumenthal, George R.; Johnston, Kathryn V.

    1994-01-01

    The Sachs-Wolfe effect is known to produce large angular scale fluctuations in the cosmic microwave background radiation (CMBR) due to gravitational potential fluctuations. We show how the angular correlation function of the CMBR can be expressed explicitly in terms of the mass autocorrelation function xi(r) in the universe. We derive analytic expressions for the angular correlation function and its multipole moments in terms of integrals over xi(r) or its second moment, J(sub 3)(r), which does not need to satisfy the sort of integral constraint that xi(r) must. We derive similar expressions for bulk flow velocity in terms of xi and J(sub 3). One interesting result that emerges directly from this analysis is that, for all angles theta, there is a substantial contribution to the correlation function from a wide range of distance r and that radial shape of this contribution does not vary greatly with angle.

  9. Bessel-Gauss beams as rigorous solutions of the Helmholtz equation.

    PubMed

    April, Alexandre

    2011-10-01

    The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

  10. Freedom of racist speech: Ego and expressive threats.

    PubMed

    White, Mark H; Crandall, Christian S

    2017-09-01

    Do claims of "free speech" provide cover for prejudice? We investigate whether this defense of racist or hate speech serves as a justification for prejudice. In a series of 8 studies (N = 1,624), we found that explicit racial prejudice is a reliable predictor of the "free speech defense" of racist expression. Participants endorsed free speech values for singing racists songs or posting racist comments on social media; people high in prejudice endorsed free speech more than people low in prejudice (meta-analytic r = .43). This endorsement was not principled-high levels of prejudice did not predict endorsement of free speech values when identical speech was directed at coworkers or the police. Participants low in explicit racial prejudice actively avoided endorsing free speech values in racialized conditions compared to nonracial conditions, but participants high in racial prejudice increased their endorsement of free speech values in racialized conditions. Three experiments failed to find evidence that defense of racist speech by the highly prejudiced was based in self-relevant or self-protective motives. Two experiments found evidence that the free speech argument protected participants' own freedom to express their attitudes; the defense of other's racist speech seems motivated more by threats to autonomy than threats to self-regard. These studies serve as an elaboration of the Justification-Suppression Model (Crandall & Eshleman, 2003) of prejudice expression. The justification of racist speech by endorsing fundamental political values can serve to buffer racial and hate speech from normative disapproval. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  11. Adhesive-bonded double-lap joints. [analytical solutions for static load carrying capacity

    NASA Technical Reports Server (NTRS)

    Hart-Smith, L. J.

    1973-01-01

    Explicit analytical solutions are derived for the static load carrying capacity of double-lap adhesive-bonded joints. The analyses extend the elastic solution Volkersen and cover adhesive plasticity, adherend stiffness imbalance and thermal mismatch between the adherends. Both elastic-plastic and bi-elastic adhesive representations lead to the explicit result that the influence of the adhesive on the maximum potential bond strength is defined uniquely by the strain energy in shear per unit area of bond. Failures induced by peel stresses at the ends of the joint are examined. This failure mode is particularly important for composite adherends. The explicit solutions are sufficiently simple to be used for design purposes

  12. Efficient scheme for parametric fitting of data in arbitrary dimensions.

    PubMed

    Pang, Ning-Ning; Tzeng, Wen-Jer; Kao, Hisen-Ching

    2008-07-01

    We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.

  13. Criticality and Connectivity in Macromolecular Charge Complexation

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

    Qin, Jian; de Pablo, Juan J.

    We examine the role of molecular connectivity and architecture on the complexation of ionic macromolecules (polyelectrolytes) of finite size. A unified framework is developed and applied to evaluate the electrostatic correlation free energy for point-like, rod-like, and coil-like molecules. That framework is generalized to molecules of variable fractal dimensions, including dendrimers. Analytical expressions for the free energy, correlation length, and osmotic pressure are derived, thereby enabling consideration of the effects of charge connectivity, fractal dimension, and backbone stiffness on the complexation behavior of a wide range of polyelectrolytes. Results are presented for regions in the immediate vicinity of the criticalmore » region and far from it. A transparent and explicit expression for the coexistence curve is derived in order to facilitate analysis of experimentally observed phase diagrams.« less

  14. Expressions of dissatisfaction and complaint by people with learning disabilities: a discourse analytic study.

    PubMed

    Jingree, Treena; Finlay, W M L

    2013-06-01

    This paper uses critical discursive psychology to examine expressions of dissatisfaction and complaint by people with learning disabilities. UK government policies stress that people with learning disabilities should have more control over their lives. Expressing dissatisfaction about services is an important aspect of this process. However, given that such individuals are often treated as incompetent, and given the delicate nature of complaining about services one might rely on for day-to-day support, this can be difficult to do. In building complaints, speakers drew on repertoires about competence and incompetence, the right to free choice as a principle, and tempered dissatisfaction to make contrasts between good and bad supporters and practice. While the complaints show many of the general features of complaints identified in previous work in the general population, they were crafted to the particular institutional context of social care, and attended both explicitly and implicitly to the particular issues of competence, power, and authority found in those services. Speakers positioned themselves as competent, and service workers as more or less competent in their roles. Issues of power in social care services were observed explicitly in the accounts, whereby people described staff as controlling and it being difficult to voice dissatisfaction. They were also implicit in the way speakers drew on the others with institutional authority for corroboration and comparison. © 2011 The British Psychological Society.

  15. Joint multifractal analysis based on the partition function approach: analytical analysis, numerical simulation and empirical application

    NASA Astrophysics Data System (ADS)

    Xie, Wen-Jie; Jiang, Zhi-Qiang; Gu, Gao-Feng; Xiong, Xiong; Zhou, Wei-Xing

    2015-10-01

    Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities.

  16. A non-planar two-loop three-point function beyond multiple polylogarithms

    NASA Astrophysics Data System (ADS)

    von Manteuffel, Andreas; Tancredi, Lorenzo

    2017-06-01

    We consider the analytic calculation of a two-loop non-planar three-point function which contributes to the two-loop amplitudes for t\\overline{t} production and γγ production in gluon fusion through a massive top-quark loop. All subtopology integrals can be written in terms of multiple polylogarithms over an irrational alphabet and we employ a new method for the integration of the differential equations which does not rely on the rationalization of the latter. The top topology integrals, instead, in spite of the absence of a massive three-particle cut, cannot be evaluated in terms of multiple polylogarithms and require the introduction of integrals over complete elliptic integrals and polylogarithms. We provide one-fold integral representations for the solutions and continue them analytically to all relevant regions of the phase space in terms of real functions, extracting all imaginary parts explicitly. The numerical evaluation of our expressions becomes straightforward in this way.

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

    Sinitsyn, Nikolai A.

    In this paper, I identify a nontrivial four-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. I argue that this system satisfies the criteria ofmore » integrability in the multistate Landau-Zener theory, which allows one to derive explicit exact analytical expressions for the transition probability matrix. Finally, I also argue that this model is likely a special case of a larger class of solvable systems, and present a six-state generalization as an example.« less

  18. A histogram-free multicanonical Monte Carlo algorithm for the construction of analytical density of states

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

    Eisenbach, Markus; Li, Ying Wai

    We report a new multicanonical Monte Carlo (MC) algorithm to obtain the density of states (DOS) for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain an analytical form for the DOS expressed in a chosen basis set, instead of a numerical array of finite resolution as in previous variants of this class of MC methods such as the multicanonical (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled by storing the visited states directly in a data set and avoiding the explicit collection of a histogram. This practice also has the advantage ofmore » avoiding undesirable artificial errors caused by the discretization and binning of continuous state variables. Our results show that this scheme is capable of obtaining converged results with a much reduced number of Monte Carlo steps, leading to a significant speedup over existing algorithms.« less

  19. Metric of two balancing Kerr particles in physical parametrization

    NASA Astrophysics Data System (ADS)

    Manko, V. S.; Ruiz, E.

    2015-11-01

    The present paper aims at elaborating a completely physical representation for the general 4-parameter family of the extended double-Kerr spacetimes describing two spinning sources in gravitational equilibrium. This involved problem is solved in a concise analytical form by using the individual Komar masses and angular momenta as arbitrary parameters, and the simplest equatorially symmetric specialization of the general expressions obtained by us yields the physical representation for the well-known Dietz-Hoenselaers superextreme case of two balancing identical Kerr constituents. The existence of the physically meaningful "black-hole-superextreme-object" equilibrium configurations permitted by the general solution may be considered as a clear indication that the spin-spin repulsion force might actually be by far stronger than expected earlier, when only the balance between two superextreme Kerr sources was thought possible. We also present the explicit analytical formulas relating the equilibrium states in the double-Kerr and double-Reissner-Nordström configurations.

  20. An analytical approach to the CMB polarization in a spatially closed background

    NASA Astrophysics Data System (ADS)

    Niazy, Pedram; Abbassi, Amir H.

    2018-03-01

    The scalar mode polarization of the cosmic microwave background is derived in a spatially closed universe from the Boltzmann equation using the line of sight integral method. The EE and TE multipole coefficients have been extracted analytically by considering some tolerable approximations such as considering the evolution of perturbation hydrodynamically and sudden transition from opacity to transparency at the time of last scattering. As the major advantage of analytic expressions, CEE,ℓS and CTE,ℓ explicitly show the dependencies on baryon density ΩB, matter density ΩM, curvature ΩK, primordial spectral index ns, primordial power spectrum amplitude As, Optical depth τreion, recombination width σt and recombination time tL. Using a realistic set of cosmological parameters taken from a fit to data from Planck, the closed universe EE and TE power spectrums in the scalar mode are compared with numerical results from the CAMB code and also latest observational data. The analytic results agree with the numerical ones on the big and moderate scales. The peak positions are in good agreement with the numerical result on these scales while the peak heights agree with that to within 20% due to the approximations have been considered for these derivations. Also, several interesting properties of CMB polarization are revealed by the analytic spectra.

  1. Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory

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

    Dixon, Lance J.; /SLAC; Drummond, James M.

    2012-02-15

    We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parametersmore » uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.« less

  2. Tacit knowledge and visual expertise in medical diagnostic reasoning: implications for medical education.

    PubMed

    Heiberg Engel, Peter Johan

    2008-01-01

    Much education--especially at the university level--has been criticized for having primarily dealt with explicit knowledge, i.e. those aspects of mental activities, which are verbal and conscious. Furthermore, research in medical diagnostic reasoning has been criticized for having focused on the specialty of intern medicine, while specialties with other skills, i.e. perceptive skills within pathology and radiology, have been ignored. To show that the concept of tacit knowledge is important in medical education-at all levels and in medical diagnostic reasoning. Describing how tacit knowledge according to Michael Polany, is experienced and expressed in day-to-day life, it is shown that there is a tacit dimension to all knowledge. Reviewing recent literature on medical diagnostic reasoning, it is shown that tacit knowledge is recognized in connection with concepts such as "non-analytical reasoning" and "dual process of reasoning." It is important that educators are trained in how explicit and implicit knowledge is attained and that tacit knowledge is included in educational programmes of all medical specialties.

  3. On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials

    NASA Astrophysics Data System (ADS)

    Doha, E. H.

    2004-01-01

    Formulae expressing explicitly the Jacobi coefficients of a general-order derivative (integral) of an infinitely differentiable function in terms of its original expansion coefficients, and formulae for the derivatives (integrals) of Jacobi polynomials in terms of Jacobi polynomials themselves are stated. A formula for the Jacobi coefficients of the moments of one single Jacobi polynomial of certain degree is proved. Another formula for the Jacobi coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its original expanded coefficients is also given. A simple approach in order to construct and solve recursively for the connection coefficients between Jacobi-Jacobi polynomials is described. Explicit formulae for these coefficients between ultraspherical and Jacobi polynomials are deduced, of which the Chebyshev polynomials of the first and second kinds and Legendre polynomials are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Jacobi and Hermite-Jacobi are developed.

  4. Analytical Applications of Monte Carlo Techniques.

    ERIC Educational Resources Information Center

    Guell, Oscar A.; Holcombe, James A.

    1990-01-01

    Described are analytical applications of the theory of random processes, in particular solutions obtained by using statistical procedures known as Monte Carlo techniques. Supercomputer simulations, sampling, integration, ensemble, annealing, and explicit simulation are discussed. (CW)

  5. The areal reduction factor: A new analytical expression for the Lazio Region in central Italy

    NASA Astrophysics Data System (ADS)

    Mineo, C.; Ridolfi, E.; Napolitano, F.; Russo, F.

    2018-05-01

    For the study and modeling of hydrological phenomena, both in urban and rural areas, a proper estimation of the areal reduction factor (ARF) is crucial. In this paper, we estimated the ARF from observed rainfall data as the ratio between the average rainfall occurring in a specific area and the point rainfall. Then, we compared the obtained ARF values with some of the most widespread empirical approaches in literature which are used when rainfall observations are not available. Results highlight that the literature formulations can lead to a substantial over- or underestimation of the ARF estimated from observed data. These findings can have severe consequences, especially in the design of hydraulic structures where empirical formulations are extensively applied. The aim of this paper is to present a new analytical relationship with an explicit dependence on the rainfall duration and area that can better represent the ARF-area trend over the area case of study. The analytical curve presented here can find an important application to estimate the ARF values for design purposes. The test study area is the Lazio Region (central Italy).

  6. Will This Case Count? The Influence of Training on Treatment.

    PubMed

    Blakeman, Rachel; Goldberger, Marianne

    2016-12-01

    Mandated use of the couch-whether specifically stated or tacitly communicated by supervisors and colleagues-to fulfill requirements for graduation or certification is a significant disservice to candidates and their patients. In its training standards, it is argued, APsaA and its member institutes should state explicitly that a treatment can qualify as a psychoanalysis, regardless of whether the patient is using the couch, as long as the process is analytic and the candidate's thinking is demonstrably analytic. The mandate, however conveyed, that one must use the couch interferes with candidates' optimal analytic functioning, jeopardizing their patients' analyses. Data from infant observation, neuroscience, and facial expression studies-unavailable to earlier generations of analysts-support a more nuanced view of use of the couch. Each analysis is unique, and some analyses might well benefit from use of both the couch and the chair at different phases of treatment, but unless this is spelled out by ApsaA and its member institutes, candidates and junior analysts will be prevented from freely contemplating the clinical benefits or detriments of their use in specific cases.

  7. 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.

  8. First-and Second-Order Displacement Transfer Functions for Structural Shape Calculations Using Analytically Predicted Surface Strains

    NASA Technical Reports Server (NTRS)

    Ko, William L.; Fleischer, Van Tran

    2012-01-01

    New first- and second-order displacement transfer functions have been developed for deformed shape calculations of nonuniform cross-sectional beam structures such as aircraft wings. The displacement transfer functions are expressed explicitly in terms of beam geometrical parameters and surface strains (uniaxial bending strains) obtained at equally spaced strain stations along the surface of the beam structure. By inputting the measured or analytically calculated surface strains into the displacement transfer functions, one could calculate local slopes, deflections, and cross-sectional twist angles of the nonuniform beam structure for mapping the overall structural deformed shapes for visual display. The accuracy of deformed shape calculations by the first- and second-order displacement transfer functions are determined by comparing these values to the analytically predicted values obtained from finite element analyses. This comparison shows that the new displacement transfer functions could quite accurately calculate the deformed shapes of tapered cantilever tubular beams with different tapered angles. The accuracy of the present displacement transfer functions also are compared to those of the previously developed displacement transfer functions.

  9. Covariance Bell inequalities

    NASA Astrophysics Data System (ADS)

    Pozsgay, Victor; Hirsch, Flavien; Branciard, Cyril; Brunner, Nicolas

    2017-12-01

    We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities is their nonlinearity; this has nontrivial consequences for the derivation of their local bound, which is not reached by deterministic local correlations. For our simplest inequality, we derive analytically tight bounds for both local and quantum correlations. An interesting application of covariance Bell inequalities is that they can act as "shared randomness witnesses": specifically, the value of the Bell expression gives device-independent lower bounds on both the dimension and the entropy of the shared random variable in a local model.

  10. Integrable models of quantum optics

    NASA Astrophysics Data System (ADS)

    Yudson, Vladimir; Makarov, Aleksander

    2017-10-01

    We give an overview of exactly solvable many-body models of quantum optics. Among them is a system of two-level atoms which interact with photons propagating in a one-dimensional (1D) chiral waveguide; exact eigenstates of this system can be explicitly constructed. This approach is used also for a system of closely located atoms in the usual (non-chiral) waveguide or in 3D space. Moreover, it is shown that for an arbitrary atomic system with a cascade spontaneous radiative decay, the fluorescence spectrum can be described by an exact analytic expression which accounts for interference of emitted photons. Open questions related with broken integrability are discussed.

  11. Effect of the qubit relaxation on transport properties of microwave photons

    NASA Astrophysics Data System (ADS)

    Sultanov, A. N.; Greenberg, Ya. S.

    2017-11-01

    In this work, using the non-Hermitian Hamiltonian method, the transmission of a single photon in a one-dimensional waveguide interacting with the cavity containing an arbitrary number of photons and the two-level artificial atom is studied with allowance for the relaxation of the latter. For transport factors, analytical expressions which explicitly take into account the qubit relaxation parameter have been obtained. The form of the transmission (reflection) coefficient when there is more than one photon in the cavity qualitatively differs from the single-photon cavity and contains the manifestation of the photon blockade effect. The qubit lifetime depends on the number of photons in the cavity.

  12. Expressions for tidal conversion at seafloor topography using physical space integrals

    NASA Astrophysics Data System (ADS)

    Schorghofer, Norbert

    2010-12-01

    The barotropic tide interacts with seafloor topography to generate internal gravity waves. Equations for streamfunction and power conversion are derived in terms of integrals over the topography in spatial coordinates. The slope of the topography does not need to be small. Explicit equations are derived up to second order in slope for general topography, and conversion by a bell-shaped topography is calculated analytically to this order. A concise formalism using Hilbert transforms is developed, the minimally converting topographic shape is discussed, and a numerical scheme for the evaluation of power conversion is designed that robustly deals with the singular integrand.

  13. Scattering-matrix approach to Casimir-Lifshitz force and heat transfer out of thermal equilibrium between arbitrary bodies

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

    Messina, Riccardo; Antezza, Mauro; CNRS, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier

    2011-10-15

    We study the radiative heat transfer and the Casimir-Lifshitz force occurring between two bodies in a system out of thermal equilibrium. We consider bodies of arbitrary shape and dielectric properties, held at two different temperatures and immersed in environmental radiation at a third different temperature. We derive explicit closed-form analytic expressions for the correlations of the electromagnetic field and for the heat transfer and Casimir-Lifshitz force in terms of the bodies' scattering matrices. We then consider some particular cases which we investigate in detail: the atom-surface and the slab-slab configurations.

  14. Influence of the electron intrinsic magnetic moment on the transverse dielectric permittivity of degenerate electron gas

    NASA Astrophysics Data System (ADS)

    Maslov, S. A.; Bobrov, V. B.; Kirillin, A. V.; Trigger, S. A.

    2018-01-01

    Using the linear response theory, the transverse dielectric permittivity of a homogeneous and isotropic system of charged particles is considered. In the ideal gas approximation for the polarization function, an explicit analytical expression for the transverse permittivity of a degenerate electron plasma, which takes into account electron spin, is found. This result describes both the Landau diamagnetism and Pauli paramagnetism in electron plasma. The influence of the electron intrinsic magnetic moment on the spatial and frequency dispersion of the transverse dielectric permittivity of degenerate electron plasma is numerically studied, that is crucial for determining the optical characteristics of plasma.

  15. Active invisibility cloaks in one dimension

    NASA Astrophysics Data System (ADS)

    Mostafazadeh, Ali

    2015-06-01

    We outline a general method of constructing finite-range cloaking potentials which render a given finite-range real or complex potential, v (x ) , unidirectionally reflectionless or invisible at a wave number, k0, of our choice. We give explicit analytic expressions for three classes of cloaking potentials which achieve this goal while preserving some or all of the other scattering properties of v (x ) . The cloaking potentials we construct are the sum of up to three constituent unidirectionally invisible potentials. We discuss their utility in making v (x ) bidirectionally invisible at k0 and demonstrate the application of our method to obtain antireflection and invisibility cloaks for a Bragg reflector.

  16. Relativistic theory of radiofrequency current drive

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

    Balescu, R.; Metens, T.

    1991-05-01

    A fully relativistic kinetic theory of rf current drive in a tokamak is developed for both the lower hybrid and the electron cyclotron mechanisms. The problem is treated as a generalization of the classical transport equations, in which the thermodynamic forces are modified by the addition of a rf-source term. In the limit of weak rf amplitude and neglecting toroidal effects (such as particle trapping), explicit analytical expressions are obtained for the rf-generated current, the dissipated power, and the current drive efficiency. These expressions are fully relativistic and are valid over the whole admissible range of frequencies and for allmore » electron temperatures. The relation between efficiency and parallel relativistic transport coefficients is exhibited. The most important relativistic effect is a dramatic broadening of the frequency range over which the rf-generated current is significantly different from zero.« less

  17. From Sommerfeld and Brillouin forerunners to optical precursors

    NASA Astrophysics Data System (ADS)

    Macke, Bruno; Ségard, Bernard

    2013-04-01

    The Sommerfeld and Brillouin forerunners generated in a single-resonance absorbing medium by an incident step-modulated pulse are theoretically considered in the double limit where the susceptibility of the medium is weak and the resonance is narrow. Combining direct Laplace-Fourier integration and calculations by the saddle-point method, we establish an explicit analytical expression of the transmitted field valid at any time, even when the two forerunners significantly overlap. We examine how their complete overlapping, occurring for shorter propagation distances, originates the formation of the unique transient currently named resonant precursor or dynamical beat. We obtain an expression of this transient identical to that usually derived within the slowly varying envelope approximation in spite of the initial discontinuity of the incident field envelope. The dynamical beats and 0π pulses generated by ultrashort incident pulses are also briefly examined.

  18. YORP torque as the function of shape harmonics

    NASA Astrophysics Data System (ADS)

    Breiter, Sławomir; Michalska, Hanna

    2008-08-01

    The second-order analytical approximation of the mean Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) torque components is given as an explicit function of the shape spherical harmonics coefficients for a sufficiently regular minor body. The results are based upon a new expression for the insolation function, significantly simpler than in previous works. Linearized plane-parallel model of the temperature distribution derived from the insolation function allows us to take into account a non-zero conductivity. Final expressions for the three average components of the YORP torque related with rotation period, obliquity and precession are given in a form of the Legendre series of the cosine of obliquity. The series have good numerical properties and can be easily truncated according to the degree of the Legendre polynomials or associated functions, with first two terms playing the principal role.

  19. 8D likelihood effective Higgs couplings extraction framework in h → 4ℓ

    DOE PAGES

    Chen, Yi; Di Marco, Emanuele; Lykken, Joe; ...

    2015-01-23

    We present an overview of a comprehensive analysis framework aimed at performing direct extraction of all possible effective Higgs couplings to neutral electroweak gauge bosons in the decay to electrons and muons, the so called ‘golden channel’. Our framework is based primarily on a maximum likelihood method constructed from analytic expressions of the fully differential cross sections for h → 4l and for the dominant irreduciblemore » $$ q\\overline{q} $$ → 4l background, where 4l = 2e2μ, 4e, 4μ. Detector effects are included by an explicit convolution of these analytic expressions with the appropriate transfer function over all center of mass variables. Utilizing the full set of observables, we construct an unbinned detector-level likelihood which is continuous in the effective couplings. We consider possible ZZ, Zγ, and γγ couplings simultaneously, allowing for general CP odd/even admixtures. A broad overview is given of how the convolution is performed and we discuss the principles and theoretical basis of the framework. This framework can be used in a variety of ways to study Higgs couplings in the golden channel using data obtained at the LHC and other future colliders.« less

  20. The mere exposure effect and recognition depend on the way you look!

    PubMed

    Willems, Sylvie; Dedonder, Jonathan; Van der Linden, Martial

    2010-01-01

    In line with Whittlesea and Price (2001), we investigated whether the memory effect measured with an implicit memory paradigm (mere exposure effect) and an explicit recognition task depended on perceptual processing strategies, regardless of whether the task required intentional retrieval. We found that manipulation intended to prompt functional implicit-explicit dissociation no longer had a differential effect when we induced similar perceptual strategies in both tasks. Indeed, the results showed that prompting a nonanalytic strategy ensured performance above chance on both tasks. Conversely, inducing an analytic strategy drastically decreased both explicit and implicit performance. Furthermore, we noted that the nonanalytic strategy involved less extensive gaze scanning than the analytic strategy and that memory effects under this processing strategy were largely independent of gaze movement.

  1. The Purpose of Analytical Models from the Perspective of a Data Provider.

    ERIC Educational Resources Information Center

    Sheehan, Bernard S.

    The purpose of analytical models is to reduce complex institutional management problems and situations to simpler proportions and compressed time frames so that human skills of decision makers can be brought to bear most effectively. Also, modeling cultivates the art of management by forcing explicit and analytical consideration of important…

  2. Setting Learning Analytics in Context: Overcoming the Barriers to Large-Scale Adoption

    ERIC Educational Resources Information Center

    Ferguson, Rebecca; Macfadyen, Leah P.; Clow, Doug; Tynan, Belinda; Alexander, Shirley; Dawson, Shane

    2014-01-01

    A core goal for most learning analytic projects is to move from small-scale research towards broader institutional implementation, but this introduces a new set of challenges because institutions are stable systems, resistant to change. To avoid failure and maximize success, implementation of learning analytics at scale requires explicit and…

  3. Higher-order jump conditions for conservation laws

    NASA Astrophysics Data System (ADS)

    Oksuzoglu, Hakan

    2018-04-01

    The hyperbolic conservation laws admit discontinuous solutions where the solution variables can have finite jumps in space and time. The jump conditions for conservation laws are expressed in terms of the speed of the discontinuity and the state variables on both sides. An example from the Gas Dynamics is the Rankine-Hugoniot conditions for the shock speed. Here, we provide an expression for the acceleration of the discontinuity in terms of the state variables and their spatial derivatives on both sides. We derive a jump condition for the shock acceleration. Using this general expression, we show how to obtain explicit shock acceleration formulas for nonlinear hyperbolic conservation laws. We start with the Burgers' equation and check the derived formula with an analytical solution. We next derive formulas for the Shallow Water Equations and the Euler Equations of Gas Dynamics. We will verify our formulas for the Euler Equations using an exact solution for the spherically symmetric blast wave problem. In addition, we discuss the potential use of these formulas for the implementation of shock fitting methods.

  4. Analytical Energy Gradients for Excited-State Coupled-Cluster Methods

    NASA Astrophysics Data System (ADS)

    Wladyslawski, Mark; Nooijen, Marcel

    The equation-of-motion coupled-cluster (EOM-CC) and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) methods have been firmly established as accurate and routinely applicable extensions of single-reference coupled-cluster theory to describe electronically excited states. An overview of these methods is provided, with emphasis on the many-body similarity transform concept that is the key to a rationalization of their accuracy. The main topic of the paper is the derivation of analytical energy gradients for such non-variational electronic structure approaches, with an ultimate focus on obtaining their detailed algebraic working equations. A general theoretical framework using Lagrange's method of undetermined multipliers is presented, and the method is applied to formulate the EOM-CC and STEOM-CC gradients in abstract operator terms, following the previous work in [P.G. Szalay, Int. J. Quantum Chem. 55 (1995) 151] and [S.R. Gwaltney, R.J. Bartlett, M. Nooijen, J. Chem. Phys. 111 (1999) 58]. Moreover, the systematics of the Lagrange multiplier approach is suitable for automation by computer, enabling the derivation of the detailed derivative equations through a standardized and direct procedure. To this end, we have developed the SMART (Symbolic Manipulation and Regrouping of Tensors) package of automated symbolic algebra routines, written in the Mathematica programming language. The SMART toolkit provides the means to expand, differentiate, and simplify equations by manipulation of the detailed algebraic tensor expressions directly. The Lagrangian multiplier formulation establishes a uniform strategy to perform the automated derivation in a standardized manner: A Lagrange multiplier functional is constructed from the explicit algebraic equations that define the energy in the electronic method; the energy functional is then made fully variational with respect to all of its parameters, and the symbolic differentiations directly yield the explicit equations for the wavefunction amplitudes, the Lagrange multipliers, and the analytical gradient via the perturbation-independent generalized Hellmann-Feynman effective density matrix. This systematic automated derivation procedure is applied to obtain the detailed gradient equations for the excitation energy (EE-), double ionization potential (DIP-), and double electron affinity (DEA-) similarity transformed equation-of-motion coupled-cluster singles-and-doubles (STEOM-CCSD) methods. In addition, the derivatives of the closed-shell-reference excitation energy (EE-), ionization potential (IP-), and electron affinity (EA-) equation-of-motion coupled-cluster singles-and-doubles (EOM-CCSD) methods are derived. Furthermore, the perturbative EOM-PT and STEOM-PT gradients are obtained. The algebraic derivative expressions for these dozen methods are all derived here uniformly through the automated Lagrange multiplier process and are expressed compactly in a chain-rule/intermediate-density formulation, which facilitates a unified modular implementation of analytic energy gradients for CCSD/PT-based electronic methods. The working equations for these analytical gradients are presented in full detail, and their factorization and implementation into an efficient computer code are discussed.

  5. Meromorphic solutions of recurrence relations and DRA method for multicomponent master integrals

    NASA Astrophysics Data System (ADS)

    Lee, Roman N.; Mingulov, Kirill T.

    2018-04-01

    We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given. The main advantage of the described approach is that the analytical properties of the solutions are very clear (the position of poles is explicit, the behavior at infinity can be easily determined). These are exactly the properties that are required for the application of the multiloop calculation method based on dimensional recurrence relations and analyticity (the DRA method).

  6. Semiclassical evaluation of quantum fidelity

    NASA Astrophysics Data System (ADS)

    Vaníček, Jiří; Heller, Eric J.

    2003-11-01

    We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform SC expression not only is tractable but it also gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform expression is accurate at times when there are 1070 semiclassical contributions. Remarkably, it also explicitly contains the “building blocks” of analytical theories of recent literature, and thus permits a direct test of the approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and show that within this approximation, the so-called “diagonal approximation” is automatic and does not require ensemble averaging.

  7. A Combined FEM/MoM/GTD Technique To Analyze Elliptically Polarized Cavity-Backed Antennas With Finite Ground Plane

    NASA Technical Reports Server (NTRS)

    Reddy, C. J.; Deshpande, M. D.; Fralick, D. T.; Cockrell, C. R.; Beck, F. B.

    1996-01-01

    Radiation pattern prediction analysis of elliptically polarized cavity-backed aperture antennas in a finite ground plane is performed using a combined Finite Element Method/Method of Moments/Geometrical Theory of Diffraction (FEM/MoM/GTD) technique. The magnetic current on the cavity-backed aperture in an infinite ground plane is calculated using the combined FEM/MoM analysis. GTD, including the slope diffraction contribution, is used to calculate the diffracted fields caused by both soft and hard polarizations at the edges of the finite ground plane. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The slope of the incident magnetic field at the diffraction points is derived and analytical expressions are presented. Numerical results for the radiation patterns of a cavity-backed circular spiral microstrip patch antenna excited by a coaxial probe in a finite rectangular ground plane are computed and compared with experimental results.

  8. CMEs' Speed, Travel Time, and Temperature: A Thermodynamic Approach

    NASA Astrophysics Data System (ADS)

    Durand-Manterola, Hector J.; Flandes, Alberto; Rivera, Ana Leonor; Lara, Alejandro; Niembro, Tatiana

    2017-12-01

    Due to their important role in space weather, coronal mass ejections or CMEs have been thoroughly studied in order to forecast their speed and transit time from the Sun to the Earth. We present a thermodynamic analytical model that describes the dynamics of CMEs. The thermodynamic approach has some advantages with respect to the hydrodynamic approach. First, it deals with the energy involved, which is a scalar quantity. Second, one may calculate the work done by the different forces separately and sum all contributions to determine the changes in speed, which simplifies the problem and allows us to obtain fully rigorous results. Our model considers the drag force, which dominates the dynamics of CMEs and the solar gravitational force, which has a much smaller effect, but it is, still, relevant enough to be considered. We derive an explicit analytical expression for the speed of CMEs in terms of its most relevant parameters and obtain an analytical expression for the CME temperature. The model is tested with a CME observed at three different heliocentric distances with three different spacecraft (SOHO, ACE, and Ulysses); also, with a set of 11 CMEs observed with the SOHO, Wind, and ACE spacecraft and, finally, with two events observed with the STEREO spacecraft. In all cases, we have a consistent agreement between the theoretical and the observed speeds and transit times. Additionally, for the set of 11 events, we estimate their temperatures at their departure position from their temperatures measured near the orbit of the Earth.

  9. Aerodynamic stability analysis of NASA J85-13/planar pressure pulse generator installation

    NASA Technical Reports Server (NTRS)

    Chung, K.; Hosny, W. M.; Steenken, W. G.

    1980-01-01

    A digital computer simulation model for the J85-13/Planar Pressure Pulse Generator (P3 G) test installation was developed by modifying an existing General Electric compression system model. This modification included the incorporation of a novel method for describing the unsteady blade lift force. This approach significantly enhanced the capability of the model to handle unsteady flows. In addition, the frequency response characteristics of the J85-13/P3G test installation were analyzed in support of selecting instrumentation locations to avoid standing wave nodes within the test apparatus and thus, low signal levels. The feasibility of employing explicit analytical expression for surge prediction was also studied.

  10. Theories and applications of second-order correlation of longitudinal velocity increments at three points in isotropic turbulence

    NASA Astrophysics Data System (ADS)

    Wu, J. Z.; Fang, L.; Shao, L.; Lu, L. P.

    2018-06-01

    In order to introduce new physics to traditional two-point correlations, we define the second-order correlation of longitudinal velocity increments at three points and obtain the analytical expressions in isotropic turbulence. By introducing the Kolmogorov 4/5 law, this three-point correlation explicitly contains velocity second- and third-order moments, which correspond to energy and energy transfer respectively. The combination of them then shows additional information of non-equilibrium turbulence by comparing to two-point correlations. Moreover, this three-point correlation shows the underlying inconsistency between numerical interpolation and three-point scaling law in numerical calculations, and inspires a preliminary model to correct this problem in isotropic turbulence.

  11. Transformation of the optical vortex dipole by an astigmatic lens

    NASA Astrophysics Data System (ADS)

    Yan, Hongwei; Lü, Baida

    2009-06-01

    The transformation of the optical vortex dipole (OVD) by an astigmatic lens is studied. The explicit propagation expression of the OVD nested in a Gaussian beam is derived and used to analytically determine the position of the OVD after the passage through the astigmatic lens. The transformation by an aberration-free lens is treated as a special case. It is shown that, depending on the propagation distance, waist width, off-axis distance and astigmatic coefficient, the motion, annihilation and revival of the OVD and the inversion of the topological charge may take place. Specifically, the creation of two OVDs may appear under certain conditions. The results are illustrated by numerical examples.

  12. Multidimensional Extension of the Generalized Chowla-Selberg Formula

    NASA Astrophysics Data System (ADS)

    Elizalde, E.

    After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous Epstein-type zeta function of the general form with A the p×p$ matrix of a quadratic form, a p vector and q a constant, is obtained. It is valid on the whole complex s-plane, is exponentially convergent and provides the residua at the poles explicitly. It reduces to the famous formula of Chowla and Selberg in the particular case p=2, , q=0. Some variations of the formula and physical applications are considered.

  13. Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

    NASA Technical Reports Server (NTRS)

    Jongen, T.; Gatski, T. B.

    1997-01-01

    The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

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

    Sinitsyn, N. A.

    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

  15. Berry phase and Hannay angle of an interacting boson system

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

    Li, S. C.; Graduate School, China Academy of Engineering Physics, Beijing 100088; Liu, J.

    2011-04-15

    In the present paper, we investigate the Berry phase and the Hannay angle of an interacting two-mode boson system and obtain their analytic expressions in explicit forms. The relation between the Berry phase and the Hannay angle is discussed. We find that, in the large-particle-number limit, the classical Hannay angle equals the particle number derivative of the quantum Berry phase except for a sign. This relationship is applicable to other many-body boson systems where the coherent-state description is available and the total particle number is conserved. The measurement of the classical Hannay angle in the many-body systems is briefly discussedmore » as well.« less

  16. Soliton polarization rotation in fiber lasers

    NASA Astrophysics Data System (ADS)

    Afanasjev, V. V.

    1995-02-01

    I have found the approximate analytical solution in explicit form for a vector soliton with an arbitrary component ratio. My solution describes the dependence of soliton intensity on polarization angle and also nonlinear polarization rotation. The analytical results agree well with the numerical simulations.

  17. Theoretical predicting of permeability evolution in damaged rock under compressive stress

    NASA Astrophysics Data System (ADS)

    Vu, M. N.; Nguyen, S. T.; To, Q. D.; Dao, N. H.

    2017-05-01

    This paper outlines an analytical model of crack growth induced permeability changes. A theoretical solution of effective permeability of cracked porous media is derived. The fluid flow obeys Poisseuille's law along the crack and Darcy's law in the porous matrix. This solution exhibits a percolation threshold for any type of crack distribution apart from a parallel crack distribution. The physical behaviour of fluid flow through a cracked porous material is well reproduced by the proposed model. The presence of this effective permeability coupling to analytical expression of crack growth under compression enables the modelling of the permeability variation due to stress-induced cracking in a porous rock. This incorporation allows the prediction of the permeability change of a porous rock embedding an anisotropic crack distribution from any initial crack density, that is, lower, around or upper to percolation threshold. The interaction between cracks is not explicitly taken into account. The model is well applicable both to micro- and macrocracks.

  18. Peculiarities of the momentum distribution functions of strongly correlated charged fermions

    NASA Astrophysics Data System (ADS)

    Larkin, A. S.; Filinov, V. S.; Fortov, V. E.

    2018-01-01

    New numerical version of the Wigner approach to quantum thermodynamics of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. An explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. Fermi statistical effects are accounted for by effective pair pseudopotential depending on coordinates, momenta and degeneracy parameter of particles and taking into account Pauli blocking of fermions. A new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been developed. Calculations of the momentum distribution functions and the pair correlation functions of degenerate ideal Fermi gas have been carried out for testing the developed approach. Comparison of the obtained momentum distribution functions of strongly correlated Coulomb systems with the Maxwell-Boltzmann and the Fermi distributions shows the significant influence of interparticle interaction both at small momenta and in high energy quantum ‘tails’.

  19. Solvable four-state Landau-Zener model of two interacting qubits with path interference

    DOE PAGES

    Sinitsyn, Nikolai A.

    2015-11-30

    In this paper, I identify a nontrivial four-state Landau-Zener model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. The model describes an experimentally accessible system of two interacting qubits, such as a localized state in a Dirac material with both valley and spin degrees of freedom or a singly charged quantum dot (QD) molecule with spin orbit coupling. Application of the linearly time-dependent magnetic field induces a sequence of quantum level crossings with possibility of interference of different trajectories in a semiclassical picture. I argue that this system satisfies the criteria ofmore » integrability in the multistate Landau-Zener theory, which allows one to derive explicit exact analytical expressions for the transition probability matrix. Finally, I also argue that this model is likely a special case of a larger class of solvable systems, and present a six-state generalization as an example.« less

  20. Stability analysis of confined V-shaped flames in high-velocity streams.

    PubMed

    El-Rabii, Hazem; Joulin, Guy; Kazakov, Kirill A

    2010-06-01

    The problem of linear stability of confined V-shaped flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained. This equation is solved analytically for V-flames anchored in high-velocity channel streams. It is demonstrated that dynamics of the flame disturbances in this case is controlled by the memory effects associated with vorticity generated by the perturbed flame. The perturbation growth rate spectrum is determined, and explicit analytical expressions for the eigenfunctions are given. It is found that the piecewise linear V structure is unstable for all values of the gas expansion coefficient. Despite the linearity of the basic pattern, however, evolutions of the V-flame disturbances are completely different from those found for freely propagating planar flames or open anchored flames. The obtained results reveal strong influence of the basic flow and the channel walls on the stability properties of confined V-flames.

  1. Multidimensional assessment of awareness in early-stage dementia: a cluster analytic approach.

    PubMed

    Clare, Linda; Whitaker, Christopher J; Nelis, Sharon M; Martyr, Anthony; Markova, Ivana S; Roth, Ilona; Woods, Robert T; Morris, Robin G

    2011-01-01

    Research on awareness in dementia has yielded variable and inconsistent associations between awareness and other factors. This study examined awareness using a multidimensional approach and applied cluster analytic techniques to identify associations between the level of awareness and other variables. Participants were 101 individuals with early-stage dementia (PwD) and their carers. Explicit awareness was assessed at 3 levels: performance monitoring in relation to memory, evaluative judgement in relation to memory, everyday activities and socio-emotional functioning, and metacognitive reflection in relation to the experience and impact of the condition. Implicit awareness was assessed with an emotional Stroop task. Different measures of explicit awareness scores were related only to a limited extent. Cluster analysis yielded 3 groups with differing degrees of explicit awareness. These groups showed no differences in implicit awareness. Lower explicit awareness was associated with greater age, lower MMSE scores, poorer recall and naming scores, lower anxiety and greater carer stress. Multidimensional assessment offers a more robust approach to classifying PwD according to level of awareness and hence to examining correlates and predictors of awareness. Copyright © 2011 S. Karger AG, Basel.

  2. Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS 2 Ⓧ S 2

    DOE PAGES

    Noronha, Jorge; Denicol, Gabriel S.

    2015-12-30

    In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime AdS 2 Ⓧ S 2. We further derive explicit analytic expressions for the momentum dependence of the single-particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density doesmore » not match the equilibrium form. The nonequilibrium contribution to the entropy density is shown to be due to higher-order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.« less

  3. Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

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

    Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.

    We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra ismore » later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a rotating quadrupole field ion trap are presented. •Exact solutions for magneto-transport in variable electromagnetic fields are shown.« less

  4. Development of a Coherent Bistatic Vegetation Model for Signal of Opportunity Applications at VHF UHF-Bands

    NASA Technical Reports Server (NTRS)

    Kurum, Mehmet; Deshpande, Manohar; Joseph, Alicia T.; O'Neill, Peggy E.; Lang, Roger H.; Eroglu, Orhan

    2017-01-01

    A coherent bistatic vegetation scattering model, based on a Monte Carlo simulation, is being developed to simulate polarimetric bi-static reflectometry at VHF/UHF-bands (240-270 MHz). The model is aimed to assess the value of geostationary satellite signals of opportunity to enable estimation of the Earth's biomass and root-zone soil moisture. An expression for bistatic scattering from a vegetation canopy is derived for the practical case of a ground-based/low altitude platforms with passive receivers overlooking vegetation. Using analytical wave theory in conjunction with distorted Born approximation (DBA), the transmit and receive antennas effects (i.e., polarization, orientation, height, etc.) are explicitly accounted for. Both the coherency nature of the model (joint phase and amplitude information) and the explicit account of system parameters (antenna, altitude, polarization, etc) enable one to perform various beamforming techniques to evaluate realistic deployment configurations. In this paper, several test scenarios will be presented and the results will be evaluated for feasibility for future biomass and root-zone soil moisture application using geostationary communication satellite signals of opportunity at low frequencies.

  5. Revisiting analytical solutions for steady interface flow in subsea aquifers: Aquitard salinity effects

    NASA Astrophysics Data System (ADS)

    Werner, Adrian D.; Robinson, Neville I.

    2018-06-01

    Existing analytical solutions for the distribution of fresh groundwater in subsea aquifers presume that the overlying offshore aquitard, represented implicitly, contains seawater. Here, we consider the case where offshore fresh groundwater is the result of freshwater discharge from onshore aquifers, and neglect paleo-freshwater sources. A recent numerical modeling investigation, involving explicit simulation of the offshore aquitard, demonstrates that offshore aquitards more likely contain freshwater in areas of upward freshwater leakage to the sea. We integrate this finding into the existing analytical solutions by providing an alternative formulation for steady interface flow in subsea aquifers, whereby the salinity in the offshore aquitard can be chosen. The new solution, taking the aquitard salinity as that of freshwater, provides a closer match to numerical modeling results in which the aquitard is represented explicitly.

  6. Adaptive steganography

    NASA Astrophysics Data System (ADS)

    Chandramouli, Rajarathnam; Li, Grace; Memon, Nasir D.

    2002-04-01

    Steganalysis techniques attempt to differentiate between stego-objects and cover-objects. In recent work we developed an explicit analytic upper bound for the steganographic capacity of LSB based steganographic techniques for a given false probability of detection. In this paper we look at adaptive steganographic techniques. Adaptive steganographic techniques take explicit steps to escape detection. We explore different techniques that can be used to adapt message embedding to the image content or to a known steganalysis technique. We investigate the advantages of adaptive steganography within an analytical framework. We also give experimental results with a state-of-the-art steganalysis technique demonstrating that adaptive embedding results in a significant number of bits embedded without detection.

  7. Aharonov-Bohm effect in graphene Möbius strips: an analytical treatment

    NASA Astrophysics Data System (ADS)

    Oliveira de Souza, Jose Fernando; de Lima Ribeiro, Carlos Alberto; Furtado, Claudio

    2017-05-01

    In this work, the influence of an Aharonov-Bohm flux on the low energy physical properties of graphene nanorings exhibiting Möbius topology is examined. Our approach lies in the continuum description of graphene, providing an analytical treatment for Aharonov-Bohm problem in the context of general relativistic confined systems, whose main goal is to understand the role of boundary conditions and their effects in such a background. We study a class of quantum rings described by a particular set of boundary conditions which combines infinite mass confinement along the transverse direction with a Möbius-type periodicity longitudinally, in order to sketch out insights into the electronic behavior of typical hard wall nanoribbons within a relativistic domain in response to the interplay between non-trivial topology and quantum interference effects. Boundary conditions are found to be only partially compatible, leading to spatial constraints on the solution, which also manifests itself in the nature of energy spectrum and persistent currents. Expressions for flux-dependent energy eigenvalues and persistent currents are explicitly calculated, as well as comparative graphs are plotted and analyzed. Both quantities are shown to alternate their expressions not only in dependence on the transverse modes, but also showing sensitivity to the allowed positions of the domain.

  8. Saying good goodbyes to your clients: A functional analytic psychotherapy (FAP) perspective.

    PubMed

    Tsai, Mavis; Gustafsson, Tore; Kanter, Jonathan; Plummer Loudon, Mary; Kohlenberg, Robert J

    2017-03-01

    Functional analytic psychotherapy (FAP) promotes client growth by shaping clients' daily life problems that also show up in session with their therapists. FAP therapists create evocative contexts within therapy that afford clients the opportunity to practice, refine, and be reinforced for new, more adaptive behaviors which then can be generalized into their outside lives. In FAP, the termination process will vary from client to client depending on the nature of the client's problems and targets. For many clients, the process can be a rich, multifaceted, final opportunity to evoke, reinforce, and promote generalization of clients' in-session improvements, particularly improvements related to vulnerable self-expression in the service of intimate and close relationships. By making explicit agreements at the outset of therapy to participate in an intentional termination process, and by later providing an evocative structure for ending therapy with vulnerable emotional expression, clients have the opportunity to develop more adaptive behaviors in the context of relationship endings which can be a painful part of the human experience. Equipped with the skills of open-hearted communication developed from an authentic relationship with their therapist, clients can leave therapy on a trajectory of further growth in interpersonal connection and living more boldly. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  9. Analytical validation of an explicit finite element model of a rolling element bearing with a localised line spall

    NASA Astrophysics Data System (ADS)

    Singh, Sarabjeet; Howard, Carl Q.; Hansen, Colin H.; Köpke, Uwe G.

    2018-03-01

    In this paper, numerically modelled vibration response of a rolling element bearing with a localised outer raceway line spall is presented. The results were obtained from a finite element (FE) model of the defective bearing solved using an explicit dynamics FE software package, LS-DYNA. Time domain vibration signals of the bearing obtained directly from the FE modelling were processed further to estimate time-frequency and frequency domain results, such as spectrogram and power spectrum, using standard signal processing techniques pertinent to the vibration-based monitoring of rolling element bearings. A logical approach to analyses of the numerically modelled results was developed with an aim to presenting the analytical validation of the modelled results. While the time and frequency domain analyses of the results show that the FE model generates accurate bearing kinematics and defect frequencies, the time-frequency analysis highlights the simulation of distinct low- and high-frequency characteristic vibration signals associated with the unloading and reloading of the rolling elements as they move in and out of the defect, respectively. Favourable agreement of the numerical and analytical results demonstrates the validation of the results from the explicit FE modelling of the bearing.

  10. The Analytic Hierarchy Process and Participatory Decisionmaking

    Treesearch

    Daniel L. Schmoldt; Daniel L. Peterson; Robert L. Smith

    1995-01-01

    Managing natural resource lands requires social, as well as biophysical, considerations. Unfortunately, it is extremely difficult to accurately assess and quantify changing social preferences, and to aggregate conflicting opinions held by diverse social groups. The Analytic Hierarchy Process (AHP) provides a systematic, explicit, rigorous, and robust mechanism for...

  11. Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

    NASA Astrophysics Data System (ADS)

    Dubinskii, Yu A.; Osipenko, A. S.

    2000-02-01

    Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

  12. The assessment of mangrove biomass and carbon in West Africa: a spatially explicit analytical framework

    Treesearch

    Wenwu Tang; Wenpeng Feng; Meijuan Jia; Jiyang Shi; Huifang Zuo; Carl C. Trettin

    2015-01-01

    Mangrove forests are highly productive and have large carbon sinks while also providing numerous goods and ecosystem services. However, effective management and conservation of the mangrove forests are often dependent on spatially explicit assessments of the resource. Given the remote and highly dispersed nature of mangroves, estimation of biomass and carbon...

  13. Putting an Ethical Lens on Learning Analytics

    ERIC Educational Resources Information Center

    West, Deborah; Huijser, Henk; Heath, David

    2016-01-01

    As learning analytics activity has increased, a variety of ethical implications and considerations have emerged, though a significant research gap remains in explicitly investigating the views of key stakeholders, such as academic staff. This paper draws on ethics-related findings from an Australian study featuring two surveys, one of…

  14. Quantum cluster theory for the polarizable continuum model. I. The CCSD level with analytical first and second derivatives.

    PubMed

    Cammi, R

    2009-10-28

    We present a general formulation of the coupled-cluster (CC) theory for a molecular solute described within the framework of the polarizable continuum model (PCM). The PCM-CC theory is derived in its complete form, called PTDE scheme, in which the correlated electronic density is used to have a self-consistent reaction field, and in an approximate form, called PTE scheme, in which the PCM-CC equations are solved assuming the fixed Hartree-Fock solvent reaction field. Explicit forms for the PCM-CC-PTDE equations are derived at the single and double (CCSD) excitation level of the cluster operator. At the same level, explicit equations for the analytical first derivatives of the PCM basic energy functional are presented, and analytical second derivatives are also discussed. The corresponding PCM-CCSD-PTE equations are given as a special case of the full theory.

  15. Implicit/explicit memory versus analytic/nonanalytic processing: rethinking the mere exposure effect.

    PubMed

    Whittlesea, B W; Price, J R

    2001-03-01

    In studies of the mere exposure effect, rapid presentation of items can increase liking without accurate recognition. The effect on liking has been explained as a misattribution of fluency caused by prior presentation. However, fluency is also a source of feelings of familiarity. It is, therefore, surprising that prior experience can enhance liking without also causing familiarity-based recognition. We suggest that when study opportunities are minimal and test items are perceptually similar, people adopt an analytic approach, attempting to recognize distinctive features. That strategy fails because rapid presentation prevents effective encoding of such features; it also prevents people from experiencing fluency and a consequent feeling of familiarity. We suggest that the liking-without-recognition effect results from using an effective (nonanalytic) strategy in judging pleasantness, but an ineffective (analytic) strategy in recognition. Explanations of the mere exposure effect based on a distinction between implicit and explicit memory are unnecessary.

  16. Theoretical Treatment of Ion Transfers in Two Polarizable Interface Systems When the Analyte Has Access to Both Interfaces.

    PubMed

    Olmos, José Manuel; Molina, Ángela; Laborda, Eduardo; Millán-Barrios, Enrique; Ortuño, Joaquín Ángel

    2018-02-06

    A new theory is presented to tackle the study of transfer processes of hydrophilic ions in two polarizable interface systems when the analyte is initially present in both aqueous phases. The treatment is applied to macrointerfaces (linear diffusion) and microholes (highly convergent diffusion), obtaining analytical equations for the current response in any voltammetric technique. The novel equations predict two signals in the current-potential curves that are symmetric when the compositions of the aqueous phases are identical while asymmetries appear otherwise. The theoretical results show good agreement with the experimental behavior of the "double transfer voltammograms" reported by Dryfe et al. in cyclic voltammetry (CV) ( Anal. Chem. 2014 , 86 , 435 - 442 ) as well as with cyclic square wave voltammetry (cSWV) experiments performed in the current work. The theoretical treatment is also extended to the situation where the target ion is lipophilic and initially present in the organic phase. The theory predicts an opposite effect of the lipophilicity of the ion on the shape of the voltammograms, which is validated experimentally via both CV and cSWV. For the above two cases, simple and manageable expressions and diagnosis criteria are derived for the qualitative and quantitative study of ion lipophilicity. The ion-transfer potentials can be easily quantified from the separation between the two signals making use of explicit analytical equations.

  17. Unruh effect for general trajectories

    NASA Astrophysics Data System (ADS)

    Obadia, N.; Milgrom, M.

    2007-03-01

    We consider two-level detectors coupled to a scalar field and moving on arbitrary trajectories in Minkowski space-time. We first derive a generic expression for the response function using a (novel) regularization procedure based on the Feynman prescription that is explicitly causal, and we compare it to other expressions used in the literature. We then use this expression to study, analytically and numerically, the time dependence of the response function in various nonstationarity situations. We show that, generically, the response function decreases like a power in the detector’s level spacing, E, for high E. It is only for stationary worldlines that the response function decays faster than any power law, in keeping with the known exponential behavior for some stationary cases. Under some conditions the (time-dependent) response function for a nonstationary worldline is well approximated by the value of the response function for a stationary worldline having the same instantaneous acceleration, torsion, and hypertorsion. While we cannot offer general conditions for this to apply, we discuss special cases; in particular, the low-energy limit for linear space trajectories.

  18. Nonequilibrium approach regarding metals from a linearised kappa distribution

    NASA Astrophysics Data System (ADS)

    Domenech-Garret, J. L.

    2017-10-01

    The widely used kappa distribution functions develop high-energy tails through an adjustable kappa parameter. The aim of this work is to show that such a parameter can itself be regarded as a function, which entangles information about the sources of disequilibrium. We first derive and analyse an expanded Fermi-Dirac kappa distribution. Later, we use this expanded form to obtain an explicit analytical expression for the kappa parameter of a heated metal on which an external electric field is applied. We show that such a kappa index causes departures from equilibrium depending on the physical magnitudes. Finally, we study the role of temperature and electric field on such a parameter, which characterises the electron population of a metal out of equilibrium.

  19. Size-dependent resonance frequencies of cantilevered and bridged nanosensors

    NASA Astrophysics Data System (ADS)

    Shi, W.; Zou, J.; Lee, K. Y.; Li, X. F.

    2018-03-01

    This paper studies transverse vibration of nanoscale cantilevered and bridged sensors carrying a nanoparticle. The nanoscale sensors are modelled as Euler-Bernoulli beams with surface effect and nanoparticle as a concentrated mass. Frequency equations of cantilevered and bridged beam-mass system are derived and exact resonance frequencies are calculated. An alternative Fredholm integral equation method is used to obtain an approximate explicit expression for the fundamental frequency for both cases. A comparison between the approximate and analytical results is made and the approximation accuracy is satisfactory. The influences of the residual surface stress, surface elasticity, and attached mass on the resonance frequencies and mode shapes are discussed. These results are useful to illustrate the surface phenomena and are helpful to design micro-/nano-mechanical sensors.

  20. Analytical study of robustness of a negative feedback oscillator by multiparameter sensitivity

    PubMed Central

    2014-01-01

    Background One of the distinctive features of biological oscillators such as circadian clocks and cell cycles is robustness which is the ability to resume reliable operation in the face of different types of perturbations. In the previous study, we proposed multiparameter sensitivity (MPS) as an intelligible measure for robustness to fluctuations in kinetic parameters. Analytical solutions directly connect the mechanisms and kinetic parameters to dynamic properties such as period, amplitude and their associated MPSs. Although negative feedback loops are known as common structures to biological oscillators, the analytical solutions have not been presented for a general model of negative feedback oscillators. Results We present the analytical expressions for the period, amplitude and their associated MPSs for a general model of negative feedback oscillators. The analytical solutions are validated by comparing them with numerical solutions. The analytical solutions explicitly show how the dynamic properties depend on the kinetic parameters. The ratio of a threshold to the amplitude has a strong impact on the period MPS. As the ratio approaches to one, the MPS increases, indicating that the period becomes more sensitive to changes in kinetic parameters. We present the first mathematical proof that the distributed time-delay mechanism contributes to making the oscillation period robust to parameter fluctuations. The MPS decreases with an increase in the feedback loop length (i.e., the number of molecular species constituting the feedback loop). Conclusions Since a general model of negative feedback oscillators was employed, the results shown in this paper are expected to be true for many of biological oscillators. This study strongly supports that the hypothesis that phosphorylations of clock proteins contribute to the robustness of circadian rhythms. The analytical solutions give synthetic biologists some clues to design gene oscillators with robust and desired period. PMID:25605374

  1. Capillary-wave dynamics and interface structure modulation in binary Bose-Einstein condensate mixtures

    NASA Astrophysics Data System (ADS)

    Indekeu, Joseph O.; Van Thu, Nguyen; Lin, Chang-You; Phat, Tran Huu

    2018-04-01

    The localized low-energy interfacial excitations, or interfacial Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically. To this end a double-parabola approximation (DPA) is performed on the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. This DPA entails a model in which analytic expressions are obtained for the excitations underlying capillary waves or ripplons for arbitrary strength K (>1 ) of the phase segregation. The dispersion relation ω (k ) ∝k3 /2 is derived directly from the Bogoliubov-de Gennes equations in the limit that the wavelength 2 π /k is much larger than the interface width. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in ω (k ) of order k5 /2 is calculated analytically within the DPA model. The combined result is tested against numerical diagonalization of the exact Bogoliubov-de Gennes equations. Satisfactory agreement is obtained in the range of physically relevant wavelengths. The ripplon dispersion relation is relevant to state-of-the-art experiments using (quasi)uniform optical-box traps. Furthermore, within the DPA model explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity ω /k to the sound velocity c . For generic mixtures consisting of condensates with unequal healing lengths, an additional modulation is predicted of the common value of the condensate densities at the interface.

  2. Perceiving emotional expressions in others: Activation likelihood estimation meta-analyses of explicit evaluation, passive perception and incidental perception of emotions.

    PubMed

    Dricu, Mihai; Frühholz, Sascha

    2016-12-01

    We conducted a series of activation likelihood estimation (ALE) meta-analyses to determine the commonalities and distinctions between separate levels of emotion perception, namely incidental perception, passive perception, and explicit evaluation of emotional expressions. Pooling together more than 180 neuroimaging experiments using facial, vocal or body expressions, our results are threefold. First, explicitly evaluating the emotions of others recruits brain regions associated with the sensory processing of expressions, such as the inferior occipital gyrus, middle fusiform gyrus and the superior temporal gyrus, and brain regions involved in low-level and high-level mindreading, namely the posterior superior temporal sulcus, the inferior frontal cortex and dorsomedial frontal cortex. Second, we show that only the sensory regions were also consistently active during the passive perception of emotional expressions. Third, we show that the brain regions involved in mindreading were active during the explicit evaluation of both facial and vocal expressions. We discuss these results in light of the existing literature and conclude by proposing a cognitive model for perceiving and evaluating the emotions of others. Copyright © 2016 Elsevier Ltd. All rights reserved.

  3. Age Differences and Cognitive Aptitudes for Implicit and Explicit Learning in Ultimate Second Language Attainment

    ERIC Educational Resources Information Center

    Granena, Gisela

    2012-01-01

    Very high-level, functional ability in foreign languages is increasingly important in many walks of life. It is also very rare, and likely requires an early start and/or a special aptitude. This study investigated the extent to which aptitude for explicit learning, defined as "analytic ability" and aptitude for implicit learning, defined…

  4. The Effectiveness of Guided Induction versus Deductive Instruction on the Development of Complex Spanish "Gustar" Structures: An Analysis of Learning Outcomes and Processes

    ERIC Educational Resources Information Center

    Cerezo, Luis; Caras, Allison; Leow, Ronald P.

    2016-01-01

    Meta-analytic research suggests an edge of explicit over implicit instruction for the development of complex L2 grammatical structures, but the jury is still out as to which type of explicit instruction--"deductive" or "inductive," where rules are respectively provided or elicited--proves more effective. Avoiding this…

  5. Gravity discharge vessel revisited: An explicit Lambert W function solution

    NASA Astrophysics Data System (ADS)

    Digilov, Rafael M.

    2017-07-01

    Based on the generalized Poiseuille equation modified by a kinetic energy correction, an explicit solution for the time evolution of a liquid column draining under gravity through an exit capillary tube is derived in terms of the Lambert W function. In contrast to the conventional exponential behavior, as implied by the Poiseuille law, a new analytical solution gives a full account for the volumetric flow rate of a fluid through a capillary of any length and improves the precision of viscosity determination. The theoretical consideration may be of interest to students as an example of how implicit equations in the field of physics can be solved analytically using the Lambert function.

  6. Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations

    NASA Astrophysics Data System (ADS)

    Demina, Maria V.; Kudryashov, Nikolay A.

    2011-03-01

    Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational, periodic, elliptic) are found for a wide class of autonomous nonlinear ordinary differential equations.

  7. Meta-analytic evidence of low convergence between implicit and explicit measures of the needs for achievement, affiliation, and power

    PubMed Central

    Köllner, Martin G.; Schultheiss, Oliver C.

    2014-01-01

    The correlation between implicit and explicit motive measures and potential moderators of this relationship were examined meta-analytically, using Hunter and Schmidt's (2004) approach. Studies from a comprehensive search in PsycINFO, data sets of our research group, a literature list compiled by an expert, and the results of a request for gray literature were examined for relevance and coded. Analyses were based on 49 papers, 56 independent samples, 6151 subjects, and 167 correlations. The correlations (ρ) between implicit and explicit measures were 0.130 (CI: 0.077–0.183) for the overall relationship, 0.116 (CI: 0.050–0.182) for affiliation, 0.139 (CI: 0.080–0.198) for achievement, and 0.038 (CI: −0.055–0.131) for power. Participant age did not moderate the size of these relationships. However, a greater proportion of males in the samples and an earlier publication year were associated with larger effect sizes. PMID:25152741

  8. Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory

    NASA Astrophysics Data System (ADS)

    Győrffy, Werner; Knizia, Gerald; Werner, Hans-Joachim

    2017-12-01

    We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series.

  9. Analytical transport network theory to guide the design of 3-D microstructural networks in energy materials: Part 1. Flow without reactions

    NASA Astrophysics Data System (ADS)

    Cocco, Alex P.; Nakajo, Arata; Chiu, Wilson K. S.

    2017-12-01

    We present a fully analytical, heuristic model - the "Analytical Transport Network Model" - for steady-state, diffusive, potential flow through a 3-D network. Employing a combination of graph theory, linear algebra, and geometry, the model explicitly relates a microstructural network's topology and the morphology of its channels to an effective material transport coefficient (a general term meant to encompass, e.g., conductivity or diffusion coefficient). The model's transport coefficient predictions agree well with those from electrochemical fin (ECF) theory and finite element analysis (FEA), but are computed 0.5-1.5 and 5-6 orders of magnitude faster, respectively. In addition, the theory explicitly relates a number of morphological and topological parameters directly to the transport coefficient, whereby the distributions that characterize the structure are readily available for further analysis. Furthermore, ATN's explicit development provides insight into the nature of the tortuosity factor and offers the potential to apply theory from network science and to consider the optimization of a network's effective resistance in a mathematically rigorous manner. The ATN model's speed and relative ease-of-use offer the potential to aid in accelerating the design (with respect to transport), and thus reducing the cost, of energy materials.

  10. Modelling the dynamics of a minimal protocell container

    NASA Astrophysics Data System (ADS)

    Nilsson Jacobi, Martin; Rasmussen, Steen; Tunstrøm, Kolbjørn

    2005-01-01

    This paper is a discussion on how reaction kinetics and three-dimensional (3D) lattice simulations can be used to elucidate the dynamical properties of micelles as a possible minimal protocell container. We start with a general discussion on the role of molecular self-assembly in prebiotic and contemporary biological systems. A simple reaction kinetic model of a micellation process of amphiphilic molecules in water is then presented and solved analytically. Amphiphilic molecules are polymers with hydrophobic (water-fearing), e.g. hydrocarbon tail groups, and hydrophilic (water-loving) head groups, e.g. fatty acids. By making a few simplifying assumptions an analytical expression for the size distribution of the resulting micelles can be derived. The main part of the paper presents and discusses a lattice gas technique for a more detailed 3D simulation of molecular self-assembly of amphiphilic polymers in aqueous environments. Water molecules, hydrocarbon tail groups and hydrophilic head groups are explicitly represented on a three-dimensional discrete lattice. Molecules move on the lattice proportional to their continuous momentum. Collision rules preserve momentum and kinetic energy. Potential energy from molecular interactions are also included explicitly. The non-trivial thermodynamics of large-scale and long-time dynamics are studied. In this paper we specifically demonstrate how, from a random initial distribution, micelles are formed and grow until they destabilize and can divide. Eventually a steady state of growing and dividing micelles is formed. Towards the end of the paper we discuss the relevance of the presented results to the design of a minimal artificial protocell.

  11. Rate-loss analysis of an efficient quantum repeater architecture

    NASA Astrophysics Data System (ADS)

    Guha, Saikat; Krovi, Hari; Fuchs, Christopher A.; Dutton, Zachary; Slater, Joshua A.; Simon, Christoph; Tittel, Wolfgang

    2015-08-01

    We analyze an entanglement-based quantum key distribution (QKD) architecture that uses a linear chain of quantum repeaters employing photon-pair sources, spectral-multiplexing, linear-optic Bell-state measurements, multimode quantum memories, and classical-only error correction. Assuming perfect sources, we find an exact expression for the secret-key rate, and an analytical description of how errors propagate through the repeater chain, as a function of various loss-and-noise parameters of the devices. We show via an explicit analytical calculation, which separately addresses the effects of the principle nonidealities, that this scheme achieves a secret-key rate that surpasses the Takeoka-Guha-Wilde bound—a recently found fundamental limit to the rate-vs-loss scaling achievable by any QKD protocol over a direct optical link—thereby providing one of the first rigorous proofs of the efficacy of a repeater protocol. We explicitly calculate the end-to-end shared noisy quantum state generated by the repeater chain, which could be useful for analyzing the performance of other non-QKD quantum protocols that require establishing long-distance entanglement. We evaluate that shared state's fidelity and the achievable entanglement-distillation rate, as a function of the number of repeater nodes, total range, and various loss-and-noise parameters of the system. We extend our theoretical analysis to encompass sources with nonzero two-pair-emission probability, using an efficient exact numerical evaluation of the quantum state propagation and measurements. We expect our results to spur formal rate-loss analysis of other repeater protocols and also to provide useful abstractions to seed analyses of quantum networks of complex topologies.

  12. Exact Maximum-Entropy Estimation with Feynman Diagrams

    NASA Astrophysics Data System (ADS)

    Netser Zernik, Amitai; Schlank, Tomer M.; Tessler, Ran J.

    2018-02-01

    A longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using perturbative Feynman calculus. The explicit expression is given as a sum over weighted trees.

  13. Phase transitions in single macromolecules: Loop-stretch transition versus loop adsorption transition in end-grafted polymer chains

    NASA Astrophysics Data System (ADS)

    Zhang, Shuangshuang; Qi, Shuanhu; Klushin, Leonid I.; Skvortsov, Alexander M.; Yan, Dadong; Schmid, Friederike

    2018-01-01

    We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter ɛ and the other is the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force F applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition and the mean position of the chain end in the case of the loop-stretch transition. Close to the transition points, both the static behavior and the dynamic behavior of chains with different length N are very well described by a scaling ansatz with the scaling parameters (ɛ - ɛ*)Nϕ (adsorption transition) and (F - F*)Nν (loop-stretch transition), respectively, where ϕ is the crossover exponent of the adsorption transition and ν is the Flory exponent. We show that both the loop-stretch and the loop adsorption transitions provide an exceptional opportunity to construct explicit analytical expressions for the crossover functions which perfectly describe all simulation results on static properties in the finite-size scaling regime. Explicit crossover functions are based on the ansatz for the analytical form of the order parameter distributions at the respective transition points. In contrast to the close similarity in equilibrium static behavior, the dynamic relaxation at the two transitions shows qualitative differences, especially in the strongly ordered regimes. This is attributed to the fact that the surface contact dynamics in a strongly adsorbed chain is governed by local processes, whereas the end height relaxation of a strongly stretched chain involves the full spectrum of Rouse modes.

  14. Effects of partial slip boundary condition and radiation on the heat and mass transfer of MHD-nanofluid flow

    NASA Astrophysics Data System (ADS)

    Abd Elazem, Nader Y.; Ebaid, Abdelhalim

    2017-12-01

    In this paper, the effect of partial slip boundary condition on the heat and mass transfer of the Cu-water and Ag-water nanofluids over a stretching sheet in the presence of magnetic field and radiation. Such partial slip boundary condition has attracted much attention due to its wide applications in industry and chemical engineering. The flow is basically governing by a system of partial differential equations which are reduced to a system of ordinary differential equations. This system has been exactly solved, where exact analytical expression has been obtained for the fluid velocity in terms of exponential function, while the temperature distribution, and the nanoparticles concentration are expressed in terms of the generalized incomplete gamma function. In addition, explicit formulae are also derived from the rates of heat transfer and mass transfer. The effects of the permanent parameters on the skin friction, heat transfer coefficient, rate of mass transfer, velocity, the temperature profile, and concentration profile have been discussed through tables and graphs.

  15. Derivation of Markov processes that violate detailed balance

    NASA Astrophysics Data System (ADS)

    Lee, Julian

    2018-03-01

    Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition. The original cyclic Markov model for the driven system is then recovered as an approximation at early times by summing over the degrees of freedom for the driving agent. I also show that the widely accepted expression for the entropy production in a cyclic Markov model is actually a time derivative of an entropy component in the extended model. Further, I present an analytic expression for the entropy component that is hidden in the cyclic Markov model.

  16. The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey's h Transformation as a Special Case

    PubMed Central

    Goerg, Georg M.

    2015-01-01

    I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert  W × F X random variable depends on a tail parameter δ ≥ 0: for δ = 0, Y ≡ X, for δ > 0 Y has heavier tails than X. For X being Gaussian it reduces to Tukey's h distribution. The Lambert W function provides an explicit inverse transformation, which can thus remove heavy tails from observed data. It also provides closed-form expressions for the cumulative distribution (cdf) and probability density function (pdf). As a special case, these yield analytic expression for Tukey's h pdf and cdf. Parameters can be estimated by maximum likelihood and applications to S&P 500 log-returns demonstrate the usefulness of the presented methodology. The R package LambertW implements most of the introduced methodology and is publicly available on CRAN. PMID:26380372

  17. Density functional perturbational orbital theory of spin polarization in electronic systems. II. Transition metal dimer complexes.

    PubMed

    Seo, Dong-Kyun

    2007-11-14

    We present a theoretical scheme for a semiquantitative analysis of electronic structures of magnetic transition metal dimer complexes within spin density functional theory (DFT). Based on the spin polarization perturbational orbital theory [D.-K. Seo, J. Chem. Phys. 125, 154105 (2006)], explicit spin-dependent expressions of the spin orbital energies and coefficients are derived, which allows to understand how spin orbitals form and change their energies and shapes when two magnetic sites are coupled either ferromagnetically or antiferromagnetically. Upon employment of the concept of magnetic orbitals in the active-electron approximation, a general mathematical formula is obtained for the magnetic coupling constant J from the analytical expression for the electronic energy difference between low-spin broken-symmetry and high-spin states. The origin of the potential exchange and kinetic exchange terms based on the one-electron picture is also elucidated. In addition, we provide a general account of the DFT analysis of the magnetic exchange interactions in compounds for which the active-electron approximation is not appropriate.

  18. Explicit Low-Thrust Guidance for Reference Orbit Targeting

    NASA Technical Reports Server (NTRS)

    Lam, Try; Udwadia, Firdaus E.

    2013-01-01

    The problem of a low-thrust spacecraft controlled to a reference orbit is addressed in this paper. A simple and explicit low-thrust guidance scheme with constrained thrust magnitude is developed by combining the fundamental equations of motion for constrained systems from analytical dynamics with a Lyapunov-based method. Examples are given for a spacecraft controlled to a reference trajectory in the circular restricted three body problem.

  19. Reference Production: Production-Internal and Addressee-Oriented Processes

    ERIC Educational Resources Information Center

    Arnold, Jennifer

    2008-01-01

    This paper reviews research on the production of referential expressions, examining the choice between explicit and attenuated lexical forms (e.g., pronouns vs. names), and between acoustically prominent and attenuated pronunciations. Both choices can be explained in terms of addressee-design, in that explicit expressions tend to be used in…

  20. The Anomalous Accretion Disk of the Cataclysmic Variable RW Sextantis

    NASA Astrophysics Data System (ADS)

    Linnell, Albert P.; Godon, P.; Hubeny, I.; Sion, E. M.; Szkody, P.

    2011-01-01

    The standard model for stable Cataclysmic Variable (CV) accretion disks (Frank, King and Raine 1992) derives an explicit analytic expression for the disk effective temperature as function of radial distance from the white dwarf (WD). That model specifies that the effective temperature, Teff(R), varies with R as ()0.25, where () represents a combination of parameters including R, the mass transfer rate M(dot), and other parameters. It is well known that fits of standard model synthetic spectra to observed CV spectra find almost no instances of agreement. We have derived a generalized expression for the radial temperature gradient, which preserves the total disk luminosity as function of M(dot) but permits a different exponent from the theoretical value of 0.25, and have applied it to RW Sex (Linnell et al.,2010,ApJ, 719,271). We find an excellent fit to observed FUSE and IUE spectra for an exponent of 0.125, curiously close to 1/2 the theoretical value. Our annulus synthetic spectra, combined to represent the accretion disk, were produced with program TLUSTY, were non-LTE and included H, He, C, Mg, Al, Si, and Fe as explicit ions. We illustrate our results with a plot showing the failure to fit RW Sex for a range of M(dot) values, our model fit to the observations, and a chi2 plot showing the selection of the exponent 0.125 as the best fit for the M(dot) range shown. (For the final model parameters see the paper cited.)

  1. Prediction of shock initiation thresholds and ignition probability of polymer-bonded explosives using mesoscale simulations

    NASA Astrophysics Data System (ADS)

    Kim, Seokpum; Wei, Yaochi; Horie, Yasuyuki; Zhou, Min

    2018-05-01

    The design of new materials requires establishment of macroscopic measures of material performance as functions of microstructure. Traditionally, this process has been an empirical endeavor. An approach to computationally predict the probabilistic ignition thresholds of polymer-bonded explosives (PBXs) using mesoscale simulations is developed. The simulations explicitly account for microstructure, constituent properties, and interfacial responses and capture processes responsible for the development of hotspots and damage. The specific mechanisms tracked include viscoelasticity, viscoplasticity, fracture, post-fracture contact, frictional heating, and heat conduction. The probabilistic analysis uses sets of statistically similar microstructure samples to directly mimic relevant experiments for quantification of statistical variations of material behavior due to inherent material heterogeneities. The particular thresholds and ignition probabilities predicted are expressed in James type and Walker-Wasley type relations, leading to the establishment of explicit analytical expressions for the ignition probability as function of loading. Specifically, the ignition thresholds corresponding to any given level of ignition probability and ignition probability maps are predicted for PBX 9404 for the loading regime of Up = 200-1200 m/s where Up is the particle speed. The predicted results are in good agreement with available experimental measurements. A parametric study also shows that binder properties can significantly affect the macroscopic ignition behavior of PBXs. The capability to computationally predict the macroscopic engineering material response relations out of material microstructures and basic constituent and interfacial properties lends itself to the design of new materials as well as the analysis of existing materials.

  2. Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

    NASA Astrophysics Data System (ADS)

    Chae, Jongchul; Litvinenko, Yuri E.

    2017-08-01

    The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na I D2 and Hα lines.

  3. Differential Higgs production at N3LO beyond threshold

    NASA Astrophysics Data System (ADS)

    Dulat, Falko; Mistlberger, Bernhard; Pelloni, Andrea

    2018-01-01

    We present several key steps towards the computation of differential Higgs boson cross sections at N3LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N3LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions. We find that while a few terms in the threshold expansion are sufficient to approximate the exact rapidity distribution well, transverse momentum distributions require a signficantly higher number of terms in the expansion to be adequately described. We find that to improve state of the art predictions for the rapidity distribution beyond NNLO even more sub-leading terms in the threshold expansion than presented in this article are required. In addition, we report on an interesting obstacle for the computation of N3LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections as supplementary material attached to this paper.

  4. Analytical solutions to optimal underactuated spacecraft formation reconfiguration

    NASA Astrophysics Data System (ADS)

    Huang, Xu; Yan, Ye; Zhou, Yang

    2015-11-01

    Underactuated systems can generally be defined as systems with fewer number of control inputs than that of the degrees of freedom to be controlled. In this paper, analytical solutions to optimal underactuated spacecraft formation reconfiguration without either the radial or the in-track control are derived. By using a linear dynamical model of underactuated spacecraft formation in circular orbits, controllability analysis is conducted for either underactuated case. Indirect optimization methods based on the minimum principle are then introduced to generate analytical solutions to optimal open-loop underactuated reconfiguration problems. Both fixed and free final conditions constraints are considered for either underactuated case and comparisons between these two final conditions indicate that the optimal control strategies with free final conditions require less control efforts than those with the fixed ones. Meanwhile, closed-loop adaptive sliding mode controllers for both underactuated cases are designed to guarantee optimal trajectory tracking in the presence of unmatched external perturbations, linearization errors, and system uncertainties. The adaptation laws are designed via a Lyapunov-based method to ensure the overall stability of the closed-loop system. The explicit expressions of the terminal convergent regions of each system states have also been obtained. Numerical simulations demonstrate the validity and feasibility of the proposed open-loop and closed-loop control schemes for optimal underactuated spacecraft formation reconfiguration in circular orbits.

  5. Differential Higgs production at N 3LO beyond threshold

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

    Dulat, Falko; Mistlberger, Bernhard; Pelloni, Andrea

    We present several key steps towards the computation of differential Higgs boson cross sections at N 3LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N 3LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions.more » We find that while a few terms in the threshold expansion are sufficient to approximate the exact rapidity distribution well, transverse momentum distributions require a signficantly higher number of terms in the expansion to be adequately described. We find that to improve state of the art predictions for the rapidity distribution beyond NNLO even more sub-leading terms in the threshold expansion than presented in this article are required. In addition, we report on an interesting obstacle for the computation of N 3LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections as supplementary material attached to this paper.« less

  6. Differential Higgs production at N 3LO beyond threshold

    DOE PAGES

    Dulat, Falko; Mistlberger, Bernhard; Pelloni, Andrea

    2018-01-29

    We present several key steps towards the computation of differential Higgs boson cross sections at N 3LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N 3LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions.more » We find that while a few terms in the threshold expansion are sufficient to approximate the exact rapidity distribution well, transverse momentum distributions require a signficantly higher number of terms in the expansion to be adequately described. We find that to improve state of the art predictions for the rapidity distribution beyond NNLO even more sub-leading terms in the threshold expansion than presented in this article are required. In addition, we report on an interesting obstacle for the computation of N 3LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections as supplementary material attached to this paper.« less

  7. Reaction Force of Micro-scale Liquid Droplets Constrained Between Parallel Plates through CFD

    NASA Astrophysics Data System (ADS)

    Free, Robert; Hekiri, Haider; Hawa, Takumi

    2012-02-01

    Micro-scale liquid droplets responding to depression between parallel plates are investigated analytically and numerically. The functional dependence of the reaction force accrued in such droplets on droplet size, surface tension, depression amount, and contact angle is explored. For both the 2D and 3D case, an analytical model is developed based on first principles. Computational fluid dynamics is then utilized to evaluate the validity of these models. The reaction force is highly nonlinear, initially increasing very slowly with increasing depression of the droplet, but eventually moving asymptotically to infinity. The force scales linearly with both the droplet free radius and surface tension of the liquid, but has a much more complicated dependence on the contact angle and depression. Explicit expressions for the reaction force have been determined, showing these dependencies. The 3D model has been largely supported by the CFD results. It very accurately predicts the reaction force on the upper plate as the droplet is crushed, accounting for the effect of contact angle, surface tension, and droplet size.

  8. Dynamic modes of quasispherical vesicles: exact analytical solutions.

    PubMed

    Guedda, M; Abaidi, M; Benlahsen, M; Misbah, C

    2012-11-01

    In this paper we introduce a simple mathematical analysis to reexamine vesicle dynamics in the quasispherical limit (small deformation) under a shear flow. In this context, a recent paper [Misbah, Phys. Rev. Lett. 96, 028104 (2006)] revealed a dynamic referred to as the vacillating-breathing (VB) mode where the vesicle main axis oscillates about the flow direction and the shape undergoes a breathinglike motion, as well as the tank-treading and tumbling (TB) regimes. Our goal here is to identify these three modes by obtaining explicit analytical expressions of the vesicle inclination angle and the shape deformation. In particular, the VB regime is put in evidence and the transition dynamics is discussed. Not surprisingly, our finding confirms the Keller-Skalak solutions (for rigid particles) and shows that the VB and TB modes coexist, and whether one prevails over the other depends on the initial conditions. An interesting additional element in the discussion is the prediction of the TB and VB modes as functions of a control parameter Γ, which can be identified as a TB-VB parameter.

  9. Instability of displacement of Oldroyd-B fluid by air in a Hele-Shaw cell

    NASA Astrophysics Data System (ADS)

    Daripa, Prabir

    2014-03-01

    We study the displacement of an Oldroyd-B fluid in a Hele-Shaw cell when driven by air. In particular, we explicitly obtain an analytical expression for the growth rate of instability which depends on the relaxation and retardation (time) constants, denoted by λ, and λ1 respectively, appearing in the Oldroyd-B constitutive relations. When these two constants are zero, we recover the classical Saffman-Taylor result for a Newtonian liquid displaced by air. Our results show that this displacement process is more unstable than the case when a Newtonian fluid is displaced by air. The analytical results are plotted and compared with numerical results on this unstable displacement process available in the literature. The agreement is found to be excellent. In particular, results show that the non-Newtonian case (i.e., Oldroyd-B) is more unstable than the Newtonian case. Supported by an NPRP Grant # 08-777-1-141 from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the author.

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

    Noronha, Jorge; Denicol, Gabriel S.

    In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime AdS 2 Ⓧ S 2. We further derive explicit analytic expressions for the momentum dependence of the single-particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density doesmore » not match the equilibrium form. The nonequilibrium contribution to the entropy density is shown to be due to higher-order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.« less

  11. Modeling and analysis of energy quantization effects on single electron inverter performance

    NASA Astrophysics Data System (ADS)

    Dan, Surya Shankar; Mahapatra, Santanu

    2009-08-01

    In this paper, for the first time, the effects of energy quantization on single electron transistor (SET) inverter performance are analyzed through analytical modeling and Monte Carlo simulations. It is shown that energy quantization mainly changes the Coulomb blockade region and drain current of SET devices and thus affects the noise margin, power dissipation, and the propagation delay of SET inverter. A new analytical model for the noise margin of SET inverter is proposed which includes the energy quantization effects. Using the noise margin as a metric, the robustness of SET inverter is studied against the effects of energy quantization. A compact expression is developed for a novel parameter quantization threshold which is introduced for the first time in this paper. Quantization threshold explicitly defines the maximum energy quantization that an SET inverter logic circuit can withstand before its noise margin falls below a specified tolerance level. It is found that SET inverter designed with CT:CG=1/3 (where CT and CG are tunnel junction and gate capacitances, respectively) offers maximum robustness against energy quantization.

  12. Computational Prediction of Shock Ignition Thresholds and Ignition Probability of Polymer-Bonded Explosives

    NASA Astrophysics Data System (ADS)

    Wei, Yaochi; Kim, Seokpum; Horie, Yasuyuki; Zhou, Min

    2017-06-01

    A computational approach is developed to predict the probabilistic ignition thresholds of polymer-bonded explosives (PBXs). The simulations explicitly account for microstructure, constituent properties, and interfacial responses and capture processes responsible for the development of hotspots and damage. The specific damage mechanisms considered include viscoelasticity, viscoplasticity, fracture, post-fracture contact, frictional heating, and heat conduction. The probabilistic analysis uses sets of statistically similar microstructure samples to mimic relevant experiments for statistical variations of material behavior due to inherent material heterogeneities. The ignition thresholds and corresponding ignition probability maps are predicted for PBX 9404 and PBX 9501 for the impact loading regime of Up = 200 --1200 m/s. James and Walker-Wasley relations are utilized to establish explicit analytical expressions for the ignition probability as a function of load intensities. The predicted results are in good agreement with available experimental measurements. The capability to computationally predict the macroscopic response out of material microstructures and basic constituent properties lends itself to the design of new materials and the analysis of existing materials. The authors gratefully acknowledge the support from Air Force Office of Scientific Research (AFOSR) and the Defense Threat Reduction Agency (DTRA).

  13. Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

    NASA Astrophysics Data System (ADS)

    Banerjee, J. R.; Ananthapuvirajah, A.

    2018-05-01

    The free vibration analysis of functionally graded beams (FGBs) and frameworks containing FGBs is carried out by applying the dynamic stiffness method and deriving the elements of the dynamic stiffness matrix in explicit algebraic form. The usually adopted rule that the material properties of the FGB vary continuously through the thickness according to a power law forms the fundamental basis of the governing differential equations of motion in free vibration. The differential equations are solved in closed analytical form when the free vibratory motion is harmonic. The dynamic stiffness matrix is then formulated by relating the amplitudes of forces to those of the displacements at the two ends of the beam. Next, the explicit algebraic expressions for the dynamic stiffness elements are derived with the help of symbolic computation. Finally the Wittrick-Williams algorithm is applied as solution technique to solve the free vibration problems of FGBs with uniform cross-section, stepped FGBs and frameworks consisting of FGBs. Some numerical results are validated against published results, but in the absence of published results for frameworks containing FGBs, consistency checks on the reliability of results are performed. The paper closes with discussion of results and conclusions.

  14. Generalized reproduction numbers and the prediction of patterns in waterborne disease

    PubMed Central

    Gatto, Marino; Mari, Lorenzo; Bertuzzo, Enrico; Casagrandi, Renato; Righetto, Lorenzo; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea

    2012-01-01

    Understanding, predicting, and controlling outbreaks of waterborne diseases are crucial goals of public health policies, but pose challenging problems because infection patterns are influenced by spatial structure and temporal asynchrony. Although explicit spatial modeling is made possible by widespread data mapping of hydrology, transportation infrastructure, population distribution, and sanitation, the precise condition under which a waterborne disease epidemic can start in a spatially explicit setting is still lacking. Here we show that the requirement that all the local reproduction numbers be larger than unity is neither necessary nor sufficient for outbreaks to occur when local settlements are connected by networks of primary and secondary infection mechanisms. To determine onset conditions, we derive general analytical expressions for a reproduction matrix , explicitly accounting for spatial distributions of human settlements and pathogen transmission via hydrological and human mobility networks. At disease onset, a generalized reproduction number (the dominant eigenvalue of ) must be larger than unity. We also show that geographical outbreak patterns in complex environments are linked to the dominant eigenvector and to spectral properties of . Tests against data and computations for the 2010 Haiti and 2000 KwaZulu-Natal cholera outbreaks, as well as against computations for metapopulation networks, demonstrate that eigenvectors of provide a synthetic and effective tool for predicting the disease course in space and time. Networked connectivity models, describing the interplay between hydrology, epidemiology, and social behavior sustaining human mobility, thus prove to be key tools for emergency management of waterborne infections. PMID:23150538

  15. The Internet and the First Amendment: School and Sexually Explicit Expression.

    ERIC Educational Resources Information Center

    Cate, Fred H.

    Rather than focus on "who" makes the determination about students' access to sexually explicit expression, this volume examines the legal issues affecting "whether" to permit that access and "how much" access to allow. In sum, this book is intended to facilitate meaningful discussion about the regulation of minors'…

  16. Unsteady lift forces on highly cambered airfoils moving through a gust

    NASA Technical Reports Server (NTRS)

    Atassi, H.; Goldstein, M.

    1974-01-01

    An unsteady airfoil theory in which the flow is linearized about the steady potential flow of the airfoil is presented. The theory is applied to an airfoil entering a gust. After transformation to the W-plane, the problem is formulated in terms of a Poisson's equation. The solutions are expanded in a Fourier-Bessel series. The theory is applied to a circular arc with arbitrary camber. Closed form expressions for the velocity and pressure on the surface of the airfoil are obtained. The unsteady aerodynamic forces are then calculated and shown to contain two terms. One in an explicit closed analytical form represents the contribution of the oncoming vortical disturbance, the other depends on a single quadrature and accounts for the effect of the wake.

  17. Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.

    PubMed

    Guérin, T; Dean, D S

    2015-12-01

    We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.

  18. Dynamic stabilization of Rayleigh-Taylor instability in an ablation front

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

    Piriz, A. R.; Di Lucchio, L.; Rodriguez Prieto, G.

    2011-01-15

    Dynamic stabilization of Rayleigh-Taylor instability in an ablation front is studied by considering a modulation in the acceleration that consists of sequences of Dirac deltas. This allows obtaining explicit analytical expressions for the instability growth rate as well as for the boundaries of the stability region. As a general rule, it is found that it is possible to stabilize all wave numbers above a certain minimum value k{sub m}, but the requirements in the modulation amplitude and frequency become more exigent with smaller k{sub m}. The essential role of compressibility is phenomenologically addressed in order to find the constraint itmore » imposes on the stability region. The results for some different wave forms of the acceleration modulation are also presented.« less

  19. Rogue-wave solutions of the Zakharov equation

    NASA Astrophysics Data System (ADS)

    Rao, Jiguang; Wang, Lihong; Liu, Wei; He, Jingsong

    2017-12-01

    Using the bilinear transformation method, we derive general rogue-wave solutions of the Zakharov equation. We present these Nth-order rogue-wave solutions explicitly in terms of Nth-order determinants whose matrix elements have simple expressions. We show that the fundamental rogue wave is a line rogue wave with a line profile on the plane ( x, y) arising from a constant background at t ≪ 0 and then gradually tending to the constant background for t ≫ 0. Higher-order rogue waves arising from a constant background and later disappearing into it describe the interaction of several fundamental line rogue waves. We also consider different structures of higher-order rogue waves. We present differences between rogue waves of the Zakharov equation and of the first type of the Davey-Stewartson equation analytically and graphically.

  20. 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

  1. The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle points

    NASA Technical Reports Server (NTRS)

    Connor, J. N. L.; Curtis, P. R.; Farrelly, D.

    1984-01-01

    Methods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.

  2. Coherent States for Kronecker Products of Non Compact Groups: Formulation and Applications

    NASA Technical Reports Server (NTRS)

    Bambah, Bindu A.; Agarwal, Girish S.

    1996-01-01

    We introduce and study the properties of a class of coherent states for the group SU(1,1) X SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the discrete series representations of SU(1,1). These are the generalization of the 'Barut Girardello' coherent states to the Kronecker Product of two non-compact groups. The resolution of the identity and the analytic phase space representation of these states is presented. This phase space representation is based on the basis of products of 'pair coherent states' rather than the standard number state canonical basis. We discuss the utility of the resulting 'bi-pair coherent states' in the context of four-mode interactions in quantum optics.

  3. Modeling of energy release systems from OTEC plants

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

    Denno, K.

    1983-12-01

    This paper presents analytical scope for the controlling functions of OTEC operation for the ultimate production of sizable bulk ..delta..T as well as H/sub 2/, N/sub 2/ and NH/sub 3/. The controlling parametric functions include the oceanic and ammonia Reynolds numbers which depend implicitly and explicitly on the ocean water velocity, mass-volume, duration of ..delta..T extraction, and the inlet and outlet water temperatures internally and externally. Solutions for the oceanic and amonia Reynolds numbers have been established setting the deciding constraints on water velocity, boundary temperatures, mass-volume as well as other plant parameters. Linkage between OTEC plant and other conventionalmore » as well as advanced energy systems has been expressed in terms of a set of balance and coordinating energy equations.« less

  4. Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

    NASA Astrophysics Data System (ADS)

    Sivaganesh, G.; Arulgnanam, A.; Seethalakshmi, A. N.; Selvaraj, S.

    2018-05-01

    We present explicit generalized analytical solutions for a network of linearly-coupled simple chaotic systems. Analytical solutions are obtained for the normalized state equations of a network of linearly-coupled systems driven by a common chaotic drive system. Two parameter bifurcation diagrams revealing the various hidden synchronization regions, such as complete, phase and phase-lag synchronization are identified using the analytical results. The synchronization dynamics and their stability are studied using phase portraits and the master stability function, respectively. Further, experimental results for linearly-coupled simple chaotic systems are presented to confirm the analytical results. The synchronization dynamics of a network of chaotic systems studied analytically is reported for the first time.

  5. More than a feeling: Pervasive influences of memory without awareness of retrieval

    PubMed Central

    Voss, Joel L.; Lucas, Heather D.; Paller, Ken A.

    2015-01-01

    The subjective experiences of recollection and familiarity have featured prominently in the search for neurocognitive mechanisms of memory. However, these two explicit expressions of memory, which involve conscious awareness of memory retrieval, are distinct from an entire category of implicit expressions of memory that do not entail such awareness. This review summarizes recent evidence showing that neurocognitive processing related to implicit memory can powerfully influence the behavioral and neural measures typically associated with explicit memory. Although there are striking distinctions between the neurocognitive processing responsible for implicit versus explicit memory, tests designed to measure only explicit memory nonetheless often capture implicit memory processing as well. In particular, the evidence described here suggests that investigations of familiarity memory are prone to the accidental capture of implicit memory processing. These findings have considerable implications for neurocognitive accounts of memory, as they suggest that many neural and behavioral measures often accepted as signals of explicit memory instead reflect the distinct operation of implicit memory mechanisms that are only sometimes related to explicit memory expressions. Proper identification of the explicit and implicit mechanisms for memory is vital to understanding the normal operation of memory, in addition to the disrupted memory capabilities associated with many neurological disorders and mental illnesses. We suggest that future progress requires utilizing neural, behavioral, and subjective evidence to dissociate implicit and explicit memory processing so as to better understand their distinct mechanisms as well as their potential relationships. When searching for the neurocognitive mechanisms of memory, it is important to keep in mind that memory involves more than a feeling. PMID:24171735

  6. Nonadiabatic dynamics of electron transfer in solution: Explicit and implicit solvent treatments that include multiple relaxation time scales

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

    Schwerdtfeger, Christine A.; Soudackov, Alexander V.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu

    2014-01-21

    The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents formore » a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.« less

  7. Simple physics-based analytical formulas for the potentials of mean force of the interaction of amino-acid side chains in water. V. Like-charged side chains.

    PubMed

    Makowski, Mariusz; Liwo, Adam; Sobolewski, Emil; Scheraga, Harold A

    2011-05-19

    A new model of side-chain-side-chain interactions for charged side-chains of amino acids, to be used in the UNRES force-field, has been developed, in which a side chain consists of a nonpolar and a charged site. The interaction energy between the nonpolar sites is composed of a Gay-Berne and a cavity term; the interaction energy between the charged sites consists of a Lennard-Jones term, a Coulombic term, a generalized-Born term, and a cavity term, while the interaction energy between the nonpolar and charged sites is composed of a Gay-Berne and a polarization term. We parametrized the energy function for the models of all six pairs of natural like-charged amino-acid side chains, namely propionate-propionate (for the aspartic acid-aspartic acid pair), butyrate-butyrate (for the glutamic acid-glutamic acid pair), propionate-butyrate (for the aspartic acid-glutamic acid pair), pentylamine cation-pentylamine cation (for the lysine-lysine pair), 1-butylguanidine cation-1-butylguanidine cation (for the arginine-arginine pair), and pentylamine cation-1-butylguanidine cation (for the lysine-arginine pair). By using umbrella-sampling molecular dynamics simulations in explicit TIP3P water, we determined the potentials of mean force of the above-mentioned pairs as functions of distance and orientation and fitted analytical expressions to them. The positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the orientation of the molecules were well represented by analytical expressions for all systems. The values of the parameters of all the energy components are physically reasonable, which justifies use of such potentials in coarse-grain protein-folding simulations. © 2011 American Chemical Society

  8. Does attitude acquisition in evaluative conditioning without explicit CS-US memory reflect implicit misattribution of affect?

    PubMed

    Mierop, Adrien; Hütter, Mandy; Stahl, Christoph; Corneille, Olivier

    2018-02-05

    Research that dissociates different types of processes within a given task using a processing tree approach suggests that attitudes may be acquired through evaluative conditioning in the absence of explicit encoding of CS-US pairings in memory. This research distinguishes explicit memory for the CS-US pairings from CS-liking acquired without encoding of CS-US pairs in explicit memory. It has been suggested that the latter effect may be due to an implicit misattribution process that is assumed to operate when US evocativeness is low. In the present research, the latter assumption was supported neither by two high-powered experiments nor by complementary meta-analytic evidence, whereas evocativeness exerted an influence on explicit memory. This pattern of findings is inconsistent with the view that CS-liking acquired without encoding of CS-US pairs in explicit memory reflects an implicit misattribution process at learning. Hence, the underlying learning process is awaiting further empirical scrutiny.

  9. A note on singularities of the 3-D Euler equation

    NASA Technical Reports Server (NTRS)

    Tanveer, S.

    1994-01-01

    In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

  10. Explicit continuous charge-based compact model for long channel heavily doped surrounding-gate MOSFETs incorporating interface traps and quantum effects

    NASA Astrophysics Data System (ADS)

    Hamzah, Afiq; Hamid, Fatimah A.; Ismail, Razali

    2016-12-01

    An explicit solution for long-channel surrounding-gate (SRG) MOSFETs is presented from intrinsic to heavily doped body including the effects of interface traps and fixed oxide charges. The solution is based on the core SRGMOSFETs model of the Unified Charge Control Model (UCCM) for heavily doped conditions. The UCCM model of highly doped SRGMOSFETs is derived to obtain the exact equivalent expression as in the undoped case. Taking advantage of the undoped explicit charge-based expression, the asymptotic limits for below threshold and above threshold have been redefined to include the effect of trap states for heavily doped cases. After solving the asymptotic limits, an explicit mobile charge expression is obtained which includes the trap state effects. The explicit mobile charge model shows very good agreement with respect to numerical simulation over practical terminal voltages, doping concentration, geometry effects, and trap state effects due to the fixed oxide charges and interface traps. Then, the drain current is obtained using the Pao-Sah's dual integral, which is expressed as a function of inversion charge densities at the source/drain ends. The drain current agreed well with the implicit solution and numerical simulation for all regions of operation without employing any empirical parameters. A comparison with previous explicit models has been conducted to verify the competency of the proposed model with the doping concentration of 1× {10}19 {{cm}}-3, as the proposed model has better advantages in terms of its simplicity and accuracy at a higher doping concentration.

  11. Theory of rotational transition in atom-diatom chemical reaction

    NASA Astrophysics Data System (ADS)

    Nakamura, Masato; Nakamura, Hiroki

    1989-05-01

    Rotational transition in atom-diatom chemical reaction is theoretically studied. A new approximate theory (which we call IOS-DW approximation) is proposed on the basis of the physical idea that rotational transition in reaction is induced by the following two different mechanisms: rotationally inelastic half collision in both initial and final arrangement channels, and coordinate transformation in the reaction zone. This theory gives a fairy compact expression for the state-to-state transition probability. Introducing the additional physically reasonable assumption that reaction (particle rearrangement) takes place in a spatially localized region, we have reduced this expression into a simpler analytical form which can explicitly give overall rotational state distribution in reaction. Numerical application was made to the H+H2 reaction and demonstrated its effectiveness for the simplicity. A further simplified most naive approximation, i.e., independent events approximation was also proposed and demonstrated to work well in the test calculation of H+H2. The overall rotational state distribution is expressed simply by a product sum of the transition probabilities for the three consecutive processes in reaction: inelastic transition in the initial half collision, transition due to particle rearrangement, and inelastic transition in the final half collision.

  12. Semiclassical evaluation of quantum fidelity

    NASA Astrophysics Data System (ADS)

    Vanicek, Jiri

    2004-03-01

    We present a numerically feasible semiclassical method to evaluate quantum fidelity (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform semiclassical expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows a Monte-Carlo evaluation, this uniform expression is accurate at times where there are 10^70 semiclassical contributions. Remarkably, the method also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and thus provide a ``defense" of the linear response theory from the famous Van Kampen objection. We point out the potential use of our uniform expression in other areas because it gives a most direct link between the quantum Feynman propagator based on the path integral and the semiclassical Van Vleck propagator based on the sum over classical trajectories. Finally, we test the applicability of our method in integrable and mixed systems.

  13. Explicit solutions for exit-only radioactive decay chains

    NASA Astrophysics Data System (ADS)

    Yuan, Ding; Kernan, Warnick

    2007-05-01

    In this study, we extended Bateman's [Proc. Cambridge Philos. Soc. 15, 423 (1910)] original work for solving radioactive decay chains and explicitly derived analytic solutions for generic exit-only radioactive decay problems under given initial conditions. Instead of using the conventional Laplace transform for solving Bateman's equations, we used a much simpler algebraic approach. Finally, we discuss methods of breaking down certain classes of large decay chains into collections of simpler chains for easy handling.

  14. Development of an analytical solution for the Budyko watershed parameter in terms of catchment physical features

    NASA Astrophysics Data System (ADS)

    Reaver, N.; Kaplan, D. A.; Jawitz, J. W.

    2017-12-01

    The Budyko hypothesis states that a catchment's long-term water and energy balances are dependent on two relatively easy to measure quantities: rainfall depth and potential evaporation. This hypothesis is expressed as a simple function, the Budyko equation, which allows for the prediction of a catchment's actual evapotranspiration and discharge from measured rainfall depth and potential evaporation, data which are widely available. However, the two main analytically derived forms of the Budyko equation contain a single unknown watershed parameter, whose value varies across catchments; variation in this parameter has been used to explain the hydrological behavior of different catchments. The watershed parameter is generally thought of as a lumped quantity that represents the influence of all catchment biophysical features (e.g. soil type and depth, vegetation type, timing of rainfall, etc). Previous work has shown that the parameter is statistically correlated with catchment properties, but an explicit expression has been elusive. While the watershed parameter can be determined empirically by fitting the Budyko equation to measured data in gauged catchments where actual evapotranspiration can be estimated, this limits the utility of the framework for predicting impacts to catchment hydrology due to changing climate and land use. In this study, we developed an analytical solution for the lumped catchment parameter for both forms of the Budyko equation. We combined these solutions with a statistical soil moisture model to obtain analytical solutions for the Budyko equation parameter as a function of measurable catchment physical features, including rooting depth, soil porosity, and soil wilting point. We tested the predictive power of these solutions using the U.S. catchments in the MOPEX database. We also compared the Budyko equation parameter estimates generated from our analytical solutions (i.e. predicted parameters) with those obtained through the calibration of the Budyko equation to discharge data (i.e. empirical parameters), and found good agreement. These results suggest that it is possible to predict the Budyko equation watershed parameter directly from physical features, even for ungauged catchments.

  15. Implicit and explicit processing of emotional facial expressions in Parkinson's disease.

    PubMed

    Wagenbreth, Caroline; Wattenberg, Lena; Heinze, Hans-Jochen; Zaehle, Tino

    2016-04-15

    Besides motor problems, Parkinson's disease (PD) is associated with detrimental emotional and cognitive functioning. Deficient explicit emotional processing has been observed, whilst patients also show impaired Theory of Mind (ToM) abilities. However, it is unclear whether this PD patients' ToM deficit is based on an inability to infer otherś emotional states or whether it is due to explicit emotional processing deficits. We investigated implicit and explicit emotional processing in PD with an affective priming paradigm in which we used pictures of human eyes for emotional primes and a lexical decision task (LDT) with emotional connoted words for target stimuli. Sixteen PD patients and sixteen matched healthy controls performed a LTD combined with an emotional priming paradigm providing emotional information through the facial eye region to assess implicit emotional processing. Second, participants explicitly evaluated the emotional status of eyes and words used in the implicit task. Compared to controls implicit emotional processing abilities were generally preserved in PD with, however, considerable alterations for happiness and disgust processing. Furthermore, we observed a general impairment of patients for explicit evaluation of emotional stimuli, which was augmented for the rating of facial expressions. This is the first study reporting results for affective priming with facial eye expressions in PD patients. Our findings indicate largely preserved implicit emotional processing, with a specific altered processing of disgust and happiness. Explicit emotional processing was considerably impaired for semantic and especially for facial stimulus material. Poor ToM abilities in PD patients might be based on deficient explicit emotional processing, with preserved ability to implicitly infer other people's feelings. Copyright © 2016 Elsevier B.V. All rights reserved.

  16. Forces and torques on rigid inclusions in an elastic environment: Resulting matrix-mediated interactions, displacements, and rotations

    NASA Astrophysics Data System (ADS)

    Puljiz, Mate; Menzel, Andreas M.

    2017-05-01

    Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance, for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical inclusions are enclosed by a homogeneous elastic medium under stick boundary conditions. Forces and torques are directly imposed from outside onto the inclusions or are externally induced between them. The inclusions respond to these forces and torques by translations and rotations against the surrounding elastic matrix. This leads to elastic matrix deformations, and in turn results in mutual long-ranged matrix-mediated interactions between the inclusions. Adapting a well-known approach from low-Reynolds-number hydrodynamics, we explicitly calculate the displacements and rotations of the inclusions from the externally imposed or induced forces and torques. Analytical expressions are presented as a function of the inclusion configuration in terms of displaceability and rotateability matrices. The role of the elastic environment is implicitly included in these relations. That is, the resulting expressions allow a calculation of the induced displacements and rotations directly from the inclusion configuration, without having to explicitly determine the deformations of the elastic environment. In contrast to the hydrodynamic case, compressibility of the surrounding medium is readily taken into account. We present the complete derivation based on the underlying equations of linear elasticity theory. In the future, the method will, for example, be helpful to characterize the behavior of externally tunable elastic composite materials, to accelerate numerical approaches, as well as to improve the quantitative interpretation of microrheological results.

  17. Research in digital adaptive flight controllers

    NASA Technical Reports Server (NTRS)

    Kaufman, H.

    1976-01-01

    A design study of adaptive control logic suitable for implementation in modern airborne digital flight computers was conducted. Both explicit controllers which directly utilize parameter identification and implicit controllers which do not require identification were considered. Extensive analytical and simulation efforts resulted in the recommendation of two explicit digital adaptive flight controllers. Interface weighted least squares estimation procedures with control logic were developed using either optimal regulator theory or with control logic based upon single stage performance indices.

  18. Simple Physics-Based Analytical Formulas for the Potentials of Mean Force of the Interaction of Amino Acid Side Chains in Water. VII. Charged-Hydrophobic/Polar and Polar-Hydrophobic/Polar Side Chains.

    PubMed

    Makowski, Mariusz; Liwo, Adam; Scheraga, Harold A

    2017-01-19

    The physics-based potentials of side-chain-side-chain interactions corresponding to pairs composed of charged and polar, polar and polar, charged and hydrophobic, and hydrophobic and hydrophobic side chains have been determined. A total of 144 four-dimensional potentials of mean force (PMFs) of all possible pairs of molecules modeling these pairs were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation, and the analytical expressions were then fitted to the PMFs. Depending on the type of interacting sites, the analytical approximation to the PMF is a sum of terms corresponding to van der Waals interactions and cavity-creation involving the nonpolar sections of the side chains and van der Waals, cavity-creation, and electrostatic (charge-dipole or dipole-dipole) interaction energies and polarization energies involving the charged or polar sections of the side chains. The model used in this work reproduces all features of the interacting pairs. The UNited RESidue force field with the new side-chain-side-chain interaction potentials was preliminarily tested with the N-terminal part of the B-domain of staphylococcal protein A (PDBL 1BDD ; a three-α-helix bundle) and UPF0291 protein YnzC from Bacillus subtilis (PDB: 2HEP ; an α-helical hairpin).

  19. Dynamic stabilization of Rayleigh-Taylor instability: Experiments with Newtonian fluids as surrogates for ablation fronts

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

    Rodriguez Prieto, G.; Piriz, A. R.; Lopez Cela, J. J.

    2013-01-15

    A previous theory on dynamic stabilization of Rayleigh-Taylor instability at interfaces between Newtonian fluids is reformulated in order to make evident the analogy of this problem with the related one on dynamic stabilization of ablation fronts in the framework of inertial confinement fusion. Explicit analytical expressions are obtained for the boundaries of the dynamically stable region which turns out to be completely analogue to the stability charts obtained for the case of ablation fronts. These results allow proposing experiments with Newtonian fluids as surrogates for studying the case of ablation fronts. Experiments with Newtonian fluids are presented which demonstrate themore » validity of the theoretical approach and encourage to pursue experimental research on ablation fronts to settle the feasibility of dynamic stabilization in the inertial confinement fusion scenario.« less

  20. A massively parallel computational approach to coupled thermoelastic/porous gas flow problems

    NASA Technical Reports Server (NTRS)

    Shia, David; Mcmanus, Hugh L.

    1995-01-01

    A new computational scheme for coupled thermoelastic/porous gas flow problems is presented. Heat transfer, gas flow, and dynamic thermoelastic governing equations are expressed in fully explicit form, and solved on a massively parallel computer. The transpiration cooling problem is used as an example problem. The numerical solutions have been verified by comparison to available analytical solutions. Transient temperature, pressure, and stress distributions have been obtained. Small spatial oscillations in pressure and stress have been observed, which would be impractical to predict with previously available schemes. Comparisons between serial and massively parallel versions of the scheme have also been made. The results indicate that for small scale problems the serial and parallel versions use practically the same amount of CPU time. However, as the problem size increases the parallel version becomes more efficient than the serial version.

  1. Quasi-steady-state analysis of coupled flashing ratchets.

    PubMed

    Levien, Ethan; Bressloff, Paul C

    2015-10-01

    We perform a quasi-steady-state (QSS) reduction of a flashing ratchet to obtain a Brownian particle in an effective potential. The resulting system is analytically tractable and yet preserves essential dynamical features of the full model. We first use the QSS reduction to derive an explicit expression for the velocity of a simple two-state flashing ratchet. In particular, we determine the relationship between perturbations from detailed balance, which are encoded in the transitions rates of the flashing ratchet, and a tilted-periodic potential. We then perform a QSS analysis of a pair of elastically coupled flashing ratchets, which reduces to a Brownian particle moving in a two-dimensional vector field. We suggest that the fixed points of this vector field accurately approximate the metastable spatial locations of the coupled ratchets, which are, in general, impossible to identify from the full system.

  2. Simple analytical relations for ship bow waves

    NASA Astrophysics Data System (ADS)

    Noblesse, Francis; Delhommeau, G.?Rard; Guilbaud, Michel; Hendrix, Dane; Yang, Chi

    Simple analytical relations for the bow wave generated by a ship in steady motion are given. Specifically, simple expressions that define the height of a ship bow wave, the distance between the ship stem and the crest of the bow wave, the rise of water at the stem, and the bow wave profile, explicitly and without calculations, in terms of the ship speed, draught, and waterline entrance angle, are given. Another result is a simple criterion that predicts, also directly and without calculations, when a ship in steady motion cannot generate a steady bow wave. This unsteady-flow criterion predicts that a ship with a sufficiently fine waterline, specifically with waterline entrance angle 2, may generate a steady bow wave at any speed. However, a ship with a fuller waterline (25E) can only generate a steady bow wave if the ship speed is higher than a critical speed, defined in terms of αE by a simple relation. No alternative criterion for predicting when a ship in steady motion does not generate a steady bow wave appears to exist. A simple expression for the height of an unsteady ship bow wave is also given. In spite of their remarkable simplicity, the relations for ship bow waves obtained in the study (using only rudimentary physical and mathematical considerations) are consistent with experimental measurements for a number of hull forms having non-bulbous wedge-shaped bows with small flare angle, and with the authors' measurements and observations for a rectangular flat plate towed at a yaw angle.

  3. Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

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

    Yoo, Jaiyul; Gong, Jinn-Ouk, E-mail: jyoo@physik.uzh.ch, E-mail: jinn-ouk.gong@apctp.org

    We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

  4. Generalized reproduction numbers and the prediction of patterns in waterborne disease.

    PubMed

    Gatto, Marino; Mari, Lorenzo; Bertuzzo, Enrico; Casagrandi, Renato; Righetto, Lorenzo; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea

    2012-11-27

    Understanding, predicting, and controlling outbreaks of waterborne diseases are crucial goals of public health policies, but pose challenging problems because infection patterns are influenced by spatial structure and temporal asynchrony. Although explicit spatial modeling is made possible by widespread data mapping of hydrology, transportation infrastructure, population distribution, and sanitation, the precise condition under which a waterborne disease epidemic can start in a spatially explicit setting is still lacking. Here we show that the requirement that all the local reproduction numbers R0 be larger than unity is neither necessary nor sufficient for outbreaks to occur when local settlements are connected by networks of primary and secondary infection mechanisms. To determine onset conditions, we derive general analytical expressions for a reproduction matrix G0, explicitly accounting for spatial distributions of human settlements and pathogen transmission via hydrological and human mobility networks. At disease onset, a generalized reproduction number Λ0 (the dominant eigenvalue of G0) must be larger than unity. We also show that geographical outbreak patterns in complex environments are linked to the dominant eigenvector and to spectral properties of G0. Tests against data and computations for the 2010 Haiti and 2000 KwaZulu-Natal cholera outbreaks, as well as against computations for metapopulation networks, demonstrate that eigenvectors of G0 provide a synthetic and effective tool for predicting the disease course in space and time. Networked connectivity models, describing the interplay between hydrology, epidemiology, and social behavior sustaining human mobility, thus prove to be key tools for emergency management of waterborne infections.

  5. What is the right formalism to search for resonances?

    NASA Astrophysics Data System (ADS)

    Mikhasenko, M.; Pilloni, A.; Nys, J.; Albaladejo, M.; Fernández-Ramírez, C.; Jackura, A.; Mathieu, V.; Sherrill, N.; Skwarnicki, T.; Szczepaniak, A. P.

    2018-03-01

    Hadron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. Hereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B→ ψ π K and B→ \\bar{D}π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.

  6. Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

    NASA Astrophysics Data System (ADS)

    Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

    2017-04-01

    Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

  7. Thermal Casimir and Casimir–Polder interactions in N parallel 2D Dirac materials

    NASA Astrophysics Data System (ADS)

    Khusnutdinov, Nail; Kashapov, Rashid; Woods, Lilia M.

    2018-07-01

    The Casimir and Casimir–Polder interactions are investigated in a stack of equally spaced graphene layers. The optical response of the individual graphene is taken into account using gauge invariant components of the polarization tensor extended to the whole complex frequency plane. The planar symmetry for the electromagnetic boundary conditions is further used to obtain explicit forms for the Casimir energy stored in the stack and the Casimir–Polder energy between an atom above the stack. Our calculations show that these fluctuation induced interactions experience strong thermal effects due to the graphene Dirac-like energy spectrum. The spatial dispersion and temperature dependence in the optical response are also found to be important for enhancing the interactions especially at smaller separations. Analytical expressions for low and high temperature limits and their comparison with corresponding expressions for an infinitely conducting planar stack are further used to expand our understanding of Casimir and Casimir–Polder energies in Dirac materials. Our results may be useful to experimentalists as new ways to probe thermal effects at the nanoscale in such universal interactions.

  8. The Havriliak-Negami relaxation and its relatives: the response, relaxation and probability density functions

    NASA Astrophysics Data System (ADS)

    Górska, K.; Horzela, A.; Bratek, Ł.; Dattoli, G.; Penson, K. A.

    2018-04-01

    We study functions related to the experimentally observed Havriliak-Negami dielectric relaxation pattern proportional in the frequency domain to [1+(iωτ0){\\hspace{0pt}}α]-β with τ0 > 0 being some characteristic time. For α = l/k< 1 (l and k being positive and relatively prime integers) and β > 0 we furnish exact and explicit expressions for response and relaxation functions in the time domain and suitable probability densities in their domain dual in the sense of the inverse Laplace transform. All these functions are expressed as finite sums of generalized hypergeometric functions, convenient to handle analytically and numerically. Introducing a reparameterization β = (2-q)/(q-1) and τ0 = (q-1){\\hspace{0pt}}1/α (1 < q < 2) we show that for 0 < α < 1 the response functions fα, β(t/τ0) go to the one-sided Lévy stable distributions when q tends to one. Moreover, applying the self-similarity property of the probability densities gα, β(u) , we introduce two-variable densities and show that they satisfy the integral form of the evolution equation.

  9. Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

    DOE PAGES

    Del Duca, Vittorio; Druc, Stefan; Drummond, James; ...

    2016-08-25

    We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they canmore » be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. In conclusion, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.« less

  10. Performing the unexplainable: Implicit task performance reveals individually reliable sequence learning without explicit knowledge

    PubMed Central

    Sanchez, Daniel J.; Gobel, Eric W.; Reber, Paul J.

    2015-01-01

    Memory-impaired patients express intact implicit perceptual–motor sequence learning, but it has been difficult to obtain a similarly clear dissociation in healthy participants. When explicit memory is intact, participants acquire some explicit knowledge and performance improvements from implicit learning may be subtle. Therefore, it is difficult to determine whether performance exceeds what could be expected on the basis of the concomitant explicit knowledge. Using a challenging new sequence-learning task, robust implicit learning was found in healthy participants with virtually no associated explicit knowledge. Participants trained on a repeating sequence that was selected randomly from a set of five. On a performance test of all five sequences, performance was best on the trained sequence, and two-thirds of the participants exhibited individually reliable improvement (by chi-square analysis). Participants could not reliably indicate which sequence had been trained by either recognition or recall. Only by expressing their knowledge via performance were participants able to indicate which sequence they had learned. PMID:21169570

  11. Implicit motives, explicit traits, and task and contextual performance at work.

    PubMed

    Lang, Jonas W B; Zettler, Ingo; Ewen, Christian; Hülsheger, Ute R

    2012-11-01

    Personality psychologists have long argued that explicit traits (as measured by questionnaires) channel the expression of implicit motives (as measured by coding imaginative verbal behavior) such that both interact in the prediction of relevant life outcome variables. In the present research, we apply these ideas in the context of industrial and organizational psychology and propose that 2 explicit traits work as channels for the expression of 3 core implicit motives in task and contextual job performance (extraversion for implicit affiliation and implicit power; explicit achievement for implicit achievement). As a test of these theoretical ideas, we report a study in which employees (N = 241) filled out a questionnaire booklet and worked on an improved modern implicit motive measure, the operant motive test. Their supervisors rated their task and contextual performance. Results support 4 of the 6 theoretical predictions and show that interactions between implicit motives and explicit traits increase the explained criterion variance in both task and contextual performance. (c) 2012 APA, all rights reserved.

  12. Utility assessment of a map-based online geo-collaboration tool.

    PubMed

    Sidlar, Christopher L; Rinner, Claus

    2009-05-01

    Spatial group decision-making processes often include both informal and analytical components. Discussions among stakeholders or planning experts are an example of an informal component. When participants discuss spatial planning projects they typically express concerns and comments by pointing to places on a map. The Argumentation Map model provides a conceptual basis for collaborative tools that enable explicit linkages of arguments to the places to which they refer. These tools allow for the input of explicitly geo-referenced arguments as well as the visual access to arguments through a map interface. In this paper, we will review previous utility studies in geo-collaboration and evaluate a case study of a Web-based Argumentation Map application. The case study was conducted in the summer of 2005 when student participants discussed planning issues on the University of Toronto St. George campus. During a one-week unmoderated discussion phase, 11 participants wrote 60 comments on issues such as safety, facilities, parking, and building aesthetics. By measuring the participants' use of geographic references, we draw conclusions on how well the software tool supported the potential of the underlying concept. This research aims to contribute to a scientific approach to geo-collaboration in which the engineering of novel spatial decision support methods is complemented by a critical assessment of their utility in controlled, realistic experiments.

  13. From wrinkling to global buckling of a ring on a curved substrate

    NASA Astrophysics Data System (ADS)

    Lagrange, R.; López Jiménez, F.; Terwagne, D.; Brojan, M.; Reis, P. M.

    2016-04-01

    We present a combined analytical approach and numerical study on the stability of a ring bound to an annular elastic substrate, which contains a circular cavity. The system is loaded by depressurizing the inner cavity. The ring is modeled as an Euler-Bernoulli beam and its equilibrium equations are derived from the mechanical energy which takes into account both stretching and bending contributions. The curvature of the substrate is considered explicitly to model the work done by its reaction force on the ring. We distinguish two different instabilities: periodic wrinkling of the ring or global buckling of the structure. Our model provides an expression for the critical pressure, as well as a phase diagram that rationalizes the transition between instability modes. Towards assessing the role of curvature, we compare our results for the critical stress and the wrinkling wavelength to their planar counterparts. We show that the critical stress is insensitive to the curvature of the substrate, while the wavelength is only affected due to the permissible discrete values of the azimuthal wavenumber imposed by the geometry of the problem. Throughout, we contrast our analytical predictions against finite element simulations.

  14. A highly accurate analytical solution for the surface fields of a short vertical wire antenna lying on a multilayer ground

    NASA Astrophysics Data System (ADS)

    Parise, M.

    2018-01-01

    A highly accurate analytical solution is derived to the electromagnetic problem of a short vertical wire antenna located on a stratified ground. The derivation consists of three steps. First, the integration path of the integrals describing the fields of the dipole is deformed and wrapped around the pole singularities and the two vertical branch cuts of the integrands located in the upper half of the complex plane. This allows to decompose the radiated field into its three contributions, namely the above-surface ground wave, the lateral wave, and the trapped surface waves. Next, the square root terms responsible for the branch cuts are extracted from the integrands of the branch-cut integrals. Finally, the extracted square roots are replaced with their rational representations according to Newton's square root algorithm, and residue theorem is applied to give explicit expressions, in series form, for the fields. The rigorous integration procedure and the convergence of square root algorithm ensure that the obtained formulas converge to the exact solution. Numerical simulations are performed to show the validity and robustness of the developed formulation, as well as its advantages in terms of time cost over standard numerical integration procedures.

  15. Torsion of a Cosserat elastic bar with square cross section: theory and experiment

    NASA Astrophysics Data System (ADS)

    Drugan, W. J.; Lakes, R. S.

    2018-04-01

    An approximate analytical solution for the displacement and microrotation vector fields is derived for pure torsion of a prismatic bar with square cross section comprised of homogeneous, isotropic linear Cosserat elastic material. This is accomplished by analytical simplification coupled with use of the principle of minimum potential energy together with polynomial representations for the desired field components. Explicit approximate expressions are derived for cross section warp and for applied torque versus angle of twist of the bar. These show that torsional rigidity exceeds the classical elasticity value, the difference being larger for slender bars, and that cross section warp is less than the classical amount. Experimental measurements on two sets of 3D printed square cross section polymeric bars, each set having a different microstructure and four different cross section sizes, revealed size effects not captured by classical elasticity but consistent with the present analysis for physically sensible values of the Cosserat moduli. The warp can allow inference of Cosserat elastic constants independently of any sensitivity the material may have to dilatation gradients; warp also facilitates inference of Cosserat constants that are difficult to obtain via size effects.

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

    Chae, Jongchul; Litvinenko, Yuri E.

    The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical resultsmore » suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.« less

  17. Retardation effects on the dispersion and propagation of plasmons in metallic nanoparticle chains

    NASA Astrophysics Data System (ADS)

    Downing, Charles A.; Mariani, Eros; Weick, Guillaume

    2018-01-01

    We consider a chain of regularly-spaced spherical metallic nanoparticles, where each particle supports three degenerate localized surface plasmons. Due to the dipolar interaction between the nanoparticles, the localized plasmons couple to form extended collective modes. Using an open quantum system approach in which the collective plasmons are interacting with vacuum electromagnetic modes and which, importantly, readily incorporates retardation via the light-matter coupling, we analytically evaluate the resulting radiative frequency shifts of the plasmonic bandstructure. For subwavelength-sized nanoparticles, our analytical treatment provides an excellent quantitative agreement with the results stemming from laborious numerical calculations based on fully-retarded solutions to Maxwell’s equations. Indeed, the explicit expressions for the plasmonic spectrum which we provide showcase how including retardation gives rise to a logarithmic singularity in the bandstructure of transverse-polarized plasmons. We further study the impact of retardation effects on the propagation of plasmonic excitations along the chain. While for the longitudinal modes, retardation has a negligible effect, we find that the retarded dipolar interaction can significantly modify the plasmon propagation in the case of transverse-polarized modes. Moreover, our results elucidate the analogy between radiative effects in nanoplasmonic systems and the cooperative Lamb shift in atomic physics.

  18. Understanding the Double Quantum Muonium RF Resonance

    NASA Astrophysics Data System (ADS)

    Kreitzman, S. R.; Cottrell, S. P.; Fleming, D. G.; Sun-Mack, S.

    A physically intuitive analytical solution to the Mu + RF Hamiltonian and lineshape is developed. The method is based on reformulating the problem in a basis set that explicitly accounts for the 1q RF transitions and identifying an isolated upper 1q quasi-eigenstate within that basis. Subsequently the double quantum resonance explicitly manifests itself via the non-zero interaction term between the pair of lower ortho-normalized 1q basis states, which in this field region are substantially the | \\uparrow \\uparrow > and | \\downarrow \\downarrow > Mu states.

  19. A Geographically Explicit Genetic Model of Worldwide Human-Settlement History

    PubMed Central

    Liu, Hua; Prugnolle, Franck; Manica, Andrea; Balloux, François

    2006-01-01

    Currently available genetic and archaeological evidence is generally interpreted as supportive of a recent single origin of modern humans in East Africa. However, this is where the near consensus on human settlement history ends, and considerable uncertainty clouds any more detailed aspect of human colonization history. Here, we present a dynamic genetic model of human settlement history coupled with explicit geographical distances from East Africa, the likely origin of modern humans. We search for the best-supported parameter space by fitting our analytical prediction to genetic data that are based on 52 human populations analyzed at 783 autosomal microsatellite markers. This framework allows us to jointly estimate the key parameters of the expansion of modern humans. Our best estimates suggest an initial expansion of modern humans ∼56,000 years ago from a small founding population of ∼1,000 effective individuals. Our model further points to high growth rates in newly colonized habitats. The general fit of the model with the data is excellent. This suggests that coupling analytical genetic models with explicit demography and geography provides a powerful tool for making inferences on human-settlement history. PMID:16826514

  20. Implicit motor learning promotes neural efficiency during laparoscopy.

    PubMed

    Zhu, Frank F; Poolton, Jamie M; Wilson, Mark R; Hu, Yong; Maxwell, Jon P; Masters, Rich S W

    2011-09-01

    An understanding of differences in expert and novice neural behavior can inform surgical skills training. Outside the surgical domain, electroencephalographic (EEG) coherence analyses have shown that during motor performance, experts display less coactivation between the verbal-analytic and motor planning regions than their less skilled counterparts. Reduced involvement of verbal-analytic processes suggests greater neural efficiency. The authors tested the utility of an implicit motor learning intervention specifically devised to promote neural efficiency by reducing verbal-analytic involvement in laparoscopic performance. In this study, 18 novices practiced a movement pattern on a laparoscopic trainer with either conscious awareness of the movement pattern (explicit motor learning) or suppressed awareness of the movement pattern (implicit motor learning). In a retention test, movement accuracy was compared between the conditions, and coactivation (EEG coherence) was assessed between the motor planning (Fz) region and both the verbal-analytic (T3) and the visuospatial (T4) cortical regions (T3-Fz and T4-Fz, respectively). Movement accuracy in the conditions was not different in a retention test (P = 0.231). Findings showed that the EEG coherence scores for the T3-Fz regions were lower for the implicit learners than for the explicit learners (P = 0.027), but no differences were apparent for the T4-Fz regions (P = 0.882). Implicit motor learning reduced EEG coactivation between verbal-analytic and motor planning regions, suggesting that verbal-analytic processes were less involved in laparoscopic performance. The findings imply that training techniques that discourage nonessential coactivation during motor performance may provide surgeons with more neural resources with which to manage other aspects of surgery.

  1. Attitudinal effects of degrading themes and sexual explicitness in video materials.

    PubMed

    Golde, J A; Strassberg, D S; Turner, C M; Lowe, K

    2000-07-01

    This study examined the independent and interactive effects of sexual explicitness and degrading themes toward women on mens' attitudes following exposure to video presentations of male-female interactions. Subjects were 83 male college students who viewed video vignettes under one of four stimulus conditions: (a) sexually explicit/degrading, (b) sexually explicit/nondegrading, (c) nonexplicit/degrading, and (d) nonexplicit/nondegrading. Results revealed that men exposed to degrading material, regardless of explicitness, were significantly more likely to express attitudes supportive of rape, while explicitness had no significant main or interactive effect on these attitudes. Further, the interaction of explicitness with degradation was found to impact scores on a measure of sexual callousness. Theoretical and clinical implications of these findings are discussed.

  2. (Implicitly) judging a book by its cover: the power of pride and shame expressions in shaping judgments of social status.

    PubMed

    Shariff, Azim F; Tracy, Jessica L; Markusoff, Jeffrey L

    2012-09-01

    How do we decide who merits social status? According to functionalist theories of emotion, the nonverbal expressions of pride and shame play a key role, functioning as automatically perceived status signals. In this view, observers automatically make status inferences about expressers on the basis of these expressions, even when contradictory contextual information about the expressers' status is available. In four studies, the authors tested whether implicit and explicit status perceptions are influenced by pride and shame expressions even when these expressions' status-related messages are contradicted by contextual information. Results indicate that emotion expressions powerfully influence implicit and explicit status inferences, at times neutralizing or even overriding situational knowledge. These findings demonstrate the irrepressible communicative power of emotion displays and indicate that status judgments can be informed as much (and often more) by automatic responses to nonverbal expressions of emotion as by rational, contextually bound knowledge.

  3. Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

    NASA Astrophysics Data System (ADS)

    Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

    2010-10-01

    Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

  4. Designing deep sequencing experiments: detecting structural variation and estimating transcript abundance.

    PubMed

    Bashir, Ali; Bansal, Vikas; Bafna, Vineet

    2010-06-18

    Massively parallel DNA sequencing technologies have enabled the sequencing of several individual human genomes. These technologies are also being used in novel ways for mRNA expression profiling, genome-wide discovery of transcription-factor binding sites, small RNA discovery, etc. The multitude of sequencing platforms, each with their unique characteristics, pose a number of design challenges, regarding the technology to be used and the depth of sequencing required for a particular sequencing application. Here we describe a number of analytical and empirical results to address design questions for two applications: detection of structural variations from paired-end sequencing and estimating mRNA transcript abundance. For structural variation, our results provide explicit trade-offs between the detection and resolution of rearrangement breakpoints, and the optimal mix of paired-read insert lengths. Specifically, we prove that optimal detection and resolution of breakpoints is achieved using a mix of exactly two insert library lengths. Furthermore, we derive explicit formulae to determine these insert length combinations, enabling a 15% improvement in breakpoint detection at the same experimental cost. On empirical short read data, these predictions show good concordance with Illumina 200 bp and 2 Kbp insert length libraries. For transcriptome sequencing, we determine the sequencing depth needed to detect rare transcripts from a small pilot study. With only 1 Million reads, we derive corrections that enable almost perfect prediction of the underlying expression probability distribution, and use this to predict the sequencing depth required to detect low expressed genes with greater than 95% probability. Together, our results form a generic framework for many design considerations related to high-throughput sequencing. We provide software tools http://bix.ucsd.edu/projects/NGS-DesignTools to derive platform independent guidelines for designing sequencing experiments (amount of sequencing, choice of insert length, mix of libraries) for novel applications of next generation sequencing.

  5. CORNAS: coverage-dependent RNA-Seq analysis of gene expression data without biological replicates.

    PubMed

    Low, Joel Z B; Khang, Tsung Fei; Tammi, Martti T

    2017-12-28

    In current statistical methods for calling differentially expressed genes in RNA-Seq experiments, the assumption is that an adjusted observed gene count represents an unknown true gene count. This adjustment usually consists of a normalization step to account for heterogeneous sample library sizes, and then the resulting normalized gene counts are used as input for parametric or non-parametric differential gene expression tests. A distribution of true gene counts, each with a different probability, can result in the same observed gene count. Importantly, sequencing coverage information is currently not explicitly incorporated into any of the statistical models used for RNA-Seq analysis. We developed a fast Bayesian method which uses the sequencing coverage information determined from the concentration of an RNA sample to estimate the posterior distribution of a true gene count. Our method has better or comparable performance compared to NOISeq and GFOLD, according to the results from simulations and experiments with real unreplicated data. We incorporated a previously unused sequencing coverage parameter into a procedure for differential gene expression analysis with RNA-Seq data. Our results suggest that our method can be used to overcome analytical bottlenecks in experiments with limited number of replicates and low sequencing coverage. The method is implemented in CORNAS (Coverage-dependent RNA-Seq), and is available at https://github.com/joel-lzb/CORNAS .

  6. An Eight-Eyed Version of Hawkins and Shohet's Clinical Supervision Model: The Addition of the Cognitive Analytic Therapy Concept of the "Observing Eye/I" as the "Observing Us"

    ERIC Educational Resources Information Center

    Darongkamas, Jurai; John, Christopher; Walker, Mark James

    2014-01-01

    This paper proposes incorporating the concept of the "observing eye/I", from cognitive analytic therapy (CAT), to Hawkins and Shohet's seven modes of supervision, comprising their transtheoretical model of supervision. Each mode is described alongside explicit examples relating to CAT. This modification using a key idea from CAT (in…

  7. What is the right formalism to search for resonances?

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

    Mikhasenko, M.; Pilloni, A.; Nys, J.

    Hmore » adron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. ereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B → ψ π K and B → D ¯ π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.« less

  8. What is the right formalism to search for resonances?

    DOE PAGES

    Mikhasenko, M.; Pilloni, A.; Nys, J.; ...

    2018-03-17

    Hmore » adron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. ereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B → ψ π K and B → D ¯ π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.« less

  9. On pseudo-hyperkähler prepotentials

    NASA Astrophysics Data System (ADS)

    Devchand, Chandrashekar; Spiro, Andrea

    2016-10-01

    An explicit surjection from a set of (locally defined) unconstrained holomorphic functions on a certain submanifold of Sp1(ℂ) × ℂ4n onto the set HKp,q of local isometry classes of real analytic pseudo-hyperkähler metrics of signature (4p, 4q) in dimension 4n is constructed. The holomorphic functions, called prepotentials, are analogues of Kähler potentials for Kähler metrics and provide a complete parameterisation of HKp,q. In particular, there exists a bijection between HKp,q and the set of equivalence classes of prepotentials. This affords the explicit construction of pseudo-hyperkähler metrics from specified prepotentials. The construction generalises one due to Galperin, Ivanov, Ogievetsky, and Sokatchev. Their work is given a coordinate-free formulation and complete, self-contained proofs are provided. The Appendix provides a vital tool for this construction: a reformulation of real analytic G-structures in terms of holomorphic frame fields on complex manifolds.

  10. The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomials coefficients using trees

    NASA Technical Reports Server (NTRS)

    Crouch, P. E.; Grossman, Robert

    1992-01-01

    This note is concerned with the explicit symbolic computation of expressions involving differential operators and their actions on functions. The derivation of specialized numerical algorithms, the explicit symbolic computation of integrals of motion, and the explicit computation of normal forms for nonlinear systems all require such computations. More precisely, if R = k(x(sub 1),...,x(sub N)), where k = R or C, F denotes a differential operator with coefficients from R, and g member of R, we describe data structures and algorithms for efficiently computing g. The basic idea is to impose a multiplicative structure on the vector space with basis the set of finite rooted trees and whose nodes are labeled with the coefficients of the differential operators. Cancellations of two trees with r + 1 nodes translates into cancellation of O(N(exp r)) expressions involving the coefficient functions and their derivatives.

  11. SYMBMAT: Symbolic computation of quantum transition matrix elements

    NASA Astrophysics Data System (ADS)

    Ciappina, M. F.; Kirchner, T.

    2012-08-01

    We have developed a set of Mathematica notebooks to compute symbolically quantum transition matrices relevant for atomic ionization processes. The utilization of a symbolic language allows us to obtain analytical expressions for the transition matrix elements required in charged-particle and laser induced ionization of atoms. Additionally, by using a few simple commands, it is possible to export these symbolic expressions to standard programming languages, such as Fortran or C, for the subsequent computation of differential cross sections or other observables. One of the main drawbacks in the calculation of transition matrices is the tedious algebraic work required when initial states other than the simple hydrogenic 1s state need to be considered. Using these notebooks the work is dramatically reduced and it is possible to generate exact expressions for a large set of bound states. We present explicit examples of atomic collisions (in First Born Approximation and Distorted Wave Theory) and laser-matter interactions (within the Dipole and Strong Field Approximations and different gauges) using both hydrogenic wavefunctions and Slater-Type Orbitals with arbitrary nlm quantum numbers as initial states. Catalogue identifier: AEMI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 71 628 No. of bytes in distributed program, including test data, etc.: 444 195 Distribution format: tar.gz Programming language: Mathematica Computer: Single machines using Linux or Windows (with cores with any clock speed, cache memory and bits in a word) Operating system: Any OS that supports Mathematica. The notebooks have been tested under Windows and Linux and with versions 6.x, 7.x and 8.x Classification: 2.6 Nature of problem: The notebooks generate analytical expressions for quantum transition matrix elements required in diverse atomic processes: ionization by ion, electron, or photon impact and ionization within the framework of strong field physics. In charged-particle collisions approaches based on perturbation theory enjoy widespread utilization. Accordingly, we have chosen the First Born Approximation and Distorted Wave theories as examples. In light-matter interactions, the main ingredient for many types of calculations is the dipole transition matrix in its different formulations, i.e. length, velocity, and acceleration gauges. In all these cases the transitions of interest occur between a bound state and a continuum state which can be described in different ways. With the notebooks developed in the present work it is possible to calculate transition matrix elements analytically for any set of quantum numbers nlm of initial hydrogenic states or Slater-Type Orbitals and for plane waves or Coulomb waves as final continuum states. Solution method: The notebooks employ symbolic computation to generate analytical expressions for transition matrix elements used in both collision and light-matter interaction physics. fba_hyd.nb - This notebook computes analytical expressions for the transition matrix of collision-induced ionization in the First Born Approximation (FBA). The transitions considered are from a bound hydrogenic state with arbitrary quantum numbers nlm to a continuum state represented by a plane wave (PW) or a Coulomb wave (CW). distorted_hyd.nb - This notebook computes analytical expressions for the transition matrix of collision-induced ionization in Distorted Wave (DW) theories. The transitions considered are from a (distorted) bound hydrogenic state with arbitrary quantum numbers nlm to a distorted-wave continuum state. The computations are based on scalar and vectorial integrals (see the text for details). dipoleLength_hyd.nb - This notebook computes analytical expressions for the dipole transition matrix in length gauge. The transitions considered are from a bound hydrogenic state with arbitrary quantum numbers nlm to a continuum state represented by a PW (the Strong Field Approximation (SFA)) or a CW (the Coulomb-Volkov Approximation (CVA)). dipoleVelocity_hyd.nb - This notebook computes analytical expressions for the dipole transition matrix in velocity gauge. The transitions considered are from a bound hydrogenic state with arbitrary quantum numbers nlm to a continuum state represented by a PW (the SFA) or a CW (the CVA). dipoleAcceleration_hyd.nb - This notebook computes analytical expressions for the dipole transition matrix in acceleration gauge. The transitions considered are from a bound hydrogenic state with arbitrary quantum numbers nlm to a continuum state represented by a PW (the SFA). For the case of the CVA we only include the transition from the 1s state to a continuum state represented by a CW. fba_STO.nb - This notebook computes analytical expressions for the transition matrix of collision-induced ionization in the FBA. The transitions considered are from a Slater-Type Orbital (STO) with arbitrary quantum numbers nlm to a continuum state represented by a PW or a CW. distorted_STO.nb - This notebook computes analytical expressions for the transition matrix of collision-induced ionization in DW theories. The transitions considered are from a (distorted) STO with arbitrary quantum numbers nlm to a distorted-wave continuum state. The computations are based on scalar and vectorial integrals (see the text for details). dipoleLength_STO.nb - This notebook computes analytical expressions for the dipole transition matrix in length gauge. The transitions considered are from an STO with arbitrary quantum numbers nlm to a continuum state represented by a PW (the SFA) or a CW (the CVA). dipoleVelocity_STO.nb - This notebook computes analytical expressions for the dipole transition matrix in velocity gauge. The transitions considered are from an STO with arbitrary quantum numbers nlm to a continuum state represented by a PW (the SFA) or a CW (the CVA). dipoleAcceleration_STO.nb - This notebook computes analytical expressions for the dipole transition matrix in acceleration gauge. The transitions considered are from an STO with arbitrary quantum numbers nlm to a continuum state represented by a PW (the SFA). The symbolic expressions obtained within each notebook can be exported to standard programming languages such as Fortran or C using the Format.m package (see the text and Ref. Sofroniou (1993) [16] for details). Running time: Computational times vary according to the transition matrix selected and quantum numbers nlm of the initial state used. The typical running time is several minutes, but it will take longer for large values of nlm.

  12. Recursive thoughts on the simulation of the flexible multibody dynamics of slender offshore structures

    NASA Astrophysics Data System (ADS)

    Schilder, J.; Ellenbroek, M.; de Boer, A.

    2017-12-01

    In this work, the floating frame of reference formulation is used to create a flexible multibody model of slender offshore structures such as pipelines and risers. It is shown that due to the chain-like topology of the considered structures, the equation of motion can be expressed in terms of absolute interface coordinates. In the presented form, kinematic constraint equations are satisfied explicitly and the Lagrange multipliers are eliminated from the equations. Hence, the structures can be conveniently coupled to finite element or multibody models of for example seabed and vessel. The chain-like topology enables the efficient use of recursive solution procedures for both transient dynamic analysis and equilibrium analysis. For this, the transfer matrix method is used. In order to improve the convergence of the equilibrium analysis, the analytical solution of an ideal catenary is used as an initial configuration, reducing the number of required iterations.

  13. High-order rogue waves of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Liu, Wei

    2017-10-01

    High-order rogue wave solutions of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin-Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

  14. Vortex breakdown incipience: Theoretical considerations

    NASA Technical Reports Server (NTRS)

    Berger, Stanley A.; Erlebacher, Gordon

    1992-01-01

    The sensitivity of the onset and the location of vortex breakdowns in concentrated vortex cores, and the pronounced tendency of the breakdowns to migrate upstream have been characteristic observations of experimental investigations; they have also been features of numerical simulations and led to questions about the validity of these simulations. This behavior seems to be inconsistent with the strong time-like axial evolution of the flow, as expressed explicitly, for example, by the quasi-cylindrical approximate equations for this flow. An order-of-magnitude analysis of the equations of motion near breakdown leads to a modified set of governing equations, analysis of which demonstrates that the interplay between radial inertial, pressure, and viscous forces gives an elliptic character to these concentrated swirling flows. Analytical, asymptotic, and numerical solutions of a simplified non-linear equation are presented; these qualitatively exhibit the features of vortex onset and location noted above.

  15. Fast and accurate Voronoi density gridding from Lagrangian hydrodynamics data

    NASA Astrophysics Data System (ADS)

    Petkova, Maya A.; Laibe, Guillaume; Bonnell, Ian A.

    2018-01-01

    Voronoi grids have been successfully used to represent density structures of gas in astronomical hydrodynamics simulations. While some codes are explicitly built around using a Voronoi grid, others, such as Smoothed Particle Hydrodynamics (SPH), use particle-based representations and can benefit from constructing a Voronoi grid for post-processing their output. So far, calculating the density of each Voronoi cell from SPH data has been done numerically, which is both slow and potentially inaccurate. This paper proposes an alternative analytic method, which is fast and accurate. We derive an expression for the integral of a cubic spline kernel over the volume of a Voronoi cell and link it to the density of the cell. Mass conservation is ensured rigorously by the procedure. The method can be applied more broadly to integrate a spherically symmetric polynomial function over the volume of a random polyhedron.

  16. Power Spectrum of a Noisy System Close to a Heteroclinic Orbit

    NASA Astrophysics Data System (ADS)

    Giner-Baldó, Jordi; Thomas, Peter J.; Lindner, Benjamin

    2017-07-01

    We consider a two-dimensional dynamical system that possesses a heteroclinic orbit connecting four saddle points. This system is not able to show self-sustained oscillations on its own. If endowed with white Gaussian noise it displays stochastic oscillations, the frequency and quality factor of which are controlled by the noise intensity. This stochastic oscillation of a nonlinear system with noise is conveniently characterized by the power spectrum of suitable observables. In this paper we explore different analytical and semianalytical ways to compute such power spectra. Besides a number of explicit expressions for the power spectrum, we find scaling relations for the frequency, spectral width, and quality factor of the stochastic heteroclinic oscillator in the limit of weak noise. In particular, the quality factor shows a slow logarithmic increase with decreasing noise of the form Q˜ [ln (1/D)]^2. Our results are compared to numerical simulations of the respective Langevin equations.

  17. Experimental study of adaptive pointing and tracking for large flexible space structures

    NASA Technical Reports Server (NTRS)

    Boussalis, D.; Bayard, D. S.; Ih, C.; Wang, S. J.; Ahmed, A.

    1991-01-01

    This paper describes an experimental study of adaptive pointing and tracking control for flexible spacecraft conducted on a complex ground experiment facility. The algorithm used in this study is based on a multivariable direct model reference adaptive control law. Several experimental validation studies were performed earlier using this algorithm for vibration damping and robust regulation, with excellent results. The current work extends previous studies by addressing the pointing and tracking problem. As is consistent with an adaptive control framework, the plant is assumed to be poorly known to the extent that only system level knowledge of its dynamics is available. Explicit bounds on the steady-state pointing error are derived as functions of the adaptive controller design parameters. It is shown that good tracking performance can be achieved in an experimental setting by adjusting adaptive controller design weightings according to the guidelines indicated by the analytical expressions for the error.

  18. Diffusing diffusivity: Rotational diffusion in two and three dimensions

    NASA Astrophysics Data System (ADS)

    Jain, Rohit; Sebastian, K. L.

    2017-06-01

    We consider the problem of calculating the probability distribution function (pdf) of angular displacement for rotational diffusion in a crowded, rearranging medium. We use the diffusing diffusivity model and following our previous work on translational diffusion [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016)], we show that the problem can be reduced to that of calculating the survival probability of a particle undergoing Brownian motion, in the presence of a sink. We use the approach to calculate the pdf for the rotational motion in two and three dimensions. We also propose new dimensionless, time dependent parameters, αr o t ,2 D and αr o t ,3 D, which can be used to analyze the experimental/simulation data to find the extent of deviation from the normal behavior, i.e., constant diffusivity, and obtain explicit analytical expressions for them, within our model.

  19. Micromechanics analysis of space simulated thermal deformations and stresses in continuous fiber reinforced composites

    NASA Technical Reports Server (NTRS)

    Bowles, David E.

    1990-01-01

    Space simulated thermally induced deformations and stresses in continuous fiber reinforced composites were investigated with a micromechanics analysis. The investigation focused on two primary areas. First, available explicit expressions for predicting the effective coefficients of thermal expansion (CTEs) for a composite were compared with each other, and with a finite element (FE) analysis, developed specifically for this study. Analytical comparisons were made for a wide range of fiber/matrix systems, and predicted values were compared with experimental data. The second area of investigation focused on the determination of thermally induced stress fields in the individual constituents. Stresses predicted from the FE analysis were compared to those predicted from a closed-form solution to the composite cylinder (CC) model, for two carbon fiber/epoxy composites. A global-local formulation, combining laminated plate theory and FE analysis, was used to determine the stresses in multidirectional laminates. Thermally induced damage initiation predictions were also made.

  20. A rigorous approach to the formulation of extended Born-Oppenheimer equation for a three-state system

    NASA Astrophysics Data System (ADS)

    Sarkar, Biplab; Adhikari, Satrajit

    If a coupled three-state electronic manifold forms a sub-Hilbert space, it is possible to express the non-adiabatic coupling (NAC) elements in terms of adiabatic-diabatic transformation (ADT) angles. Consequently, we demonstrate: (a) Those explicit forms of the NAC terms satisfy the Curl conditions with non-zero Divergences; (b) The formulation of extended Born-Oppenheimer (EBO) equation for any three-state BO system is possible only when there exists coordinate independent ratio of the gradients for each pair of ADT angles leading to zero Curls at and around the conical intersection(s). With these analytic advancements, we formulate a rigorous EBO equation and explore its validity as well as necessity with respect to the approximate one (Sarkar and Adhikari, J Chem Phys 2006, 124, 074101) by performing numerical calculations on two different models constructed with different chosen forms of the NAC elements.

  1. On the variability of the Charnock constant and the functional dependence of the drag coefficient on wind speed: Part II-Observations

    NASA Astrophysics Data System (ADS)

    Bye, John A. T.; Wolff, Jörg-Olaf; Lettmann, Karsten A.

    2014-07-01

    An analytical expression for the 10 m drag law in terms of the 10 m wind speed at the maximum in the 10 m drag coefficient, and the Charnock constant is presented, which is based on the results obtained from a model of the air-sea interface derived in Bye et al. (2010). This drag law is almost independent of wave age and over the mid-range of wind speeds (5-17 ms-1) is very similar to the drag law based on observed data presented in Foreman and Emeis (2010). The linear fit of the observed data which incorporates a constant into the traditional definition of the drag coefficient is shown to arise to first-order as a consequence of the momentum exchange across the air-sea boundary layer brought about by wave generation and spray production which are explicitly represented in the theoretical model.

  2. Generalized cable equation model for myelinated nerve fiber.

    PubMed

    Einziger, Pinchas D; Livshitz, Leonid M; Mizrahi, Joseph

    2005-10-01

    Herein, the well-known cable equation for nonmyelinated axon model is extended analytically for myelinated axon formulation. The myelinated membrane conductivity is represented via the Fourier series expansion. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficients, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the entire periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent nonmyelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the myelinated axon model. Hill's equation is explicitly integrated for the specific choice of piecewise constant membrane conductivity profile, thereby resulting in an explicit closed form expression for the transmembrane potential in terms of trigonometric functions. The Floquet's modes are recognized as the nerve fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model, provided that the periodic membrane point-wise passivity constraint is properly modified. Indeed, the modified condition, enforcing the periodic membrane passivity constraint on the average conductivity only leads, for the first time, to the inclusion of the nerve fiber activation modes in our novel model. The validity of the generalized transmission-line and cable equation models for a myelinated nerve fiber, is verified herein through a rigorous Green's function formulation and numerical simulations for transmembrane potential induced in three-dimensional myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.

  3. Computing the Sensitivity Kernels for 2.5-D Seismic Waveform Inversion in Heterogeneous, Anisotropic Media

    NASA Astrophysics Data System (ADS)

    Zhou, Bing; Greenhalgh, S. A.

    2011-10-01

    2.5-D modeling and inversion techniques are much closer to reality than the simple and traditional 2-D seismic wave modeling and inversion. The sensitivity kernels required in full waveform seismic tomographic inversion are the Fréchet derivatives of the displacement vector with respect to the independent anisotropic model parameters of the subsurface. They give the sensitivity of the seismograms to changes in the model parameters. This paper applies two methods, called `the perturbation method' and `the matrix method', to derive the sensitivity kernels for 2.5-D seismic waveform inversion. We show that the two methods yield the same explicit expressions for the Fréchet derivatives using a constant-block model parameterization, and are available for both the line-source (2-D) and the point-source (2.5-D) cases. The method involves two Green's function vectors and their gradients, as well as the derivatives of the elastic modulus tensor with respect to the independent model parameters. The two Green's function vectors are the responses of the displacement vector to the two directed unit vectors located at the source and geophone positions, respectively; they can be generally obtained by numerical methods. The gradients of the Green's function vectors may be approximated in the same manner as the differential computations in the forward modeling. The derivatives of the elastic modulus tensor with respect to the independent model parameters can be obtained analytically, dependent on the class of medium anisotropy. Explicit expressions are given for two special cases—isotropic and tilted transversely isotropic (TTI) media. Numerical examples are given for the latter case, which involves five independent elastic moduli (or Thomsen parameters) plus one angle defining the symmetry axis.

  4. Cross-cultural evidence that the nonverbal expression of pride is an automatic status signal.

    PubMed

    Tracy, Jessica L; Shariff, Azim F; Zhao, Wanying; Henrich, Joseph

    2013-02-01

    To test whether the pride expression is an implicit, reliably developing signal of high social status in humans, the authors conducted a series of experiments that measured implicit and explicit cognitive associations between pride displays and high-status concepts in two culturally disparate populations--North American undergraduates and Fijian villagers living in a traditional, small-scale society. In both groups, pride displays produced strong implicit associations with high status, despite Fijian social norms discouraging overt displays of pride. Also in both groups, implicit and explicit associations between emotion expressions and status were dissociated; despite the cross-cultural implicit association between pride displays and high status, happy displays were, cross-culturally, the more powerful status indicator at an explicit level, and among Fijians, happy and pride displays were equally strongly implicitly associated with status. Finally, a cultural difference emerged: Fijians viewed happy displays as more deserving of high status than did North Americans, both implicitly and explicitly. Together, these findings suggest that the display and recognition of pride may be part of a suite of adaptations for negotiating status relationships, but that the high-status message of pride is largely communicated through implicit cognitive processes. 2013 APA, all rights reserved

  5. An Analytical Dynamics Approach to the Control of Mechanical Systems

    NASA Astrophysics Data System (ADS)

    Mylapilli, Harshavardhan

    A new and novel approach to the control of nonlinear mechanical systems is presented in this study. The approach is inspired by recent results in analytical dynamics that deal with the theory of constrained motion. The control requirements on the dynamical system are viewed from an analytical dynamics perspective and the theory of constrained motion is used to recast these control requirements as constraints on the dynamical system. Explicit closed form expressions for the generalized nonlinear control forces are obtained by using the fundamental equation of mechanics. The control so obtained is optimal at each instant of time and causes the constraints to be exactly satisfied. No linearizations and/or approximations of the nonlinear dynamical system are made, and no a priori structure is imposed on the nature of nonlinear controller. Three examples dealing with highly nonlinear complex dynamical systems that are chosen from diverse areas of discrete and continuum mechanics are presented to demonstrate the control approach. The first example deals with the energy control of underactuated inhomogeneous nonlinear lattices (or chains), the second example deals with the synchronization of the motion of multiple coupled slave gyros with that of a master gyro, and the final example deals with the control of incompressible hyperelastic rubber-like thin cantilever beams. Numerical simulations accompanying these examples show the ease, simplicity and the efficacy with which the control methodology can be applied and the accuracy with which the desired control objectives can be met.

  6. A fast method to compute Three-Dimensional Infrared Radiative Transfer in non scattering medium

    NASA Astrophysics Data System (ADS)

    Makke, Laurent; Musson-Genon, Luc; Carissimo, Bertrand

    2014-05-01

    The Atmospheric Radiation field has seen the development of more accurate and faster methods to take into account absoprtion in participating media. Radiative fog appears with clear sky condition due to a significant cooling during the night, so scattering is left out. Fog formation modelling requires accurate enough method to compute cooling rates. Thanks to High Performance Computing, multi-spectral approach of Radiative Transfer Equation resolution is most often used. Nevertheless, the coupling of three-dimensionnal radiative transfer with fluid dynamics is very detrimental to the computational cost. To reduce the time spent in radiation calculations, the following method uses analytical absorption functions fitted by Sasamori (1968) on Yamamoto's charts (Yamamoto,1956) to compute a local linear absorption coefficient. By averaging radiative properties, this method eliminates the spectral integration. For an isothermal atmosphere, analytical calculations lead to an explicit formula between emissivities functions and linear absorption coefficient. In the case of cooling to space approximation, this analytical expression gives very accurate results compared to correlated k-distribution. For non homogeneous paths, we propose a two steps algorithm. One-dimensional radiative quantities and linear absorption coefficient are computed by a two-flux method. Then, three-dimensional RTE under the grey medium assumption is solved with the DOM. Comparisons with measurements of radiative quantities during ParisFOG field (2006) shows the cability of this method to handle strong vertical variations of pressure/temperature and gases concentrations.

  7. An explicit closed-form analytical solution for European options under the CGMY model

    NASA Astrophysics Data System (ADS)

    Chen, Wenting; Du, Meiyu; Xu, Xiang

    2017-01-01

    In this paper, we consider the analytical pricing of European path-independent options under the CGMY model, which is a particular type of pure jump Le´vy process, and agrees well with many observed properties of the real market data by allowing the diffusions and jumps to have both finite and infinite activity and variation. It is shown that, under this model, the option price is governed by a fractional partial differential equation (FPDE) with both the left-side and right-side spatial-fractional derivatives. In comparison to derivatives of integer order, fractional derivatives at a point not only involve properties of the function at that particular point, but also the information of the function in a certain subset of the entire domain of definition. This ;globalness; of the fractional derivatives has added an additional degree of difficulty when either analytical methods or numerical solutions are attempted. Albeit difficult, we still have managed to derive an explicit closed-form analytical solution for European options under the CGMY model. Based on our solution, the asymptotic behaviors of the option price and the put-call parity under the CGMY model are further discussed. Practically, a reliable numerical evaluation technique for the current formula is proposed. With the numerical results, some analyses of impacts of four key parameters of the CGMY model on European option prices are also provided.

  8. Parametrizations of three-body hadronic B - and D -decay amplitudes in terms of analytic and unitary meson-meson form factors

    NASA Astrophysics Data System (ADS)

    Boito, D.; Dedonder, J.-P.; El-Bennich, B.; Escribano, R.; Kamiński, R.; Leśniak, L.; Loiseau, B.

    2017-12-01

    We introduce parametrizations of hadronic three-body B and D weak decay amplitudes that can be readily implemented in experimental analyses and are a sound alternative to the simplistic and widely used sum of Breit-Wigner type amplitudes, also known as the isobar model. These parametrizations can be particularly useful in the interpretation of C P asymmetries in the Dalitz plots. They are derived from previous calculations based on a quasi-two-body factorization approach in which two-body hadronic final-state interactions are fully taken into account in terms of unitary S - and P -wave π π , π K , and K K ¯ form factors. These form factors can be determined rigorously, fulfilling fundamental properties of quantum field-theory amplitudes such as analyticity and unitarity, and are in agreement with the low-energy behavior predicted by effective theories of QCD. They are derived from sets of coupled-channel equations using T -matrix elements constrained by experimental meson-meson phase shifts and inelasticities, chiral symmetry, and asymptotic QCD. We provide explicit amplitude expressions for the decays B±→π+π-π±, B →K π+π-, B±→K+K-K±, D+→π-π+π+, D+→K-π+π+, and D0→KS0π+π-, for which we have shown in previous studies that this approach is phenomenologically successful; in addition, we provide expressions for the D0→KS0K+K- decay. Other three-body hadronic channels can be parametrized likewise.

  9. A Fractal Permeability Model for Shale Oil Reservoir

    NASA Astrophysics Data System (ADS)

    Zhang, Tao; Dong, Mingzhe; Li, Yajun

    2018-01-01

    In this work, a fractal analytical model is proposed to predict the permeability of shale reservoir. The proposed model explicitly relates the permeability to the micro-structural parameters (tortuosity, pore area fractal dimensions, porosity and slip velocity coefficient) of shale.

  10. Predicted range expansion of Chinese tallow tree (Triadica sebifera) in forestlands of the southern United States

    Treesearch

    Hsiao-Hsuan Wang; William Grant; Todd Swannack; Jianbang Gan; William Rogers; Tomasz Koralewski; James Miller; John W. Taylor Jr.

    2011-01-01

    We present an integrated approach for predicting future range expansion of an invasive species (Chinese tallow tree) that incorporates statistical forecasting and analytical techniques within a spatially explicit, agent-based, simulation framework.

  11. Quantitative Analysis of Fullerene Nanomaterials in Environmental Systems: A Critical Review

    PubMed Central

    Isaacson, Carl W.; Kleber, Markus; Field, Jennifer A.

    2009-01-01

    The increasing production and use of fullerene nanomaterials has led to calls for more information regarding the potential impacts that releases of these materials may have on human and environmental health. Fullerene nanomaterials, which are comprised of both fullerenes and surface-functionalized fullerenes, are used in electronic, optic, medical and cosmetic applications. Measuring fullerene nanomaterial concentrations in natural environments is difficult because they exhibit a duality of physical and chemical characteristics as they transition from hydrophobic to polar forms upon exposure to water. In aqueous environments, this is expressed as their tendency to initially (i) self assemble into aggregates of appreciable size and hydrophobicity, and subsequently (ii) interact with the surrounding water molecules and other chemical constituents in natural environments thereby acquiring negative surface charge. Fullerene nanomaterials may therefore deceive the application of any single analytical method that is applied with the assumption that fullerenes have but one defining characteristic (e.g., hydrophobicity). [1] We find that analytical procedures are needed to account for the potentially transitory nature of fullerenes in natural environments through the use of approaches that provide chemically-explicit information including molecular weight and the number and identity of surface functional groups. [2] We suggest that sensitive and mass-selective detection, such as that offered by mass spectrometry when combined with optimized extraction procedures, offers the greatest potential to achieve this goal. [3] With this review, we show that significant improvements in analytical rigor would result from an increased availability of well characterized authentic standards, reference materials, and isotopically-labeled internal standards. Finally, the benefits of quantitative and validated analytical methods for advancing the knowledge on fullerene occurrence, fate, and behavior are indicated. PMID:19764203

  12. SOCIO-ETHICAL ISSUES IN PERSONALIZED MEDICINE: A SYSTEMATIC REVIEW OF ENGLISH LANGUAGE HEALTH TECHNOLOGY ASSESSMENTS OF GENE EXPRESSION PROFILING TESTS FOR BREAST CANCER PROGNOSIS.

    PubMed

    Ali-Khan, Sarah E; Black, Lee; Palmour, Nicole; Hallett, Michael T; Avard, Denise

    2015-01-01

    There have been multiple calls for explicit integration of ethical, legal, and social issues (ELSI) in health technology assessment (HTA) and addressing ELSI has been highlighted as key in optimizing benefits in the Omics/Personalized Medicine field. This study examines HTAs of an early clinical example of Personalized Medicine (gene expression profile tests [GEP] for breast cancer prognosis) aiming to: (i) identify ELSI; (ii) assess whether ELSIs are implicitly or explicitly addressed; and (iii) report methodology used for ELSI integration. A systematic search for HTAs (January 2004 to September 2012), followed by descriptive and qualitative content analysis. Seventeen HTAs for GEP were retrieved. Only three (18%) explicitly presented ELSI, and only one reported methodology. However, all of the HTAs included implicit ELSI. Eight themes of implicit and explicit ELSI were identified. "Classical" ELSI including privacy, informed consent, and concerns about limited patient/clinician genetic literacy were always presented explicitly. Some ELSI, including the need to understand how individual patients' risk tolerances affect clinical decision-making after reception of GEP results, were presented both explicitly and implicitly in HTAs. Others, such as concern about evidentiary deficiencies for clinical utility of GEP tests, occurred only implicitly. Despite a wide variety of important ELSI raised, these were rarely explicitly addressed in HTAs. Explicit treatment would increase their accessibility to decision-makers, and may augment HTA efficiency maximizing their utility. This is particularly important where complex Personalized Medicine applications are rapidly expanding choices for patients, clinicians and healthcare systems.

  13. The Soil Foam Drainage Equation - an alternative model for unsaturated flow in porous media

    NASA Astrophysics Data System (ADS)

    Assouline, Shmuel; Lehmann, Peter; Hoogland, Frouke; Or, Dani

    2017-04-01

    The analogy between the geometry and dynamics of wet foam drainage and gravity drainage of unsaturated porous media expands modeling capabilities for capillary flows and supplements the standard Richards equation representation. The governing equation for draining foam (or a soil variant termed the soil foam drainage equation - SFDE) obviates the need for macroscopic unsaturated hydraulic conductivity function by an explicit account of diminishing flow pathway sizes as the medium gradually drains. Potential advantages of the proposed drainage foam formalism include direct description of transient flow without requiring constitutive functions; evolution of capillary cross sections that provides consistent description of self-regulating internal fluxes (e.g., towards field capacity); and a more intuitive geometrical picture of capillary flow across textural boundaries. We will present new and simple analytical expressions for drainage rates and volumes from unsaturated porous media subjected to different boundary conditions that are in good agreement with the numerical solution of the SFDE and experimental results. The foam drainage methodology expands the range of tools available for describing and quantifying unsaturated flows and provides geometrically tractable links between evolution of liquid configuration and flow dynamics in unsaturated porous media. The resulting geometrical representation of capillary drainage could improve understanding of colloid and pathogen transport. The explicit geometrical interpretation of flow pathways underlying the hydraulic functions used by the Richards equation offers new insights that benefit both approaches.

  14. Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

    NASA Astrophysics Data System (ADS)

    Jost, Jürgen; Keßler, Enno; Tolksdorf, Jürgen; Wu, Ruijun; Zhu, Miaomiao

    2018-02-01

    We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler-Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivière's regularity theory and Riesz potential theory.

  15. Measures and metrics for software development

    NASA Technical Reports Server (NTRS)

    1984-01-01

    The evaluations of and recommendations for the use of software development measures based on the practical and analytical experience of the Software Engineering Laboratory are discussed. The basic concepts of measurement and system of classification for measures are described. The principal classes of measures defined are explicit, analytic, and subjective. Some of the major software measurement schemes appearing in the literature are derived. The applications of specific measures in a production environment are explained. These applications include prediction and planning, review and assessment, and evaluation and selection.

  16. Revisiting the debate on the relationship between display rules and performance: considering the explicitness of display rules.

    PubMed

    Christoforou, Paraskevi S; Ashforth, Blake E

    2015-01-01

    We argue that the strength with which the organization communicates expectations regarding the appropriate emotional expression toward customers (i.e., explicitness of display rules) has an inverted U-shaped relationship with service delivery behaviors, customer satisfaction, and sales performance. Further, we argue that service organizations need a particular blend of explicitness of display rules and role discretion for the purpose of optimizing sales performance. As hypothesized, findings from 2 samples of salespeople suggest that either high or low explicitness of display rules impedes service delivery behaviors and sales performance, which peaks at moderate explicitness of display rules and high role discretion. The findings also suggest that the explicitness of display rules has a positive relationship with customer satisfaction. (c) 2015 APA, all rights reserved.

  17. Fluctuation theorem for the effusion of an ideal gas.

    PubMed

    Cleuren, B; Van den Broeck, C; Kawai, R

    2006-08-01

    The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.

  18. Analytic derivation of bacterial growth laws from a simple model of intracellular chemical dynamics.

    PubMed

    Pandey, Parth Pratim; Jain, Sanjay

    2016-09-01

    Experiments have found that the growth rate and certain other macroscopic properties of bacterial cells in steady-state cultures depend upon the medium in a surprisingly simple manner; these dependencies are referred to as 'growth laws'. Here we construct a dynamical model of interacting intracellular populations to understand some of the growth laws. The model has only three population variables: an amino acid pool, a pool of enzymes that transport an external nutrient and produce the amino acids, and ribosomes that catalyze their own and the enzymes' production from the amino acids. We assume that the cell allocates its resources between the enzyme sector and the ribosomal sector to maximize its growth rate. We show that the empirical growth laws follow from this assumption and derive analytic expressions for the phenomenological parameters in terms of the more basic model parameters. Interestingly, the maximization of the growth rate of the cell as a whole implies that the cell allocates resources to the enzyme and ribosomal sectors in inverse proportion to their respective 'efficiencies'. The work introduces a mathematical scheme in which the cellular growth rate can be explicitly determined and shows that two large parameters, the number of amino acid residues per enzyme and per ribosome, are useful for making approximations.

  19. Capture zones for simple aquifers

    USGS Publications Warehouse

    McElwee, Carl D.

    1991-01-01

    Capture zones showing the area influenced by a well within a certain time are useful for both aquifer protection and cleanup. If hydrodynamic dispersion is neglected, a deterministic curve defines the capture zone. Analytical expressions for the capture zones can be derived for simple aquifers. However, the capture zone equations are transcendental and cannot be explicitly solved for the coordinates of the capture zone boundary. Fortunately, an iterative scheme allows the solution to proceed quickly and efficiently even on a modest personal computer. Three forms of the analytical solution must be used in an iterative scheme to cover the entire region of interest, after the extreme values of the x coordinate are determined by an iterative solution. The resulting solution is a discrete one, and usually 100-1000 intervals along the x-axis are necessary for a smooth definition of the capture zone. The presented program is written in FORTRAN and has been used in a variety of computing environments. No graphics capability is included with the program; it is assumed the user has access to a commercial package. The superposition of capture zones for multiple wells is expected to be satisfactory if the spacing is not too close. Because this program deals with simple aquifers, the results rarely will be the final word in a real application.

  20. On the renormalisation of the diffusion asymptotics in the problem of reflection of a narrow optical beam from a biological medium

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

    Appanov, A Yu; Barabanenkov, Yu N

    2005-12-31

    An analytic hybrid method is considered for solving the stationary radiation transfer equation in the problem on reflection of a narrow laser beam from biological media such as the 2% aqueous solution of intralipid and erythrocyte suspension with the volume concentration (hematocrit) H=0.41. The method is based on the reciprocity of the Green function in the radiation transfer theory and on the iteration solution of the integral equation for this function. As a result, the ray intensity is represented as a sum of two terms. The first of them describes the contribution of finite-order scattering to the intensity of amore » beam diffusely reflected from the medium. The second term contains the explicit analytic expression for a spatially distributed effective source of diffuse radiation emerging from the deep layers of the medium to the surface. This approach substantially improves the diffusion approximation for the problem under study and allows one to obtain the uniform asymptotics of the reflection coefficient at the specified interval of distances between the radiation source and detector on the medium surface with the relative error within {+-}6% for the 2% intralipid emulsion and erythrocyte suspension (H=0.41). (radiation scattering)« less

  1. Analytical Solutions for an Escape Problem in a Disc with an Arbitrary Distribution of Exit Holes Along Its Boundary

    NASA Astrophysics Data System (ADS)

    Marshall, J. S.

    2016-12-01

    We analytically construct solutions for the mean first-passage time and splitting probabilities for the escape problem of a particle moving with continuous Brownian motion in a confining planar disc with an arbitrary distribution (i.e., of any number, size and spacing) of exit holes/absorbing sections along its boundary. The governing equations for these quantities are Poisson's equation with a (non-zero) constant forcing term and Laplace's equation, respectively, and both are subject to a mixture of homogeneous Neumann and Dirichlet boundary conditions. Our solutions are expressed as explicit closed formulae written in terms of a parameterising variable via a conformal map, using special transcendental functions that are defined in terms of an associated Schottky group. They are derived by exploiting recent results for a related problem of fluid mechanics that describes a unidirectional flow over "no-slip/no-shear" surfaces, as well as results from potential theory, all of which were themselves derived using the same theory of Schottky groups. They are exact up to the determination of a finite set of mapping parameters, which is performed numerically. Their evaluation also requires the numerical inversion of the parameterising conformal map. Computations for a series of illustrative examples are also presented.

  2. Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

    PubMed

    Predoi, Mihai Valentin

    2014-09-01

    The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

  3. A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.

    PubMed

    Hall, A J; Minchin, P E H

    2013-12-01

    A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants. © 2013 John Wiley & Sons Ltd.

  4. IOL calculation using paraxial matrix optics.

    PubMed

    Haigis, Wolfgang

    2009-07-01

    Matrix methods have a long tradition in paraxial physiological optics. They are especially suited to describe and handle optical systems in a simple and intuitive manner. While these methods are more and more applied to calculate the refractive power(s) of toric intraocular lenses (IOL), they are hardly used in routine IOL power calculations for cataract and refractive surgery, where analytical formulae are commonly utilized. Since these algorithms are also based on paraxial optics, matrix optics can offer rewarding approaches to standard IOL calculation tasks, as will be shown here. Some basic concepts of matrix optics are introduced and the system matrix for the eye is defined, and its application in typical IOL calculation problems is illustrated. Explicit expressions are derived to determine: predicted refraction for a given IOL power; necessary IOL power for a given target refraction; refractive power for a phakic IOL (PIOL); predicted refraction for a thick lens system. Numerical examples with typical clinical values are given for each of these expressions. It is shown that matrix optics can be applied in a straightforward and intuitive way to most problems of modern routine IOL calculation, in thick or thin lens approximation, for aphakic or phakic eyes.

  5. Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity

    NASA Astrophysics Data System (ADS)

    Lázaro, Mario

    2018-01-01

    In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices. Viscoelasticity leads to a frequency dependence of this latter. In this work, a novel closed-form expression to estimate complex eigenvalues is derived. The key point is to consider the damping model as perturbed by a continuous fictitious parameter. Assuming then the eigensolutions as function of this parameter, the computation of the eigenvalues sensitivity leads to an ordinary differential equation, from whose solution arises the proposed analytical formula. The resulting expression explicitly depends on the viscoelasticity (frequency derivatives of the damping function), the nonproportionality (influence of the modal damping matrix off-diagonal terms). Eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue. The method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix. Frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems.

  6. Expressed wishes and incidence of euthanasia in advanced lung cancer patients.

    PubMed

    Pardon, Koen; Deschepper, Reginald; Vander Stichele, Robert; Bernheim, Jan L; Mortier, Freddy; Schallier, Denis; Germonpré, Paul; Galdermans, Daniella; Van Kerckhoven, Willem; Deliens, Luc

    2012-10-01

    This study explores expressed wishes and requests for euthanasia (i.e. administration of lethal drugs at the explicit request of the patient), and incidence of end-of-life decisions with possible life-shortening effects (ELDs) in advanced lung cancer patients in Flanders, Belgium. We performed a prospective, longitudinal, observational study of a consecutive sample of advanced lung cancer patients and selected those who died within 18 months of diagnosis. Immediately after death, the pulmonologist/oncologist and general practitioner (GP) of the patient filled in a questionnaire. Information was available for 105 out of 115 deaths. According to the specialist or GP, one in five patients had expressed a wish for euthanasia; and three in four of these had made an explicit and repeated request. One in two of these received euthanasia. Of the patients who had expressed a wish for euthanasia but had not made an explicit and repeated request, none received euthanasia. Patients with a palliative treatment goal at inclusion were more likely to receive euthanasia. Death was preceded by an ELD in 62.9% of patients. To conclude, advanced lung cancer patients who expressed a euthanasia wish were often determined. Euthanasia was performed significantly more among patients whose treatment goal after diagnosis was exclusively palliative.

  7. A Statistical Physicist's Approach to Biological Motion: From the the Kinesin Walk to Muscle Contraction

    NASA Astrophysics Data System (ADS)

    Vicsek, Tamas

    1997-03-01

    It is demonstrated that a wide range of experimental results on biological motion can be successfully interpreted in terms of statistical physics motivated models taking into account the relevant microscopic details of motor proteins and allowing analytic solutions. Two important examples are considered, i) the motion of a single kinesin molecule along microtubules inside individual cells and ii) muscle contraction which is a macroscopic phenomenon due to the collective action of a large number of myosin heads along actin filaments. i) Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. Here we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads showing all of these properties. The analytic treatment of our model results in a very good fit to the experimental data and practically has no free parameters. ii) Myosin is an ATPase enzyme that converts the chemical energy stored in ATP molecules into mechanical work. During muscle contraction, the myosin cross-bridges attach to the actin filaments and exert force on them yielding a relative sliding of the actin and myosin filaments. In this paper we present a simple mechanochemical model for the cross-bridge interaction involving the relevant kinetic data and providing simple analytic solutions for the mechanical properties of muscle contraction, such as the force-velocity relationship or the relative number of the attached cross-bridges. So far the only analytic formula which could be fitted to the measured force-velocity curves has been the well known Hill equation containing parameters lacking clear microscopic origin. The main advantages of our new approach are that it explicitly connects the mechanical data with the kinetic data and the concentration of the ATP and ATPase products and as such it leads to new analytic solutions which agree extremely well with a wide range of experimental curves, while the parameters of the corresponding expressions have well defined microscopic meaning.

  8. Optimal time-domain technique for pulse width modulation in power electronics

    NASA Astrophysics Data System (ADS)

    Mayergoyz, I.; Tyagi, S.

    2018-05-01

    Optimal time-domain technique for pulse width modulation is presented. It is based on exact and explicit analytical solutions for inverter circuits, obtained for any sequence of input voltage rectangular pulses. Two optimal criteria are discussed and illustrated by numerical examples.

  9. Spatially-explicit models of global tree density.

    PubMed

    Glick, Henry B; Bettigole, Charlie; Maynard, Daniel S; Covey, Kristofer R; Smith, Jeffrey R; Crowther, Thomas W

    2016-08-16

    Remote sensing and geographic analysis of woody vegetation provide means of evaluating the distribution of natural resources, patterns of biodiversity and ecosystem structure, and socio-economic drivers of resource utilization. While these methods bring geographic datasets with global coverage into our day-to-day analytic spheres, many of the studies that rely on these strategies do not capitalize on the extensive collection of existing field data. We present the methods and maps associated with the first spatially-explicit models of global tree density, which relied on over 420,000 forest inventory field plots from around the world. This research is the result of a collaborative effort engaging over 20 scientists and institutions, and capitalizes on an array of analytical strategies. Our spatial data products offer precise estimates of the number of trees at global and biome scales, but should not be used for local-level estimation. At larger scales, these datasets can contribute valuable insight into resource management, ecological modelling efforts, and the quantification of ecosystem services.

  10. Dissociation of Neural Substrates of Response Inhibition to Negative Information between Implicit and Explicit Facial Go/Nogo Tasks: Evidence from an Electrophysiological Study

    PubMed Central

    Sun, Shiyue; Carretié, Luis; Zhang, Lei; Dong, Yi; Zhu, Chunyan; Luo, Yuejia; Wang, Kai

    2014-01-01

    Background Although ample evidence suggests that emotion and response inhibition are interrelated at the behavioral and neural levels, neural substrates of response inhibition to negative facial information remain unclear. Thus we used event-related potential (ERP) methods to explore the effects of explicit and implicit facial expression processing in response inhibition. Methods We used implicit (gender categorization) and explicit emotional Go/Nogo tasks (emotion categorization) in which neutral and sad faces were presented. Electrophysiological markers at the scalp and the voxel level were analyzed during the two tasks. Results We detected a task, emotion and trial type interaction effect in the Nogo-P3 stage. Larger Nogo-P3 amplitudes during sad conditions versus neutral conditions were detected with explicit tasks. However, the amplitude differences between the two conditions were not significant for implicit tasks. Source analyses on P3 component revealed that right inferior frontal junction (rIFJ) was involved during this stage. The current source density (CSD) of rIFJ was higher with sad conditions compared to neutral conditions for explicit tasks, rather than for implicit tasks. Conclusions The findings indicated that response inhibition was modulated by sad facial information at the action inhibition stage when facial expressions were processed explicitly rather than implicitly. The rIFJ may be a key brain region in emotion regulation. PMID:25330212

  11. Explicit ions/implicit water generalized Born model for nucleic acids

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

    Tolokh, Igor S.; Thomas, Dennis G.; Onufriev, Alexey V.

    Ion atmosphere around highly charged nucleic acid molecules plays a significant role in their dynamics, structure and interactions. Here we utilized the implicit solvent framework to develop a model for the explicit treatment of ions interacting with nucleic acid molecules. The proposed explicit ions/implicit water model is based on a significantly modified generalized Born (GB) model, and utilizes a non-standard approach to defining the solute/solvent dielectric boundary. Specifically, the model includes modifications to the GB interaction terms for the case of multiple interacting solutes – disconnected dielectric boundary around the solute-ion or ion-ion pairs. Fully analytical description of all energymore » components for charge-charge interactions is provided. The effectiveness of the approach is demonstrated by calculating the potential of mean force (PMF) for Na+-Cl− ion pair and by carrying out a set of Monte Carlo (MC) simulations of mono- and trivalent ions interacting with DNA and RNA duplexes. The monovalent (Na+) and trivalent (CoHex3+) counterion distributions predicted by the model are in close quantitative agreement with all-atom explicit water molecular dynamics simulations used as reference. Expressed in the units of energy, the maximum deviations of local ion concentrations from the reference are within kBT. The proposed explicit ions/implicit water GB model is able to resolve subtle features and differences of CoHex distributions around DNA and RNA duplexes. These features include preferential CoHex binding inside the major groove of RNA duplex, in contrast to CoHex biding at the "external" surface of the sugar-phosphate backbone of DNA duplex; these differences in the counterion binding patters were shown earlier to be responsible for the observed drastic differences in condensation propensities between short DNA and RNA duplexes. MC simulations of CoHex ions interacting with homopolymeric poly(dA·dT) DNA duplex with modified (de-methylated) and native Thymine bases are used to explore the physics behind CoHex-Thymine interactions. The simulations suggest that the ion desolvation penalty due to proximity to the low dielectric volume of the methyl group can contribute significantly to CoHex-Thymine interactions. Compared to the steric repulsion between the ion and the methyl group, the desolvation penalty interaction has a longer range, and may be important to consider in the context of methylation effects on DNA condensation.« less

  12. Explicit ions/implicit water generalized Born model for nucleic acids

    NASA Astrophysics Data System (ADS)

    Tolokh, Igor S.; Thomas, Dennis G.; Onufriev, Alexey V.

    2018-05-01

    The ion atmosphere around highly charged nucleic acid molecules plays a significant role in their dynamics, structure, and interactions. Here we utilized the implicit solvent framework to develop a model for the explicit treatment of ions interacting with nucleic acid molecules. The proposed explicit ions/implicit water model is based on a significantly modified generalized Born (GB) model and utilizes a non-standard approach to define the solute/solvent dielectric boundary. Specifically, the model includes modifications to the GB interaction terms for the case of multiple interacting solutes—disconnected dielectric boundary around the solute-ion or ion-ion pairs. A fully analytical description of all energy components for charge-charge interactions is provided. The effectiveness of the approach is demonstrated by calculating the potential of mean force for Na+-Cl- ion pair and by carrying out a set of Monte Carlo (MC) simulations of mono- and trivalent ions interacting with DNA and RNA duplexes. The monovalent (Na+) and trivalent (CoHex3+) counterion distributions predicted by the model are in close quantitative agreement with all-atom explicit water molecular dynamics simulations used as reference. Expressed in the units of energy, the maximum deviations of local ion concentrations from the reference are within kBT. The proposed explicit ions/implicit water GB model is able to resolve subtle features and differences of CoHex distributions around DNA and RNA duplexes. These features include preferential CoHex binding inside the major groove of the RNA duplex, in contrast to CoHex biding at the "external" surface of the sugar-phosphate backbone of the DNA duplex; these differences in the counterion binding patters were earlier shown to be responsible for the observed drastic differences in condensation propensities between short DNA and RNA duplexes. MC simulations of CoHex ions interacting with the homopolymeric poly(dA.dT) DNA duplex with modified (de-methylated) and native thymine bases are used to explore the physics behind CoHex-thymine interactions. The simulations suggest that the ion desolvation penalty due to proximity to the low dielectric volume of the methyl group can contribute significantly to CoHex-thymine interactions. Compared to the steric repulsion between the ion and the methyl group, the desolvation penalty interaction has a longer range and may be important to consider in the context of methylation effects on DNA condensation.

  13. Not on the Face Alone: Perception of Contextualized Face Expressions in Huntington's Disease

    ERIC Educational Resources Information Center

    Aviezer, Hillel; Bentin, Shlomo; Hassin, Ran R.; Meschino, Wendy S.; Kennedy, Jeanne; Grewal, Sonya; Esmail, Sherali; Cohen, Sharon; Moscovitch, Morris

    2009-01-01

    Numerous studies have demonstrated that Huntington's disease mutation-carriers have deficient explicit recognition of isolated facial expressions. There are no studies, however, which have investigated the recognition of facial expressions embedded within an emotional body and scene context. Real life facial expressions are typically embedded in…

  14. Solvent effects in time-dependent self-consistent field methods. II. Variational formulations and analytical gradients

    DOE PAGES

    Bjorgaard, J. A.; Velizhanin, K. A.; Tretiak, S.

    2015-08-06

    This study describes variational energy expressions and analytical excited state energy gradients for time-dependent self-consistent field methods with polarizable solvent effects. Linear response, vertical excitation, and state-specific solventmodels are examined. Enforcing a variational ground stateenergy expression in the state-specific model is found to reduce it to the vertical excitation model. Variational excited state energy expressions are then provided for the linear response and vertical excitation models and analytical gradients are formulated. Using semiempiricalmodel chemistry, the variational expressions are verified by numerical and analytical differentiation with respect to a static external electric field. Lastly, analytical gradients are further tested by performingmore » microcanonical excited state molecular dynamics with p-nitroaniline.« less

  15. Some rules for polydimensional squeezing

    NASA Technical Reports Server (NTRS)

    Manko, Vladimir I.

    1994-01-01

    The review of the following results is presented: For mixed state light of N-mode electromagnetic field described by Wigner function which has generic Gaussian form, the photon distribution function is obtained and expressed explicitly in terms of Hermite polynomials of 2N-variables. The momenta of this distribution are calculated and expressed as functions of matrix invariants of the dispersion matrix. The role of new uncertainty relation depending on photon state mixing parameter is elucidated. New sum rules for Hermite polynomials of several variables are found. The photon statistics of polymode even and odd coherent light and squeezed polymode Schroedinger cat light is given explicitly. Photon distribution for polymode squeezed number states expressed in terms of multivariable Hermite polynomials is discussed.

  16. Correlations and analytical approaches to co-evolving voter models

    NASA Astrophysics Data System (ADS)

    Ji, M.; Xu, C.; Choi, C. W.; Hui, P. M.

    2013-11-01

    The difficulty in formulating analytical treatments in co-evolving networks is studied in light of the Vazquez-Eguíluz-San Miguel voter model (VM) and a modified VM (MVM) that introduces a random mutation of the opinion as a noise in the VM. The density of active links, which are links that connect the nodes of opposite opinions, is shown to be highly sensitive to both the degree k of a node and the active links n among the neighbors of a node. We test the validity in the formalism of analytical approaches and show explicitly that the assumptions behind the commonly used homogeneous pair approximation scheme in formulating a mean-field theory are the source of the theory's failure due to the strong correlations between k, n and n2. An improved approach that incorporates spatial correlation to the nearest-neighbors explicitly and a random approximation for the next-nearest neighbors is formulated for the VM and the MVM, and it gives better agreement with the simulation results. We introduce an empirical approach that quantifies the correlations more accurately and gives results in good agreement with the simulation results. The work clarifies why simply mean-field theory fails and sheds light on how to analyze the correlations in the dynamic equations that are often generated in co-evolving processes.

  17. 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.

  18. Investigation of the feasibility of an analytical method of accounting for the effects of atmospheric drag on satellite motion

    NASA Technical Reports Server (NTRS)

    Bozeman, Robert E.

    1987-01-01

    An analytic technique for accounting for the joint effects of Earth oblateness and atmospheric drag on close-Earth satellites is investigated. The technique is analytic in the sense that explicit solutions to the Lagrange planetary equations are given; consequently, no numerical integrations are required in the solution process. The atmospheric density in the technique described is represented by a rotating spherical exponential model with superposed effects of the oblate atmosphere and the diurnal variations. A computer program implementing the process is discussed and sample output is compared with output from program NSEP (Numerical Satellite Ephemeris Program). NSEP uses a numerical integration technique to account for atmospheric drag effects.

  19. 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.

  20. Analytical modeling of soliton interactions in a nonlocal nonlinear medium analogous to gravitational force

    NASA Astrophysics Data System (ADS)

    Zeng, Shihao; Chen, Manna; Zhang, Ting; Hu, Wei; Guo, Qi; Lu, Daquan

    2018-01-01

    We illuminate an analytical model of soliton interactions in lead glass by analogizing to a gravitational force system. The orbits of spiraling solitons under a long-range interaction are given explicitly and demonstrated to follow Newton's second law of motion and the Binet equation by numerical simulations. The condition for circular orbits is obtained and the oscillating orbits are proved not to be closed. We prove the analogy between the nonlocal nonlinear optical system and gravitational system and specify the quantitative relation of the quantity between the two models.

  1. Hill Problem Analytical Theory to the Order Four. Application to the Computation of Frozen Orbits around Planetary Satellites

    NASA Technical Reports Server (NTRS)

    Lara, Martin; Palacian, Jesus F.

    2007-01-01

    Frozen orbits of the Hill problem are determined in the double averaged problem, where short and long period terms are removed by means of Lie transforms. The computation of initial conditions of corresponding quasi periodic solutions in the non-averaged problem is straightforward for the perturbation method used provides the explicit equations of the transformation that connects the averaged and non-averaged models. A fourth order analytical theory reveals necessary for the accurate computation of quasi periodic, frozen orbits.

  2. The Legal Recognition of Sign Languages

    ERIC Educational Resources Information Center

    De Meulder, Maartje

    2015-01-01

    This article provides an analytical overview of the different types of explicit legal recognition of sign languages. Five categories are distinguished: constitutional recognition, recognition by means of general language legislation, recognition by means of a sign language law or act, recognition by means of a sign language law or act including…

  3. CTE method and interaction solutions for the Kadomtsev-Petviashvili equation

    NASA Astrophysics Data System (ADS)

    Ren, Bo

    2017-02-01

    The consistent tanh expansion method is applied to the Kadomtsev-Petviashvili equation. The interaction solutions among one soliton and other types of solitary waves, such as multiple resonant soliton solutions and cnoidal waves, are explicitly given. Some special concrete interaction solutions are discussed both in analytical and graphical ways.

  4. Influence of Familiar Features on Diagnosis: Instantiated Features in an Applied Setting

    ERIC Educational Resources Information Center

    Dore, Kelly L.; Brooks, Lee R.; Weaver, Bruce; Norman, Geoffrey R.

    2012-01-01

    Medical diagnosis can be viewed as a categorization task. There are two mechanisms whereby humans make categorical judgments: "analytical reasoning," based on explicit consideration of features and "nonanalytical reasoning," an unconscious holistic process of matching against prior exemplars. However, there is evidence that prior experience can…

  5. Knowing English Grammar--An Important Aid in Second Language Learning

    ERIC Educational Resources Information Center

    Cleary, Colin

    2004-01-01

    This article discusses a small-scale study that explored students', teachers', and university lecturers' beliefs about the value of studying English grammar in foreign and second language learning. A major debate in second language acquisition literature has been concerned with experiential (implicit) learning as opposed to analytical (explicit)…

  6. Completeness of the Coulomb Wave Functions in Quantum Mechanics

    ERIC Educational Resources Information Center

    Mukunda, N.

    1978-01-01

    Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

  7. DEVELOPMENTS AT U.S. EPA IN ADDRESSING UNCERTAINTY IN RISK ASSESSMENT

    EPA Science Inventory

    An emerging trend in risk assessment is to be more explicit about uncertainties, both during the analytical procedures and in communicating results. In February 1 992, then-Deputy EPA Administrator Henry Habicht set out Agency goals in a memorandum stating that the Agency will "p...

  8. Transnationalisation within School Education:The Interconnection between Actors, Structures and Mechanisms

    ERIC Educational Resources Information Center

    Schneider, Claudia

    2017-01-01

    The current literature of school education, transnationalisation and migration explores actors, structures and social mechanisms, however, tends to focus on these analytical levels separately. This article advocates a more explicit analysis of the interconnections of structures, actors and mechanisms within and across schools and wider national…

  9. Hippocampal Contribution to Implicit Configuration Memory Expressed via Eye Movements During Scene Exploration

    PubMed Central

    Ryals, Anthony J.; Wang, Jane X.; Polnaszek, Kelly L.; Voss, Joel L.

    2015-01-01

    Although hippocampus unequivocally supports explicit/ declarative memory, fewer findings have demonstrated its role in implicit expressions of memory. We tested for hippocampal contributions to an implicit expression of configural/relational memory for complex scenes using eye-movement tracking during functional magnetic resonance imaging (fMRI) scanning. Participants studied scenes and were later tested using scenes that resembled study scenes in their overall feature configuration but comprised different elements. These configurally similar scenes were used to limit explicit memory, and were intermixed with new scenes that did not resemble studied scenes. Scene configuration memory was expressed through eye movements reflecting exploration overlap (EO), which is the viewing of the same scene locations at both study and test. EO reliably discriminated similar study-test scene pairs from study-new scene pairs, was reliably greater for similarity-based recognition hits than for misses, and correlated with hippocampal fMRI activity. In contrast, subjects could not reliably discriminate similar from new scenes by overt judgments, although ratings of familiarity were slightly higher for similar than new scenes. Hippocampal fMRI correlates of this weak explicit memory were distinct from EO-related activity. These findings collectively suggest that EO was an implicit expression of scene configuration memory associated with hippocampal activity. Visual exploration can therefore reflect implicit hippocampal-related memory processing that can be observed in eye-movement behavior during naturalistic scene viewing. PMID:25620526

  10. Two-point function of a quantum scalar field in the interior region of a Reissner-Nordstrom black hole

    NASA Astrophysics Data System (ADS)

    Lanir, Assaf; Levi, Adam; Ori, Amos; Sela, Orr

    2018-01-01

    We derive explicit expressions for the two-point function of a massless scalar field in the interior region of a Reissner-Nordstrom black hole, in both the Unruh and the Hartle-Hawking quantum states. The two-point function is expressed in terms of the standard l m ω modes of the scalar field (those associated with a spherical harmonic Yl m and a temporal mode e-i ω t), which can be conveniently obtained by solving an ordinary differential equation, the radial equation. These explicit expressions are the internal analogs of the well-known results in the external region (originally derived by Christensen and Fulling), in which the two-point function outside the black hole is written in terms of the external l m ω modes of the field. They allow the computation of ⟨Φ2⟩ren and the renormalized stress-energy tensor inside the black hole, after the radial equation has been solved (usually numerically). In the second part of the paper, we provide an explicit expression for the trace of the renormalized stress-energy tensor of a minimally coupled massless scalar field (which is nonconformal), relating it to the d'Alembertian of ⟨Φ2⟩ren . This expression proves itself useful in various calculations of the renormalized stress-energy tensor.

  11. Measuring Explicit Word Learning of Preschool Children: A Development Study.

    PubMed

    Kelley, Elizabeth Spencer

    2017-08-15

    The purpose of this article is to present preliminary results related to the development of a new measure of explicit word learning. The measure incorporated elements of explicit vocabulary instruction and dynamic assessment and was designed to be sensitive to differences in word learning skill and to be feasible for use in clinical settings. The explicit word learning measure included brief teaching trials and repeated fine-grained measurement of semantic knowledge and production of 3 novel words (2 verbs and 1 adjective). Preschool children (N = 23) completed the measure of explicit word learning; standardized, norm-referenced measures of expressive and receptive vocabulary; and an incidental word learning task. The measure of explicit word learning provided meaningful information about word learning. Performance on the explicit measure was related to existing vocabulary knowledge and incidental word learning. Findings from this development study indicate that further examination of the measure of explicit word learning is warranted. The measure may have the potential to identify children who are poor word learners. https://doi.org/10.23641/asha.5170738.

  12. A potential energy surface for the process H2 + H2O yielding H + H + H2O - Ab initio calculations and analytical representation

    NASA Technical Reports Server (NTRS)

    Schwenke, David W.; Walch, Stephen P.; Taylor, Peter R.

    1991-01-01

    Extensive ab initio calculations on the ground state potential energy surface of H2 + H2O were performed using a large contracted Gaussian basis set and a high level of correlation treatment. An analytical representation of the potential energy surface was then obtained which reproduces the calculated energies with an overall root-mean-square error of only 0.64 mEh. The analytic representation explicitly includes all nine internal degrees of freedom and is also well behaved as the H2 dissociates; it thus can be used to study collision-induced dissociation or recombination of H2. The strategy used to minimize the number of energy calculations is discussed, as well as other advantages of the present method for determining the analytical representation.

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

    Safari, L., E-mail: laleh.safari@ist.ac.at; Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu; Santos, J. P.

    Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the independent particle model constructed from nonrelativistic screened hydrogenic wave functions. The range of validity of this analytical expression is checked by comparing the analytically obtained form factors with the ones obtained within the Hartee-Fock method. As an example, we apply our analytical expression for the atomic form factor to evaluate the differential cross section for Rayleigh scattering off neutral atoms.

  14. Analytical model for the radio-frequency sheath

    NASA Astrophysics Data System (ADS)

    Czarnetzki, Uwe

    2013-12-01

    A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

  15. Analytical model for the radio-frequency sheath.

    PubMed

    Czarnetzki, Uwe

    2013-12-01

    A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

  16. Large-deviation theory for diluted Wishart random matrices

    NASA Astrophysics Data System (ADS)

    Castillo, Isaac Pérez; Metz, Fernando L.

    2018-03-01

    Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology, and economy. In this work, we develop a theory for the eigenvalue fluctuations of diluted Wishart random matrices based on the replica approach of disordered systems. We derive an analytical expression for the cumulant generating function of the number of eigenvalues IN(x ) smaller than x ∈R+ , from which all cumulants of IN(x ) and the rate function Ψx(k ) controlling its large-deviation probability Prob[IN(x ) =k N ] ≍e-N Ψx(k ) follow. Explicit results for the mean value and the variance of IN(x ) , its rate function, and its third cumulant are discussed and thoroughly compared to numerical diagonalization, showing very good agreement. The present work establishes the theoretical framework put forward in a recent letter [Phys. Rev. Lett. 117, 104101 (2016), 10.1103/PhysRevLett.117.104101] as an exact and compelling approach to deal with eigenvalue fluctuations of sparse random matrices.

  17. Exact solutions for sound radiation from a moving monopole above an impedance plane.

    PubMed

    Ochmann, Martin

    2013-04-01

    The acoustic field of a monopole source moving with constant velocity at constant height above an infinite locally reacting plane can be expressed in analytical form by combining the Lorentz transformation with the method of superimposing complex or real point sources. For a plane with masslike response, the solution in Lorentz space consists of a superposition of monopoles only and therefore, does not differ in principle from the solution for the corresponding stationary boundary value problem. However, by considering a frequency independent surface impedance, e.g., with pure absorbing behavior, the half-space Green's function is now comprised of not only a line of monopoles but also of dipoles. For certain field points at a special line g, this solution can be written explicitly by using an exponential integral. For arbitrary field points, the method of stationary phase leads to an asymptotic solution for the reflection coefficient which agrees with prior results from the literature.

  18. Deformation of a flexible disk bonded to an elastic half space-application to the lung.

    PubMed

    Lai-Fook, S J; Hajji, M A; Wilson, T A

    1980-08-01

    An analysis is presented of the deformation of a homogeneous, isotropic, elastic half space subjected to a constant radial strain in a circular area on the boundary. Explicit analytic expressions for the normal and radial displacements and the shear stress on the boundary are used to interpret experiments performed on inflated pig lungs. The boundary strain was induced by inflating or deflating the lung after bonding a flexible disk to the lung surface. The prediction that the surface bulges outward for positive boundary strain and inward for negative strain was observed in the experiments. Poisson's ratio at two transpulmonary pressures was measured, by use of the normal displacement equation evaluated at the surface. A direct estimate of Poisson's ratio was possible because the normal displacement of the surface depended uniquely on the compressibility of the material. Qualitative comparisons between theory and experiment support the use of continuum analyses in evaluating the behavior of the lung parenchyma when subjected to small local distortions.

  19. Unsteady free convection flow of viscous fluids with analytical results by employing time-fractional Caputo-Fabrizio derivative (without singular kernel)

    NASA Astrophysics Data System (ADS)

    Ali Shah, Nehad; Mahsud, Yasir; Ali Zafar, Azhar

    2017-10-01

    This article introduces a theoretical study for unsteady free convection flow of an incompressible viscous fluid. The fluid flows near an isothermal vertical plate. The plate has a translational motion with time-dependent velocity. The equations governing the fluid flow are expressed in fractional differential equations by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Explicit solutions for velocity, temperature and solute concentration are obtained by applying the Laplace transform technique. As the fractional parameter approaches to one, solutions for the ordinary fluid model are extracted from the general solutions of the fractional model. The results showed that, for the fractional model, the obtained solutions for velocity, temperature and concentration exhibit stationary jumps discontinuity across the plane at t=0 , while the solutions are continuous functions in the case of the ordinary model. Finally, numerical results for flow features at small-time are illustrated through graphs for various pertinent parameters.

  20. Ghost-gluon vertex in the presence of the Gribov horizon

    NASA Astrophysics Data System (ADS)

    Mintz, B. W.; Palhares, L. F.; Sorella, S. P.; Pereira, A. D.

    2018-02-01

    We consider Yang-Mills theories quantized in the Landau gauge in the presence of the Gribov horizon via the refined Gribov-Zwanziger (RGZ) framework. As the restriction of the gauge path integral to the Gribov region is taken into account, the resulting gauge field propagators display a nontrivial infrared behavior, being very close to the ones observed in lattice gauge field theory simulations. In this work, we explore a higher correlation function in the refined Gribov-Zwanziger theory: the ghost-gluon interaction vertex, at one-loop level. We show explicit compatibility with kinematical constraints, as required by the Ward identities of the theory, and obtain analytical expressions in the limit of vanishing gluon momentum. We find that the RGZ results are nontrivial in the infrared regime, being compatible with lattice Yang-Mills simulations in both SU(2) and SU(3), as well as with solutions from Schwinger-Dyson equations in different truncation schemes, Functional Renormalization Group analysis, and the renormalization group-improved Curci-Ferrari model.

  1. Temperament and typology.

    PubMed

    Blandin, Kesstan

    2013-02-01

    This paper takes a cue from Harvard neuroscientists Jerome Kagan and Nancy Snidman's (2004) comment that Jung's work on typology has remarkable relevance to their research on neurobiological correlates of temperament and develops the links between the theorists separated by almost a century. The paper begins with a brief review of temperament traits in personality psychology. Kagan and Snidman's 11-year longitudinal study is then analysed and correlated with Jung's psychological attitude types of introversion and extraversion, demonstrating that Jung's close empirical observations of human nature fit explicitly with objective measurements of neurobiological sensitivity thresholds and their expression in temperament. Emerging research on neurobiologically sensitive adults and children from Aron (1997, 2004, 2011) and differential susceptibility theory (DST) is presented as extrapolating the same links between temperament and physiological sensitivity found in Jung's introversion and Kagan and Snidman's high-reactive type. The paper concludes with a consideration of the subjective psyche as a necessary aspect to understanding the self and human consciousness as whole. © 2013, The Society of Analytical Psychology.

  2. Bethe Ansatz solutions for highest states in Script N = 4 SYM and AdS/CFT duality

    NASA Astrophysics Data System (ADS)

    Beccaria, Matteo; DelDebbio, Luigi

    2006-09-01

    We consider the operators with highest anomalous dimension Δ in the compact rank-one sectors fraktur sfraktur u(1|1) and fraktur sfraktur u(2) of Script N = 4 super Yang-Mills. We study the flow of Δ from weak to strong 't Hooft coupling λ by solving (i) the all-loop gauge Bethe Ansatz, (ii) the quantum string Bethe Ansatz. The two calculations are carefully compared in the strong coupling limit and exhibit different exponents ν in the leading order expansion Δ ~ λν. We find ν = 1/2 and ν = 1/4 for the gauge or string solution. This strong coupling discrepancy is not unexpected, and it provides an explicit example where the gauge Bethe Ansatz solution cannot be trusted at large λ. Instead, the string solution perfectly reproduces the Gubser-Klebanov-Polyakov law Δ = 2n1/2 λ1/4. In particular, we provide an analytic expression for the integer level n as a function of the U(1) charge in both sectors.

  3. The Adler D-function for N = 1 SQCD regularized by higher covariant derivatives in the three-loop approximation

    NASA Astrophysics Data System (ADS)

    Kataev, A. L.; Kazantsev, A. E.; Stepanyantz, K. V.

    2018-01-01

    We calculate the Adler D-function for N = 1 SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the D-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for N = 1 SQCD is found in this scheme to the order O (αs2). The problem of scheme-dependence of the D-function and the NSVZ-like equation is briefly discussed.

  4. J functions for the process ud→WA

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

    Bardin, D. Yu., E-mail: bardin@nu.jinr.ru; Kalinovskaya, L. V., E-mail: kalinov@mail.cern.ch; Uglov, E. D., E-mail: e.uglov@gmail.com

    In this paper we present a description of the universal approach for analytic calculations for a certain class of J functions for six topologies of the boxes for the process ud → WA. These functions J arise at the reduction of the infrared divergent box diagrams. The standard Passarino–Veltman reduction of the four-point box diagram with an internal photon line connecting two external lines on the mass shell leads to infrared-divergent and mass-singular D{sub 0} functions. In the system SANC a systematic procedure is adopted to separate both types of singularities into the simplest objects, namely C{sub 0} functions. Themore » functions J, in turn, are represented as certain linear combinations of the standard D{sub 0} and C{sub 0} functions. The subtracted J functions are free of both types of singularities and are expressed as explicit and compact linear combinations of dilogarithm functions. We present extensive comparisons of numerical results of SANC with those obtained with the aid of the LoopTools package.« less

  5. Novel and general approach to linear filter design for contrast-to-noise ratio enhancement of magnetic resonance images with multiple interfering features in the scene

    NASA Astrophysics Data System (ADS)

    Soltanian-Zadeh, Hamid; Windham, Joe P.

    1992-04-01

    Maximizing the minimum absolute contrast-to-noise ratios (CNRs) between a desired feature and multiple interfering processes, by linear combination of images in a magnetic resonance imaging (MRI) scene sequence, is attractive for MRI analysis and interpretation. A general formulation of the problem is presented, along with a novel solution utilizing the simple and numerically stable method of Gram-Schmidt orthogonalization. We derive explicit solutions for the case of two interfering features first, then for three interfering features, and, finally, using a typical example, for an arbitrary number of interfering feature. For the case of two interfering features, we also provide simplified analytical expressions for the signal-to-noise ratios (SNRs) and CNRs of the filtered images. The technique is demonstrated through its applications to simulated and acquired MRI scene sequences of a human brain with a cerebral infarction. For these applications, a 50 to 100% improvement for the smallest absolute CNR is obtained.

  6. Temperature-Dependent Implicit-Solvent Model of Polyethylene Glycol in Aqueous Solution.

    PubMed

    Chudoba, Richard; Heyda, Jan; Dzubiella, Joachim

    2017-12-12

    A temperature (T)-dependent coarse-grained (CG) Hamiltonian of polyethylene glycol/oxide (PEG/PEO) in aqueous solution is reported to be used in implicit-solvent material models in a wide temperature (i.e., solvent quality) range. The T-dependent nonbonded CG interactions are derived from a combined "bottom-up" and "top-down" approach. The pair potentials calculated from atomistic replica-exchange molecular dynamics simulations in combination with the iterative Boltzmann inversion are postrefined by benchmarking to experimental data of the radius of gyration. For better handling and a fully continuous transferability in T-space, the pair potentials are conveniently truncated and mapped to an analytic formula with three structural parameters expressed as explicit continuous functions of T. It is then demonstrated that this model without further adjustments successfully reproduces other experimentally known key thermodynamic properties of semidilute PEG solutions such as the full equation of state (i.e., T-dependent osmotic pressure) for various chain lengths as well as their cloud point (or collapse) temperature.

  7. Concept of contrast transfer function for edge illumination x-ray phase-contrast imaging and its comparison with the free-space propagation technique.

    PubMed

    Diemoz, Paul C; Vittoria, Fabio A; Olivo, Alessandro

    2016-05-16

    Previous studies on edge illumination (EI) X-ray phase-contrast imaging (XPCi) have investigated the nature and amplitude of the signal provided by this technique. However, the response of the imaging system to different object spatial frequencies was never explicitly considered and studied. This is required in order to predict the performance of a given EI setup for different classes of objects. To this scope, in the present work we derive analytical expressions for the contrast transfer function of an EI imaging system, using the approximation of near-field regime, and study its dependence upon the main experimental parameters. We then exploit these results to compare the frequency response of an EI system with respect of that of a free-space propagation XPCi one. The results achieved in this work can be useful for predicting the signals obtainable for different types of objects and also as a basis for new retrieval methods.

  8. Effect of magnetic helicity upon rectilinear propagation of charged particles in random magnetic fields

    NASA Technical Reports Server (NTRS)

    Earl, James A.

    1992-01-01

    When charged particles spiral along a large constant magnetic field, their trajectories are scattered by any random field components that are superposed on the guiding field. If the random field configuration embodies helicity, the scattering is asymmetrical with respect to a plane perpendicular to the guiding field, for particles moving into the forward hemisphere are scattered at different rates from those moving into the backward hemisphere. This asymmetry gives rise to new terms in the transport equations that describe propagation of charged particles. Helicity has virtually no impact on qualitative features of the diffusive mode of propagation. However, characteristic velocities of the coherent modes that appear after a highly anisotropic injection exhibit an asymmetry related to helicity. Explicit formulas, which embody the effects of helicity, are given for the anisotropies, the coefficient diffusion, and the coherent velocities. Predictions derived from these expressions are in good agreement with Monte Carlo simulations of particle transport, but the simulations reveal certain phenomena whose explanation calls for further analytical work.

  9. Symmetry Reductions and Group-Invariant Radial Solutions to the n-Dimensional Wave Equation

    NASA Astrophysics Data System (ADS)

    Feng, Wei; Zhao, Songlin

    2018-01-01

    In this paper, we derive explicit group-invariant radial solutions to a class of wave equation via symmetry group method. The optimal systems of one-dimensional subalgebras for the corresponding radial wave equation are presented in terms of the known point symmetries. The reductions of the radial wave equation into second-order ordinary differential equations (ODEs) with respect to each symmetry in the optimal systems are shown. Then we solve the corresponding reduced ODEs explicitly in order to write out the group-invariant radial solutions for the wave equation. Finally, several analytical behaviours and smoothness of the resulting solutions are discussed.

  10. A new approach to the Schrödinger equation with rational potentials

    NASA Astrophysics Data System (ADS)

    Dong, Ming-de; Chu, Jue-Hui

    1984-04-01

    A new analytic theory is established for the Schrödinger equation with a rational potential, including a complete classification of the regular eigenfunctions into three different types, an exact method of obtaining wavefunctions, an explicit formulation of the spectral equation (3 x 3 determinant) etc. All representations are exhibited in a unifying way via function-theoretic methods and therefore given in explicit form, in contrast to the prevailing discussion appealing to perturbation or variation methods or continued-fraction techniques. The irregular eigenfunctions at infinity can be obtained analogously and will be discussed separately as another solvable case for singular potentials.

  11. Self-sustained peristaltic waves: Explicit asymptotic solutions

    NASA Astrophysics Data System (ADS)

    Dudchenko, O. A.; Guria, G. Th.

    2012-02-01

    A simple nonlinear model for the coupled problem of fluid flow and contractile wall deformation is proposed to describe peristalsis. In the context of the model the ability of a transporting system to perform autonomous peristaltic pumping is interpreted as the ability to propagate sustained waves of wall deformation. Piecewise-linear approximations of nonlinear functions are used to analytically demonstrate the existence of traveling-wave solutions. Explicit formulas are derived which relate the speed of self-sustained peristaltic waves to the rheological properties of the transporting vessel and the transported fluid. The results may contribute to the development of diagnostic and therapeutic procedures for cases of peristaltic motility disorders.

  12. Decision support systems in health economics.

    PubMed

    Quaglini, S; Dazzi, L; Stefanelli, M; Barosi, G; Marchetti, M

    1999-08-01

    This article describes a system addressed to different health care professionals for building, using, and sharing decision support systems for resource allocation. The system deals with selected areas, namely the choice of diagnostic tests, the therapy planning, and the instrumentation purchase. Decision support is based on decision-analytic models, incorporating an explicit knowledge representation of both the medical domain knowledge and the economic evaluation theory. Application models are built on top of meta-models, that are used as guidelines for making explicit both the cost and effectiveness components. This approach improves the transparency and soundness of the collaborative decision-making process and facilitates the result interpretation.

  13. Vocation in theology-based nursing theories.

    PubMed

    Lundmark, Mikael

    2007-11-01

    By using the concepts of intrinsicality/extrinsicality as analytic tools, the theology-based nursing theories of Ann Bradshaw and Katie Eriksson are analyzed regarding their explicit and/or implicit understanding of vocation as a motivational factor for nursing. The results show that both theories view intrinsic values as guarantees against reducing nursing practice to mechanistic applications of techniques and as being a way of reinforcing a high ethical standard. The theories explicitly (Bradshaw) or implicitly (Eriksson) advocate a vocational understanding of nursing as being essential for nursing theories. Eriksson's theory has a potential for conceptualizing an understanding of extrinsic and intrinsic motivational factors for nursing but one weakness in the theory could be the risk of slipping over to moral judgments where intrinsic factors are valued as being superior to extrinsic. Bradshaw's theory is more complex and explicit in understanding the concept of vocation and is theologically more plausible, although also more confessional.

  14. MPDATA: Third-order accuracy for variable flows

    NASA Astrophysics Data System (ADS)

    Waruszewski, Maciej; Kühnlein, Christian; Pawlowska, Hanna; Smolarkiewicz, Piotr K.

    2018-04-01

    This paper extends the multidimensional positive definite advection transport algorithm (MPDATA) to third-order accuracy for temporally and spatially varying flows. This is accomplished by identifying the leading truncation error of the standard second-order MPDATA, performing the Cauchy-Kowalevski procedure to express it in a spatial form and compensating its discrete representation-much in the same way as the standard MPDATA corrects the first-order accurate upwind scheme. The procedure of deriving the spatial form of the truncation error was automated using a computer algebra system. This enables various options in MPDATA to be included straightforwardly in the third-order scheme, thereby minimising the implementation effort in existing code bases. Following the spirit of MPDATA, the error is compensated using the upwind scheme resulting in a sign-preserving algorithm, and the entire scheme can be formulated using only two upwind passes. Established MPDATA enhancements, such as formulation in generalised curvilinear coordinates, the nonoscillatory option or the infinite-gauge variant, carry over to the fully third-order accurate scheme. A manufactured 3D analytic solution is used to verify the theoretical development and its numerical implementation, whereas global tracer-transport benchmarks demonstrate benefits for chemistry-transport models fundamental to air quality monitoring, forecasting and control. A series of explicitly-inviscid implicit large-eddy simulations of a convective boundary layer and explicitly-viscid simulations of a double shear layer illustrate advantages of the fully third-order-accurate MPDATA for fluid dynamics applications.

  15. A GIS based spatially-explicit sensitivity and uncertainty analysis approach for multi-criteria decision analysis.

    PubMed

    Feizizadeh, Bakhtiar; Jankowski, Piotr; Blaschke, Thomas

    2014-03-01

    GIS multicriteria decision analysis (MCDA) techniques are increasingly used in landslide susceptibility mapping for the prediction of future hazards, land use planning, as well as for hazard preparedness. However, the uncertainties associated with MCDA techniques are inevitable and model outcomes are open to multiple types of uncertainty. In this paper, we present a systematic approach to uncertainty and sensitivity analysis. We access the uncertainty of landslide susceptibility maps produced with GIS-MCDA techniques. A new spatially-explicit approach and Dempster-Shafer Theory (DST) are employed to assess the uncertainties associated with two MCDA techniques, namely Analytical Hierarchical Process (AHP) and Ordered Weighted Averaging (OWA) implemented in GIS. The methodology is composed of three different phases. First, weights are computed to express the relative importance of factors (criteria) for landslide susceptibility. Next, the uncertainty and sensitivity of landslide susceptibility is analyzed as a function of weights using Monte Carlo Simulation and Global Sensitivity Analysis. Finally, the results are validated using a landslide inventory database and by applying DST. The comparisons of the obtained landslide susceptibility maps of both MCDA techniques with known landslides show that the AHP outperforms OWA. However, the OWA-generated landslide susceptibility map shows lower uncertainty than the AHP-generated map. The results demonstrate that further improvement in the accuracy of GIS-based MCDA can be achieved by employing an integrated uncertainty-sensitivity analysis approach, in which the uncertainty of landslide susceptibility model is decomposed and attributed to model's criteria weights.

  16. A GIS based spatially-explicit sensitivity and uncertainty analysis approach for multi-criteria decision analysis☆

    PubMed Central

    Feizizadeh, Bakhtiar; Jankowski, Piotr; Blaschke, Thomas

    2014-01-01

    GIS multicriteria decision analysis (MCDA) techniques are increasingly used in landslide susceptibility mapping for the prediction of future hazards, land use planning, as well as for hazard preparedness. However, the uncertainties associated with MCDA techniques are inevitable and model outcomes are open to multiple types of uncertainty. In this paper, we present a systematic approach to uncertainty and sensitivity analysis. We access the uncertainty of landslide susceptibility maps produced with GIS-MCDA techniques. A new spatially-explicit approach and Dempster–Shafer Theory (DST) are employed to assess the uncertainties associated with two MCDA techniques, namely Analytical Hierarchical Process (AHP) and Ordered Weighted Averaging (OWA) implemented in GIS. The methodology is composed of three different phases. First, weights are computed to express the relative importance of factors (criteria) for landslide susceptibility. Next, the uncertainty and sensitivity of landslide susceptibility is analyzed as a function of weights using Monte Carlo Simulation and Global Sensitivity Analysis. Finally, the results are validated using a landslide inventory database and by applying DST. The comparisons of the obtained landslide susceptibility maps of both MCDA techniques with known landslides show that the AHP outperforms OWA. However, the OWA-generated landslide susceptibility map shows lower uncertainty than the AHP-generated map. The results demonstrate that further improvement in the accuracy of GIS-based MCDA can be achieved by employing an integrated uncertainty–sensitivity analysis approach, in which the uncertainty of landslide susceptibility model is decomposed and attributed to model's criteria weights. PMID:25843987

  17. Critical Thinking in Critical Care: Five Strategies to Improve Teaching and Learning in the Intensive Care Unit.

    PubMed

    Hayes, Margaret M; Chatterjee, Souvik; Schwartzstein, Richard M

    2017-04-01

    Critical thinking, the capacity to be deliberate about thinking, is increasingly the focus of undergraduate medical education, but is not commonly addressed in graduate medical education. Without critical thinking, physicians, and particularly residents, are prone to cognitive errors, which can lead to diagnostic errors, especially in a high-stakes environment such as the intensive care unit. Although challenging, critical thinking skills can be taught. At this time, there is a paucity of data to support an educational gold standard for teaching critical thinking, but we believe that five strategies, routed in cognitive theory and our personal teaching experiences, provide an effective framework to teach critical thinking in the intensive care unit. The five strategies are: make the thinking process explicit by helping learners understand that the brain uses two cognitive processes: type 1, an intuitive pattern-recognizing process, and type 2, an analytic process; discuss cognitive biases, such as premature closure, and teach residents to minimize biases by expressing uncertainty and keeping differentials broad; model and teach inductive reasoning by utilizing concept and mechanism maps and explicitly teach how this reasoning differs from the more commonly used hypothetico-deductive reasoning; use questions to stimulate critical thinking: "how" or "why" questions can be used to coach trainees and to uncover their thought processes; and assess and provide feedback on learner's critical thinking. We believe these five strategies provide practical approaches for teaching critical thinking in the intensive care unit.

  18. A GIS based spatially-explicit sensitivity and uncertainty analysis approach for multi-criteria decision analysis

    NASA Astrophysics Data System (ADS)

    Feizizadeh, Bakhtiar; Jankowski, Piotr; Blaschke, Thomas

    2014-03-01

    GIS multicriteria decision analysis (MCDA) techniques are increasingly used in landslide susceptibility mapping for the prediction of future hazards, land use planning, as well as for hazard preparedness. However, the uncertainties associated with MCDA techniques are inevitable and model outcomes are open to multiple types of uncertainty. In this paper, we present a systematic approach to uncertainty and sensitivity analysis. We access the uncertainty of landslide susceptibility maps produced with GIS-MCDA techniques. A new spatially-explicit approach and Dempster-Shafer Theory (DST) are employed to assess the uncertainties associated with two MCDA techniques, namely Analytical Hierarchical Process (AHP) and Ordered Weighted Averaging (OWA) implemented in GIS. The methodology is composed of three different phases. First, weights are computed to express the relative importance of factors (criteria) for landslide susceptibility. Next, the uncertainty and sensitivity of landslide susceptibility is analyzed as a function of weights using Monte Carlo Simulation and Global Sensitivity Analysis. Finally, the results are validated using a landslide inventory database and by applying DST. The comparisons of the obtained landslide susceptibility maps of both MCDA techniques with known landslides show that the AHP outperforms OWA. However, the OWA-generated landslide susceptibility map shows lower uncertainty than the AHP-generated map. The results demonstrate that further improvement in the accuracy of GIS-based MCDA can be achieved by employing an integrated uncertainty-sensitivity analysis approach, in which the uncertainty of landslide susceptibility model is decomposed and attributed to model's criteria weights.

  19. Critical Thinking in Critical Care: Five Strategies to Improve Teaching and Learning in the Intensive Care Unit

    PubMed Central

    Chatterjee, Souvik; Schwartzstein, Richard M.

    2017-01-01

    Critical thinking, the capacity to be deliberate about thinking, is increasingly the focus of undergraduate medical education, but is not commonly addressed in graduate medical education. Without critical thinking, physicians, and particularly residents, are prone to cognitive errors, which can lead to diagnostic errors, especially in a high-stakes environment such as the intensive care unit. Although challenging, critical thinking skills can be taught. At this time, there is a paucity of data to support an educational gold standard for teaching critical thinking, but we believe that five strategies, routed in cognitive theory and our personal teaching experiences, provide an effective framework to teach critical thinking in the intensive care unit. The five strategies are: make the thinking process explicit by helping learners understand that the brain uses two cognitive processes: type 1, an intuitive pattern-recognizing process, and type 2, an analytic process; discuss cognitive biases, such as premature closure, and teach residents to minimize biases by expressing uncertainty and keeping differentials broad; model and teach inductive reasoning by utilizing concept and mechanism maps and explicitly teach how this reasoning differs from the more commonly used hypothetico-deductive reasoning; use questions to stimulate critical thinking: “how” or “why” questions can be used to coach trainees and to uncover their thought processes; and assess and provide feedback on learner’s critical thinking. We believe these five strategies provide practical approaches for teaching critical thinking in the intensive care unit. PMID:28157389

  20. Explicit asymmetric bounds for robust stability of continuous and discrete-time systems

    NASA Technical Reports Server (NTRS)

    Gao, Zhiqiang; Antsaklis, Panos J.

    1993-01-01

    The problem of robust stability in linear systems with parametric uncertainties is considered. Explicit stability bounds on uncertain parameters are derived and expressed in terms of linear inequalities for continuous systems, and inequalities with quadratic terms for discrete-times systems. Cases where system parameters are nonlinear functions of an uncertainty are also examined.

  1. Iranian Pre-University Student's Retention of Collocations: Implicit Exposure or Explicit Instruction

    ERIC Educational Resources Information Center

    Gheisari, Nouzar; Yousofi, Nouroldin

    2016-01-01

    The effectiveness of different teaching methods of collocational expressions in ESL/EFL contexts of education has been a point of debate for more than two decades, with some believing in explicit and the others in implicit instruction of collocations. In this regard, the present study aimed at finding about which kind of instruction is more…

  2. Why love has wings and sex has not: how reminders of love and sex influence creative and analytic thinking.

    PubMed

    Förster, Jens; Epstude, Kai; Ozelsel, Amina

    2009-11-01

    This article examines cognitive links between romantic love and creativity and between sexual desire and analytic thought based on construal level theory. It suggests that when in love, people typically focus on a long-term perspective, which should enhance holistic thinking and thereby creative thought, whereas when experiencing sexual encounters, they focus on the present and on concrete details enhancing analytic thinking. Because people automatically activate these processing styles when in love or when they experience sex, subtle or even unconscious reminders of love versus sex should suffice to change processing modes. Two studies explicitly or subtly reminded participants of situations of love or sex and found support for this hypothesis.

  3. 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.

  4. A constitutive law for continuous fiber reinforced brittle matrix composites with fiber fragmentation and stress recovery

    NASA Astrophysics Data System (ADS)

    Neumeister, Jonas M.

    1993-08-01

    THE TENSILE BEHAVIOR of a brittle matrix composite is studied for post matrix crack saturation conditions. Scatter of fiber strength following the Weibull distribution as well as the influence of the major microstructural variables is considered. The stress in a fiber is assumed to recover linearly around a failure due to a fiber-matrix interface behavior mainly ruled by friction. The constitutive behavior for such a composite is analysed. Results are given for a simplified and a refined approximate description and compared with an analysis resulting from the exact analytical theory of fiber fragmentation. It is shown that the stress-strain relation for the refined model excellently follows the exact solution and gives the location of the maximum to within 1% in both stress and strain; for most materials the agreement is even better. Also it is shown that all relations can be normalized to depend on only two variables; a stress reference and the Weibull exponent. For systems with low scatter in fiber strength the simplified model is sufficient to determine the stress maximum but not the postcritical behavior. In addition, the simplified model gives explicit analytical expressions for the maximum stress and corresponding strain. None of the models contain any volume dependence or statistical scatter, but the maximum stress given by the stress-strain relation constitutes an upper bound for the ultimate tensile strength of the composite.

  5. Size-dependent nonlinear bending of micro/nano-beams made of nanoporous biomaterials including a refined truncated cube cell

    NASA Astrophysics Data System (ADS)

    Sahmani, S.; Aghdam, M. M.

    2017-12-01

    Morphology and pore size plays an essential role in the mechanical properties as well as the associated biological capability of a porous structure made of biomaterials. The objective of the current study is to predict the Young's modulus and Poisson's ratio of nanoporous biomaterials including refined truncated cube cells based on a hyperbolic shear deformable beam model. Analytical relationships for the mechanical properties of nanoporous biomaterials are given as a function of the refined cell's dimensions. After that, the size dependency in the nonlinear bending behavior of micro/nano-beams made of such nanoporous biomaterials is analyzed using the nonlocal strain gradient elasticity theory. It is assumed that the micro/nano-beam has one movable end under axial compression in conjunction with a uniform distributed lateral load. The Galerkin method together with an improved perturbation technique is employed to propose explicit analytical expression for nonlocal strain gradient load-deflection curves of the micro/nano-beams made of nanoporous biomaterials subjected to uniform transverse distributed load. It is found that through increment of the pore size, the micro/nano-beam will undergo much more deflection corresponding to a specific distributed load due to the reduction in the stiffness of nanoporous biomaterial. This pattern is more prominent for lower value of applied axial compressive load at the free end of micro/nano-beam.

  6. Local box-counting dimensions of discrete quantum eigenvalue spectra: Analytical connection to quantum spectral statistics

    NASA Astrophysics Data System (ADS)

    Sakhr, Jamal; Nieminen, John M.

    2018-03-01

    Two decades ago, Wang and Ong, [Phys. Rev. A 55, 1522 (1997)], 10.1103/PhysRevA.55.1522 hypothesized that the local box-counting dimension of a discrete quantum spectrum should depend exclusively on the nearest-neighbor spacing distribution (NNSD) of the spectrum. In this Rapid Communication, we validate their hypothesis by deriving an explicit formula for the local box-counting dimension of a countably-infinite discrete quantum spectrum. This formula expresses the local box-counting dimension of a spectrum in terms of single and double integrals of the NNSD of the spectrum. As applications, we derive an analytical formula for Poisson spectra and closed-form approximations to the local box-counting dimension for spectra having Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE), and Gaussian symplectic ensemble (GSE) spacing statistics. In the Poisson and GOE cases, we compare our theoretical formulas with the published numerical data of Wang and Ong and observe excellent agreement between their data and our theory. We also study numerically the local box-counting dimensions of the Riemann zeta function zeros and the alternate levels of GOE spectra, which are often used as numerical models of spectra possessing GUE and GSE spacing statistics, respectively. In each case, the corresponding theoretical formula is found to accurately describe the numerically computed local box-counting dimension.

  7. Explicitly represented polygon wall boundary model for the explicit MPS method

    NASA Astrophysics Data System (ADS)

    Mitsume, Naoto; Yoshimura, Shinobu; Murotani, Kohei; Yamada, Tomonori

    2015-05-01

    This study presents an accurate and robust boundary model, the explicitly represented polygon (ERP) wall boundary model, to treat arbitrarily shaped wall boundaries in the explicit moving particle simulation (E-MPS) method, which is a mesh-free particle method for strong form partial differential equations. The ERP model expresses wall boundaries as polygons, which are explicitly represented without using the distance function. These are derived so that for viscous fluids, and with less computational cost, they satisfy the Neumann boundary condition for the pressure and the slip/no-slip condition on the wall surface. The proposed model is verified and validated by comparing computed results with the theoretical solution, results obtained by other models, and experimental results. Two simulations with complex boundary movements are conducted to demonstrate the applicability of the E-MPS method to the ERP model.

  8. The explicit and implicit dance in psychoanalytic change.

    PubMed

    Fosshage, James L

    2004-02-01

    How the implicit/non-declarative and explicit/declarative cognitive domains interact is centrally important in the consideration of effecting change within the psychoanalytic arena. Stern et al. (1998) declare that long-lasting change occurs in the domain of implicit relational knowledge. In the view of this author, the implicit and explicit domains are intricately intertwined in an interactive dance within a psychoanalytic process. The author views that a spirit of inquiry (Lichtenberg, Lachmann & Fosshage 2002) serves as the foundation of the psychoanalytic process. Analyst and patient strive to explore, understand and communicate and, thereby, create a 'spirit' of interaction that contributes, through gradual incremental learning, to new implicit relational knowledge. This spirit, as part of the implicit relational interaction, is a cornerstone of the analytic relationship. The 'inquiry' more directly brings explicit/declarative processing to the foreground in the joint attempt to explore and understand. The spirit of inquiry in the psychoanalytic arena highlights both the autobiographical scenarios of the explicit memory system and the mental models of the implicit memory system as each contributes to a sense of self, other, and self with other. This process facilitates the extrication and suspension of the old models, so that new models based on current relational experience can be gradually integrated into both memory systems for lasting change.

  9. Explicit Analytical Solution of a Pendulum with Periodically Varying Length

    ERIC Educational Resources Information Center

    Yang, Tianzhi; Fang, Bo; Li, Song; Huang, Wenhu

    2010-01-01

    A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper,…

  10. Coherent control in simple quantum systems

    NASA Technical Reports Server (NTRS)

    Prants, Sergey V.

    1995-01-01

    Coherent dynamics of two, three, and four-level quantum systems, simultaneously driven by concurrent laser pulses of arbitrary and different forms, is treated by using a nonperturbative, group-theoretical approach. The respective evolution matrices are calculated in an explicit form. General aspects of controllability of few-level atoms by using laser fields are treated analytically.

  11. Linking climate change and fish conservation efforts using spatially explicit decision support tools

    Treesearch

    Douglas P. Peterson; Seth J. Wenger; Bruce E. Rieman; Daniel J. Isaak

    2013-01-01

    Fisheries professionals are increasingly tasked with incorporating climate change projections into their decisions. Here we demonstrate how a structured decision framework, coupled with analytical tools and spatial data sets, can help integrate climate and biological information to evaluate management alternatives. We present examples that link downscaled climate...

  12. The Impact of College Experiences on Conventional Career Logic

    ERIC Educational Resources Information Center

    Baumgardner, Steve R.

    1976-01-01

    The factors students consider in choosing a college major were scaled on an analytic-intuitive dimension. Differences in thinking orientation were found to be associated with students's sex, area of study, and year in school. Overall, the apparent lack of explicit rationality in student educational decisions appears to be adaptive. (Author)

  13. Assessing housing growth when census boundaries change

    Treesearch

    Alexandra D. Syphard; Susan I. Stewart; Jason McKeefry; Roger B. Hammer; Jeremy S. Fried; Sherry Holcomb; Volker C. Radeloff

    2009-01-01

    The US Census provides the primary source of spatially explicit social data, but changing block boundaries complicate analyses of housing growth over time. We compared procedures for reconciling housing density data between 1990 and 2000 census block boundaries in order to assess the sensitivity of analytical methods to estimates of housing growth in Oregon. Estimates...

  14. Performance Assessment in Serious Games: Compensating for the Effects of Randomness

    ERIC Educational Resources Information Center

    Westera, Wim

    2016-01-01

    This paper is about performance assessment in serious games. We conceive serious gaming as a process of player-lead decision taking. Starting from combinatorics and item-response theory we provide an analytical model that makes explicit to what extent observed player performances (decisions) are blurred by chance processes (guessing behaviors). We…

  15. Validating Grammaticality Judgment Tests: Evidence from Two New Psycholinguistic Measures

    ERIC Educational Resources Information Center

    Vafaee, Payman; Suzuki, Yuichi; Kachisnke, Ilina

    2017-01-01

    Several previous factor-analytic studies on the construct validity of grammaticality judgment tests (GJTs) concluded that untimed GJTs measure explicit knowledge (EK) and timed GJTs measure implicit knowledge (IK) (Bowles, 2011; R. Ellis, 2005; R. Ellis & Loewen, 2007). It has also been shown that, irrespective of the time condition chosen,…

  16. Metalinguistic Knowledge and Cognitive Style in Polish Classroom Learners of English

    ERIC Educational Resources Information Center

    Zietek, Agnieszka A.; Roehr, Karen

    2011-01-01

    In this exploratory study, we investigated the relationship between level of English metalinguistic knowledge, or explicit knowledge about the English language, and cognitive style on the wholist/analytic dimension in an intact group of young adult Polish learners of English as a foreign language. Contrary to expectation, metalinguistic knowledge…

  17. Sign(al)s: Living and Learning as Semiotic Engagement

    ERIC Educational Resources Information Center

    Stables, Andrew

    2006-01-01

    Cartesian mind-body dualism, while often explicitly denied, has left a legacy of conceptions that remain highly influential in education. I argue that trends in both analytic and continental philosophy of language point towards a post-Cartesian settlement in which the distinction between "signs" and "signals" is collapsed, and which thus construes…

  18. Constitutive Modelling and Deformation Band Angle Predictions for High Porosity Sandstones

    NASA Astrophysics Data System (ADS)

    Richards, M. C.; Issen, K. A.; Ingraham, M. D.

    2017-12-01

    The development of a field-scale deformation model requires a constitutive framework that is capable of representing known material behavior and able to be calibrated using available mechanical response data. This work employs the principle of hyperplasticity (e.g., Houlsby and Puzrin, 2006) to develop such a constitutive framework for high porosity sandstone. Adapting the works of Zimmerman et al. (1986) and Collins and Houlsby (1997), the mechanical data set of Ingraham et al. (2013 a, b) was used to develop a specific constitutive framework for Castlegate sandstone, a high porosity fluvial-deposited reservoir analog rock. Using the mechanical data set of Ingraham et al. (2013 a, b), explicit expressions and material parameters of the elastic moduli and strain tensors were obtained. With these expressions, analytical and numerical techniques were then employed to partition the total mechanical strain into elastic, coupled, and plastic strain components. With the partitioned strain data, yield surfaces in true-stress space, coefficients of internal friction, dilatancy factors, along with the theorectical predictions of the deformation band angles were obtained. These results were also evaluated against band angle values obtained from a) measurements on specimen jackets (Ingraham et al., 2013a), b) plane fits through located acoustic emissions (AE) events (Ingraham et al. 2013b), and c) X-ray micro-computed tomography (micro-CT) calculations.

  19. Phase transition and thermodynamic geometry of f (R ) AdS black holes in the grand canonical ensemble

    NASA Astrophysics Data System (ADS)

    Li, Gu-Qiang; Mo, Jie-Xiong

    2016-06-01

    The phase transition of a four-dimensional charged AdS black hole solution in the R +f (R ) gravity with constant curvature is investigated in the grand canonical ensemble, where we find novel characteristics quite different from that in the canonical ensemble. There exists no critical point for T -S curve while in former research critical point was found for both the T -S curve and T -r+ curve when the electric charge of f (R ) black holes is kept fixed. Moreover, we derive the explicit expression for the specific heat, the analog of volume expansion coefficient and isothermal compressibility coefficient when the electric potential of f (R ) AdS black hole is fixed. The specific heat CΦ encounters a divergence when 0 <Φ b . This finding also differs from the result in the canonical ensemble, where there may be two, one or no divergence points for the specific heat CQ . To examine the phase structure newly found in the grand canonical ensemble, we appeal to the well-known thermodynamic geometry tools and derive the analytic expressions for both the Weinhold scalar curvature and Ruppeiner scalar curvature. It is shown that they diverge exactly where the specific heat CΦ diverges.

  20. Forces Associated with Nonlinear Nonholonomic Constraint Equations

    NASA Technical Reports Server (NTRS)

    Roithmayr, Carlos M.; Hodges, Dewey H.

    2010-01-01

    A concise method has been formulated for identifying a set of forces needed to constrain the behavior of a mechanical system, modeled as a set of particles and rigid bodies, when it is subject to motion constraints described by nonholonomic equations that are inherently nonlinear in velocity. An expression in vector form is obtained for each force; a direction is determined, together with the point of application. This result is a consequence of expressing constraint equations in terms of dot products of vectors rather than in the usual way, which is entirely in terms of scalars and matrices. The constraint forces in vector form are used together with two new analytical approaches for deriving equations governing motion of a system subject to such constraints. If constraint forces are of interest they can be brought into evidence in explicit dynamical equations by employing the well-known nonholonomic partial velocities associated with Kane's method; if they are not of interest, equations can be formed instead with the aid of vectors introduced here as nonholonomic partial accelerations. When the analyst requires only the latter, smaller set of equations, they can be formed directly; it is not necessary to expend the labor to form the former, larger set first and subsequently perform matrix multiplications.

  1. Flat bases of invariant polynomials and P-matrices of E{sub 7} and E{sub 8}

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

    Talamini, Vittorino

    2010-02-15

    Let G be a compact group of linear transformations of a Euclidean space V. The G-invariant C{sup {infinity}} functions can be expressed as C{sup {infinity}} functions of a finite basic set of G-invariant homogeneous polynomials, sometimes called an integrity basis. The mathematical description of the orbit space V/G depends on the integrity basis too: it is realized through polynomial equations and inequalities expressing rank and positive semidefiniteness conditions of the P-matrix, a real symmetric matrix determined by the integrity basis. The choice of the basic set of G-invariant homogeneous polynomials forming an integrity basis is not unique, so it ismore » not unique the mathematical description of the orbit space too. If G is an irreducible finite reflection group, Saito et al. [Commun. Algebra 8, 373 (1980)] characterized some special basic sets of G-invariant homogeneous polynomials that they called flat. They also found explicitly the flat basic sets of invariant homogeneous polynomials of all the irreducible finite reflection groups except of the two largest groups E{sub 7} and E{sub 8}. In this paper the flat basic sets of invariant homogeneous polynomials of E{sub 7} and E{sub 8} and the corresponding P-matrices are determined explicitly. Using the results here reported one is able to determine easily the P-matrices corresponding to any other integrity basis of E{sub 7} or E{sub 8}. From the P-matrices one may then write down the equations and inequalities defining the orbit spaces of E{sub 7} and E{sub 8} relatively to a flat basis or to any other integrity basis. The results here obtained may be employed concretely to study analytically the symmetry breaking in all theories where the symmetry group is one of the finite reflection groups E{sub 7} and E{sub 8} or one of the Lie groups E{sub 7} and E{sub 8} in their adjoint representations.« less

  2. A Framework for Integrating Environmental Justice in Regulatory Analysis

    PubMed Central

    Nweke, Onyemaechi C.

    2011-01-01

    With increased interest in integrating environmental justice into the process for developing environmental regulations in the United States, analysts and decision makers are confronted with the question of what methods and data can be used to assess disproportionate environmental health impacts. However, as a first step to identifying data and methods, it is important that analysts understand what information on equity impacts is needed for decision making. Such knowledge originates from clearly stated equity objectives and the reflection of those objectives throughout the analytical activities that characterize Regulatory Impact Analysis (RIA), a process that is traditionally used to inform decision making. The framework proposed in this paper advocates structuring analyses to explicitly provide pre-defined output on equity impacts. Specifically, the proposed framework emphasizes: (a) defining equity objectives for the proposed regulatory action at the onset of the regulatory process, (b) identifying specific and related sub-objectives for key analytical steps in the RIA process, and (c) developing explicit analytical/research questions to assure that stated sub-objectives and objectives are met. In proposing this framework, it is envisioned that information on equity impacts informs decision-making in regulatory development, and that this is achieved through a systematic and consistent approach that assures linkages between stated equity objectives, regulatory analyses, selection of policy options, and the design of compliance and enforcement activities. PMID:21776235

  3. First-order analytic propagation of satellites in the exponential atmosphere of an oblate planet

    NASA Astrophysics Data System (ADS)

    Martinusi, Vladimir; Dell'Elce, Lamberto; Kerschen, Gaëtan

    2017-04-01

    The paper offers the fully analytic solution to the motion of a satellite orbiting under the influence of the two major perturbations, due to the oblateness and the atmospheric drag. The solution is presented in a time-explicit form, and takes into account an exponential distribution of the atmospheric density, an assumption that is reasonably close to reality. The approach involves two essential steps. The first one concerns a new approximate mathematical model that admits a closed-form solution with respect to a set of new variables. The second step is the determination of an infinitesimal contact transformation that allows to navigate between the new and the original variables. This contact transformation is obtained in exact form, and afterwards a Taylor series approximation is proposed in order to make all the computations explicit. The aforementioned transformation accommodates both perturbations, improving the accuracy of the orbit predictions by one order of magnitude with respect to the case when the atmospheric drag is absent from the transformation. Numerical simulations are performed for a low Earth orbit starting at an altitude of 350 km, and they show that the incorporation of drag terms into the contact transformation generates an error reduction by a factor of 7 in the position vector. The proposed method aims at improving the accuracy of analytic orbit propagation and transforming it into a viable alternative to the computationally intensive numerical methods.

  4. Can We Distinguish Emotions from Faces? Investigation of Implicit and Explicit Processes of Peak Facial Expressions.

    PubMed

    Xiao, Ruiqi; Li, Xianchun; Li, Lin; Wang, Yanmei

    2016-01-01

    Most previous studies on facial expression recognition have focused on the moderate emotions; to date, few studies have been conducted to investigate the explicit and implicit processes of peak emotions. In the current study, we used transiently peak intense expression images of athletes at the winning or losing point in competition as materials, and investigated the diagnosability of peak facial expressions at both implicit and explicit levels. In Experiment 1, participants were instructed to evaluate isolated faces, isolated bodies, and the face-body compounds, and eye-tracking movement was recorded. The results revealed that the isolated body and face-body congruent images were better recognized than isolated face and face-body incongruent images, indicating that the emotional information conveyed by facial cues was ambiguous, and the body cues influenced facial emotion recognition. Furthermore, eye movement records showed that the participants displayed distinct gaze patterns for the congruent and incongruent compounds. In Experiment 2A, the subliminal affective priming task was used, with faces as primes and bodies as targets, to investigate the unconscious emotion perception of peak facial expressions. The results showed that winning face prime facilitated reaction to winning body target, whereas losing face prime inhibited reaction to winning body target, suggesting that peak facial expressions could be perceived at the implicit level. In general, the results indicate that peak facial expressions cannot be consciously recognized but can be perceived at the unconscious level. In Experiment 2B, revised subliminal affective priming task and a strict awareness test were used to examine the validity of unconscious perception of peak facial expressions found in Experiment 2A. Results of Experiment 2B showed that reaction time to both winning body targets and losing body targets was influenced by the invisibly peak facial expression primes, which indicated the unconscious perception of peak facial expressions.

  5. Can We Distinguish Emotions from Faces? Investigation of Implicit and Explicit Processes of Peak Facial Expressions

    PubMed Central

    Xiao, Ruiqi; Li, Xianchun; Li, Lin; Wang, Yanmei

    2016-01-01

    Most previous studies on facial expression recognition have focused on the moderate emotions; to date, few studies have been conducted to investigate the explicit and implicit processes of peak emotions. In the current study, we used transiently peak intense expression images of athletes at the winning or losing point in competition as materials, and investigated the diagnosability of peak facial expressions at both implicit and explicit levels. In Experiment 1, participants were instructed to evaluate isolated faces, isolated bodies, and the face-body compounds, and eye-tracking movement was recorded. The results revealed that the isolated body and face-body congruent images were better recognized than isolated face and face-body incongruent images, indicating that the emotional information conveyed by facial cues was ambiguous, and the body cues influenced facial emotion recognition. Furthermore, eye movement records showed that the participants displayed distinct gaze patterns for the congruent and incongruent compounds. In Experiment 2A, the subliminal affective priming task was used, with faces as primes and bodies as targets, to investigate the unconscious emotion perception of peak facial expressions. The results showed that winning face prime facilitated reaction to winning body target, whereas losing face prime inhibited reaction to winning body target, suggesting that peak facial expressions could be perceived at the implicit level. In general, the results indicate that peak facial expressions cannot be consciously recognized but can be perceived at the unconscious level. In Experiment 2B, revised subliminal affective priming task and a strict awareness test were used to examine the validity of unconscious perception of peak facial expressions found in Experiment 2A. Results of Experiment 2B showed that reaction time to both winning body targets and losing body targets was influenced by the invisibly peak facial expression primes, which indicated the unconscious perception of peak facial expressions. PMID:27630604

  6. An Analytical Model for Two-Order Asperity Degradation of Rock Joints Under Constant Normal Stiffness Conditions

    NASA Astrophysics Data System (ADS)

    Li, Yingchun; Wu, Wei; Li, Bo

    2018-05-01

    Jointed rock masses during underground excavation are commonly located under the constant normal stiffness (CNS) condition. This paper presents an analytical formulation to predict the shear behaviour of rough rock joints under the CNS condition. The dilatancy and deterioration of two-order asperities are quantified by considering the variation of normal stress. We separately consider the dilation angles of waviness and unevenness, which decrease to zero as the normal stress approaches the transitional stress. The sinusoidal function naturally yields the decay of dilation angle as a function of relative normal stress. We assume that the magnitude of transitional stress is proportionate to the square root of asperity geometric area. The comparison between the analytical prediction and experimental data shows the reliability of the analytical model. All the parameters involved in the analytical model possess explicit physical meanings and are measurable from laboratory tests. The proposed model is potentially practicable for assessing the stability of underground structures at various field scales.

  7. Boundary enhanced effects on the existence of quadratic solitons

    NASA Astrophysics Data System (ADS)

    Chen, Manna; Zhang, Ting; Li, Wenjie; Lu, Daquan; Guo, Qi; Hu, Wei

    2018-05-01

    We investigate, both analytically and numerically, the boundary enhanced effects exerted on the quadratic solitons consisting of fundamental waves and oscillatory second harmonics in the presence of boundary conditions. The nonlocal analogy predicts that the soliton for fundamental wave is supported by the balance between equivalent nonlinear confinement and diffraction (or dispersion). Under Snyder and Mitchell's strongly nonlocal approximation, we obtain the analytical soliton solutions both with and without the boundary conditions to show the impact of boundary conditions. We can distinguish explicitly the nonlinear confinement between the second harmonic mutual interaction and the enhanced effects caused by remote boundaries. Those boundary enhanced effects on the existence of solitons can be positive or negative, which depend on both sample size and nonlocal parameter. The piecewise existence regime of solitons can be explained analytically. The analytical soliton solutions are verified by the numerical ones and the discrepancy between them is also discussed.

  8. What values in design? The challenge of incorporating moral values into design.

    PubMed

    Manders-Huits, Noëmi

    2011-06-01

    Recently, there is increased attention to the integration of moral values into the conception, design, and development of emerging IT. The most reviewed approach for this purpose in ethics and technology so far is Value-Sensitive Design (VSD). This article considers VSD as the prime candidate for implementing normative considerations into design. Its methodology is considered from a conceptual, analytical, normative perspective. The focus here is on the suitability of VSD for integrating moral values into the design of technologies in a way that joins in with an analytical perspective on ethics of technology. Despite its promising character, it turns out that VSD falls short in several respects: (1) VSD does not have a clear methodology for identifying stakeholders, (2) the integration of empirical methods with conceptual research within the methodology of VSD is obscure, (3) VSD runs the risk of committing the naturalistic fallacy when using empirical knowledge for implementing values in design, (4) the concept of values, as well as their realization, is left undetermined and (5) VSD lacks a complimentary or explicit ethical theory for dealing with value trade-offs. For the normative evaluation of a technology, I claim that an explicit and justified ethical starting point or principle is required. Moreover, explicit attention should be given to the value aims and assumptions of a particular design. The criteria of adequacy for such an approach or methodology follow from the evaluation of VSD as the prime candidate for implementing moral values in design.

  9. The Association Between Implicit and Explicit Attitudes Toward Smoking and Support for Tobacco Control Measures

    PubMed Central

    Chassin, Laurie; Presson, Clark C.

    2013-01-01

    Introduction: This study examined the association between implicit and explicit attitudes toward smoking and support for tobacco control policies. Methods: Participants were from an ongoing longitudinal study of the natural history of smoking who also completed a web-based assessment of implicit attitudes toward smoking (N = 1,337). Multiple regression was used to test the association between covariates (sex, age, educational attainment, parent status, and smoking status), implicit attitude toward smoking, and explicit attitude toward smoking and support for tobacco control policies. The moderating effect of the covariates on the relation between attitudes and support for policies was also tested. Results: Females, those with higher educational attainment, parents, and nonsmokers expressed more support for tobacco control policy measures. For nonsmokers, only explicit attitude was significantly associated with support for policies. For smokers, both explicit and implicit attitudes were significantly associated with support. The effect of explicit attitude was stronger for those with lower educational attainment. Conclusions: Both explicit and implicit smoking attitudes are important for building support for tobacco control policies, particularly among smokers. More research is needed on how to influence explicit and implicit attitudes to inform policy advocacy campaigns. PMID:22581941

  10. The association between implicit and explicit attitudes toward smoking and support for tobacco control measures.

    PubMed

    Macy, Jonathan T; Chassin, Laurie; Presson, Clark C

    2013-01-01

    This study examined the association between implicit and explicit attitudes toward smoking and support for tobacco control policies. Participants were from an ongoing longitudinal study of the natural history of smoking who also completed a web-based assessment of implicit attitudes toward smoking (N = 1,337). Multiple regression was used to test the association between covariates (sex, age, educational attainment, parent status, and smoking status), implicit attitude toward smoking, and explicit attitude toward smoking and support for tobacco control policies. The moderating effect of the covariates on the relation between attitudes and support for policies was also tested. Females, those with higher educational attainment, parents, and nonsmokers expressed more support for tobacco control policy measures. For nonsmokers, only explicit attitude was significantly associated with support for policies. For smokers, both explicit and implicit attitudes were significantly associated with support. The effect of explicit attitude was stronger for those with lower educational attainment. Both explicit and implicit smoking attitudes are important for building support for tobacco control policies, particularly among smokers. More research is needed on how to influence explicit and implicit attitudes to inform policy advocacy campaigns.

  11. Q-controlled amplitude modulation atomic force microscopy in liquids: An analysis

    NASA Astrophysics Data System (ADS)

    Hölscher, H.; Schwarz, U. D.

    2006-08-01

    An analysis of amplitude modulation atomic force microscopy in liquids is presented with respect to the application of the Q-Control technique. The equation of motion is solved by numerical and analytic methods with and without Q-Control in the presence of a simple model interaction force adequate for many liquid environments. In addition, the authors give an explicit analytical formula for the tip-sample indentation showing that higher Q factors reduce the tip-sample force. It is found that Q-Control suppresses unwanted deformations of the sample surface, leading to the enhanced image quality reported in several experimental studies.

  12. Analytical formulation of selected activities of the remote manipulator system

    NASA Technical Reports Server (NTRS)

    Zimmerman, K. J.

    1977-01-01

    Existing analysis of Orbiter-RMS-Payload kinematics were surveyed, including equations dealing with the two body kinematics in the presence of a massless RMS and compares analytical explicit solutions with numerical solutions. For the following operational phases of the RMS numerical demonstration, problems are provided: (1) payload capture; (2) payload stowage and removal from cargo bay; and (3) payload deployment. The equation of motion provided accounted for RMS control forces and torque moments and could be extended to RMS flexibility and control loop simulation without increasing the degrees of freedom of the two body system.

  13. Front-form spinors in the Weinberg-Soper formalism and generalized Melosh transformations for any spin

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

    Ahluwalia, D.V.; Sawicki, M.

    Using the Weinberg-Soper formalism we construct the front-form ([ital j],0)[direct sum](0,[ital j]) spinors. Explicit expressions for the generalized Melosh transformations up to spin two are obtained. The formalism, without explicitly invoking any wave equations, reproduces the spin-1/2 front-form results of Melosh, Lepage and Brodsky, and Dziembowski.

  14. Emotion regulation and mania risk: Differential responses to implicit and explicit cues to regulate.

    PubMed

    Ajaya, Yatrika; Peckham, Andrew D; Johnson, Sheri L

    2016-03-01

    People prone to mania use emotion regulation (ER) strategies well when explicitly coached to do so in laboratory settings, but they find these strategies ineffective in daily life. We hypothesized that, compared with control participants, mania-prone people would show ER deficits when they received implicit, but not explicit, cues to use ER. Undergraduates (N = 66) completed the Hypomanic Personality Scale (HPS) and were randomly assigned to one of three experimental conditions: automatic ER (scrambled sentence primes), deliberate ER (verbal instructions), or control (no priming or instructions to use ER). Then, participants played a videogame designed to evoke anger. Emotion responses were measured with a multi-modal assessment of self-reported affect, psychophysiology, and facial expressions. Respiratory sinus arrhythmia (RSA) was used to index ER. The videogame effectively elicited subjective anger, angry facial expressions, and heart rate increases when keys malfunctioned. As hypothesized, persons who were more mania prone showed greater RSA increases in the deliberate ER condition than in the automatic or control conditions. One potential limitation is the use of an analog sample. Findings suggest that those at risk for mania require more explicit instruction to engage ER effectively. Copyright © 2015 Elsevier Ltd. All rights reserved.

  15. Learning to Express Gratitude in Mandarin Chinese through Web-Based Instruction

    ERIC Educational Resources Information Center

    Yang, Li

    2016-01-01

    This study explored the effectiveness of a self-access website as a tool to teach expressions of gratitude to learners of Mandarin Chinese. The web-based instruction included explicit instruction on how to express gratitude appropriately in Mandarin and various consciousness-raising exercises/activities. Two groups of learners who differed in…

  16. Moments from Cumulants and Vice Versa

    ERIC Educational Resources Information Center

    Withers, Christopher S.; Nadarajah, Saralees

    2009-01-01

    Moments and cumulants are expressed in terms of each other using Bell polynomials. Inbuilt routines for the latter make these expressions amenable to use by algebraic manipulation programs. One of the four formulas given is an explicit version of Kendall's use of Faa di Bruno's chain rule to express cumulants in terms of moments.

  17. Effects of task demands on the early neural processing of fearful and happy facial expressions

    PubMed Central

    Itier, Roxane J.; Neath-Tavares, Karly N.

    2017-01-01

    Task demands shape how we process environmental stimuli but their impact on the early neural processing of facial expressions remains unclear. In a within-subject design, ERPs were recorded to the same fearful, happy and neutral facial expressions presented during a gender discrimination, an explicit emotion discrimination and an oddball detection tasks, the most studied tasks in the field. Using an eye tracker, fixation on the face nose was enforced using a gaze-contingent presentation. Task demands modulated amplitudes from 200–350ms at occipito-temporal sites spanning the EPN component. Amplitudes were more negative for fearful than neutral expressions starting on N170 from 150–350ms, with a temporo-occipital distribution, whereas no clear effect of happy expressions was seen. Task and emotion effects never interacted in any time window or for the ERP components analyzed (P1, N170, EPN). Thus, whether emotion is explicitly discriminated or irrelevant for the task at hand, neural correlates of fearful and happy facial expressions seem immune to these task demands during the first 350ms of visual processing. PMID:28315309

  18. The wire optical test: a thorough analytical study in and out of caustic surface, and advantages of a dynamical adaptation

    NASA Astrophysics Data System (ADS)

    Alejandro Juárez-Reyes, Salvador; Sosa-Sánchez, Citlalli Teresa; Silva-Ortigoza, Gilberto; de Jesús Cabrera-Rosas, Omar; Espíndola-Ramos, Ernesto; Ortega-Vidals, Paula

    2018-03-01

    Among the best known non-interferometric optical tests are the wire test, the Foucault test and Ronchi test with a low frequency grating. Since the wire test is the seed to understand the other ones, the aim of the present work is to do a thorough study of this test for a lens with symmetry of revolution and to do this study for any configuration of the object and detection planes where both planes could intersect: two, one or no branches of the caustic region (including the marginal and paraxial foci). To this end, we calculated the vectorial representation for the caustic region, and we found the analytical expression for the pattern; we report that the analytical pattern explicitly depends on the magnitude of a branch of the caustic. With the analytical pattern we computed a set of simulations of a dynamical adaptation of the optical wire test. From those simulations, we have done a thorough analysis of the topological structure of the pattern; so we explain how the multiple image formation process and the image collapse process take place for each configuration, in particular, when both the wire and the detection planes are placed inside the caustic region, which has not been studied before. For the first time, we remark that not only the intersections of the object and detection planes with the caustic are important in the change of pattern topology; but also the projection of the intersection between the caustic and the object plane mapped onto the detection plane; and the virtual projection of the intersection between the caustic and the detection plane mapped onto the object plane. We present that for the new configurations of the optical system, the wire image is curves of the Tschirnhausen’s cubic, the piriform and the deformed eight-curve types.

  19. Precipitate shape fitting and reconstruction by means of 3D Zernike functions

    NASA Astrophysics Data System (ADS)

    Callahan, P. G.; De Graef, M.

    2012-01-01

    3D Zernike functions are defined and used for the reconstruction of precipitate shapes. These functions are orthogonal over the unit ball and allow for an arbitrary shape, scaled to fit inside an embedding sphere, to be decomposed into 3D harmonics. Explicit expressions are given for the general Zernike moments, correcting typographical errors in the literature. Explicit expressions of the Zernike moments for the ellipsoid and the cube are given. The 3D Zernike functions and moments are applied to the reconstruction of γ' precipitate shapes in two Ni-based superalloys, one with nearly cuboidal precipitate shapes, and one with more complex dendritic shapes.

  20. Evaluation of algorithms for point cloud surface reconstruction through the analysis of shape parameters

    NASA Astrophysics Data System (ADS)

    Cao, Lu; Verbeek, Fons J.

    2012-03-01

    In computer graphics and visualization, reconstruction of a 3D surface from a point cloud is an important research area. As the surface contains information that can be measured, i.e. expressed in features, the application of surface reconstruction can be potentially important for application in bio-imaging. Opportunities in this application area are the motivation for this study. In the past decade, a number of algorithms for surface reconstruction have been proposed. Generally speaking, these methods can be separated into two categories: i.e., explicit representation and implicit approximation. Most of the aforementioned methods are firmly based in theory; however, so far, no analytical evaluation between these methods has been presented. The straightforward way of evaluation has been by convincing through visual inspection. Through evaluation we search for a method that can precisely preserve the surface characteristics and that is robust in the presence of noise. The outcome will be used to improve reliability in surface reconstruction of biological models. We, therefore, use an analytical approach by selecting features as surface descriptors and measure these features in varying conditions. We selected surface distance, surface area and surface curvature as three major features to compare quality of the surface created by the different algorithms. Our starting point has been ground truth values obtained from analytical shapes such as the sphere and the ellipsoid. In this paper we present four classical surface reconstruction methods from the two categories mentioned above, i.e. the Power Crust, the Robust Cocone, the Fourier-based method and the Poisson reconstruction method. The results obtained from our experiments indicate that Poisson reconstruction method performs the best in the presence of noise.

  1. Multi-model predictive control based on LMI: from the adaptation of the state-space model to the analytic description of the control law

    NASA Astrophysics Data System (ADS)

    Falugi, P.; Olaru, S.; Dumur, D.

    2010-08-01

    This article proposes an explicit robust predictive control solution based on linear matrix inequalities (LMIs). The considered predictive control strategy uses different local descriptions of the system dynamics and uncertainties and thus allows the handling of less conservative input constraints. The computed control law guarantees constraint satisfaction and asymptotic stability. The technique is effective for a class of nonlinear systems embedded into polytopic models. A detailed discussion of the procedures which adapt the partition of the state space is presented. For the practical implementation the construction of suitable (explicit) descriptions of the control law are described upon concrete algorithms.

  2. An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems.

    PubMed

    Joyce, Duncan; Parnell, William J; Assier, Raphaël C; Abrahams, I David

    2017-05-01

    In Parnell & Abrahams (2008 Proc. R. Soc. A 464 , 1461-1482. (doi:10.1098/rspa.2007.0254)), a homogenization scheme was developed that gave rise to explicit forms for the effective antiplane shear moduli of a periodic unidirectional fibre-reinforced medium where fibres have non-circular cross section. The explicit expressions are rational functions in the volume fraction. In that scheme, a (non-dilute) approximation was invoked to determine leading-order expressions. Agreement with existing methods was shown to be good except at very high volume fractions. Here, the theory is extended in order to determine higher-order terms in the expansion. Explicit expressions for effective properties can be derived for fibres with non-circular cross section, without recourse to numerical methods. Terms appearing in the expressions are identified as being associated with the lattice geometry of the periodic fibre distribution, fibre cross-sectional shape and host/fibre material properties. Results are derived in the context of antiplane elasticity but the analogy with the potential problem illustrates the broad applicability of the method to, e.g. thermal, electrostatic and magnetostatic problems. The efficacy of the scheme is illustrated by comparison with the well-established method of asymptotic homogenization where for fibres of general cross section, the associated cell problem must be solved by some computational scheme.

  3. An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems

    PubMed Central

    Joyce, Duncan

    2017-01-01

    In Parnell & Abrahams (2008 Proc. R. Soc. A 464, 1461–1482. (doi:10.1098/rspa.2007.0254)), a homogenization scheme was developed that gave rise to explicit forms for the effective antiplane shear moduli of a periodic unidirectional fibre-reinforced medium where fibres have non-circular cross section. The explicit expressions are rational functions in the volume fraction. In that scheme, a (non-dilute) approximation was invoked to determine leading-order expressions. Agreement with existing methods was shown to be good except at very high volume fractions. Here, the theory is extended in order to determine higher-order terms in the expansion. Explicit expressions for effective properties can be derived for fibres with non-circular cross section, without recourse to numerical methods. Terms appearing in the expressions are identified as being associated with the lattice geometry of the periodic fibre distribution, fibre cross-sectional shape and host/fibre material properties. Results are derived in the context of antiplane elasticity but the analogy with the potential problem illustrates the broad applicability of the method to, e.g. thermal, electrostatic and magnetostatic problems. The efficacy of the scheme is illustrated by comparison with the well-established method of asymptotic homogenization where for fibres of general cross section, the associated cell problem must be solved by some computational scheme. PMID:28588412

  4. Explicit robust schemes for implementation of a class of principal value-based constitutive models: Symbolic and numeric implementation

    NASA Technical Reports Server (NTRS)

    Arnold, S. M.; Saleeb, A. F.; Tan, H. Q.; Zhang, Y.

    1993-01-01

    The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, special purpose functions (running under MACSYMA) are developed for the symbolic derivation, evaluation, and automatic FORTRAN code generation of explicit expressions for the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid over the entire deformation range, since the singularities resulting from repeated principal-stretch values have been theoretically removed. The required computational algorithms are outlined, and the resulting FORTRAN computer code is presented.

  5. An analytical fuzzy-based approach to ?-gain optimal control of input-affine nonlinear systems using Newton-type algorithm

    NASA Astrophysics Data System (ADS)

    Milic, Vladimir; Kasac, Josip; Novakovic, Branko

    2015-10-01

    This paper is concerned with ?-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone-Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for ?-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton's method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.

  6. Opening up the Profession: Inclusive Messages for Pre-Service Teachers from a Pedagogy Textbook

    ERIC Educational Resources Information Center

    Brass, Amber

    2016-01-01

    Textbooks are a ubiquitous part of classrooms in all levels of education. Whilst textbooks used in tertiary content subjects have been examined in several studies, research focused on textbooks used in mathematics pedagogy subjects is scarce. Using a discourse analytic framework, this paper presents data about the implicit and explicit messages…

  7. Handling Errors as They Arise in Whole-Class Interactions

    ERIC Educational Resources Information Center

    Ingram, Jenni; Pitt, Andrea; Baldry, Fay

    2015-01-01

    There has been a long history of research into errors and their role in the teaching and learning of mathematics. This research has led to a change to pedagogical recommendations from avoiding errors to explicitly using them in lessons. In this study, 22 mathematics lessons were video-recorded and transcribed. A conversation analytic (CA) approach…

  8. Adding uncertainty to forest inventory plot locations: effects on analyses using geospatial data

    Treesearch

    Alexia A. Sabor; Volker C. Radeloff; Ronald E. McRoberts; Murray Clayton; Susan I. Stewart

    2007-01-01

    The Forest Inventory and Analysis (FIA) program of the USDA Forest Service alters plot locations before releasing data to the public to ensure landowner confidentiality and sample integrity, but using data with altered plot locations in conjunction with other spatially explicit data layers produces analytical results with unknown amounts of error. We calculated the...

  9. The Dispersion Relation for the 1/sinh(exp 2) Potential in the Classical Limit

    NASA Technical Reports Server (NTRS)

    Campbell, Joel

    2009-01-01

    The dispersion relation for the inverse hyperbolic potential is calculated in the classical limit. This is shown for both the low amplitude phonon branch and the high amplitude soliton branch. It is shown these results qualitatively follow that previously found for the inverse squared potential where explicit analytic solutions are known.

  10. Something to sink your teeth into: The presence of teeth augments ERPs to mouth expressions.

    PubMed

    daSilva, Elizabeth B; Crager, Kirsten; Geisler, Danika; Newbern, Powell; Orem, Benjamin; Puce, Aina

    2016-02-15

    If the whites of the sclera can impact neural processing of eye expressions (Hardee, Thompson, & Puce, 2008; Whalen et al., 1998), do seen teeth affect neural responses to mouth expressions? Twenty participants (10 females; ages 22-31) viewed avatar mouth images depicting grimaces, smiles and open mouth expressions that were presented with and without teeth. A continuous 256 channel electroencephalogram (EEG) was recorded while subjects completed two tasks: an implicit task evaluating stimulus color and an explicit task evaluating mouth expression valence. Event related potential (ERP) peak amplitudes and latencies and area under the curve (AUC) were measured in individual subject averaged ERPs. Statistical testing revealed a main effect of the presence of Teeth for P100, N170, and vertex positive potential (VPP) amplitudes and for slow positive wave (SPW) AUC. Task by teeth interactions occurred for P250 amplitude, underscoring how explicit task demands can influence neural processing. Arousal ratings co-varied with teeth presence, suggesting that low-level visual features such as teeth may drive the saliency of emotional expressions, and lie at the core of differences in neural processing to different emotional expressions. Copyright © 2015 Elsevier Inc. All rights reserved.

  11. Analytic representations of mK , FK, mη, and Fη in two loop S U (3 ) chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Ananthanarayan, B.; Bijnens, Johan; Friot, Samuel; Ghosh, Shayan

    2018-06-01

    In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in S U (3 ) chiral perturbation theory. These involve sunset diagrams and their derivatives evaluated at p2=mP2 (P =π , K , η ). Recalling that there are three mass scales in this theory, mπ, mK and mη, there are instances when the finite part of the sunset diagrams do not admit an expression in terms of elementary functions, and have therefore been evaluated numerically in the past. In a recent publication, an expansion in the external momentum was performed to obtain approximate analytic expressions for mπ and Fπ, the pion mass and decay constant. We provide fully analytic exact expressions for mK and mη, the kaon and eta masses, and FK and Fη, the kaon and eta decay constants. These expressions, calculated using Mellin-Barnes methods, are in the form of double series in terms of two mass ratios. A numerical analysis of the results to evaluate the relative size of contributions coming from loops, chiral logarithms as well as phenomenological low-energy constants is presented. We also present a set of approximate analytic expressions for mK, FK, mη and Fη that facilitate comparisons with lattice results. Finally, we show how exact analytic expressions for mπ and Fπ may be obtained, the latter having been used in conjunction with the results for FK to produce a recently published analytic representation of FK/Fπ.

  12. Complex eigenvalue analysis of rotating structures

    NASA Technical Reports Server (NTRS)

    Patel, J. S.; Seltzer, S. M.

    1972-01-01

    A FORTRAN subroutine to NASTRAN which constructs coriolis and centripetal acceleration matrices, and a centrifugal load vector due to spin about a selected point or about the mass center of the structure is discussed. The rigid translational degrees of freedom can be removed by using a transformation matrix T and its explicitly given inverse. These matrices are generated in the subroutine and their explicit expressions are given.

  13. The Impact of a Systematic and Explicit Vocabulary Intervention in Spanish with Spanish-Speaking English Learners in First Grade

    ERIC Educational Resources Information Center

    Cena, Johanna; Baker, Doris Luft; Kame'enui, Edward J.; Baker, Scott K.; Park, Yonghan; Smolkowski, Keith

    2013-01-01

    This study examined the impact of a 15-min daily explicit vocabulary intervention in Spanish on expressive and receptive vocabulary knowledge and oral reading fluency in Spanish, and on language proficiency in English. Fifty Spanish-speaking English learners who received 90 min of Spanish reading instruction in an early transition model were…

  14. Differential Fairness Decisions and Brain Responses after Expressed Emotions of Others in Boys with Autism Spectrum Disorders

    ERIC Educational Resources Information Center

    Klapwijk, Eduard T.; Aghajani, Moji; Lelieveld, Gert-Jan; van Lang, Natasja D. J.; Popma, Arne; van der Wee, Nic J. A.; Colins, Olivier F.; Vermeiren, Robert R. J. M.

    2017-01-01

    Little is known about how emotions expressed by others influence social decisions and associated brain responses in autism spectrum disorders (ASD). We investigated the neural mechanisms underlying fairness decisions in response to explicitly expressed emotions of others in boys with ASD and typically developing (TD) boys. Participants with ASD…

  15. Dimensional transitions in thermodynamic properties of ideal Maxwell-Boltzmann gases

    NASA Astrophysics Data System (ADS)

    Aydin, Alhun; Sisman, Altug

    2015-04-01

    An ideal Maxwell-Boltzmann gas confined in various rectangular nanodomains is considered under quantum size effects. Thermodynamic quantities are calculated from their relations with the partition function, which consists of triple infinite summations over momentum states in each direction. To obtain analytical expressions, summations are converted to integrals for macrosystems by a continuum approximation, which fails at the nanoscale. To avoid both the numerical calculation of summations and the failure of their integral approximations at the nanoscale, a method which gives an analytical expression for a single particle partition function (SPPF) is proposed. It is shown that a dimensional transition in momentum space occurs at a certain magnitude of confinement. Therefore, to represent the SPPF by lower-dimensional analytical expressions becomes possible, rather than numerical calculation of summations. Considering rectangular domains with different aspect ratios, a comparison of the results of derived expressions with those of summation forms of the SPPF is made. It is shown that analytical expressions for the SPPF give very precise results with maximum relative errors of around 1%, 2% and 3% at exactly the transition point for single, double and triple transitions, respectively. Based on dimensional transitions, expressions for free energy, entropy, internal energy, chemical potential, heat capacity and pressure are given analytically valid for any scale.

  16. White and Black American Children’s Implicit Intergroup Bias

    PubMed Central

    Newheiser, Anna-Kaisa; Olson, Kristina R.

    2011-01-01

    Despite a decline in explicit prejudice, adults and children from majority groups (e.g., White Americans) often express bias implicitly, as assessed by the Implicit Association Test. In contrast, minority-group (e.g., Black American) adults on average show no bias on the IAT. In the present research, representing the first empirical investigation of whether Black children’s IAT responses parallel those of Black adults, we examined implicit bias in 7–11-year-old White and Black American children. Replicating previous findings with adults, whereas White children showed a robust ingroup bias, Black children showed no bias. Additionally, we investigated the role of valuing status in the development of implicit bias. For Black children, explicit preference for high status predicted implicit outgroup bias: Black children who explicitly expressed high preference for rich (vs. poor) people showed an implicit preference for Whites comparable in magnitude to White children’s ingroup bias. Implications for research on intergroup bias are discussed. PMID:22184478

  17. Symmetry boost of the fidelity of Shor factoring

    NASA Astrophysics Data System (ADS)

    Nam, Y. S.; Blümel, R.

    2018-05-01

    In Shor's algorithm quantum subroutines occur with the structure F U F-1 , where F is a unitary transform and U is performing a quantum computation. Examples are quantum adders and subunits of quantum modulo adders. In this paper we show, both analytically and numerically, that if, in analogy to spin echoes, F and F-1 can be implemented symmetrically when executing Shor's algorithm on actual, imperfect quantum hardware, such that F and F-1 have the same hardware errors, a symmetry boost in the fidelity of the combined F U F-1 quantum operation results when compared to the case in which the errors in F and F-1 are independently random. Running the complete gate-by-gate implemented Shor algorithm, we show that the symmetry-induced fidelity boost can be as large as a factor 4. While most of our analytical and numerical results concern the case of over- and under-rotation of controlled rotation gates, in the numerically accessible case of Shor's algorithm with a small number of qubits, we show explicitly that the symmetry boost is robust with respect to more general types of errors. While, expectedly, additional error types reduce the symmetry boost, we show explicitly, by implementing general off-diagonal SU (N ) errors (N =2 ,4 ,8 ), that the boost factor scales like a Lorentzian in δ /σ , where σ and δ are the error strengths of the diagonal over- and underrotation errors and the off-diagonal SU (N ) errors, respectively. The Lorentzian shape also shows that, while the boost factor may become small with increasing δ , it declines slowly (essentially like a power law) and is never completely erased. We also investigate the effect of diagonal nonunitary errors, which, in analogy to unitary errors, reduce but never erase the symmetry boost. Going beyond the case of small quantum processors, we present analytical scaling results that show that the symmetry boost persists in the practically interesting case of a large number of qubits. We illustrate this result explicitly for the case of Shor factoring of the semiprime RSA-1024, where, analytically, focusing on over- and underrotation errors, we obtain a boost factor of about 10. In addition, we provide a proof of the fidelity product formula, including its range of applicability.

  18. Analytical transmission cross-coefficients for pink beam X-ray microscopy based on compound refractive lenses.

    PubMed

    Falch, Ken Vidar; Detlefs, Carsten; Snigirev, Anatoly; Mathiesen, Ragnvald H

    2018-01-01

    Analytical expressions for the transmission cross-coefficients for x-ray microscopes based on compound refractive lenses are derived based on Gaussian approximations of the source shape and energy spectrum. The effects of partial coherence, defocus, beam convergence, as well as lateral and longitudinal chromatic aberrations are accounted for and discussed. Taking the incoherent limit of the transmission cross-coefficients, a compact analytical expression for the modulation transfer function of the system is obtained, and the resulting point, line and edge spread functions are presented. Finally, analytical expressions for optimal numerical aperture, coherence ratio, and bandwidth are given. Copyright © 2017 Elsevier B.V. All rights reserved.

  19. Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

    NASA Technical Reports Server (NTRS)

    Tamma, Kumar K.; D'Costa, Joseph F.

    1991-01-01

    This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

  20. Characterizing Aeroelastic Systems Using Eigenanalysis, Explicitly Retaining The Aerodynamic Degrees of Freedom

    NASA Technical Reports Server (NTRS)

    Heeg, Jennifer; Dowell, Earl H.

    2001-01-01

    Discrete time aeroelastic models with explicitly retained aerodynamic modes have been generated employing a time marching vortex lattice aerodynamic model. This paper presents analytical results from eigenanalysis of these models. The potential of these models to calculate the behavior of modes that represent damped system motion (noncritical modes) in addition to the simple harmonic modes is explored. A typical section with only structural freedom in pitch is examined. The eigenvalues are examined and compared to experimental data. Issues regarding the convergence of the solution with regard to refining the aerodynamic discretization are investigated. Eigenvector behavior is examined; the eigenvector associated with a particular eigenvalue can be viewed as the set of modal participation factors for that particular mode. For the present formulation of the equations of motion, the vorticity for each aerodynamic element appears explicitly as an element of each eigenvector in addition to the structural dynamic generalized coordinates. Thus, modal participation of the aerodynamic degrees of freedom can be assessed in M addition to participation of structural degrees of freedom.

  1. Time course of implicit processing and explicit processing of emotional faces and emotional words.

    PubMed

    Frühholz, Sascha; Jellinghaus, Anne; Herrmann, Manfred

    2011-05-01

    Facial expressions are important emotional stimuli during social interactions. Symbolic emotional cues, such as affective words, also convey information regarding emotions that is relevant for social communication. Various studies have demonstrated fast decoding of emotions from words, as was shown for faces, whereas others report a rather delayed decoding of information about emotions from words. Here, we introduced an implicit (color naming) and explicit task (emotion judgment) with facial expressions and words, both containing information about emotions, to directly compare the time course of emotion processing using event-related potentials (ERP). The data show that only negative faces affected task performance, resulting in increased error rates compared to neutral faces. Presentation of emotional faces resulted in a modulation of the N170, the EPN and the LPP components and these modulations were found during both the explicit and implicit tasks. Emotional words only affected the EPN during the explicit task, but a task-independent effect on the LPP was revealed. Finally, emotional faces modulated source activity in the extrastriate cortex underlying the generation of the N170, EPN and LPP components. Emotional words led to a modulation of source activity corresponding to the EPN and LPP, but they also affected the N170 source on the right hemisphere. These data show that facial expressions affect earlier stages of emotion processing compared to emotional words, but the emotional value of words may have been detected at early stages of emotional processing in the visual cortex, as was indicated by the extrastriate source activity. Copyright © 2011 Elsevier B.V. All rights reserved.

  2. Verbs and attention to relational roles in English and Tamil*

    PubMed Central

    SETHURAMAN, NITYA; SMITH, LINDA B.

    2013-01-01

    English-learning children have been shown to reliably use cues from argument structure in learning verbs. However, languages pair overtly expressed arguments with verbs to varying extents, raising the question of whether children learning all languages expect the same, universal mapping between arguments and relational roles. Three experiments examined this question by asking how strongly early-learned verbs by themselves, without their corresponding explicitly expressed arguments, point to ‘conceptual arguments’ – the relational roles in a scene. Children aged two to four years and adult speakers of two languages that differ structurally in terms of whether the arguments of a verb are explicitly expressed more (English) or less (Tamil) frequently were compared in their mapping of verbs, presented without any overtly expressed arguments, to a range of scenes. The results suggest different developmental trajectories for language learners, as well as different patterns of adult interpretation, and offer new ways of thinking about the nature of verbs cross-linguistically. PMID:22289295

  3. Grin and bear it: the influence of manipulated facial expression on the stress response.

    PubMed

    Kraft, Tara L; Pressman, Sarah D

    2012-01-01

    In the study reported here, we investigated whether covertly manipulating positive facial expressions would influence cardiovascular and affective responses to stress. Participants (N = 170) naive to the purpose of the study completed two different stressful tasks while holding chopsticks in their mouths in a manner that produced a Duchenne smile, a standard smile, or a neutral expression. Awareness was manipulated by explicitly asking half of all participants in the smiling groups to smile (and giving the other half no instructions related to smiling). Findings revealed that all smiling participants, regardless of whether they were aware of smiling, had lower heart rates during stress recovery than the neutral group did, with a slight advantage for those with Duchenne smiles. Participants in the smiling groups who were not explicitly asked to smile reported less of a decrease in positive affect during a stressful task than did the neutral group. These findings show that there are both physiological and psychological benefits from maintaining positive facial expressions during stress.

  4. Dissolving Bubbles in Glass

    NASA Technical Reports Server (NTRS)

    Weinberg, M. C.; Oronato, P. I.; Uhlmann, D. R.

    1984-01-01

    Analytical expression used to calculate time it takes for stationary bubbles of oxygen and carbon dioxide to dissolve from glass melt. Technique based on analytical expression for bubble radius as function time, with consequences of surface tension included.

  5. Shared Book Reading Promotes Not Only Language Development, But Also Grapheme Awareness in German Kindergarten Children

    PubMed Central

    Wesseling, Patricia B. C.; Christmann, Corinna A.; Lachmann, Thomas

    2017-01-01

    Effects of shared book reading on expressive vocabulary and grapheme awareness without letter instruction in German kindergarteners (longitudinal; N = 69, 3;0–4;8 years) were investigated. Expressive vocabulary was measured by using a standardized test; grapheme awareness was measured by asking children to identify one grapheme per trial presented amongst non-letter distractors. Two methods of shared book reading were investigated, literacy enrichment (additional books) and teacher training in shared book reading strategies, both without explicit letter instruction. Whereas positive effects of shared book reading on expressive vocabulary were evident in numerous previous studies, the impact of shared book reading on grapheme awareness has not yet been investigated. Both methods resulted in positive effects on children’s expressive vocabulary and grapheme awareness over a period of 6 months. Thus, early shared book reading may not only be considered to be a tool for promoting the development of expressive vocabulary, but also for implicit acquisition of grapheme awareness. The latter is considered an important precondition required for the explicit learning of grapheme–phoneme conversion rules (letter knowledge). PMID:28377732

  6. Shared Book Reading Promotes Not Only Language Development, But Also Grapheme Awareness in German Kindergarten Children.

    PubMed

    Wesseling, Patricia B C; Christmann, Corinna A; Lachmann, Thomas

    2017-01-01

    Effects of shared book reading on expressive vocabulary and grapheme awareness without letter instruction in German kindergarteners (longitudinal; N = 69, 3;0-4;8 years) were investigated. Expressive vocabulary was measured by using a standardized test; grapheme awareness was measured by asking children to identify one grapheme per trial presented amongst non-letter distractors. Two methods of shared book reading were investigated, literacy enrichment (additional books) and teacher training in shared book reading strategies, both without explicit letter instruction. Whereas positive effects of shared book reading on expressive vocabulary were evident in numerous previous studies, the impact of shared book reading on grapheme awareness has not yet been investigated. Both methods resulted in positive effects on children's expressive vocabulary and grapheme awareness over a period of 6 months. Thus, early shared book reading may not only be considered to be a tool for promoting the development of expressive vocabulary, but also for implicit acquisition of grapheme awareness. The latter is considered an important precondition required for the explicit learning of grapheme-phoneme conversion rules (letter knowledge).

  7. st-Alphabets: On the Feasibility in the Explicit Use of Extended Relational Alphabets in Classifier Systems

    NASA Astrophysics Data System (ADS)

    Toledo-Suárez, Carlos D.

    It is proposed a way of increasing the cardinality of an alphabet used to write rules in a learning classifier system that extends the idea of relational schemata. Theoretical justifications regarding the possible reduction in the amount of rules for the solution of problems such extended alphabets (st-alphabets) imply are shown. It is shown that when expressed as bipolar neural networks, the matching process of rules over st-alphabets strongly resembles a gene expression mechanism applied to a system over {0,1,#}. In spite of the apparent drawbacks the explicit use of such relational alphabets would imply, their successful implementation in an information gain based classifier system (IGCS) is presented.

  8. Analytic Morse/long-range potential energy surfaces and "adiabatic-hindered-rotor" treatment for a symmetric top-linear molecule dimer: A case study of CH3F-H2

    NASA Astrophysics Data System (ADS)

    Zhang, Xiao-Long; Ma, Yong-Tao; Zhai, Yu; Li, Hui

    2018-03-01

    A first effective six-dimensional ab initio potential energy surface (PES) for CH3F-H2 which explicitly includes the intramolecular Q3 stretching normal mode of the CH3F monomer is presented. The electronic structure computations have been carried out at the explicitly correlated coupled cluster level of theory [CCSD(T)-F12a] with an augmented correlation-consistent triple zeta basis set. Five-dimensional analytical intermolecular PESs for ν3(CH3F) = 0 and 1 are then obtained by fitting the vibrationally averaged potentials to the Morse/Long-Range (MLR) potential function form. The MLR function form is applied to the nonlinear molecule-linear molecule case for the first time. These fits to 25 015 points have root-mean-square deviations of 0.74 cm-1 and 0.082 cm-1 for interaction energies less than 0.0 cm-1. Using the adiabatic hindered-rotor approximation, three-dimensional PESs for CH3F-paraH2 are generated from the 5D PESs over all possible orientations of the hydrogen monomer. The infrared and microwave spectra for CH3F-paraH2 dimer are predicted for the first time. These analytic PESs can be used for modeling the dynamical behavior in CH3F-(H2)N clusters, including the possible appearance of microscopic superfluidity.

  9. Age-related differences in brain activity during implicit and explicit processing of fearful facial expressions.

    PubMed

    Zsoldos, Isabella; Cousin, Emilie; Klein-Koerkamp, Yanica; Pichat, Cédric; Hot, Pascal

    2016-11-01

    Age-related differences in neural correlates underlying implicit and explicit emotion processing are unclear. Within the framework of the Frontoamygdalar Age-related Differences in Emotion model (St Jacques et al., 2009), our objectives were to examine the behavioral and neural modifications that occur with age for both processes. During explicit and implicit processing of fearful faces, we expected to observe less amygdala activity in older adults (OA) than in younger adults (YA), associated with poorer recognition performance in the explicit task, and more frontal activity during implicit processing, suggesting compensation. At a behavioral level, explicit recognition of fearful faces was impaired in OA compared with YA. We did not observe any cerebral differences between OA and YA during the implicit task, whereas in the explicit task, OA recruited more frontal, parietal, temporal, occipital, and cingulate areas. Our findings suggest that automatic processing of emotion may be preserved during aging, whereas deliberate processing is impaired. Additional neural recruitment in OA did not appear to compensate for their behavioral deficits. Copyright © 2016 Elsevier B.V. All rights reserved.

  10. Analytic approximations to the modon dispersion relation. [in oceanography

    NASA Technical Reports Server (NTRS)

    Boyd, J. P.

    1981-01-01

    Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

  11. Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

    DOE PAGES

    Jia, Shaoyang; Pennington, M. R.

    2017-08-01

    With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

  12. Analytical Approach to (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional Kadomtsev-Petviashvili Equation

    NASA Astrophysics Data System (ADS)

    Sarıaydın, Selin; Yıldırım, Ahmet

    2010-05-01

    In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation utt -uxx-uyy-(u2)xx-uxxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation uxt -6ux 2 +6uuxx -uxxxx -uyy -uzz = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically.

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

    PubMed Central

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

    2015-01-01

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

  14. Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

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

    Jia, Shaoyang; Pennington, M. R.

    With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

  15. Analysis of random point images with the use of symbolic computation codes and generalized Catalan numbers

    NASA Astrophysics Data System (ADS)

    Reznik, A. L.; Tuzikov, A. V.; Solov'ev, A. A.; Torgov, A. V.

    2016-11-01

    Original codes and combinatorial-geometrical computational schemes are presented, which are developed and applied for finding exact analytical formulas that describe the probability of errorless readout of random point images recorded by a scanning aperture with a limited number of threshold levels. Combinatorial problems encountered in the course of the study and associated with the new generalization of Catalan numbers are formulated and solved. An attempt is made to find the explicit analytical form of these numbers, which is, on the one hand, a necessary stage of solving the basic research problem and, on the other hand, an independent self-consistent problem.

  16. Explicit correlation treatment of the six-dimensional potential energy surface and predicted infrared spectra for OCS-H2

    NASA Astrophysics Data System (ADS)

    Liu, Jing-Min; Zhai, Yu; Li, Hui

    2017-07-01

    An effective six-dimensional ab initio potential energy surface (PES) for H2-OCS which explicitly includes the intramolecular stretch normal modes of carbonyl sulfide (OCS) is presented. The electronic structure computations are carried out using the explicitly correlated coupled cluster [CCSD(T)-F12] method with the augmented correlation-consistent aug-cc-pVTZ basis set, and the accuracy is critically tested by performing a series of benchmark calculations. Analytic four-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies to the Morse/long-range potential model. These fits to 13 485 points have a root-mean-square deviation (RMSD) of 0.16 cm-1. The combined radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to evaluate the rovibrational energy levels for five isotopic species of the OCS-hydrogen complexes. The predicted transition frequencies and intensities based on the resulting vibrationally averaged PESs are in good agreement with the available experimental values, whose RMSDs are smaller than 0.004 cm-1 for five different species of OCS-hydrogen complexes. The calculated infrared band origin shifts for all five species of OCS-hydrogen complexes are only 0.03 cm-1 smaller than the corresponding experimental values. These validate the high quality of our PESs which can be used for modeling OCS doped in hydrogen clusters to further study quantum solution and microscopic superfluidity. In addition, the analytic coordinate transformation functions between isotopologues are also derived due to the center of mass shifting of different isotope substitutes.

  17. Explicit analytical tuning rules for digital PID controllers via the magnitude optimum criterion.

    PubMed

    Papadopoulos, Konstantinos G; Yadav, Praveen K; Margaris, Nikolaos I

    2017-09-01

    Analytical tuning rules for digital PID type-I controllers are presented regardless of the process complexity. This explicit solution allows control engineers 1) to make an accurate examination of the effect of the controller's sampling time to the control loop's performance both in the time and frequency domain 2) to decide when the control has to be I, PI and when the derivative, D, term has to be added or omitted 3) apply this control action to a series of stable benchmark processes regardless of their complexity. The former advantages are considered critical in industry applications, since 1) most of the times the choice of the digital controller's sampling time is based on heuristics and past criteria, 2) there is little a-priori knowledge of the controlled process making the choice of the type of the controller a trial and error exercise 3) model parameters change often depending on the control loop's operating point making in this way, the problem of retuning the controller's parameter a much challenging issue. Basis of the proposed control law is the principle of the PID tuning via the Magnitude Optimum criterion. The final control law involves the controller's sampling time T s within the explicit solution of the controller's parameters. Finally, the potential of the proposed method is justified by comparing its performance with the conventional PID tuning when controlling the same process. Further investigation regarding the choice of the controller's sampling time T s is also presented and useful conclusions for control engineers are derived. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  18. Effects of task demands on the early neural processing of fearful and happy facial expressions.

    PubMed

    Itier, Roxane J; Neath-Tavares, Karly N

    2017-05-15

    Task demands shape how we process environmental stimuli but their impact on the early neural processing of facial expressions remains unclear. In a within-subject design, ERPs were recorded to the same fearful, happy and neutral facial expressions presented during a gender discrimination, an explicit emotion discrimination and an oddball detection tasks, the most studied tasks in the field. Using an eye tracker, fixation on the face nose was enforced using a gaze-contingent presentation. Task demands modulated amplitudes from 200 to 350ms at occipito-temporal sites spanning the EPN component. Amplitudes were more negative for fearful than neutral expressions starting on N170 from 150 to 350ms, with a temporo-occipital distribution, whereas no clear effect of happy expressions was seen. Task and emotion effects never interacted in any time window or for the ERP components analyzed (P1, N170, EPN). Thus, whether emotion is explicitly discriminated or irrelevant for the task at hand, neural correlates of fearful and happy facial expressions seem immune to these task demands during the first 350ms of visual processing. Copyright © 2017 Elsevier B.V. All rights reserved.

  19. Navy Interest Inventory: Approach Development

    DTIC Science & Technology

    2006-12-01

    lacking social skills” • Investigative is “analytical, intelligent , skeptical and having academic talent– lacking interpersonal skills” • Artistic is...explicit scales to assess RIASEC types or methods to convert their interest scale scores to Holland’s system. Gottfredson and Holland (1996) have given...universality of vocational interest structure among racial/ethnic minorities. American Psychologist, 53, 728-736. Gottfredson , G. D., & Holland, J. L. (1996

  20. Effective diffusion of confined active Brownian swimmers.

    PubMed

    Sandoval, Mario; Dagdug, Leornardo

    2014-12-01

    We theoretically find the effect of confinement and thermal fluctuations on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian dynamics simulations and we obtain excellent agreement.

  1. A Multiple Group Measurement Model of Children's Reports of Parental Socioeconomic Status. Discussion Papers No. 531-78.

    ERIC Educational Resources Information Center

    Mare, Robert D.; Mason, William M.

    An important class of applications of measurement error or constrained factor analytic models consists of comparing models for several populations. In such cases, it is appropriate to make explicit statistical tests of model similarity across groups and to constrain some parameters of the models to be equal across groups using a priori substantive…

  2. Therapists' Attitudes about and Preferences to Use Relationship Focused Interventions: New Tools to Measure a Critical Component of Functional Analytic Psychotherapy (FAP)

    ERIC Educational Resources Information Center

    Terry, Christeine M.; Kohlenberg, Robert J.

    2012-01-01

    The primary study aims were to create reliable measures of therapists' attitudes about and preferences to use Relationship Focused Interventions (RFIs), and investigate factors that influence them. Explicit and implicit measures of therapists' attitudes and preferences were administered to a national sample of mental health trainees and FAP…

  3. Aircraft electric field measurements: Calibration and ambient field retrieval

    NASA Technical Reports Server (NTRS)

    Koshak, William J.; Bailey, Jeff; Christian, Hugh J.; Mach, Douglas M.

    1994-01-01

    An aircraft locally distorts the ambient thundercloud electric field. In order to determine the field in the absence of the aircraft, an aircraft calibration is required. In this work a matrix inversion method is introduced for calibrating an aircraft equipped with four or more electric field sensors and a high-voltage corona point that is capable of charging the aircraft. An analytic, closed form solution for the estimate of a (3 x 3) aircraft calibration matrix is derived, and an absolute calibration experiment is used to improve the relative magnitudes of the elements of this matrix. To demonstrate the calibration procedure, we analyze actual calibration date derived from a Lear jet 28/29 that was equipped with five shutter-type field mill sensors (each with sensitivities of better than 1 V/m) located on the top, bottom, port, starboard, and aft positions. As a test of the calibration method, we analyze computer-simulated calibration data (derived from known aircraft and ambient fields) and explicitly determine the errors involved in deriving the variety of calibration matrices. We extend our formalism to arrive at an analytic solution for the ambient field, and again carry all errors explicitly.

  4. A unifying theory for genetic epidemiological analysis of binary disease data

    PubMed Central

    2014-01-01

    Background Genetic selection for host resistance offers a desirable complement to chemical treatment to control infectious disease in livestock. Quantitative genetics disease data frequently originate from field studies and are often binary. However, current methods to analyse binary disease data fail to take infection dynamics into account. Moreover, genetic analyses tend to focus on host susceptibility, ignoring potential variation in infectiousness, i.e. the ability of a host to transmit the infection. This stands in contrast to epidemiological studies, which reveal that variation in infectiousness plays an important role in the progression and severity of epidemics. In this study, we aim at filling this gap by deriving an expression for the probability of becoming infected that incorporates infection dynamics and is an explicit function of both host susceptibility and infectiousness. We then validate this expression according to epidemiological theory and by simulating epidemiological scenarios, and explore implications of integrating this expression into genetic analyses. Results Our simulations show that the derived expression is valid for a range of stochastic genetic-epidemiological scenarios. In the particular case of variation in susceptibility only, the expression can be incorporated into conventional quantitative genetic analyses using a complementary log-log link function (rather than probit or logit). Similarly, if there is moderate variation in both susceptibility and infectiousness, it is possible to use a logarithmic link function, combined with an indirect genetic effects model. However, in the presence of highly infectious individuals, i.e. super-spreaders, the use of any model that is linear in susceptibility and infectiousness causes biased estimates. Thus, in order to identify super-spreaders, novel analytical methods using our derived expression are required. Conclusions We have derived a genetic-epidemiological function for quantitative genetic analyses of binary infectious disease data, which, unlike current approaches, takes infection dynamics into account and allows for variation in host susceptibility and infectiousness. PMID:24552188

  5. A unifying theory for genetic epidemiological analysis of binary disease data.

    PubMed

    Lipschutz-Powell, Debby; Woolliams, John A; Doeschl-Wilson, Andrea B

    2014-02-19

    Genetic selection for host resistance offers a desirable complement to chemical treatment to control infectious disease in livestock. Quantitative genetics disease data frequently originate from field studies and are often binary. However, current methods to analyse binary disease data fail to take infection dynamics into account. Moreover, genetic analyses tend to focus on host susceptibility, ignoring potential variation in infectiousness, i.e. the ability of a host to transmit the infection. This stands in contrast to epidemiological studies, which reveal that variation in infectiousness plays an important role in the progression and severity of epidemics. In this study, we aim at filling this gap by deriving an expression for the probability of becoming infected that incorporates infection dynamics and is an explicit function of both host susceptibility and infectiousness. We then validate this expression according to epidemiological theory and by simulating epidemiological scenarios, and explore implications of integrating this expression into genetic analyses. Our simulations show that the derived expression is valid for a range of stochastic genetic-epidemiological scenarios. In the particular case of variation in susceptibility only, the expression can be incorporated into conventional quantitative genetic analyses using a complementary log-log link function (rather than probit or logit). Similarly, if there is moderate variation in both susceptibility and infectiousness, it is possible to use a logarithmic link function, combined with an indirect genetic effects model. However, in the presence of highly infectious individuals, i.e. super-spreaders, the use of any model that is linear in susceptibility and infectiousness causes biased estimates. Thus, in order to identify super-spreaders, novel analytical methods using our derived expression are required. We have derived a genetic-epidemiological function for quantitative genetic analyses of binary infectious disease data, which, unlike current approaches, takes infection dynamics into account and allows for variation in host susceptibility and infectiousness.

  6. Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form

    USGS Publications Warehouse

    Greenwood, J. Arthur; Landwehr, J. Maciunas; Matalas, N.C.; Wallis, J.R.

    1979-01-01

    Distributions whose inverse forms are explicitly defined, such as Tukey's lambda, may present problems in deriving their parameters by more conventional means. Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions.

  7. Special solutions to Chazy equation

    NASA Astrophysics Data System (ADS)

    Varin, V. P.

    2017-02-01

    We consider the classical Chazy equation, which is known to be integrable in hypergeometric functions. But this solution has remained purely existential and was never used numerically. We give explicit formulas for hypergeometric solutions in terms of initial data. A special solution was found in the upper half plane H with the same tessellation of H as that of the modular group. This allowed us to derive some new identities for the Eisenstein series. We constructed a special solution in the unit disk and gave an explicit description of singularities on its natural boundary. A global solution to Chazy equation in elliptic and theta functions was found that allows parametrization of an arbitrary solution to Chazy equation. The results have applications to analytic number theory.

  8. Nonlinear truncation error analysis of finite difference schemes for the Euler equations

    NASA Technical Reports Server (NTRS)

    Klopfer, G. H.; Mcrae, D. S.

    1983-01-01

    It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

  9. Explicit equilibria in a kinetic model of gambling

    NASA Astrophysics Data System (ADS)

    Bassetti, F.; Toscani, G.

    2010-06-01

    We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the evolution of wealth in a pure gambling process, where the entire sum of wealths of two agents is up for gambling, and randomly shared between the agents. For this equation the analytical form of the steady states is found for various realizations of the random fraction of the sum which is shared to the agents. Among others, the exponential distribution appears as steady state in case of a uniformly distributed random fraction, while Gamma distribution appears for a random fraction which is Beta distributed. The case in which the gambling game is only conservative-in-the-mean is shown to lead to an explicit heavy tailed distribution.

  10. Delivering Faster Congestion Feedback with the Mark-Front Strategy

    NASA Technical Reports Server (NTRS)

    Liu, Chunlei; Jain, Raj

    2001-01-01

    Computer networks use congestion feedback from the routers and destinations to control the transmission load. Delivering timely congestion feedback is essential to the performance of networks. Reaction to the congestion can be more effective if faster feedback is provided. Current TCP/IP networks use timeout, duplicate Acknowledgement Packets (ACKs) and explicit congestion notification (ECN) to deliver the congestion feedback, each provides a faster feedback than the previous method. In this paper, we propose a markfront strategy that delivers an even faster congestion feedback. With analytical and simulation results, we show that mark-front strategy reduces buffer size requirement, improves link efficiency and provides better fairness among users. Keywords: Explicit Congestion Notification, mark-front, congestion control, buffer size requirement, fairness.

  11. Two-point derivative dispersion relations

    NASA Astrophysics Data System (ADS)

    Ferreira, Erasmo; Sesma, Javier

    2013-03-01

    A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to construct the real part and consist of new mathematical structures of double infinite summations of derivatives. In this new form the derivatives are calculated at the generic value of the energy E and separately at the reference point E = m that is the lower limit of the integration. This new form may be more interesting in certain circumstances and directly shows the origin of the difficulties in convergence that were present in the old truncated forms called standard-derivative dispersion relations (DDR). For all cases in which the reductions of the double to single sums were obtained in our previous work, leading to explicit demonstration of convergence, these new expressions are seen to be identical to the previous ones. We present, as a glossary, the most simplified explicit results for the DDR's in the cases of imaginary amplitudes of forms (E/m)λ[ln (E/m)]n that cover the cases of practical interest in particle physics phenomenology at high energies. We explicitly study the expressions for the cases with λ negative odd integers, that require identification of cancelation of singularities, and provide the corresponding final results.

  12. Closed-form analytical solutions of high-temperature heat pipe startup and frozen startup limitation

    NASA Technical Reports Server (NTRS)

    Cao, Y.; Faghri, A.

    1992-01-01

    Previous numerical and experimental studies indicate that the high-temperature heat pipe startup process is characterized by a moving hot zone with relatively sharp fronts. Based on the above observation, a flat-front model for an approximate analytical solution is proposed. A closed-form solution related to the temperature distribution in the hot zone and the hot zone length as a function of time are obtained. The analytical results agree well with the corresponding experimental data, and provide a quick prediction method for the heat pipe startup performance. Finally, a heat pipe limitation related to the frozen startup process is identified, and an explicit criterion for the high-temperature heat pipe startup is derived. The frozen startup limit identified in this paper provides a fundamental guidance for high-temperature heat pipe design.

  13. Airside HVAC BESTEST: HVAC Air-Distribution System Model Test Cases for ASHRAE Standard 140

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

    Judkoff, Ronald; Neymark, Joel; Kennedy, Mike D.

    This paper summarizes recent work to develop new airside HVAC equipment model analytical verification test cases for ANSI/ASHRAE Standard 140, Standard Method of Test for the Evaluation of Building Energy Analysis Computer Programs. The analytical verification test method allows comparison of simulation results from a wide variety of building energy simulation programs with quasi-analytical solutions, further described below. Standard 140 is widely cited for evaluating software for use with performance-path energy efficiency analysis, in conjunction with well-known energy-efficiency standards including ASHRAE Standard 90.1, the International Energy Conservation Code, and other international standards. Airside HVAC Equipment is a common area ofmore » modelling not previously explicitly tested by Standard 140. Integration of the completed test suite into Standard 140 is in progress.« less

  14. Analytical Sociology: A Bungean Appreciation

    NASA Astrophysics Data System (ADS)

    Wan, Poe Yu-ze

    2012-10-01

    Analytical sociology, an intellectual project that has garnered considerable attention across a variety of disciplines in recent years, aims to explain complex social processes by dissecting them, accentuating their most important constituent parts, and constructing appropriate models to understand the emergence of what is observed. To achieve this goal, analytical sociologists demonstrate an unequivocal focus on the mechanism-based explanation grounded in action theory. In this article I attempt a critical appreciation of analytical sociology from the perspective of Mario Bunge's philosophical system, which I characterize as emergentist systemism. I submit that while the principles of analytical sociology and those of Bunge's approach share a lot in common, the latter brings to the fore the ontological status and explanatory importance of supra-individual actors (as concrete systems endowed with emergent causal powers) and macro-social mechanisms (as processes unfolding in and among social systems), and therefore it does not stipulate that every causal explanation of social facts has to include explicit references to individual-level actors and mechanisms. In this sense, Bunge's approach provides a reasonable middle course between the Scylla of sociological reification and the Charybdis of ontological individualism, and thus serves as an antidote to the untenable "strong program of microfoundations" to which some analytical sociologists are committed.

  15. Theoretical and experimental evidence of Fano-like resonances in simple monomode photonic circuits

    NASA Astrophysics Data System (ADS)

    Mouadili, A.; El Boudouti, E. H.; Soltani, A.; Talbi, A.; Akjouj, A.; Djafari-Rouhani, B.

    2013-04-01

    A simple photonic device consisting of two dangling side resonators grafted at two sites on a waveguide is designed in order to obtain sharp resonant states inside the transmission gaps without introducing any defects in the structure. This results from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or placed between two zeros of transmission, the so-called Fano resonances. A general analytical expression for the transmission coefficient is given for various systems of this kind. The amplitude of the transmission is obtained following the Fano form. The full width at half maximum of the resonances as well as the asymmetric Fano parameter are discussed explicitly as function of the geometrical parameters of the system. In addition to the usual asymmetric Fano resonance, we show that this system may exhibit an electromagnetic induced transparency resonance as well as well as a particular case where such resonances collapse in the transmission coefficient. Also, we give a comparison between the phase of the determinant of the scattering matrix, the so-called Friedel phase, and the phase of the transmission amplitude. The analytical results are obtained by means of the Green's function method, whereas the experiments are carried out using coaxial cables in the radio-frequency regime. These results should have important consequences for designing integrated devices such as narrow-frequency optical or microwave filters and high-speed switches. This system is proposed as a simpler alternative to coupled-micoresonators.

  16. Modeling of matter-wave solitons in a nonlinear inductor-capacitor network through a Gross-Pitaevskii equation with time-dependent linear potential

    NASA Astrophysics Data System (ADS)

    Kengne, E.; Lakhssassi, A.; Liu, W. M.

    2017-08-01

    A lossless nonlinear L C transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed. We find that the potential parameter of the GP equation of the system does not affect the different regions of the MI. Neglecting the chemical potential in the GP equation, we derive exact analytical solutions which describe the propagation of both bright and dark solitary waves on continuous-wave (cw) backgrounds. Using the found exact analytical solutions of the GP equation, we investigate numerically the transmission of both bright and dark solitary voltage signals in the network. Our numerical studies show that the amplitude of a bright solitary voltage signal and the depth of a dark solitary voltage signal as well as their width, their motion, and their behavior depend on (i) the propagation frequencies, (ii) the potential parameter, and (iii) the amplitude of the cw background. The GP equation derived in this paper with a time-dependent linear potential opens up different ideas that may be of considerable theoretical interest for the management of matter-wave solitons in nonlinear L C transmission networks.

  17. Reading affect in the face and voice: neural correlates of interpreting communicative intent in children and adolescents with autism spectrum disorders.

    PubMed

    Wang, A Ting; Lee, Susan S; Sigman, Marian; Dapretto, Mirella

    2007-06-01

    Understanding a speaker's communicative intent in everyday interactions is likely to draw on cues such as facial expression and tone of voice. Prior research has shown that individuals with autism spectrum disorders (ASD) show reduced activity in brain regions that respond selectively to the face and voice. However, there is also evidence that activity in key regions can be increased if task demands allow for explicit processing of emotion. To examine the neural circuitry underlying impairments in interpreting communicative intentions in ASD using irony comprehension as a test case, and to determine whether explicit instructions to attend to facial expression and tone of voice will elicit more normative patterns of brain activity. Eighteen boys with ASD (aged 7-17 years, full-scale IQ >70) and 18 typically developing (TD) boys underwent functional magnetic resonance imaging at the Ahmanson-Lovelace Brain Mapping Center, University of California, Los Angeles. Blood oxygenation level-dependent brain activity during the presentation of short scenarios involving irony. Behavioral performance (accuracy and response time) was also recorded. Reduced activity in the medial prefrontal cortex and right superior temporal gyrus was observed in children with ASD relative to TD children during the perception of potentially ironic vs control scenarios. Importantly, a significant group x condition interaction in the medial prefrontal cortex showed that activity was modulated by explicit instructions to attend to facial expression and tone of voice only in the ASD group. Finally, medial prefrontal cortex activity was inversely related to symptom severity in children with ASD such that children with greater social impairment showed less activity in this region. Explicit instructions to attend to facial expression and tone of voice can elicit increased activity in the medial prefrontal cortex, part of a network important for understanding the intentions of others, in children with ASD. These findings suggest a strategy for future intervention research.

  18. Analytical saturated domain orientation textures and electromechanical properties of ferroelectric ceramics due to electric/mechanical poling

    NASA Astrophysics Data System (ADS)

    Li, F. X.; Rajapakse, R. K. N. D.

    2007-03-01

    Saturated domain orientation textures of three types of pseudocubic (tetragonal, rhombohedral, and orthorhombic) ferroelectric ceramics after complete electric and uniaxial tension (compression) poling is studied analytically in this paper. A one-dimensional orientation distribution function (ODF) of the domain polar vectors is explicitly derived from the uniform inverse pole figures of the poling field axes on a stereographic projection with respect to the fixed crystallite coordinates. The analytical ODF is used to obtain the analytical solutions of saturated polarization and strain after electric/mechanical poling. Based on the closed form solution of the saturated domain orientation textures, the resultant intrinsic electromechanical properties of ferroelectric ceramics, which depend only on the ODF and properties of the corresponding single crystals, are obtained. The results show how the macroscopic symmetries of ferroelectric crystals change from 4mm (tetragonal), 3m (rhombohedral), and mm2 (orthorhombic) single crystals to a ∞mm (transversely isotropic) completely poled ceramic.

  19. Matter field Kähler metric in heterotic string theory from localisation

    NASA Astrophysics Data System (ADS)

    Blesneag, Ştefan; Buchbinder, Evgeny I.; Constantin, Andrei; Lukas, Andre; Palti, Eran

    2018-04-01

    We propose an analytic method to calculate the matter field Kähler metric in heterotic compactifications on smooth Calabi-Yau three-folds with Abelian internal gauge fields. The matter field Kähler metric determines the normalisations of the N = 1 chiral superfields, which enter the computation of the physical Yukawa couplings. We first derive the general formula for this Kähler metric by a dimensional reduction of the relevant supergravity theory and find that its T-moduli dependence can be determined in general. It turns out that, due to large internal gauge flux, the remaining integrals localise around certain points on the compactification manifold and can, hence, be calculated approximately without precise knowledge of the Ricci-flat Calabi-Yau metric. In a final step, we show how this local result can be expressed in terms of the global moduli of the Calabi-Yau manifold. The method is illustrated for the family of Calabi-Yau hypersurfaces embedded in P^1× P^3 and we obtain an explicit result for the matter field Kähler metric in this case.

  20. Bound and resonance states of positronic copper atoms

    NASA Astrophysics Data System (ADS)

    Yamashita, Takuma; Umair, Muhammad; Kino, Yasushi

    2017-10-01

    We report a theoretical calculation for the bound and S-wave resonance states of the positronic copper atom (e+Cu). A positron is a positively charged particle; therefore, a positronic atom has an attractive correlation between the positron and electron. A Gaussian expansion method is adopted to directly describe this correlation as well as the strong repulsive interaction with the nucleus. The correlation between the positron and electron is much more important than that between electrons in an analogous system of Cu-, although the formation of a positronium (Ps) in e+Cu is not expressed in the ground state structure explicitly. Resonance states are calculated with a complex scaling method and identified above the first excited state of the copper atom. Resonance states below Ps (n = 2) + Cu+ classified to a dipole series show agreement with a simple analytical law. Comparison of the resonance energies and widths of e+Cu with those of e+K, of which the potential energy of the host atom resembles that of e+Cu, reveals that the positions of the resonance for the e+Cu dipole series deviate equally from those of e+K.

  1. Axial postbuckling analysis of multilayer functionally graded composite nanoplates reinforced with GPLs based on nonlocal strain gradient theory

    NASA Astrophysics Data System (ADS)

    Sahmani, S.; Aghdam, M. M.

    2017-11-01

    In this paper, a new size-dependent inhomogeneous plate model is constructed to analyze the nonlinear buckling and postbuckling characteristics of multilayer functionally graded composite nanoplates reinforced with graphene platelet (GPL) nanofillers under axial compressive load. To this purpose, the nonlocal strain gradient theory of elasticity is implemented into a refined hyperbolic shear deformation plate theory. The mechanical properties of multilayer graphene platelet-reinforced composite (GPLRC) nanoplates are evaluated based upon the Halpin-Tsai micromechanical scheme. The weight fraction of randomly dispersed GPLs remain constant in each individual layer, which results in U-GPLRC nanoplate, or changes layerwise in accordance with three different functionally graded patterns, which make X-GPLRC, O-GPLRC and A-GPLRC nanoplates. Via a two-stepped perturbation technique, explicit analytical expressions for nonlocal strain gradient stability paths are established for layerwise functionally graded GPLRC nanoplates. It is demonstrated that both the nonlocal and strain gradient size dependencies are more significant for multilayer GPLRC nanoplates filling by GPL nanofillers with higher length-to-thickness and width-to-thickness ratios.

  2. Transient aging in fractional Brownian and Langevin-equation motion.

    PubMed

    Kursawe, Jochen; Schulz, Johannes; Metzler, Ralf

    2013-12-01

    Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic-time and ensemble averages behave differently-from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time t(a). In particular, it turns out that for fractional Langevin-equation motion the aging dependence on t(a) is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.

  3. Coherent nonlinear optical response of single-layer black phosphorus: third-harmonic generation

    NASA Astrophysics Data System (ADS)

    Margulis, Vladimir A.; Muryumin, Evgeny E.; Gaiduk, Evgeny A.

    2017-10-01

    We theoretically calculate the nonlinear optical (NLO) response of phosphorene (a black phosphorus monolayer) to a normally incident and linearly polarized coherent laser radiation of frequency ω, resulting in the generation of radiation at frequency 3ω. We derive explicit analytic expressions for four independent nonvanishing elements of the third-order NLO susceptibility tensor, describing the third-harmonic generation (THG) from phosphorene. The final formulas are numerically evaluated for typical values of the system's parameters to explore how the efficiency of the THG varies with both the frequency and the polarization direction of the incident radiation. The results obtained show a resonant enhancement of the THG efficiency when the pump photon energy ℏω approaches a value of one third of the bandgap energy Eg (≈1.5 eV) of phosphorene. It is also shown that the THG efficiency exhibits a specific polarization dependence, allowing the THG to be used for determining the orientation of phosphorene's crystallographic axes. Our findings highlight the material's potential for practical application in nanoscale photonic devices such as frequency convertors operating in the near-infrared spectral range.

  4. Second-order hydrodynamics and universality in non-conformal holographic fluids

    NASA Astrophysics Data System (ADS)

    Kleinert, Philipp; Probst, Jonas

    2016-12-01

    We study second-order hydrodynamic transport in strongly coupled non-conformal field theories with holographic gravity duals in asymptotically anti-de Sitter space. We first derive new Kubo formulae for five second-order transport coefficients in non-conformal fluids in (3 + 1) dimensions. We then apply them to holographic RG flows induced by scalar operators of dimension Δ = 3. For general background solutions of the dual bulk geometry, we find explicit expressions for the five transport coefficients at infinite coupling and show that a specific combination, tilde{H}=2η {τ}_{π }-2(κ -{κ}^{ast})-{λ}_2 , always vanishes. We prove analytically that the Haack-Yarom identity H = 2 ητ π - 4λ1 - λ2 = 0, which is known to be true for conformal holographic fluids at infinite coupling, also holds when taking into account leading non-conformal corrections. The numerical results we obtain for two specific families of RG flows suggest that H vanishes regardless of conformal symmetry. Our work provides further evidence that the Haack-Yarom identity H = 0 may be universally satisfied by strongly coupled fluids.

  5. Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

    NASA Astrophysics Data System (ADS)

    Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

    2018-03-01

    The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

  6. Scalar curvature in conformal geometry of Connes-Landi noncommutative manifolds

    NASA Astrophysics Data System (ADS)

    Liu, Yang

    2017-11-01

    We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative two tori, the quantum part of the curvature consists of actions of the modular derivation through two local curvature functions. Explicit expressions for those functions are obtained for all even dimensions (greater than two). In dimension four, the one variable function shows striking similarity to the analytic functions of the characteristic classes appeared in the Atiyah-Singer local index formula, namely, it is roughly a product of the j-function (which defines the A ˆ -class of a manifold) and an exponential function (which defines the Chern character of a bundle). By performing two different computations for the variation of the Einstein-Hilbert action, we obtain deep internal relations between two local curvature functions. Straightforward verification for those relations gives a strong conceptual confirmation for the whole computational machinery we have developed so far, especially the Mathematica code hidden behind the paper.

  7. Effects of counter-rotating-wave terms of the driving field on the spectrum of resonance fluorescence

    NASA Astrophysics Data System (ADS)

    Yan, Yiying; Lü, Zhiguo; Zheng, Hang

    2013-11-01

    We investigate the fluorescence spectrum of a two-level system driven by a monochromatic classical field by the Born-Markovian master equation based on a unitary transformation. The main purpose is to understand the effects of counter-rotating-wave terms of the driving on spectral features of the fluorescence. We have derived an analytical expression for the fluorescence spectrum, which is different from Mollow's theory, while Mollow's result on resonance is the limiting case of ours in moderately weak driving regimes. Our results demonstrate precisely that the counter-rotating-wave terms of the driving play an important role in the fluorescence spectrum for intense driving: (i) the counter-rotating coupling suppresses the red sideband in the Mollow triplet and it enhances the blue one in explicitly contrast to the well-known equal intensity of the sideband in Mollow's theory, (ii) the higher-order Mollow triplets appear as a characteristic spectral feature arising from counter-rotating-wave terms of the driving, and (iii) a significant frequency shift of the sidebands is observed, which depends on both the detuning and driving strength.

  8. Comparison between four dissimilar solar panel configurations

    NASA Astrophysics Data System (ADS)

    Suleiman, K.; Ali, U. A.; Yusuf, Ibrahim; Koko, A. D.; Bala, S. I.

    2017-12-01

    Several studies on photovoltaic systems focused on how it operates and energy required in operating it. Little attention is paid on its configurations, modeling of mean time to system failure, availability, cost benefit and comparisons of parallel and series-parallel designs. In this research work, four system configurations were studied. Configuration I consists of two sub-components arranged in parallel with 24 V each, configuration II consists of four sub-components arranged logically in parallel with 12 V each, configuration III consists of four sub-components arranged in series-parallel with 8 V each, and configuration IV has six sub-components with 6 V each arranged in series-parallel. Comparative analysis was made using Chapman Kolmogorov's method. The derivation for explicit expression of mean time to system failure, steady state availability and cost benefit analysis were performed, based on the comparison. Ranking method was used to determine the optimal configuration of the systems. The results of analytical and numerical solutions of system availability and mean time to system failure were determined and it was found that configuration I is the optimal configuration.

  9. Analytical tools in accelerator physics

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

    Litvinenko, V.N.

    2010-09-01

    This paper is a sub-set of my lectures presented in the Accelerator Physics course (USPAS, Santa Rosa, California, January 14-25, 2008). It is based on my notes I wrote during period from 1976 to 1979 in Novosibirsk. Only few copies (in Russian) were distributed to my colleagues in Novosibirsk Institute of Nuclear Physics. The goal of these notes is a complete description starting from the arbitrary reference orbit, explicit expressions for 4-potential and accelerator Hamiltonian and finishing with parameterization with action and angle variables. To a large degree follow logic developed in Theory of Cyclic Particle Accelerators by A.A.Kolmensky andmore » A.N.Lebedev [Kolomensky], but going beyond the book in a number of directions. One of unusual feature is these notes use of matrix function and Sylvester formula for calculating matrices of arbitrary elements. Teaching the USPAS course motivated me to translate significant part of my notes into the English. I also included some introductory materials following Classical Theory of Fields by L.D. Landau and E.M. Liftsitz [Landau]. A large number of short notes covering various techniques are placed in the Appendices.« less

  10. The Imperative in Chinese.

    ERIC Educational Resources Information Center

    Hashimoto, Anne Yue

    A preliminary study of the syntactic characteristics of the imperative construction in modern Chinese is presented. The term "imperative" is used to refer to the type of syntactic construction which is marked by an implicit or explicit second person subject, and which expresses a direct command. Indirect or implied commands expressed by a…

  11. Parametrizing growth in dark energy and modified gravity models

    NASA Astrophysics Data System (ADS)

    Resco, Miguel Aparicio; Maroto, Antonio L.

    2018-02-01

    It is well known that an extremely accurate parametrization of the growth function of matter density perturbations in Λ CDM cosmology, with errors below 0.25%, is given by f (a )=Ωmγ(a ) with γ ≃0.55 . In this work, we show that a simple modification of this expression also provides a good description of growth in modified gravity theories. We consider the model-independent approach to modified gravity in terms of an effective Newton constant written as μ (a ,k )=Geff/G and show that f (a )=β (a )Ωmγ(a ) provides fits to the numerical solutions with similar accuracy to that of Λ CDM . In the time-independent case with μ =μ (k ), simple analytic expressions for β (μ ) and γ (μ ) are presented. In the time-dependent (but scale-independent) case μ =μ (a ), we show that β (a ) has the same time dependence as μ (a ). As an example, explicit formulas are provided in the Dvali-Gabadadze-Porrati (DGP) model. In the general case, for theories with μ (a ,k ), we obtain a perturbative expansion for β (μ ) around the general relativity case μ =1 which, for f (R ) theories, reaches an accuracy below 1%. Finally, as an example we apply the obtained fitting functions in order to forecast the precision with which future galaxy surveys will be able to measure the μ parameter.

  12. On the spin separation of algebraic two-component relativistic Hamiltonians: Molecular properties

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

    Li, Zhendong; Xiao, Yunlong; Liu, Wenjian, E-mail: liuwjbdf@gmail.com

    2014-08-07

    The idea for separating the algebraic exact two-component (X2C) relativistic Hamiltonians into spin-free (sf) and spin-dependent terms [Z. Li, Y. Xiao, and W. Liu, J. Chem. Phys. 137, 154114 (2012)] is extended to both electric and magnetic molecular properties. Taking the spin-free terms (which are correct to infinite order in α ≈ 1/137) as zeroth order, the spin-dependent terms can be treated to any desired order via analytic derivative technique. This is further facilitated by unified Sylvester equations for the response of the decoupling and renormalization matrices to single or multiple perturbations. For practical purposes, explicit expressions of order α{supmore » 2} in spin are also given for electric and magnetic properties, as well as two-electron spin-orbit couplings. At this order, the response of the decoupling and renormalization matrices is not required, such that the expressions are very compact and completely parallel to those based on the Breit-Pauli (BP) Hamiltonian. However, the former employ sf-X2C wave functions, whereas the latter can only use nonrelativistic wave functions. As the sf-X2C terms can readily be interfaced with any nonrelativistic program, the implementation of the O(α{sup 2}) spin-orbit corrections to sf-X2C properties requires only marginal revisions of the routines for evaluating the BP type of corrections.« less

  13. On the spin separation of algebraic two-component relativistic Hamiltonians: Molecular properties

    NASA Astrophysics Data System (ADS)

    Li, Zhendong; Xiao, Yunlong; Liu, Wenjian

    2014-08-01

    The idea for separating the algebraic exact two-component (X2C) relativistic Hamiltonians into spin-free (sf) and spin-dependent terms [Z. Li, Y. Xiao, and W. Liu, J. Chem. Phys. 137, 154114 (2012)] is extended to both electric and magnetic molecular properties. Taking the spin-free terms (which are correct to infinite order in α ≈ 1/137) as zeroth order, the spin-dependent terms can be treated to any desired order via analytic derivative technique. This is further facilitated by unified Sylvester equations for the response of the decoupling and renormalization matrices to single or multiple perturbations. For practical purposes, explicit expressions of order α2 in spin are also given for electric and magnetic properties, as well as two-electron spin-orbit couplings. At this order, the response of the decoupling and renormalization matrices is not required, such that the expressions are very compact and completely parallel to those based on the Breit-Pauli (BP) Hamiltonian. However, the former employ sf-X2C wave functions, whereas the latter can only use nonrelativistic wave functions. As the sf-X2C terms can readily be interfaced with any nonrelativistic program, the implementation of the O(α ^2) spin-orbit corrections to sf-X2C properties requires only marginal revisions of the routines for evaluating the BP type of corrections.

  14. Neoclassical poloidal and toroidal rotation in tokamaks

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

    Kim, Y.B.; Diamond, P.H.; Groebner, R.J.

    1991-08-01

    Explicit expressions for the neoclassical poloidal and toroidal rotation speeds of primary ion and impurity species are derived via the Hirshman and Sigmar moment approach. The rotation speeds of the primary ion can be significantly different from those of impurities in various interesting cases. The rapid increase of impurity poloidal rotation in the edge region of H-mode discharges in tokamaks can be explained by a rapid steepening of the primary ion pressure gradient. Depending on ion collisionality, the poloidal rotation speed of the primary ions at the edge can be quite small and the flow direction may be opposite tomore » that of the impurities. This may cast considerable doubts on current L to H bifurcation models based on primary ion poloidal rotation only. Also, the difference between the toroidal rotation velocities of primary ions and impurities is not negligible in various cases. In Ohmic plasmas, the parallel electric field induces a large impurity toroidal rotation close to the magnetic axis, which seems to agree with experimental observations. In the ion banana and plateau regime, there can be non-negligible disparities between primary ion and impurity toroidal rotation velocities due to the ion density and temperature gradients. Detailed analytic expressions for the primary ion and impurity rotation speeds are presented, and the methodology for generalization to the case of several impurity species is also presented for future numerical evaluation.« less

  15. Recursive-operator method in vibration problems for rod systems

    NASA Astrophysics Data System (ADS)

    Rozhkova, E. V.

    2009-12-01

    Using linear differential equations with constant coefficients describing one-dimensional dynamical processes as an example, we show that the solutions of these equations and systems are related to the solution of the corresponding numerical recursion relations and one does not have to compute the roots of the corresponding characteristic equations. The arbitrary functions occurring in the general solution of the homogeneous equations are determined by the initial and boundary conditions or are chosen from various classes of analytic functions. The solutions of the inhomogeneous equations are constructed in the form of integro-differential series acting on the right-hand side of the equation, and the coefficients of the series are determined from the same recursion relations. The convergence of formal solutions as series of a more general recursive-operator construction was proved in [1]. In the special case where the solutions of the equation can be represented in separated variables, the power series can be effectively summed, i.e., expressed in terms of elementary functions, and coincide with the known solutions. In this case, to determine the natural vibration frequencies, one obtains algebraic rather than transcendental equations, which permits exactly determining the imaginary and complex roots of these equations without using the graphic method [2, pp. 448-449]. The correctness of the obtained formulas (differentiation formulas, explicit expressions for the series coefficients, etc.) can be verified directly by appropriate substitutions; therefore, we do not prove them here.

  16. Turbulence-enhanced bottom melting of a horizontal glacier--lake interface

    NASA Astrophysics Data System (ADS)

    Keitzl, T.; Mellado, J. P.; Notz, D.

    2014-12-01

    We use laboratory tank experiments and direct numerical simulations to investigate the meltrates of a horizontal bottom glacier--lake interface as a function of lake temperature. Existing parameterisations of such meltrates are usually based on empirical fits to field observations. To understand the meltrates of an ice--water interface more systematically we study an idealised system in terms of its temperature-driven buoyancy forcing. In such systems, the meltrate can be expressed analytically for a stable stratification. Here we investigate the unstable case and present how the meltrate depends on the lake temperature when the water beneath the ice is overturning and turbulent. We use laboratory tank experiments and direct numerical simulations to study an idealised ice--water boundary. The laboratory tank experiments provide robust observation-based mean-temperature profiles. The numerical simulations provide the full three-dimensional structure of the turbulent flow down to scales not accessible in the laboratory, with a minimum 0.2mm gridspacing. Our laboratory mean-temperature profiles agree well with the numerical simulations and lend credibility to our numerical setup. The structure of the turbulent flow in our simulations is well described by two self-similar subregions, a diffusion-dominated inner layer close to the ice and a turbulence-dominated outer layer far from the ice. We provide an explicit expression for the parameterisation of the meltrate of a horizontal glacier--lake interface as a function of lake temperature.

  17. Analytical expressions for the log-amplitude correlation function of a plane wave through anisotropic atmospheric refractive turbulence.

    PubMed

    Gudimetla, V S Rao; Holmes, Richard B; Smith, Carey; Needham, Gregory

    2012-05-01

    The effect of anisotropic Kolmogorov turbulence on the log-amplitude correlation function for plane-wave fields is investigated using analysis, numerical integration, and simulation. A new analytical expression for the log-amplitude correlation function is derived for anisotropic Kolmogorov turbulence. The analytic results, based on the Rytov approximation, agree well with a more general wave-optics simulation based on the Fresnel approximation as well as with numerical evaluations, for low and moderate strengths of turbulence. The new expression reduces correctly to previously published analytic expressions for isotropic turbulence. The final results indicate that, as asymmetry becomes greater, the Rytov variance deviates from that given by the standard formula. This deviation becomes greater with stronger turbulence, up to moderate turbulence strengths. The anisotropic effects on the log-amplitude correlation function are dominant when the separation of the points is within the Fresnel length. In the direction of stronger turbulence, there is an enhanced dip in the correlation function at a separation close to the Fresnel length. The dip is diminished in the weak-turbulence axis, suggesting that energy redistribution via focusing and defocusing is dominated by the strong-turbulence axis. The new analytical expression is useful when anisotropy is observed in relevant experiments. © 2012 Optical Society of America

  18. Extraction of CP Properties of the H(125) Boson Discovered in Proton-Proton Collisions at√s = 7 and 8 TeV with the CMS Detector at the LHC

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

    Chen, Yi

    In this thesis we build a novel analysis framework to perform the direct extraction ofall possible effective Higgs boson couplings to the neutral electroweak gauge bosonsin the H → ZZ (*) → 4 channel also referred to as the golden channel. We use analytic expressions of the full decay differential cross sections for the H → V V → 4process, and the dominant irreducible standard model q q → 4 background where¯4 = 2e2µ, 4e, 4µ. Detector effects are included through an explicit convolution ofthese analytic expressions with transfer functions that model the detector responsesas well as acceptance and efficiencymore » effects. Using the full set of decay observables, weconstruct an unbinned 8-dimensional detector level likelihood function which is continuous in the effective couplings, and includes systematics. All potential anomalouscouplings of HV V where V = Z, γ are considered, allowing for general CP even/oddadmixtures and any possible phases. We measure the CP -odd mixing between thetree-level HZZ coupling and higher order CP -odd couplings to be compatible withzero, and in the range [-0.40, 0.43], and the mixing between HZZ tree-level couplingand higher order CP -even coupling to be in the ranges [-0.66, -0.57] U [-0.15, 1.00];namely compatible with a standard model Higgs. We discuss the expected precisionin determining the various HV V couplings in future LHC runs. A powerful and at first glance surprising prediction of the analysis is that with 100-400 fb -1 , the goldenchannel will be able to start probing the couplings of the Higgs boson to diphotons inthe 4 channel. We discuss the implications and further optimization of the methodsfor the next LHC runs.« less

  19. Effects of molecular and particle scatterings on the model parameter for remote-sensing reflectance.

    PubMed

    Lee, ZhongPing; Carder, Kendall L; Du, KePing

    2004-09-01

    For optically deep waters, remote-sensing reflectance (r(rs)) is traditionally expressed as the ratio of the backscattering coefficient (b(b)) to the sum of absorption and backscattering coefficients (a + b(b)) that multiples a model parameter (g, or the so-called f'/Q). Parameter g is further expressed as a function of b(b)/(a + b(b)) (or b(b)/a) to account for its variation that is due to multiple scattering. With such an approach, the same g value will be derived for different a and b(b) values that provide the same ratio. Because g is partially a measure of the angular distribution of upwelling light, and the angular distribution from molecular scattering is quite different from that of particle scattering; g values are expected to vary with different scattering distributions even if the b(b)/a ratios are the same. In this study, after numerically demonstrating the effects of molecular and particle scatterings on the values of g, an innovative r(rs) model is developed. This new model expresses r(rs) in two separate terms: one governed by the phase function of molecular scattering and one governed by the phase function of particle scattering, with a model parameter introduced for each term. In this way the phase function effects from molecular and particle scatterings are explicitly separated and accounted for. This new model provides an analytical tool to understand and quantify the phase-function effects on r(rs), and a platform to calculate r(rs) spectrum quickly and accurately that is required for remote-sensing applications.

  20. Electroweak corrections to hadronic production of W bosons at large transverse momenta

    NASA Astrophysics Data System (ADS)

    Kühn, Johann H.; Kulesza, A.; Pozzorini, S.; Schulze, M.

    2008-07-01

    To match the precision of present and future measurements of W-boson production at hadron colliders electroweak radiative corrections must be included in the theory predictions. In this paper we consider their effect on the transverse momentum ( p) distribution of W bosons, with emphasis on large p. We evaluate the full electroweak O(α) corrections to the processes pp→W+jet and pp¯→W+jet including virtual and real photonic contributions. We present the explicit expressions in analytical form for the virtual corrections and provide results for the real corrections, discussing in detail the treatment of soft and collinear singularities. We also provide compact approximate expressions which are valid in the high-energy region, where the electroweak corrections are strongly enhanced by logarithms of sˆ/MW2. These expressions describe the complete asymptotic behaviour at one loop as well as the leading and next-to-leading logarithms at two loops. Numerical results are presented for proton-proton collisions at 14 TeV and proton-antiproton collisions at 2 TeV. The corrections are negative and their size increases with p. At the LHC, where transverse momenta of 2 TeV or more can be reached, the one- and two-loop corrections amount up to -40% and +10%, respectively, and will be important for a precise analysis of W production. At the Tevatron, transverse momenta up to 300 GeV are within reach. In this case the electroweak corrections amount up to -10% and are thus larger than the expected statistical error.

  1. Neurocognitive mechanisms underlying the experience of flow.

    PubMed

    Dietrich, Arne

    2004-12-01

    Recent theoretical and empirical work in cognitive science and neuroscience is brought into contact with the concept of the flow experience. After a brief exposition of brain function, the explicit-implicit distinction is applied to the effortless information processing that is so characteristic of the flow state. The explicit system is associated with the higher cognitive functions of the frontal lobe and medial temporal lobe structures and has evolved to increase cognitive flexibility. In contrast, the implicit system is associated with the skill-based knowledge supported primarily by the basal ganglia and has the advantage of being more efficient. From the analysis of this flexibility/efficiency trade-off emerges a thesis that identifies the flow state as a period during which a highly practiced skill that is represented in the implicit system's knowledge base is implemented without interference from the explicit system. It is proposed that a necessary prerequisite to the experience of flow is a state of transient hypofrontality that enables the temporary suppression of the analytical and meta-conscious capacities of the explicit system. Examining sensory-motor integration skills that seem to typify flow such as athletic performance, writing, and free-jazz improvisation, the new framework clarifies how this concept relates to creativity and opens new avenues of research.

  2. Effects of divided attention and speeded responding on implicit and explicit retrieval of artificial grammar knowledge.

    PubMed

    Helman, Shaun; Berry, Dianne C

    2003-07-01

    The artificial grammar (AG) learning literature (see, e.g., Mathews et al., 1989; Reber, 1967) has relied heavily on a single measure of implicitly acquired knowledge. Recent work comparing this measure (string classification) with a more indirect measure in which participants make liking ratings of novel stimuli (e.g., Manza & Bornstein, 1995; Newell & Bright, 2001) has shown that string classification (which we argue can be thought of as an explicit, rather than an implicit, measure of memory) gives rise to more explicit knowledge of the grammatical structure in learning strings and is more resilient to changes in surface features and processing between encoding and retrieval. We report data from two experiments that extend these findings. In Experiment 1, we showed that a divided attention manipulation (at retrieval) interfered with explicit retrieval of AG knowledge but did not interfere with implicit retrieval. In Experiment 2, we showed that forcing participants to respond within a very tight deadline resulted in the same asymmetric interference pattern between the tasks. In both experiments, we also showed that the type of information being retrieved influenced whether interference was observed. The results are discussed in terms of the relatively automatic nature of implicit retrieval and also with respect to the differences between analytic and nonanalytic processing (Whittlesea & Price, 2001).

  3. Examining the Affordances of Dual Cognitive Processing to Explain the Development of High School Students' Nature of Science Views

    ERIC Educational Resources Information Center

    Jackson, Luke M.

    2017-01-01

    This mixed method study was aimed at examining the influence of dual processing (Type 1 and Type 2 thinking) on the development of high school students' nature of science (NOS) views. Type 1 thinking is intuitive, experiential, and heuristic. Type 2 thinking is rational, analytical, and explicit. Three research questions were asked: (1) Do the…

  4. Compact Q-balls in the complex signum-Gordon model

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

    Arodz, H.; Lis, J.

    2008-05-15

    We discuss Q-balls in the complex signum-Gordon model in d-dimensional space for d=1, 2, 3. The Q-balls have strictly finite size. Their total energy is a powerlike function of the conserved U(1) charge with the exponent equal to (d+2)(d+3){sup -1}. In the cases d=1 and d=3 explicit analytic solutions are presented.

  5. Phase estimation without a priori phase knowledge in the presence of loss

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

    Kolodynski, Jan; Demkowicz-Dobrzanski, Rafal

    2010-11-15

    We find the optimal scheme for quantum phase estimation in the presence of loss when no a priori knowledge on the estimated phase is available. We prove analytically an explicit lower bound on estimation uncertainty, which shows that, as a function of the number of probes, quantum precision enhancement amounts at most to a constant factor improvement over classical strategies.

  6. New Tests to Measure Individual Differences in Matching and Labelling Facial Expressions of Emotion, and Their Association with Ability to Recognise Vocal Emotions and Facial Identity

    PubMed Central

    Palermo, Romina; O’Connor, Kirsty B.; Davis, Joshua M.; Irons, Jessica; McKone, Elinor

    2013-01-01

    Although good tests are available for diagnosing clinical impairments in face expression processing, there is a lack of strong tests for assessing “individual differences” – that is, differences in ability between individuals within the typical, nonclinical, range. Here, we develop two new tests, one for expression perception (an odd-man-out matching task in which participants select which one of three faces displays a different expression) and one additionally requiring explicit identification of the emotion (a labelling task in which participants select one of six verbal labels). We demonstrate validity (careful check of individual items, large inversion effects, independence from nonverbal IQ, convergent validity with a previous labelling task), reliability (Cronbach’s alphas of.77 and.76 respectively), and wide individual differences across the typical population. We then demonstrate the usefulness of the tests by addressing theoretical questions regarding the structure of face processing, specifically the extent to which the following processes are common or distinct: (a) perceptual matching and explicit labelling of expression (modest correlation between matching and labelling supported partial independence); (b) judgement of expressions from faces and voices (results argued labelling tasks tap into a multi-modal system, while matching tasks tap distinct perceptual processes); and (c) expression and identity processing (results argued for a common first step of perceptual processing for expression and identity). PMID:23840821

  7. New tests to measure individual differences in matching and labelling facial expressions of emotion, and their association with ability to recognise vocal emotions and facial identity.

    PubMed

    Palermo, Romina; O'Connor, Kirsty B; Davis, Joshua M; Irons, Jessica; McKone, Elinor

    2013-01-01

    Although good tests are available for diagnosing clinical impairments in face expression processing, there is a lack of strong tests for assessing "individual differences"--that is, differences in ability between individuals within the typical, nonclinical, range. Here, we develop two new tests, one for expression perception (an odd-man-out matching task in which participants select which one of three faces displays a different expression) and one additionally requiring explicit identification of the emotion (a labelling task in which participants select one of six verbal labels). We demonstrate validity (careful check of individual items, large inversion effects, independence from nonverbal IQ, convergent validity with a previous labelling task), reliability (Cronbach's alphas of.77 and.76 respectively), and wide individual differences across the typical population. We then demonstrate the usefulness of the tests by addressing theoretical questions regarding the structure of face processing, specifically the extent to which the following processes are common or distinct: (a) perceptual matching and explicit labelling of expression (modest correlation between matching and labelling supported partial independence); (b) judgement of expressions from faces and voices (results argued labelling tasks tap into a multi-modal system, while matching tasks tap distinct perceptual processes); and (c) expression and identity processing (results argued for a common first step of perceptual processing for expression and identity).

  8. Oxytocin enhances pupil dilation and sensitivity to ‘hidden’ emotional expressions

    PubMed Central

    Wessberg, Johan; Ellingsen, Dan-Mikael; Chelnokova, Olga; Olausson, Håkan; Laeng, Bruno

    2013-01-01

    Sensing others’ emotions through subtle facial expressions is a highly important social skill. We investigated the effects of intranasal oxytocin treatment on the evaluation of explicit and ‘hidden’ emotional expressions and related the results to individual differences in sensitivity to others’ subtle expressions of anger and happiness. Forty healthy volunteers participated in this double-blind, placebo-controlled crossover study, which shows that a single dose of intranasal oxytocin (40 IU) enhanced or ‘sharpened’ evaluative processing of others’ positive and negative facial expression for both explicit and hidden emotional information. Our results point to mechanisms that could underpin oxytocin’s prosocial effects in humans. Importantly, individual differences in baseline emotional sensitivity predicted oxytocin’s effects on the ability to sense differences between faces with hidden emotional information. Participants with low emotional sensitivity showed greater oxytocin-induced improvement. These participants also showed larger task-related pupil dilation, suggesting that they also allocated the most attentional resources to the task. Overall, oxytocin treatment enhanced stimulus-induced pupil dilation, consistent with oxytocin enhancement of attention towards socially relevant stimuli. Since pupil dilation can be associated with increased attractiveness and approach behaviour, this effect could also represent a mechanism by which oxytocin increases human affiliation. PMID:22648957

  9. Oxytocin enhances pupil dilation and sensitivity to 'hidden' emotional expressions.

    PubMed

    Leknes, Siri; Wessberg, Johan; Ellingsen, Dan-Mikael; Chelnokova, Olga; Olausson, Håkan; Laeng, Bruno

    2013-10-01

    Sensing others' emotions through subtle facial expressions is a highly important social skill. We investigated the effects of intranasal oxytocin treatment on the evaluation of explicit and 'hidden' emotional expressions and related the results to individual differences in sensitivity to others' subtle expressions of anger and happiness. Forty healthy volunteers participated in this double-blind, placebo-controlled crossover study, which shows that a single dose of intranasal oxytocin (40 IU) enhanced or 'sharpened' evaluative processing of others' positive and negative facial expression for both explicit and hidden emotional information. Our results point to mechanisms that could underpin oxytocin's prosocial effects in humans. Importantly, individual differences in baseline emotional sensitivity predicted oxytocin's effects on the ability to sense differences between faces with hidden emotional information. Participants with low emotional sensitivity showed greater oxytocin-induced improvement. These participants also showed larger task-related pupil dilation, suggesting that they also allocated the most attentional resources to the task. Overall, oxytocin treatment enhanced stimulus-induced pupil dilation, consistent with oxytocin enhancement of attention towards socially relevant stimuli. Since pupil dilation can be associated with increased attractiveness and approach behaviour, this effect could also represent a mechanism by which oxytocin increases human affiliation.

  10. Analytic integration of real-virtual counterterms in NNLO jet cross sections I

    NASA Astrophysics Data System (ADS)

    Aglietti, Ugo; Del Duca, Vittorio; Duhr, Claude; Somogyi, Gábor; Trócsányi, Zoltán

    2008-09-01

    We present analytic evaluations of some integrals needed to give explicitly the integrated real-virtual counterterms, based on a recently proposed subtraction scheme for next-to-next-to-leading order (NNLO) jet cross sections. After an algebraic reduction of the integrals, integration-by-parts identities are used for the reduction to master integrals and for the computation of the master integrals themselves by means of differential equations. The results are written in terms of one- and two-dimensional harmonic polylogarithms, once an extension of the standard basis is made. We expect that the techniques described here will be useful in computing other integrals emerging in calculations in perturbative quantum field theories.

  11. Linear dimension reduction and Bayes classification

    NASA Technical Reports Server (NTRS)

    Decell, H. P., Jr.; Odell, P. L.; Coberly, W. A.

    1978-01-01

    An explicit expression for a compression matrix T of smallest possible left dimension K consistent with preserving the n variate normal Bayes assignment of X to a given one of a finite number of populations and the K variate Bayes assignment of TX to that population was developed. The Bayes population assignment of X and TX were shown to be equivalent for a compression matrix T explicitly calculated as a function of the means and covariances of the given populations.

  12. Does Islam play a role in anti-immigrant sentiment? An experimental approach.

    PubMed

    Creighton, Mathew J; Jamal, Amaney

    2015-09-01

    Are Muslim immigrants subjected to targeted opposition (i.e., Islamophobia) on their pathway to US citizenship? Using a list experiment and a representative sample of the US population, we compare explicit and implicit opposition to Muslim and Christian immigrants. We find that Muslim immigrants, relative to Christian immigrants, experience greater explicit resistance. However, when social desirability bias is taken into account via the list experiment, we find that opposition to Christian and Muslim immigrants is the same. The explanation is that respondents conceal a significant amount of opposition to Christian immigrants. Muslim immigrants, on the other hand, are afforded no such protection. We find that religiosity or denomination do not play a significant role in determining implicit or explicit opposition. We conclude that Islamophobia, which is only explicitly expressed, is best understood as reflective of social desirability bias from which Muslim immigrants do not benefit. Copyright © 2015 Elsevier Inc. All rights reserved.

  13. Young Adults' Implicit and Explicit Attitudes towards the Sexuality of Older Adults.

    PubMed

    Thompson, Ashley E; O'Sullivan, Lucia F; Byers, E Sandra; Shaughnessy, Krystelle

    2014-09-01

    Sexual interest and capacity can extend far into later life and result in many positive health outcomes. Yet there is little support for sexual expression in later life, particularly among young adults. This study assessed and compared young adults' explicit and implicit attitudes towards older adult sexuality. A sample of 120 participants (18-24 years; 58% female) completed a self-report (explicit) measure and a series of Implicit Association Tests capturing attitudes towards sexuality among older adults. Despite reporting positive explicit attitudes, young people revealed an implicit bias against the sexual lives of older adults. In particular, young adults demonstrated implicit biases favouring general, as compared to sexual, activities and young adults as compared to older adults. Moreover, the bias favouring general activities was amplified with regard to older adults as compared to younger adults. Our findings challenge the validity of research relying on self-reports of attitudes about older adult sexuality.

  14. Reactions to Humorous Sexual Stimuli as a Function of Sexual Activeness and Satisfaction.

    ERIC Educational Resources Information Center

    Prerost, Frank J.

    1984-01-01

    Assessed male (N=60) and female (N=60) responses to pictorial humorous sexual material in relationship to degree of sexual expression and personal satisfaction with sexual behavior. Results showed persons with active and satisfying sexual expression enjoyed sexually explicit cartoons and showed less preference for aggressive themes. (LLL)

  15. Cross-Cultural Evidence that the Nonverbal Expression of Pride Is an Automatic Status Signal

    ERIC Educational Resources Information Center

    Tracy, Jessica L.; Shariff, Azim F.; Zhao, Wanying; Henrich, Joseph

    2013-01-01

    To test whether the pride expression is an implicit, reliably developing signal of high social status in humans, the authors conducted a series of experiments that measured implicit and explicit cognitive associations between pride displays and high-status concepts in two culturally disparate populations--North American undergraduates and Fijian…

  16. 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

  17. Viscous damping and spring force in periodic perforated planar microstructures when the Reynolds’ equation cannot be applied

    PubMed Central

    Homentcovschi, Dorel; Miles, Ronald N.

    2010-01-01

    A model of squeeze-film behavior is developed based on Stokes’ equations for viscous, compressible isothermal flows. The flow domain is an axisymmetrical, unit cell approximation of a planar, periodic, perforated microstructure. The model is developed for cases when the lubrication approximation cannot be applied. The complex force generated by vibrations of the diaphragm driving the flow has two components: the damping force and the spring force. While for large frequencies the spring force dominates, at low (acoustical) frequencies the damping force is the most important part. The analytical approach developed here yields an explicit formula for both forces. In addition, using a finite element software package, the damping force is also obtained numerically. A comparison is made between the analytic result, numerical solution, and some experimental data found in the literature, which validates the analytic formula and provides compelling arguments about its value in designing microelectomechanical devices. PMID:20329828

  18. Upon the Shoulders of Giants: Open-Source Hardware and Software in Analytical Chemistry.

    PubMed

    Dryden, Michael D M; Fobel, Ryan; Fobel, Christian; Wheeler, Aaron R

    2017-04-18

    Isaac Newton famously observed that "if I have seen further it is by standing on the shoulders of giants." We propose that this sentiment is a powerful motivation for the "open-source" movement in scientific research, in which creators provide everything needed to replicate a given project online, as well as providing explicit permission for users to use, improve, and share it with others. Here, we write to introduce analytical chemists who are new to the open-source movement to best practices and concepts in this area and to survey the state of open-source research in analytical chemistry. We conclude by considering two examples of open-source projects from our own research group, with the hope that a description of the process, motivations, and results will provide a convincing argument about the benefits that this movement brings to both creators and users.

  19. Event-by-Event Simulations of Early Gluon Fields in High Energy Nuclear Collisions

    NASA Astrophysics Data System (ADS)

    Nickel, Matthew; Rose, Steven; Fries, Rainer

    2017-09-01

    Collisions of heavy ions are carried out at ultra relativistic speeds at the Relativistic Heavy Ion Collider and the Large Hadron Collider to create Quark Gluon Plasma. The earliest stages of such collisions are dominated by the dynamics of classical gluon fields. The McLerran-Venugopalan (MV) model of color glass condensate provides a model for this process. Previous research has provided an analytic solution for event averaged observables in the MV model. Using the High Performance Research Computing Center (HPRC) at Texas A&M, we have developed a C++ code to explicitly calculate the initial gluon fields and energy momentum tensor event by event using the analytic recursive solution. The code has been tested against previously known analytic results up to fourth order. We have also have been able to test the convergence of the recursive solution at high orders in time and studied the time evolution of color glass condensate.

  20. Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

    NASA Astrophysics Data System (ADS)

    Minesaki, Yukitaka

    2018-04-01

    We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

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