Vibration and stability of cracked hollow-sectional beams

NASA Astrophysics Data System (ADS)

Zheng, D. Y.; Fan, S. C.

2003-10-01

This paper presents simple tools for the vibration and stability analysis of cracked hollow-sectional beams. It comprises two parts. In the first, the influences of sectional cracks are expressed in terms of flexibility induced. Each crack is assigned with a local flexibility coefficient, which is derived by virtue of theories of fracture mechanics. The flexibility coefficient is a function of the depth of a crack. The general formulae are derived and expressed in integral form. It is then transformed to explicit form through 128-point Gauss quadrature. According to the depth of the crack, the formulae are derived under two scenarios. The first is for shallow cracks, of which the penetration depth is contained within the top solid-sectional region. The second is for deeper penetration, in which the crack goes into the middle hollow-sectional region. The explicit formulae are best-fitted equations generated by the least-squares method. The best-fitted curves are presented. From the curves, the flexibility coefficients can be read out easily, while the explicit expressions facilitate easy implementation in computer analysis. In the second part, the flexibility coefficients are employed in the vibration and stability analysis of hollow-sectional beams. The cracked beam is treated as an assembly of sub-segments linked up by rotational springs. Division of segments are made coincident with the location of cracks or any abrupt change of sectional property. The crack's flexibility coefficient then serves as that of the rotational spring. Application of the Hamilton's principle leads to the governing equations, which are subsequently solved through employment of a simple technique. It is a kind of modified Fourier series, which is able to represent any order of continuity of the vibration/buckling modes. Illustrative numerical examples are included.

Wave energy transfer in elastic half-spaces with soft interlayers.

PubMed

Glushkov, Evgeny; Glushkova, Natalia; Fomenko, Sergey

2015-04-01

The paper deals with guided waves generated by a surface load in a coated elastic half-space. The analysis is based on the explicit integral and asymptotic expressions derived in terms of Green's matrix and given loads for both laminate and functionally graded substrates. To perform the energy analysis, explicit expressions for the time-averaged amount of energy transferred in the time-harmonic wave field by every excited guided or body wave through horizontal planes and lateral cylindrical surfaces have been also derived. The study is focused on the peculiarities of wave energy transmission in substrates with soft interlayers that serve as internal channels for the excited guided waves. The notable features of the source energy partitioning in such media are the domination of a single emerging mode in each consecutive frequency subrange and the appearance of reverse energy fluxes at certain frequencies. These effects as well as modal and spatial distribution of the wave energy coming from the source into the substructure are numerically analyzed and discussed.

Derivation and application of the reciprocity relations for radiative transfer with internal illumination

NASA Technical Reports Server (NTRS)

Cogley, A. C.

1975-01-01

A Green's function formulation is used to derive basic reciprocity relations for planar radiative transfer in a general medium with internal illumination. Reciprocity (or functional symmetry) allows an explicit and generalized development of the equivalence between source and probability functions. Assuming similar symmetry in three-dimensional space, a general relationship is derived between planar-source intensity and point-source total directional energy. These quantities are expressed in terms of standard (universal) functions associated with the planar medium, while all results are derived from the differential equation of radiative transfer.

Transport coefficients for the shear dynamo problem at small Reynolds numbers.

PubMed

Singh, Nishant K; Sridhar, S

2011-05-01

We build on the formulation developed in S. Sridhar and N. K. Singh [J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients α(il) and η(il) are derived. We prove that when the velocity field is nonhelical, the transport coefficient α(il) vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X(3) and time τ; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Rädler, M. Rheinhardt, and P. J. Käpylä [Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor η(il)(τ). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter. © 2011 American Physical Society

Transport coefficients for the shear dynamo problem at small Reynolds numbers

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

Singh, Nishant K.; Joint Astronomy Programme, Indian Institute of Science, Bangalore 560 012; Sridhar, S.

2011-05-15

We build on the formulation developed in S. Sridhar and N. K. Singh [J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients {alpha}{sub il} and {eta}{sub iml} are derived. We prove that when the velocity field is nonhelical, the transport coefficient {alpha}{sub il} vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynoldsmore » number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X{sub 3} and time {tau}; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Raedler, M. Rheinhardt, and P. J. Kaepylae [Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor {eta}{sub ij}({tau}). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.« less

Determination of angle of light deflection in higher-derivative gravity theories

NASA Astrophysics Data System (ADS)

Xu, Chenmei; Yang, Yisong

2018-03-01

Gravitational light deflection is known as one of three classical tests of general relativity and the angle of deflection may be computed explicitly using approximate or exact solutions describing the gravitational force generated from a point mass. In various generalized gravity theories, however, such explicit determination is often impossible due to the difficulty in obtaining an exact expression for the deflection angle. In this work, we present some highly effective globally convergent iterative methods to determine the angle of semiclassical gravitational deflection in higher- and infinite-derivative formalisms of quantum gravity theories. We also establish the universal properties that the deflection angle always stays below the classical Einstein angle and is a strictly decreasing function of the incident photon energy, in these formalisms.

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

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2008-03-01

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

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

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2008-03-21

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

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

NASA Astrophysics Data System (ADS)

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

2003-01-01

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

A Truncated Cauchy Distribution

ERIC Educational Resources Information Center

Nadarajah, Saralees; Kotz, Samuel

2006-01-01

A truncated version of the Cauchy distribution is introduced. Unlike the Cauchy distribution, this possesses finite moments of all orders and could therefore be a better model for certain practical situations. One such situation in finance is discussed. Explicit expressions for the moments of the truncated distribution are also derived.

Pharmacokinetic Steady-States Highlight Interesting Target-Mediated Disposition Properties.

PubMed

Gabrielsson, Johan; Peletier, Lambertus A

2017-05-01

In this paper, we derive explicit expressions for the concentrations of ligand L, target R and ligand-target complex RL at steady state for the classical model describing target-mediated drug disposition, in the presence of a constant-rate infusion of ligand. We demonstrate that graphing the steady-state values of ligand, target and ligand-target complex, we obtain striking and often singular patterns, which yield a great deal of insight and understanding about the underlying processes. Deriving explicit expressions for the dependence of L, R and RL on the infusion rate, and displaying graphs of the relations between L, R and RL, we give qualitative and quantitive information for the experimentalist about the processes involved. Understanding target turnover is pivotal for optimising these processes when target-mediated drug disposition (TMDD) prevails. By a combination of mathematical analysis and simulations, we also show that the evolution of the three concentration profiles towards their respective steady-states can be quite complex, especially for lower infusion rates. We also show how parameter estimates obtained from iv bolus studies can be used to derive steady-state concentrations of ligand, target and complex. The latter may serve as a template for future experimental designs.

Choice of threshold line angle for binary phase-only filters

NASA Astrophysics Data System (ADS)

Vijaya Kumar, Bhagavatula; Hendrix, Charles D.

1993-10-01

The choice of threshold line angle (TLA) is an important issue in designing Binary Phase-Only Filters (BPOFs). In this paper, we derive expressions that explicitly relate the TLA to correlation peak intensity. We also show some examples that illustrate the effect of choosing the wrong TLA.

Nonlinear field equations for aligning self-propelled rods.

PubMed

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

2012-12-28

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

Equivalence of quantum Boltzmann equation and Kubo formula for dc conductivity

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

Su, Z.B.; Chen, L.Y.

1990-02-01

This paper presents a derivation of the quantum Boltzmann equation for linear dc transport with a correction term to Mahan-Hansch's equations and derive a formal solution to it. Based on this formal solution, the authors find the electric conductivity can be expressed as the retarded current-current correlation. Therefore, the authors explicitly demonstrate the equivalence of the two most important theoretical methods: quantum Boltzmann equation and Kubo formula.

Two-photon excitation cross-section in light and intermediate atoms

NASA Technical Reports Server (NTRS)

Omidvar, K.

1980-01-01

The method of explicit summation over the intermediate states is used along with LS coupling to derive an expression for two-photon absorption cross section in light and intermediate atoms in terms of integrals over radial wave functions. Two selection rules, one exact and one approximate, are also derived. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum defect method are used. A relationship between the cross section and the oscillator strengths is derived. Cross sections due to selected transitions in nitrogen, oxygen, and chlorine are given. The expression for the cross section is useful in calculating the two-photon absorption in light and intermediate atoms.

A massive Feynman integral and some reduction relations for Appell functions

NASA Astrophysics Data System (ADS)

Shpot, M. A.

2007-12-01

New explicit expressions are derived for the one-loop two-point Feynman integral with arbitrary external momentum and masses m12 and m22 in D dimensions. The results are given in terms of Appell functions, manifestly symmetric with respect to the masses mi2. Equating our expressions with previously known results in terms of Gauss hypergeometric functions yields reduction relations for the involved Appell functions that are apparently new mathematical results.

Higher-order jump conditions for conservation laws

NASA Astrophysics Data System (ADS)

Oksuzoglu, Hakan

2018-04-01

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

Mathematical Model of Bubble Sloshing Dynamics for Cryogenic Liquid Helium in Orbital Spacecraft Dewar Container

NASA Technical Reports Server (NTRS)

Hung, R. J.; Pan, H. L.

1995-01-01

A generalized mathematical model is investigated of sloshing dynamics for dewar containers, partially filled with a liquid of cryogenic superfluid helium 2, driven by both gravity gradient and jitter accelerations applicable to two types of scientific spacecrafts, which are eligible to carry out spinning motion and/or slew motion to perform scientific observations during normal spacecraft operation. Two examples are given for the Gravity Probe-B (GP-B) with spinning motion, and the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) with slew motion, which are responsible for the sloshing dynamics. Explicit mathematical expressions for the modelling of sloshing dynamics to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics will be based on the noninertial frame spacecraft bound coordinate, and we will solve the time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. Explicit mathematical expressions of boundary conditions lo cover capillary force effects on the liquid-vapor interface in microgravity environments are also derived. Results of the simulations of the mathematical model are illustrated.

Sloshing dynamics on rotating helium dewar tank

NASA Technical Reports Server (NTRS)

Hung, R. J.

1993-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics were based on the non-inertia frame spacecraft bound coordinate, and solve time dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers were derived. Results were widely published in the open journals.

Numerical studies of the surface tension effect of cryogenic liquid helium

NASA Technical Reports Server (NTRS)

Hung, R. J.

1994-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose of performing scientific observation during the normal spacecraft operation is investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics has been based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers, have been derived.

Degree Distribution of Position-Dependent Ball-Passing Networks in Football Games

NASA Astrophysics Data System (ADS)

Narizuka, Takuma; Yamamoto, Ken; Yamazaki, Yoshihiro

2015-08-01

We propose a simple stochastic model describing the position-dependent ball-passing network in football (soccer) games. In this network, a player in a certain area in a divided field is a node, and a pass between two nodes corresponds to an edge. Our stochastic process model is characterized by the consecutive choice of a node depending on its intrinsic fitness. We derive an explicit expression for the degree distribution and find that the derived distribution reproduces that for actual data reasonably well.

Explicit formula for the Holevo bound for two-parameter qubit-state estimation problem

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

Suzuki, Jun, E-mail: junsuzuki@uec.ac.jp

The main contribution of this paper is to derive an explicit expression for the fundamental precision bound, the Holevo bound, for estimating any two-parameter family of qubit mixed-states in terms of quantum versions of Fisher information. The obtained formula depends solely on the symmetric logarithmic derivative (SLD), the right logarithmic derivative (RLD) Fisher information, and a given weight matrix. This result immediately provides necessary and sufficient conditions for the following two important classes of quantum statistical models; the Holevo bound coincides with the SLD Cramér-Rao bound and it does with the RLD Cramér-Rao bound. One of the important results ofmore » this paper is that a general model other than these two special cases exhibits an unexpected property: the structure of the Holevo bound changes smoothly when the weight matrix varies. In particular, it always coincides with the RLD Cramér-Rao bound for a certain choice of the weight matrix. Several examples illustrate these findings.« less

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

NASA Astrophysics Data System (ADS)

Doha, E. H.

2004-01-01

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

Scattering matrices of Lamb waves at irregular surface and void defects.

PubMed

Feng, Feilong; Shen, Jianzhong; Lin, Shuyu

2012-08-01

Time-harmonic solution of Lamb wave scattering in a plane-strain waveguide with irregular thickness is investigated based on stair-step discretization and stepwise mode matching. The transfer relations of the transmission matrices and reflection matrices are derived in both directions of the waveguide. With these, an explicit expression of the scattering matrix is derived. When the scattering region of an inner irregular defect is geometrically divided into several parts composed of sub-waveguides with variable thicknesses and void regions with vertical free edges corresponding to the plate surfaces, the scattering matrix of the whole region could then be derived by modal matching along the artificial boundaries, as explicit functions of all the scattering matrices of the sub-waveguides and reflection matrices of the free edges. The effectiveness of the formulation is examined by numerical examples; the calculated scattering coefficients are in good accordance with those obtained from numerical simulation models. Copyright © 2012 Elsevier B.V. All rights reserved.

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

PubMed

Chevalier, Michael W; El-Samad, Hana

2012-08-28

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

Solutions for the conductivity of multi-coated spheres and spherically symmetric inclusion problems

NASA Astrophysics Data System (ADS)

Pham, Duc Chinh

2018-02-01

Variational results on the macroscopic conductivity (thermal, electrical, etc.) of the multi-coated sphere assemblage have been used to derive the explicit expression of the respective field (thermal, electrical, etc.) within the spheres in d dimensions (d=2,3). A differential substitution approach has been developed to construct various explicit expressions or determining equations for the effective spherically symmetric inclusion problems, which include those with radially variable conductivity, different radially variable transverse and normal conductivities, and those involving imperfect interfaces, in d dimensions. When the volume proportion of the outermost spherical shell increases toward 1, one obtains the respective exact results for the most important specific cases: the dilute solutions for the compound inhomogeneities suspended in a major matrix phase. Those dilute solution results are also needed for other effective medium approximation schemes.

Some Remarks about Semiclassical Trace Invariants and Quantum Normal Forms

NASA Astrophysics Data System (ADS)

Guillemin, Victor; Paul, Thierry

2010-02-01

In this paper we explore the connection between semi-classical and quantum Birkhoff canonical forms (BCF) for Schrödinger operators. In particular we give a “non-symbolic” operator theoretic derivation of the quantum Birkhoff canonical form and provide an explicit recipe for expressing the quantum BCF in terms of the semi-classical BCF.

On the tidal-energy tensor for two homogeneous coaxial ellipsoids

NASA Astrophysics Data System (ADS)

Caimmi, R.; Secco, L.

2001-10-01

The tidal-energy tensor for two homogeneous and coaxial ellipsoids, one lying completely within the other, is investigated in connection with the tidal action exerted by the outer ellipsoid on the inner one. Making reference to the explicit expression found in a previous paper of ours, it is shown that the generic component of the tidal-energy tensor, (i) may be expressed as the product of the corresponding component of the self-energy tensor related to the inner ellipsoid, by the density ratio, and the shape factor ratio, and (ii) equals the one due to any homogeneous, outer ellipsoid, for which the product of the density and a specified shape factor remains unchanged; in particular, the outer ellipsoid may be similar and similarly placed with respect to the inner one. In addition, an explicit expression for the Clausius-virial tensor is derived. Analogous results for the corresponding scalar quantities are also given. Further attention is paid to the particular case of spheroids.

Dimensionless Numbers Expressed in Terms of Common CVD Process Parameters

NASA Technical Reports Server (NTRS)

Kuczmarski, Maria A.

1999-01-01

A variety of dimensionless numbers related to momentum and heat transfer are useful in Chemical Vapor Deposition (CVD) analysis. These numbers are not traditionally calculated by directly using reactor operating parameters, such as temperature and pressure. In this paper, these numbers have been expressed in a form that explicitly shows their dependence upon the carrier gas, reactor geometry, and reactor operation conditions. These expressions were derived for both monatomic and diatomic gases using estimation techniques for viscosity, thermal conductivity, and heat capacity. Values calculated from these expressions compared well to previously published values. These expressions provide a relatively quick method for predicting changes in the flow patterns resulting from changes in the reactor operating conditions.

Chaotic processes using the two-parameter derivative with non-singular and non-local kernel: Basic theory and applications

NASA Astrophysics Data System (ADS)

Doungmo Goufo, Emile Franc

2016-08-01

After having the issues of singularity and locality addressed recently in mathematical modelling, another question regarding the description of natural phenomena was raised: How influent is the second parameter β of the two-parameter Mittag-Leffler function E α , β ( z ) , z ∈ ℂ ? To answer this question, we generalize the newly introduced one-parameter derivative with non-singular and non-local kernel [A. Atangana and I. Koca, Chaos, Solitons Fractals 89, 447 (2016); A. Atangana and D. Bealeanu (e-print)] by developing a similar two-parameter derivative with non-singular and non-local kernel based on Eα,β(z). We exploit the Agarwal/Erdelyi higher transcendental functions together with their Laplace transforms to explicitly establish the Laplace transform's expressions of the two-parameter derivatives, necessary for solving related fractional differential equations. Explicit expression of the associated two-parameter fractional integral is also established. Concrete applications are done on atmospheric convection process by using Lorenz non-linear simple system. Existence result for the model is provided and a numerical scheme established. As expected, solutions exhibit chaotic behaviors for α less than 0.55, and this chaos is not interrupted by the impact of β. Rather, this second parameter seems to indirectly squeeze and rotate the solutions, giving an impression of twisting. The whole graphics seem to have completely changed its orientation to a particular direction. This is a great observation that clearly shows the substantial impact of the second parameter of Eα,β(z), certainly opening new doors to modeling with two-parameter derivatives.

Chaotic processes using the two-parameter derivative with non-singular and non-local kernel: Basic theory and applications.

PubMed

Doungmo Goufo, Emile Franc

2016-08-01

After having the issues of singularity and locality addressed recently in mathematical modelling, another question regarding the description of natural phenomena was raised: How influent is the second parameter β of the two-parameter Mittag-Leffler function Eα,β(z), z∈ℂ? To answer this question, we generalize the newly introduced one-parameter derivative with non-singular and non-local kernel [A. Atangana and I. Koca, Chaos, Solitons Fractals 89, 447 (2016); A. Atangana and D. Bealeanu (e-print)] by developing a similar two-parameter derivative with non-singular and non-local kernel based on Eα , β(z). We exploit the Agarwal/Erdelyi higher transcendental functions together with their Laplace transforms to explicitly establish the Laplace transform's expressions of the two-parameter derivatives, necessary for solving related fractional differential equations. Explicit expression of the associated two-parameter fractional integral is also established. Concrete applications are done on atmospheric convection process by using Lorenz non-linear simple system. Existence result for the model is provided and a numerical scheme established. As expected, solutions exhibit chaotic behaviors for α less than 0.55, and this chaos is not interrupted by the impact of β. Rather, this second parameter seems to indirectly squeeze and rotate the solutions, giving an impression of twisting. The whole graphics seem to have completely changed its orientation to a particular direction. This is a great observation that clearly shows the substantial impact of the second parameter of Eα , β(z), certainly opening new doors to modeling with two-parameter derivatives.

Basic governing equations for the flight regimes of aeroassisted orbital transfer vehicles

NASA Technical Reports Server (NTRS)

Lee, J.-H.

1984-01-01

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are given explicitly. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, is derived by solving the system of master equations accounting for the multiple-level transitions.

Basic Governing Equations for the Flight Regimes of Aeroassisted Orbital Transfer Vehicles

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1985-01-01

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are explicitly given. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, are derived by solving the system of master equations accounting for the multiple-level transitions.

Algorithms for Computing the Magnetic Field, Vector Potential, and Field Derivatives for Circular Current Loops in Cylindrical Coordinates

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

Walstrom, Peter Lowell

A numerical algorithm for computing the field components B r and B z and their r and z derivatives with open boundaries in cylindrical coordinates for circular current loops is described. An algorithm for computing the vector potential is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations (especially for the field derivatives) are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. Since cel can evaluate complete elliptic integrals of a fairlymore » general type, in some cases the elliptic integrals can be evaluated without first reducing them to forms containing standard Legendre forms. The algorithms avoid the numerical difficulties that many of the textbook solutions have for points near the axis because of explicit factors of 1=r or 1=r 2 in the some of the expressions.« less

Large-deviation properties of Brownian motion with dry friction.

PubMed

Chen, Yaming; Just, Wolfram

2014-10-01

We investigate piecewise-linear stochastic models with regard to the probability distribution of functionals of the stochastic processes, a question that occurs frequently in large deviation theory. The functionals that we are looking into in detail are related to the time a stochastic process spends at a phase space point or in a phase space region, as well as to the motion with inertia. For a Langevin equation with discontinuous drift, we extend the so-called backward Fokker-Planck technique for non-negative support functionals to arbitrary support functionals, to derive explicit expressions for the moments of the functional. Explicit solutions for the moments and for the distribution of the so-called local time, the occupation time, and the displacement are derived for the Brownian motion with dry friction, including quantitative measures to characterize deviation from Gaussian behavior in the asymptotic long time limit.

Exact sum rules for inhomogeneous drums

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

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

2013-09-15

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

Higher-order formulas of amplitude-dependent tune shift caused by a sextupole magnetic field distribution

NASA Astrophysics Data System (ADS)

Soutome, Kouichi; Tanaka, Hitoshi

2017-06-01

Nowadays, designs for ring-based light sources use multibend lattices for achieving a very small emittance of around 100 pmrad. In this type of storage ring, the chromaticity correcting sextupoles generally have greater strengths than those used in typical third-generation light sources. Therefore, controlling lattice nonlinearity such as amplitude-dependent tune shift (ADTS) is important for enabling stable operations and smooth beam commissioning. As the strength of the sextupoles increases, their higher-order terms contribute significantly to ADTS, rendering well-known lowest-order formulas inadequate for describing tune variations at large horizontal amplitudes. In response, we have derived explicit expressions of ADTS up to the fourth order in sextupole strength based on the canonical perturbation theory, assuming that the amplitude of a vertical betatron oscillation is smaller compared with the horizontal one. The new formulas express the horizontal and vertical betatron tune variations as functions of the action variables: Jx and Jy up to O (Jx2) and O (Jy) . The derived formulas were applied to a five-bend achromat lattice designed for the SPring-8 upgrade. By comparing the calculated results with the tracking simulations, we found that (1) the formulas accurately express ADTS around a horizontal amplitude of ˜10 mm and (2) the nonlinear terms of the fourth order in sextupole strength govern the behaviors of circulating electrons at large horizontal amplitudes. In this paper, we present explicit expressions of fourth-order formulas of ADTS and provide some examples to illustrate their effectiveness.

Thickness-shear mode quartz crystal resonators in viscoelastic fluid media

NASA Astrophysics Data System (ADS)

Arnau, A.; Jiménez, Y.; Sogorb, T.

2000-10-01

An extended Butterworth-Van Dyke (EBVD) model to characterize a thickness-shear mode quartz crystal resonator in a semi-infinite viscoelastic medium is derived by means of analysis of the lumped elements model described by Cernosek et al. [R. W. Cernosek, S. J. Martin, A. R. Hillman, and H. L. Bandey, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 1399 (1998)]. The EBVD model parameters are related to the viscoelastic properties of the medium. A capacitance added to the motional branch of the EBVD model has to be included when the elastic properties of the fluid are considered. From this model, an explicit expression for the frequency shift of a quartz crystal sensor in viscoelastic media is obtained. By combining the expressions for shifts in the motional series resonant frequency and in the motional resistance, a simple equation that relates only one unknown (the loss factor of the fluid) to those measurable quantities, and two simple explicit expressions for determining the viscoelastic properties of semi-infinite fluid media have been derived. The proposed expression for the parameter Δf/ΔR is compared with the corresponding ratio obtained with data computed from the complete admittance model. Relative errors below 4.5%, 3%, and 1.2% (for the ratios of the load surface mechanical impedance to the quartz shear characteristic impedance of 0.3, 0.25, and 0.1, respectively), are obtained in the range of the cases analyzed. Experimental data from the literature are used to validate the model.

Unbiased nonorthogonal bases for tomographic reconstruction

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

Sainz, Isabel; Klimov, Andrei B.; Roa, Luis

2010-05-15

We have developed a general method for constructing a set of nonorthogonal bases with equal separations between all different basis states in prime dimensions. The results are that the corresponding biorthogonal counterparts are pairwise unbiased with the components of the original bases. Using these bases, we derive an explicit expression for the optimal tomography in nonorthogonal bases. A special two-dimensional case is analyzed separately.

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

NASA Astrophysics Data System (ADS)

Monrolin, Nicolas; Praud, Olivier; Plouraboué, Franck

2018-06-01

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

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

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

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

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

An alternative model for a partially coherent elliptical dark hollow beam

NASA Astrophysics Data System (ADS)

Li, Xu; Wang, Fei; Cai, Yangjian

2011-04-01

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

Conditionally Teleported States Using Optical Squeezers and Photon Counting

NASA Astrophysics Data System (ADS)

Fan, Hong-Yi; Fan, Yue; Cheng, Hai-Ling

2002-04-01

By virtue of the neat expression of the two-mode squeezing operator in the Einstein, Podolsky and Rosen entangled state representation, we provide a new approach for discussing the teleportation scheme using optical squeezers and photon counting devices. We derive the explicit form of the teleported states, so that the conditional property of teleportation and teleportation fidelity of this protocol can be seen more clearly. The derivation is concise. The project supported by the President Foundation of the Chinese Academy of Sciences and National Natural Science Foundation of China

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

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

NASA Technical Reports Server (NTRS)

Blumenthal, George R.; Johnston, Kathryn V.

1994-01-01

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

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

NASA Astrophysics Data System (ADS)

Zhou, Bing; Greenhalgh, S. A.

2011-10-01

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

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

NASA Astrophysics Data System (ADS)

Bastianello, Alvise; Piroli, Lorenzo; Calabrese, Pasquale

2018-05-01

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

Active motion on curved surfaces

NASA Astrophysics Data System (ADS)

Castro-Villarreal, Pavel; Sevilla, Francisco J.

2018-05-01

A theoretical analysis of active motion on curved surfaces is presented in terms of a generalization of the telegrapher equation. Such a generalized equation is explicitly derived as the polar approximation of the hierarchy of equations obtained from the corresponding Fokker-Planck equation of active particles diffusing on curved surfaces. The general solution to the generalized telegrapher equation is given for a pulse with vanishing current as initial data. Expressions for the probability density and the mean squared geodesic displacement are given in the limit of weak curvature. As an explicit example of the formulated theory, the case of active motion on the sphere is presented, where oscillations observed in the mean squared geodesic displacement are explained.

The Darboux transformation of the derivative nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Xu, Shuwei; He, Jingsong; Wang, Lihong

2011-07-01

The n-fold Darboux transformation (DT) is a 2 × 2 matrix for the Kaup-Newell (KN) system. In this paper, each element of this matrix is expressed by a ratio of the (n + 1) × (n + 1) determinant and n × n determinant of eigenfunctions. Using these formulae, the expressions of the q[n] and r[n] in the KN system are generated by the n-fold DT. Further, under the reduction condition, the rogue wave, rational traveling solution, dark soliton, bright soliton, breather solution and periodic solution of the derivative nonlinear Schrödinger equation are given explicitly by different seed solutions. In particular, the rogue wave and rational traveling solution are two kinds of new solutions. The complete classification of these solutions generated by one-fold DT is given.

Efficient scheme for parametric fitting of data in arbitrary dimensions.

PubMed

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

2008-07-01

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

Criticality and Connectivity in Macromolecular Charge Complexation

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

Qin, Jian; de Pablo, Juan J.

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

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

NASA Technical Reports Server (NTRS)

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

2001-01-01

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

The high-frequency dispersion coefficient for the Rayleigh velocity in a vertically inhomogeneous anisotropic half-space.

PubMed

Shuvalov, A L

2008-05-01

For an arbitrary anisotropic half-space with continuous vertical variation of material properties, an explicit closed-form expression for the coefficient B of high-frequency dispersion of the Rayleigh velocity v(R)(omega) approximately v(R)(0)(1+B/omega) is derived. The result involves two matrices, one consisting of the surface-traction derivatives in velocity and the other of its Wentzel-Kramers-Brillouin coefficients, which are contracted with an amplitude vector of the Rayleigh wave in the reference homogeneous half-space. The "ingredients" are routinely defined through the fundamental elasticity matrix and its first derivative, both taken at v=v(R)(0) and referred to the surface.

Lagrange thermodynamic potential and intrinsic variables for He-3 He-4 dilute solutions

NASA Technical Reports Server (NTRS)

Jackson, H. W.

1983-01-01

For a two-fluid model of dilute solutions of He-3 in liquid He-4, a thermodynamic potential is constructed that provides a Lagrangian for deriving equations of motion by a variational procedure. This Lagrangian is defined for uniform velocity fields as a (negative) Legendre transform of total internal energy, and its primary independent variables, together with their thermodynamic conjugates, are identified. Here, similarities between relations in classical physics and quantum statistical mechanics serve as a guide for developing an alternate expression for this function that reveals its character as the difference between apparent kinetic energy and intrinsic internal energy. When the He-3 concentration in the mixtures tends to zero, this expression reduces to Zilsel's formula for the Lagrangian for pure liquid He-4. An investigation of properties of the intrinsic internal energy leads to the introduction of intrinsic chemical potentials along with other intrinsic variables for the mixtures. Explicit formulas for these variables are derived for a noninteracting elementary excitation model of the fluid. Using these formulas and others also derived from quantum statistical mechanics, another equivalent expression for the Lagrangian is generated.

Superfluid helium sloshing dynamics induced oscillations and fluctuations of angular momentum, force and moment actuated on spacecraft driven by gravity gradient or jitter acceleration associated with slew motion

NASA Technical Reports Server (NTRS)

Hung, R. J.

1994-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by the gravity gradient and jitter accelerations associated with slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) for slew motion which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid-vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers have also been derived. Examples are also given for cases applicable to the AXAF-S spacecraft sloshing dynamics associated with slew motion.

Generalized Freud's equation and level densities with polynomial potential

NASA Astrophysics Data System (ADS)

Boobna, Akshat; Ghosh, Saugata

2013-08-01

We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.

Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

NASA Astrophysics Data System (ADS)

Bertini, L.; de Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C.

2002-05-01

We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager-Machlup theory in the SNS; a general Hamilton-Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton-Jacobi equation, we obtain a logically independent derivation of this result.

Conformally Invariant Powers of the Laplacian, Q-Curvature, and Tractor Calculus

NASA Astrophysics Data System (ADS)

Gover, A. Rod; Peterson, Lawrence J.

We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian. Conformal tractor calculus is the natural induced bundle calculus associated to the conformal Cartan connection. Applications discussed include standard formulae for these operators in terms of the Levi-Civita connection and its curvature and a direct definition and formula for T. Branson's so-called Q-curvature (which integrates to a global conformal invariant) as well as generalisations of the operators and the Q-curvature. Among examples, the operators of order 4, 6 and 8 and the related Q-curvatures are treated explicitly. The algorithm exploits the ambient metric construction of Fefferman and Graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions. This is partly based on [12], where the relationship of the normal standard tractor bundle to the ambient construction is described.

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

Explicit robust schemes for implementation of a class of principal value-based constitutive models: Theoretical development

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Arnold, S. M.

1991-01-01

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, explicit forms for the corresponding material tangent stiffness tensors are developed, and these are valid for the entire deformation range; i.e., with both distinct as well as repeated principal-stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain-energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials. The forms derived are also amenable for use with symbolic-manipulation packages for systematic code generation.

Exact sum rules for inhomogeneous systems containing a zero mode

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

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

2014-10-15

We show that the formulas for the sum rules for the eigenvalues of inhomogeneous systems that we have obtained in two recent papers are incomplete when the system contains a zero mode. We prove that there are finite contributions of the zero mode to the sum rules and we explicitly calculate the expressions for the sum rules of order one and two. The previous results for systems that do not contain a zero mode are unaffected. - Highlights: • We discuss the sum rules of the eigenvalues of inhomogeneous systems containing a zero mode. • We derive the explicit expressionsmore » for sum rules of order one and two. • We perform accurate numerical tests of these results for three examples.« less

The usefulness of Poynting's theorem in magnetic turbulence

NASA Astrophysics Data System (ADS)

Treumann, Rudolf A.; Baumjohann, Wolfgang

2017-12-01

We rewrite Poynting's theorem, already used in a previous publication Treumann and Baumjohann (2017a) to derive relations between the turbulent magnetic and electric power spectral densities, to make explicit where the mechanical contributions enter. We then make explicit use of the relativistic transformation of the turbulent electric fluctuations to obtain expressions which depend only on the magnetic and velocity fluctuations. Any electric fluctuations play just an intermediate role. Equations are constructed for the turbulent conductivity spectrum in Alfvénic and non-Alfvénic turbulence in extension of the results in the above citation. An observation-based discussion of their use in application to solar wind turbulence is given. The inertial range solar wind turbulence exhibits signs of chaos and self-organization.

Gyrokinetic theory for particle and energy transport in fusion plasmas

NASA Astrophysics Data System (ADS)

Falessi, Matteo Valerio; Zonca, Fulvio

2018-03-01

A set of equations is derived describing the macroscopic transport of particles and energy in a thermonuclear plasma on the energy confinement time. The equations thus derived allow studying collisional and turbulent transport self-consistently, retaining the effect of magnetic field geometry without postulating any scale separation between the reference state and fluctuations. Previously, assuming scale separation, transport equations have been derived from kinetic equations by means of multiple-scale perturbation analysis and spatio-temporal averaging. In this work, the evolution equations for the moments of the distribution function are obtained following the standard approach; meanwhile, gyrokinetic theory has been used to explicitly express the fluctuation induced fluxes. In this way, equations for the transport of particles and energy up to the transport time scale can be derived using standard first order gyrokinetics.

Single-Particle Quantum Dynamics in a Magnetic Lattice

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

Venturini, Marco

2001-02-01

We study the quantum dynamics of a spinless charged-particle propagating through a magnetic lattice in a transport line or storage ring. Starting from the Klein-Gordon equation and by applying the paraxial approximation, we derive a Schroedinger-like equation for the betatron motion. A suitable unitary transformation reduces the problem to that of a simple harmonic oscillator. As a result we are able to find an explicit expression for the particle wavefunction.

Fluctuation theorem for entropy production during effusion of an ideal gas with momentum transfer.

PubMed

Wood, Kevin; Van den Broeck, C; Kawai, R; Lindenberg, Katja

2007-06-01

We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Cleuren [Phys. Rev. E 74, 021117 (2006)], we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.

Gluons and gravitons at one loop from ambitwistor strings

NASA Astrophysics Data System (ADS)

Geyer, Yvonne; Monteiro, Ricardo

2018-03-01

We present new and explicit formulae for the one-loop integrands of scattering amplitudes in non-supersymmetric gauge theory and gravity, valid for any number of particles. The results exhibit the colour-kinematics duality in gauge theory and the double-copy relation to gravity, in a form that was recently observed in supersymmetric theories. The new formulae are expressed in a particular representation of the loop integrand, with only one quadratic propagator, which arises naturally from the framework of the loop-level scattering equations. The starting point in our work are the expressions based on the scattering equations that were recently derived from ambitwistor string theory. We turn these expressions into explicit formulae depending only on the loop momentum, the external momenta and the external polarisations. These formulae are valid in any number of spacetime dimensions for pure Yang-Mills theory (gluon) and its natural double copy, NS-NS gravity (graviton, dilaton, B-field), and we also present formulae in four spacetime dimensions for pure gravity (graviton). We perform several tests of our results, such as checking gauge invariance and directly matching our four-particle formulae to previously known expressions. While these tests would be elaborate in a Feynman-type representation of the loop integrand, they become straightforward in the representation we use.

Discrete ordinates solutions of nongray radiative transfer with diffusely reflecting walls

NASA Technical Reports Server (NTRS)

Menart, J. A.; Lee, Haeok S.; Kim, Tae-Kuk

1993-01-01

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

Prolongation structures of nonlinear evolution equations. II

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1976-01-01

The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear Schroedinger equation. The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is open - i.e., does not terminate as a set of structure relations of a finite-dimensional Lie group. We introduce the use of multiple pseudopotentials to generate multiple Baecklund transformation, and derive the double Baecklund transformation. This symmetric transformation concisely expresses the (usually conjectured) theorem of permutability, which must consequently apply to all solutions irrespective of asymptotic constraints.

Thermodynamics and Phase Transition from Regular Bardeen Black Hole Surrounded by Quintessence

NASA Astrophysics Data System (ADS)

Saleh, Mahamat; Thomas, Bouetou Bouetou; Kofane, Timoleon Crepin

2018-05-01

In this paper, thermodynamics and phase transition are investigated for the regular Bardeen black hole surrounded by quintessence. Considering the metric of the Bardeen spacetime surrounded by quintessence, we derived the Unruh-Verlinde temperature. Using the first law of thermodynamics, we derived the expressions of the Hawking temperature as well as the specific heat for the black hole. Explicitly, their behaviors were plotted. It results that the magnetic monopole charge β as well as the presence of quintessence decrease the temperature and induce a thermodynamics phase transition in the spacetime. Moreover, when increasing the density of quintessence, the transition point moves to lower entropies.

Covariance Bell inequalities

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

PubMed

Sels, Dries; Brosens, Fons

2013-10-01

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

Expressions for tidal conversion at seafloor topography using physical space integrals

NASA Astrophysics Data System (ADS)

Schorghofer, Norbert

2010-12-01

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

New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

PubMed Central

Abd-Elhameed, W. M.

2014-01-01

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. PMID:25386599

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

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

Moutarde, H.

2015-04-10

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

A general mass term for bigravity

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

Cusin, Giulia; Durrer, Ruth; Guarato, Pietro

2016-04-01

We introduce a new formalism to study perturbations of Hassan-Rosen bigravity theory, around general backgrounds for the two dynamical metrics. In particular, we derive the general expression for the mass term of the perturbations and we explicitly compute it for cosmological settings. We study tensor perturbations in a specific branch of bigravity using this formalism. We show that the tensor sector is affected by a late-time instability, which sets in when the mass matrix is no longer positive definite.

On the effect of the degeneracy among dark energy parameters

NASA Astrophysics Data System (ADS)

Gong, Yungui; Gao, Qing

2014-01-01

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

Semi-classical approach to transitionless quantum driving: Explicitness and Locality

NASA Astrophysics Data System (ADS)

Loewe, Benjamin; Hipolito, Rafael; Goldbart, Paul M.

Berry has shown that, via a reverse engineering strategy, non-adiabatic transitions in time-dependent quantum systems can be stifled through the introduction of a specific auxiliary hamiltonian. This hamiltonian comes, however, expressed as a formal sum of outer products of the original instantaneous eigenstates and their time-derivatives. Generically, how to create such an operator in the laboratory is thus not evident. Furthermore, the operator may be non- local. By following a semi-classical approach, we obtain a recipe that yields the auxiliary hamiltonian explicitly in terms of the fundamental operators of the system (e.g., position and momentum). By using this formalism, we are able to ascertain criteria for the locality of the auxiliary hamiltonian, and also to determine its exact form in certain special cases.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Korte, John J.

1991-01-01

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required for the upwind PNS code are approximately equal to an explicit PNS MacCormack's code and existing implicit PNS solvers.

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

PubMed

Bashir, Ali; Bansal, Vikas; Bafna, Vineet

2010-06-18

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

Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.

PubMed

Guérin, T; Dean, D S

2015-12-01

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

Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms

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

Pederson, Mark R., E-mail: mark.pederson@science.doe.gov

2015-02-14

A recent modification of the Perdew-Zunger self-interaction-correction to the density-functional formalism has provided a framework for explicitly restoring unitary invariance to the expression for the total energy. The formalism depends upon construction of Löwdin orthonormalized Fermi-orbitals which parametrically depend on variational quasi-classical electronic positions. Derivatives of these quasi-classical electronic positions, required for efficient minimization of the self-interaction corrected energy, are derived and tested, here, on atoms. Total energies and ionization energies in closed-shell singlet atoms, where correlation is less important, using the Perdew-Wang 1992 Local Density Approximation (PW92) functional, are in good agreement with experiment and non-relativistic quantum-Monte-Carlo results albeitmore » slightly too low.« less

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

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

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism.more » Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.« less

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

DOE PAGES

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; ...

2017-07-03

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism.more » Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.« less

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

NASA Astrophysics Data System (ADS)

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

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Intrinsic operators for the electromagnetic nuclear current

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

J. Adam, Jr.; H. Arenhovel

1996-09-01

The intrinsic electromagnetic nuclear meson exchange charge and current operators arising from a separation of the center-of-mass motion are derived for a one-boson-exchange model for the nuclear interaction with scalar, pseudoscalar and vector meson exchange including leading order relativistic terms. Explicit expressions for the meson exchange operators corresponding to the different meson types are given in detail for a two-nucleon system. These intrinsic operators are to be evaluated between intrinsic wave functions in their center-of-mass frame.

Angularly symmetric splitting of a light beam upon reflection and refraction at an air-dielectric plane boundary: reply.

PubMed

Azzam, R M A

2016-05-01

The simplified explicit expressions derived by Andersen [J. Opt. Soc. Am. A33, 984 (2016)JOAOD60740-323210.1364/JOSAA.32.000984], that relate to angularly symmetric beam splitting by reflection and refraction at an air-dielectric interface recently described by Azzam [J. Opt. Soc. Am. A32, 2436 (2015)JOAOD60740-323210.1364/JOSAA.32.002436], are welcome. A few additional remarks are also included in my reply to Andersen's comment.

Gas evolution from spheres

NASA Astrophysics Data System (ADS)

Longhurst, G. R.

1991-04-01

Gas evolution from spherical solids or liquids where no convective processes are active is analyzed. Three problem classes are considered: (1) constant concentration boundary, (2) Henry's law (first order) boundary, and (3) Sieverts' law (second order) boundary. General expressions are derived for dimensionless times and transport parameters appropriate to each of the classes considered. However, in the second order case, the non-linearities of the problem require the presence of explicit dimensional variables in the solution. Sample problems are solved to illustrate the method.

Soret motion in non-ionic binary molecular mixtures

NASA Astrophysics Data System (ADS)

Leroyer, Yves; Würger, Alois

2011-08-01

We study the Soret coefficient of binary molecular mixtures with dispersion forces. Relying on standard transport theory for liquids, we derive explicit expressions for the thermophoretic mobility and the Soret coefficient. Their sign depends on composition, the size ratio of the two species, and the ratio of Hamaker constants. Our results account for several features observed in experiment, such as a linear variation with the composition; they confirm the general rule that small molecules migrate to the warm, and large ones to the cold.

A new dipole-free sum-over-states expression for the second hyperpolarizability

NASA Astrophysics Data System (ADS)

Pérez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.

2008-02-01

The generalized Thomas-Kuhn sum rules are used to eliminate the explicit dependence on dipolar terms in the traditional sum-over-states (SOS) expression for the second hyperpolarizability to derive a new, yet equivalent, SOS expression. This new dipole-free expression may be better suited to study the second hyperpolarizability of nondipolar systems such as quadrupolar, octupolar, and dodecapolar structures. The two expressions lead to the same fundamental limits of the off-resonance second hyperpolarizability; and when applied to a particle in a box and a clipped harmonic oscillator, have the same frequency dependence. We propose that the new dipole-free equation, when used in conjunction with the standard SOS expression, can be used to develop a three-state model of the dispersion of the third-order susceptibility that can be applied to molecules in cases where normally many more states would have been required. Furthermore, a comparison between the two expressions can be used as a convergence test of molecular orbital calculations when applied to the second hyperpolarizability.

Wigner molecules: natural orbitals of strongly correlated two-electron harmonium.

PubMed

Cioslowski, Jerzy; Buchowiecki, Marcin

2006-08-14

Explicit asymptotic expressions for natural orbitals and their occupancies are derived for the harmonium atom at the strong-correlation limit at which the confinement strength omega tends to zero. Unlike in systems with moderate correlation effects, the occupancies at the omega-->0 limit (derived from occupation amplitudes with alternating sign patterns) are vanishingly small and asymptotically independent of the angular momentum, forming a geometric progression with the scale factor proportional to omega(1/3) and the common ratio of ca. 0.0186. The radial components of the natural orbitals are given by products of polynomials and Gaussian functions that, as expected, peak at approximately half of the equilibrium interelectron distance.

Synchronization error estimation and controller design for delayed Lur'e systems with parameter mismatches.

PubMed

He, Wangli; Qian, Feng; Han, Qing-Long; Cao, Jinde

2012-10-01

This paper investigates the problem of master-slave synchronization of two delayed Lur'e systems in the presence of parameter mismatches. First, by analyzing the corresponding synchronization error system, synchronization with an error level, which is referred to as quasi-synchronization, is established. Some delay-dependent quasi-synchronization criteria are derived. An estimation of the synchronization error bound is given, and an explicit expression of error levels is obtained. Second, sufficient conditions on the existence of feedback controllers under a predetermined error level are provided. The controller gains are obtained by solving a set of linear matrix inequalities. Finally, a delayed Chua's circuit is chosen to illustrate the effectiveness of the derived results.

The neutrino–neutrino interaction effects in supernovae: The point of view from the ‘matter’ basis

DOE PAGES

Galais, Sebastien; Kneller, James; Volpe, Cristina

2012-01-19

We consider the Hamiltonian for neutrino oscillations in matter in the case of arbitrary potentials including off-diagonal complex terms. We derive the expressions for the corresponding Hamiltonian in the basis of the instantaneous eigenstates in matter, in terms of quantities one can derive from the flavor-basis Hamiltonian and its derivative, for an arbitrary number of neutrino flavors. We make our expressions explicit for the two-neutrino flavor case and apply our results to the neutrino propagation in core-collapse supernovae where the Hamiltonian includes both coupling to matter and to neutrinos. We show that the neutrino flavor evolution depends on the mixingmore » matrix derivatives involving not only the derivative of the matter mixing angles but also of the phases. In particular, we point out the important role of the phase derivatives, that appear due to the neutrino-neutrino interaction, and show how it can cause an oscillating degeneracy between the diagonal elements of the Hamiltonian in the basis of the eigenstates in matter. Lastly, our results also reveal that the end of the synchronization regime is due to a rapid increase of the phase derivative and identify the condition to be fulfilled for the onset of bipolar oscillations involving both the off-diagonal neutrino-neutrino interaction contributions and the vacuum terms.« less

Alternative derivation of an exchange-only density-functional optimized effective potential

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

Joubert, D. P.

2007-10-15

An alternative derivation of the exchange-only density-functional optimized effective potential equation is given. It is shown that the localized Hartree-Fock-common energy denominator Green's function approximation (LHF-CEDA) for the density-functional exchange potential proposed independently by Della Sala and Goerling [J. Chem. Phys. 115, 5718 (2001)] and Gritsenko and Baerends [Phys. Rev. A 64, 42506 (2001)] can be derived as an approximation to the OEP exchange potential in a similar way that the KLI approximation [Phys. Rev. A 45, 5453 (1992)] was derived. An exact expression for the correction term to the LHF-CEDA approximation can thus be found. The correction term canmore » be expressed in terms of the first-order perturbation-theory many-electron wave function shift when the Kohn-Sham Hamiltonian is subjected to a perturbation equal to the difference between the density-functional exchange potential and the Hartree-Fock nonlocal potential, expressed in terms of the Kohn-Sham orbitals. An explicit calculation shows that the density weighted mean of the correction term is zero, confirming that the LHF-CEDA approximation can be interpreted as a mean-field approximation. The corrected LHF-CEDA equation and the optimized effective potential equation are shown to be identical, with information distributed differently between terms in the equations. For a finite system the correction term falls off at least as fast as 1/r{sup 4} for large r.« less

Alternative derivation of an exchange-only density-functional optimized effective potential

NASA Astrophysics Data System (ADS)

Joubert, D. P.

2007-10-01

An alternative derivation of the exchange-only density-functional optimized effective potential equation is given. It is shown that the localized Hartree-Fock common energy denominator Green’s function approximation (LHF-CEDA) for the density-functional exchange potential proposed independently by Della Sala and Görling [J. Chem. Phys. 115, 5718 (2001)] and Gritsenko and Baerends [Phys. Rev. A 64, 42506 (2001)] can be derived as an approximation to the OEP exchange potential in a similar way that the KLI approximation [Phys. Rev. A 45, 5453 (1992)] was derived. An exact expression for the correction term to the LHF-CEDA approximation can thus be found. The correction term can be expressed in terms of the first-order perturbation-theory many-electron wave function shift when the Kohn-Sham Hamiltonian is subjected to a perturbation equal to the difference between the density-functional exchange potential and the Hartree-Fock nonlocal potential, expressed in terms of the Kohn-Sham orbitals. An explicit calculation shows that the density weighted mean of the correction term is zero, confirming that the LHF-CEDA approximation can be interpreted as a mean-field approximation. The corrected LHF-CEDA equation and the optimized effective potential equation are shown to be identical, with information distributed differently between terms in the equations. For a finite system the correction term falls off at least as fast as 1/r4 for large r .

Gurtin-Murdoch surface elasticity theory revisit: An orbital-free density functional theory perspective

NASA Astrophysics Data System (ADS)

Zhu, Yichao; Wei, Yihai; Guo, Xu

2017-12-01

In the present paper, the well-established Gurtin-Murdoch theory of surface elasticity (Gurtin and Murdoch, 1975, 1978) is revisited from an orbital-free density functional theory (OFDFT) perspective by taking the boundary layer into consideration. Our analysis indicates that firstly, the quantities introduced in the Gurtin-Murdoch theory of surface elasticity can all find their explicit expressions in the derived OFDFT-based theoretical model. Secondly, the derived expression for surface energy density captures a competition between the surface normal derivatives of the electron density and the electrostatic potential, which well rationalises the onset of signed elastic constants that are observed both experimentally and computationally. Thirdly, the established model naturally yields an inversely linear relationship between the materials surface stiffness and its size, which conforms to relevant findings in literature. Since the proposed OFDFT-based model is established under arbitrarily imposed boundary condition of electron density, electrostatic potential and external load, it also has the potential of being used to investigate the electro-mechanical behaviour of nanoscale materials manifesting surface effect.

Two-dimensional dispersion of magnetostatic volume spin waves

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Application of unsteady airfoil theory to rotary wings

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.; Kvaternik, R. G.

1981-01-01

A clarification is presented on recent work concerning the application of unsteady airfoil theory to rotary wings. The application of this theory may be seen as consisting of four steps: (1) the selection of an appropriate unsteady airfoil theory; (2) the resolution of that velocity which is the resultant of aerodynamic and dynamic velocities at a point on the elastic axis into radial, tangential and perpendicular components, and the angular velocity of a blade section about the deformed axis; (3) the expression of lift and pitching moments in terms of the three components; and (4) the derivation of explicit expressions for the components in terms of flight velocity, induced flow, rotor rotational speed, blade motion variables, etc.

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

Silin, D.; Goloshubin, G.

Analysis of compression wave propagation in a poroelastic medium predicts a peak of reflection from a high-permeability layer in the low-frequency end of the spectrum. An explicit formula expresses the resonant frequency through the elastic moduli of the solid skeleton, the permeability of the reservoir rock, the fluid viscosity and compressibility, and the reservoir thickness. This result is obtained through a low-frequency asymptotic analysis of Biot's model of poroelasticity. A review of the derivation of the main equations from the Hooke's law, momentum and mass balance equations, and Darcy's law suggests an alternative new physical interpretation of some coefficients ofmore » the classical poroelasticity. The velocity of wave propagation, the attenuation factor, and the wave number, are expressed in the form of power series with respect to a small dimensionless parameter. The absolute value of this parameter is equal to the product of the kinematic reservoir fluid mobility and the wave frequency. Retaining only the leading terms of the series leads to explicit and relatively simple expressions for the reflection and transmission coefficients for a planar wave crossing an interface between two permeable media, as well as wave reflection from a thin highly-permeable layer (a lens). Practical applications of the obtained asymptotic formulae are seismic modeling, inversion, and at-tribute analysis.« less

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

NASA Astrophysics Data System (ADS)

Izvekov, Sergei

2017-03-01

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

Dynamic imaging model and parameter optimization for a star tracker.

PubMed

Yan, Jinyun; Jiang, Jie; Zhang, Guangjun

2016-03-21

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

Fully Anisotropic Rotational Diffusion Tensor from Molecular Dynamics Simulations.

PubMed

Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

2018-05-31

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

A virtual-system coupled multicanonical molecular dynamics simulation: Principles and applications to free-energy landscape of protein-protein interaction with an all-atom model in explicit solvent

NASA Astrophysics Data System (ADS)

Higo, Junichi; Umezawa, Koji; Nakamura, Haruki

2013-05-01

We propose a novel generalized ensemble method, a virtual-system coupled multicanonical molecular dynamics (V-McMD), to enhance conformational sampling of biomolecules expressed by an all-atom model in an explicit solvent. In this method, a virtual system, of which physical quantities can be set arbitrarily, is coupled with the biomolecular system, which is the target to be studied. This method was applied to a system of an Endothelin-1 derivative, KR-CSH-ET1, known to form an antisymmetric homodimer at room temperature. V-McMD was performed starting from a configuration in which two KR-CSH-ET1 molecules were mutually distant in an explicit solvent. The lowest free-energy state (the most thermally stable state) at room temperature coincides with the experimentally determined native complex structure. This state was separated to other non-native minor clusters by a free-energy barrier, although the barrier disappeared with elevated temperature. V-McMD produced a canonical ensemble faster than a conventional McMD method.

The Anomalous Accretion Disk of the Cataclysmic Variable RW Sextantis

NASA Astrophysics Data System (ADS)

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

2011-01-01

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

The network level reproduction number for infectious diseases with both vertical and horizontal transmission.

PubMed

Xue, Ling; Scoglio, Caterina

2013-05-01

A wide range of infectious diseases are both vertically and horizontally transmitted. Such diseases are spatially transmitted via multiple species in heterogeneous environments, typically described by complex meta-population models. The reproduction number, R0, is a critical metric predicting whether the disease can invade the meta-population system. This paper presents the reproduction number for a generic disease vertically and horizontally transmitted among multiple species in heterogeneous networks, where nodes are locations, and links reflect outgoing or incoming movement flows. The metapopulation model for vertically and horizontally transmitted diseases is gradually formulated from two species, two-node network models. We derived an explicit expression of R0, which is the spectral radius of a matrix reduced in size with respect to the original next generation matrix. The reproduction number is shown to be a function of vertical and horizontal transmission parameters, and the lower bound is the reproduction number for horizontal transmission. As an application, the reproduction number and its bounds for the Rift Valley fever zoonosis, where livestock, mosquitoes, and humans are the involved species are derived. By computing the reproduction number for different scenarios through numerical simulations, we found the reproduction number is affected by livestock movement rates only when parameters are heterogeneous across nodes. To summarize, our study contributes the reproduction number for vertically and horizontally transmitted diseases in heterogeneous networks. This explicit expression is easily adaptable to specific infectious diseases, affording insights into disease evolution. Copyright © 2013 Elsevier Inc. All rights reserved.

On the derivation of the semiclassical approximation to the quantum propagator

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

Fischer, Stefan G., E-mail: stefan.fischer@physik.uni-freiburg.de; Buchleitner, Andreas

2015-07-15

In order to rigorously derive the amplitude factor of the semiclassical approximation to the quantum propagator, we extend an existing method originally devised to evaluate Gaussian path-integral expressions. Using a result which relates the determinant of symmetric block-tridiagonal matrices to the determinants of their blocks, two difference equations are obtained. The first one allows to establish the connection of the amplitude factor to Jacobi’s accessory equations in the continuous-time limit, while the second one leads to an additional factor which, however, contributes to the final result only in exceptional cases. In order to demonstrate the wide applicability of these differencemore » equations, we treat explicitly the case where the time-sliced Lagrangian is written in generalized coordinates, for which a general derivation has so far been unavailable.« less

On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity

NASA Astrophysics Data System (ADS)

Vallée, Claude; Fortuné, Danielle; Lerintiu, Camelia

2008-11-01

Elastic materials are governed by a constitutive law relating the second Piola-Kirchhoff stress tensor Σ and the right Cauchy-Green strain tensor C=FF. Isotropic elastic materials are the special cases for which the Cauchy stress tensor σ depends solely on the left Cauchy-Green strain tensor B=FF. In this Note we revisit the following property of isotropic hyperelastic materials: if the constitutive law relating Σ and C is derivable from a potential ϕ, then σ and lnB are related by a constitutive law derived from the compound potential ϕ○exp. We give a new and concise proof which is based on an explicit integral formula expressing the derivative of the exponential of a tensor. To cite this article: C. Vallée et al., C. R. Mecanique 336 (2008).

Explicit Formulae for the Continued Fraction Convergents of "Square Root of D"

ERIC Educational Resources Information Center

Braza, Peter A.

2010-01-01

The formulae for the convergents of continued fractions are always given recursively rather than in explicit form. This article derives explicit formulae for the convergents of the continued fraction expansions for square roots.

Holographic entanglement for Chern-Simons terms

NASA Astrophysics Data System (ADS)

Azeyanagi, Tatsuo; Loganayagam, R.; Ng, Gim Seng

2017-02-01

We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS2 k+1. This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong's derivation applied to the corresponding anomaly polynomial. In lower dimensions ( k = 1 , 2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k ≥ 3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.

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

NASA Astrophysics Data System (ADS)

Li, Can; Deng, Wei-Hua

2014-07-01

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

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

PubMed

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

2017-02-01

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

The construction of meaning.

PubMed

Kintsch, Walter; Mangalath, Praful

2011-04-01

We argue that word meanings are not stored in a mental lexicon but are generated in the context of working memory from long-term memory traces that record our experience with words. Current statistical models of semantics, such as latent semantic analysis and the Topic model, describe what is stored in long-term memory. The CI-2 model describes how this information is used to construct sentence meanings. This model is a dual-memory model, in that it distinguishes between a gist level and an explicit level. It also incorporates syntactic information about how words are used, derived from dependency grammar. The construction of meaning is conceptualized as feature sampling from the explicit memory traces, with the constraint that the sampling must be contextually relevant both semantically and syntactically. Semantic relevance is achieved by sampling topically relevant features; local syntactic constraints as expressed by dependency relations ensure syntactic relevance. Copyright © 2010 Cognitive Science Society, Inc.

High-order noise filtering in nontrivial quantum logic gates.

PubMed

Green, Todd; Uys, Hermann; Biercuk, Michael J

2012-07-13

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.

Communication: Relaxation-limited electronic currents in extended reservoir simulations

NASA Astrophysics Data System (ADS)

Gruss, Daniel; Smolyanitsky, Alex; Zwolak, Michael

2017-10-01

Open-system approaches are gaining traction in the simulation of charge transport in nanoscale and molecular electronic devices. In particular, "extended reservoir" simulations, where explicit reservoir degrees of freedom are present, allow for the computation of both real-time and steady-state properties but require relaxation of the extended reservoirs. The strength of this relaxation, γ, influences the conductance, giving rise to a "turnover" behavior analogous to Kramers turnover in chemical reaction rates. We derive explicit, general expressions for the weak and strong relaxation limits. For weak relaxation, the conductance increases linearly with γ and every electronic state of the total explicit system contributes to the electronic current according to its "reduced" weight in the two extended reservoir regions. Essentially, this represents two conductors in series—one at each interface with the implicit reservoirs that provide the relaxation. For strong relaxation, a "dual" expression-one with the same functional form-results, except now proportional to 1/γ and dependent on the system of interest's electronic states, reflecting that the strong relaxation is localizing electrons in the extended reservoirs. Higher order behavior (e.g., γ2 or 1/γ2) can occur when there is a gap in the frequency spectrum. Moreover, inhomogeneity in the frequency spacing can give rise to a pseudo-plateau regime. These findings yield a physically motivated approach to diagnosing numerical simulations and understanding the influence of relaxation, and we examine their occurrence in both simple models and a realistic, fluctuating graphene nanoribbon.

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

NASA Astrophysics Data System (ADS)

Banerjee, J. R.; Ananthapuvirajah, A.

2018-05-01

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

Derivation of Markov processes that violate detailed balance

NASA Astrophysics Data System (ADS)

Lee, Julian

2018-03-01

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

From non-trivial geometries to power spectra and vice versa

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

The statistical kinematical theory of X-ray diffraction as applied to reciprocal-space mapping

PubMed

Nesterets; Punegov

2000-11-01

The statistical kinematical X-ray diffraction theory is developed to describe reciprocal-space maps (RSMs) from deformed crystals with defects of the structure. The general solutions for coherent and diffuse components of the scattered intensity in reciprocal space are derived. As an example, the explicit expressions for intensity distributions in the case of spherical defects and of a mosaic crystal were obtained. The theory takes into account the instrumental function of the triple-crystal diffractometer and can therefore be used for experimental data analysis.

Geometry of Thin Nematic Elastomer Sheets

NASA Astrophysics Data System (ADS)

Aharoni, Hillel; Sharon, Eran; Kupferman, Raz

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

On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model

NASA Astrophysics Data System (ADS)

Chu, Weiqi; Li, Xiantao

2018-01-01

We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori-Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.

A link representation for gravity amplitudes

NASA Astrophysics Data System (ADS)

He, Song

2013-10-01

We derive a link representation for all tree amplitudes in supergravity, from a recent conjecture by Cachazo and Skinner. The new formula explicitly writes amplitudes as contour integrals over constrained link variables, with an integrand naturally expressed in terms of determinants, or equivalently tree diagrams. Important symmetries of the amplitude, such as supersymmetry, parity and (partial) permutation invariance, are kept manifest in the formulation. We also comment on rewriting the formula in a GL( k)-invariant manner, which may serve as a starting point for the generalization to possible Grassmannian contour integrals.

Darboux coordinates and instanton corrections in projective superspace

NASA Astrophysics Data System (ADS)

Crichigno, P. Marcos; Jain, Dharmesh

2012-10-01

By demanding consistency of the Legendre transform construction of hyperkähler metrics in projective superspace, we derive the expression for the Darboux coordinates on the hyperkähler manifold. We apply these results to study the Coulomb branch moduli space of 4D, {N}=2 super-Yang-Mills theory (SYM) on {{{R}}^3}× {S^1} , recovering the results by GMN. We also apply this method to study the electric corrections to the moduli space of 5D, {N}=1 SYM on {{{R}}^3}× {T^2} and give the Darboux coordinates explicitly.

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

PubMed Central

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2016-01-01

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

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

Pramanik, Souvik, E-mail: souvick.in@gmail.com; Moussa, Mohamed, E-mail: mohamed.ibrahim@fsc.bu.edu.eg; Faizal, Mir, E-mail: f2mir@uwaterloo.ca

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. Withmore » this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.« less

Exact relations between homoclinic and periodic orbit actions in chaotic systems

NASA Astrophysics Data System (ADS)

Li, Jizhou; Tomsovic, Steven

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

Zarifi, Keyvan; Gershman, Alex B.

2006-12-01

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

An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes

NASA Astrophysics Data System (ADS)

Barlow, Nathaniel S.; Weinstein, Steven J.; Faber, Joshua A.

2017-07-01

An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the weak- and strong-deflection limits are explicitly satisfied while maintaining accuracy at intermediate values of impact parameter via the method of asymptotic approximants (Barlow et al 2017 Q. J. Mech. Appl. Math. 70 21-48). To this end, the strong deflection limit for a prograde orbit around an extremal black hole is examined, and the full non-vanishing asymptotic behavior is determined. The derived approximant may be an attractive alternative to computationally expensive elliptical integrals used in black hole simulations.

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

NASA Astrophysics Data System (ADS)

Rack, Heinz-Joachim

2017-07-01

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

Analytic theory of orbit contraction

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

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

PubMed

Dricu, Mihai; Frühholz, Sascha

2016-12-01

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

A unifying theory for genetic epidemiological analysis of binary disease data

PubMed Central

2014-01-01

Background Genetic selection for host resistance offers a desirable complement to chemical treatment to control infectious disease in livestock. Quantitative genetics disease data frequently originate from field studies and are often binary. However, current methods to analyse binary disease data fail to take infection dynamics into account. Moreover, genetic analyses tend to focus on host susceptibility, ignoring potential variation in infectiousness, i.e. the ability of a host to transmit the infection. This stands in contrast to epidemiological studies, which reveal that variation in infectiousness plays an important role in the progression and severity of epidemics. In this study, we aim at filling this gap by deriving an expression for the probability of becoming infected that incorporates infection dynamics and is an explicit function of both host susceptibility and infectiousness. We then validate this expression according to epidemiological theory and by simulating epidemiological scenarios, and explore implications of integrating this expression into genetic analyses. Results Our simulations show that the derived expression is valid for a range of stochastic genetic-epidemiological scenarios. In the particular case of variation in susceptibility only, the expression can be incorporated into conventional quantitative genetic analyses using a complementary log-log link function (rather than probit or logit). Similarly, if there is moderate variation in both susceptibility and infectiousness, it is possible to use a logarithmic link function, combined with an indirect genetic effects model. However, in the presence of highly infectious individuals, i.e. super-spreaders, the use of any model that is linear in susceptibility and infectiousness causes biased estimates. Thus, in order to identify super-spreaders, novel analytical methods using our derived expression are required. Conclusions We have derived a genetic-epidemiological function for quantitative genetic analyses of binary infectious disease data, which, unlike current approaches, takes infection dynamics into account and allows for variation in host susceptibility and infectiousness. PMID:24552188

A unifying theory for genetic epidemiological analysis of binary disease data.

PubMed

Lipschutz-Powell, Debby; Woolliams, John A; Doeschl-Wilson, Andrea B

2014-02-19

Genetic selection for host resistance offers a desirable complement to chemical treatment to control infectious disease in livestock. Quantitative genetics disease data frequently originate from field studies and are often binary. However, current methods to analyse binary disease data fail to take infection dynamics into account. Moreover, genetic analyses tend to focus on host susceptibility, ignoring potential variation in infectiousness, i.e. the ability of a host to transmit the infection. This stands in contrast to epidemiological studies, which reveal that variation in infectiousness plays an important role in the progression and severity of epidemics. In this study, we aim at filling this gap by deriving an expression for the probability of becoming infected that incorporates infection dynamics and is an explicit function of both host susceptibility and infectiousness. We then validate this expression according to epidemiological theory and by simulating epidemiological scenarios, and explore implications of integrating this expression into genetic analyses. Our simulations show that the derived expression is valid for a range of stochastic genetic-epidemiological scenarios. In the particular case of variation in susceptibility only, the expression can be incorporated into conventional quantitative genetic analyses using a complementary log-log link function (rather than probit or logit). Similarly, if there is moderate variation in both susceptibility and infectiousness, it is possible to use a logarithmic link function, combined with an indirect genetic effects model. However, in the presence of highly infectious individuals, i.e. super-spreaders, the use of any model that is linear in susceptibility and infectiousness causes biased estimates. Thus, in order to identify super-spreaders, novel analytical methods using our derived expression are required. We have derived a genetic-epidemiological function for quantitative genetic analyses of binary infectious disease data, which, unlike current approaches, takes infection dynamics into account and allows for variation in host susceptibility and infectiousness.

Analytical Energy Gradients for Excited-State Coupled-Cluster Methods

NASA Astrophysics Data System (ADS)

Wladyslawski, Mark; Nooijen, Marcel

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

Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations

NASA Astrophysics Data System (ADS)

Demina, Maria V.; Kudryashov, Nikolay A.

2011-03-01

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

On hydrostatic flows in isentropic coordinates

NASA Astrophysics Data System (ADS)

Bokhove, Onno

2000-01-01

The hydrostatic primitive equations of motion which have been used in large-scale weather prediction and climate modelling over the last few decades are analysed with variational methods in an isentropic Eulerian framework. The use of material isentropic coordinates for the Eulerian hydrostatic equations is known to have distinct conceptual advantages since fluid motion is, under inviscid and statically stable circumstances, confined to take place on quasi-horizontal isentropic surfaces. First, an Eulerian isentropic Hamilton's principle, expressed in terms of fluid parcel variables, is therefore derived by transformation of a Lagrangian Hamilton's principle to an Eulerian one. This Eulerian principle explicitly describes the boundary dynamics of the time-dependent domain in terms of advection of boundary isentropes sB; these are the values the isentropes have at their intersection with the (lower) boundary. A partial Legendre transform for only the interior variables yields an Eulerian ‘action’ principle. Secondly, Noether's theorem is used to derive energy and potential vorticity conservation from the Eulerian Hamilton's principle. Thirdly, these conservation laws are used to derive a wave-activity invariant which is second-order in terms of small-amplitude disturbances relative to a resting or moving basic state. Linear stability criteria are derived but only for resting basic states. In mid-latitudes a time- scale separation between gravity and vortical modes occurs. Finally, this time-scale separation suggests that conservative geostrophic and ageostrophic approximations can be made to the Eulerian action principle for hydrostatic flows. Approximations to Eulerian variational principles may be more advantageous than approximations to Lagrangian ones because non-dimensionalization and scaling tend to be based on Eulerian estimates of the characteristic scales involved. These approximations to the stratified hydrostatic formulation extend previous approximations to the shallow- water equations. An explicit variational derivation is given of an isentropic version of Hoskins & Bretherton's model for atmospheric fronts.

Exact Maximum-Entropy Estimation with Feynman Diagrams

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

A compressible near-wall turbulence model for boundary layer calculations

NASA Technical Reports Server (NTRS)

So, R. M. C.; Zhang, H. S.; Lai, Y. G.

1992-01-01

A compressible near-wall two-equation model is derived by relaxing the assumption of dynamical field similarity between compressible and incompressible flows. This requires justifications for extending the incompressible models to compressible flows and the formulation of the turbulent kinetic energy equation in a form similar to its incompressible counterpart. As a result, the compressible dissipation function has to be split into a solenoidal part, which is not sensitive to changes of compressibility indicators, and a dilational part, which is directly affected by these changes. This approach isolates terms with explicit dependence on compressibility so that they can be modeled accordingly. An equation that governs the transport of the solenoidal dissipation rate with additional terms that are explicitly dependent on the compressibility effects is derived similarly. A model with an explicit dependence on the turbulent Mach number is proposed for the dilational dissipation rate. Thus formulated, all near-wall incompressible flow models could be expressed in terms of the solenoidal dissipation rate and straight-forwardly extended to compressible flows. Therefore, the incompressible equations are recovered correctly in the limit of constant density. The two-equation model and the assumption of constant turbulent Prandtl number are used to calculate compressible boundary layers on a flat plate with different wall thermal boundary conditions and free-stream Mach numbers. The calculated results, including the near-wall distributions of turbulence statistics and their limiting behavior, are in good agreement with measurements. In particular, the near-wall asymptotic properties are found to be consistent with incompressible behavior; thus suggesting that turbulent flows in the viscous sublayer are not much affected by compressibility effects.

Viscosity and thermal conductivity of moderately dense gas mixtures.

NASA Technical Reports Server (NTRS)

Wakeham, W. A.; Kestin, J.; Mason, E. A.; Sandler, S. I.

1972-01-01

Derivation of a simple, semitheoretical expression for the initial density dependence of the viscosity and thermal conductivity of gaseous mixtures in terms of the appropriate properties of the pure components and of their interaction quantities. The derivation is based on Enskog's theory of dense gases and yields an equation in which the composition dependence of the linear factor in the density expansion is explicit. The interaction quantities are directly related to those of the mixture extrapolated to zero density and to a universal function valid for all gases. The reliability of the formulation is assessed with respect to the viscosity of several binary mixtures. It is found that the calculated viscosities of binary mixtures agree with the experimental data with a precision which is comparable to that of the most precise measurements.

Reference Production: Production-Internal and Addressee-Oriented Processes

ERIC Educational Resources Information Center

Arnold, Jennifer

2008-01-01

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

Nonlinear equations of dynamics for spinning paraboloidal antennas

NASA Technical Reports Server (NTRS)

Utku, S.; Shoemaker, W. L.; Salama, M.

1983-01-01

The nonlinear strain-displacement and velocity-displacement relations of spinning imperfect rotational paraboloidal thin shell antennas are derived for nonaxisymmetrical deformations. Using these relations with the admissible trial functions in the principle functional of dynamics, the nonlinear equations of stress inducing motion are expressed in the form of a set of quasi-linear ordinary differential equations of the undetermined functions by means of the Rayleigh-Ritz procedure. These equations include all nonlinear terms up to and including the third degree. Explicit expressions are given for the coefficient matrices appearing in these equations. Both translational and rotational off-sets of the axis of revolution (and also the apex point of the paraboloid) with respect to the spin axis are considered. Although the material of the antenna is assumed linearly elastic, it can be anisotropic.

Mordell integrals and Giveon-Kutasov duality

NASA Astrophysics Data System (ADS)

Giasemidis, Georgios; Tierz, Miguel

2016-01-01

We solve, for finite N, the matrix model of supersymmetric U( N) Chern-Simons theory coupled to N f massive hypermultiplets of R-charge 1/2 , together with a Fayet-Iliopoulos term. We compute the partition function by identifying it with a determinant of a Hankel matrix, whose entries are parametric derivatives (of order N f - 1) of Mordell integrals. We obtain finite Gauss sums expressions for the partition functions. We also apply these results to obtain an exhaustive test of Giveon-Kutasov (GK) duality in the N=3 setting, by systematic computation of the matrix models involved. The phase factor that arises in the duality is then obtained explicitly. We give an expression characterized by modular arithmetic (mod 4) behavior that holds for all tested values of the parameters (checked up to N f = 12 flavours).

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

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

Krebs, H., E-mail: hermann.krebs@rub.de; Epelbaum, E., E-mail: evgeny.epelbaum@rub.de; Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93016

We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of themore » continuity equation.« less

A generalized modal shock spectra method for spacecraft loads analysis

NASA Technical Reports Server (NTRS)

Trubert, M.; Salama, M.

1979-01-01

Unlike the traditional shock spectra approach, the generalization presented in this paper permits elastic interaction between the spacecraft and launch vehicle in order to obtain accurate bounds on the spacecraft response and structural loads. In addition, the modal response from a previous launch vehicle transient analysis - with or without a dummy spacecraft - is exploited in order to define a modal impulse as a simple idealization of the actual forcing function. The idealized modal forcing function is then used to derive explicit expressions for an estimate of the bound on the spacecraft structural response and forces.

Magnetic field effects on peristaltic flow of blood in a non-uniform channel

NASA Astrophysics Data System (ADS)

Latha, R.; Rushi Kumar, B.

2017-11-01

The objective of this paper is to carry out the effect of the MHD on the peristaltic transport of blood in a non-uniform channel have been explored under long wavelength approximation with low (zero) Reynolds number. Blood is made of an incompressible, viscous and electrically conducting. Explicit expressions for the axial velocity, axial pressure gradient are derived using long wavelength assumptions with slip and regularity conditions. It is determined that the pressure gradient diminishes as the couple stress parameter increments and it decreases as the magnetic parameter increments. We additionally concentrate the embedded parameters through graphs.

An implicit iterative algorithm with a tuning parameter for Itô Lyapunov matrix equations

NASA Astrophysics Data System (ADS)

Zhang, Ying; Wu, Ai-Guo; Sun, Hui-Jie

2018-01-01

In this paper, an implicit iterative algorithm is proposed for solving a class of Lyapunov matrix equations arising in Itô stochastic linear systems. A tuning parameter is introduced in this algorithm, and thus the convergence rate of the algorithm can be changed. Some conditions are presented such that the developed algorithm is convergent. In addition, an explicit expression is also derived for the optimal tuning parameter, which guarantees that the obtained algorithm achieves its fastest convergence rate. Finally, numerical examples are employed to illustrate the effectiveness of the given algorithm.

Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model

NASA Astrophysics Data System (ADS)

Farajpour, A.; Mohammadi, M.; Shahidi, A. R.; Mahzoon, M.

2011-08-01

In this article, the buckling behavior of nanoscale circular plates under uniform radial compression is studied. Small-scale effect is taken into consideration. Using nonlocal elasticity theory the governing equations are derived for the circular single-layered graphene sheets (SLGS). Explicit expressions for the buckling loads are obtained for clamped and simply supported boundary conditions. It is shown that nonlocal effects play an important role in the buckling of circular nanoplates. The effects of the small scale on the buckling loads considering various parameters such as the radius of the plate and mode numbers are investigated.

Robust and accurate vectorization of line drawings.

PubMed

Hilaire, Xavier; Tombre, Karl

2006-06-01

This paper presents a method for vectorizing the graphical parts of paper-based line drawings. The method consists of separating the input binary image into layers of homogeneous thickness, skeletonizing each layer, segmenting the skeleton by a method based on random sampling, and simplifying the result. The segmentation method is robust with a best bound of 50 percent noise reached for indefinitely long primitives. Accurate estimation of the recognized vector's parameters is enabled by explicitly computing their feasibility domains. Theoretical performance analysis and expression of the complexity of the segmentation method are derived. Experimental results and comparisons with other vectorization systems are also provided.

Heavy-tailed fractional Pearson diffusions.

PubMed

Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N

2017-11-01

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

Parametric decay of plasma waves near the upper-hybrid resonance

DOE PAGES

Dodin, I. Y.; Arefiev, A. V.

2017-03-28

An intense X wave propagating perpendicularly to dc magnetic field is unstable with respect to a parametric decay into an electron Bernstein wave and a lower-hybrid wave. A modified theory of this effect is proposed that extends to the high-intensity regime, where the instability rate γ ceases to be a linear function of the incident-wave amplitude. An explicit formula for γ is derived and expressed in terms of cold-plasma parameters. Here, theory predictions are in reasonable agreement with the results of the particle-in-cell simulations presented in a separate publication.

Damping behavior of nano-fibrous composites with viscous interface in anti-plane shear

NASA Astrophysics Data System (ADS)

Wang, Xu

2017-06-01

By using the composite cylinder assemblage model, we derive an explicit expression of the specific damping capacity of nano-fibrous composite with viscous interface when subjected to time-harmonic anti-plane shear loads. The fiber and the matrix are first endowed with separate and distinct Gurtin-Murdoch surface elasticities, and rate-dependent sliding occurs on the fiber-matrix interface. Our analysis indicates that the effective damping of the composite depends on five dimensionless parameters: the fiber volume fraction, the stiffness ratio, two parameters arising from surface elasticity and one parameter due to interface sliding.

RNA sequencing of transformed lymphoblastoid cells from siblings discordant for autism spectrum disorders reveals transcriptomic and functional alterations: Evidence for sex-specific effects.

PubMed

Tylee, Daniel S; Espinoza, Alfred J; Hess, Jonathan L; Tahir, Muhammad A; McCoy, Sarah Y; Rim, Joshua K; Dhimal, Totadri; Cohen, Ori S; Glatt, Stephen J

2017-03-01

Genome-wide expression studies of samples derived from individuals with autism spectrum disorder (ASD) and their unaffected siblings have been widely used to shed light on transcriptomic differences associated with this condition. Females have historically been under-represented in ASD genomic studies. Emerging evidence from studies of structural genetic variants and peripheral biomarkers suggest that sex-differences may exist in the biological correlates of ASD. Relatively few studies have explicitly examined whether sex-differences exist in the transcriptomic signature of ASD. The present study quantified genome-wide expression values by performing RNA sequencing on transformed lymphoblastoid cell lines and identified transcripts differentially expressed between same-sex, proximal-aged sibling pairs. We found that performing separate analyses for each sex improved our ability to detect ASD-related transcriptomic differences; we observed a larger number of dysregulated genes within our smaller set of female samples (n = 12 sibling pairs), as compared with the set of male samples (n = 24 sibling pairs), with small, but statistically significant overlap between the sexes. Permutation-based gene-set analyses and weighted gene co-expression network analyses also supported the idea that the transcriptomic signature of ASD may differ between males and females. We discuss our findings in the context of the relevant literature, underscoring the need for future ASD studies to explicitly account for differences between the sexes. Autism Res 2017, 10: 439-455. © 2016 International Society for Autism Research, Wiley Periodicals, Inc. © 2016 International Society for Autism Research, Wiley Periodicals, Inc.

Current capabilities for simulating the extreme distortion of thin structures subjected to severe impacts

NASA Technical Reports Server (NTRS)

Key, Samuel W.

1993-01-01

The explicit transient dynamics technology in use today for simulating the impact and subsequent transient dynamic response of a structure has its origins in the 'hydrocodes' dating back to the late 1940's. The growth in capability in explicit transient dynamics technology parallels the growth in speed and size of digital computers. Computer software for simulating the explicit transient dynamic response of a structure is characterized by algorithms that use a large number of small steps. In explicit transient dynamics software there is a significant emphasis on speed and simplicity. The finite element technology used to generate the spatial discretization of a structure is based on a compromise between completeness of the representation for the physical processes modelled and speed in execution. That is, since it is expected in every calculation that the deformation will be finite and the material will be strained beyond the elastic range, the geometry and the associated gradient operators must be reconstructed, as well as complex stress-strain models evaluated at every time step. As a result, finite elements derived for explicit transient dynamics software use the simplest and barest constructions possible for computational efficiency while retaining an essential representation of the physical behavior. The best example of this technology is the four-node bending quadrilateral derived by Belytschko, Lin and Tsay. Today, the speed, memory capacity and availability of computer hardware allows a number of the previously used algorithms to be 'improved.' That is, it is possible with today's computing hardware to modify many of the standard algorithms to improve their representation of the physical process at the expense of added complexity and computational effort. The purpose is to review a number of these algorithms and identify the improvements possible. In many instances, both the older, faster version of the algorithm and the improved and somewhat slower version of the algorithm are found implemented together in software. Specifically, the following seven algorithmic items are examined: the invariant time derivatives of stress used in material models expressed in rate form; incremental objectivity and strain used in the numerical integration of the material models; the use of one-point element integration versus mean quadrature; shell elements used to represent the behavior of thin structural components; beam elements based on stress-resultant plasticity versus cross-section integration; the fidelity of elastic-plastic material models in their representation of ductile metals; and the use of Courant subcycling to reduce computational effort.

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

ERIC Educational Resources Information Center

Cate, Fred H.

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

Stochastic modelling of the hydrologic operation of rainwater harvesting systems

NASA Astrophysics Data System (ADS)

Guo, Rui; Guo, Yiping

2018-07-01

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

Role of Rayleigh numbers on characteristics of double diffusive salt fingers

NASA Astrophysics Data System (ADS)

Rehman, F.; Singh, O. P.

2018-05-01

Double diffusion convection, driven by two constituents of the fluid with different molecular diffusivity, is widely applied in oceanography and large number of other fields like astrophysics, geology, chemistry and metallurgy. In case of ocean, heat (T) and salinity (S) are the two components with varying diffusivity, where heat diffuses hundred times faster than salt. Component (T) stabilizes the system whereas components (S) destabilizes the system with overall density remains stable and forms the rising and sinking fingers known as salt fingers. Recent observations suggest that salt finger characteristics such as growth rates, wavenumber, and fluxes are strongly depending on the Rayleigh numbers as major driving force. In this paper, we corroborate this observation with the help of experiments, numerical simulations and linear theory. An eigenvalue expression for growth rate is derived from the linearized governing equations with explicit dependence on Rayleigh numbers, density stability ratio, Prandtl number and diffusivity ratio. Expressions for fastest growing fingers are also derived as a function various non-dimensional parameter. The predicted results corroborate well with the data reported from the field measurements, experiments and numerical simulations.

Algorithms for Computing the Magnetic Field, Vector Potential, and Field Derivatives for a Thin Solenoid with Uniform Current Density

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

Walstrom, Peter Lowell

A numerical algorithm for computing the field components B r and B z and their r and z derivatives with open boundaries in cylindrical coordinates for radially thin solenoids with uniform current density is described in this note. An algorithm for computing the vector potential A θ is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. The (apparently) new feature of themore » algorithms described in this note applies to cases where the field point is outside of the bore of the solenoid and the field-point radius approaches the solenoid radius. Since the elliptic integrals of the third kind normally used in computing B z and A θ become infinite in this region of parameter space, fields for points with the axial coordinate z outside of the ends of the solenoid and near the solenoid radius are treated by use of elliptic integrals of the third kind of modified argument, derived by use of an addition theorem. Also, the algorithms also avoid the numerical difficulties the textbook solutions have for points near the axis arising from explicit factors of 1/r or 1/r 2 in the some of the expressions.« less

PP/PS anisotropic stereotomography

NASA Astrophysics Data System (ADS)

Nag, Steinar; Alerini, Mathias; Ursin, Bjørn

2010-04-01

Stereotomography is a slope tomographic method which gives good results for background velocity model estimation in 2-D isotropic media. We develop here the extension of the method to 3-D general anisotropic media for PP and PS events. We do not take into account the issue of shear wave degeneracy. As in isotropic media, the sensitivity matrix of the inversion can be computed by paraxial ray tracing. We introduce a `constant Z stereotomography' approach, which can reduce the size of the sensitivity matrix. Based on ray perturbation theory, we give all the derivatives of stereotomography data parameters with respect to model parameters in a 3-D general anisotropic medium. These general formulas for the derivatives can also be used in other applications that rely on anisotropic ray perturbation theory. In particular, we obtain derivatives of the phase velocity with respect to position, phase angle and elastic medium parameters, all for general anisotropic media. The derivatives are expressed using the Voigt notation for the elastic medium parameters. We include a Jacobian that allows to change the model parametrization from Voigt to Thomsen parameters. Explicit expressions for the derivatives of the data are given for the case of 2-D tilted transversely isotropic (TTI) media. We validate the method by single-parameter estimation of each Thomsen parameter field of a 2-D TTI synthetic model, where data are modelled by ray tracing. For each Thomsen parameter, the estimated velocity field fits well with the true velocity field.

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

PubMed Central

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

2015-01-01

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

Photon-number statistics in resonance fluorescence

NASA Astrophysics Data System (ADS)

Lenstra, D.

1982-12-01

The theory of photon-number statistics in resonance fluorescence is treated, starting with the general formula for the emission probability of n photons during a given time interval T. The results fully confirm formerly obtained results by Cook that were based on the theory of atomic motion in a traveling wave. General expressions for the factorial moments are derived and explicit results for the mean and the variance are given. It is explicitly shown that the distribution function tends to a Gaussian when T becomes much larger than the natural lifetime of the excited atom. The speed of convergence towards the Gaussian is found to be typically slow, that is, the third normalized central moment (or the skewness) is proportional to T-12. However, numerical results illustrate that the overall features of the distribution function are already well represented by a Gaussian when T is larger than a few natural lifetimes only, at least if the intensity of the exciting field is not too small and its detuning is not too large.

Effect of spatial coherence on the scintillation properties of a dark hollow beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Yuan, Yangsheng; Chen, Yahong; Liang, Chunhao; Cai, Yangjian; Baykal, Yahya

2013-03-01

With the help of a tensor method, we derive an explicit expression for the on-axis scintillation index of a circular partially coherent dark hollow (DH) beam in weakly turbulent atmosphere. The derived formula can be applied to study the scintillation properties of a partially coherent Gaussian beam and a partially coherent flat-topped (FT) beam. The effect of spatial coherence on the scintillation properties of DH beam, FT beam and Gaussian beam is studied numerically and comparatively. Our results show that the advantage of a DH beam over a FT beam and a Gaussian beam for reducing turbulence-induced scintillation increases particularly at long propagation distances with the decrease of spatial coherence or the increase of the atmospheric turbulence, which will be useful for long-distance free-space optical communications.

Temperature extrapolation of multicomponent grand canonical free energy landscapes

NASA Astrophysics Data System (ADS)

Mahynski, Nathan A.; Errington, Jeffrey R.; Shen, Vincent K.

2017-08-01

We derive a method for extrapolating the grand canonical free energy landscape of a multicomponent fluid system from one temperature to another. Previously, we introduced this statistical mechanical framework for the case where kinetic energy contributions to the classical partition function were neglected for simplicity [N. A. Mahynski et al., J. Chem. Phys. 146, 074101 (2017)]. Here, we generalize the derivation to admit these contributions in order to explicitly illustrate the differences that result. Specifically, we show how factoring out kinetic energy effects a priori, in order to consider only the configurational partition function, leads to simpler mathematical expressions that tend to produce more accurate extrapolations than when these effects are included. We demonstrate this by comparing and contrasting these two approaches for the simple cases of an ideal gas and a non-ideal, square-well fluid.

Large deviation function for a driven underdamped particle in a periodic potential

NASA Astrophysics Data System (ADS)

Fischer, Lukas P.; Pietzonka, Patrick; Seifert, Udo

2018-02-01

Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one-dimensional periodic potential. Two different approaches to the large deviation function of the particle current are presented. First, we derive an explicit expression for the large deviation functional of the empirical phase space density, which replaces the level 2.5 functional used for overdamped dynamics. Using this approach, we obtain several bounds on the large deviation function of the particle current. We compare these to bounds for overdamped dynamics that have recently been derived, motivated by the thermodynamic uncertainty relation. Second, we provide a method to calculate the large deviation function via the cumulant generating function. We use this method to assess the tightness of the bounds in a numerical case study for a cosine potential.

The spin-temperature theory of dynamic nuclear polarization and nuclear spin-lattice relaxation

NASA Technical Reports Server (NTRS)

Byvik, C. E.; Wollan, D. S.

1974-01-01

A detailed derivation of the equations governing dynamic nuclear polarization (DNP) and nuclear spin lattice relaxation by use of the spin temperature theory has been carried to second order in a perturbation expansion of the density matrix. Nuclear spin diffusion in the rapid diffusion limit and the effects of the coupling of the electron dipole-dipole reservoir (EDDR) with the nuclear spins are incorporated. The complete expression for the dynamic nuclear polarization has been derived and then examined in detail for the limit of well resolved solid effect transitions. Exactly at the solid effect transition peaks, the conventional solid-effect DNP results are obtained, but with EDDR effects on the nuclear relaxation and DNP leakage factor included. Explicit EDDR contributions to DNP are discussed, and a new DNP effect is predicted.

Time-fractional Cahn-Allen and time-fractional Klein-Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis

NASA Astrophysics Data System (ADS)

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

2018-03-01

This research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn-Allen (CA) and time-fractional Klein-Gordon (KG) equations with Riemann-Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented.

[Application of general retention time formula for gradient liquid chromatography in the studies of ladder-like gradient elution].

PubMed

Sun, Xiaoli; Hao, Weiqiang; Wang, Junde; Di, Bin; Chen, Qiang; Zhuang, Wei; Yu, Qiang; Zhang, Peipei

2013-08-01

By not explicitly specifying the type of solvent strength model, the features of ladder-like gradient elution were studied based on the general retention time formula that was derived in our previous work. For the case where the solute is eluted at like gradient, we derived the expression that connects the mobile phase composition (phiR), at which the solute is eluted from the column, with the gradient slope (B). It was shown that phiR will increase with the increase of B in this case. For the case where the solute is eluted at the last isocratic segment of the ladder-like gradient, it was proven that the retention time (tR) will correlate linearly with the reciprocal of the gradient slope (1/B) when the initial and final mobile phase compositions are set to be constant. In experiments, by taking biphenyl as the sample, the values of retention time in isocratic and gradient elution were measured on a C18 column by using a mixture of methanol and water as the mobile phase. The experimental values were found to be well consistent with the theoretical values that were calculated from the expressions. These expressions will be helpful to understand the features of the ladder-like gradient in practice.

From Sommerfeld and Brillouin forerunners to optical precursors

NASA Astrophysics Data System (ADS)

Macke, Bruno; Ségard, Bernard

2013-04-01

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

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

PubMed

Martirosyan, A; Saakian, David B

2011-08-01

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

YORP torque as the function of shape harmonics

NASA Astrophysics Data System (ADS)

Breiter, Sławomir; Michalska, Hanna

2008-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

PubMed

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

2016-04-15

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

Explicit expressions of self-diffusion coefficient, shear viscosity, and the Stokes-Einstein relation for binary mixtures of Lennard-Jones liquids

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

Ohtori, Norikazu, E-mail: ohtori@chem.sc.niigata-u.ac.jp; Ishii, Yoshiki

Explicit expressions of the self-diffusion coefficient, D{sub i}, and shear viscosity, η{sub sv}, are presented for Lennard-Jones (LJ) binary mixtures in the liquid states along the saturated vapor line. The variables necessary for the expressions were derived from dimensional analysis of the properties: atomic mass, number density, packing fraction, temperature, and the size and energy parameters used in the LJ potential. The unknown dependence of the properties on each variable was determined by molecular dynamics (MD) calculations for an equimolar mixture of Ar and Kr at the temperature of 140 K and density of 1676 kg m{sup −3}. The scalingmore » equations obtained by multiplying all the single-variable dependences can well express D{sub i} and η{sub sv} evaluated by the MD simulation for a whole range of compositions and temperatures without any significant coupling between the variables. The equation for D{sub i} can also explain the dual atomic-mass dependence, i.e., the average-mass and the individual-mass dependence; the latter accounts for the “isotope effect” on D{sub i}. The Stokes-Einstein (SE) relation obtained from these equations is fully consistent with the SE relation for pure LJ liquids and that for infinitely dilute solutions. The main differences from the original SE relation are the presence of dependence on the individual mass and on the individual energy parameter. In addition, the packing-fraction dependence turned out to bridge another gap between the present and original SE relations as well as unifying the SE relation between pure liquids and infinitely dilute solutions.« less

Spectral singularities, threshold gain, and output intensity for a slab laser with mirrors

NASA Astrophysics Data System (ADS)

Doğan, Keremcan; Mostafazadeh, Ali; Sarısaman, Mustafa

2018-05-01

We explore the consequences of the emergence of linear and nonlinear spectral singularities in TE modes of a homogeneous slab of active optical material that is placed between two mirrors. We use the results together with two basic postulates regarding the behavior of laser light emission to derive explicit expressions for the laser threshold condition and output intensity for these modes of the slab and discuss their physical implications. In particular, we reveal the details of the dependence of the threshold gain and output intensity on the position and properties of the mirrors and on the real part of the refractive index of the gain material.

Quantum SU(2|1) supersymmetric Calogero-Moser spinning systems

NASA Astrophysics Data System (ADS)

Fedoruk, Sergey; Ivanov, Evgeny; Lechtenfeld, Olaf; Sidorov, Stepan

2018-04-01

SU(2|1) supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an N=4 supersymmetrization of the quantum U(2) spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra \\widehat{su}(2\\Big|1) . The full system admits an SU(2|1) covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum SU(2|1) generators in both sectors as well as for the total system, and we determine the relevant energy spectra, degeneracies, and the sets of physical states.

Pulse propagation, dispersion, and energy in magnetic materials.

PubMed

Scalora, Michael; D'Aguanno, Giuseppe; Mattiucci, Nadia; Akozbek, Neset; Bloemer, Mark J; Centini, Marco; Sibilia, Concita; Bertolotti, Mario

2005-12-01

We discuss pulse propagation effects in generic, electrically and magnetically dispersive media that may display large material discontinuities, such as a surface boundary. Using the known basic constitutive relations between the fields, and an explicit Taylor expansion to describe the dielectric susceptibility and magnetic permeability, we derive expressions for energy density and energy dissipation rates, and equations of motion for the coupled electric and magnetic fields. We then solve the equations of motion in the presence of a single interface, and find that in addition to the now-established negative refraction process an energy exchange occurs between the electric and magnetic fields as the pulse traverses the boundary.

Convergence of high order perturbative expansions in open system quantum dynamics.

PubMed

Xu, Meng; Song, Linze; Song, Kai; Shi, Qiang

2017-02-14

We propose a new method to directly calculate high order perturbative expansion terms in open system quantum dynamics. They are first written explicitly in path integral expressions. A set of differential equations are then derived by extending the hierarchical equation of motion (HEOM) approach. As two typical examples for the bosonic and fermionic baths, specific forms of the extended HEOM are obtained for the spin-boson model and the Anderson impurity model. Numerical results are then presented for these two models. General trends of the high order perturbation terms as well as the necessary orders for the perturbative expansions to converge are analyzed.

Transform-limited-pulse representation of excitation with natural incoherent light

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

Chenu, Aurélia, E-mail: aurelia.chenu@utoronto.ca; Brumer, Paul, E-mail: pbrumer@chem.utoronto.ca

2016-01-28

The excitation of molecular systems by natural incoherent light relevant, for example, to photosynthetic light-harvesting is examined. We show that the result of linear excitation with natural incoherent light can be obtained using incident light described in terms of transform limited pulses, as opposed to conventional classical representations with explicit random character. The derived expressions allow for computations to be done directly for any thermal light spectrum using a simple wave function formalism and provide a route to the experimental determination of natural incoherent excitation using pulsed laser techniques. Pulses associated with solar and cosmic microwave background radiation are providedmore » as examples.« less

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

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

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

2011-10-15

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

Analysis of delamination related fracture processes in composites

NASA Technical Reports Server (NTRS)

Armanios, Erian A.

1992-01-01

An anisotropic thin walled closed section beam theory was developed based on an asymptotical analysis of the shell energy functional. The displacement field is not assumed a priori and emerges as a result of the analysis. In addition to the classical out-of-plane torsional warping, two new contributions are identified namely, axial strain and bending warping. A comparison of the derived governing equations confirms the theory developed by Reissner and Tsai. Also, explicit closed form expressions for the beam stiffness coefficients, the stress and displacement fields are provided. The predictions of the present theory were validated by comparison with finite element simulation, other closed form analyses and test data.

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

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

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

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

Higher-derivative operators and effective field theory for general scalar-tensor theories

NASA Astrophysics Data System (ADS)

Solomon, Adam R.; Trodden, Mark

2018-02-01

We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order operators only, and demonstrate this using several different techniques, such as reduction of order and explicit field redefinitions. These methods are applied, in particular, to the much-studied Horndeski theories. The goal is to clarify the application of effective field theory techniques in the context of popular cosmological models, and to explicitly demonstrate how and when higher-derivative operators can be cast into lower-derivative forms suitable for numerical solution techniques.

Revisiting the Logan plot to account for non-negligible blood volume in brain tissue.

PubMed

Schain, Martin; Fazio, Patrik; Mrzljak, Ladislav; Amini, Nahid; Al-Tawil, Nabil; Fitzer-Attas, Cheryl; Bronzova, Juliana; Landwehrmeyer, Bernhard; Sampaio, Christina; Halldin, Christer; Varrone, Andrea

2017-08-18

Reference tissue-based quantification of brain PET data does not typically include correction for signal originating from blood vessels, which is known to result in biased outcome measures. The bias extent depends on the amount of radioactivity in the blood vessels. In this study, we seek to revisit the well-established Logan plot and derive alternative formulations that provide estimation of distribution volume ratios (DVRs) that are corrected for the signal originating from the vasculature. New expressions for the Logan plot based on arterial input function and reference tissue were derived, which included explicit terms for whole blood radioactivity. The new methods were evaluated using PET data acquired using [ 11 C]raclopride and [ 18 F]MNI-659. The two-tissue compartment model (2TCM), with which signal originating from blood can be explicitly modeled, was used as a gold standard. DVR values obtained for [ 11 C]raclopride using the either blood-based or reference tissue-based Logan plot were systematically underestimated compared to 2TCM, and for [ 18 F]MNI-659, a proportionality bias was observed, i.e., the bias varied across regions. The biases disappeared when optimal blood-signal correction was used for respective tracer, although for the case of [ 18 F]MNI-659 a small but systematic overestimation of DVR was still observed. The new method appears to remove the bias introduced due to absence of correction for blood volume in regular graphical analysis and can be considered in clinical studies. Further studies are however required to derive a generic mapping between plasma and whole-blood radioactivity levels.

Approximate analytical relationships for linear optimal aeroelastic flight control laws

NASA Astrophysics Data System (ADS)

Kassem, Ayman Hamdy

1998-09-01

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

Banding of NMR-derived Methyl Order Parameters: Implications for Protein Dynamics

PubMed Central

Sharp, Kim A.; Kasinath, Vignesh; Wand, A. Joshua

2014-01-01

Our understanding of protein folding, stability and function has begun to more explicitly incorporate dynamical aspects. Nuclear magnetic resonance has emerged as a powerful experimental method for obtaining comprehensive site-resolved insight into protein motion. It has been observed that methyl-group motion tends to cluster into three “classes” when expressed in terms of the popular Lipari-Szabo model-free squared generalized order parameter. Here the origins of the three classes or bands in the distribution of order parameters are examined. As a first step, a Bayesian based approach, which makes no a priori assumption about the existence or number of bands, is developed to detect the banding of O2axis values derived either from NMR experiments or molecular dynamics simulations. The analysis is applied to seven proteins with extensive molecular dynamics simulations of these proteins in explicit water to examine the relationship between O2 and fine details of the motion of methyl bearing side chains. All of the proteins studied display banding, with some subtle differences. We propose a very simple yet plausible physical mechanism for banding. Finally, our Bayesian method is used to analyze the measured distributions of methyl group motions in the catabolite activating protein and several of its mutants in various liganded states and discuss the functional implications of the observed banding to protein dynamics and function. PMID:24677353

The Inverse Optimal Control Problem for a Three-Loop Missile Autopilot

NASA Astrophysics Data System (ADS)

Hwang, Donghyeok; Tahk, Min-Jea

2018-04-01

The performance characteristics of the autopilot must have a fast response to intercept a maneuvering target and reasonable robustness for system stability under the effect of un-modeled dynamics and noise. By the conventional approach, the three-loop autopilot design is handled by time constant, damping factor and open-loop crossover frequency to achieve the desired performance requirements. Note that the general optimal theory can be also used to obtain the same gain as obtained from the conventional approach. The key idea of using optimal control technique for feedback gain design revolves around appropriate selection and interpretation of the performance index for which the control is optimal. This paper derives an explicit expression, which relates the weight parameters appearing in the quadratic performance index to the design parameters such as open-loop crossover frequency, phase margin, damping factor, or time constant, etc. Since all set of selection of design parameters do not guarantee existence of optimal control law, explicit inequalities, which are named the optimality criteria for the three-loop autopilot (OC3L), are derived to find out all set of design parameters for which the control law is optimal. Finally, based on OC3L, an efficient gain selection procedure is developed, where time constant is set to design objective and open-loop crossover frequency and phase margin as design constraints. The effectiveness of the proposed technique is illustrated through numerical simulations.

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

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

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

2013-08-01

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

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2012-11-01

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

The RKGL method for the numerical solution of initial-value problems

NASA Astrophysics Data System (ADS)

Prentice, J. S. C.

2008-04-01

We introduce the RKGL method for the numerical solution of initial-value problems of the form y'=f(x,y), y(a)=[alpha]. The method is a straightforward modification of a classical explicit Runge-Kutta (RK) method, into which Gauss-Legendre (GL) quadrature has been incorporated. The idea is to enhance the efficiency of the method by reducing the number of times the derivative f(x,y) needs to be computed. The incorporation of GL quadrature serves to enhance the global order of the method by, relative to the underlying RK method. Indeed, the RKGL method has a global error of the form Ahr+1+Bh2m, where r is the order of the RK method and m is the number of nodes used in the GL component. In this paper we derive this error expression and show that RKGL is consistent, convergent and strongly stable.

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

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

The renormalization group and the implicit function theorem for amplitude equations

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

Kirkinis, Eleftherios

2008-07-15

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen et al., Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation formore » both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases.« less

Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads

NASA Astrophysics Data System (ADS)

Asemi, H. R.; Asemi, S. R.; Farajpour, A.; Mohammadi, M.

2015-04-01

The potential applications of piezoelectric nanofilms (PNFs) and double-piezoelectric-nanofilm (DPNF) systems as nanoelectromechanical mass sensors are examined. The PNFs carrying multiple nanoparticles at arbitrary locations are modeled as rectangular nonlocal plates with attached concentrated masses. Using the nonlocal elasticity theory and Hamilton's principle, the differential equations of motion are derived for both PNF-based and DPNF-based nanosensors. The influences of small scale, initial stress and temperature change on the frequency shifts of the nanoelectromechanical sensors are taken into consideration. Explicit expressions are derived for the resonance frequencies of the nanosensors by employing the Galerkin method. The present results show that when the value of nonlocal parameter decreases, the frequency shifts of piezoelectric nanosensors increase. Further, the frequency shifts of DPNF-based mass sensors are always greater than those of PNF-based mass sensors. The present work would be helpful in the design of nanoelectromechanical mass sensors using PNFs.

Species abundance distribution and population dynamics in a two-community model of neutral ecology

NASA Astrophysics Data System (ADS)

Vallade, M.; Houchmandzadeh, B.

2006-11-01

Explicit formulas for the steady-state distribution of species in two interconnected communities of arbitrary sizes are derived in the framework of Hubbell’s neutral model of biodiversity. Migrations of seeds from both communities as well as mutations in both of them are taken into account. These results generalize those previously obtained for the “island-continent” model and they allow an analysis of the influence of the ratio of the sizes of the two communities on the dominance/diversity equilibrium. Exact expressions for species abundance distributions are deduced from a master equation for the joint probability distribution of species in the two communities. Moreover, an approximate self-consistent solution is derived. It corresponds to a generalization of previous results and it proves to be accurate over a broad range of parameters. The dynamical correlations between the abundances of a species in both communities are also discussed.

Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of Al-Salam Carlitz I polynomials

NASA Astrophysics Data System (ADS)

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

2005-12-01

Two formulae expressing explicitly the derivatives and moments of Al-Salam-Carlitz I polynomials of any degree and for any order in terms of Al-Salam-Carlitz I themselves are proved. Two other formulae for the expansion coefficients of general-order derivatives Dpqf(x), and for the moments xellDpqf(x), of an arbitrary function f(x) in terms of its original expansion coefficients are also obtained. Application of these formulae for solving q-difference equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Al-Salam-Carlitz I polynomials and any system of basic hypergeometric orthogonal polynomials, belonging to the q-Hahn class, is described.

Asymptotic Linear Spectral Statistics for Spiked Hermitian Random Matrices

NASA Astrophysics Data System (ADS)

Passemier, Damien; McKay, Matthew R.; Chen, Yang

2015-07-01

Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked correlation), non-central Wishart with rank-one non-centrality, and a related class of non-central matrices. For a generic linear statistic, we derive simple and explicit CLT expressions as the matrix dimensions grow large. For all three ensembles under consideration, we find that the primary effect of the spike is to introduce an correction term to the asymptotic mean of the linear spectral statistic, which we characterize with simple formulas. The utility of our proposed framework is demonstrated through application to three different linear statistics problems: the classical likelihood ratio test for a population covariance, the capacity analysis of multi-antenna wireless communication systems with a line-of-sight transmission path, and a classical multiple sample significance testing problem.

Active colloids in the context of chemical kinetics

NASA Astrophysics Data System (ADS)

Oshanin, G.; Popescu, M. N.; Dietrich, S.

2017-03-01

We study a mesoscopic model of a chemically active colloidal particle which on certain parts of its surface promotes chemical reactions in the surrounding solution. For reasons of simplicity and conceptual clarity, we focus on the case in which only electrically neutral species are present in the solution and on chemical reactions which are described by first order kinetics. Within a self-consistent approach we explicitly determine the steady state product and reactant number density fields around the colloid as functionals of the interaction potentials of the various molecular species in solution with the colloid. By using a reciprocal theorem, this allows us to compute and to interpret—in a transparent way in terms of the classical Smoluchowski theory of chemical kinetics—the external force needed to keep such a catalytically active colloid at rest (stall force) or, equivalently, the corresponding velocity of the colloid if it is free to move. We use the particular case of triangular-well interaction potentials as a benchmark example for applying the general theoretical framework developed here. For this latter case, we derive explicit expressions for the dependences of the quantities of interest on the diffusion coefficients of the chemical species, the reaction rate constant, the coverage by catalyst, the size of the colloid, as well as on the parameters of the interaction potentials. These expressions provide a detailed picture of the phenomenology associated with catalytically-active colloids and self-diffusiophoresis.

Electromagnetic fields and potentials generated by massless charged particles

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

Azzurli, Francesco, E-mail: francesco.azzurli@gmail.com; Lechner, Kurt, E-mail: lechner@pd.infn.it; INFN, Sezione di Padova, Via F. Marzolo, 8, 35131 Padova

2014-10-15

We provide for the first time the exact solution of Maxwell’s equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard–Wiechert field the electromagnetic field acquires singular δ-like contributions whose support and dimensionality depend crucially on whether the motion is (a) linear, (b) accelerated unbounded, (c) accelerated bounded. In the first two cases the particle generates amore » planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string. - Highlights: • First exact solution of Maxwell’s equations for massless charges in arbitrary motion. • Explicit expressions of electromagnetic fields and potentials. • Derivations are rigorous and based on distribution theory. • The form of the field depends heavily on whether the motion is bounded or unbounded. • The electromagnetic field contains unexpected Dirac-delta-function contributions.« less

Evaluation of risk assessment guideline levels for the chemical warfare agents mustard, GB, and VX.

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

Hartmann, H.; Environmental Assessment

2002-06-01

The U.S. Army has estimated acute lethality guideline levels for inhalation of the chemical warfare agents mustard, GB, and VX. These levels are expressed as dosages measured in milligram-minutes per cubic meter (mg-min/m3). The National Advisory Council has also proposed acute emergency guideline levels (AEGLs) for the agents. The AEGLs are threshold exposure limits for the general public for mild effects, serious adverse effects, and lethality. They are expressed as air concentrations (in units of mg/m3) and are applicable to emergency exposure periods ranging from 10 min to 8 h. The report discusses strengths and deficiencies in the levels, importantmore » parameters (i.e., exposure time, breathing rate) that need to be explicitly addressed in deriving the guideline levels, and possible impacts that could result from using AEGLs instead of guideline dosages in future assessments.« less

Two-body loss rates for reactive collisions of cold atoms

NASA Astrophysics Data System (ADS)

Cop, C.; Walser, R.

2018-01-01

We present an effective two-channel model for reactive collisions of cold atoms. It augments elastic molecular channels with an irreversible, inelastic loss channel. Scattering is studied with the distorted-wave Born approximation and yields general expressions for angular momentum resolved cross sections as well as two-body loss rates. Explicit expressions are obtained for piecewise constant potentials. A pole expansion reveals simple universal shape functions for cross sections and two-body loss rates in agreement with the Wigner threshold laws. This is applied to collisions of metastable 20Ne and 21Ne atoms, which decay primarily through exothermic Penning or associative ionization processes. From a numerical solution of the multichannel Schrödinger equation using the best currently available molecular potentials, we have obtained synthetic scattering data. Using the two-body loss shape functions derived in this paper, we can match these scattering data very well.

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

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

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.

Higgs decay into two photons in a warped extra dimension

NASA Astrophysics Data System (ADS)

Hahn, Juliane; Hörner, Clara; Malm, Raoul; Neubert, Matthias; Novotny, Kristiane; Schmell, Christoph

2014-05-01

A detailed five-dimensional calculation of the Higgs-boson decay into two photons is performed in both the minimal and the custodially protected Randall-Sundrum (RS) model, where the Standard Model (SM) fields propagate in the bulk and the scalar sector lives on or near the IR brane. It is explicitly shown that the gauge invariance of the sum of diagrams involving bosonic fields in the SM also applies to the case of these RS scenarios. An exact expression for the amplitude in terms of the five-dimensional (5D) gauge-boson and fermion propagators is presented, which includes the full dependence on the Higgs-boson mass. Closed expressions for the 5D -boson propagators in the minimal and the custodial RS model are derived, which are valid to all orders in . In contrast to the fermion case, the result for the bosonic contributions to the amplitude is insensitive to the details of the localization of the Higgs profile on or near the IR brane. The various RS predictions for the rate of the process are compared with the latest LHC data, and exclusion regions for the RS model parameters are derived.

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

PubMed

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

2000-07-01

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

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

PubMed

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

2012-09-01

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

Continuum Fatigue Damage Modeling for Use in Life Extending Control

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.

1994-01-01

This paper develops a simplified continuum (continuous wrp to time, stress, etc.) fatigue damage model for use in Life Extending Controls (LEC) studies. The work is based on zero mean stress local strain cyclic damage modeling. New nonlinear explicit equation forms of cyclic damage in terms of stress amplitude are derived to facilitate the continuum modeling. Stress based continuum models are derived. Extension to plastic strain-strain rate models are also presented. Application of these models to LEC applications is considered. Progress toward a nonzero mean stress based continuum model is presented. Also, new nonlinear explicit equation forms in terms of stress amplitude are also derived for this case.

Calibration of piezoelectric RL shunts with explicit residual mode correction

NASA Astrophysics Data System (ADS)

Høgsberg, Jan; Krenk, Steen

2017-01-01

Piezoelectric RL (resistive-inductive) shunts are passive resonant devices used for damping of dominant vibration modes of a flexible structure and their efficiency relies on the precise calibration of the shunt components. In the present paper improved calibration accuracy is attained by an extension of the local piezoelectric transducer displacement by two additional terms, representing the flexibility and inertia contributions from the residual vibration modes not directly addressed by the shunt damping. This results in an augmented dynamic model for the targeted resonant vibration mode, in which the residual contributions, represented by two correction factors, modify both the apparent transducer capacitance and the shunt circuit impedance. Explicit expressions for the correction of the shunt circuit inductance and resistance are presented in a form that is generally applicable to calibration formulae derived on the basis of an assumed single-mode structure, where modal interaction has been neglected. A design procedure is devised and subsequently verified by a numerical example, which demonstrates that effective mitigation can be obtained for an arbitrary vibration mode when the residual mode correction is included in the calibration of the RL shunt.

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

NASA Technical Reports Server (NTRS)

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

2017-01-01

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

An explicit asymptotic model for the surface wave in a viscoelastic half-space based on applying Rabotnov's fractional exponential integral operators

NASA Astrophysics Data System (ADS)

Wilde, M. V.; Sergeeva, N. V.

2018-05-01

An explicit asymptotic model extracting the contribution of a surface wave to the dynamic response of a viscoelastic half-space is derived. Fractional exponential Rabotnov's integral operators are used for describing of material properties. The model is derived by extracting the principal part of the poles corresponding to the surface waves after applying Laplace and Fourier transforms. The simplified equations for the originals are written by using power series expansions. Padè approximation is constructed to unite short-time and long-time models. The form of this approximation allows to formulate the explicit model using a fractional exponential Rabotnov's integral operator with parameters depending on the properties of surface wave. The applicability of derived models is studied by comparing with the exact solutions of a model problem. It is revealed that the model based on Padè approximation is highly effective for all the possible time domains.

Transformation of the optical vortex dipole by an astigmatic lens

NASA Astrophysics Data System (ADS)

Yan, Hongwei; Lü, Baida

2009-06-01

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

N-point functions in rolling tachyon background

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

Jokela, Niko; Keski-Vakkuri, Esko; Department of Physics, P.O. Box 64, FIN-00014, University of Helsinki

2009-04-15

We study n-point boundary correlation functions in timelike boundary Liouville theory, relevant for open string multiproduction by a decaying unstable D brane. We give an exact result for the one-point function of the tachyon vertex operator and show that it is consistent with a previously proposed relation to a conserved charge in string theory. We also discuss when the one-point amplitude vanishes. Using a straightforward perturbative expansion, we find an explicit expression for a tachyon n-point amplitude for all n, however the result is still a toy model. The calculation uses a new asymptotic approximation for Toeplitz determinants, derived bymore » relating the system to a Dyson gas at finite temperature.« less

A method for determining electrophoretic and electroosmotic mobilities using AC and DC electric field particle displacements.

PubMed

Oddy, M H; Santiago, J G

2004-01-01

We have developed a method for measuring the electrophoretic mobility of submicrometer, fluorescently labeled particles and the electroosmotic mobility of a microchannel. We derive explicit expressions for the unknown electrophoretic and the electroosmotic mobilities as a function of particle displacements resulting from alternating current (AC) and direct current (DC) applied electric fields. Images of particle displacements are captured using an epifluorescent microscope and a CCD camera. A custom image-processing code was developed to determine image streak lengths associated with AC measurements, and a custom particle tracking velocimetry (PTV) code was devised to determine DC particle displacements. Statistical analysis was applied to relate mobility estimates to measured particle displacement distributions.

Large D-2 theory of superconducting fluctuations in a magnetic field and its application to iron pnictides.

PubMed

Murray, James M; Tesanović, Zlatko

2010-07-16

A Ginzburg-Landau approach to fluctuations of a layered superconductor in a magnetic field is used to show that the interlayer coupling can be incorporated within an interacting self-consistent theory of a single layer, in the limit of a large number of neighboring layers. The theory exhibits two phase transitions-a vortex liquid-to-solid transition is followed by a Bose-Einstein condensation into the Abrikosov lattice-illustrating the essential role of interlayer coupling. By using this theory, explicit expressions for magnetization, specific heat, and fluctuation conductivity are derived. We compare our results with recent experimental data on the iron-pnictide superconductors.

Factorizable Upwind Schemes: The Triangular Unstructured Grid Formulation

NASA Technical Reports Server (NTRS)

Sidilkover, David; Nielsen, Eric J.

2001-01-01

The upwind factorizable schemes for the equations of fluid were introduced recently. They facilitate achieving the Textbook Multigrid Efficiency (TME) and are expected also to result in the solvers of unparalleled robustness. The approach itself is very general. Therefore, it may well become a general framework for the large-scale, Computational Fluid Dynamics. In this paper we outline the triangular grid formulation of the factorizable schemes. The derivation is based on the fact that the factorizable schemes can be expressed entirely using vector notation. without explicitly mentioning a particular coordinate frame. We, describe the resulting discrete scheme in detail and present some computational results verifying the basic properties of the scheme/solver.

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

PubMed

Mei, Chiang C; Jing, Haixiao

2016-10-01

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

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

Sinitsyn, N. A.

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

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

Unseren, M.A.

A rigid body model for the entire system which accounts for the load distribution scheme proposed in Part 1 as well as for the dynamics of the manipulators and the kinematic constraints is derived in the joint space. A technique is presented for expressing the object dynamics in terms of the joint variables of both manipulators which leads to a positive definite and symmetric inertia matrix. The model is then transformed to obtain reduced order equations of motion and a separate set of equations which govern the behavior of the internal contact forces. The control architecture is applied to themore » model which results in the explicit decoupling of the position and internal contact force-controlled degrees of freedom (DOF).« less

Dissipation in a rotating frame: Master equation, effective temperature, and Lamb shift

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

Verso, Alvise; Ankerhold, Joachim

Motivated by recent realizations of microwave-driven nonlinear resonators in superconducting circuits, the impact of environmental degrees of freedom is analyzed as seen from a rotating frame. A system plus reservoir model is applied to consistently derive in the weak coupling limit the master equation for the reduced density in the moving frame and near the first bifurcation threshold. The concept of an effective temperature is introduced to analyze to what extent a detailed balance relation exists. Explicit expressions are also found for the Lamb-shift. Results for ohmic baths are in agreement with experimental findings, while for structured environments population inversionmore » is predicted that may qualitatively explain recent observations.« less

Vector solution for the mean electromagnetic fields in a layer of random particles

NASA Technical Reports Server (NTRS)

Lang, R. H.; Seker, S. S.; Levine, D. M.

1986-01-01

The mean electromagnetic fields are found in a layer of randomly oriented particles lying over a half space. A matrix-dyadic formulation of Maxwell's equations is employed in conjunction with the Foldy-Lax approximation to obtain equations for the mean fields. A two variable perturbation procedure, valid in the limit of small fractional volume, is then used to derive uncoupled equations for the slowly varying amplitudes of the mean wave. These equations are solved to obtain explicit expressions for the mean electromagnetic fields in the slab region in the general case of arbitrarily oriented particles and arbitrary polarization of the incident radiation. Numerical examples are given for the application to remote sensing of vegetation.

Foraging swarms as Nash equilibria of dynamic games.

PubMed

Özgüler, Arif Bülent; Yildiz, Aykut

2014-06-01

The question of whether foraging swarms can form as a result of a noncooperative game played by individuals is shown here to have an affirmative answer. A dynamic game played by N agents in 1-D motion is introduced and models, for instance, a foraging ant colony. Each agent controls its velocity to minimize its total work done in a finite time interval. The game is shown to have a unique Nash equilibrium under two different foraging location specifications, and both equilibria display many features of a foraging swarm behavior observed in biological swarms. Explicit expressions are derived for pairwise distances between individuals of the swarm, swarm size, and swarm center location during foraging.

Berry phase and Hannay angle of an interacting boson system

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

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

2011-04-15

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

Target detection using microwave irradiances from natural sources: A passive, local and global surveillance system

NASA Technical Reports Server (NTRS)

Stacey, J. M.

1984-01-01

Detection of metal objects on or near the Earth's surface was investigated using existing, passive, microwave sensors operating from Earth orbit. The range equations are derived from basic microwave principles and theories and the expressions are given explicitly to estimate the signal to noise ratio for detecting metal targets operating as bistatic scatterers. Actual measurements are made on a range of metal objects observed from orbit using existing passive microwave receiving systems. The details of the measurements and the results are tabulated and discussed. The advantages of a passive microwave sensor as it is applied to surveillance of metal objects as viewed from aerial platforms or from orbit, are examined.

Integrands for QCD rational terms and {N} = {4} SYM from massive CSW rules

NASA Astrophysics Data System (ADS)

Elvang, Henriette; Freedman, Daniel Z.; Kiermaier, Michael

2012-06-01

We use massive CSW rules to derive explicit compact expressions for integrands of rational terms in QCD with any number of external legs. Specifically, we present all- n integrands for the one-loop all-plus and one-minus gluon amplitudes in QCD. We extract the finite part of spurious external-bubble contributions systematically; this is crucial for the application of integrand-level CSW rules in theories without supersymmetry. Our approach yields integrands that are independent of the choice of CSW reference spinor even before integration. Furthermore, we present a recursive derivation of the recently proposed massive CSW-style vertex expansion for massive tree amplitudes and loop integrands on the Coulomb-branch of {N} = {4} SYM. The derivation requires a careful study of boundary terms in all-line shift recursion relations, and provides a rigorous (albeit indirect) proof of the recently proposed construction of massive amplitudes from soft-limits of massless on-shell amplitudes. We show that the massive vertex expansion manifestly preserves all holomorphic and half of the anti-holomorphic supercharges, diagram-by-diagram, even off-shell.

Multipole expansions and Fock symmetry of the hydrogen atom

NASA Astrophysics Data System (ADS)

Meremianin, A. V.; Rost, J.-M.

2006-10-01

The main difficulty in utilizing the O(4) symmetry of the hydrogen atom in practical calculations is the dependence of the Fock stereographic projection on energy. This is due to the fact that the wavefunctions of the states with different energies are proportional to the hyperspherical harmonics (HSH) corresponding to different points on the hypersphere. Thus, the calculation of the matrix elements reduces to the problem of re-expanding HSH in terms of HSH depending on different points on the hypersphere. We solve this problem by applying the technique of multipole expansions for four-dimensional HSH. As a result, we obtain the multipole expansions whose coefficients are the matrix elements of the boost operator taken between hydrogen wavefunctions (i.e., hydrogen form factors). The explicit expressions for those coefficients are derived. It is shown that the hydrogen matrix elements can be presented as derivatives of an elementary function. Such an operator representation is convenient for the derivation of recurrence relations connecting matrix elements between states corresponding to different values of the quantum numbers n and l.

Generalised Transfer Functions of Neural Networks

NASA Astrophysics Data System (ADS)

Fung, C. F.; Billings, S. A.; Zhang, H.

1997-11-01

When artificial neural networks are used to model non-linear dynamical systems, the system structure which can be extremely useful for analysis and design, is buried within the network architecture. In this paper, explicit expressions for the frequency response or generalised transfer functions of both feedforward and recurrent neural networks are derived in terms of the network weights. The derivation of the algorithm is established on the basis of the Taylor series expansion of the activation functions used in a particular neural network. This leads to a representation which is equivalent to the non-linear recursive polynomial model and enables the derivation of the transfer functions to be based on the harmonic expansion method. By mapping the neural network into the frequency domain information about the structure of the underlying non-linear system can be recovered. Numerical examples are included to demonstrate the application of the new algorithm. These examples show that the frequency response functions appear to be highly sensitive to the network topology and training, and that the time domain properties fail to reveal deficiencies in the trained network structure.

Non-classical and potential symmetry analysis of Richard's equation for moisture flow in soil

NASA Astrophysics Data System (ADS)

Wiltshire, Ron; El-Kafri, Manal

2004-01-01

This paper focuses upon the derivation of the non-classical symmetries of Bluman and Cole as they apply to Richard's equation for water flow in an unsaturated uniform soil. It is shown that the determining equations for the non-classical case lead to four highly non-linear equations which have been solved in five particular cases. In each case the corresponding similarity ansatz has been derived and Richard's equation is reduced to an ordinary differential equation. Explicit solutions are produced when possible. Richard's equation is also expressed as a potential system and in reviewing the classical Lie solutions a new symmetry is derived together with its similarity ansatz. Determining equations are then produced for the potential system using the non-classical algorithm. This results in an under-determined set of equations and an example symmetry that reveals a missing classical case is presented. An example of a classical and a non-classical symmetry reduction applied to the infiltration of moisture in soil is presented. The condition for surface invariance is used to demonstrate the equivalence of a classical Lie and a potential symmetry.

Semantic Interference and Facilitation: Understanding the Integration of Spatial Distance and Conceptual Similarity During Sentence Reading.

PubMed

Guerra, Ernesto; Knoeferle, Pia

2018-01-01

Existing evidence has shown a processing advantage (or facilitation) when representations derived from a non-linguistic context (spatial proximity depicted by gambling cards moving together) match the semantic content of an ensuing sentence. A match, inspired by conceptual metaphors such as 'similarity is closeness' would, for instance, involve cards moving closer together and the sentence relates similarity between abstract concepts such as war and battle. However, other studies have reported a disadvantage (or interference) for congruence between the semantic content of a sentence and representations of spatial distance derived from this sort of non-linguistic context. In the present article, we investigate the cognitive mechanisms underlying the interaction between the representations of spatial distance and sentence processing. In two eye-tracking experiments, we tested the predictions of a mechanism that considers the competition, activation, and decay of visually and linguistically derived representations as key aspects in determining the qualitative pattern and time course of that interaction. Critical trials presented two playing cards, each showing a written abstract noun; the cards turned around, obscuring the nouns, and moved either farther apart or closer together. Participants then read a sentence expressing either semantic similarity or difference between these two nouns. When instructed to attend to the nouns on the cards (Experiment 1), participants' total reading times revealed interference between spatial distance (e.g., closeness) and semantic relations (similarity) as soon as the sentence explicitly conveyed similarity. But when instructed to attend to the cards (Experiment 2), cards approaching (vs. moving apart) elicited first interference (when similarity was implicit) and then facilitation (when similarity was made explicit) during sentence reading. We discuss these findings in the context of a competition mechanism of interference and facilitation effects.

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

PubMed

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

2013-02-01

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

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

PubMed

Cammi, R

2009-10-28

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

A constitutive rheological model for agglomerating blood derived from nonequilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Tsimouri, Ioanna Ch.; Stephanou, Pavlos S.; Mavrantzas, Vlasis G.

2018-03-01

Red blood cells tend to aggregate in the presence of plasma proteins, forming structures known as rouleaux. Here, we derive a constitutive rheological model for human blood which accounts for the formation and dissociation of rouleaux using the generalized bracket formulation of nonequilibrium thermodynamics. Similar to the model derived by Owens and co-workers ["A non-homogeneous constitutive model for human blood. Part 1. Model derivation and steady flow," J. Fluid Mech. 617, 327-354 (2008)] through polymer network theory, each rouleau in our model is represented as a dumbbell; the corresponding structural variable is the conformation tensor of the dumbbell. The kinetics of rouleau formation and dissociation is treated as in the work of Germann et al. ["Nonequilibrium thermodynamic modeling of the structure and rheology of concentrated wormlike micellar solutions," J. Non-Newton. Fluid Mech. 196, 51-57 (2013)] by assuming a set of reversible reactions, each characterized by a forward and a reverse rate constant. The final set of evolution equations for the microstructure of each rouleau and the expression for the stress tensor turn out to be very similar to those of Owens and co-workers. However, by explicitly considering a mechanism for the formation and breakage of rouleaux, our model further provides expressions for the aggregation and disaggregation rates appearing in the final transport equations, which in the kinetic theory-based network model of Owens were absent and had to be specified separately. Despite this, the two models are found to provide similar descriptions of experimental data on the size distribution of rouleaux.

Environmental Media Phase-Tracking Units in the Classroom

ERIC Educational Resources Information Center

Langseth, David E.

2009-01-01

When teaching phase partitioning concepts for solutes in porous media, and other multi-phase environmental systems, explicitly tracking the environmental media phase with which a substance of interest (S0I) is associated can enhance the students' understanding of the fundamental concepts and derivations. It is common to explicitly track the…

Unruh effect for general trajectories

NASA Astrophysics Data System (ADS)

Obadia, N.; Milgrom, M.

2007-03-01

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

Statistical Mechanical Model for Adsorption Coupled with SAFT-VR Mie Equation of State.

PubMed

Franco, Luís F M; Economou, Ioannis G; Castier, Marcelo

2017-10-24

We extend the SAFT-VR Mie equation of state to calculate adsorption isotherms by considering explicitly the residual energy due to the confinement effect. Assuming a square-well potential for the fluid-solid interactions, the structure imposed by the fluid-solid interface is calculated using two different approaches: an empirical expression proposed by Travalloni et al. ( Chem. Eng. Sci. 65 , 3088 - 3099 , 2010 ), and a new theoretical expression derived by applying the mean value theorem. Adopting the SAFT-VR Mie ( Lafitte et al. J. Chem. Phys. , 139 , 154504 , 2013 ) equation of state to describe the fluid-fluid interactions, and solving the phase equilibrium criteria, we calculate adsorption isotherms for light hydrocarbons adsorbed in a carbon molecular sieve and for carbon dioxide, nitrogen, and water adsorbed in a zeolite. Good results are obtained from the model using either approach. Nonetheless, the theoretical expression seems to correlate better the experimental data than the empirical one, possibly implying that a more reliable way to describe the structure ensures a better description of the thermodynamic behavior.

A Bayesian Surrogate for Regional Skew in Flood Frequency Analysis

NASA Astrophysics Data System (ADS)

Kuczera, George

1983-06-01

The problem of how to best utilize site and regional flood data to infer the shape parameter of a flood distribution is considered. One approach to this problem is given in Bulletin 17B of the U.S. Water Resources Council (1981) for the log-Pearson distribution. Here a lesser known distribution is considered, namely, the power normal which fits flood data as well as the log-Pearson and has a shape parameter denoted by λ derived from a Box-Cox power transformation. The problem of regionalizing λ is considered from an empirical Bayes perspective where site and regional flood data are used to infer λ. The distortive effects of spatial correlation and heterogeneity of site sampling variance of λ are explicitly studied with spatial correlation being found to be of secondary importance. The end product of this analysis is the posterior distribution of the power normal parameters expressing, in probabilistic terms, what is known about the parameters given site flood data and regional information on λ. This distribution can be used to provide the designer with several types of information. The posterior distribution of the T-year flood is derived. The effect of nonlinearity in λ on inference is illustrated. Because uncertainty in λ is explicitly allowed for, the understatement in confidence limits due to fixing λ (analogous to fixing log skew) is avoided. Finally, it is shown how to obtain the marginal flood distribution which can be used to select a design flood with specified exceedance probability.

Frequency domain analysis of noise in simple gene circuits

NASA Astrophysics Data System (ADS)

Cox, Chris D.; McCollum, James M.; Austin, Derek W.; Allen, Michael S.; Dar, Roy D.; Simpson, Michael L.

2006-06-01

Recent advances in single cell methods have spurred progress in quantifying and analyzing stochastic fluctuations, or noise, in genetic networks. Many of these studies have focused on identifying the sources of noise and quantifying its magnitude, and at the same time, paying less attention to the frequency content of the noise. We have developed a frequency domain approach to extract the information contained in the frequency content of the noise. In this article we review our work in this area and extend it to explicitly consider sources of extrinsic and intrinsic noise. First we review applications of the frequency domain approach to several simple circuits, including a constitutively expressed gene, a gene regulated by transitions in its operator state, and a negatively autoregulated gene. We then review our recent experimental study, in which time-lapse microscopy was used to measure noise in the expression of green fluorescent protein in individual cells. The results demonstrate how changes in rate constants within the gene circuit are reflected in the spectral content of the noise in a manner consistent with the predictions derived through frequency domain analysis. The experimental results confirm our earlier theoretical prediction that negative autoregulation not only reduces the magnitude of the noise but shifts its content out to higher frequency. Finally, we develop a frequency domain model of gene expression that explicitly accounts for extrinsic noise at the transcriptional and translational levels. We apply the model to interpret a shift in the autocorrelation function of green fluorescent protein induced by perturbations of the translational process as a shift in the frequency spectrum of extrinsic noise and a decrease in its weighting relative to intrinsic noise.

Characterizing Thematized Derivative Schema by the Underlying Emergent Structures

ERIC Educational Resources Information Center

Garcia, Mercedes; Llinares, Salvador; Sanchez-Matamoros, Gloria

2011-01-01

This paper reports on different underlying structures of the derivative schema of three undergraduate students that were considered to be at the trans level of development of the derivative schema (action-process-object-schema). The derivative schema is characterized in terms of the students' ability to explicitly transfer the relationship between…

COFFDROP: A Coarse-Grained Nonbonded Force Field for Proteins Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of Amino Acids.

PubMed

Andrews, Casey T; Elcock, Adrian H

2014-11-11

We describe the derivation of a set of bonded and nonbonded coarse-grained (CG) potential functions for use in implicit-solvent Brownian dynamics (BD) simulations of proteins derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acids. Bonded potential functions were derived from 1 μs MD simulations of each of the 20 canonical amino acids, with histidine modeled in both its protonated and neutral forms; nonbonded potential functions were derived from 1 μs MD simulations of every possible pairing of the amino acids (231 different systems). The angle and dihedral probability distributions and radial distribution functions sampled during MD were used to optimize a set of CG potential functions through use of the iterative Boltzmann inversion (IBI) method. The optimized set of potential functions-which we term COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins)-quantitatively reproduced all of the "target" MD distributions. In a first test of the force field, it was used to predict the clustering behavior of concentrated amino acid solutions; the predictions were directly compared with the results of corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. In a second test, BD simulations of the small protein villin headpiece were carried out at concentrations that have recently been studied in all-atom explicit-solvent MD simulations by Petrov and Zagrovic ( PLoS Comput. Biol. 2014 , 5 , e1003638). The anomalously strong intermolecular interactions seen in the MD study were reproduced in the COFFDROP simulations; a simple scaling of COFFDROP's nonbonded parameters, however, produced results in better accordance with experiment. Overall, our results suggest that potential functions derived from simulations of pairwise amino acid interactions might be of quite broad applicability, with COFFDROP likely to be especially useful for modeling unfolded or intrinsically disordered proteins.

COFFDROP: A Coarse-Grained Nonbonded Force Field for Proteins Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of Amino Acids

PubMed Central

2015-01-01

We describe the derivation of a set of bonded and nonbonded coarse-grained (CG) potential functions for use in implicit-solvent Brownian dynamics (BD) simulations of proteins derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acids. Bonded potential functions were derived from 1 μs MD simulations of each of the 20 canonical amino acids, with histidine modeled in both its protonated and neutral forms; nonbonded potential functions were derived from 1 μs MD simulations of every possible pairing of the amino acids (231 different systems). The angle and dihedral probability distributions and radial distribution functions sampled during MD were used to optimize a set of CG potential functions through use of the iterative Boltzmann inversion (IBI) method. The optimized set of potential functions—which we term COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins)—quantitatively reproduced all of the “target” MD distributions. In a first test of the force field, it was used to predict the clustering behavior of concentrated amino acid solutions; the predictions were directly compared with the results of corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. In a second test, BD simulations of the small protein villin headpiece were carried out at concentrations that have recently been studied in all-atom explicit-solvent MD simulations by Petrov and Zagrovic (PLoS Comput. Biol.2014, 5, e1003638). The anomalously strong intermolecular interactions seen in the MD study were reproduced in the COFFDROP simulations; a simple scaling of COFFDROP’s nonbonded parameters, however, produced results in better accordance with experiment. Overall, our results suggest that potential functions derived from simulations of pairwise amino acid interactions might be of quite broad applicability, with COFFDROP likely to be especially useful for modeling unfolded or intrinsically disordered proteins. PMID:25400526

Pairing fluctuations and the superfluid density through the BCS-BEC crossover

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

Taylor, E.; Griffin, A.; Fukushima, N.

2006-12-15

We derive an expression for the superfluid density of a uniform two-component Fermi gas through the BCS-BEC crossover in terms of the thermodynamic potential in the presence of an imposed superfluid flow. Treating the pairing fluctuations in a Gaussian approximation following the approach of Nozieres and Schmitt-Rink, we use this definition of {rho}{sub s} to obtain an explicit result which is valid at finite temperatures and over the full BCS-BEC crossover. It is crucial that the BCS gap {delta}, the chemical potential {mu}, and {rho}{sub s} all include the effect of fluctuations at the same level in a self-consistent manner.more » We show that the normal fluid density {rho}{sub n}{identical_to}n-{rho}{sub s} naturally separates into a sum of contributions from Fermi BCS quasiparticles ({rho}{sub n}{sup F}) and Bose collective modes ({rho}{sub n}{sup B}). The expression for {rho}{sub n}{sup F} is just Landau's formula for a BCS Fermi superfluid but now calculated over the BCS-BEC crossover. The expression for the Bose contribution {rho}{sub n}{sup B} is more complicated and only reduces to Landau's formula for a Bose superfluid in the extreme BEC limit, where all the fermions have formed stable Bose pairs and the Bogoliubov excitations of the associated molecular Bose condensate are undamped. In a companion paper, we present numerical calculations of {rho}{sub s} using an expression equivalent to the one derived in this paper, over the BCS-BEC crossover, including unitarity, and at finite temperatures.« less

Efficient summary statistical representation when change localization fails.

PubMed

Haberman, Jason; Whitney, David

2011-10-01

People are sensitive to the summary statistics of the visual world (e.g., average orientation/speed/facial expression). We readily derive this information from complex scenes, often without explicit awareness. Given the fundamental and ubiquitous nature of summary statistical representation, we tested whether this kind of information is subject to the attentional constraints imposed by change blindness. We show that information regarding the summary statistics of a scene is available despite limited conscious access. In a novel experiment, we found that while observers can suffer from change blindness (i.e., not localize where change occurred between two views of the same scene), observers could nevertheless accurately report changes in the summary statistics (or "gist") about the very same scene. In the experiment, observers saw two successively presented sets of 16 faces that varied in expression. Four of the faces in the first set changed from one emotional extreme (e.g., happy) to another (e.g., sad) in the second set. Observers performed poorly when asked to locate any of the faces that changed (change blindness). However, when asked about the ensemble (which set was happier, on average), observer performance remained high. Observers were sensitive to the average expression even when they failed to localize any specific object change. That is, even when observers could not locate the very faces driving the change in average expression between the two sets, they nonetheless derived a precise ensemble representation. Thus, the visual system may be optimized to process summary statistics in an efficient manner, allowing it to operate despite minimal conscious access to the information presented.

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

PubMed

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

2015-01-01

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

On explicit algebraic stress models for complex turbulent flows

NASA Technical Reports Server (NTRS)

Gatski, T. B.; Speziale, C. G.

1992-01-01

Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

The explicit form of the rate function for semi-Markov processes and its contractions

NASA Astrophysics Data System (ADS)

Sughiyama, Yuki; Kobayashi, Testuya J.

2018-03-01

We derive the explicit form of the rate function for semi-Markov processes. Here, the ‘random time change trick’ plays an essential role. Also, by exploiting the contraction principle of large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the level 2.5 rate function for Markov processes to semi-Markov cases.

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

PubMed

Christoforou, Paraskevi S; Ashforth, Blake E

2015-01-01

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

Deriving an explicit hepatic clearance equation accounting for plasma protein binding and hepatocellular uptake.

PubMed

Yoon, Miyoung; Clewell, Harvey J; Andersen, Melvin E

2013-02-01

High throughput in vitro biochemical and cell-based assays have the promise to provide more mechanism-based assessments of the adverse effects of large numbers of chemicals. One of the most challenging hurdles for interpreting in vitro toxicity findings is the need for reverse dosimetry tools that estimate the exposures that will give concentrations in vivo similar to the active concentrations in vitro. Recent experience using IVIVE approaches to estimate in vivo pharmacokinetics (Wetmore et al., 2012) identified the need to develop a hepatic clearance equation that explicitly accounted for a broader set of protein binding and membrane transport processes and did not depend on a well-mixed description of the liver compartment. Here we derive an explicit steady-state hepatic clearance equation that includes these factors. In addition to the derivation, we provide simple computer code to calculate steady-state extraction for any combination of blood flow, membrane transport processes and plasma protein-chemical binding rates. This expanded equation provides a tool to estimate hepatic clearance for a more diverse array of compounds. Copyright © 2012 Elsevier Ltd. All rights reserved.

A finite parallel zone model to interpret and extend Giddings' coupling theory for the eddy-dispersion in porous chromatographic media.

PubMed

Desmet, Gert

2013-11-01

The finite length parallel zone (FPZ)-model is proposed as an alternative model for the axial- or eddy-dispersion caused by the occurrence of local velocity biases or flow heterogeneities in porous media such as those used in liquid chromatography columns. The mathematical plate height expression evolving from the model shows that the A- and C-term band broadening effects that can originate from a given velocity bias should be coupled in an exponentially decaying way instead of harmonically as proposed in Giddings' coupling theory. In the low and high velocity limit both models converge, while a 12% difference can be observed in the (practically most relevant) intermediate range of reduced velocities. Explicit expressions for the A- and C-constants appearing in the exponential decay-based plate height expression have been derived for each of the different possible velocity bias levels (single through-pore and particle level, multi-particle level and trans-column level). These expressions allow to directly relate the band broadening originating from these different levels to the local fundamental transport parameters, hence offering the possibility to include a velocity-dependent and, if, needed retention factor-dependent transversal dispersion coefficient. Having developed the mathematics for the general case wherein a difference in retention equilibrium establishes between the two parallel zones, the effect of any possible local variations in packing density and/or retention capacity on the eddy-dispersion can be explicitly accounted for as well. It is furthermore also shown that, whereas the lumped transport parameter model used in the basic variant of the FPZ-model only provides a first approximation of the true decay constant, the model can be extended by introducing a constant correction factor to correctly account for the continuous transversal dispersion transport in the velocity bias zones. Copyright © 2013 Elsevier B.V. All rights reserved.

An exergy approach to efficiency evaluation of desalination

NASA Astrophysics Data System (ADS)

Ng, Kim Choon; Shahzad, Muhammad Wakil; Son, Hyuk Soo; Hamed, Osman A.

2017-05-01

This paper presents an evaluation process efficiency based on the consumption of primary energy for all types of practical desalination methods available hitherto. The conventional performance ratio has, thus far, been defined with respect to the consumption of derived energy, such as the electricity or steam, which are susceptible to the conversion losses of power plants and boilers that burned the input primary fuels. As derived energies are usually expressed by the units, either kWh or Joules, these units cannot differentiate the grade of energy supplied to the processes accurately. In this paper, the specific energy consumption is revisited for the efficacy of all large-scale desalination plants. In today's combined production of electricity and desalinated water, accomplished with advanced cogeneration concept, the input exergy of fuels is utilized optimally and efficiently in a temperature cascaded manner. By discerning the exergy destruction successively in the turbines and desalination processes, the relative contribution of primary energy to the processes can be accurately apportioned to the input primary energy. Although efficiency is not a law of thermodynamics, however, a common platform for expressing the figures of merit explicit to the efficacy of desalination processes can be developed meaningfully that has the thermodynamic rigor up to the ideal or thermodynamic limit of seawater desalination for all scientists and engineers to aspire to.

A kinetic model for heterogeneous condensation of vapor on an insoluble spherical particle.

PubMed

Luo, Xisheng; Fan, Yu; Qin, Fenghua; Gui, Huaqiao; Liu, Jianguo

2014-01-14

A kinetic model is developed to describe the heterogeneous condensation of vapor on an insoluble spherical particle. This new model considers two mechanisms of cluster growth: direct addition of water molecules from the vapor and surface diffusion of adsorbed water molecules on the particle. The effect of line tension is also included in the model. For the first time, the exact expression of evaporation coefficient is derived for heterogeneous condensation of vapor on an insoluble spherical particle by using the detailed balance. The obtained expression of evaporation coefficient is proved to be also correct in the homogeneous condensation and the heterogeneous condensation on a planar solid surface. The contributions of the two mechanisms to heterogeneous condensation including the effect of line tension are evaluated and analysed. It is found that the cluster growth via surface diffusion of adsorbed water molecules on the particle is more important than the direct addition from the vapor. As an example of our model applications, the growth rate of the cap shaped droplet on the insoluble spherical particle is derived. Our evaluation shows that the growth rate of droplet in heterogeneous condensation is larger than that in homogeneous condensation. These results indicate that an explicit kinetic model is benefit to the study of heterogeneous condensation on an insoluble spherical particle.

Cross-section fluctuations in chaotic scattering systems.

PubMed

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

2016-10-01

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

Phase transition and thermodynamic geometry of f (R ) AdS black holes in the grand canonical ensemble

NASA Astrophysics Data System (ADS)

Li, Gu-Qiang; Mo, Jie-Xiong

2016-06-01

The phase transition of a four-dimensional charged AdS black hole solution in the R +f (R ) gravity with constant curvature is investigated in the grand canonical ensemble, where we find novel characteristics quite different from that in the canonical ensemble. There exists no critical point for T -S curve while in former research critical point was found for both the T -S curve and T -r+ curve when the electric charge of f (R ) black holes is kept fixed. Moreover, we derive the explicit expression for the specific heat, the analog of volume expansion coefficient and isothermal compressibility coefficient when the electric potential of f (R ) AdS black hole is fixed. The specific heat CΦ encounters a divergence when 0 <Φ b . This finding also differs from the result in the canonical ensemble, where there may be two, one or no divergence points for the specific heat CQ . To examine the phase structure newly found in the grand canonical ensemble, we appeal to the well-known thermodynamic geometry tools and derive the analytic expressions for both the Weinhold scalar curvature and Ruppeiner scalar curvature. It is shown that they diverge exactly where the specific heat CΦ diverges.