Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy.

PubMed

Ansumali, S; Karlin, I V; Arcidiacono, S; Abbas, A; Prasianakis, N I

2007-03-23

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.

Induced drag ideal efficiency factor of arbitrary lateral-vertical wing forms

NASA Technical Reports Server (NTRS)

Deyoung, J.

1980-01-01

A relatively simple equation is presented for estimating the induced drag ideal efficiency factor e for arbitrary cross sectional wing forms. This equation is based on eight basic but varied wing configurations which have exact solutions. The e function which relates the basic wings is developed statistically and is a continuous function of configuration geometry. The basic wing configurations include boxwings shaped as a rectangle, ellipse, and diamond; the V-wing; end-plate wing; 90 degree cruciform; circle dumbbell; and biplane. Example applications of the e equations are made to many wing forms such as wings with struts which form partial span rectangle dumbbell wings; bowtie, cruciform, winglet, and fan wings; and multiwings. Derivations are presented in the appendices of exact closed form solutions found of e for the V-wing and 90 degree cruciform wing and for an asymptotic solution for multiwings.

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

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

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

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

Trajectory And Heating Of A Hypervelocity Projectile

NASA Technical Reports Server (NTRS)

Tauber, Michael E.

1992-01-01

Technical paper presents derivation of approximate, closed-form equation for relationship between velocity of projectile and density of atmosphere. Results of calculations based on approximate equation agree well with results from numerical integrations of exact equations of motion. Comparisons of results presented in series of graphs.

Exact solutions to model surface and volume charge distributions

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Partition-free approach to open quantum systems in harmonic environments: An exact stochastic Liouville equation

NASA Astrophysics Data System (ADS)

McCaul, G. M. G.; Lorenz, C. D.; Kantorovich, L.

2017-03-01

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system, termed the extended stochastic Liouville-von Neumann equation. Our approach generalizes previous work based on Caldeira-Leggett models and a partitioned initial density matrix. This provides a simple, yet exact, closed-form description for the evolution of open systems from equilibriated initial conditions. The applicability of this model and the potential for numerical implementations are also discussed.

Closed-form solutions of performability. [modeling of a degradable buffer/multiprocessor system

NASA Technical Reports Server (NTRS)

Meyer, J. F.

1981-01-01

Methods which yield closed form performability solutions for continuous valued variables are developed. The models are similar to those employed in performance modeling (i.e., Markovian queueing models) but are extended so as to account for variations in structure due to faults. In particular, the modeling of a degradable buffer/multiprocessor system is considered whose performance Y is the (normalized) average throughput rate realized during a bounded interval of time. To avoid known difficulties associated with exact transient solutions, an approximate decomposition of the model is employed permitting certain submodels to be solved in equilibrium. These solutions are then incorporated in a model with fewer transient states and by solving the latter, a closed form solution of the system's performability is obtained. In conclusion, some applications of this solution are discussed and illustrated, including an example of design optimization.

Nonminimally coupled massive scalar field in a 2D black hole: Exactly solvable model

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

Frolov, V.; Zelnikov, A.

2001-06-15

We study a nonminimal massive scalar field in the background of a two-dimensional black hole spacetime. We consider the black hole which is the solution of the 2D dilaton gravity derived from string-theoretical models. We find an explicit solution in a closed form for all modes and the Green function of the scalar field with an arbitrary mass and a nonminimal coupling to the curvature. Greybody factors, the Hawking radiation, and 2>{sup ren} are calculated explicitly for this exactly solvable model.

Reflection and Non-Reflection of Particle Wavepackets

ERIC Educational Resources Information Center

Cox, Timothy; Lekner, John

2008-01-01

Exact closed-form solutions of the time-dependent Schrodinger equation are obtained, describing the propagation of wavepackets in the neighbourhood of a potential. Examples given include zero reflection, total reflection and partial reflection of the wavepacket, for the sech[superscript 2]x/a, 1/x[superscript 2] and delta(x) potentials,…

Computerized Diagnostic Testing: Problems and Possibilities.

ERIC Educational Resources Information Center

McArthur, David L.

The use of computers to build diagnostic inferences is explored in two contexts. In computerized monitoring of liquid oxygen systems for the space shuttle, diagnoses are exact because they can be derived within a world which is closed. In computerized classroom testing of reading comprehension, programs deliver a constrained form of adaptive…

A General Closed-Form Solution for the Lunar Reconnaissance Orbiter (LRO) Antenna Pointing System

NASA Technical Reports Server (NTRS)

Shah, Neerav; Chen, J. Roger; Hashmall, Joseph A.

2010-01-01

The National Aeronautics and Space Administration s (NASA) Lunar Reconnaissance Orbiter (LRO) launched on June 18, 2009 from the Cape Canaveral Air Force Station aboard an Atlas V launch vehicle into a direct insertion trajectory to the Moon LRO, designed, built, and operated by the NASA Goddard Space Flight Center in Greenbelt, MD, is gathering crucial data on the lunar environment that will help astronauts prepare for long-duration lunar expeditions. During the mission s nominal life of one year its six instruments and one technology demonstrator will find safe landing site, locate potential resources, characterize the radiation environment and test new technology. To date, LRO has been operating well within the bounds of its requirements and has been collecting excellent science data images taken from the LRO Camera Narrow Angle Camera (LROC NAC) of the Apollo landing sites have appeared on cable news networks. A significant amount of information on LRO s science instruments is provided at the LRO mission webpage. LRO s Attitude Control System (ACS), in addition to controlling the orientation of the spacecraft is also responsible for pointing the High Gain Antenna (HGA). A dual-axis (or double-gimbaled) antenna, deployed on a meter-long boom, is required to point at a selected Earth ground station. Due to signal loss over the distance from the Moon to Earth, pointing precision for the antenna system is very tight. Since the HGA has to be deployed in spaceflight, its exact geometry relative to the spacecraft body is uncertain. In addition, thermal distortions and mechanical errors/tolerances must be characterized and removed to realize the greatest gain from the antenna system. These reasons necessitate the need for an in-flight calibration. Once in orbit around the moon, a series of attitude maneuvers was conducted to provide data needed to determine optimal parameters to load onboard, which would account for the environmental and mechanical errors at any antenna orientation. The nominal geometry for the HGA involves an outer gimbal axis that is exactly perpendicular to the inner gimbal axis, and a target direction that is exactly perpendicular to the outer gimbal axis. For this nominal geometry, closed-form solutions of the desired gimbal angles are simple to get for a desired target direction specified in the spacecraft body fame. If the gimbal axes and the antenna boresight are slightly misaligned, the nominal closed-form solution is not sufficiently accurate for computing the gimbal angles needed to point at a target. In this situation, either a general closed-form solution has to be developed for a mechanism with general geometries, or a correction scheme has to be applied to the nominal closed-form solutions. The latter has been adopted for Solar Dynamics Observatory (SDO) as can be seen in Reference 1, and the former has been used for LRO. The advantage of the general closed-form solution is the use of a small number of parameters for the correction of nominal solutions, especially in the regions near singularities. Singularities here refer to cases when the nominal closed-form solutions have two or more solutions. Algorithm complexity, however, is the disadvantage of the general closed-form solution.

Lunar Tire Close-up

NASA Image and Video Library

2017-02-23

This is a close-up of an exact replica of the Apollo-era Lunar Roving Vehicle Wheel, of which twelve originals still rest on the surface of the Moon. The tire was designed to flex under load, without air, and was formed from a mesh of plated piano wire. Metal straps were hand riveted onto the mesh to reduce sinking into loose lunar soils. These replica wheels were tested in NASA Glenn's SLOPE Lab to establish a baseline for future improvements.

The Effective Resistance of the -Cycle Graph with Four Nearest Neighbors

NASA Astrophysics Data System (ADS)

Chair, Noureddine

2014-02-01

The exact expression for the effective resistance between any two vertices of the -cycle graph with four nearest neighbors , is given. It turns out that this expression is written in terms of the effective resistance of the -cycle graph , the square of the Fibonacci numbers, and the bisected Fibonacci numbers. As a consequence closed form formulas for the total effective resistance, the first passage time, and the mean first passage time for the simple random walk on the the -cycle graph with four nearest neighbors are obtained. Finally, a closed form formula for the effective resistance of with all first neighbors removed is obtained.

Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

NASA Astrophysics Data System (ADS)

Schatz, Konrad; Friedrich, Bretislav; Becker, Simon; Schmidt, Burkhard

2018-05-01

We make use of the quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasisolvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasisolvability of the time-independent Schrödinger equation as well as the corresponding finite sets of exact analytic solutions. We do so for this prototypical trigonometric system as well as for its anti-isospectral hyperbolic counterpart. An examination of the algebraic and numerical spectra of these two systems reveals mutually closely related patterns. The QHJ approach allows us to retrieve the closed-form solutions for the spherical and planar pendula and the Razavy system that had been obtained in our earlier work via supersymmetric quantum mechanics as well as to find a cornucopia of additional exact analytic solutions.

On prototypical wave transmission across a junction of waveguides with honeycomb structure

NASA Astrophysics Data System (ADS)

Sharma, Basant Lal

2018-02-01

An exact expression for the scattering matrix associated with a junction generated by partial unzipping along the zigzag direction of armchair tubes is presented. The assumed simple, but representative, model, for scalar wave transmission can be interpreted in terms of the transport of the out-of-plane phonons in the ribbon-side vis-a-vis the radial phonons in the tubular-side of junction, based on the nearest-neighbor interactions between lattice sites. The exact solution for the `bondlength' in `broken' versus intact bonds can be constructed via a standard application of the Wiener-Hopf technique. The amplitude distribution of outgoing phonons, far away from the junction on either side of it, is obtained in closed form by the mode-matching method; eventually, this leads to the provision of the scattering matrix. As the main result of the paper, a succinct and closed form expression for the accompanying reflection and transmission coefficients is provided along with a detailed derivation using the Chebyshev polynomials. Applications of the analysis presented in this paper include linear wave transmission in nanotubes, nanoribbons, and monolayers of honeycomb lattices containing carbon-like units.

Fingering patterns in magnetic fluids: Perturbative solutions and the stability of exact stationary shapes

NASA Astrophysics Data System (ADS)

Anjos, Pedro H. A.; Lira, Sérgio A.; Miranda, José A.

2018-04-01

We examine the formation of interfacial patterns when a magnetic liquid droplet (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. By using a vortex-sheet formalism, we find exact stationary solutions for the fluid-fluid interface in the form of n -fold polygonal shapes. A weakly nonlinear, mode-coupling method is then utilized to find time-evolving perturbative solutions for the interfacial patterns. The stability of such nonzero surface tension exact solutions is checked and discussed, by trying to systematically approach the exact stationary shapes through perturbative solutions containing an increasingly larger number of participating Fourier modes. Our results indicate that the exact stationary solutions of the problem are stable, and that a good matching between exact and perturbative shape solutions is achieved just by using a few Fourier modes. The stability of such solutions is substantiated by a linearization process close to the stationary shape, where a system of mode-coupling equations is diagonalized, determining the eigenvalues which dictate the stability of a fixed point.

Perturbation solutions of combustion instability problems

NASA Technical Reports Server (NTRS)

Googerdy, A.; Peddieson, J., Jr.; Ventrice, M.

1979-01-01

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Abundant closed form solutions of the conformable time fractional Sawada-Kotera-Ito equation using (G‧ / G) -expansion method

NASA Astrophysics Data System (ADS)

Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.

2018-06-01

In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.

Morse oscillator propagator in the high temperature limit I: Theory

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

Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae

2017-02-15

In an earlier work of the author the time evolution of Morse oscillator was studied analytically and exactly at low temperatures whereupon optical correlation functions were calculated using Morse oscillator coherent states were employed. Morse oscillator propagator in the high temperature limit is derived and a closed form of its corresponding canonical partition function is obtained. Both diagonal and off-diagonal forms of Morse oscillator propagator are derived in the high temperature limit. Partition functions of diatomic molecules are calculated. - Highlights: • Derives the quantum propagator of Morse oscillator in the high temperature limit. • Uses the resulting diagonal propagatormore » to derive a closed form of Morse oscillator partition function. • Provides a more sophisticated formula of the quantum propagator to test the accuracy of the herein results.« less

Contents or Ideology? A Case Study of Mathematical Teaching in North Korea

ERIC Educational Resources Information Center

Karp, Alexander; Lee, JungHang

2010-01-01

This article addresses mathematics education in one of the most closed countries in the world, North Korea. It is known that ideology permeates all aspects of life in North Korea, but how exactly do the ideological and substantive mathematical components interact in mathematics education there? What concrete form does this interaction take in…

Exact Solutions for Stokes' Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach

NASA Astrophysics Data System (ADS)

Aziz, Taha; Aziz, A.; Khalique, C. M.

2016-07-01

The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

Turbulence regeneration in pipe flow at moderate Reynolds numbers.

PubMed

Hof, Björn; van Doorne, Casimir W H; Westerweel, Jerry; Nieuwstadt, Frans T M

2005-11-18

We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves.

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

NASA Astrophysics Data System (ADS)

Conway, John T.; Cohl, Howard S.

2010-06-01

A new method is presented for Fourier decomposition of the Helmholtz Green function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Green function are split into their half advanced + half retarded and half advanced-half retarded components, and closed form solutions for these components are then obtained in terms of a Horn function and a Kampé de Fériet function respectively. Series solutions for the Fourier coefficients are given in terms of associated Legendre functions, Bessel and Hankel functions and a hypergeometric function. These series are derived either from the closed form 2-dimensional hypergeometric solutions or from an integral representation, or from both. A simple closed form far-field solution for the general Fourier coefficient is derived from the Hankel series. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented. Fourth order ordinary differential equations for the Fourier coefficients are also given and discussed briefly.

On the Spectrum of the Plenoptic Function.

PubMed

Gilliam, Christopher; Dragotti, Pier-Luigi; Brookes, Mike

2014-02-01

The plenoptic function is a powerful tool to analyze the properties of multi-view image data sets. In particular, the understanding of the spectral properties of the plenoptic function is essential in many computer vision applications, including image-based rendering. In this paper, we derive for the first time an exact closed-form expression of the plenoptic spectrum of a slanted plane with finite width and use this expression as the elementary building block to derive the plenoptic spectrum of more sophisticated scenes. This is achieved by approximating the geometry of the scene with a set of slanted planes and evaluating the closed-form expression for each plane in the set. We then use this closed-form expression to revisit uniform plenoptic sampling. In this context, we derive a new Nyquist rate for the plenoptic sampling of a slanted plane and a new reconstruction filter. Through numerical simulations, on both real and synthetic scenes, we show that the new filter outperforms alternative existing filters.

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

PubMed

Demidenko, Eugene

2017-09-01

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

Efficient modeling of interconnects and capacitive discontinuities in high-speed digital circuits. Thesis

NASA Technical Reports Server (NTRS)

Oh, K. S.; Schutt-Aine, J.

1995-01-01

Modeling of interconnects and associated discontinuities with the recent advances high-speed digital circuits has gained a considerable interest over the last decade although the theoretical bases for analyzing these structures were well-established as early as the 1960s. Ongoing research at the present time is focused on devising methods which can be applied to more general geometries than the ones considered in earlier days and, at the same time, improving the computational efficiency and accuracy of these methods. In this thesis, numerically efficient methods to compute the transmission line parameters of a multiconductor system and the equivalent capacitances of various strip discontinuities are presented based on the quasi-static approximation. The presented techniques are applicable to conductors embedded in an arbitrary number of dielectric layers with two possible locations of ground planes at the top and bottom of the dielectric layers. The cross-sections of conductors can be arbitrary as long as they can be described with polygons. An integral equation approach in conjunction with the collocation method is used in the presented methods. A closed-form Green's function is derived based on weighted real images thus avoiding nested infinite summations in the exact Green's function; therefore, this closed-form Green's function is numerically more efficient than the exact Green's function. All elements associated with the moment matrix are computed using the closed-form formulas. Various numerical examples are considered to verify the presented methods, and a comparison of the computed results with other published results showed good agreement.

Outage Probability of MRC for κ-μ Shadowed Fading Channels under Co-Channel Interference.

PubMed

Chen, Changfang; Shu, Minglei; Wang, Yinglong; Yang, Ming; Zhang, Chongqing

2016-01-01

In this paper, exact closed-form expressions are derived for the outage probability (OP) of the maximal ratio combining (MRC) scheme in the κ-μ shadowed fading channels, in which both the independent and correlated shadowing components are considered. The scenario assumes the received desired signals are corrupted by the independent Rayleigh-faded co-channel interference (CCI) and background white Gaussian noise. To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series. Then the incomplete generalized moment-generating function (IG-MGF) of the received signal-to-interference-plus-noise ratio (SINR) is derived in the closed form. By using the IG-MGF results, closed-form expressions for the OP of MRC scheme are obtained over the κ-μ shadowed fading channels. Simulation results are included to validate the correctness of the analytical derivations. These new statistical results can be applied to the modeling and analysis of several wireless communication systems, such as body centric communications.

Outage Probability of MRC for κ-μ Shadowed Fading Channels under Co-Channel Interference

PubMed Central

Chen, Changfang; Shu, Minglei; Wang, Yinglong; Yang, Ming; Zhang, Chongqing

2016-01-01

In this paper, exact closed-form expressions are derived for the outage probability (OP) of the maximal ratio combining (MRC) scheme in the κ-μ shadowed fading channels, in which both the independent and correlated shadowing components are considered. The scenario assumes the received desired signals are corrupted by the independent Rayleigh-faded co-channel interference (CCI) and background white Gaussian noise. To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series. Then the incomplete generalized moment-generating function (IG-MGF) of the received signal-to-interference-plus-noise ratio (SINR) is derived in the closed form. By using the IG-MGF results, closed-form expressions for the OP of MRC scheme are obtained over the κ-μ shadowed fading channels. Simulation results are included to validate the correctness of the analytical derivations. These new statistical results can be applied to the modeling and analysis of several wireless communication systems, such as body centric communications. PMID:27851817

Outage Analysis of Dual-hop Cognitive Networks with Relay Selection over Nakagami-m Fading Environment

NASA Astrophysics Data System (ADS)

Zhang, Zongsheng; Pi, Xurong

2014-09-01

In this paper, we investigate the outage performance of decode-and-forward cognitive relay networks for Nakagami-m fading channels, with considering both best relay selection and interference constraints. Focusing on the relay selection and making use of the underlay cognitive approach, an exact closed-form outage probability expression is derived in an independent, non-identical distributed Nakagami-m environment. The closed-form outage probability provides an efficient means to evaluate the effects of the maximum allowable interference power, number of cognitive relays, and channel conditions between the primary user and cognitive users. Finally, we present numerical results to validate the theory analysis. Moreover, from the simulation results, we obtain that the system can obtain the full diversity.

Partial differential equation-based localization of a monopole source from a circular array.

PubMed

Ando, Shigeru; Nara, Takaaki; Levy, Tsukassa

2013-10-01

Wave source localization from a sensor array has long been the most active research topics in both theory and application. In this paper, an explicit and time-domain inversion method for the direction and distance of a monopole source from a circular array is proposed. The approach is based on a mathematical technique, the weighted integral method, for signal/source parameter estimation. It begins with an exact form of the source-constraint partial differential equation that describes the unilateral propagation of wide-band waves from a single source, and leads to exact algebraic equations that include circular Fourier coefficients (phase mode measurements) as their coefficients. From them, nearly closed-form, single-shot and multishot algorithms are obtained that is suitable for use with band-pass/differential filter banks. Numerical evaluation and several experimental results obtained using a 16-element circular microphone array are presented to verify the validity of the proposed method.

Electromagnetic fields radiated from a lightning return stroke - Application of an exact solution to Maxwell's equations

NASA Technical Reports Server (NTRS)

Le Vine, D. M.; Meneghini, R.

1978-01-01

A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.

Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians

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

Longhi, Stefano, E-mail: stefano.longhi@fisi.polimi.it

Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H{sup -hat} (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H{sup -hat} (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for themore » Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization.« less

Natural Vibration Analysis of Clamped Rectangular Orthotropic Plates

NASA Astrophysics Data System (ADS)

dalaei, m.; kerr, a. d.

The natural vibrations of clamped rectangular orthotropic plates are analyzed using the extended Kantorovich method. The developed iterative scheme converges very rapidly to the final result. The obtained natural frequencies are evaluated for a square plate made of Kevlar 49 Epoxy and the obtained results are compared with those published by Kanazawa and Kawai, and by Leissa. The agreement was found to be very close. As there are no exact analytical solutions for clamped rectangular plates, the generated closed form expression for the natural modes, and the corresponding natural frequencies, are very suitable for use in engineering analyses.

Two-ball Newton's cradle

NASA Astrophysics Data System (ADS)

Glendinning, Paul

2011-12-01

Newton's cradle for two balls with Hertzian interactions is considered as a hybrid system, and this makes it possible to derive return maps for the motion between collisions in an exact form despite the fact that the three-halves interaction law cannot be solved in closed form. The return maps depend on a constant whose value can only be determined numerically, but solutions can be written down explicitly in terms of this parameter, and we compare this with the results of simulations. The results are in fact independent of the details of the interaction potential.

Viscosity of a concentrated suspension of rigid monosized particles

NASA Astrophysics Data System (ADS)

Brouwers, H. J. H.

2010-05-01

This paper addresses the relative viscosity of concentrated suspensions loaded with unimodal hard particles. So far, exact equations have only been put forward in the dilute limit, e.g., by Einstein [A. Einstein, Ann. Phys. 19, 289 (1906) (in German); Ann. Phys. 34, 591 (1911) (in German)] for spheres. For larger concentrations, a number of phenomenological models for the relative viscosity was presented, which depend on particle concentration only. Here, an original and exact closed form expression is derived based on geometrical considerations that predicts the viscosity of a concentrated suspension of monosized particles. This master curve for the suspension viscosity is governed by the relative viscosity-concentration gradient in the dilute limit (for spheres the Einstein limit) and by random close packing of the unimodal particles in the concentrated limit. The analytical expression of the relative viscosity is thoroughly compared with experiments and simulations reported in the literature, concerning both dilute and concentrated suspensions of spheres, and good agreement is found.

Closed solutions to a differential-difference equation and an associated plate solidification problem.

PubMed

Layeni, Olawanle P; Akinola, Adegbola P; Johnson, Jesse V

2016-01-01

Two distinct and novel formalisms for deriving exact closed solutions of a class of variable-coefficient differential-difference equations arising from a plate solidification problem are introduced. Thereupon, exact closed traveling wave and similarity solutions to the plate solidification problem are obtained for some special cases of time-varying plate surface temperature.

Sample distribution in peak mode isotachophoresis

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

Rubin, Shimon; Schwartz, Ortal; Bercovici, Moran, E-mail: mberco@technion.ac.il

We present an analytical study of peak mode isotachophoresis (ITP), and provide closed form solutions for sample distribution and electric field, as well as for leading-, trailing-, and counter-ion concentration profiles. Importantly, the solution we present is valid not only for the case of fully ionized species, but also for systems of weak electrolytes which better represent real buffer systems and for multivalent analytes such as proteins and DNA. The model reveals two major scales which govern the electric field and buffer distributions, and an additional length scale governing analyte distribution. Using well-controlled experiments, and numerical simulations, we verify andmore » validate the model and highlight its key merits as well as its limitations. We demonstrate the use of the model for determining the peak concentration of focused sample based on known buffer and analyte properties, and show it differs significantly from commonly used approximations based on the interface width alone. We further apply our model for studying reactions between multiple species having different effective mobilities yet co-focused at a single ITP interface. We find a closed form expression for an effective-on rate which depends on reactants distributions, and derive the conditions for optimizing such reactions. Interestingly, the model reveals that maximum reaction rate is not necessarily obtained when the concentration profiles of the reacting species perfectly overlap. In addition to the exact solutions, we derive throughout several closed form engineering approximations which are based on elementary functions and are simple to implement, yet maintain the interplay between the important scales. Both the exact and approximate solutions provide insight into sample focusing and can be used to design and optimize ITP-based assays.« less

A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers

NASA Astrophysics Data System (ADS)

Kumar, V. R. Sanal; Sankar, Vigneshwaran; Chandrasekaran, Nichith; Saravanan, Vignesh; Natarajan, Vishnu; Padmanabhan, Sathyan; Sukumaran, Ajith; Mani, Sivabalan; Rameshkumar, Tharikaa; Nagaraju Doddi, Hema Sai; Vysaprasad, Krithika; Sharan, Sharad; Murugesh, Pavithra; Shankar, S. Ganesh; Nejaamtheen, Mohammed Niyasdeen; Baskaran, Roshan Vignesh; Rahman Mohamed Rafic, Sulthan Ariff; Harisrinivasan, Ukeshkumar; Srinivasan, Vivek

2018-02-01

A closed-form analytical model is developed for estimating the 3D boundary-layer-displacement thickness of an internal flow system at the Sanal flow choking condition for adiabatic flows obeying the physics of compressible viscous fluids. At this unique condition the boundary-layer blockage induced fluid-throat choking and the adiabatic wall-friction persuaded flow choking occur at a single sonic-fluid-throat location. The beauty and novelty of this model is that without missing the flow physics we could predict the exact boundary-layer blockage of both 2D and 3D cases at the sonic-fluid-throat from the known values of the inlet Mach number, the adiabatic index of the gas and the inlet port diameter of the internal flow system. We found that the 3D blockage factor is 47.33 % lower than the 2D blockage factor with air as the working fluid. We concluded that the exact prediction of the boundary-layer-displacement thickness at the sonic-fluid-throat provides a means to correctly pinpoint the causes of errors of the viscous flow solvers. The methodology presented herein with state-of-the-art will play pivotal roles in future physical and biological sciences for a credible verification, calibration and validation of various viscous flow solvers for high-fidelity 2D/3D numerical simulations of real-world flows. Furthermore, our closed-form analytical model will be useful for the solid and hybrid rocket designers for the grain-port-geometry optimization of new generation single-stage-to-orbit dual-thrust-motors with the highest promising propellant loading density within the given envelope without manifestation of the Sanal flow choking leading to possible shock waves causing catastrophic failures.

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

NASA Astrophysics Data System (ADS)

Shodja, H. M.; Khorshidi, A.

2013-04-01

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

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

Liemert, André, E-mail: andre.liemert@ilm.uni-ulm.de; Kienle, Alwin

Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiativemore » transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.« less

Dual representation of lattice QCD with worldlines and worldsheets of Abelian color fluxes

NASA Astrophysics Data System (ADS)

Marchis, Carlotta; Gattringer, Christof

2018-02-01

We present a new dual representation for lattice QCD in terms of wordlines and worldsheets. The exact reformulation is carried out using the recently developed Abelian color flux method where the action is decomposed into commuting minimal terms that connect different colors on neighboring sites. Expanding the Boltzmann factors for these commuting terms allows one to reorganize the gauge field contributions according to links such that the gauge fields can be integrated out in closed form. The emerging constraints give the dual variables the structure of worldlines for the fermions and worldsheets for the gauge degrees of freedom. The partition sum has the form of a strong coupling expansion, and with the Abelian color flux approach discussed here all coefficients of the expansion are known in closed form. We present the dual form for three cases: pure SU(3) lattice gauge theory, strong coupling QCD and full QCD, and discuss in detail the constraints for the color fluxes and their physical interpretation.

Transfer matrix approach to the persistent current in quantum rings: Application to hybrid normal-superconducting rings

NASA Astrophysics Data System (ADS)

Nava, Andrea; Giuliano, Rosa; Campagnano, Gabriele; Giuliano, Domenico

2016-11-01

Using the properties of the transfer matrix of one-dimensional quantum mechanical systems, we derive an exact formula for the persistent current across a quantum mechanical ring pierced by a magnetic flux Φ as a single integral of a known function of the system's parameters. Our approach provides exact results at zero temperature, which can be readily extended to a finite temperature T . We apply our technique to exactly compute the persistent current through p -wave and s -wave superconducting-normal hybrid rings, deriving full plots of the current as a function of the applied flux at various system's scales. Doing so, we recover at once a number of effects such as the crossover in the current periodicity on increasing the size of the ring and the signature of the topological phase transition in the p -wave case. In the limit of a large ring size, resorting to a systematic expansion in inverse powers of the ring length, we derive exact analytic closed-form formulas, applicable to a number of cases of physical interest.

A closed-form solution to tensor voting: theory and applications.

PubMed

Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gérard

2012-08-01

We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway.

Chiral behavior of K →π l ν decay form factors in lattice QCD with exact chiral symmetry

NASA Astrophysics Data System (ADS)

Aoki, S.; Cossu, G.; Feng, X.; Fukaya, H.; Hashimoto, S.; Kaneko, T.; Noaki, J.; Onogi, T.; Jlqcd Collaboration

2017-08-01

We calculate the form factors of the K →π l ν semileptonic decays in three-flavor lattice QCD and study their chiral behavior as a function of the momentum transfer and the Nambu-Goldstone boson masses. Chiral symmetry is exactly preserved by using the overlap quark action, which enables us to directly compare the lattice data with chiral perturbation theory (ChPT). We generate gauge ensembles at a lattice spacing of 0.11 fm with four pion masses covering 290-540 MeV and a strange quark mass ms close to its physical value. By using the all-to-all quark propagator, we calculate the vector and scalar form factors with high precision. Their dependence on ms and the momentum transfer is studied by using the reweighting technique and the twisted boundary conditions for the quark fields. We compare the results for the semileptonic form factors with ChPT at next-to-next-to-leading order in detail. While many low-energy constants appear at this order, we make use of our data of the light meson electromagnetic form factors in order to control the chiral extrapolation. We determine the normalization of the form factors as f+(0 )=0.9636 (36 )(-35+57) and observe reasonable agreement of their shape with experiment.

A generalization of Bertrand's theorem to surfaces of revolution

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

Zagryadskii, Oleg A; Kudryavtseva, Elena A; Fedoseev, Denis A

We prove a generalization of Bertrand's theorem to the case of abstract surfaces of revolution that have no 'equators'. We prove a criterion for exactly two central potentials to exist on this type of surface (up to an additive and a multiplicative constant) for which all bounded orbits are closed and there is a bounded nonsingular noncircular orbit. We prove a criterion for the existence of exactly one such potential. We study the geometry and classification of the corresponding surfaces with the aforementioned pair of potentials (gravitational and oscillatory) or unique potential (oscillatory). We show that potentials of the requiredmore » form do not exist on surfaces that do not belong to any of the classes described. Bibliography: 33 titles.« less

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

NASA Astrophysics Data System (ADS)

Chicurel-Uziel, Enrique

2007-08-01

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

Recovery time in quantum dynamics of wave packets

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

Strekalov, M. L., E-mail: strekalov@kinetics.nsc.ru

2017-01-15

A wave packet formed by a linear superposition of bound states with an arbitrary energy spectrum returns arbitrarily close to the initial state after a quite long time. A method in which quantum recovery times are calculated exactly is developed. In particular, an exact analytic expression is derived for the recovery time in the limiting case of a two-level system. In the general case, the reciprocal recovery time is proportional to the Gauss distribution that depends on two parameters (mean value and variance of the return probability). The dependence of the recovery time on the mean excitation level of themore » system is established. The recovery time is the longest for the maximal excitation level.« less

On a new class of completely integrable nonlinear wave equations. I. Infinitely many conservation laws

NASA Astrophysics Data System (ADS)

Nutku, Y.

1985-06-01

We point out a class of nonlinear wave equations which admit infinitely many conserved quantities. These equations are characterized by a pair of exact one-forms. The implication that they are closed gives rise to equations, the characteristics and Riemann invariants of which are readily obtained. The construction of the conservation laws requires the solution of a linear second-order equation which can be reduced to canonical form using the Riemann invariants. The hodograph transformation results in a similar linear equation. We discuss also the symplectic structure and Bäcklund transformations associated with these equations.

Concise calculation of the scaling function, exponents, and probability functional of the Edwards-Wilkinson equation with correlated noise

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

Yu, Y.; Pang, N.; Halpin-Healy, T.

1994-12-01

The linear Langevin equation proposed by Edwards and Wilkinson [Proc. R. Soc. London A 381, 17 (1982)] is solved in closed form for noise of arbitrary space and time correlation. Furthermore, the temporal development of the full probability functional describing the height fluctuations is derived exactly, exhibiting an interesting evolution between two distinct Gaussian forms. We determine explicitly the dynamic scaling function for the interfacial width for any given initial condition, isolate the early-time behavior, and discover an invariance that was unsuspected in this problem of arbitrary spatiotemporal noise.

Exact simulation of max-stable processes.

PubMed

Dombry, Clément; Engelke, Sebastian; Oesting, Marco

2016-06-01

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

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Closed-form solution of the Ogden-Hill's compressible hyperelastic model for ramp loading

NASA Astrophysics Data System (ADS)

Berezvai, Szabolcs; Kossa, Attila

2017-05-01

This article deals with the visco-hyperelastic modelling approach for compressible polymer foam materials. Polymer foams can exhibit large elastic strains and displacements in case of volumetric compression. In addition, they often show significant rate-dependent properties. This material behaviour can be accurately modelled using the visco-hyperelastic approach, in which the large strain viscoelastic description is combined with the rate-independent hyperelastic material model. In case of polymer foams, the most widely used compressible hyperelastic material model, the so-called Ogden-Hill's model, was applied, which is implemented in the commercial finite element (FE) software Abaqus. The visco-hyperelastic model is defined in hereditary integral form, therefore, obtaining a closed-form solution for the stress is not a trivial task. However, the parameter-fitting procedure could be much faster and accurate if closed-form solution exists. In this contribution, exact stress solutions are derived in case of uniaxial, biaxial and volumetric compression loading cases using ramp-loading history. The analytical stress solutions are compared with the stress results in Abaqus using FE analysis. In order to highlight the benefits of the analytical closed-form solution during the parameter-fitting process experimental work has been carried out on a particular open-cell memory foam material. The results of the material identification process shows significant accuracy improvement in the fitting procedure by applying the derived analytical solutions compared to the so-called separated approach applied in the engineering practice.

A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories

NASA Astrophysics Data System (ADS)

Li, Wenliang

2018-04-01

We propose a framework for Lorentz-invariant Lagrangian field theories where Ostrogradsky's scalar ghosts could be absent. A key ingredient is the generalized Kronecker delta. The general Lagrangians are reformulated in the language of differential forms. The absence of higher order equations of motion for the scalar modes stems from the basic fact that every exact form is closed. The well-established Lagrangian theories for spin-0, spin-1, p-form, spin-2 fields have natural formulations in this framework. We also propose novel building blocks for Lagrangian field theories. Some of them are novel nonlinear derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar ghosts are absent in these fully nonlinear theories.

Analytically derived switching functions for exact H2+ eigenstates

NASA Astrophysics Data System (ADS)

Thorson, W. R.; Kimura, M.; Choi, J. H.; Knudson, S. K.

1981-10-01

Electron translation factors (ETF's) appropriate for slow atomic collisions may be constructed using switching functions. In this paper we derive a set of switching functions for the H2+ system by an analytical "two-center decomposition" of the exact molecular eigenstates. These switching functions are closely approximated by the simple form f=bη, where η is the "angle variable" of prolate spheroidal coordinates. For given united atom angular momentum quantum numbers (l,m), the characteristic parameter blm depends only on the quantity c2=-ɛR22, where ɛ is the electronic binding energy and R the internuclear distance in a.u. The resulting parameters are in excellent agreement with those found in our earlier work by a heuristic "optimization" scheme based on a study of coupling matrix-element behavior for a number of H2+ states. An approximate extension to asymmetric cases (HeH2+) has also been made. Nonadiabatic couplings based on these switching functions have been used in recent close-coupling calculations for H+-H(1s) collisions and He2+-H(1s) collisions at energies 1.0-20 keV.

Transverse vibration of Bernoulli Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution

NASA Astrophysics Data System (ADS)

Maiz, Santiago; Bambill, Diana V.; Rossit, Carlos A.; Laura, P. A. A.

2007-06-01

The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of the machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. An exact solution for the title problem is obtained in closed-form fashion, considering general boundary conditions by means of translational and rotatory springs at both ends. The model allows to analyze the influence of the masses and their rotatory inertia on the dynamic behavior of beams with all the classic boundary conditions, and also, as particular cases, to determine the frequencies of continuous beams.

Exact wave functions of two-electron quantum rings.

PubMed

Loos, Pierre-François; Gill, Peter M W

2012-02-24

We demonstrate that the Schrödinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational solutions can be found for any value of the angular momentum and that the singlet and triplet manifolds, which are degenerate, have distinct geometric phases. We also study the nodal structure associated with these two-electron states.

Collision Dynamics of Rydberg Atoms and Molecules at Ultralow Energies

DTIC Science & Technology

2005-12-31

body recombination between electrons, ions and neural gas atoms. We wish to study the interaction and collisions between two Rydberg atoms in the...transitions, Exact solutions of Stark mixing in atomic hydro- where Ekjn is the Levi - Civita antisymmetric symbol gen induced by the time-dependent...L and U do not close under commutation to form a Lie algebra because [Ui, Uj] = (-2g)iCijkLk, where cijk is the Levi - Civita antisymmetric symbol for

Equilibration in finite Bose systems

NASA Astrophysics Data System (ADS)

Wolschin, Georg

2018-06-01

The equilibration of a finite Bose system is modeled using a gradient expansion of the collision integral that leads to a nonlinear transport equation. For constant transport coefficients, it is solved in closed form through a nonlinear transformation. Using schematic initial conditions, the exact solution and the equilibration time are derived and compared to the corresponding case for fermions. Applications to the fast equilibration of the gluon system created initially in relativistic heavy-ion collisions, and to cold quantum gases are envisaged.

Nonparaxial wave beams and packets with general astigmatism

NASA Astrophysics Data System (ADS)

Kiselev, A. P.; Plachenov, A. B.; Chamorro-Posada, P.

2012-04-01

We present exact solutions of the wave equation involving an arbitrary wave form with a phase closely similar to the general astigmatic phase of paraxial wave optics. Special choices of the wave form allow general astigmatic beamlike and pulselike waves with a Gaussian-type unrestricted localization in space and time. These solutions are generalizations of the known Bateman-type waves obtained from the connection existing between beamlike solutions of the paraxial parabolic equation and relatively undistorted wave solutions of the wave equation. As a technical tool, we present a full description of parametrizations of 2×2 symmetric matrices with positive imaginary part, which arise in the theory of Gaussian beams.

Asymptotic/numerical analysis of supersonic propeller noise

NASA Technical Reports Server (NTRS)

Myers, M. K.; Wydeven, R.

1989-01-01

An asymptotic analysis based on the Mach surface structure of the field of a supersonic helical source distribution is applied to predict thickness and loading noise radiated by high speed propeller blades. The theory utilizes an integral representation of the Ffowcs-Williams Hawkings equation in a fully linearized form. The asymptotic results are used for chordwise strips of the blade, while required spanwise integrations are performed numerically. The form of the analysis enables predicted waveforms to be interpreted in terms of Mach surface propagation. A computer code developed to implement the theory is described and found to yield results in close agreement with more exact computations.

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

Exact RG flow equations and quantum gravity

NASA Astrophysics Data System (ADS)

de Alwis, S. P.

2018-03-01

We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.

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

PubMed

Bougoffa, Lazhar

2014-01-01

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

An exact solution for the solidification of a liquid slab of binary mixture

NASA Technical Reports Server (NTRS)

Antar, B. N.; Collins, F. G.; Aumalia, A. E.

1986-01-01

The time dependent temperature and concentration profiles of a one dimensional finite slab of a binary liquid alloy is investigated during solidification. The governing equations are reduced to a set of coupled, nonlinear initial value problems using the method outlined by Meyer. Two methods will be used to solve these equations. The first method uses a Runge-Kutta-Fehlberg integrator to solve the equations numerically. The second method comprises of finding closed form solutions of the equations.

The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations

NASA Technical Reports Server (NTRS)

Osher, Stanley

1989-01-01

Simple inequalities for the Riemann problem for a Hamilton-Jacobi equation in N space dimension when neither the initial data nor the Hamiltonian need be convex (or concave) are presented. The initial data is globally continuous, affine in each orthant, with a possible jump in normal derivative across each coordinate plane, x sub i = 0. The inequalities become equalities wherever a maxmin equals a minmax and thus an exact closed form solution to this problem is then obtained.

Statistics of Sxy estimates

NASA Technical Reports Server (NTRS)

Freilich, M. H.; Pawka, S. S.

1987-01-01

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman (1957), the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxy(tot). In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum-likelihood estimator for a posterior estimation is outlined.

Critical behavior of a relativistic Bose gas.

PubMed

Pandita, P N

2014-03-01

We show that the thermodynamic behavior of relativistic ideal Bose gas, recently studied numerically by Grether et al., can be obtained analytically. Using the analytical results, we obtain the critical behavior of the relativistic Bose gas exactly for all the regimes. We show that these analytical results reduce to those of Grether et al. in different regimes of the Bose gas. Furthermore, we also obtain an analytically closed-form expression for the energy density for the Bose gas that is valid in all regimes.

Exact analytical thermodynamic expressions for a Brownian heat engine

NASA Astrophysics Data System (ADS)

Taye, Mesfin Asfaw

2015-09-01

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

Exact analytical thermodynamic expressions for a Brownian heat engine.

PubMed

Taye, Mesfin Asfaw

2015-09-01

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

Exact solutions for laminated composite cylindrical shells in cylindrical bending

NASA Technical Reports Server (NTRS)

Yuan, F. G.

1992-01-01

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

Large Deformation Behavior of Long Shallow Cylindrical Composite Panels

NASA Technical Reports Server (NTRS)

Carper, Douglas M.; Hyer, Michael W.; Johnson, Eric R.

1991-01-01

An exact solution is presented for the large deformation response of a simply supported orthotropic cylindrical panel subjected to a uniform line load along a cylinder generator. The cross section of the cylinder is circular and deformations up to the fully snapped through position are investigated. The orthotropic axes are parallel to the generator and circumferential directions. The governing equations are derived using laminated plate theory, nonlinear strain-displacement relations, and applying variational principles. The response is investigated for the case of a panel loaded exactly at midspan and for a panel with the load offset from midspan. The mathematical formulation is one dimensional in the circumferential coordinate. Solutions are obtained in closed-form. An experimental apparatus was designed to load the panels. Experimental results of displacement controlled tests performed on graphite-epoxy curved panels are compared with analytical predictions.

Efficient Approaches for Evaluating the Planar Microstrip Green's Function and its Applications to the Analysis of Microstrip Antennas.

NASA Astrophysics Data System (ADS)

Barkeshli, Sina

A relatively simple and efficient closed form asymptotic representation of the microstrip dyadic surface Green's function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the planar microstrip configuration. Surprisingly, this asymptotic solution remains accurate even for very small (almost two tenths of a wavelength) lateral separation of the source and field points. The present asymptotic Green's function will thus allow a very efficient calculation of the currents excited on microstrip antenna patches/feed lines and monolithic millimeter and microwave integrated circuit (MIMIC) elements based on a moment method (MM) solution of an integral equation for these currents. The kernal of the latter integral equation is the present asymptotic form of the microstrip Green's function. It is noted that the conventional Sommerfeld integral representation of the microstrip surface Green's function is very poorly convergent when used in this MM formulation. In addition, an efficient exact steepest descent path integral form employing a radially propagating representation of the microstrip dyadic Green's function is also derived which exhibits a relatively faster convergence when compared to the conventional Sommerfeld integral representation. The same steepest descent form could also be obtained by deforming the integration contour of the conventional Sommerfeld representation; however, the radially propagating integral representation exhibits better convergence properties for laterally separated source and field points even before the steepest descent path of integration is used. Numerical results based on the efficient closed form asymptotic solution for the microstrip surface Green's function developed in this work are presented for the mutual coupling between a pair of dipoles on a single layer grounded dielectric slab. The accuracy of the latter calculations is confirmed by comparison with results based on an exact integral representation for that Green's function.

Perturbational blowup solutions to the compressible Euler equations with damping.

PubMed

Cheung, Ka Luen

2016-01-01

The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant. With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Conservational PDF Equations of Turbulence

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2010-01-01

Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

Creation of quasi-Dirac points in the Floquet band structure of bilayer graphene.

PubMed

Cheung, W M; Chan, K S

2017-06-01

We study the Floquet quasi-energy band structure of bilayer graphene when it is illuminated by two laser lights with frequencies [Formula: see text] and [Formula: see text] using Floquet theory. We focus on the dynamical gap formed by the conduction band with Floquet index  =  -1 and the valence band with Floquet index  =  +1 to understand how Dirac points can be formed. It is found that the dynamical gap does not have rotation symmetry in the momentum space, and quasi-Dirac points, where the conduction and valence bands almost touch, can be created when the dynamical gap closes along some directions with suitably chosen radiation parameters. We derive analytical expressions for the direction dependence of the dynamical gaps using Lowdin perturbation theory to gain a better understanding of the formation of quasi-Dirac points. When both radiations are circularly polarized, the gap can be exactly zero along some directions, when only the first and second order perturbations are considered. Higher order perturbations can open a very small gap in this case. When both radiations are linearly polarized, the gap can be exactly zero up to the fourth order perturbation and more than one quasi-Dirac point is formed. We also study the electron velocity around a dynamical gap and show that the magnitude of the velocity drops to values close to zero when the k vector is near to the gap minimum. The direction of the velocity also changes around the gap minimum, and when the gap is larger in value the change in the velocity direction is more gradual. The warping effect does not affect the formation of a Dirac point along the k x axis, while it prevents its formation when there is phase shift between the two radiations.

The microscopic structure of an exactly solvable model binary solution that exhibits two closed loops in the phase diagram.

PubMed

Lungu, Radu P; Huckaby, Dale A

2008-07-21

An exactly solvable lattice model describing a binary solution is considered where rodlike molecules of types AA and BB cover the links of a honeycomb lattice, the neighboring molecular ends having three-body and orientation-dependent bonding interactions. At phase coexistence of AA-rich and BB-rich phases, the average fraction of each type of triangle of neighboring molecular ends is calculated exactly. The fractions of the different types of triangles are then used to deduce the local microscopic structure of the coexisting phases for a case of the model that contains two closed loops in the phase diagram.

Black Hole Mass and Spin from the 2:3 Twin-peak QPOs in Microquasars

NASA Astrophysics Data System (ADS)

Mondal, Soumen

2010-01-01

In the Galactic microquasars with double peak kHz quasi-periodic oscillations (QPOs) detected in X-ray fluxes, the ratio of the twin-peak frequencies is exactly, or almost exactly 2:3. This rather strongly supports the fact that they originate a few gravitational radii away from its center due to two modes of accretion disk oscillations. Numerical investigations suggest that post-shock matter, before they settle down in a subsonic branch, execute oscillations in the neighborhood region of "shock transition". This shock may excite QPO mechanism. The radial and vertical epicyclic modes of oscillating matter exactly match with these twin-peak QPOs. In fully general relativistic transonic flows, we investigate that shocks may form very close to the horizon around highly spinning Kerr black holes and appear as extremum in the inviscid flows. The extreme shock location provides upper limit of QPOs and hence fixes "lower cutoff" of the spin. We conclude that the 2:3 ratio exactly occurs for spin parameters a >= 0.87 and almost exactly, for wide range of spin parameter, for example, XTE 1550-564, and GRO 1655-40 a>0.87, GRS 1915+105 a>0.83, XTE J1650-500 a>0.78, and H 1743-322 a>0.68. We also make an effort to measure unknown mass for XTE J1650-500(9.1 ~ 14.1 M sun) and H 1743-322(6.6 ~ 11.3 M sun).

LETTER TO THE EDITOR: Exact energy distribution function in a time-dependent harmonic oscillator

NASA Astrophysics Data System (ADS)

Robnik, Marko; Romanovski, Valery G.; Stöckmann, Hans-Jürgen

2006-09-01

Following a recent work by Robnik and Romanovski (2006 J. Phys. A: Math. Gen. 39 L35, 2006 Open Syst. Inf. Dyn. 13 197-222), we derive an explicit formula for the universal distribution function of the final energies in a time-dependent 1D harmonic oscillator, whose functional form does not depend on the details of the frequency ω(t) and is closely related to the conservation of the adiabatic invariant. The normalized distribution function is P(x) = \\pi^{-1} (2\\mu^2 - x^2)^{-\\frac{1}{2}} , where x=E_1- \\skew3\\bar{E}_1 ; E1 is the final energy, \\skew3\\bar{E}_1 is its average value and µ2 is the variance of E1. \\skew3\\bar{E}_1 and µ2 can be calculated exactly using the WKB approach to all orders.

Exactly solved models on planar graphs with vertices in {Z}^3

NASA Astrophysics Data System (ADS)

Kels, Andrew P.

2017-12-01

It is shown how exactly solved edge interaction models on the square lattice, may be extended onto more general planar graphs, with edges connecting a subset of next nearest neighbour vertices of {Z}3 . This is done by using local deformations of the square lattice, that arise through the use of the star-triangle relation. Similar to Baxter’s Z-invariance property, these local deformations leave the partition function invariant up to some simple factors coming from the star-triangle relation. The deformations used here extend the usual formulation of Z-invariance, by requiring the introduction of oriented rapidity lines which form directed closed paths in the rapidity graph of the model. The quasi-classical limit is also considered, in which case the deformations imply a classical Z-invariance property, as well as a related local closure relation, for the action functional of a system of classical discrete Laplace equations.

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

NASA Astrophysics Data System (ADS)

Mejía, José; Zapata, Camilo; Botero, Alonso

2017-01-01

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

Solution of the Eshelby problem in gradient elasticity for multilayer spherical inclusions

NASA Astrophysics Data System (ADS)

Volkov-Bogorodskii, D. B.; Lurie, S. A.

2016-03-01

We consider gradient models of elasticity which permit taking into account the characteristic scale parameters of the material. We prove the Papkovich-Neuber theorems, which determine the general form of the gradient solution and the structure of scale effects. We derive the Eshelby integral formula for the gradient moduli of elasticity, which plays the role of the closing equation in the self-consistent three-phase method. In the gradient theory of deformations, we consider the fundamental Eshelby-Christensen problem of determining the effective elastic properties of dispersed composites with spherical inclusions; the exact solution of this problem for classical models was obtained in 1976. This paper is the first to present the exact analytical solution of the Eshelby-Christensen problem for the gradient theory, which permits estimating the influence of scale effects on the stress state and the effective properties of the dispersed composites under study.We also analyze the influence of scale factors.

A hydrophobic gate in an ion channel: the closed state of the nicotinic acetylcholine receptor

NASA Astrophysics Data System (ADS)

Beckstein, Oliver; Sansom, Mark S. P.

2006-06-01

The nicotinic acetylcholine receptor (nAChR) is the prototypic member of the 'Cys-loop' superfamily of ligand-gated ion channels which mediate synaptic neurotransmission, and whose other members include receptors for glycine, γ-aminobutyric acid and serotonin. Cryo-electron microscopy has yielded a three-dimensional structure of the nAChR in its closed state. However, the exact nature and location of the channel gate remains uncertain. Although the transmembrane pore is constricted close to its center, it is not completely occluded. Rather, the pore has a central hydrophobic zone of radius about 3 Å. Model calculations suggest that such a constriction may form a hydrophobic gate, preventing movement of ions through a channel. We present a detailed and quantitative simulation study of the hydrophobic gating model of the nicotinic receptor, in order to fully evaluate this hypothesis. We demonstrate that the hydrophobic constriction of the nAChR pore indeed forms a closed gate. Potential of mean force (PMF) calculations reveal that the constriction presents a barrier of height about 10 kT to the permeation of sodium ions, placing an upper bound on the closed channel conductance of 0.3 pS. Thus, a 3 Å radius hydrophobic pore can form a functional barrier to the permeation of a 1 Å radius Na+ ion. Using a united-atom force field for the protein instead of an all-atom one retains the qualitative features but results in differing conductances, showing that the PMF is sensitive to the detailed molecular interactions.

Strip Yield Model Numerical Application to Different Geometries and Loading Conditions

NASA Technical Reports Server (NTRS)

Hatamleh, Omar; Forman, Royce; Shivakumar, Venkataraman; Lyons, Jed

2006-01-01

A new numerical method based on the strip-yield analysis approach was developed for calculating the Crack Tip Opening Displacement (CTOD). This approach can be applied for different crack configurations having infinite and finite geometries, and arbitrary applied loading conditions. The new technique adapts the boundary element / dislocation density method to obtain crack-face opening displacements at any point on a crack, and succeeds by obtaining requisite values as a series of definite integrals, the functional parts of each being evaluated exactly in a closed form.

Brownian thermal noise in functional optical surfaces

NASA Astrophysics Data System (ADS)

Kroker, S.; Dickmann, J.; Rojas Hurtado, C. B.; Heinert, D.; Nawrodt, R.; Levin, Y.; Vyatchanin, S. P.

2017-07-01

We present a formalism to compute Brownian thermal noise in functional optical surfaces such as grating reflectors, photonic crystal slabs, or complex metamaterials. Such computations are based on a specific readout variable, typically a surface integral of a dielectric interface displacement weighed by a form factor. This paper shows how to relate this form factor to Maxwell's stress tensor computed on all interfaces of the moving surface. As an example, we examine Brownian thermal noise in monolithic T-shaped grating reflectors. The previous computations by Heinert et al. [Phys. Rev. D 88, 042001 (2013), 10.1103/PhysRevD.88.042001] utilizing a simplified readout form factor produced estimates of thermal noise that are tens of percent higher than those of the exact analysis in the present paper. The relation between the form factor and Maxwell's stress tensor implies a close correlation between the optical properties of functional optical surfaces and thermal noise.

"Nonspecific" cholinesterase and acetylcholinesterase in rat tissues: molecular forms, structural and catalytic properties, and significance of the two enzyme systems.

PubMed Central

Vigny, M; Gisiger, V; Massoulié, J

1978-01-01

"Nonspecific" cholinesterase (acylcholine acylhydrolase; EC 3.1.1.8) from various rat tissues has been found to exist in several stable molecular forms that appear as exact counterparts of molecular forms of acetylcholinesterase (acetylcholine hydrolase; EC 3.1.1.7). The sedimentation pattern of cholinesterase was similar to that of acetylcholinesterase with a small but significant shift between the sedimentation coefficients of the corresponding forms. Extraction yields in different media also demonstrated a close parallelism between the two enzyme systems. Other properties, such as thermal stability and catalytic characteristics, indicated both differences and similarities. In spite of the structural resemblance implied by their physicochemical properties, cholinesterase did not crossreact with antibodies against acetylcholinesterase. The nature of the relationships revealed by these studies and their bearing on the physiological significance of cholinesterases are discussed. PMID:78492

Addition by subtraction in coupled-cluster theory: a reconsideration of the CC and CI interface and the nCC hierarchy.

PubMed

Bartlett, Rodney J; Musiał, Monika

2006-11-28

The nCC hierarchy of coupled-cluster approximations, where n guarantees exactness for n electrons and all products of n electrons are derived and applied to several illustrative problems. The condition of exactness for n=2 defines nCCSD=2CC, with nCCSDT=3CC and nCCSDTQ=4CC being exact for three and four electrons. To achieve this, the minimum number of diagrams is evaluated, which is less than in the corresponding CC model. For all practical purposes, nCC is also the proper definition of a size-extensive CI. 2CC is also an orbitally invariant coupled electron pair approximation. The numerical results of nCC are close to those for the full CC variant, and in some cases are closer to the full CI reference result. As 2CC is exact for separated electron pairs, it is the natural zeroth-order approximation for the correlation problem in molecules with other effects introduced as these units start to interact. The nCC hierarchy of approximations has all the attractive features of CC including its size extensivity, orbital invariance, and orbital insensitivity, but in a conceptually appealing form suited to bond breaking, while being computationally less demanding. Excited states from the equation of motion (EOM-2CC) are also reported, which show results frequently approaching those of EOM-CCSDT.

Localized solutions of Lugiato-Lefever equations with focused pump.

PubMed

Cardoso, Wesley B; Salasnich, Luca; Malomed, Boris A

2017-12-04

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

An exact and efficient first passage time algorithm for reaction-diffusion processes on a 2D-lattice

NASA Astrophysics Data System (ADS)

Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.

2014-01-01

We present an exact and efficient algorithm for reaction-diffusion-nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

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

Bezzola, Andri, E-mail: andri.bezzola@gmail.com; Bales, Benjamin B., E-mail: bbbales2@gmail.com; Alkire, Richard C., E-mail: r-alkire@uiuc.edu

2014-01-01

We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for largemore » ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.« less

Random matrix theory of singular values of rectangular complex matrices I: Exact formula of one-body distribution function in fixed-trace ensemble

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

Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

The fixed-trace ensemble of random complex matrices is the fundamental model that excellently describes the entanglement in the quantum states realized in a coupled system by its strongly chaotic dynamical evolution [see H. Kubotani, S. Adachi, M. Toda, Phys. Rev. Lett. 100 (2008) 240501]. The fixed-trace ensemble fully takes into account the conservation of probability for quantum states. The present paper derives for the first time the exact analytical formula of the one-body distribution function of singular values of random complex matrices in the fixed-trace ensemble. The distribution function of singular values (i.e. Schmidt eigenvalues) of a quantum state ismore » so important since it describes characteristics of the entanglement in the state. The derivation of the exact analytical formula utilizes two recent achievements in mathematics, which appeared in 1990s. The first is the Kaneko theory that extends the famous Selberg integral by inserting a hypergeometric type weight factor into the integrand to obtain an analytical formula for the extended integral. The second is the Petkovsek-Wilf-Zeilberger theory that calculates definite hypergeometric sums in a closed form.« less

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

PubMed

Netz, Roland R

2018-05-14

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

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

NASA Astrophysics Data System (ADS)

Netz, Roland R.

2018-05-01

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

Linear approximations of nonlinear systems

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Su, R.

1983-01-01

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Exactly solvable model of the two-dimensional electrical double layer.

PubMed

Samaj, L; Bajnok, Z

2005-12-01

We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike unit charges in the stability-against-collapse regime of reduced inverse temperatures 0< or = beta < 2. If there is a potential difference between the bulk interior of the electrolyte and the grounded electrode, the electrolyte region close to the electrode (known as the electrical double layer) carries some nonzero surface charge density. The model is mappable onto an integrable semi-infinite sine-Gordon theory with Dirichlet boundary conditions. The exact form-factor and boundary state information gained from the mapping provide asymptotic forms of the charge and number density profiles of electrolyte particles at large distances from the interface. The result for the asymptotic behavior of the induced electric potential, related to the charge density via the Poisson equation, confirms the validity of the concept of renormalized charge and the corresponding saturation hypothesis. It is documented on the nonperturbative result for the asymptotic density profile at a strictly nonzero beta that the Debye-Hückel beta-->0 limit is a delicate issue.

Verification assessment of piston boundary conditions for Lagrangian simulation of compressible flow similarity solutions

DOE PAGES

Ramsey, Scott D.; Ivancic, Philip R.; Lilieholm, Jennifer F.

2015-12-10

This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the code and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in Lagrangian compressible flow simulations as rigid boundary-driven flow, even if no such “piston”more » is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in Lagrangian compressible flow solvers. Finally, the consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common code verification analysis metrics (e.g., shock strength/position errors and global convergence rates).« less

Verification assessment of piston boundary conditions for Lagrangian simulation of compressible flow similarity solutions

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

Ramsey, Scott D.; Ivancic, Philip R.; Lilieholm, Jennifer F.

This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the code and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in Lagrangian compressible flow simulations as rigid boundary-driven flow, even if no such “piston”more » is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in Lagrangian compressible flow solvers. Finally, the consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common code verification analysis metrics (e.g., shock strength/position errors and global convergence rates).« less

Simplified Antenna Group Determination of RS Overhead Reduced Massive MIMO for Wireless Sensor Networks.

PubMed

Lee, Byung Moo

2017-12-29

Massive multiple-input multiple-output (MIMO) systems can be applied to support numerous internet of things (IoT) devices using its excessive amount of transmitter (TX) antennas. However, one of the big obstacles for the realization of the massive MIMO system is the overhead of reference signal (RS), because the number of RS is proportional to the number of TX antennas and/or related user equipments (UEs). It has been already reported that antenna group-based RS overhead reduction can be very effective to the efficient operation of massive MIMO, but the method of deciding the number of antennas needed in each group is at question. In this paper, we propose a simplified determination scheme of the number of antennas needed in each group for RS overhead reduced massive MIMO to support many IoT devices. Supporting many distributed IoT devices is a framework to configure wireless sensor networks. Our contribution can be divided into two parts. First, we derive simple closed-form approximations of the achievable spectral efficiency (SE) by using zero-forcing (ZF) and matched filtering (MF) precoding for the RS overhead reduced massive MIMO systems with channel estimation error. The closed-form approximations include a channel error factor that can be adjusted according to the method of the channel estimation. Second, based on the closed-form approximation, we present an efficient algorithm determining the number of antennas needed in each group for the group-based RS overhead reduction scheme. The algorithm depends on the exact inverse functions of the derived closed-form approximations of SE. It is verified with theoretical analysis and simulation that the proposed algorithm works well, and thus can be used as an important tool for massive MIMO systems to support many distributed IoT devices.

Simplified Antenna Group Determination of RS Overhead Reduced Massive MIMO for Wireless Sensor Networks

PubMed Central

2017-01-01

Massive multiple-input multiple-output (MIMO) systems can be applied to support numerous internet of things (IoT) devices using its excessive amount of transmitter (TX) antennas. However, one of the big obstacles for the realization of the massive MIMO system is the overhead of reference signal (RS), because the number of RS is proportional to the number of TX antennas and/or related user equipments (UEs). It has been already reported that antenna group-based RS overhead reduction can be very effective to the efficient operation of massive MIMO, but the method of deciding the number of antennas needed in each group is at question. In this paper, we propose a simplified determination scheme of the number of antennas needed in each group for RS overhead reduced massive MIMO to support many IoT devices. Supporting many distributed IoT devices is a framework to configure wireless sensor networks. Our contribution can be divided into two parts. First, we derive simple closed-form approximations of the achievable spectral efficiency (SE) by using zero-forcing (ZF) and matched filtering (MF) precoding for the RS overhead reduced massive MIMO systems with channel estimation error. The closed-form approximations include a channel error factor that can be adjusted according to the method of the channel estimation. Second, based on the closed-form approximation, we present an efficient algorithm determining the number of antennas needed in each group for the group-based RS overhead reduction scheme. The algorithm depends on the exact inverse functions of the derived closed-form approximations of SE. It is verified with theoretical analysis and simulation that the proposed algorithm works well, and thus can be used as an important tool for massive MIMO systems to support many distributed IoT devices. PMID:29286339

Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Zhong, Yiyuan; Chen, Chaojian; Tang, Jingtian; Kalscheuer, Thomas; Maurer, Hansruedi; Li, Yang

2018-03-01

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are derived for a polyhedral body with a polynomial mass contrast of order higher than one (that is quadratic and cubic orders). Three synthetic models (a prismatic body with depth-dependent density contrasts, an irregular polyhedron with linear density contrast and a tetrahedral body with horizontally and vertically varying density contrasts) are used to verify the correctness and the efficiency of our newly developed closed-form solutions. Excellent agreements are obtained between our solutions and other published exact solutions. In addition, stability tests are performed to demonstrate that our exact solutions can safely be used to detect shallow subsurface targets.

Model error in covariance structure models: Some implications for power and Type I error

PubMed Central

Coffman, Donna L.

2010-01-01

The present study investigated the degree to which violation of the parameter drift assumption affects the Type I error rate for the test of close fit and power analysis procedures proposed by MacCallum, Browne, and Sugawara (1996) for both the test of close fit and the test of exact fit. The parameter drift assumption states that as sample size increases both sampling error and model error (i.e. the degree to which the model is an approximation in the population) decrease. Model error was introduced using a procedure proposed by Cudeck and Browne (1992). The empirical power for both the test of close fit, in which the null hypothesis specifies that the Root Mean Square Error of Approximation (RMSEA) ≤ .05, and the test of exact fit, in which the null hypothesis specifies that RMSEA = 0, is compared with the theoretical power computed using the MacCallum et al. (1996) procedure. The empirical power and theoretical power for both the test of close fit and the test of exact fit are nearly identical under violations of the assumption. The results also indicated that the test of close fit maintains the nominal Type I error rate under violations of the assumption. PMID:21331302

A note on the solutions of some nonlinear equations arising in third-grade fluid flows: an exact approach.

PubMed

Aziz, Taha; Mahomed, F M

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.

Fitness Probability Distribution of Bit-Flip Mutation.

PubMed

Chicano, Francisco; Sutton, Andrew M; Whitley, L Darrell; Alba, Enrique

2015-01-01

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.

On traveling waves in beams

NASA Technical Reports Server (NTRS)

Leonard, Robert W; Budiansky, Bernard

1954-01-01

The basic equations of Timoshenko for the motion of vibrating nonuniform beams, which allow for effects of transverse shear deformation and rotary inertia, are presented in several forms, including one in which the equations are written in the directions of the characteristics. The propagation of discontinuities in moment and shear, as governed by these equations, is discussed. Numerical traveling-wave solutions are obtained for some elementary problems of finite uniform beams for which the propagation velocities of bending and shear discontinuities are taken to be equal. These solutions are compared with modal solutions of Timoshenko's equations and, in some cases, with exact closed solutions. (author)

Lectures on the scattering of light. [by dielectric sphere

NASA Technical Reports Server (NTRS)

Saxon, D. S.

1974-01-01

The exact (Mie) theory for the scattering of a plane wave by a dielectric sphere is presented. Since this infinite series solution is computationally impractical for large spheres, another formulation is given in terms of an integral equation valid for a bounded, but otherwise general array of scatterers. This equation is applied to the scattering by a single sphere, and several methods are suggested for approximating the scattering cross section in closed form. A tensor scattering matrix is introduced, in terms of which some general scattering theorems are derived. The application of the formalism to multiple scattering is briefly considered.

A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

PubMed Central

Mahomed, F. M.

2014-01-01

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed. PMID:25143962

Clinical chemistry as scientific discipline: historical perspectives.

PubMed

Büttner, J

1994-12-31

The fundamental ideas which underlie clinical chemistry as an independent scientific field were formed over the course of centuries. Exactly 200 years ago the first modern concepts for this discipline were formulated in close connection with the restructuring of medical education during the French Revolution on the one hand, and the emergence of a new idea of a 'clinic' on the other hand. However, not until 1840 was clinical chemistry institutionalized as academic subject and simultaneously integrated into medical teaching. After about 1860, clinical chemistry was practiced by the clinicians themselves in close relationship with clinical activities, yet again with emphasis on teaching. In this period, clinics and hospitals established 'clinical laboratories'. With the start of the 20th century, after biochemistry had developed into an independent scientific field, clinical chemistry continued to evolve in close relationship with that latter discipline. This was particularly true in the United States, where an 'American School of Clinical Biochemistry' emerged which was to greatly influence the field.

Wave vector modification of the infinite order sudden approximation

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

Sachs, J.G.; Bowman, J.M.

1980-10-15

A simple method is proposed to modify the infinite order sudden approximation (IOS) in order to extend its region of quantitative validity. The method involves modifying the phase of the IOS scattering matrix to include a part calculated at the outgoing relative kinetic energy as well as a part calculated at the incoming kinetic energy. An immediate advantage of this modification is that the resulting S matrix is symmetric. We also present a closely related method in which the relative kinetic energies used in the calculation of the phase are determined from quasiclassical trajectory calculations. A set of trajectories ismore » run with the initial state being the incoming state, and another set is run with the initial state being the outgoing state, and the average final relative kinetic energy of each set is obtained. One part of the S-operator phase is then calculated at each of these kinetic energies. We apply these methods to vibrationally inelastic collinear collisions of an atom and a harmonic oscillator, and calculate transition probabilities P/sub n/1..-->..nf for three model systems. For systems which are sudden, or nearly so, the agreement with exact quantum close-coupling calculations is substantially improved over standard IOS ones when ..delta..n=such thatub f/-n/sub i/ is large, and the corresponding transition probability is small, i.e., less than 0.1. However, the modifications we propose will not improve the accuracy of the IOS transition probabilities for any collisional system unless the standard form of IOS already gives at least qualitative agreement with exact quantal calculations. We also suggest comparisons between some classical quantities and sudden predictions which should help in determining the validity of the sudden approximation. This is useful when exact quantal data is not available for comparison.« less

Wave vector modification of the infinite order sudden approximation

NASA Astrophysics Data System (ADS)

Sachs, Judith Grobe; Bowman, Joel M.

1980-10-01

A simple method is proposed to modify the infinite order sudden approximation (IOS) in order to extend its region of quantitative validity. The method involves modifying the phase of the IOS scattering matrix to include a part calculated at the outgoing relative kinetic energy as well as a part calculated at the incoming kinetic energy. An immediate advantage of this modification is that the resulting S matrix is symmetric. We also present a closely related method in which the relative kinetic energies used in the calculation of the phase are determined from quasiclassical trajectory calculations. A set of trajectories is run with the initial state being the incoming state, and another set is run with the initial state being the outgoing state, and the average final relative kinetic energy of each set is obtained. One part of the S-operator phase is then calculated at each of these kinetic energies. We apply these methods to vibrationally inelastic collinear collisions of an atom and a harmonic oscillator, and calculate transition probabilities Pn1→nf for three model systems. For systems which are sudden, or nearly so, the agreement with exact quantum close-coupling calculations is substantially improved over standard IOS ones when Δn=‖nf-ni‖ is large, and the corresponding transition probability is small, i.e., less than 0.1. However, the modifications we propose will not improve the accuracy of the IOS transition probabilities for any collisional system unless the standard form of IOS already gives at least qualitative agreement with exact quantal calculations. We also suggest comparisons between some classical quantities and sudden predictions which should help in determining the validity of the sudden approximation. This is useful when exact quantal data is not available for comparison.

Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations.

PubMed

Chavanis, P-H; Sire, C

2004-08-01

We determine an exact asymptotic expression of the blow-up time t(coll) for self-gravitating Brownian particles or bacterial populations (chemotaxis) close to the critical point in d=3. We show that t(coll) = t(*) (eta- eta(c) )(-1/2) with t(*) =0.917 677 02..., where eta represents the inverse temperature (for Brownian particles) or the mass (for bacterial colonies), and eta(c) is the critical value of eta above which the system blows up. This result is in perfect agreement with the numerical solution of the Smoluchowski-Poisson system. We also determine the exact asymptotic expression of the relaxation time close to but above the critical temperature and derive a large time asymptotic expansion for the density profile exactly at the critical point.

Closed timelike curves produced by pairs of moving cosmic strings - Exact solutions

NASA Technical Reports Server (NTRS)

Gott, J. Richard, III

1991-01-01

Exact solutions of Einstein's field equations are presented for the general case of two moving straight cosmic strings that do not intersect. The solutions for parallel cosmic strings moving in opposite directions show closed timelike curves (CTCs) that circle the two strings as they pass, allowing observers to visit their own past. Similar results occur for nonparallel strings, and for masses in (2+1)-dimensional spacetime. For finite string loops the possibility that black-hole formation may prevent the formation of CTCs is discussed.

Random matrix models, double-time Painlevé equations, and wireless relaying

NASA Astrophysics Data System (ADS)

Chen, Yang; Haq, Nazmus S.; McKay, Matthew R.

2013-06-01

This paper gives an in-depth study of a multiple-antenna wireless communication scenario in which a weak signal received at an intermediate relay station is amplified and then forwarded to the final destination. The key quantity determining system performance is the statistical properties of the signal-to-noise ratio (SNR) γ at the destination. Under certain assumptions on the encoding structure, recent work has characterized the SNR distribution through its moment generating function, in terms of a certain Hankel determinant generated via a deformed Laguerre weight. Here, we employ two different methods to describe the Hankel determinant. First, we make use of ladder operators satisfied by orthogonal polynomials to give an exact characterization in terms of a "double-time" Painlevé differential equation, which reduces to Painlevé V under certain limits. Second, we employ Dyson's Coulomb fluid method to derive a closed form approximation for the Hankel determinant. The two characterizations are used to derive closed-form expressions for the cumulants of γ, and to compute performance quantities of engineering interest.

Programmable logic construction kits for hyper-real-time neuronal modeling.

PubMed

Guerrero-Rivera, Ruben; Morrison, Abigail; Diesmann, Markus; Pearce, Tim C

2006-11-01

Programmable logic designs are presented that achieve exact integration of leaky integrate-and-fire soma and dynamical synapse neuronal models and incorporate spike-time dependent plasticity and axonal delays. Highly accurate numerical performance has been achieved by modifying simpler forward-Euler-based circuitry requiring minimal circuit allocation, which, as we show, behaves equivalently to exact integration. These designs have been implemented and simulated at the behavioral and physical device levels, demonstrating close agreement with both numerical and analytical results. By exploiting finely grained parallelism and single clock cycle numerical iteration, these designs achieve simulation speeds at least five orders of magnitude faster than the nervous system, termed here hyper-real-time operation, when deployed on commercially available field-programmable gate array (FPGA) devices. Taken together, our designs form a programmable logic construction kit of commonly used neuronal model elements that supports the building of large and complex architectures of spiking neuron networks for real-time neuromorphic implementation, neurophysiological interfacing, or efficient parameter space investigations.

Evolutionary games with self-questioning adaptive mechanism and the Ising model

NASA Astrophysics Data System (ADS)

Liu, J.; Xu, C.; Hui, P. M.

2017-09-01

A class of evolutionary games using a self-questioning strategy switching mechanism played in a population of connected agents is shown to behave as an Ising model Hamiltonian of spins connected in the same way. The payoff parameters combine to give the coupling between spins and an external magnetic field. The mapping covers the prisoner's dilemma, snowdrift and stag hunt games in structured populations. A well-mixed system is used to illustrate the equivalence. In a chain of agents/spins, the mapping to Ising model leads to an exact solution to the games effortlessly. The accuracy of standard approximations on the games can then be quantified. The site approximation is found to show varied accuracies depending on the payoff parameters, and the link approximation is shown to give the exact result in a chain but not in a closed form. The mapping established here connects two research areas, with each having much to offer to the other.

Nonlinear image registration with bidirectional metric and reciprocal regularization

PubMed Central

Ying, Shihui; Li, Dan; Xiao, Bin; Peng, Yaxin; Du, Shaoyi; Xu, Meifeng

2017-01-01

Nonlinear registration is an important technique to align two different images and widely applied in medical image analysis. In this paper, we develop a novel nonlinear registration framework based on the diffeomorphic demons, where a reciprocal regularizer is introduced to assume that the deformation between two images is an exact diffeomorphism. In detail, first, we adopt a bidirectional metric to improve the symmetry of the energy functional, whose variables are two reciprocal deformations. Secondly, we slack these two deformations into two independent variables and introduce a reciprocal regularizer to assure the deformations being the exact diffeomorphism. Then, we utilize an alternating iterative strategy to decouple the model into two minimizing subproblems, where a new closed form for the approximate velocity of deformation is calculated. Finally, we compare our proposed algorithm on two data sets of real brain MR images with two relative and conventional methods. The results validate that our proposed method improves accuracy and robustness of registration, as well as the gained bidirectional deformations are actually reciprocal. PMID:28231342

Discrete breathers in an array of self-excited oscillators: Exact solutions and stability.

PubMed

Shiroky, I B; Gendelman, O V

2016-10-01

We consider dynamics of array of coupled self-excited oscillators. The model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs) and exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone but lose stability via Neimark-Sacker bifurcation in the vicinity of the bandgap boundary. Besides the well-known DBs with exponential localization, the considered system possesses novel type of solutions-discrete breathers with main frequency in the propagation zone of the chain. In these regimes, the energy irradiation into the chain is balanced by the self-excitation. The amplitude of oscillations is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in the closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.

Discrete breathers in an array of self-excited oscillators: Exact solutions and stability

NASA Astrophysics Data System (ADS)

Shiroky, I. B.; Gendelman, O. V.

2016-10-01

We consider dynamics of array of coupled self-excited oscillators. The model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs) and exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone but lose stability via Neimark-Sacker bifurcation in the vicinity of the bandgap boundary. Besides the well-known DBs with exponential localization, the considered system possesses novel type of solutions—discrete breathers with main frequency in the propagation zone of the chain. In these regimes, the energy irradiation into the chain is balanced by the self-excitation. The amplitude of oscillations is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in the closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.

Closed form solutions of two time fractional nonlinear wave equations

NASA Astrophysics Data System (ADS)

Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

2018-06-01

In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

An Exactly Solvable Spin Chain Related to Hahn Polynomials

NASA Astrophysics Data System (ADS)

Stoilova, Neli I.; van der Jeugt, Joris

2011-03-01

We study a linear spin chain which was originally introduced by Shi et al. [Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength contains a parameter α and depends on the parity of the chain site. Extending the model by a second parameter β, it is shown that the single fermion eigenstates of the Hamiltonian can be computed in explicit form. The components of these eigenvectors turn out to be Hahn polynomials with parameters (α,β) and (α+1,β-1). The construction of the eigenvectors relies on two new difference equations for Hahn polynomials. The explicit knowledge of the eigenstates leads to a closed form expression for the correlation function of the spin chain. We also discuss some aspects of a q-extension of this model.

Primordial black holes in linear and non-linear regimes

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

Allahyari, Alireza; Abolhasani, Ali Akbar; Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir

We revisit the formation of primordial black holes (PBHs) in the radiation-dominated era for both linear and non-linear regimes, elaborating on the concept of an apparent horizon. Contrary to the expectation from vacuum models, we argue that in a cosmological setting a density fluctuation with a high density does not always collapse to a black hole. To this end, we first elaborate on the perturbation theory for spherically symmetric space times in the linear regime. Thereby, we introduce two gauges. This allows to introduce a well defined gauge-invariant quantity for the expansion of null geodesics. Using this quantity, we arguemore » that PBHs do not form in the linear regime irrespective of the density of the background. Finally, we consider the formation of PBHs in non-linear regimes, adopting the spherical collapse picture. In this picture, over-densities are modeled by closed FRW models in the radiation-dominated era. The difference of our approach is that we start by finding an exact solution for a closed radiation-dominated universe. This yields exact results for turn-around time and radius. It is important that we take the initial conditions from the linear perturbation theory. Additionally, instead of using uniform Hubble gauge condition, both density and velocity perturbations are admitted in this approach. Thereby, the matching condition will impose an important constraint on the initial velocity perturbations δ {sup h} {sub 0} = −δ{sub 0}/2. This can be extended to higher orders. Using this constraint, we find that the apparent horizon of a PBH forms when δ > 3 at turn-around time. The corrections also appear from the third order. Moreover, a PBH forms when its apparent horizon is outside the sound horizon at the re-entry time. Applying this condition, we infer that the threshold value of the density perturbations at horizon re-entry should be larger than δ {sub th} > 0.7.« less

Exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral harmonics

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

High-energy effective theory for matter on close Randall-Sundrum branes

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

Rham, Claudia de; Webster, Samuel

2005-09-15

Extending the analysis of C. de Rham and S. Webster [Phys. Rev. D 71, 124025 (2005)], we obtain a formal expression for the coupling between brane matter and the radion in a Randall-Sundrum braneworld. This effective theory is correct to all orders in derivatives of the radion in the limit of small brane separation, and, in particular, contains no higher than second derivatives. In the case of cosmological symmetry the theory can be obtained in closed form and reproduces the five-dimensional behavior. Perturbations in the tensor and scalar sectors are then studied. When the branes are moving, the effective Newtonianmore » constant on the brane is shown to depend both on the distance between the branes and on their velocity. In the small-distance limit, we compute the exact dependence between the four-dimensional and the five-dimensional Newtonian constants.« less

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

A {3,2}-Order Bending Theory for Laminated Composite and Sandwich Beams

NASA Technical Reports Server (NTRS)

Cook, Geoffrey M.; Tessler, Alexander

1998-01-01

A higher-order bending theory is derived for laminated composite and sandwich beams thus extending the recent {1,2}-order theory to include third-order axial effect without introducing additional kinematic variables. The present theory is of order {3,2} and includes both transverse shear and transverse normal deformations. A closed-form solution to the cylindrical bending problem is derived and compared with the corresponding exact elasticity solution. The numerical comparisons are focused on the most challenging material systems and beam aspect ratios which include moderate-to-thick unsymmetric composite and sandwich laminates. Advantages and limitations of the theory are discussed.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Analytic solutions for single and multiple cylinders of gravitating polytropes in magnetostatic equilibrium

NASA Technical Reports Server (NTRS)

Lerche, I.; Low, B. C.

1980-01-01

Exact analytic solutions for the static equilibrium of a gravitating plasma polytrope in the presence of magnetic fields are presented. The means of generating various equilibrium configurations to illustrate directly the complex physical relationships between pressure, magnetic fields, and gravity in self-gravitating systems is demonstrated. One of the solutions is used to model interstellar clouds suspended by magnetic fields against the galactic gravity such as may be formed by the Parker (1966) instability. It is concluded that the pinching effect of closed loops of magnetic fields in the clouds may be a dominant agent in further collapsing the clouds following their formation.

Hawking radiation in sonic black holes.

PubMed

Giovanazzi, S

2005-02-18

I present a microscopic description of Hawking radiation in sonic black holes. A one-dimensional Fermi-degenerate liquid squeezed by a smooth barrier forms a transonic flow, a sonic analog of a black hole. The quantum treatment of the noninteracting case establishes a close relationship between sonic Hawking radiation and quantum tunneling through the barrier. Quasiparticle excitations appear at the barrier and are then radiated with a thermal distribution in exact agreement with Hawking's formula. The signature of the radiation can be found in the dynamic structure factor, which can be measured in a scattering experiment. The possibility for experimental verification of this new transport phenomenon for ultracold atoms is discussed.

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

Song, Kai; Song, Linze; Shi, Qiang, E-mail: qshi@iccas.ac.cn

Based on the path integral approach, we derive a new realization of the exact non-Markovian stochastic Schrödinger equation (SSE). The main difference from the previous non-Markovian quantum state diffusion (NMQSD) method is that the complex Gaussian stochastic process used for the forward propagation of the wave function is correlated, which may be used to reduce the amplitude of the non-Markovian memory term at high temperatures. The new SSE is then written into the recently developed hierarchy of pure states scheme, in a form that is more closely related to the hierarchical equation of motion approach. Numerical simulations are then performedmore » to demonstrate the efficiency of the new method.« less

Analogies between Kirchhoff plates and functionally graded Saint-Venant beams under torsion

NASA Astrophysics Data System (ADS)

Barretta, Raffaele; Luciano, Raimondo

2015-05-01

Exact solutions of elastic Kirchhoff plates are available only for special geometries, loadings and kinematic boundary constraints. An effective solution procedure, based on an analogy between functionally graded orthotropic Saint-Venant beams under torsion and inhomogeneous isotropic Kirchhoff plates, with no kinematic boundary constraints, is proposed. The result extends the one contributed in Barretta (Acta Mech 224(12):2955-2964, 2013) for the special case of homogeneous Saint-Venant beams under torsion. Closed-form solutions for displacement, bending-twisting moment and curvature fields of an elliptic plate, corresponding to a functionally graded orthotropic beam, are evaluated. A new benchmark for computational mechanics is thus provided.

Gödel universes in string theory

NASA Astrophysics Data System (ADS)

Barrow, John D.; Dabrowski, Mariusz P.

1998-11-01

We show that homogeneous Gödel spacetimes need not contain closed timelike curves in low-energy-effective string theories. We find exact solutions for the Gödel metric in string theory for the full O(α') action including both dilaton and axion fields. The results are valid for bosonic, heterotic and super-strings. To first order in the inverse string tension α', these solutions display a simple relation between the angular velocity of the Gödel universe, Ω, and the inverse string tension of the form α'=1/Ω2 in the absence of the axion field. The generalization of this relationship is also found when the axion field is present.

The Fundamental Solutions for the Stress Intensity Factors of Modes I, II And III. The Axially Symmetric Problem

NASA Astrophysics Data System (ADS)

Rogowski, B.

2015-05-01

The subject of the paper are Green's functions for the stress intensity factors of modes I, II and III. Green's functions are defined as a solution to the problem of an elastic, transversely isotropic solid with a penny-shaped or an external crack under general axisymmetric loadings acting along a circumference on the plane parallel to the crack plane. Exact solutions are presented in a closed form for the stress intensity factors under each type of axisymmetric ring forces as fundamental solutions. Numerical examples are employed and conclusions which can be utilized in engineering practice are formulated.

Exact partition functions for deformed N=2 theories with N_f=4 flavours

NASA Astrophysics Data System (ADS)

Beccaria, Matteo; Fachechi, Alberto; Macorini, Guido; Martina, Luigi

2016-12-01

We consider the Ω-deformed N=2 SU(2) gauge theory in four dimensions with N f = 4 massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters ɛ 1 , ɛ 2, the scalar field expectation value a, and the hypermultiplet masses m = ( m 1 , m 2 , m 3 , m 4). Motivated by recent findings in the N={2}^{*} theory, we explore the theories that are characterized by special fixed ratios ɛ 2 /ɛ 1 and m /ɛ 1 and propose a simple condition on the structure of the multi-instanton contributions to the prepotential determining the effective action. This condition determines a finite set Π N of special points such that the prepotential has N poles at fixed positions independent on the instanton number. In analogy with what happens in the N={2}^{*} gauge theory, the full prepotential of the Π N theories may be given in closed form as an explicit function of a and the modular parameter q appearing in special combinations of Eisenstein series and Jacobi theta functions with well defined modular properties. The resulting finite pole partition functions are related by AGT correspondence to special 4-point spherical conformal blocks of the Virasoro algebra. We examine in full details special cases where the closed expression of the block is known and confirms our Ansatz. We systematically study the special features of Zamolodchikov's recursion for the Π N conformal blocks. As a result, we provide a novel effective recursion relation that can be exactly solved and allows to prove the conjectured closed expressions analytically in the case of the Π1 and Π2 conformal blocks.

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

NASA Astrophysics Data System (ADS)

Krapez, J.-C.

2018-07-01

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

Design equations for the assessment and FRP-strengthening of reinforced rectangular concrete columns under combined biaxial bending and axial loads

NASA Astrophysics Data System (ADS)

Alessandri, S.; Monti, G.

2008-05-01

A simple procedure is proposed for the assessment of reinforced rectangular concrete columns under combined biaxial bending and axial loads and for the design of a correct amount of FRP-strengthening for underdesigned concrete sections. Approximate closed-form equations are developed based on the load contour method originally proposed by Bresler for reinforced concrete sections. The 3D failure surface is approximated along its contours, at a constant axial load, by means of equations given as the sum of the acting/resisting moment ratio in the directions of principal axes of the sections, raised to a power depending on the axial load, the steel reinforcement ratio, and the section shape. The method is extended to FRP-strengthened sections. Moreover, to make it possible to apply the load contour method in a more practical way, simple closed-form equations are developed for rectangular reinforced concrete sections with a two-way steel reinforcement and FRP strengthenings on each side. A comparison between the approach proposed and the fiber method (which is considered exact) shows that the simplified equations correctly represent the section interaction diagram.

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.

Classical Control System Design: A non-Graphical Method for Finding the Exact System Parameters

NASA Astrophysics Data System (ADS)

Hussein, Mohammed Tawfik

2008-06-01

The Root Locus method of control system design was developed in the 1940's. It is a set of rules that helps in sketching the path traced by the roots of the closed loop characteristic equation of the system, as a parameter such as a controller gain, k, is varied. The procedure provides approximate sketching guidelines. Designs on control systems using the method are therefore not exact. This paper aims at a non-graphical method for finding the exact system parameters to place a pair of complex conjugate poles on a specified damping ratio line. The overall procedure is based on the exact solution of complex equations on the PC using numerical methods.

General theory for calculating disorder-averaged Green's function correlators within the coherent potential approximation

NASA Astrophysics Data System (ADS)

Zhou, Chenyi; Guo, Hong

2017-01-01

We report a diagrammatic method to solve the general problem of calculating configurationally averaged Green's function correlators that appear in quantum transport theory for nanostructures containing disorder. The theory treats both equilibrium and nonequilibrium quantum statistics on an equal footing. Since random impurity scattering is a problem that cannot be solved exactly in a perturbative approach, we combine our diagrammatic method with the coherent potential approximation (CPA) so that a reliable closed-form solution can be obtained. Our theory not only ensures the internal consistency of the diagrams derived at different levels of the correlators but also satisfies a set of Ward-like identities that corroborate the conserving consistency of transport calculations within the formalism. The theory is applied to calculate the quantum transport properties such as average ac conductance and transmission moments of a disordered tight-binding model, and results are numerically verified to high precision by comparing to the exact solutions obtained from enumerating all possible disorder configurations. Our formalism can be employed to predict transport properties of a wide variety of physical systems where disorder scattering is important.

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

Quantum Field Theory in Two Dimensions: Light-front Versus Space-like Solutions

NASA Astrophysics Data System (ADS)

Martinovic̆, L'ubomír

2017-07-01

A few non-perturbative topics of quantum field theory in D=1+1 are studied in both the conventional (SL) and light-front (LF) versions. First, we give a concise review of the recently proposed quantization of the two-dimensional massless LF fields. The LF version of bosonization follows in a simple and natural way including the bosonized form of the Thirring model. As a further application, we demonstrate the closeness of the 2D massless LF quantum fields to conformal field theory (CFT). We calculate several correlation functions including those between the components of the LF energy-momentum tensor and derive the LF version of the Virasoro algebra. Using the Euclidean time variable, we can immediately transform calculated quantities to the (anti)holomorphic form. The results found are in agreement with those from CFT. Finally, we show that the proposed framework provides us with the elements needed for an independent LF study of exactly solvable models. We compute the non-perturbative correlation functions from the exact operator solution of the LF Thirring model and compare it to the analogous results in the SL theory. While the vacuum effects are automatically taken into account in the LF case, the non-trivial vacuum structure has to be incorported by an explicit diagonalization of the SL Hamiltonians, to obtain the equivalently complete solution.

Scribbling on the blank sheet: Eddington's structuralist conception of objects

NASA Astrophysics Data System (ADS)

French, Steven

Although Eddington's philosophy of physics has been subjected to critical re-evaluation in recent years, neither the exact nature of his structuralist views nor his response to criticism by the likes of Braithwaite have been made clear. In this paper I trace, in particular, the incorporation into Eddington's structuralism of the non-classical indistinguishability of quantum objects. His metaphysical view of such objects as the product of group-theoretical analysis is crucial for understanding his response to Braithwaite's criticisms of the whole structuralist endeavor. These criticisms closely resemble more recent attacks on structural realism in the philosophy of science. I conclude with a brief comparison between these more modern forms of structuralism and Eddington's.

Performance analysis of dual-hop optical wireless communication systems over k-distribution turbulence channel with pointing error

NASA Astrophysics Data System (ADS)

Mishra, Neha; Sriram Kumar, D.; Jha, Pranav Kumar

2017-06-01

In this paper, we investigate the performance of the dual-hop free space optical (FSO) communication systems under the effect of strong atmospheric turbulence together with misalignment effects (pointing error). We consider a relay assisted link using decode and forward (DF) relaying protocol between source and destination with the assumption that Channel State Information is available at both transmitting and receiving terminals. The atmospheric turbulence channels are modeled by k-distribution with pointing error impairment. The exact closed form expression is derived for outage probability and bit error rate and illustrated through numerical plots. Further BER results are compared for the different modulation schemes.

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

NASA Astrophysics Data System (ADS)

Ismail-Beigi, Sohrab

2010-05-01

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

Anisotropic exchange interaction induced by a single photon in semiconductor microcavities

NASA Astrophysics Data System (ADS)

Chiappe, G.; Fernández-Rossier, J.; Louis, E.; Anda, E. V.

2005-12-01

We investigate coupling of localized spins in a semiconductor quantum dot embedded in a microcavity. The lowest cavity mode and the quantum dot exciton are coupled and close in energy, forming a polariton. The fermions forming the exciton interact with localized spins via exchange. Exact diagonalization of a Hamiltonian in which photons, spins, and excitons are treated quantum mechanically shows that a single polariton induces a sizable indirect anisotropic exchange interaction between spins. At sufficiently low temperatures strong ferromagnetic correlations show up without an appreciable increase in exciton population. In the case of a (Cd,Mn)Te quantum dot, Mn-Mn ferromagnetic coupling is still significant at 1 K : spin-spin correlation around 3 for exciton occupation smaller than 0.3. We find that the interaction mediated by photon-polaritons is 10 times stronger than the one induced by a classical field for equal Rabi splitting.

On the degrees of freedom of reduced-rank estimators in multivariate regression

PubMed Central

Mukherjee, A.; Chen, K.; Wang, N.; Zhu, J.

2015-01-01

Summary We study the effective degrees of freedom of a general class of reduced-rank estimators for multivariate regression in the framework of Stein's unbiased risk estimation. A finite-sample exact unbiased estimator is derived that admits a closed-form expression in terms of the thresholded singular values of the least-squares solution and hence is readily computable. The results continue to hold in the high-dimensional setting where both the predictor and the response dimensions may be larger than the sample size. The derived analytical form facilitates the investigation of theoretical properties and provides new insights into the empirical behaviour of the degrees of freedom. In particular, we examine the differences and connections between the proposed estimator and a commonly-used naive estimator. The use of the proposed estimator leads to efficient and accurate prediction risk estimation and model selection, as demonstrated by simulation studies and a data example. PMID:26702155

Deflection of a flexural cantilever beam

NASA Astrophysics Data System (ADS)

Sherbourne, A. N.; Lu, F.

The behavior of a flexural elastoplastic cantilever beam is investigated in which geometric nonlinearities are considered. The result of an elastica analysis by Frisch-Fay (1962) is extended to include postyield behavior. Although a closed-form solution is not possible, as in the elastic case, simple algebraic equations are derived involving only one unknown variable, which can also be expressed in the standard form of elliptic integrals if so desired. The results, in comparison with those of the small deflection analyses, indicate that large deflection analyses are necessary when the relative depth of the beam is very small over the length. The present exact solution can be used as a reference by those who resort to a finite element method for more complicated problems. It can also serve as a building block to other beam problems such as a simply supported beam or a beam with multiple loads.

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.

Cosmology with decaying cosmological constant—exact solutions and model testing

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

Szydłowski, Marek; Stachowski, Aleksander, E-mail: marek.szydlowski@uj.edu.pl, E-mail: aleksander.stachowski@uj.edu.pl

We study dynamics of Λ(t) cosmological models which are a natural generalization of the standard cosmological model (the ΛCDM model). We consider a class of models: the ones with a prescribed form of Λ(t)=Λ{sub bare}+α{sup 2}/t{sup 2}. This type of a Λ(t) parametrization is motivated by different cosmological approaches. We interpret the model with running Lambda (Λ(t)) as a special model of an interacting cosmology with the interaction term −dΛ(t)/dt in which energy transfer is between dark matter and dark energy sectors. For the Λ(t) cosmology with a prescribed form of Λ(t) we have found the exact solution in themore » form of Bessel functions. Our model shows that fractional density of dark energy Ω{sub e} is constant and close to zero during the early evolution of the universe. We have also constrained the model parameters for this class of models using the astronomical data such as SNIa data, BAO, CMB, measurements of H(z) and the Alcock-Paczyński test. In this context we formulate a simple criterion of variability of Λ with respect to t in terms of variability of the jerk or sign of estimator (1−Ω{sub m},0−Ω{sub Λ,0}). The case study of our model enable us to find an upper limit α{sup 2} < 0.012 (2σ C.L.) describing the variation from the cosmological constant while the LCDM model seems to be consistent with various data.« less

New exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in multi-temperature electron plasmas

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu; Zeng, Zhi-Fang

2017-10-01

In this paper, we aim to introduce a new form of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation for the long waves of small amplitude with slow dependence on the transverse coordinate. By using the Hirota's bilinear form and the extended homoclinic test approach, new exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are presented. Moreover, the properties and characteristics for these new exact periodic solitary-wave solutions are discussed with some figures.

The mu-derivative and its applications to finding exact solutions of the Cahn-Hilliard, Korteveg-de Vries, and Burgers equations.

PubMed

Mitlin, Vlad

2005-10-15

A new transformation termed the mu-derivative is introduced. Applying it to the Cahn-Hilliard equation yields dynamical exact solutions. It is shown that the mu-transformed Cahn-Hilliard equation can be presented in a separable form. This transformation also yields dynamical exact solutions and separable forms for other nonlinear models such as the modified Korteveg-de Vries and the Burgers equations. The general structure of a nonlinear partial differential equation that becomes separable upon applying the mu-derivative is described.

Chapter 5. Hidden Symmetry and Exact Solutions in Einstein Gravity

NASA Astrophysics Data System (ADS)

Yasui, Y.; Houri, T.

Conformal Killing-Yano tensors are introduced as ageneralization of Killing vectors. They describe symmetries of higher-dimensional rotating black holes. In particular, a rank-2 closed conformal Killing-Yano tensor generates the tower of both hidden symmetries and isometries. We review a classification of higher-dimensional spacetimes admitting such a tensor, and present exact solutions to the Einstein equations for these spacetimes.

Critical frontier of the Potts and percolation models on triangular-type and kagome-type lattices. II. Numerical analysis

NASA Astrophysics Data System (ADS)

Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F. Y.

2010-06-01

In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu’s result is exact, and for the kagome-type lattices Wu’s expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu’s analysis is the derivation of lattice-dependent constants A,B,C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q -state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n×n):(n×n) , n≤4 , for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1×1):(n×n) for 1≤n≤6 .

A relativistic gravity train

NASA Astrophysics Data System (ADS)

Parker, Edward

2017-08-01

A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl's theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.

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

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

Human physiological benefits of viewing nature: EEG responses to exact and statistical fractal patterns.

PubMed

Hagerhall, C M; Laike, T; Küller, M; Marcheschi, E; Boydston, C; Taylor, R P

2015-01-01

Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as opposed to fractal patterns which repeat exactly at different scales. This raises the question of whether human responses like preference and relaxation are being driven by fractal geometry in general or by the specific form of fractal geometry found in nature. In this study we consider both types of fractals (statistical and exact) and morph one type into the other. Based on the Koch curve, nine visual stimuli were produced in which curves of three different fractal dimensions evolve gradually from an exact to a statistical fractal. The patterns were shown for one minute each to thirty-five subjects while qEEG was continuously recorded. The results showed that the responses to statistical and exact fractals differ, and that the natural form of the fractal is important for inducing alpha responses, an indicator of a wakefully relaxed state and internalized attention.

The Galaxy Count Correlation Function in Redshift Space Revisited

NASA Astrophysics Data System (ADS)

Campagne, J.-E.; Plaszczynski, S.; Neveu, J.

2017-08-01

In the near future, cosmology will enter the wide and deep galaxy survey era, enabling high-precision studies of the large-scale structure of the universe in three dimensions. To test cosmological models and determine their parameters accurately, it is necessary to use data with exact theoretical expectations expressed in observational parameter space (angles and redshift). The data-driven, galaxy number count fluctuations on redshift shells can be used to build correlation functions ξ (θ ,{z}1,{z}2) on and between shells to probe the baryonic acoustic oscillations and distance-redshift distortions, as well as gravitational lensing and other relativistic effects. To obtain a numerical estimation of ξ (θ ,{z}1,{z}2) from a cosmological model, it is typical to use either a closed form derived from a tripolar spherical expansion or to compute the power spectrum {C}{\\ell }({z}1,{z}2) and perform a Legendre polynomial {P}{\\ell }(\\cos θ ) expansion. Here, we present a new derivation of a ξ (θ ,{z}1,{z}2) closed form using the spherical harmonic expansion and proceeding to an infinite sum over multipoles thanks to an addition theorem. We demonstrate that this new expression is perfectly compatible with the existing closed forms but is simpler to establish and manipulate. We provide formulas for the leading density and redshift-space contributions, but also show how Doppler-like and lensing terms can be easily included in this formalism. We have implemented and made publicly available software for computing those correlations efficiently, without any Limber approximation, and validated this software with the CLASSgal code. It is available at https://gitlab.in2p3.fr/campagne/AngPow.

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers.

PubMed

Cui, Jiaxin; Zhang, Yiyun; Cheng, Dazhi; Li, Dawei; Zhou, Xinlin

2017-01-01

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation.

Practical auxiliary basis implementation of Rung 3.5 functionals

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

Janesko, Benjamin G., E-mail: b.janesko@tcu.edu; Scalmani, Giovanni; Frisch, Michael J.

2014-07-21

Approximate exchange-correlation functionals for Kohn-Sham density functional theory often benefit from incorporating exact exchange. Exact exchange is constructed from the noninteracting reference system's nonlocal one-particle density matrix γ(r{sup -vector},r{sup -vector}′). Rung 3.5 functionals attempt to balance the strengths and limitations of exact exchange using a new ingredient, a projection of γ(r{sup -vector},r{sup -vector} ′) onto a semilocal model density matrix γ{sub SL}(ρ(r{sup -vector}),∇ρ(r{sup -vector}),r{sup -vector}−r{sup -vector} ′). γ{sub SL} depends on the electron density ρ(r{sup -vector}) at reference point r{sup -vector}, and is closely related to semilocal model exchange holes. We present a practical implementation of Rung 3.5 functionals, expandingmore » the r{sup -vector}−r{sup -vector} ′ dependence of γ{sub SL} in an auxiliary basis set. Energies and energy derivatives are obtained from 3D numerical integration as in standard semilocal functionals. We also present numerical tests of a range of properties, including molecular thermochemistry and kinetics, geometries and vibrational frequencies, and bandgaps and excitation energies. Rung 3.5 functionals typically provide accuracy intermediate between semilocal and hybrid approximations. Nonlocal potential contributions from γ{sub SL} yield interesting successes and failures for band structures and excitation energies. The results enable and motivate continued exploration of Rung 3.5 functional forms.« less

On Fully Developed Channel Flows: Some Solutions and Limitations, and Effects of Compressibility, Variable Properties, and Body Forces

NASA Technical Reports Server (NTRS)

Maslen, Stephen H.

1959-01-01

An examination of the effects of compressibility, variable properties, and body forces on fully developed laminar flow has indicated several limitations on such streams. In the absence of a pressure gradient, but presence of a body force (e.g., gravity), an exact fully developed gas flow results. For a liquid this follows also for the case of a constant streamwise pressure gradient. These motions are exact in the sense of a Couette flow. In the liquid case two solutions (not a new result) can occur for the same boundary conditions. An approximate analytic solution was found which agrees closely with machine calculations.In the case of approximately exact flows, it turns out that for large temperature variations across the channel the effects of convection (due to, say, a wall temperature gradient) and frictional heating must be negligible. In such a case the energy and momentum equations are separated, and the solutions are readily obtained. If the temperature variations are small, then both convection effects and frictional heating can consistently be considered. This case becomes the constant-property incompressible case (or quasi-incompressible case for free-convection flows) considered by many authors. Finally there is a brief discussion of cases wherein streamwise variations of all quantities are allowed but only a such form that independent variables are separable. For the case where the streamwise velocity varies inversely as the square root distance along the channel a solution is given.

Fast Quaternion Attitude Estimation from Two Vector Measurements

NASA Technical Reports Server (NTRS)

Markley, F. Landis; Bauer, Frank H. (Technical Monitor)

2001-01-01

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. Existing closed-form attitude estimates based on Wahba's optimality criterion for two arbitrarily weighted observations are somewhat slow to evaluate. This paper presents two new fast quaternion attitude estimation algorithms using two vector observations, one optimal and one suboptimal. The suboptimal method gives the same estimate as the TRIAD algorithm, at reduced computational cost. Simulations show that the TRIAD estimate is almost as accurate as the optimal estimate in representative test scenarios.

FUEL ELEMENT FOR NUCLEAR REACTORS

DOEpatents

Bassett, C.H.

1961-11-21

A fuel element is designed which is particularly adapted for reactors of high power density used to generate steam for the production of electricity. The fuel element consists of inner and outer concentric tubes forming an annular chamber within which is contained fissionable fuel pellet segments, wedge members interposed between the fuel segments, and a spring which, acting with wedge members, urges said fuel pellets radially into contact against the inner surface of the outer tube. The wedge members may be a fertile material convertible into fissionable fuel material by absorbing neutrons emitted from the fissionable fuel pellet segments. The costly grinding of cylindrical fuel pellets to close tolerances for snug engagement is reduced because the need to finish the exact size is eliminated. (AEC)

An 'unconditional-like' structure for the conditional estimator of odds ratio from 2 x 2 tables.

PubMed

Hanley, James A; Miettinen, Olli S

2006-02-01

In the estimation of the odds ratio (OR), the conditional maximum-likelihood estimate (cMLE) is preferred to the more readily computed unconditional one (uMLE). However, the exact cMLE does not have a closed form to help divine it from the uMLE or to understand in what circumstances the difference between the two is appreciable. Here, the cMLE is shown to have the same 'ratio of cross-products' structure as its unconditional counterpart, but with two of the cell frequencies augmented, so as to shrink the unconditional estimator towards unity. The augmentation involves a factor, similar to the finite population correction, derived from the minimum of the marginal totals.

Joint Transmit Antenna Selection and Power Allocation for ISDF Relaying Mobile-to-Mobile Sensor Networks

PubMed Central

Xu, Lingwei; Zhang, Hao; Gulliver, T. Aaron

2016-01-01

The outage probability (OP) performance of multiple-relay incremental-selective decode-and-forward (ISDF) relaying mobile-to-mobile (M2M) sensor networks with transmit antenna selection (TAS) over N-Nakagami fading channels is investigated. Exact closed-form OP expressions for both optimal and suboptimal TAS schemes are derived. The power allocation problem is formulated to determine the optimal division of transmit power between the broadcast and relay phases. The OP performance under different conditions is evaluated via numerical simulation to verify the analysis. These results show that the optimal TAS scheme has better OP performance than the suboptimal scheme. Further, the power allocation parameter has a significant influence on the OP performance. PMID:26907282

You can run, you can hide: The epidemiology and statistical mechanics of zombies

NASA Astrophysics Data System (ADS)

Alemi, Alexander A.; Bierbaum, Matthew; Myers, Christopher R.; Sethna, James P.

2015-11-01

We use a popular fictional disease, zombies, in order to introduce techniques used in modern epidemiology modeling, and ideas and techniques used in the numerical study of critical phenomena. We consider variants of zombie models, from fully connected continuous time dynamics to a full scale exact stochastic dynamic simulation of a zombie outbreak on the continental United States. Along the way, we offer a closed form analytical expression for the fully connected differential equation, and demonstrate that the single person per site two dimensional square lattice version of zombies lies in the percolation universality class. We end with a quantitative study of the full scale US outbreak, including the average susceptibility of different geographical regions.

The Pearson walk with shrinking steps in two dimensions

NASA Astrophysics Data System (ADS)

Serino, C. A.; Redner, S.

2010-01-01

We study the shrinking Pearson random walk in two dimensions and greater, in which the direction of the Nth step is random and its length equals λN-1, with λ<1. As λ increases past a critical value λc, the endpoint distribution in two dimensions, P(r), changes from having a global maximum away from the origin to being peaked at the origin. The probability distribution for a single coordinate, P(x), undergoes a similar transition, but exhibits multiple maxima on a fine length scale for λ close to λc. We numerically determine P(r) and P(x) by applying a known algorithm that accurately inverts the exact Bessel function product form of the Fourier transform for the probability distributions.

Occupation probabilities and fluctuations in the asymmetric simple inclusion process

NASA Astrophysics Data System (ADS)

Reuveni, Shlomi; Hirschberg, Ori; Eliazar, Iddo; Yechiali, Uri

2014-04-01

The asymmetric simple inclusion process (ASIP), a lattice-gas model of unidirectional transport and aggregation, was recently proposed as an "inclusion" counterpart of the asymmetric simple exclusion process. In this paper we present an exact closed-form expression for the probability that a given number of particles occupies a given set of consecutive lattice sites. Our results are expressed in terms of the entries of Catalan's trapezoids—number arrays which generalize Catalan's numbers and Catalan's triangle. We further prove that the ASIP is asymptotically governed by the following: (i) an inverse square-root law of occupation, (ii) a square-root law of fluctuation, and (iii) a Rayleigh law for the distribution of interexit times. The universality of these results is discussed.

Spectral edge: gradient-preserving spectral mapping for image fusion.

PubMed

Connah, David; Drew, Mark S; Finlayson, Graham D

2015-12-01

This paper describes a novel approach to image fusion for color display. Our goal is to generate an output image whose gradient matches that of the input as closely as possible. We achieve this using a constrained contrast mapping paradigm in the gradient domain, where the structure tensor of a high-dimensional gradient representation is mapped exactly to that of a low-dimensional gradient field which is then reintegrated to form an output. Constraints on output colors are provided by an initial RGB rendering. Initially, we motivate our solution with a simple "ansatz" (educated guess) for projecting higher-D contrast onto color gradients, which we expand to a more rigorous theorem to incorporate color constraints. The solution to these constrained optimizations is closed-form, allowing for simple and hence fast and efficient algorithms. The approach can map any N-D image data to any M-D output and can be used in a variety of applications using the same basic algorithm. In this paper, we focus on the problem of mapping N-D inputs to 3D color outputs. We present results in five applications: hyperspectral remote sensing, fusion of color and near-infrared or clear-filter images, multilighting imaging, dark flash, and color visualization of magnetic resonance imaging diffusion-tensor imaging.

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.

From quantum affine groups to the exact dynamical correlation function of the Heisenberg model

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

Bougourzi, A.H.; Couture, M.; Kacir, M.

1997-01-20

The exact form factors of the Heisenberg models XXX and XXZ have been recently computed through the quantum affine symmetry of XXZ model in the thermodynamic limit. The authors use them to derive an exact formula for the contribution of two spinons to the dynamical correlation function of XXX model at zero temperature.

von Kármán swirling flow between a rotating and a stationary smooth disk: Experiment

NASA Astrophysics Data System (ADS)

Mukherjee, Aryesh; Steinberg, Victor

2018-01-01

Precise measurements of the torque in a von Kármán swirling flow between a rotating and a stationary smooth disk in three Newtonian fluids with different dynamic viscosities are reported. From these measurements the dependence of the normalized torque, called the friction coefficient, on Re is found to be of the form Cf=1.17 (±0.03 ) Re-0.46±0.003 where the scaling exponent and coefficient are close to that predicted theoretically for an infinite, unshrouded, and smooth rotating disk which follows from an exact similarity solution of the Navier-Stokes equations, obtained by von Kármán. An error analysis shows that deviations from the theory can be partially caused by background errors. Measurements of the azimuthal Vθ and axial velocity profiles along radial and axial directions reveal that the flow core rotates at Vθ/r Ω ≃0.22 (up to z ≈4 cm from the rotating disk and up to r0/R ≃0.25 in the radial direction) in spite of the small aspect ratio of the vessel. Thus the friction coefficient shows scaling close to that obtained from the von Kármán exact similarity solution, but the observed rotating core provides evidence of the Batchelor-like solution [Q. J. Mech. Appl. Math. 4, 29 (1951), 10.1093/qjmam/4.1.29] different from the von Kármán [Z. Angew. Math. Mech. 1, 233 (1921), 10.1002/zamm.19210010401] or Stewartson [Proc. Camb. Philos. Soc. 49, 333 (1953), 10.1017/S0305004100028437] one.

Reduced Dynamics of the Non-holonomic Whipple Bicycle

NASA Astrophysics Data System (ADS)

Boyer, Frédéric; Porez, Mathieu; Mauny, Johan

2018-06-01

Though the bicycle is a familiar object of everyday life, modeling its full nonlinear three-dimensional dynamics in a closed symbolic form is a difficult issue for classical mechanics. In this article, we address this issue without resorting to the usual simplifications on the bicycle kinematics nor its dynamics. To derive this model, we use a general reduction-based approach in the principal fiber bundle of configurations of the three-dimensional bicycle. This includes a geometrically exact model of the contacts between the wheels and the ground, the explicit calculation of the kernel of constraints, along with the dynamics of the system free of any external forces, and its projection onto the kernel of admissible velocities. The approach takes benefits of the intrinsic formulation of geometric mechanics. Along the path toward the final equations, we show that the exact model of the bicycle dynamics requires to cope with a set of non-symmetric constraints with respect to the structural group of its configuration fiber bundle. The final reduced dynamics are simulated on several examples representative of the bicycle. As expected the constraints imposed by the ground contacts, as well as the energy conservation, are satisfied, while the dynamics can be numerically integrated in real time.

Synchronization in complex oscillator networks and smart grids.

PubMed

Dörfler, Florian; Chertkov, Michael; Bullo, Francesco

2013-02-05

The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here, we present a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically correct for almost all networks; and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks, such as electrical power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex network scenarios and in smart grid applications.

Exact solution of the Lifshitz equations governing the growth of fluctuations in cosmology

NASA Technical Reports Server (NTRS)

Adams, P. J.; Canuto, V.

1975-01-01

The exact solution of the Lifshitz equations governing the cosmological evolution of an initial fluctuation is presented. Lifshitz results valid for squares of the sound velocity equal to zero and 1/3 are extended in closed form to any equation of state where the pressure equals the total energy density times the square of the sound velocity. The solutions embody all the results found previously for special cases of the square of the sound velocity. It is found that the growth of any initial fluctuation is only an exponential function of time with an exponent of not more than 4/3 and is insufficient to produce galaxies unless the initial fluctuation is very large. A possible way to produce very large initial fluctuations by modifying the equation of state by including gravitational interactions is also examined. It is found that a phase transition can occur at baryonic density of 1 nucleon per cubic Planck length or equivalently, at a time of about 10 to the -43rd power sec. At those early times, the masses allowed by causality requirements are too small to be of interest in galaxy formation.

Exact outage analysis of the effect of co-channel interference on secured multi-hop relaying networks

NASA Astrophysics Data System (ADS)

Quang Nguyen, Sang; Kong, Hyung Yun

2016-11-01

In this article, the presence of multi-hop relaying, eavesdropper and co-channel interference (CCI) in the same system model is investigated. Specifically, the effect of CCI on a secured multi-hop relaying network is studied, in which the source communicates with the destination via multi-relay-hopping under the presence of an eavesdropper and CCI at each node. The optimal relay at each cluster is selected to help forward the message from the source to the destination. We apply two relay selection approaches to such a system model, i.e. the optimal relay is chosen based on (1) the maximum channel gain from the transmitter to all relays in the desired cluster and (2) the minimum channel gain from the eavesdropper to all relays in each cluster. For the performance evaluation and comparison, we derived the exact closed form of the secrecy outage probability of the two approaches. That analysis is verified by Monte Carlo simulation. Finally, the effects of the number of hops, the transmit power at the source, relays and the external sources, the distance between the external sources and each node in the system, and the location of the eavesdropper are presented and discussed.

Quantum propagation across cosmological singularities

NASA Astrophysics Data System (ADS)

Gielen, Steffen; Turok, Neil

2017-05-01

The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.

No-infill 3D Printing

NASA Astrophysics Data System (ADS)

Wei, Xiao-Ran; Zhang, Yu-He; Geng, Guo-Hua

2016-09-01

In this paper, we examined how printing the hollow objects without infill via fused deposition modeling, one of the most widely used 3D-printing technologies, by partitioning the objects to shell parts. More specifically, we linked the partition to the exact cover problem. Given an input watertight mesh shape S, we developed region growing schemes to derive a set of surfaces that had inside surfaces that were printable without support on the mesh for the candidate parts. We then employed Monte Carlo tree search over the candidate parts to obtain the optimal set cover. All possible candidate subsets of exact cover from the optimal set cover were then obtained and the bounded tree was used to search the optimal exact cover. We oriented each shell part to the optimal position to guarantee the inside surface was printed without support, while the outside surface was printed with minimum support. Our solution can be applied to a variety of models, closed-hollowed or semi-closed, with or without holes, as evidenced by experiments and performance evaluation on our proposed algorithm.

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with K=(±1,0)

NASA Astrophysics Data System (ADS)

Schmid, Christoph

2009-03-01

We show that there is exact dragging of the axis directions of local inertial frames by a weighted average of the cosmological energy currents via gravitomagnetism for all linear perturbations of all Friedmann-Robertson-Walker (FRW) universes and of Einstein’s static closed universe, and for all energy-momentum-stress tensors and in the presence of a cosmological constant. This includes FRW universes arbitrarily close to the Milne Universe and the de Sitter universe. Hence the postulate formulated by Ernst Mach about the physical cause for the time-evolution of inertial axes is shown to hold in general relativity for linear perturbations of FRW universes.—The time-evolution of local inertial axes (relative to given local fiducial axes) is given experimentally by the precession angular velocity Ω→gyro of local gyroscopes, which in turn gives the operational definition of the gravitomagnetic field: B→g≡-2Ω→gyro. The gravitomagnetic field is caused by energy currents J→ɛ via the momentum constraint, Einstein’s G0^i^ equation, (-Δ+μ2)A→g=-16πGNJ→ɛ with B→g=curlA→g. This equation is analogous to Ampère’s law, but it holds for all time-dependent situations. Δ is the de Rham-Hodge Laplacian, and Δ=-curlcurl for the vorticity sector in Riemannian 3-space.—In the solution for an open universe the 1/r2-force of Ampère is replaced by a Yukawa force Yμ(r)=(-d/dr)[(1/R)exp⁡(-μr)], form-identical for FRW backgrounds with K=(-1,0). Here r is the measured geodesic distance from the gyroscope to the cosmological source, and 2πR is the measured circumference of the sphere centered at the gyroscope and going through the source point. The scale of the exponential cutoff is the H-dot radius, where H is the Hubble rate, dot is the derivative with respect to cosmic time, and μ2=-4(dH/dt). Analogous results hold in closed FRW universes and in Einstein’s closed static universe.—We list six fundamental tests for the principle formulated by Mach: all of them are explicitly fulfilled by our solutions.—We show that only energy currents in the toroidal vorticity sector with ℓ=1 can affect the precession of gyroscopes. We show that the harmonic decomposition of toroidal vorticity fields in terms of vector spherical harmonics X→ℓm- has radial functions which are form-identical for the 3-sphere, the hyperbolic 3-space, and Euclidean 3-space, and are form-identical with the spherical Bessel-, Neumann-, and Hankel functions.—The Appendix gives the de Rham-Hodge Laplacian on vorticity fields in Riemannian 3-spaces by equations connecting the calculus of differential forms with the curl notation. We also give the derivation the Weitzenböck formula for the difference between the de Rham-Hodge Laplacian Δ and the “rough” Laplacian ∇2 on vector fields.

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with K=({+-}1,0)

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

Schmid, Christoph

We show that there is exact dragging of the axis directions of local inertial frames by a weighted average of the cosmological energy currents via gravitomagnetism for all linear perturbations of all Friedmann-Robertson-Walker (FRW) universes and of Einstein's static closed universe, and for all energy-momentum-stress tensors and in the presence of a cosmological constant. This includes FRW universes arbitrarily close to the Milne Universe and the de Sitter universe. Hence the postulate formulated by Ernst Mach about the physical cause for the time-evolution of inertial axes is shown to hold in general relativity for linear perturbations of FRW universes. -more » The time-evolution of local inertial axes (relative to given local fiducial axes) is given experimentally by the precession angular velocity {omega}-vector{sub gyro} of local gyroscopes, which in turn gives the operational definition of the gravitomagnetic field: B-vector{sub g}{identical_to}-2{omega}-vector{sub gyro}. The gravitomagnetic field is caused by energy currents J-vector{sub {epsilon}} via the momentum constraint, Einstein's G{sup 0-}circumflex{sub i-circumflex} equation, (-{delta}+{mu}{sup 2})A-vector{sub g}=-16{pi}G{sub N}J-vector{sub {epsilon}} with B-vector{sub g}=curl A-vector{sub g}. This equation is analogous to Ampere's law, but it holds for all time-dependent situations. {delta} is the de Rham-Hodge Laplacian, and {delta}=-curl curl for the vorticity sector in Riemannian 3-space. - In the solution for an open universe the 1/r{sup 2}-force of Ampere is replaced by a Yukawa force Y{sub {mu}}(r)=(-d/dr)[(1/R)exp(-{mu}r)], form-identical for FRW backgrounds with K=(-1,0). Here r is the measured geodesic distance from the gyroscope to the cosmological source, and 2{pi}R is the measured circumference of the sphere centered at the gyroscope and going through the source point. The scale of the exponential cutoff is the H-dot radius, where H is the Hubble rate, dot is the derivative with respect to cosmic time, and {mu}{sup 2}=-4(dH/dt). Analogous results hold in closed FRW universes and in Einstein's closed static universe.--We list six fundamental tests for the principle formulated by Mach: all of them are explicitly fulfilled by our solutions.--We show that only energy currents in the toroidal vorticity sector with l=1 can affect the precession of gyroscopes. We show that the harmonic decomposition of toroidal vorticity fields in terms of vector spherical harmonics X-vector{sub lm}{sup -} has radial functions which are form-identical for the 3-sphere, the hyperbolic 3-space, and Euclidean 3-space, and are form-identical with the spherical Bessel-, Neumann-, and Hankel functions. - The Appendix gives the de Rham-Hodge Laplacian on vorticity fields in Riemannian 3-spaces by equations connecting the calculus of differential forms with the curl notation. We also give the derivation the Weitzenboeck formula for the difference between the de Rham-Hodge Laplacian {delta} and the ''rough'' Laplacian {nabla}{sup 2} on vector fields.« less

Close the Hidden Funding Gaps in Our Schools. K-12 Policy

ERIC Educational Resources Information Center

Hall, Daria; Ushomirsky, Natasha

2010-01-01

Everyone knows that low-income and minority students often face steep hurdles. Although these challenges sometimes have roots outside of school, compelling evidence shows that great teachers and well-run schools can have powerful effects on student learning and help close achievement gaps. Yet in most parts of the country, people do exactly the…

Closed Analytic Solution for the Potential and Equations of Motion in the Presence of a Gravitating Oblate Spheroid

NASA Astrophysics Data System (ADS)

Atkinson, William

2008-10-01

A closed analytic solution for the potential due to a gravitating solid oblate spheroid, derived in oblate spheroidal coordinates in this paper, is shown to be much simpler than those obtained either in cylindrical coordinates (MacMillan) or in spherical coordinates (McCullough). The derivation in oblate spheroidal coordinates is also much simpler to follow than those of the MacMillan or McCullough. The potential solution is applied in exacting a closed solution for the equations of motion for an object rolling on the surface of the spheroid subjected only to the gravitational force component tangential to the surface of the spheroid. The exact solution was made possible by the fact that the force can be represented as separable functions of the coordinates only in oblate spheroidal coordinates. The derivation is a good demonstration of the use of curvilinear coordinates to problems in classical mechanics, potential theory, and mathematical physics for both undergraduate and graduate students.

Gödel metrics with chronology protection in Horndeski gravities

NASA Astrophysics Data System (ADS)

Geng, Wei-Jian; Li, Shou-Long; Lü, H.; Wei, Hao

2018-05-01

Gödel universe, one of the most interesting exact solutions predicted by General Relativity, describes a homogeneous rotating universe containing naked closed time-like curves (CTCs). It was shown that such CTCs are the consequence of the null energy condition in General Relativity. In this paper, we show that the Gödel-type metrics with chronology protection can emerge in Einstein-Horndeski gravity. We construct such exact solutions also in Einstein-Horndeski-Maxwell and Einstein-Horndeski-Proca theories.

Orientifolding of the ABJ Fermi gas

NASA Astrophysics Data System (ADS)

Okuyama, Kazumi

2016-03-01

The grand partition functions of ABJ theory can be factorized into even and odd parts under the reflection of fermion coordinate in the Fermi gas approach. In some cases, the even/odd part of ABJ grand partition function is equal to that of {N}=5O(n)× USp({n}^') theory, hence it is natural to think of the even/odd projection of grand partition function as an orientifolding of ABJ Fermi gas system. By a systematic WKB analysis, we determine the coefficients in the perturbative part of grand potential of such orientifold ABJ theory. We also find the exact form of the first few "half-instanton" corrections coming from the twisted sector of the reflection of fermion coordinate. For the Chern-Simons level k = 2 ,4 ,8 we find closed form expressions of the grand partition functions of orientifold ABJ theory, and for k = 2 , 4 we prove the functional relations among the grand partition functions conjectured in arXiv:1410.7658.

Vector spherical quasi-Gaussian vortex beams

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2014-02-01

Model equations for describing and efficiently computing the radiation profiles of tightly spherically focused higher-order electromagnetic beams of vortex nature are derived stemming from a vectorial analysis with the complex-source-point method. This solution, termed as a high-order quasi-Gaussian (qG) vortex beam, exactly satisfies the vector Helmholtz and Maxwell's equations. It is characterized by a nonzero integer degree and order (n,m), respectively, an arbitrary waist w0, a diffraction convergence length known as the Rayleigh range zR, and an azimuthal phase dependency in the form of a complex exponential corresponding to a vortex beam. An attractive feature of the high-order solution is the rigorous description of strongly focused (or strongly divergent) vortex wave fields without the need of either the higher-order corrections or the numerically intensive methods. Closed-form expressions and computational results illustrate the analysis and some properties of the high-order qG vortex beams based on the axial and transverse polarization schemes of the vector potentials with emphasis on the beam waist.

A Study of Chemically Reactive Species and Thermal Radiation Effects on an Unsteady MHD Free Convection Flow Through a Porous Medium Past a Flat Plate with Ramped Wall Temperature

NASA Astrophysics Data System (ADS)

Pandit, K. K.; Sarma, D.; Singh, S. I.

2017-12-01

An investigation of the effects of a chemical reaction and thermal radiation on unsteady MHD free convection heat and mass transfer flow of an electrically conducting, viscous, incompressible fluid past a vertical infinite flat plate embedded in a porous medium is carried out. The flow is induced by a general time-dependent movement of the vertical plate, and the cases of ramped temperature and isothermal plates are studied. An exact solution of the governing equations is obtained in closed form by the Laplace Transform technique. Some applications of practical interest for different types of plate motions are discussed. The numerical values of fluid velocity, temperature and species concentration are displayed graphically whereas the numerical values of skin friction, Nusselt number and Sherwood number are presented in a tabular form for various values of pertinent flow parameters for both ramped temperature and isothermal plates.

The passage of an infinite swept airfoil through an oblique gust. [approximate solution for aerodynamic response

NASA Technical Reports Server (NTRS)

Adamczyk, J. L.

1974-01-01

An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

NASA Astrophysics Data System (ADS)

Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell

2017-06-01

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon-polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed.

Applications of computer algebra to distributed parameter systems

NASA Technical Reports Server (NTRS)

Storch, Joel A.

1993-01-01

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

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

NASA Astrophysics Data System (ADS)

Sahadevan, R.; Rajakumar, S.

2008-03-01

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

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers

PubMed Central

Cui, Jiaxin; Zhang, Yiyun; Cheng, Dazhi; Li, Dawei; Zhou, Xinlin

2017-01-01

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation. PMID:28824513

The exact analysis of contingency tables in medical research.

PubMed

Mehta, C R

1994-01-01

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

The Poisson-Boltzmann theory for the two-plates problem: some exact results.

PubMed

Xing, Xiang-Jun

2011-12-01

The general solution to the nonlinear Poisson-Boltzmann equation for two parallel charged plates, either inside a symmetric electrolyte, or inside a 2q:-q asymmetric electrolyte, is found in terms of Weierstrass elliptic functions. From this we derive some exact asymptotic results for the interaction between charged plates, as well as the exact form of the renormalized surface charge density.

Traveling front solutions to directed diffusion-limited aggregation, digital search trees, and the Lempel-Ziv data compression algorithm.

PubMed

Majumdar, Satya N

2003-08-01

We use the traveling front approach to derive exact asymptotic results for the statistics of the number of particles in a class of directed diffusion-limited aggregation models on a Cayley tree. We point out that some aspects of these models are closely connected to two different problems in computer science, namely, the digital search tree problem in data structures and the Lempel-Ziv algorithm for data compression. The statistics of the number of particles studied here is related to the statistics of height in digital search trees which, in turn, is related to the statistics of the length of the longest word formed by the Lempel-Ziv algorithm. Implications of our results to these computer science problems are pointed out.

Traveling front solutions to directed diffusion-limited aggregation, digital search trees, and the Lempel-Ziv data compression algorithm

NASA Astrophysics Data System (ADS)

Majumdar, Satya N.

2003-08-01

We use the traveling front approach to derive exact asymptotic results for the statistics of the number of particles in a class of directed diffusion-limited aggregation models on a Cayley tree. We point out that some aspects of these models are closely connected to two different problems in computer science, namely, the digital search tree problem in data structures and the Lempel-Ziv algorithm for data compression. The statistics of the number of particles studied here is related to the statistics of height in digital search trees which, in turn, is related to the statistics of the length of the longest word formed by the Lempel-Ziv algorithm. Implications of our results to these computer science problems are pointed out.

Isaac Newton and the astronomical refraction.

PubMed

Lehn, Waldemar H

2008-12-01

In a short interval toward the end of 1694, Isaac Newton developed two mathematical models for the theory of the astronomical refraction and calculated two refraction tables, but did not publish his theory. Much effort has been expended, starting with Biot in 1836, in the attempt to identify the methods and equations that Newton used. In contrast to previous work, a closed form solution is identified for the refraction integral that reproduces the table for his first model (in which density decays linearly with elevation). The parameters of his second model, which includes the exponential variation of pressure in an isothermal atmosphere, have also been identified by reproducing his results. The implication is clear that in each case Newton had derived exactly the correct equations for the astronomical refraction; furthermore, he was the first to do so.

Brownian motion of massive skyrmions in magnetic thin films

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

Troncoso, Roberto E., E-mail: r.troncoso.c@gmail.com; Núñez, Álvaro S., E-mail: alnunez@dfi.uchile.cl

2014-12-15

We report on the thermal effects on the motion of current-driven massive magnetic skyrmions. The reduced equation for the motion of skyrmion has the form of a stochastic generalized Thiele’s equation. We propose an ansatz for the magnetization texture of a non-rigid single skyrmion that depends linearly with the velocity. By using this ansatz it is found that the skyrmion mass tensor is closely related to intrinsic skyrmion parameters, such as Gilbert damping, skyrmion-charge and dissipative force. We have found an exact expression for the average drift velocity as well as the mean-square velocity of the skyrmion. The longitudinal andmore » transverse mobility of skyrmions for small spin-velocity of electrons is also determined and found to be independent of the skyrmion mass.« less

A proof of the Woodward-Lawson sampling method for a finite linear array

NASA Technical Reports Server (NTRS)

Somers, Gary A.

1993-01-01

An extension of the continuous aperture Woodward-Lawson sampling theorem has been developed for a finite linear array of equidistant identical elements with arbitrary excitations. It is shown that by sampling the array factor at a finite number of specified points in the far field, the exact array factor over all space can be efficiently reconstructed in closed form. The specified sample points lie in real space and hence are measurable provided that the interelement spacing is greater than approximately one half of a wavelength. This paper provides insight as to why the length parameter used in the sampling formulas for discrete arrays is larger than the physical span of the lattice points in contrast with the continuous aperture case where the length parameter is precisely the physical aperture length.

Controlled Self-Assembly of Low-Dimensional Alq3 Nanostructures from 1D Nanowires to 2D Plates via Intermolecular Interactions

NASA Astrophysics Data System (ADS)

Gu, Jianmin; Yin, Baipeng; Fu, Shaoyan; Jin, Cuihong; Liu, Xin; Bian, Zhenpan; Li, Jianjun; Wang, Lu; Li, Xiaoyu

2018-03-01

Due to the intense influence of the shape and size of the photon building blocks on the limitation and guidance of optical waves, an important strategy is the fabrication of different structures. Herein, organic semiconductor tris-(8-hydroxyquinoline)aluminium (Alq3) nanostructures with controllable morphology, ranging from one-dimensional nanowires to two-dimensional plates, have been prepared through altering intermolecular interactions with employing the anti-solvent diffusion cooperate with solvent-volatilization induced self-assembly method. The morphologies of the formed nanostructures, which are closely related to the stacking modes of the molecules, can be exactly controlled by altering the polarity of anti-solvents that can influence various intermolecular interactions. The synthesis strategy reported here can potentially be extended to other functional organic nanomaterials.

Simulation of Benchmark Cases with the Terminal Area Simulation System (TASS)

NASA Technical Reports Server (NTRS)

Ahmad, Nash'at; Proctor, Fred

2011-01-01

The hydrodynamic core of the Terminal Area Simulation System (TASS) is evaluated against different benchmark cases. In the absence of closed form solutions for the equations governing atmospheric flows, the models are usually evaluated against idealized test cases. Over the years, various authors have suggested a suite of these idealized cases which have become standards for testing and evaluating the dynamics and thermodynamics of atmospheric flow models. In this paper, simulations of three such cases are described. In addition, the TASS model is evaluated against a test case that uses an exact solution of the Navier-Stokes equations. The TASS results are compared against previously reported simulations of these banchmark cases in the literature. It is demonstrated that the TASS model is highly accurate, stable and robust.

Ceramics: Durability and radiation effects

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

Ewing, R.C.; Lutze, W.; Weber, W.J.

1996-05-01

At present, there are three seriously considered options for the disposition of excess weapons plutonium: (1) incorporation, partial burn-up and direct disposal of MOX-fuel; (2) vitrification with defense waste and disposal as glass {open_quotes}logs{close_quotes}; (3) deep borehole disposal. The first two options provide a safeguard due to the high activity of fission products in the irradiated fuel and the defense waste. The latter option has only been examined in a preliminary manner, and the exact form of the plutonium has not been identified. In this paper, we review the potential for the immobilization of plutonium in highly durable crystalline ceramicsmore » apatite, pyrochlore, zirconolite, monazite and zircon. Based on available data, we propose zircon as the preferred crystalline ceramic for the permanent disposition of excess weapons plutonium.« less

The IR emission features - Emission from PAH molecules and amorphous carbon particles

NASA Technical Reports Server (NTRS)

Allamandola, L. J.; Tielens, A. G. G. M.; Barker, J. R.

1987-01-01

Techniques for the assessment of the importance of the various forms of PAHs, and recent infrared observations concerning the PAH problem, are considered. Spectroscopic data suggest that the observed interstellar spectrum is due to both free molecule-sized PAHs producing the narrow features, and amorphous carbon particles contributing to the broad underlying components. Explanations for the multicomponent emission spectrum are discussed. A model of the emission mechanism for the example of chrysene is presented, and an exact treatment of the IR fluorescence from highly vibrationally excited large molecules shows that species containing 20-30 carbon atoms are responsible for the narrow features, although the spectra more closely resemble those of amorphous carbon particles. It is suggested that future emphasis should be placed on the spatial characteristics of the component spectra.

Symbolic Computational Approach to the Marangoni Convection Problem With Soret Diffusion

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond

1998-01-01

A recently reported solution for stationary stability of a thermosolutal system with Soret diffusion is re-derived and examined using a symbolic computational package. Symbolic computational languages are well suited for such an analysis and facilitate a pragmatic approach that is adaptable to similar problems. Linearization of the equations, normal mode analysis, and extraction of the final solution are performed in a Mathematica notebook format. An exact solution is obtained for stationary stability in the limit of zero gravity. A closed form expression is also obtained for the location of asymptotes in relevant parameter, (Sm(sub c), Mac(sub c)), space. The stationary stability behavior is conveniently examined within the symbolic language environment. An abbreviated version of the Mathematica notebook is given in the Appendix.

Superexchange and spin-glass formation in semimagnetic semiconductors

NASA Astrophysics Data System (ADS)

Rusin, Tomasz M.

1996-05-01

The Mn-Mn superexchange interaction in semimagnetic semiconductors A1-xMnxB (where A=Zn, Cd and B=S, Se, Te) is studied within the three-level model of the band structure. We focus on the dependence of the interaction on the interion distance Jdd(r)=J0f(r). In the present work, the function f(r) is obtained analytically. This, only weakly material-dependent function is found to decrease with Mn-Mn distance much slower than its Gaussian approximation derived previously. The exact form of the decay of the superexchange can be approximated by a power law J0r-8.5. This is close to an experimental result, J0r-6.8, determined on the basis of the spin-glass transition temperature on the composition.

Photocounting distributions for exponentially decaying sources.

PubMed

Teich, M C; Card, H C

1979-05-01

Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model.

Simulation of Benchmark Cases with the Terminal Area Simulation System (TASS)

NASA Technical Reports Server (NTRS)

Ahmad, Nashat N.; Proctor, Fred H.

2011-01-01

The hydrodynamic core of the Terminal Area Simulation System (TASS) is evaluated against different benchmark cases. In the absence of closed form solutions for the equations governing atmospheric flows, the models are usually evaluated against idealized test cases. Over the years, various authors have suggested a suite of these idealized cases which have become standards for testing and evaluating the dynamics and thermodynamics of atmospheric flow models. In this paper, simulations of three such cases are described. In addition, the TASS model is evaluated against a test case that uses an exact solution of the Navier-Stokes equations. The TASS results are compared against previously reported simulations of these benchmark cases in the literature. It is demonstrated that the TASS model is highly accurate, stable and robust.

Efficiently computing exact geodesic loops within finite steps.

PubMed

Xin, Shi-Qing; He, Ying; Fu, Chi-Wing

2012-06-01

Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.

Exact semiclassical expansions for one-dimensional quantum oscillators

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

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

1997-12-01

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

Notes on the ExactPack Implementation of the DSD Explosive Arc Solver

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

Kaul, Ann; Doebling, Scott William

It has been shown above that the discretization scheme implemented in the ExactPack solver for the DSD Explosive Arc equation is consistent with the Explosive Arc PDE. In addition, a stability analysis has provided a CFL condition for a stable time step. Together, consistency and stability imply convergence of the scheme, which is expected to be close to first-order in time and second-order in space. It is understood that the nonlinearity of the underlying PDE will affect this rate somewhat.

Minimal gravity and Frobenius manifolds: bulk correlation on sphere and disk

NASA Astrophysics Data System (ADS)

Aleshkin, Konstantin; Belavin, Vladimir; Rim, Chaiho

2017-11-01

There are two alternative approaches to the minimal gravity — direct Liouville approach and matrix models. Recently there has been a certain progress in the matrix model approach, growing out of presence of a Frobenius manifold (FM) structure embedded in the theory. The previous studies were mainly focused on the spherical topology. Essentially, it was shown that the action principle of Douglas equation allows to define the free energy and to compute the correlation numbers if the resonance transformations are properly incorporated. The FM structure allows to find the explicit form of the resonance transformation as well as the closed expression for the partition function. In this paper we elaborate on the case of gravitating disk. We focus on the bulk correlators and show that in the similar way as in the closed topology the generating function can be formulated using the set of flat coordinates on the corresponding FM. Moreover, the resonance transformations, which follow from the spherical topology consideration, are exactly those needed to reproduce FZZ result of the Liouville gravity approach.

Anorectal closing mechanisms.

PubMed

Wilson, P M

1977-05-28

The thrust of this contribution is contained in an analysis of the refined sealing devices which supplement the co-operative interactions between the anorectum and its surroundings. They include an active smooth-muscle complex which, with elastic tissue, is closely related to vascular anal cushions. These, when distended, plug the anal lumen and complete continence. Additional objectives are: (i) to draw attention to new concepts on the nature of haemorrhoids; (ii) to add illustrations to support the idea of tripartite sealing plugs in the form of anal "cushions"; (iii) to note discrepancies in the literature on the exact siting of the pectinate/dentate line in the anal canal which have a bearing on the theory of the anal cushion; (iv) to give reasons why the musculus submucosae ani should not be termed Treitz's muscle; (v) to review some morphological, pressure, motility and electromyographic sutdies of the neuromusculature of the anorectal region in normal subjects and in patients with haemorrhoids; and (vi) to add explanations and suggestions to fit the concept of the anal cushion into a broader framework of use to the surgeon.

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

Dubrovsky, V. G.; Topovsky, A. V.

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums ofmore » special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.« less

Nonlinear spike-and-slab sparse coding for interpretable image encoding.

PubMed

Shelton, Jacquelyn A; Sheikh, Abdul-Saboor; Bornschein, Jörg; Sterne, Philip; Lücke, Jörg

2015-01-01

Sparse coding is a popular approach to model natural images but has faced two main challenges: modelling low-level image components (such as edge-like structures and their occlusions) and modelling varying pixel intensities. Traditionally, images are modelled as a sparse linear superposition of dictionary elements, where the probabilistic view of this problem is that the coefficients follow a Laplace or Cauchy prior distribution. We propose a novel model that instead uses a spike-and-slab prior and nonlinear combination of components. With the prior, our model can easily represent exact zeros for e.g. the absence of an image component, such as an edge, and a distribution over non-zero pixel intensities. With the nonlinearity (the nonlinear max combination rule), the idea is to target occlusions; dictionary elements correspond to image components that can occlude each other. There are major consequences of the model assumptions made by both (non)linear approaches, thus the main goal of this paper is to isolate and highlight differences between them. Parameter optimization is analytically and computationally intractable in our model, thus as a main contribution we design an exact Gibbs sampler for efficient inference which we can apply to higher dimensional data using latent variable preselection. Results on natural and artificial occlusion-rich data with controlled forms of sparse structure show that our model can extract a sparse set of edge-like components that closely match the generating process, which we refer to as interpretable components. Furthermore, the sparseness of the solution closely follows the ground-truth number of components/edges in the images. The linear model did not learn such edge-like components with any level of sparsity. This suggests that our model can adaptively well-approximate and characterize the meaningful generation process.

Nonlinear Spike-And-Slab Sparse Coding for Interpretable Image Encoding

PubMed Central

Shelton, Jacquelyn A.; Sheikh, Abdul-Saboor; Bornschein, Jörg; Sterne, Philip; Lücke, Jörg

2015-01-01

Sparse coding is a popular approach to model natural images but has faced two main challenges: modelling low-level image components (such as edge-like structures and their occlusions) and modelling varying pixel intensities. Traditionally, images are modelled as a sparse linear superposition of dictionary elements, where the probabilistic view of this problem is that the coefficients follow a Laplace or Cauchy prior distribution. We propose a novel model that instead uses a spike-and-slab prior and nonlinear combination of components. With the prior, our model can easily represent exact zeros for e.g. the absence of an image component, such as an edge, and a distribution over non-zero pixel intensities. With the nonlinearity (the nonlinear max combination rule), the idea is to target occlusions; dictionary elements correspond to image components that can occlude each other. There are major consequences of the model assumptions made by both (non)linear approaches, thus the main goal of this paper is to isolate and highlight differences between them. Parameter optimization is analytically and computationally intractable in our model, thus as a main contribution we design an exact Gibbs sampler for efficient inference which we can apply to higher dimensional data using latent variable preselection. Results on natural and artificial occlusion-rich data with controlled forms of sparse structure show that our model can extract a sparse set of edge-like components that closely match the generating process, which we refer to as interpretable components. Furthermore, the sparseness of the solution closely follows the ground-truth number of components/edges in the images. The linear model did not learn such edge-like components with any level of sparsity. This suggests that our model can adaptively well-approximate and characterize the meaningful generation process. PMID:25954947

Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.

PubMed

Petrinović, Davor; Brezović, Marko

2011-04-01

We propose a method for direct digital frequency synthesis (DDS) using a cubic spline piecewise-polynomial model for a phase-to-sinusoid amplitude converter (PSAC). This method offers maximum smoothness of the output signal. Closed-form expressions for the cubic polynomial coefficients are derived in the spectral domain and the performance analysis of the model is given in the time and frequency domains. We derive the closed-form performance bounds of such DDS using conventional metrics: rms and maximum absolute errors (MAE) and maximum spurious free dynamic range (SFDR) measured in the discrete time domain. The main advantages of the proposed PSAC are its simplicity, analytical tractability, and inherent numerical stability for high table resolutions. Detailed guidelines for a fixed-point implementation are given, based on the algebraic analysis of all quantization effects. The results are verified on 81 PSAC configurations with the output resolutions from 5 to 41 bits by using a bit-exact simulation. The VHDL implementation of a high-accuracy DDS based on the proposed PSAC with 28-bit input phase word and 32-bit output value achieves SFDR of its digital output signal between 180 and 207 dB, with a signal-to-noise ratio of 192 dB. Its implementation requires only one 18 kB block RAM and three 18-bit embedded multipliers in a typical field-programmable gate array (FPGA) device. © 2011 IEEE

Exact partition functions for the Ω-deformed {N}={2}^{ast } SU(2) gauge theory

NASA Astrophysics Data System (ADS)

Beccaria, Matteo; Macorini, Guido

2016-07-01

We study the low energy effective action of the Ω-deformed {N}={2}^{ast } SU(2) gauge theory. It depends on the deformation parameters ɛ 1, ɛ 2, the scalar field expectation value a, and the hypermultiplet mass m. We explore the plane (m/ɛ_1,ɛ_2/ɛ_1) looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit ɛ 2 → 0. We propose a simple condition on the structure of poles of the k-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value a and the modular parameter q appearing in special combinations of Eisenstein series and Dedekind η function. As a byproduct, the modular anomaly equation can be tested at all orders at these points. We discuss these special features from the point of view of the AGT correspondence and provide explicit toroidal 1-blocks in non-trivial closed form. The full list of solutions with 1, 2, 3, and 4 poles is determined and described in details.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

An Astronomical Test of CCD Photometric Precision

NASA Technical Reports Server (NTRS)

Koch, David; Dunham, Edward; Borucki, William; Jenkins, Jon; DeVingenzi, D. (Technical Monitor)

1998-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Fluticasone propionate/formoterol for COPD management: a randomized controlled trial

PubMed Central

Papi, A; Dokic, D; Tzimas, W; Mészáros, I; Olech-Cudzik, A; Koroknai, Z; McAulay, K; Mersmann, S; Dalvi, PS; Overend, T

2017-01-01

Purpose To evaluate fluticasone propionate/formoterol (FP/FORM) in COPD. Patients and methods COPD patients with forced expiratory volume in 1 s (FEV1) ≤50% predicted and ≥1 moderate/severe COPD exacerbation in the last 12 months were randomized to FP/FORM 500/20 or 250/10 µg bid, or formoterol (FORM) 12 µg bid for 52 weeks. The primary outcome was the annualized rate of moderate/severe COPD exacerbations. Results In total, 1,765 patients were randomized. There were fewer discontinuations with FP/FORM 500/20 µg (20.6%) and 250/10 µg (24.0%) compared with FORM (26.1%). None of the two FP/FORM doses reduced the moderate/severe exacerbation rate versus FORM (rate ratios [RR]: 0.93; P≤0.402). There was a trend toward a lower moderate/severe exacerbation rate with FP/FORM 500/20 µg versus FORM in patients with ≥2 exacerbations in the preceding year (RR: 0.79; P=0.084). Pre- and post-dose FEV1 and forced vital capacity were greater with FP/FORM 500/20 µg versus FORM (P≤0.039). There was a trend toward a lower EXAcerbations of Chronic pulmonary disease Tool (EXACT) exacerbation rate with FP/FORM 500/20 µg versus FORM (RR: 0.87; P=0.077). There were more St George’s Respiratory Questionnaire for COPD (SGRQ-C) responders with FP/FORM 500/20 µg than FORM (odds ratios [OR] at weeks 6, 23 and 52 ≥1.28; P≤0.054). EXACT-respiratory symptoms total and breathlessness scores were lower with both FP/FORM 500/20 µg and 250/10 µg versus FORM (P≤0.066). Acute β2-agonist-induced effects and 24-hour Holter findings were similar for all treatments. Mean 24-hour urinary cortisol was similarly reduced with both FP/FORM doses. Radiologically confirmed pneumonia was seen in 2.4%, 3.2% and 1.5% of FP/FORM 500/20 µg, FP/FORM 250/10 µg and FORM-treated patients, respectively. Adverse events were otherwise similar across treatment groups. Conclusion FP/FORM did not reduce exacerbation rates versus FORM. Numerical benefits were observed with FP/FORM 500/20 µg versus FORM for secondary variables, including lung function, EXACT exacerbations, SGRQ-C and EXACT-respiratory symptoms total and breathlessness scores. Few efficacy differences were evident between FP/FORM 250/10 µg and FORM. Pneumonia was more frequent in FP/FORM-treated patients, although the absolute difference was low. Adverse events were otherwise similar between treatments. PMID:28740376

Fluticasone propionate/formoterol for COPD management: a randomized controlled trial.

PubMed

Papi, A; Dokic, D; Tzimas, W; Mészáros, I; Olech-Cudzik, A; Koroknai, Z; McAulay, K; Mersmann, S; Dalvi, P S; Overend, T

2017-01-01

To evaluate fluticasone propionate/formoterol (FP/FORM) in COPD. COPD patients with forced expiratory volume in 1 s (FEV 1 ) ≤50% predicted and ≥1 moderate/severe COPD exacerbation in the last 12 months were randomized to FP/FORM 500/20 or 250/10 µg bid, or formoterol (FORM) 12 µg bid for 52 weeks. The primary outcome was the annualized rate of moderate/severe COPD exacerbations. In total, 1,765 patients were randomized. There were fewer discontinuations with FP/FORM 500/20 µg (20.6%) and 250/10 µg (24.0%) compared with FORM (26.1%). None of the two FP/FORM doses reduced the moderate/severe exacerbation rate versus FORM (rate ratios [RR]: 0.93; P ≤0.402). There was a trend toward a lower moderate/severe exacerbation rate with FP/FORM 500/20 µg versus FORM in patients with ≥2 exacerbations in the preceding year (RR: 0.79; P =0.084). Pre- and post-dose FEV 1 and forced vital capacity were greater with FP/FORM 500/20 µg versus FORM ( P ≤0.039). There was a trend toward a lower EXAcerbations of Chronic pulmonary disease Tool (EXACT) exacerbation rate with FP/FORM 500/20 µg versus FORM (RR: 0.87; P =0.077). There were more St George's Respiratory Questionnaire for COPD (SGRQ-C) responders with FP/FORM 500/20 µg than FORM (odds ratios [OR] at weeks 6, 23 and 52 ≥1.28; P ≤0.054). EXACT-respiratory symptoms total and breathlessness scores were lower with both FP/FORM 500/20 µg and 250/10 µg versus FORM ( P ≤0.066). Acute β 2 -agonist-induced effects and 24-hour Holter findings were similar for all treatments. Mean 24-hour urinary cortisol was similarly reduced with both FP/FORM doses. Radiologically confirmed pneumonia was seen in 2.4%, 3.2% and 1.5% of FP/FORM 500/20 µg, FP/FORM 250/10 µg and FORM-treated patients, respectively. Adverse events were otherwise similar across treatment groups. FP/FORM did not reduce exacerbation rates versus FORM. Numerical benefits were observed with FP/FORM 500/20 µg versus FORM for secondary variables, including lung function, EXACT exacerbations, SGRQ-C and EXACT-respiratory symptoms total and breathlessness scores. Few efficacy differences were evident between FP/FORM 250/10 µg and FORM. Pneumonia was more frequent in FP/FORM-treated patients, although the absolute difference was low. Adverse events were otherwise similar between treatments.

Electronic transport across a junction between armchair graphene nanotube and zigzag nanoribbon. Transmission in an armchair nanotube without a zigzag half-line of dimers

NASA Astrophysics Data System (ADS)

Sharma, Basant Lal

2018-05-01

Based on the well known nearest-neighbor tight-binding approximation for graphene, an exact expression for the electronic conductance across a zigzag nanoribbon/armchair nanotube junction is presented for non-interacting electrons. The junction results from the removal of a half-row of zigzag dimers in armchair nanotube, or equivalently by partial rolling of zigzag nanoribbon and insertion of a half-row of zigzag dimers in between. From the former point of view, a discrete form of Dirichlet condition is imposed on a zigzag half-line of dimers assuming the vanishing of wave function outside the physical structure. A closed form expression is provided for the reflection and transmission moduli for the outgoing wave modes for each given electronic wave mode incident from either side of the junction. It is demonstrated that such a contact junction between the nanotube and nanoribbon exhibits negligible backscattering, and the transmission has been found to be nearly ballistic. In contrast to the previously reported studies for partially unzipped carbon nanotubes (CNTs), using the same tight binding model, it is found that due to the "defect" there is certain amount of mixing between the electronic wave modes with even and odd reflection symmetries. But the junction remains a perfect valley filter for CNTs at certain energy ranges. Applications aside from the electronic case, include wave propagation in quasi-one-dimensional honeycomb structures of graphene-like constitution. The paper includes several numerical calculations, analytical derivations, and graphical results, which complement the provision of succinct closed form expressions.

Fourier-Legendre expansion of the one-electron density matrix of ground-state two-electron atoms.

PubMed

Ragot, Sébastien; Ruiz, María Belén

2008-09-28

The density matrix rho(r,r(')) of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials P(l)(cos theta=rr(')rr(')). Application is here made to harmonically trapped electron pairs (i.e., Moshinsky's and Hooke's atoms), for which exact wavefunctions are known, and to the helium atom, using a near-exact wavefunction. In the present approach, generic closed form expressions are derived for the series coefficients of rho(r,r(')). The series expansions are shown to converge rapidly in each case, with respect to both the electron number and the kinetic energy. In practice, a two-term expansion accounts for most of the correlation effects, so that the correlated density matrices of the atoms at issue are essentially a linear functions of P(l)(cos theta)=cos theta. For example, in the case of Hooke's atom, a two-term expansion takes in 99.9% of the electrons and 99.6% of the kinetic energy. The correlated density matrices obtained are finally compared to their determinantal counterparts, using a simplified representation of the density matrix rho(r,r(')), suggested by the Legendre expansion. Interestingly, two-particle correlation is shown to impact the angular delocalization of each electron, in the one-particle space spanned by the r and r(') variables.

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

Ballesteros, Ángel, E-mail: angelb@ubu.es; Enciso, Alberto, E-mail: aenciso@icmat.es; Herranz, Francisco J., E-mail: fjherranz@ubu.es

In this paper we quantize the N-dimensional classical Hamiltonian system H=(|q|)/(2(η+|q|)) p{sup 2}−k/(η+|q|) , that can be regarded as a deformation of the Coulomb problem with coupling constant k, that it is smoothly recovered in the limit η→0. Moreover, the kinetic energy term in H is just the one corresponding to an N-dimensional Taub–NUT space, a fact that makes this system relevant from a geometric viewpoint. Since the Hamiltonian H is known to be maximally superintegrable, we propose a quantization prescription that preserves such superintegrability in the quantum mechanical setting. We show that, to this end, one must choose asmore » the kinetic part of the Hamiltonian the conformal Laplacian of the underlying Riemannian manifold, which combines the usual Laplace–Beltrami operator on the Taub–NUT manifold and a multiple of its scalar curvature. As a consequence, we obtain a novel exactly solvable deformation of the quantum Coulomb problem, whose spectrum is computed in closed form for positive values of η and k, and showing that the well-known maximal degeneracy of the flat system is preserved in the deformed case. Several interesting algebraic and physical features of this new exactly solvable quantum system are analyzed, and the quantization problem for negative values of η and/or k is also sketched.« less

The effect of dissipative inhomogeneous medium on the statistics of the wave intensity

NASA Technical Reports Server (NTRS)

Saatchi, Sasan S.

1993-01-01

One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not essential were discussed.

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Larson, Mats G.; Barth, Timothy J.

1999-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Inclusive heavy flavor hadroproduction in NLO QCD: The exact analytic result

NASA Astrophysics Data System (ADS)

Czakon, M.; Mitov, A.

2010-01-01

We present the first exact analytic result for all partonic channels contributing to the total cross section for the production of a pair of heavy flavors in hadronic collisions in NLO QCD. Our calculation is a step in the derivation of the top quark pair production cross section at NNLO in QCD, which is a cornerstone of the precision LHC program. Our results uncover the analytical structures behind observables with heavy flavors at higher orders. They also reveal surprising and non-trivial implications for kinematics close to partonic threshold.

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

Svendsen, Harald G.

In this paper we study a solution of heterotic string theory corresponding to a rotating Kerr-Taub-NUT spacetime. It has an exact CFT description as a heterotic coset model, and a Lagrangian formulation as a gauged WZNW model. It is a generalization of a recently discussed stringy Taub-NUT solution, and is interesting as another laboratory for studying the fate of closed timelike curves and cosmological singularities in string theory. We extend the computation of the exact metric and dilaton to this rotating case, and then discuss some properties of the metric, with particular emphasis on the curvature singularities.

Exact solutions for network rewiring models

NASA Astrophysics Data System (ADS)

Evans, T. S.

2007-03-01

Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree distribution is found and its exact solution and generating solution are given.

Sample size requirements for the design of reliability studies: precision consideration.

PubMed

Shieh, Gwowen

2014-09-01

In multilevel modeling, the intraclass correlation coefficient based on the one-way random-effects model is routinely employed to measure the reliability or degree of resemblance among group members. To facilitate the advocated practice of reporting confidence intervals in future reliability studies, this article presents exact sample size procedures for precise interval estimation of the intraclass correlation coefficient under various allocation and cost structures. Although the suggested approaches do not admit explicit sample size formulas and require special algorithms for carrying out iterative computations, they are more accurate than the closed-form formulas constructed from large-sample approximations with respect to the expected width and assurance probability criteria. This investigation notes the deficiency of existing methods and expands the sample size methodology for the design of reliability studies that have not previously been discussed in the literature.

Vortex/surface interaction

NASA Technical Reports Server (NTRS)

Bodstein, G. C. R.; George, A. R.; Hui, C. Y.

1993-01-01

This paper considers the interaction of a vortex generated upstream in a flow field with a downstream aerodynamic surface that possesses a large chord. The flow is assumed to be steady, incompressible, inviscid and irrotational, and the surface to be semiinfinite. The vortex is considered to be a straight vortex filament. To lowest order the problem is modeled using potential theory, where the 3D Laplace's equation for the velocity potential on the surface is solved exactly. The closed-form equation for pressure distribution obtained from this theory is found to have a square root singularity at the leading-edge. It also converges, as x goes to infinity, to the solution of the 2D point-vortex/infinite plane problem. The pressure coefficient presents an anti-symmetric behavior, near the leading-edge and a symmetric behavior as x goes to infinity.

CBR anisotropy from primordial gravitational waves in inflationary cosmologies

NASA Astrophysics Data System (ADS)

Allen, Bruce; Koranda, Scott

1994-09-01

We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early Universe. These temperature fluctuations are described by an angular correlation function C(γ). A new (more concise and general) derivation of C(γ) is given, and evaluated for inflationary-universe cosmologies. This yields standard results for angles γ greater than a few degrees, but new results for smaller angles, because we do not make standard long-wavelength approximations to the gravitational wave mode functions. The function C(γ) may be expanded in a series of Legendre polynomials; we use numerical methods to compare the coefficients of the resulting expansion in our exact calculation with standard (approximate) results. We also report some progress towards finding a closed form expression for C(γ).

Thermal noise in aqueous quadrupole micro- and nano-traps

DOE PAGES

Park, Jae; Krstić, Predrag S.

2012-02-27

Recent simulations and experiments with aqueous quadrupole micro-traps have confirmed a possibility for control and localization of motion of a charged particle in a water environment, also predicting a possibility of further reduction of the trap size to tens of nano-meters for trapping charged bio-molecules and DNA segments. We study the random thermal noise due to Brownian motion in water which significantly influences the trapping of particles in an aqueous environment. We derive the exact, closed-form expressions for the thermal fluctuations of position and velocity of a trapped particle and thoroughly examine the properties of the rms for the fluctuationsmore » as functions of the system parameters and time. The instantaneous signal transferring mechanism between the velocity and position fluctuations could not be achieved in the previous phase-average approaches.« less

Correlators in tensor models from character calculus

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2017-11-01

We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz) character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.

Application of Newton's method to the postbuckling of rings under pressure loadings

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

The postbuckling response of circular rings (or long cylinders) is examined. The rings are subjected to four types of external pressure loadings; each type of pressure is defined by its magnitude and direction at points on the buckled ring. Newton's method is applied to the nonlinear differential equations of the exact inextensional theory for the ring problem. A zeroth approximation for the solution of the nonlinear equations, based on the mode shape corresponding to the first buckling pressure, is derived in closed form for each of the four types of pressure. The zeroth approximation is used to start the iteration cycle in Newton's method to compute numerical solutions of the nonlinear equations. The zeroth approximations for the postbuckling pressure-deflection curves are compared with the converged solutions from Newton's method and with similar results reported in the literature.

Nonlinear dynamics investigation in few-cycle laser seeding of quantum cascade lasers: role of permanent dipole moment

NASA Astrophysics Data System (ADS)

Wu, Erheng; Cao, Qing; You, Jun; Liu, Chengpu

2017-06-01

The ultrafast dynamics in the few-cycle laser seeding of quantum cascade laser (QCL) is numerically investigated via the exact solution of the full-wave Maxwell-Bloch equations. It is found that, with or without taking permanent dipole moment (PDM) into account, the QCL emission is quite different: beyond the fundamental frequency band, additional high and low bands occur for that with PDM, which forms an ultra-broad quasi-comb. The origin for this is closely related to the generation of second order harmonic and direct-current components as a result of PDM breaking down the parity symmetry. Moreover, the carrier-envelope-phase (CEP) of laser seed is locked to the QCL output, no matter with or without PDM, and this phase controlled QCL maybe has more wide and convenient applications in related fields.

The probabilistic convolution tree: efficient exact Bayesian inference for faster LC-MS/MS protein inference.

PubMed

Serang, Oliver

2014-01-01

Exact Bayesian inference can sometimes be performed efficiently for special cases where a function has commutative and associative symmetry of its inputs (called "causal independence"). For this reason, it is desirable to exploit such symmetry on big data sets. Here we present a method to exploit a general form of this symmetry on probabilistic adder nodes by transforming those probabilistic adder nodes into a probabilistic convolution tree with which dynamic programming computes exact probabilities. A substantial speedup is demonstrated using an illustration example that can arise when identifying splice forms with bottom-up mass spectrometry-based proteomics. On this example, even state-of-the-art exact inference algorithms require a runtime more than exponential in the number of splice forms considered. By using the probabilistic convolution tree, we reduce the runtime to O(k log(k)2) and the space to O(k log(k)) where k is the number of variables joined by an additive or cardinal operator. This approach, which can also be used with junction tree inference, is applicable to graphs with arbitrary dependency on counting variables or cardinalities and can be used on diverse problems and fields like forward error correcting codes, elemental decomposition, and spectral demixing. The approach also trivially generalizes to multiple dimensions.

The Probabilistic Convolution Tree: Efficient Exact Bayesian Inference for Faster LC-MS/MS Protein Inference

PubMed Central

Serang, Oliver

2014-01-01

Exact Bayesian inference can sometimes be performed efficiently for special cases where a function has commutative and associative symmetry of its inputs (called “causal independence”). For this reason, it is desirable to exploit such symmetry on big data sets. Here we present a method to exploit a general form of this symmetry on probabilistic adder nodes by transforming those probabilistic adder nodes into a probabilistic convolution tree with which dynamic programming computes exact probabilities. A substantial speedup is demonstrated using an illustration example that can arise when identifying splice forms with bottom-up mass spectrometry-based proteomics. On this example, even state-of-the-art exact inference algorithms require a runtime more than exponential in the number of splice forms considered. By using the probabilistic convolution tree, we reduce the runtime to and the space to where is the number of variables joined by an additive or cardinal operator. This approach, which can also be used with junction tree inference, is applicable to graphs with arbitrary dependency on counting variables or cardinalities and can be used on diverse problems and fields like forward error correcting codes, elemental decomposition, and spectral demixing. The approach also trivially generalizes to multiple dimensions. PMID:24626234

Statistics on continuous IBD data: Exact distribution evaluation for a pair of full(half)-sibs and a pair of a (great-) grandchild with a (great-) grandparent

PubMed Central

Stefanov, Valeri T

2002-01-01

Background Pairs of related individuals are widely used in linkage analysis. Most of the tests for linkage analysis are based on statistics associated with identity by descent (IBD) data. The current biotechnology provides data on very densely packed loci, and therefore, it may provide almost continuous IBD data for pairs of closely related individuals. Therefore, the distribution theory for statistics on continuous IBD data is of interest. In particular, distributional results which allow the evaluation of p-values for relevant tests are of importance. Results A technology is provided for numerical evaluation, with any given accuracy, of the cumulative probabilities of some statistics on continuous genome data for pairs of closely related individuals. In the case of a pair of full-sibs, the following statistics are considered: (i) the proportion of genome with 2 (at least 1) haplotypes shared identical-by-descent (IBD) on a chromosomal segment, (ii) the number of distinct pieces (subsegments) of a chromosomal segment, on each of which exactly 2 (at least 1) haplotypes are shared IBD. The natural counterparts of these statistics for the other relationships are also considered. Relevant Maple codes are provided for a rapid evaluation of the cumulative probabilities of such statistics. The genomic continuum model, with Haldane's model for the crossover process, is assumed. Conclusions A technology, together with relevant software codes for its automated implementation, are provided for exact evaluation of the distributions of relevant statistics associated with continuous genome data on closely related individuals. PMID:11996673

Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Abuasad, Salah; Hashim, Ishak

2018-04-01

In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

Exact p-values for pairwise comparison of Friedman rank sums, with application to comparing classifiers.

PubMed

Eisinga, Rob; Heskes, Tom; Pelzer, Ben; Te Grotenhuis, Manfred

2017-01-25

The Friedman rank sum test is a widely-used nonparametric method in computational biology. In addition to examining the overall null hypothesis of no significant difference among any of the rank sums, it is typically of interest to conduct pairwise comparison tests. Current approaches to such tests rely on large-sample approximations, due to the numerical complexity of computing the exact distribution. These approximate methods lead to inaccurate estimates in the tail of the distribution, which is most relevant for p-value calculation. We propose an efficient, combinatorial exact approach for calculating the probability mass distribution of the rank sum difference statistic for pairwise comparison of Friedman rank sums, and compare exact results with recommended asymptotic approximations. Whereas the chi-squared approximation performs inferiorly to exact computation overall, others, particularly the normal, perform well, except for the extreme tail. Hence exact calculation offers an improvement when small p-values occur following multiple testing correction. Exact inference also enhances the identification of significant differences whenever the observed values are close to the approximate critical value. We illustrate the proposed method in the context of biological machine learning, were Friedman rank sum difference tests are commonly used for the comparison of classifiers over multiple datasets. We provide a computationally fast method to determine the exact p-value of the absolute rank sum difference of a pair of Friedman rank sums, making asymptotic tests obsolete. Calculation of exact p-values is easy to implement in statistical software and the implementation in R is provided in one of the Additional files and is also available at http://www.ru.nl/publish/pages/726696/friedmanrsd.zip .

Closed-form solutions of the Wheeler-DeWitt equation in a scalar-vector field cosmological model by Lie symmetries

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos; Vakili, Babak

2016-01-01

We apply as selection rule to determine the unknown functions of a cosmological model the existence of Lie point symmetries for the Wheeler-DeWitt equation of quantum gravity. Our cosmological setting consists of a flat Friedmann-Robertson-Walker metric having the scale factor a( t), a scalar field with potential function V(φ ) minimally coupled to gravity and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f(φ ). Then, the Lie symmetries of this dynamical system are investigated by utilizing the behavior of the corresponding minisuperspace under the infinitesimal generator of the desired symmetries. It is shown that by applying the Lie symmetry condition the form of the coupling function and also the scalar field potential function may be explicitly determined so that we are able to solve the Wheeler-DeWitt equation. Finally, we show how we can use the Lie symmetries in order to construct conservation laws and exact solutions for the field equations.

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

NASA Technical Reports Server (NTRS)

Goldstein, Marvin E.

2001-01-01

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

Differential Forms: A New Tool in Economics

NASA Astrophysics Data System (ADS)

Mimkes, Jürgen

Econophysics is the transfer of methods from natural to socio-economic sciences. This concept has first been applied to finance1, but it is now also used in various applications of economics and social sciences [2,3]. The present paper focuses on problems in macro economics and growth. 1. Neoclassical theory [4, 5] neglects the “ex post” property of income and growth. Income Y(K, L) is assumed to be a function of capital and labor. But functions cannot model the “ex post” character of income. 2. Neoclassical theory is based on a Cobb Douglas function [6] with variable elasticity α, which may be fitted to economic data. But an undefined elasticity α leads to a descriptive rather than a predictive economic theory. The present paper introduces a new tool - differential forms and path dependent integrals - to macro economics. This is a solution to the problems above: 1. The integral of not exact differential forms is path dependent and can only be calculated “ex post” like income and economic growth. 2. Not exact differential forms can be made exact by an integrating factor, this leads to a new, well defined, unique production function F and a predictive economic theory.

A review of plague persistence with special emphasis on fleas

USGS Publications Warehouse

Wimsatt, Jeffrey; Biggins, Dean E.

2009-01-01

Here, we note a potentially pivotal role for fleas. These epizootic plague vectors should be closely studied with newer more exacting methods to determine their potential to serve as participants in or accomplices to a plague persistence reservoir.

New stochastic approach for extreme response of slow drift motion of moored floating structures

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

Kato, Shunji; Okazaki, Takashi

1995-12-31

A new stochastic method for investigating the flow drift response statistics of moored floating structures is described. Assuming that wave drift excitation process can be driven by a Gaussian white noise process, an exact stochastic equation governing a time evolution of the response Probability Density Function (PDF) is derived on a basis of Projection operator technique in the field of statistical physics. In order to get an approximate solution of the GFP equation, the authors develop the renormalized perturbation technique which is a kind of singular perturbation methods and solve the GFP equation taken into account up to third ordermore » moments of a non-Gaussian excitation. As an example of the present method, a closed form of the joint PDF is derived for linear response in surge motion subjected to a non-Gaussian wave drift excitation and it is represented by the product of a form factor and the quasi-Cauchy PDFs. In this case, the motion displacement and velocity processes are not mutually independent if the excitation process has a significant third order moment. From a comparison between the response PDF by the present solution and the exact one derived by Naess, it is found that the present solution is effective for calculating both the response PDF and the joint PDF. Furthermore it is shown that the displacement-velocity independence is satisfied if the damping coefficient in equation of motion is not so large and that both the non-Gaussian property of excitation and the damping coefficient should be taken into account for estimating the probability exceedance of the response.« less

Exact and approximate solutions for the decades-old Michaelis-Menten equation: Progress-curve analysis through integrated rate equations.

PubMed

Goličnik, Marko

2011-01-01

The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century. Copyright © 2011 Wiley Periodicals, Inc.

Couple stress fluid flow in a rotating channel with peristalsis

NASA Astrophysics Data System (ADS)

Abd elmaboud, Y.; Abdelsalam, Sara I.; Mekheimer, Kh. S.

2018-04-01

This article describes a new model for obtaining closed-form semi-analytical solutions of peristaltic flow induced by sinusoidal wave trains propagating with constant speed on the walls of a two-dimensional rotating infinite channel. The channel rotates with a constant angular speed about the z - axis and is filled with couple stress fluid. The governing equations of the channel deformation and the flow rate inside the channel are derived using the lubrication theory approach. The resulting equations are solved, using the homotopy perturbation method (HPM), for exact solutions to the longitudinal velocity distribution, pressure gradient, flow rate due to secondary velocity, and pressure rise per wavelength. The effect of various values of physical parameters, such as, Taylor's number and couple stress parameter, together with some interesting features of peristaltic flow are discussed through graphs. The trapping phenomenon is investigated for different values of parameters under consideration. It is shown that Taylor's number and the couple stress parameter have an increasing effect on the longitudinal velocity distribution till half of the channel, on the flow rate due to secondary velocity, and on the number of closed streamlines circulating the bolus.

Magnetohydrodynamic motion of a two-fluid plasma

DOE PAGES

Burby, Joshua W.

2017-07-21

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Magnetohydrodynamic motion of a two-fluid plasma

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

Burby, Joshua W.

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Lognormal Approximations of Fault Tree Uncertainty Distributions.

PubMed

El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P

2018-01-26

Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.

Is Surgical Navigation Useful During Closed Reduction of Nasal Bone Fractures?

PubMed

Kim, Seon Tae; Jung, Joo Hyun; Kang, Il Gyu

2017-05-01

To report the case of a 42-year-old woman with a nasal bone fracture that was easily treated using a surgical navigation system. In this clinical report, the authors suggest that intraoperative surgical navigation systems are useful diagnostically and for localizing sites of nasal bone fractures exactly. The patient underwent successful closed reduction of the nasal bone fracture. Surgical navigation is a useful tool for identifying nasal bone fracture locations and for guiding closed reduction. Surgical navigation is recommended when nasal bone fractures are complicated or not well reduced using the ordinary method.

Closed loop models for analyzing the effects of simulator characteristics. [digital simulation of human operators

NASA Technical Reports Server (NTRS)

Baron, S.; Muralidharan, R.; Kleinman, D. L.

1978-01-01

The optimal control model of the human operator is used to develop closed loop models for analyzing the effects of (digital) simulator characteristics on predicted performance and/or workload. Two approaches are considered: the first utilizes a continuous approximation to the discrete simulation in conjunction with the standard optimal control model; the second involves a more exact discrete description of the simulator in a closed loop multirate simulation in which the optimal control model simulates the pilot. Both models predict that simulator characteristics can have significant effects on performance and workload.

Gyro-gauge-independent formulation of the guiding-center reduction to arbitrary order in the Larmor radius

NASA Astrophysics Data System (ADS)

de Guillebon, L.; Vittot, M.

2013-10-01

Guiding-center reduction is studied using gyro-gauge-independent coordinates. The Lagrangian 1-form of charged particle dynamics is Lie transformed without introducing a gyro-gauge, but using directly the unit vector of the component of the velocity perpendicular to the magnetic field as the coordinate corresponding to Larmor gyration. The reduction is shown to provide a maximal reduction for the Lagrangian and to work for all orders in the Larmor radius, following exactly the same procedure as when working with the standard gauge-dependent coordinate. The gauge-dependence is removed from the coordinate system by using a constrained variable for the gyro-angle. The closed 1-form dθ is replaced by a more general non-closed 1-form, which is equal to dθ in the gauge-dependent case. The gauge vector is replaced by a more general connection in the definition of the gradient, which behaves as a covariant derivative, in perfect agreement with the circle-bundle picture. This explains some results of previous works, whose gauge-independent expressions did not correspond to gauge fixing but did indeed correspond to connection fixing. In addition, some general results are obtained for the guiding-center reduction. The expansion is polynomial in the cotangent of the pitch-angle as an effect of the structure of the Lagrangian, preserved by Lie derivatives. The induction for the reduction is shown to rely on the inversion of a matrix, which is the same for all orders higher than three. It is inverted and explicit induction relations are obtained to go to an arbitrary order in the perturbation expansion. The Hamiltonian and symplectic representations of the guiding-center reduction are recovered, but conditions for the symplectic representation at each order are emphasized.

Nonlinear equation of the modes in circular slab waveguides and its application.

PubMed

Zhu, Jianxin; Zheng, Jia

2013-11-20

In this paper, circularly curved inhomogeneous waveguides are transformed into straight inhomogeneous waveguides first by a conformal mapping. Then, the differential transfer matrix method is introduced and adopted to deduce the exact dispersion relation for modes. This relation itself is complex and difficult to solve, but it can be approximated by a simpler nonlinear equation in practical applications, which is close to the exact relation and quite easy to analyze. Afterward, optimized asymptotic solutions are obtained and act as initial guesses for the following Newton's iteration. Finally, very accurate solutions are achieved in the numerical experiment.

Asymptotic symmetries in p-form theories

NASA Astrophysics Data System (ADS)

Afshar, Hamid; Esmaeili, Erfan; Sheikh-Jabbari, M. M.

2018-05-01

We consider ( p + 1)-form gauge fields in flat (2 p + 4)-dimensions for which radiation and Coulomb solutions have the same asymptotic fall-off behavior. Imposing appropriate fall-off behavior on fields and adopting a Maxwell-type action, we construct the boundary term which renders the action principle well-defined in the Lorenz gauge. We then compute conserved surface charges and the corresponding asymptotic charge algebra associated with nontrivial gauge transformations. We show that for p ≥ 1, there are three sets of conserved asymptotic charges associated with exact, coexact and zero-mode parts of the corresponding p-form gauge transformations on the asymptotic S 2 p+2. The coexact and zero-mode charges are higher form extensions of the four dimensional electrodynamics ( p = 0), and are commuting. Charges associated with exact gauge transformations have no counterparts in four dimensions and form infinite copies of Heisenberg algebras. We briefly discuss physical implications of these charges and their algebra.

Variational Dirac-Hartree-Fock calculation of the Breit interaction

NASA Astrophysics Data System (ADS)

Goldman, S. P.

1988-04-01

The calculation of the retarded version of the Breit interaction in the context of the VDHF method is discussed. With the use of Slater-type basis functions, all the terms involved can be calculated in closed form. The results are expressed as an expansion in powers of one-electron energy differences and linear combinations of hypergeometric functions. Convergence is fast and high accuracy is obtained with a small number of terms in the expansion even for high values of the nuclear charge. An added advantage is that the lowest order cancellations occurring in the retardation terms are accounted for exactly a priori. A comparison of the number of terms in the total expansion needed for an accuracy of 12 significant digits in the total energy, as well as a comparison of the results with an without retardation and in the local potential approximation, are presented for the carbon isoelectronic sequence.

SER Analysis of MPPM-Coded MIMO-FSO System over Uncorrelated and Correlated Gamma-Gamma Atmospheric Turbulence Channels

NASA Astrophysics Data System (ADS)

Khallaf, Haitham S.; Garrido-Balsells, José M.; Shalaby, Hossam M. H.; Sampei, Seiichi

2015-12-01

The performance of multiple-input multiple-output free space optical (MIMO-FSO) communication systems, that adopt multipulse pulse position modulation (MPPM) techniques, is analyzed. Both exact and approximate symbol-error rates (SERs) are derived for both cases of uncorrelated and correlated channels. The effects of background noise, receiver shot-noise, and atmospheric turbulence are taken into consideration in our analysis. The random fluctuations of the received optical irradiance, produced by the atmospheric turbulence, is modeled by the widely used gamma-gamma statistical distribution. Uncorrelated MIMO channels are modeled by the α-μ distribution. A closed-form expression for the probability density function of the optical received irradiance is derived for the case of correlated MIMO channels. Using our analytical expressions, the degradation of the system performance with the increment of the correlation coefficients between MIMO channels is corroborated.

Unsteady Newton-Busemann flow theory. Part 2: Bodies of revolution

NASA Technical Reports Server (NTRS)

Hui, W. H.; Tobak, M.

1981-01-01

Newtonian flow theory for unsteady flow past oscillating bodies of revolution at very high Mach numbers is completed by adding a centrifugal force correction to the impact pressures. Exact formulas for the unsteady pressure and the stability derivatives are obtained in closed form and are applicable to bodies of revolution that have arbitrary shapes, arbitrary thicknesses, and either sharp or blunt noses. The centrifugal force correction arising from the curved trajectories followed by the fluid particles in unsteady flow cannot be neglected even for the case of a circular cone. With this correction, the present theory is in excellent agreement with experimental results for sharp cones and for cones with small nose bluntness; gives poor agreement with the results of experiments in air for bodies with moderate or large nose bluntness. The pitching motions of slender power-law bodies of revulution are shown to be always dynamically stable according to Newton-Busemann theory.

Equivalency principle for magnetoelectroelastic multiferroics with arbitrary microstructure: The phase field approach

NASA Astrophysics Data System (ADS)

Ni, Yong; He, Linghui; Khachaturyan, Armen G.

2010-07-01

A phase field method is proposed to determine the equilibrium fields of a magnetoelectroelastic multiferroic with arbitrarily distributed constitutive constants under applied loadings. This method is based on a developed generalized Eshelby's equivalency principle, in which the elastic strain, electrostatic, and magnetostatic fields at the equilibrium in the original heterogeneous system are exactly the same as those in an equivalent homogeneous magnetoelectroelastic coupled or uncoupled system with properly chosen distributed effective eigenstrain, polarization, and magnetization fields. Finding these effective fields fully solves the equilibrium elasticity, electrostatics, and magnetostatics in the original heterogeneous multiferroic. The paper formulates a variational principle proving that the effective fields are minimizers of appropriate close-form energy functional. The proposed phase field approach produces the energy minimizing effective fields (and thus solving the general multiferroic problem) as a result of artificial relaxation process described by the Ginzburg-Landau-Khalatnikov kinetic equations.

Black hole solutions in d = 5 Chern-Simons gravity

NASA Astrophysics Data System (ADS)

Brihaye, Yves; Radu, Eugen

2013-11-01

The five dimensional Einstein-Gauss-Bonnet gravity with a negative cosmological constant becomes, for a special value of the Gauss-Bonnet coupling constant, a Chern-Simons (CS) theory of gravity. In this work we discuss the properties of several different types of black object solutions of this model. Special attention is paid to the case of spinning black holes with equal-magnitude angular momenta which posses a regular horizon of spherical topology. Closed form solutions are obtained in the small angular momentum limit. Nonperturbative solutions are constructed by solving numerically the equations of the model. Apart from that, new exact solutions describing static squashed black holes and black strings are also discussed. The action and global charges of all configurations studied in this work are obtained by using the quasilocal formalism with boundary counterterms generalized for the case of a d = 5 CS theory.

Unraveling different chemical fingerprints between a champagne wine and its aerosols.

PubMed

Liger-Belair, Gérard; Cilindre, Clara; Gougeon, Régis D; Lucio, Marianna; Gebefügi, Istvan; Jeandet, Philippe; Schmitt-Kopplin, Philippe

2009-09-29

As champagne or sparkling wine is poured into a glass, the myriad of ascending bubbles collapse and radiate a multitude of tiny droplets above the free surface into the form of very characteristic and refreshing aerosols. Ultrahigh-resolution MS was used as a nontargeted approach to discriminate hundreds of surface active compounds that are preferentially partitioning in champagne aerosols; thus, unraveling different chemical fingerprints between the champagne bulk and its aerosols. Based on accurate exact mass analysis and database search, tens of these compounds overconcentrating in champagne aerosols were unambiguously discriminated and assigned to compounds showing organoleptic interest or being aromas precursors. By drawing a parallel between the fizz of the ocean and the fizz in Champagne wines, our results closely link bursting bubbles and flavor release; thus, supporting the idea that rising and collapsing bubbles act as a continuous paternoster lift for aromas in every glass of champagne.

Reclassification of Xuhuaishuia manganoxidans Wang et al. 2015 as a later heterotypic synonym of Brevirhabdus pacifica Wu et al. 2015 and emendation of the species description.

PubMed

Liu, Yang; Lai, Qiliang; Xu, Xue-Wei; Wu, Yue-Hong; Cheng, Hong; Zhang, Xiao-Hua; Wang, Long; Shao, Zongze

2017-08-01

A polyphasic taxonomic study was undertaken to clarify the exact position of type strain DY6-4T of Xuhuaishuia manganoxidans. A combination of physiological properties of X. manganoxidans DY6-4T was consistent with those of type strain 22DY15T of Brevirhabdus pacifica. The 16S rRNA gene sequence analyses indicated that X. manganoxidans DY6-4T and B. pacifica 22DY15T shared 100 % similarity and formed a monophyletic group. The close relationship between the two strains was underpinned by the results of chemotaxonomic characteristics, including the fatty acids, quinone and polar lipids. The digital DNA-DNA hybridization and average nucleotide identity values between the two strains were 99.90 and 99.98 %, respectively. Based on these results, we propose that Xuhuaishuia manganoxidans is a later heterotypic synonym of Brevirhabdus pacifica.

[Nursing: the meaning of this profession to nurses. A first approach].

PubMed

Luchesi, Luciana Barizon; Santos, Claudia Benedita dos

2005-01-01

In an attempt to understand, tell and, why not, participate a little in the history of Nursing, we proposed to study the prejudices and negative stereotypes that have permeated this profession over time. This is a before-after experimental type of study in a population of adolescents regularly enrolled in the eleventh grade of a Brazilian public school. The intervention took the form of a lecture about the profession and a questionnaire with closed questions which was applied before and after the lecture. Conclusions were based on the results of binomial and McNemar's non-parametric tests for the significance of changes. Although the statistically significant presence of prejudice and negatives stereotypes was not found, the results of the intervention were in line with expectations, since the changes(or tendency towards changes) took place exactly in those subgroups that showed a greater frequency of stereotypes.

Unraveling different chemical fingerprints between a champagne wine and its aerosols

PubMed Central

Liger-Belair, Gérard; Cilindre, Clara; Gougeon, Régis D.; Lucio, Marianna; Gebefügi, Istvan; Jeandet, Philippe; Schmitt-Kopplin, Philippe

2009-01-01

As champagne or sparkling wine is poured into a glass, the myriad of ascending bubbles collapse and radiate a multitude of tiny droplets above the free surface into the form of very characteristic and refreshing aerosols. Ultrahigh-resolution MS was used as a nontargeted approach to discriminate hundreds of surface active compounds that are preferentially partitioning in champagne aerosols; thus, unraveling different chemical fingerprints between the champagne bulk and its aerosols. Based on accurate exact mass analysis and database search, tens of these compounds overconcentrating in champagne aerosols were unambiguously discriminated and assigned to compounds showing organoleptic interest or being aromas precursors. By drawing a parallel between the fizz of the ocean and the fizz in Champagne wines, our results closely link bursting bubbles and flavor release; thus, supporting the idea that rising and collapsing bubbles act as a continuous paternoster lift for aromas in every glass of champagne. PMID:19805335

Adiabatic Berry phase in an atom-molecule conversion system

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

Fu Libin; Center for Applied Physics and Technology, Peking University, Beijing 100084; Liu Jie, E-mail: liu_jie@iapcm.ac.c

2010-11-15

We investigate the Berry phase of adiabatic quantum evolution in the atom-molecule conversion system that is governed by a nonlinear Schroedinger equation. We find that the Berry phase consists of two parts: the usual Berry connection term and a novel term from the nonlinearity brought forth by the atom-molecule coupling. The total geometric phase can be still viewed as the flux of the magnetic field of a monopole through the surface enclosed by a closed path in parameter space. The charge of the monopole, however, is found to be one third of the elementary charge of the usual quantized monopole.more » We also derive the classical Hannay angle of a geometric nature associated with the adiabatic evolution. It exactly equals minus Berry phase, indicating a novel connection between Berry phase and Hannay angle in contrast to the usual derivative form.« less

An Analytical Time–Domain Expression for the Net Ripple Produced by Parallel Interleaved Converters

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

Johnson, Brian B.; Krein, Philip T.

We apply modular arithmetic and Fourier series to analyze the superposition of N interleaved triangular waveforms with identical amplitudes and duty-ratios. Here, interleaving refers to the condition when a collection of periodic waveforms with identical periods are each uniformly phase-shifted across one period. The main result is a time-domain expression which provides an exact representation of the summed and interleaved triangular waveforms, where the peak amplitude and parameters of the time-periodic component are all specified in closed-form. Analysis is general and can be used to study various applications in multi-converter systems. This model is unique not only in that itmore » reveals a simple and intuitive expression for the net ripple, but its derivation via modular arithmetic and Fourier series is distinct from prior approaches. The analytical framework is experimentally validated with a system of three parallel converters under time-varying operating conditions.« less

An Improved Correlation between Impression and Uniaxial Creep

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

Hsueh, Chun-Hway; Miranda, Pedro; Becher, Paul F

2006-01-01

A semiempirical correlation between impression and uniaxial creep has been established by Hyde et al. [Int. J. Mech. Sci. 35, 451 (1993) ] using finite element results for materials exhibiting general power-law creep with the stress exponent n in the range 2 {<=} n {<=} 15. Here, we derive the closed-form solution for a special case of viscoelastic materials, i.e., n = 1, subjected to impression creep and obtain the exact correlation between impression and uniaxial creep. This analytical solution serves as a checkpoint for the finite element results. We then perform finite element analyses for the general case tomore » derive a semiempirical correlation, which agrees well with both analytical viscoelastic results and the existing experimental data. Our improved correlation agrees with the correlation of Hyde et al. for n {>=} 4, and the difference increases with decreasing n for n<4.« less

Diffusion with stochastic resetting at power-law times.

PubMed

Nagar, Apoorva; Gupta, Shamik

2016-06-01

What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals τ distributed as a power law ∼τ^{-(1+α)};α>0? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for α<1, to one that is time independent for α>1. The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal α that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.

Excitation basis for (3+1)d topological phases

NASA Astrophysics Data System (ADS)

Delcamp, Clement

2017-12-01

We consider an exactly solvable model in 3+1 dimensions, based on a finite group, which is a natural generalization of Kitaev's quantum double model. The corresponding lattice Hamiltonian yields excitations located at torus-boundaries. By cutting open the three-torus, we obtain a manifold bounded by two tori which supports states satisfying a higher-dimensional version of Ocneanu's tube algebra. This defines an algebraic structure extending the Drinfel'd double. Its irreducible representations, labeled by two fluxes and one charge, characterize the torus-excitations. The tensor product of such representations is introduced in order to construct a basis for (3+1)d gauge models which relies upon the fusion of the defect excitations. This basis is defined on manifolds of the form Σ × S_1 , with Σ a two-dimensional Riemann surface. As such, our construction is closely related to dimensional reduction from (3+1)d to (2+1)d topological orders.

Discrete conservation properties for shallow water flows using mixed mimetic spectral elements

NASA Astrophysics Data System (ADS)

Lee, D.; Palha, A.; Gerritsma, M.

2018-03-01

A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of calculus with respect to the standard Lagrange basis functions in one dimension. These are used to construct tensor product solution spaces which satisfy the generalized Stokes theorem, as well as the annihilation of the gradient operator by the curl and the curl by the divergence. This allows for the exact conservation of first order moments (mass, vorticity), as well as higher moments (energy, potential enstrophy), subject to the truncation error of the time stepping scheme. The continuity equation is solved in the strong form, such that mass conservation holds point wise, while the momentum equation is solved in the weak form such that vorticity is globally conserved. While mass, vorticity and energy conservation hold for any quadrature rule, potential enstrophy conservation is dependent on exact spatial integration. The method possesses a weak form statement of geostrophic balance due to the compatible nature of the solution spaces and arbitrarily high order spatial error convergence.

Rover mast calibration, exact camera pointing, and camara handoff for visual target tracking

NASA Technical Reports Server (NTRS)

Kim, Won S.; Ansar, Adnan I.; Steele, Robert D.

2005-01-01

This paper presents three technical elements that we have developed to improve the accuracy of the visual target tracking for single-sol approach-and-instrument placement in future Mars rover missions. An accurate, straightforward method of rover mast calibration is achieved by using a total station, a camera calibration target, and four prism targets mounted on the rover. The method was applied to Rocky8 rover mast calibration and yielded a 1.1-pixel rms residual error. Camera pointing requires inverse kinematic solutions for mast pan and tilt angles such that the target image appears right at the center of the camera image. Two issues were raised. Mast camera frames are in general not parallel to the masthead base frame. Further, the optical axis of the camera model in general does not pass through the center of the image. Despite these issues, we managed to derive non-iterative closed-form exact solutions, which were verified with Matlab routines. Actual camera pointing experiments aver 50 random target image paints yielded less than 1.3-pixel rms pointing error. Finally, a purely geometric method for camera handoff using stereo views of the target has been developed. Experimental test runs show less than 2.5 pixels error on high-resolution Navcam for Pancam-to-Navcam handoff, and less than 4 pixels error on lower-resolution Hazcam for Navcam-to-Hazcam handoff.

Closed-Suction Drainage and Cerebrospinal Fluid Leakage Following Microvascular Decompression : A Retrospective Comparison Study

PubMed Central

Kim, Young-Hoon; Kim, Chae-Yong; Oh, Chang Wan

2013-01-01

Objective We performed this study to investigate whether the use of closed-suction drainage following microvascular decompression (MVD) causes cerebrospinal fluid (CSF) leakage. Methods Between 2004 and 2011, a total of 157 patients with neurovascular compression were treated with MVD. MVD was performed for hemifacial spasm in 150 (95.5%) cases and for trigeminal neuralgia in 7 (4.5%) cases. The mean age of the patients was 49.8±9.6 years (range, 20-69). Dural substitutes were used in 44 (28.0%) patients. Ninety-two patients (58.6%) were underwent a 4-5 cm craniotomy using drainage (drainage group), and 65 (41.4%) did a small 2-2.5 cm retromastoid craniectomy without closed-suction drainage (no-drainage group). Results Eleven (7.0%) patients experienced CSF leakage following MVD based on the criteria of this study; all of these patients were in the drainage group. In the unadjusted analyses, the incidence of CSF leakage was significantly related with the use of closed-suction drainage following MVD (12.0% in the drainage group vs. 0% in the no-drainage group, respectively; p=0.003; Fisher's exact test). Those who received dural substitutes and the elderly (cut-off value=60 years) exhibited a tendency to develop CSF leakage (p=0.075 and p=0.090, respectively; Fisher's exact test). In the multivariate analysis, only the use of closed-suction drainage was significantly and independently associated with the development of CSF leakage following MVD (odds ratio=9.900; 95% confidence interval, 1.418 to infinity; p=0.017). Conclusion The use of closed-suction drainage following MVD appears to be related to the development of CSF leakage. PMID:24175025

Familial Sinistrals Avoid Exact Numbers

PubMed Central

Sauerland, Uli; Gotzner, Nicole

2013-01-01

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

Familial sinistrals avoid exact numbers.

PubMed

Sauerland, Uli; Gotzner, Nicole

2013-01-01

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

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

Derrida, B.; Meir, R.

We consider the evolution of configurations in a layered feed-forward neural network. Exact expressions for the evolution of the distance between two configurations are obtained in the thermodynamic limit. Our results show that the distance between two arbitrarily close configurations always increases, implying chaotic behavior, even in the phase of good retrieval.

Citation Matching in Sanskrit Corpora Using Local Alignment

NASA Astrophysics Data System (ADS)

Prasad, Abhinandan S.; Rao, Shrisha

Citation matching is the problem of finding which citation occurs in a given textual corpus. Most existing citation matching work is done on scientific literature. The goal of this paper is to present methods for performing citation matching on Sanskrit texts. Exact matching and approximate matching are the two methods for performing citation matching. The exact matching method checks for exact occurrence of the citation with respect to the textual corpus. Approximate matching is a fuzzy string-matching method which computes a similarity score between an individual line of the textual corpus and the citation. The Smith-Waterman-Gotoh algorithm for local alignment, which is generally used in bioinformatics, is used here for calculating the similarity score. This similarity score is a measure of the closeness between the text and the citation. The exact- and approximate-matching methods are evaluated and compared. The methods presented can be easily applied to corpora in other Indic languages like Kannada, Tamil, etc. The approximate-matching method can in particular be used in the compilation of critical editions and plagiarism detection in a literary work.

ADHD and math - The differential effect on calculation and estimation.

PubMed

Ganor-Stern, Dana; Steinhorn, Ofir

2018-05-31

Adults with ADHD were compared to controls when solving multiplication problems exactly and when estimating the results of multidigit multiplication problems relative to reference numbers. The ADHD participants were slower than controls in the exact calculation and in the estimation tasks, but not less accurate. The ADHD participants were similar to controls in showing enhanced accuracy and speed for smaller problem sizes, for trials in which the reference numbers were smaller (vs. larger) than the exact answers and for reference numbers that were far (vs. close) from the exact answer. The two groups similarly used the approximated calculation and the sense of magnitude strategies. They differed however in strategy execution, mainly of the approximated calculation strategy, which requires working memory resources. The increase in reaction time associated with using the approximated calculation strategy was larger for the ADHD compared to the control participants. Thus, ADHD seems to selectively impair calculation processes in estimation tasks that rely on working memory, but it does not hamper estimation skills that are based on sense of magnitude. The educational implications of these findings are discussed. Copyright © 2018. Published by Elsevier B.V.

Rotationally mediated selective adsorption as a probe of isotropic and anisotropic molecule. Surface interaction potentials: HD(J)/Ag(111)

NASA Astrophysics Data System (ADS)

Uy, C. F.; Hogg, C. S.; Cowin, J. P.; Whaley, K. B.; Light, J. C.; Sibener, S. J.

1982-08-01

Rotationally mediated selective adsorption scattering resonances are used to make an experimental and theoretical study of the laterally averaged interaction potential between HD and a weakly corrugated system, Ag(111). The experimentally observed resonances determine the vibrational levels of the HD/Ag(111) physisorption potential as a function of bound rotational state. These vibrational levels show J-dependent shifts due to the orientational anisotropy of the potential. Exact quantum scattering calculations using a full laterally averaged potential of the form V sub o(z,0) = v sub o (z) (1 + beta P sub 2 (cos theta)) have been carried out to obtain rotationally inelastic transition probabilities. Experimental and theoretical resonance energies are compared for two forms of v sub o(z), a Morse and a variable exponent potential, as a function of Beta, and are found to be very close to the first order perturbed energies of a free rotor in bound states of v sub o(z). Both potential forms give equally good fits to the data, yielding an optimum value of the asymmetry parameter, Beta approx. -0.05. The determination of Beta is relatively insensitive to small changes in the v sub o(z) well depth.

Physical Meaning of Virtual Kohn-Sham Orbitals and Orbital Energies: An Ideal Basis for the Description of Molecular Excitations.

PubMed

van Meer, R; Gritsenko, O V; Baerends, E J

2014-10-14

In recent years, several benchmark studies on the performance of large sets of functionals in time-dependent density functional theory (TDDFT) calculations of excitation energies have been performed. The tested functionals do not approximate exact Kohn-Sham orbitals and orbital energies closely. We highlight the advantages of (close to) exact Kohn-Sham orbitals and orbital energies for a simple description, very often as just a single orbital-to-orbital transition, of molecular excitations. Benchmark calculations are performed for the statistical average of orbital potentials (SAOP) functional for the potential [J. Chem. Phys. 2000, 112, 1344; 2001, 114, 652], which approximates the true Kohn-Sham potential much better than LDA, GGA, mGGA, and hybrid potentials do. An accurate Kohn-Sham potential does not only perform satisfactorily for calculated vertical excitation energies of both valence and Rydberg transitions but also exhibits appealing properties of the KS orbitals including occupied orbital energies close to ionization energies, virtual-occupied orbital energy gaps very close to excitation energies, realistic shapes of virtual orbitals, leading to straightforward interpretation of most excitations as single orbital transitions. We stress that such advantages are completely lost in time-dependent Hartree-Fock and partly in hybrid approaches. Many excitations and excitation energies calculated with local density, generalized gradient, and hybrid functionals are spurious. There is, with an accurate KS, or even the LDA or GGA potentials, nothing problematic about the "band gap" in molecules: the HOMO-LUMO gap is close to the first excitation energy (the optical gap).

Straight spinning cosmic strings in Brans-Dicke gravity

NASA Astrophysics Data System (ADS)

Dos Santos, S. Mittmann; da Silva, J. M. Hoff; Cindra, J. L.

2018-03-01

An exact solution of straight spinning cosmic strings in Brans-Dicke theory of gravitation is presented. The possibility of the existence of closed time-like curves around these cosmic strings is analyzed. Furthermore, the stability about the formation of the topological defect discussed here is checked. It is shown that the existence of a suitable choice for the integration constants in which closed time-like curves are not allowed. We also study the (im)possibility of using the obtained spacetime in the rotational curves problem.

Bullying of medical students.

PubMed

Mukhtar, Fatima; Daud, Seema; Manzoor, Iram; Amjad, Ibtesaam; Saeed, Kamran; Naeem, Mehvish; Javed, Mehwish

2010-12-01

To assess the frequency and forms of bullying experienced by medical students, and the associated factors. Cross-sectional questionnaire-based survey. The study was conducted at a private Medical College of Lahore, from January to February 2010. All the students of first and fourth year classes were included in the study with voluntary and anonymous participation. Self administered-questionnaires were given to the students which were completed by them in the presence of the surveyor. A modified version of the British Medical Associations (BMA) medical student's welfare and education survey form was used for data collection. The data was recorded and analyzed using the statistical package for social sciences version 16.0. Data was described in the form of frequencies and percentages. Chi-square test and Fisher exact test were used to test statistical significance between categorical variables at p < 0.05. More than half the students 70 (66%) had experienced some form of bullying in the past 6 months at the Medical College. It was found that 70% (49) of the students who were bullied were females. Sixty-seven percent of students reported experiencing a bullying episode at least once in a month, 26% less than once in a month and 7% at least once in a week. The most common forms were verbal abuse (n=44, 63%) and behavioural gestures i.e. making faces (n=36, 51%), followed by having been ignored or excluded (n=20, 29%). The common perpetrators of all types of bullying were fellow students followed by Professors. Feeling lonely or sad (p=0.024), not having a close friend (p=0.049) and knowledge amongst respondents regarding the availability of support services in their college (p=0.019) were significantly associated with being bullied. Most medical students reported of having been bullied in the last 6 months at the College, with verbal abuse being the commonest form of maltreatment and fellow students followed by Professors being the frequent perpetrators. A history of feeling lonely or sad, not having a close friend and knowledge amongst respondents regarding the availability of support services in their college were significantly associated with these experiences.

Exact short-time height distribution for the flat Kardar-Parisi-Zhang interface

NASA Astrophysics Data System (ADS)

Smith, Naftali R.; Meerson, Baruch

2018-05-01

We determine the exact short-time distribution -lnPf(" close=")H ,t )">H ,t =Sf(H )/√{t } of the one-point height H =h (x =0 ,t ) of an evolving 1 +1 Kardar-Parisi-Zhang (KPZ) interface for flat initial condition. This is achieved by combining (i) the optimal fluctuation method, (ii) a time-reversal symmetry of the KPZ equation in 1 +1 dimension, and (iii) the recently determined exact short-time height distribution -lnPst(H ) of the latter, one encounters two branches: an analytic and a nonanalytic. The analytic branch is nonphysical beyond a critical value of H where a second-order dynamical phase transition occurs. Here we show that, remarkably, it is the analytic branch of Sst(H ) which determines the large-deviation function Sf(H ) of the flat interface via a simple mapping Sf(H )=2-3 /2Sst

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