Structural Reliability Analysis and Optimization: Use of Approximations

NASA Technical Reports Server (NTRS)

Grandhi, Ramana V.; Wang, Liping

1999-01-01

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.

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.

A continued fraction resummation form of bath relaxation effect in the spin-boson model

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

Gong, Zhihao; Tang, Zhoufei; Wu, Jianlan, E-mail: jianlanwu@zju.edu.cn

2015-02-28

In the spin-boson model, a continued fraction form is proposed to systematically resum high-order quantum kinetic expansion (QKE) rate kernels, accounting for the bath relaxation effect beyond the second-order perturbation. In particular, the analytical expression of the sixth-order QKE rate kernel is derived for resummation. With higher-order correction terms systematically extracted from higher-order rate kernels, the resummed quantum kinetic expansion approach in the continued fraction form extends the Pade approximation and can fully recover the exact quantum dynamics as the expansion order increases.

Dynamics of Nonlinear Excitation of the High-Order Mode in a Single-Mode Step-Index Optical Fiber

NASA Astrophysics Data System (ADS)

Burdin, V.; Bourdine, A.

2018-04-01

This work is concerned with approximate model of higher-order mode nonlinear excitation in a singlemode silica optical fiber. We present some results of simulation for step-index optical fiber under femtosecond optical pulse launching, which confirm ability of relatively stable higher-order mode excitation in such singlemode optical fiber over sufficiently narrow range of launched optical power variation.

Spline function approximation techniques for image geometric distortion representation. [for registration of multitemporal remote sensor imagery

NASA Technical Reports Server (NTRS)

Anuta, P. E.

1975-01-01

Least squares approximation techniques were developed for use in computer aided correction of spatial image distortions for registration of multitemporal remote sensor imagery. Polynomials were first used to define image distortion over the entire two dimensional image space. Spline functions were then investigated to determine if the combination of lower order polynomials could approximate a higher order distortion with less computational difficulty. Algorithms for generating approximating functions were developed and applied to the description of image distortion in aircraft multispectral scanner imagery. Other applications of the techniques were suggested for earth resources data processing areas other than geometric distortion representation.

Construction of special eye models for investigation of chromatic and higher-order aberrations of eyes.

PubMed

Zhai, Yi; Wang, Yan; Wang, Zhaoqi; Liu, Yongji; Zhang, Lin; He, Yuanqing; Chang, Shengjiang

2014-01-01

An achromatic element eliminating only longitudinal chromatic aberration (LCA) while maintaining transverse chromatic aberration (TCA) is established for the eye model, which involves the angle formed by the visual and optical axis. To investigate the impacts of higher-order aberrations on vision, the actual data of higher-order aberrations of human eyes with three typical levels are introduced into the eye model along visual axis. Moreover, three kinds of individual eye models are established to investigate the impacts of higher-order aberrations, chromatic aberration (LCA+TCA), LCA and TCA on vision under the photopic condition, respectively. Results show that for most human eyes, the impact of chromatic aberration on vision is much stronger than that of higher-order aberrations, and the impact of LCA in chromatic aberration dominates. The impact of TCA is approximately equal to that of normal level higher-order aberrations and it can be ignored when LCA exists.

Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

PubMed

Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

2014-01-01

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

Accurate Estimate of Some Propagation Characteristics for the First Higher Order Mode in Graded Index Fiber with Simple Analytic Chebyshev Method

NASA Astrophysics Data System (ADS)

Dutta, Ivy; Chowdhury, Anirban Roy; Kumbhakar, Dharmadas

2013-03-01

Using Chebyshev power series approach, accurate description for the first higher order (LP11) mode of graded index fibers having three different profile shape functions are presented in this paper and applied to predict their propagation characteristics. These characteristics include fractional power guided through the core, excitation efficiency and Petermann I and II spot sizes with their approximate analytic formulations. We have shown that where two and three Chebyshev points in LP11 mode approximation present fairly accurate results, the values based on our calculations involving four Chebyshev points match excellently with available exact numerical results.

Kurtosis Approach Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation Keywords: Independent Component Analysis, Kurtosis, Higher order statistics.

Third-order dissipative hydrodynamics from the entropy principle

NASA Astrophysics Data System (ADS)

El, Andrej; Xu, Zhe; Greiner, Carsten

2010-06-01

We review the entropy based derivation of third-order hydrodynamic equations and compare their solutions in one-dimensional boost-invariant geometry with calculations by the partonic cascade BAMPS. We demonstrate that Grad's approximation, which underlies the derivation of both Israel-Stewart and third-order equations, describes the transverse spectra from BAMPS with high accuracy. At the same time solutions of third-order equations are much closer to BAMPS results than solutions of Israel-Stewart equations. Introducing a resummation scheme for all higher-oder corrections to one-dimensional hydrodynamic equation we demonstrate the importance of higher-order terms if the Knudsen number is large.

Variationally consistent approximation scheme for charge transfer

NASA Technical Reports Server (NTRS)

Halpern, A. M.

1978-01-01

The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groups of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximation to the amplitude.

Predicting synchrony in heterogeneous pulse coupled oscillators

NASA Astrophysics Data System (ADS)

Talathi, Sachin S.; Hwang, Dong-Uk; Miliotis, Abraham; Carney, Paul R.; Ditto, William L.

2009-08-01

Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically coupled neurons, we present a general theory that extends beyond the weak-coupling approximation, to account for higher-order PRC corrections in the derivation of an approximate discrete map, the stable fixed point of which can predict the domain of 1:1 phase locked synchronous states generated by the PCO network.

Higher-order kinetic expansion of quantum dissipative dynamics: mapping quantum networks to kinetic networks.

PubMed

Wu, Jianlan; Cao, Jianshu

2013-07-28

We apply a new formalism to derive the higher-order quantum kinetic expansion (QKE) for studying dissipative dynamics in a general quantum network coupled with an arbitrary thermal bath. The dynamics of system population is described by a time-convoluted kinetic equation, where the time-nonlocal rate kernel is systematically expanded of the order of off-diagonal elements of the system Hamiltonian. In the second order, the rate kernel recovers the expression of the noninteracting-blip approximation method. The higher-order corrections in the rate kernel account for the effects of the multi-site quantum coherence and the bath relaxation. In a quantum harmonic bath, the rate kernels of different orders are analytically derived. As demonstrated by four examples, the higher-order QKE can reliably predict quantum dissipative dynamics, comparing well with the hierarchic equation approach. More importantly, the higher-order rate kernels can distinguish and quantify distinct nontrivial quantum coherent effects, such as long-range energy transfer from quantum tunneling and quantum interference arising from the phase accumulation of interactions.

Nuclear magnetic resonance signal dynamics of liquids in the presence of distant dipolar fields, revisited

PubMed Central

Barros, Wilson; Gochberg, Daniel F.; Gore, John C.

2009-01-01

The description of the nuclear magnetic resonance magnetization dynamics in the presence of long-range dipolar interactions, which is based upon approximate solutions of Bloch–Torrey equations including the effect of a distant dipolar field, has been revisited. New experiments show that approximate analytic solutions have a broader regime of validity as well as dependencies on pulse-sequence parameters that seem to have been overlooked. In order to explain these experimental results, we developed a new method consisting of calculating the magnetization via an iterative formalism where both diffusion and distant dipolar field contributions are treated as integral operators incorporated into the Bloch–Torrey equations. The solution can be organized as a perturbative series, whereby access to higher order terms allows one to set better boundaries on validity regimes for analytic first-order approximations. Finally, the method legitimizes the use of simple analytic first-order approximations under less demanding experimental conditions, it predicts new pulse-sequence parameter dependencies for the range of validity, and clarifies weak points in previous calculations. PMID:19425789

Transformation of general binary MRF minimization to the first-order case.

PubMed

Ishikawa, Hiroshi

2011-06-01

We introduce a transformation of general higher-order Markov random field with binary labels into a first-order one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higher-order multi-label MRF energies that combines the new reduction with the fusion-move and QPBO algorithms. While many computer vision problems today are formulated as energy minimization problems, they have mostly been limited to using first-order energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higher-order interactions. Our algorithm challenges this restriction that limits the representational power of the models so that higher-order energies can be used to capture the rich statistics of natural scenes. We also show that some minimization methods can be considered special cases of the present framework, as well as comparing the new method experimentally with other such techniques.

Generalized Skyrme model with the loosely bound potential

NASA Astrophysics Data System (ADS)

Gudnason, Sven Bjarke; Zhang, Baiyang; Ma, Nana

2016-12-01

We study a generalization of the loosely bound Skyrme model which consists of the Skyrme model with a sixth-order derivative term—motivated by its fluidlike properties—and the second-order loosely bound potential—motivated by lowering the classical binding energies of higher-charged Skyrmions. We use the rational map approximation for the Skyrmion of topological charge B =4 , calculate the binding energy of the latter, and estimate the systematic error in using this approximation. In the parameter space that we can explore within the rational map approximation, we find classical binding energies as low as 1.8%, and once taking into account the contribution from spin-isospin quantization, we obtain binding energies as low as 5.3%. We also calculate the contribution from the sixth-order derivative term to the electric charge density and axial coupling.

Higher-order harmonics of limited diffraction Bessel beams

PubMed

Ding; Lu

2000-03-01

We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.

High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bryan A. (Technical Monitor)

2002-01-01

In this paper we derive fully-discrete Central WENO (CWENO) schemes for approximating solutions of one dimensional Hamilton-Jacobi (HJ) equations, which combine our previous works. We introduce third and fifth-order accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core ingredient is the derivation of our schemes is a high-order CWENO reconstructions in space.

The Epoch of Disk Formation: z is Approximately l to Today

NASA Technical Reports Server (NTRS)

Kassin, Susan; Gardner, Jonathan; Weiner, Ben; Faber, Sandra

2012-01-01

We present data on galaxy kinematics, morphologies, and star-formation rates over 0.1 less than z less than 1.2 for approximately 500 blue galaxies. These data show how systems like our own Milky-Way have come into being. At redshifts around 1, about half the age of the Universe ago, Milky-Way mass galaxies were different beasts than today. They had a significant amount of disturbed motions, disturbed morphologies, shallower potential wells, higher specific star-formation rates, and likely higher gas fractions. Since redshift approximately 1, galaxies have decreased in disturbed motions, increased in rotation velocity and potential well depth, become more well-ordered morphologically, and decreased in specific star-formation rate. We find interrelationships between these measurements. Galaxy kinematics are correlated with morphology and specific star-formation rate such that galaxies with the fastest rotation velocities and the least amounts of disturbed motions have the most well-ordered morphologies and the lowest specific star-formation rates. The converse is true. Moreover, we find that the rate at which galaxies become more well-ordered kinematically (i.e., increased rotation velocity, decreased disturbed motions) and morphologically is directly proportional to their stellar mass.

Corrections to the one-photon approximation in the 0+-->2+ transition of 12C

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

Paul Gueye; Madeleine Bernheim; J. F. Danel

2001-04-18

Contribution of higher order effects to the one-photon exchange approximation were studied in the first excited state of 12C by comparing inclusive inelastic scattering cross sections of electrons and positrons obtained at the Saclay Linear Accelerator. The data were compared to a distorted wave Born approximation (DWBA)calculation. The results indicate an effect less than 2% within 2sigma, compatible with what was observed in recent elastic scattering measurements.

Topographical scattering of gravity waves

NASA Astrophysics Data System (ADS)

Miles, J. W.; Chamberlain, P. G.

1998-04-01

A systematic hierarchy of partial differential equations for linear gravity waves in water of variable depth is developed through the expansion of the average Lagrangian in powers of [mid R:][nabla del, Hamilton operator][mid R:] (h=depth, [nabla del, Hamilton operator]h=slope). The first and second members of this hierarchy, the Helmholtz and conventional mild-slope equations, are second order. The third member is fourth order but may be approximated by Chamberlain & Porter's (1995) ‘modified mild-slope’ equation, which is second order and comprises terms in [nabla del, Hamilton operator]2h and ([nabla del, Hamilton operator]h)2 that are absent from the mild-slope equation. Approximate solutions of the mild-slope and modified mild-slope equations for topographical scattering are determined through an iterative sequence, starting from a geometrical-optics approximation (which neglects reflection), then a quasi-geometrical-optics approximation, and on to higher-order results. The resulting reflection coefficient for a ramp of uniform slope is compared with the results of numerical integrations of each of the mild-slope equation (Booij 1983), the modified mild-slope equation (Porter & Staziker 1995), and the full linear equations (Booij 1983). Also considered is a sequence of sinusoidal sandbars, for which Bragg resonance may yield rather strong reflection and for which the modified mild-slope approximation is in close agreement with Mei's (1985) asymptotic approximation.

Relativistic wide-angle galaxy bispectrum on the light cone

NASA Astrophysics Data System (ADS)

Bertacca, Daniele; Raccanelli, Alvise; Bartolo, Nicola; Liguori, Michele; Matarrese, Sabino; Verde, Licia

2018-01-01

Given the important role that the galaxy bispectrum has recently acquired in cosmology and the scale and precision of forthcoming galaxy clustering observations, it is timely to derive the full expression of the large-scale bispectrum going beyond approximated treatments which neglect integrated terms or higher-order bias terms or use the Limber approximation. On cosmological scales, relativistic effects that arise from observing the past light cone alter the observed galaxy number counts, therefore leaving their imprints on N-point correlators at all orders. In this paper we compute for the first time the bispectrum including all general relativistic, local and integrated, effects at second order, the tracers' bias at second order, geometric effects as well as the primordial non-Gaussianity contribution. This is timely considering that future surveys will probe scales comparable to the horizon where approximations widely used currently may not hold; neglecting these effects may introduce biases in estimation of cosmological parameters as well as primordial non-Gaussianity.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Basement-involved faults and deep structures in the West Philippine Basin: constrains from gravity field

NASA Astrophysics Data System (ADS)

Wang, Gang; Jiang, Suhua; Li, Sanzhong; Zhang, Huixuan; Lei, Jianping; Gao, Song; Zhao, Feiyu

2017-06-01

To reveal the basement-involved faults and deep structures of the West Philippine Basin (WPB), the gravitational responses caused by these faults are observed and analyzed based on the latest spherical gravity model: WGM2012 Model. By mapping the free-air and Bouguer gravity anomalies, several main faults and some other linear structures are located and observed in the WPB. Then, by conducting a 2D discrete multi-scale wavelet decomposition, the Bouguer anomalies are decomposed into the first- to eighth-order detail and approximation fields (the first- to eighth-order Details and Approximations). The first- to third-order Details reflect detailed and localized geological information of the crust at different depths, and of which the higher-order reflects gravity field of the deeper depth. The first- to fourth-order Approximations represent the regional gravity fields at different depths of the crust, respectively. The fourth-order Approximation represents the regional gravity fluctuation caused by the density inhomogeneity of Moho interface. Therefore, taking the fourth-order Approximation as input, and adopting Parker-Oldenburg interactive inversion, We calculated the depth of Moho interface in the WPB. Results show that the Moho interface depth in the WPB ranges approximately from 8 to 12 km, indicating that there is typical oceanic crust in the basin. In the Urdaneta Plateau and the Benham Rise, the Moho interface depths are about 14 and 16 km, respectively, which provides a piece of evidence to support that the Banham Rise could be a transitional crust caused by a large igneous province. The second-order vertical derivative and the horizontal derivatives in direction 0° and 90° are computed based on the data of the third-order Detail, and most of the basement-involved faults and structures in the WPB, such as the Central Basin Fault Zone, the Gagua Ridge, the Luzon-Okinawa Fault Zone, and the Mindanao Fault Zone are interpreted by the gravity derivatives.

Bridging Literacy Acquisition and Self-Regulated Learning: Using a SRL Framework to Support Struggling Readers

ERIC Educational Resources Information Center

Holtzheuser, Sierra; McNamara, John

2014-01-01

Reading is conceptualized as a hierarchy of component skills where lower order emergent literacy skills set the foundation for higher order reading skills such as fluency and comprehension. Approximately 20% of readers struggle within this hierarchical process (Fielding, Kerr, & Rosier, 2007). Struggling readers are susceptible to the Matthew…

Higher order corrections to mixed QCD-EW contributions to Higgs boson production in gluon fusion

NASA Astrophysics Data System (ADS)

Bonetti, Marco; Melnikov, Kirill; Tancredi, Lorenzo

2018-03-01

We present an estimate of the next-to-leading-order (NLO) QCD corrections to mixed QCD-electroweak contributions to the Higgs boson production cross section in gluon fusion, combining the recently computed three-loop virtual corrections and the approximate treatment of real emission in the soft approximation. We find that the NLO QCD corrections to the mixed QCD-electroweak contributions are nearly identical to NLO QCD corrections to QCD Higgs production. Our result confirms an earlier estimate of these O (α αs2) effects by Anastasiou et al. [J. High Energy Phys. 04 (2009) 003, 10.1088/1126-6708/2009/04/003] and provides further support for the factorization approximation of QCD and electroweak corrections.

Stochastic Optimal Prediction with Application to Averaged Euler Equations

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

Bell, John; Chorin, Alexandre J.; Crutchfield, William

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.

Symbolic Algebra Development for Higher-Order Electron Propagator Formulation and Implementation.

PubMed

Tamayo-Mendoza, Teresa; Flores-Moreno, Roberto

2014-06-10

Through the use of symbolic algebra, implemented in a program, the algebraic expression of the elements of the self-energy matrix for the electron propagator to different orders were obtained. In addition, a module for the software package Lowdin was automatically generated. Second- and third-order electron propagator results have been calculated to test the correct operation of the program. It was found that the Fortran 90 modules obtained automatically with our algorithm succeeded in calculating ionization energies with the second- and third-order electron propagator in the diagonal approximation. The strategy for the development of this symbolic algebra program is described in detail. This represents a solid starting point for the automatic derivation and implementation of higher-order electron propagator methods.

Formulation of aerodynamic prediction techniques for hypersonic configuration design

NASA Technical Reports Server (NTRS)

1979-01-01

An investigation of approximate theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at moderate hypersonic speeds was performed. Emphasis was placed on approaches that would be responsive to preliminary configuration design level of effort. Supersonic second order potential theory was examined in detail to meet this objective. Shock layer integral techniques were considered as an alternative means of predicting gross aerodynamic characteristics. Several numerical pilot codes were developed for simple three dimensional geometries to evaluate the capability of the approximate equations of motion considered. Results from the second order computations indicated good agreement with higher order solutions and experimental results for a variety of wing like shapes and values of the hypersonic similarity parameter M delta approaching one.

Beyond electronegativity and local hardness: Higher-order equalization criteria for determination of a ground-state electron density.

PubMed

Ayers, Paul W; Parr, Robert G

2008-08-07

Higher-order global softnesses, local softnesses, and softness kernels are defined along with their hardness inverses. The local hardness equalization principle recently derived by the authors is extended to arbitrary order. The resulting hierarchy of equalization principles indicates that the electronegativity/chemical potential, local hardness, and local hyperhardnesses all are constant when evaluated for the ground-state electron density. The new equalization principles can be used to test whether a trial electron density is an accurate approximation to the true ground-state density and to discover molecules with desired reactive properties, as encapsulated by their chemical reactivity indicators.

Identification of stochastic interactions in nonlinear models of structural mechanics

NASA Astrophysics Data System (ADS)

Kala, Zdeněk

2017-07-01

In the paper, the polynomial approximation is presented by which the Sobol sensitivity analysis can be evaluated with all sensitivity indices. The nonlinear FEM model is approximated. The input area is mapped using simulations runs of Latin Hypercube Sampling method. The domain of the approximation polynomial is chosen so that it were possible to apply large number of simulation runs of Latin Hypercube Sampling method. The method presented also makes possible to evaluate higher-order sensitivity indices, which could not be identified in case of nonlinear FEM.

Redshift Evolution of Non-Gaussianity in Cosmic Large-Scale Structure

NASA Astrophysics Data System (ADS)

Sullivan, James; Wiegand, Alexander; Eisenstein, Daniel

2018-01-01

We probe the higher-order galaxy clustering in the final data release (DR12) of the Sloan Digital Sky Survey using germ-grain Minkowski Functionals (MFs). Our data selection contains 979,430 BOSS galaxies from both the northern and southern galactic caps over the redshift range 0.2 - 0.6. We extract the higher-order parts of the MFs and find deviations from the case without higher order MFs with chi-squared values of order 1000 for 24 degrees of freedom across the entire data selection. We show the MFs to be sensitive to contributions up to the five-point correlation function across the entire data selection. We measure significant redshift evolution in the higher-order functionals for the first time, with a percentage growth between redshift bins of approximately 20 % in both galactic caps. This is a nearly a factor of 2 greater than similar growth in the two-point correlation function and will allow for tests of non-linear structure growth by comparing the three-point and higher-order parts to their expected theoretical values. The SAO REU program is funded by the National Science Foundation REU and Department of Defense ASSURE programs under NSF Grant AST-1659473, and by the Smithsonian Institution.

Stokes waves revisited: Exact solutions in the asymptotic limit

NASA Astrophysics Data System (ADS)

Davies, Megan; Chattopadhyay, Amit K.

2016-03-01

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic "secular variation" in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n -ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory: Convergence analysis of the dual fermion technique

NASA Astrophysics Data System (ADS)

Gukelberger, Jan; Kozik, Evgeny; Hafermann, Hartmut

2017-07-01

The dual fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work, we compute the dual fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact diagrammatic determinant Monte Carlo simulations to systematically assess convergence of the dual fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT Néel transition, the dual fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered (4 ≤U /t ≤12 ), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find, however, that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.

Higher-order ice-sheet modelling accelerated by multigrid on graphics cards

NASA Astrophysics Data System (ADS)

Brædstrup, Christian; Egholm, David

2013-04-01

Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.

A three-dimensional parabolic equation model of sound propagation using higher-order operator splitting and Padé approximants.

PubMed

Lin, Ying-Tsong; Collis, Jon M; Duda, Timothy F

2012-11-01

An alternating direction implicit (ADI) three-dimensional fluid parabolic equation solution method with enhanced accuracy is presented. The method uses a square-root Helmholtz operator splitting algorithm that retains cross-multiplied operator terms that have been previously neglected. With these higher-order cross terms, the valid angular range of the parabolic equation solution is improved. The method is tested for accuracy against an image solution in an idealized wedge problem. Computational efficiency improvements resulting from the ADI discretization are also discussed.

Higgs radiation off top quarks at the Tevatron and the LHC.

PubMed

Beenakker, W; Dittmaier, S; Krämer, M; Plümper, B; Spira, M; Zerwas, P M

2001-11-12

Higgs bosons can be searched for in the channels pp macro/pp-->tt macro H + X at the Fermilab Tevatron and the Cern Large Hadron Collider (LHC). We have calculated the QCD corrections to these processes in the standard model at next-to-leading order. The higher-order corrections reduce the renormalization and factorization scale dependence considerably and stabilize the theoretical predictions for the cross sections. At the central scale mu = (2m(t)+M(H))/2 the properly defined K factors are slightly below unity for the Tevatron (K approximately 0.8) and slightly above unity for the LHC (K approximately 1.2).

Periodicity of high-order neural functions

NASA Technical Reports Server (NTRS)

Kellaway, P.; Borda, R. P.; Frost, J. D.; Carrie, J. R. G.; Coats, A. C.

1973-01-01

The results of recent studies on higher order, integrative processes in the central nervous system are reported. Attempts were made to determine whether these processes exhibit any ongoing rhythmicity which might manifest itself in alterations of attention and alertness. Experiments were also designed to determine if a periodicity approximating that of the REM could be detected in various parameters of brain electrical activity.

Approximate solution of space and time fractional higher order phase field equation

NASA Astrophysics Data System (ADS)

Shamseldeen, S.

2018-03-01

This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

MLFMA-accelerated Nyström method for ultrasonic scattering - Numerical results and experimental validation

NASA Astrophysics Data System (ADS)

Gurrala, Praveen; Downs, Andrew; Chen, Kun; Song, Jiming; Roberts, Ron

2018-04-01

Full wave scattering models for ultrasonic waves are necessary for the accurate prediction of voltage signals received from complex defects/flaws in practical nondestructive evaluation (NDE) measurements. We propose the high-order Nyström method accelerated by the multilevel fast multipole algorithm (MLFMA) as an improvement to the state-of-the-art full-wave scattering models that are based on boundary integral equations. We present numerical results demonstrating improvements in simulation time and memory requirement. Particularly, we demonstrate the need for higher order geom-etry and field approximation in modeling NDE measurements. Also, we illustrate the importance of full-wave scattering models using experimental pulse-echo data from a spherical inclusion in a solid, which cannot be modeled accurately by approximation-based scattering models such as the Kirchhoff approximation.

Communication: Accurate higher-order van der Waals coefficients between molecules from a model dynamic multipole polarizability

DOE PAGES

Tao, Jianmin; Rappe, Andrew M.

2016-01-20

Due to the absence of the long-range van der Waals (vdW) interaction, conventional density functional theory (DFT) often fails in the description of molecular complexes and solids. In recent years, considerable progress has been made in the development of the vdW correction. However, the vdW correction based on the leading-order coefficient C 6 alone can only achieve limited accuracy, while accurate modeling of higher-order coefficients remains a formidable task, due to the strong non-additivity effect. Here, we apply a model dynamic multipole polarizability within a modified single-frequency approximation to calculate C 8 and C 10 between small molecules. We findmore » that the higher-order vdW coefficients from this model can achieve remarkable accuracy, with mean absolute relative deviations of 5% for C 8 and 7% for C 10. As a result, inclusion of accurate higher-order contributions in the vdW correction will effectively enhance the predictive power of DFT in condensed matter physics and quantum chemistry.« less

Validity of the Born approximation for beyond Gaussian weak lensing observables

DOE PAGES

Petri, Andrea; Haiman, Zoltan; May, Morgan

2017-06-06

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show thatmore » deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O(Φ 3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O(Φ 4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5σ. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.« less

Validity of the Born approximation for beyond Gaussian weak lensing observables

NASA Astrophysics Data System (ADS)

Petri, Andrea; Haiman, Zoltán; May, Morgan

2017-06-01

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N -body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O (Φ3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O (Φ4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5 σ . Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.

Scattering from very rough layers under the geometric optics approximation: further investigation.

PubMed

Pinel, Nicolas; Bourlier, Christophe

2008-06-01

Scattering from very rough homogeneous layers is studied in the high-frequency limit (under the geometric optics approximation) by taking the shadowing effect into account. To do so, the iterated Kirchhoff approximation, recently developed by Pinel et al. [Waves Random Complex Media17, 283 (2007)] and reduced to the geometric optics approximation, is used and investigated in more detail. The contributions from the higher orders of scattering inside the rough layer are calculated under the iterated Kirchhoff approximation. The method can be applied to rough layers of either very rough or perfectly flat lower interfaces, separating either lossless or lossy media. The results are compared with the PILE (propagation-inside-layer expansion) method, recently developed by Déchamps et al. [J. Opt. Soc. Am. A23, 359 (2006)], and accelerated by the forward-backward method with spectral acceleration. They highlight that there is very good agreement between the developed method and the reference numerical method for all scattering orders and that the method can be applied to root-mean-square (RMS) heights at least down to 0.25lambda.

Quaternary borocarbides: New class of intermetallic superconductors

NASA Technical Reports Server (NTRS)

Nagarajan, R.; Gupta, L. C.; Dhar, S. K.; Mazumdar, Chandan; Hossain, Zakir; Godart, C.; Levy-Clement, C.; Padalia, B. D.; Vijayaraghavan, R.

1995-01-01

Our recent discovery of superconductivity (SC) in the four-element multiphase Y-Ni-B-C system at an elevated temperature (TC approximately 12 K) has opened up great possibilities of identifying new superconducting materials and generating new physics. Superconductivity with Tc (greater than 20 K) higher than that known so far in bulk intermetallics has been observed in multiphase Y-Pd-B-C and Th-Pd-B-C systems and a family of single phase materials RENi2B2C (RE= Y, rare earth) have been found. Our investigations show YNi2B2C to be a strong coupling hard type-II SC. HC2(T) exhibits an unconventional temperature dependence. Specific heat and magnetization studies reveal coexistence of SC and magnetism in RNi2B2C (R = Ho, Er, Tm) with magnetic ordering temperatures (Tc approximately 8 K, 10.5 K, 11 K and Tm approximately 5 K, approximately 7K, approximately 4 K respectively) that are remarkably higher than those in known magnetic superconductors . Mu-SR studies suggest the possibility of Ni atoms carrying a moment in TmNi2B2C. Resistivity results suggests a double re-entrant transition (SC-normal-SC) in HoNi2B2C. RENi2B2C (RE = Ce, Nd, Gd) do not show SC down to 4.2 K. The Nd- and Gd-compounds order magnetically at approximately 4.5 K and approximately 19.5 K, respectively. Two SC transitions are observed in Y-Pd-B-C (Tc approximately 22 K, approximately 10 K) and in Th-Pd-B-C (Tc approximately 20 K, approximately 14 K) systems, which indicate that there are at least two structures which support SC in these borocarbides. In our multiphase ThNi2B2C we observe SC at approximately 6 K. No SC was seen in multiphase UNi2B2C, UPd2B2C, UOs2Ge2C and UPd5B3C(0.35) down to 4.2 K. Tc in YNi2B2C is depressed by substitutions (Gd, Th and U at Y-sites and Fe, Co at Ni-sites).

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

NASA Astrophysics Data System (ADS)

Heumann, Holger; Rapetti, Francesca

2017-04-01

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

Complete Hamiltonian analysis of cosmological perturbations at all orders

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

Nandi, Debottam; Shankaranarayanan, S., E-mail: debottam@iisertvm.ac.in, E-mail: shanki@iisertvm.ac.in

2016-06-01

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the 'gauge-fixing' issues and extend the analysis to scalar field models and show that our approach can be applied to any order of perturbation for any first order derivative fields. In the case of Galilean scalar fields, our procedure can extract constrained relations at all orders in perturbations leading to the fact that there is no extra degrees of freedom due to the presence of higher time derivatives of the field in themore » Lagrangian. We compare and contrast our approach to the Lagrangian approach (Chen et al. [2006]) for extracting higher order correlations and show that our approach is efficient and robust and can be applied to any model of gravity and matter fields without invoking slow-roll approximation.« less

Constraining modified theories of gravity with the galaxy bispectrum

NASA Astrophysics Data System (ADS)

Yamauchi, Daisuke; Yokoyama, Shuichiro; Tashiro, Hiroyuki

2017-12-01

We explore the use of the galaxy bispectrum induced by the nonlinear gravitational evolution as a possible probe to test general scalar-tensor theories with second-order equations of motion. We find that time dependence of the leading second-order kernel is approximately characterized by one parameter, the second-order index, which is expected to trace the higher-order growth history of the Universe. We show that our new parameter can significantly carry new information about the nonlinear growth of structure. We forecast future constraints on the second-order index as well as the equation-of-state parameter and the growth index.

An h-p Taylor-Galerkin finite element method for compressible Euler equations

NASA Technical Reports Server (NTRS)

Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.

1991-01-01

An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

Analytical treatment of self-phase-modulation beyond the slowly varying envelope approximation

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

Syrchin, M.S.; Zheltikov, A.M.; International Laser Center, M.V. Lomonosov Moscow State University, 119899 Moscow

Analytical treatment of the self-phase-modulation of an ultrashort light pulse is extended beyond the slowly varying envelope approximation. The resulting wave equation is modified to include corrections to self-phase-modulation due to higher-order spatial and temporal derivatives. Analytical solutions are found in the limiting regimes of high nonlinearities and very short pulses. Our results reveal features that can significantly impact both pulse shape and the evolution of the phase.

A Hierarchy of Transport Approximations for High Energy Heavy (HZE) Ions

NASA Technical Reports Server (NTRS)

Wilson, John W.; Lamkin, Stanley L.; Hamidullah, Farhat; Ganapol, Barry D.; Townsend, Lawrence W.

1989-01-01

The transport of high energy heavy (HZE) ions through bulk materials is studied neglecting energy dependence of the nuclear cross sections. A three term perturbation expansion appears to be adequate for most practical applications for which penetration depths are less than 30 g per sq cm of material. The differential energy flux is found for monoenergetic beams and for realistic ion beam spectral distributions. An approximate formalism is given to estimate higher-order terms.

Fast and Analytical EAP Approximation from a 4th-Order Tensor.

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

Fast and Analytical EAP Approximation from a 4th-Order Tensor

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data. PMID:23365552

Failure of geometric electromagnetism in the adiabatic vector Kepler problem

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

Anglin, J.R.; Schmiedmayer, J.

2004-02-01

The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wire's magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only the particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher-order postadiabatic corrections make the orbits precess, but recent analysis of this 'vector Kepler problem' has shown that the effective Hamiltonian incorporating a postadiabatic scalar potential ('geometric electromagnetism') fails to predict themore » precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the postadiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a 1/r{sup 3} singularity which is an artifact of the adiabatic approximation.« less

On the acceleration of charged particles at relativistic shock fronts

NASA Technical Reports Server (NTRS)

Kirk, J. G.; Schneider, P.

1987-01-01

The diffusive acceleration of highly relativistic particles at a shock is reconsidered. Using the same physical assumptions as Blandford and Ostriker (1978), but dropping the restriction to nonrelativistic shock velocities, the authors find approximate solutions of the particle kinetic equation by generalizing the diffusion approximation to higher order terms in the anisotropy of the particle distribution. The general solution of the transport equation on either side of the shock is constructed, which involves the solution of an eigenvalue problem. By matching the two solutions at the shock, the spectral index of the resulting power law is found by taking into account a sufficiently large number of eigenfunctions. Low-order truncation corresponds to the standard diffusion approximation and to a somewhat more general method described by Peacock (1981). In addition to the energy spectrum, the method yields the angular distribution of the particles and its spatial dependence.

Quantifying the effect of finite spectral bandwidth on extinction coefficient of species in laser absorption spectroscopy

NASA Astrophysics Data System (ADS)

Singh, Manjeet; Singh, Jaswant; Singh, Baljit; Ghanshyam, C.

2016-11-01

The aim of this study is to quantify the finite spectral bandwidth effect on laser absorption spectroscopy for a wide-band laser source. Experimental analysis reveals that the extinction coefficient of an analyte is affected by the bandwidth of the spectral source, which may result in the erroneous conclusions. An approximate mathematical model has been developed for optical intensities having Gaussian line shape, which includes the impact of source's spectral bandwidth in the equation for spectroscopic absorption. This is done by introducing a suitable first order and second order bandwidth approximation in the Beer-Lambert law equation for finite bandwidth case. The derived expressions were validated using spectroscopic analysis with higher SBW on a test sample, Rhodamine B. The concentrations calculated using proposed approximation, were in significant agreement with the true values when compared with those calculated with conventional approach.

Cosmic microwave background bispectrum from primordial magnetic fields on large angular scales.

PubMed

Seshadri, T R; Subramanian, Kandaswamy

2009-08-21

Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher-order effect. We propose a novel probe of stochastic primordial magnetic fields that exploits the characteristic CMB non-Gaussianity that they induce. We compute the CMB bispectrum (b(l1l2l3)) induced by such fields on large angular scales. We find a typical value of l1(l1 + 1)l3(l3 + 1)b(l1l2l3) approximately 10(-22), for magnetic fields of strength B0 approximately 3 nG and with a nearly scale invariant magnetic spectrum. Observational limits on the bispectrum allow us to set upper limits on B0 approximately 35 nG.

Polarization-resolved simulations of multiple-order rainbows using realistic raindrop shapes

NASA Astrophysics Data System (ADS)

Haußmann, Alexander

2016-05-01

This paper presents selected results of a simulation study of the first five (primary-quinary) rainbow orders based on a realistic, size-dependent shape model for falling raindrops, taking into account that the drops' bottom part is flattened to higher degree than the dome-like top part. Moreover, broad drop size distributions are included in the simulations, as it is one goal of this paper to analyze, whether the predicted amplification and attenuation patterns for higher-order rainbows, as derived from previous simulations with monodisperse drop sizes, will still be pronounced under the conditions of natural rainfall. Secondly, deviations of the multiple rainbow orders' polarization state from the reference case of spherical drops are discussed. It is shown that each rainbow order may contain a small amount of circularly polarized light due to total internal reflections. Thirdly, it is investigated, how the conditions that generate twinned primary rainbows will affect the higher orders. For the simulations, geometric-optic ray tracing of the full Stokes vector as well as an approximate approach using appropriately shifted Debye series data is applied.

Renormalization group analysis of the Reynolds stress transport equation

NASA Technical Reports Server (NTRS)

Rubinstein, R.; Barton, J. M.

1992-01-01

The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.

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

Ip, Hiu Yan; Schmidt, Fabian, E-mail: iphys@mpa-garching.mpg.de, E-mail: fabians@mpa-garching.mpg.de

Density perturbations in cosmology, i.e. spherically symmetric adiabatic perturbations of a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime, are locally exactly equivalent to a different FLRW solution, as long as their wavelength is much larger than the sound horizon of all fluid components. This fact is known as the 'separate universe' paradigm. However, no such relation is known for anisotropic adiabatic perturbations, which correspond to an FLRW spacetime with large-scale tidal fields. Here, we provide a closed, fully relativistic set of evolutionary equations for the nonlinear evolution of such modes, based on the conformal Fermi (CFC) frame. We show explicitly that the tidal effectsmore » are encoded by the Weyl tensor, and are hence entirely different from an anisotropic Bianchi I spacetime, where the anisotropy is sourced by the Ricci tensor. In order to close the system, certain higher derivative terms have to be dropped. We show that this approximation is equivalent to the local tidal approximation of Hui and Bertschinger [1]. We also show that this very simple set of equations matches the exact evolution of the density field at second order, but fails at third and higher order. This provides a useful, easy-to-use framework for computing the fully relativistic growth of structure at second order.« less

Efficient 3D geometric and Zernike moments computation from unstructured surface meshes.

PubMed

Pozo, José María; Villa-Uriol, Maria-Cruz; Frangi, Alejandro F

2011-03-01

This paper introduces and evaluates a fast exact algorithm and a series of faster approximate algorithms for the computation of 3D geometric moments from an unstructured surface mesh of triangles. Being based on the object surface reduces the computational complexity of these algorithms with respect to volumetric grid-based algorithms. In contrast, it can only be applied for the computation of geometric moments of homogeneous objects. This advantage and restriction is shared with other proposed algorithms based on the object boundary. The proposed exact algorithm reduces the computational complexity for computing geometric moments up to order N with respect to previously proposed exact algorithms, from N(9) to N(6). The approximate series algorithm appears as a power series on the rate between triangle size and object size, which can be truncated at any desired degree. The higher the number and quality of the triangles, the better the approximation. This approximate algorithm reduces the computational complexity to N(3). In addition, the paper introduces a fast algorithm for the computation of 3D Zernike moments from the computed geometric moments, with a computational complexity N(4), while the previously proposed algorithm is of order N(6). The error introduced by the proposed approximate algorithms is evaluated in different shapes and the cost-benefit ratio in terms of error, and computational time is analyzed for different moment orders.

Speeding up spin-component-scaled third-order pertubation theory with the chain of spheres approximation: the COSX-SCS-MP3 method

NASA Astrophysics Data System (ADS)

Izsák, Róbert; Neese, Frank

2013-07-01

The 'chain of spheres' approximation, developed earlier for the efficient evaluation of the self-consistent field exchange term, is introduced here into the evaluation of the external exchange term of higher order correlation methods. Its performance is studied in the specific case of the spin-component-scaled third-order Møller--Plesset perturbation (SCS-MP3) theory. The results indicate that the approximation performs excellently in terms of both computer time and achievable accuracy. Significant speedups over a conventional method are obtained for larger systems and basis sets. Owing to this development, SCS-MP3 calculations on molecules of the size of penicillin (42 atoms) with a polarised triple-zeta basis set can be performed in ∼3 hours using 16 cores of an Intel Xeon E7-8837 processor with a 2.67 GHz clock speed, which represents a speedup by a factor of 8-9 compared to the previously most efficient algorithm. Thus, the increased accuracy offered by SCS-MP3 can now be explored for at least medium-sized molecules.

Tangent Adjoint Methods In a Higher-Order Space-Time Discontinuous-Galerkin Solver For Turbulent Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo; Murman, Scott; Blonigan, Patrick; Garai, Anirban

2017-01-01

Presented space-time adjoint solver for turbulent compressible flows. Confirmed failure of traditional sensitivity methods for chaotic flows. Assessed rate of exponential growth of adjoint for practical 3D turbulent simulation. Demonstrated failure of short-window sensitivity approximations.

Excitation energies from particle-particle random phase approximation with accurate optimized effective potentials

NASA Astrophysics Data System (ADS)

Jin, Ye; Yang, Yang; Zhang, Du; Peng, Degao; Yang, Weitao

2017-10-01

The optimized effective potential (OEP) that gives accurate Kohn-Sham (KS) orbitals and orbital energies can be obtained from a given reference electron density. These OEP-KS orbitals and orbital energies are used here for calculating electronic excited states with the particle-particle random phase approximation (pp-RPA). Our calculations allow the examination of pp-RPA excitation energies with the exact KS density functional theory (DFT). Various input densities are investigated. Specifically, the excitation energies using the OEP with the electron densities from the coupled-cluster singles and doubles method display the lowest mean absolute error from the reference data for the low-lying excited states. This study probes into the theoretical limit of the pp-RPA excitation energies with the exact KS-DFT orbitals and orbital energies. We believe that higher-order correlation contributions beyond the pp-RPA bare Coulomb kernel are needed in order to achieve even higher accuracy in excitation energy calculations.

Higher order approximation to the Hill problem dynamics about the libration points

NASA Astrophysics Data System (ADS)

Lara, Martin; Pérez, Iván L.; López, Rosario

2018-06-01

An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture all the relevant periodic orbits originated from the libration points within a reasonable accuracy, the normalization is approached in complex variables. The validity of the solution extends to energy values considerably far away from that of the libration points and, therefore, can be used in the computation of Halo orbits as an alternative to the classical Lindstedt-Poincaré approach. Furthermore, the theory correctly predicts the existence of the two-lane bridge of periodic orbits linking the families of planar and vertical Lyapunov orbits.

Theoretical studies of floating-reference method for NIR blood glucose sensing

NASA Astrophysics Data System (ADS)

Shi, Zhenzhi; Yang, Yue; Zhao, Huijuan; Chen, Wenliang; Liu, Rong; Xu, Kexin

2011-03-01

Non-invasive blood glucose monitoring using NIR light has been suffered from the variety of optical background that is mainly caused by the change of human body, such as the change of temperature, water concentration, and so on. In order to eliminate these internal influence and external interference a so called floating-reference method has been proposed to provide an internal reference. From the analysis of the diffuse reflectance spectrum, a position has been found where diffuse reflection of light is not sensitive to the glucose concentrations. Our previous work has proved the existence of reference position using diffusion equation. However, since glucose monitoring generally use the NIR light in region of 1000-2000nm, diffusion equation is not valid because of the high absorption coefficient and small source-detector separations. In this paper, steady-state high-order approximate model is used to further investigate the existence of the floating reference position in semi-infinite medium. Based on the analysis of different optical parameters on the impact of spatially resolved reflectance of light, we find that the existence of the floating-reference position is the result of the interaction of optical parameters. Comparing to the results of Monte Carlo simulation, the applicable region of diffusion approximation and higher-order approximation for the calculation of floating-reference position is discussed at the wavelength of 1000nm-1800nm, using the intralipid solution of different concentrations. The results indicate that when the reduced albedo is greater than 0.93, diffusion approximation results are more close to simulation results, otherwise the high order approximation is more applicable.

Calculation of Protein Heat Capacity from Replica-Exchange Molecular Dynamics Simulations with Different Implicit Solvent Models

DTIC Science & Technology

2008-10-30

rigorous Poisson-based methods generally apply a Lee-Richards mo- lecular surface.9 This surface is considered the de facto description for continuum...definition and calculation of the Born radii. To evaluate the Born radii, two approximations are invoked. The first is the Coulomb field approximation (CFA...energy term, and depending on the particular GB formulation, higher-order non- Coulomb correction terms may be added to the Born radii to account for the

On the loop approximation in nucleon QCD sum rules

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

Drukarev, E. G., E-mail: drukarev@thd.pnpi.spb.ru; Ryskin, M. G.; Sadovnikova, V. A.

There was a general belief that the nucleon QCD sum rules which include only the quark loops and thus contain only the condensates of dimension d = 3 and d = 4 have only a trivial solution. We demonstrate that there is also a nontrivial solution. We show that it can be treated as the lowest order approximation to the solution which includes the higher terms of the Operator Product Expansion. Inclusion of the radiative corrections improves the convergence of the series.

Arbitrary-level hanging nodes for adaptive hphp-FEM approximations in 3D

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

Pavel Kus; Pavel Solin; David Andrs

2014-11-01

In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hphp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.

Production of e+e- Pairs Accompanied by Nuclear Dissociation in Ultra-peripheral Heavy Ion Collisions

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

Adams, J.; Adler, C.; Aggarwal, M.M.

2004-04-07

We present the first data on e{sup +}e{sup -} pair production accompanied by nuclear breakup in ultra-peripheral gold-gold collisions at a center of mass energy of 200 GeV per nucleon pair. The nuclear breakup requirement selects events at small impact parameters, where higher-order corrections to the pair production cross section should be enhanced. We compare the pair kinematic distributions with two calculations: one based on the equivalent photon approximation, and the other using lowest-order quantum electrodynamics (QED); the latter includes the photon virtuality. The cross section, pair mass, rapidity and angular distributions are in good agreement with both calculations. Themore » pair transverse momentum, p{sub T}, spectrum agrees with the QED calculation, but not with the equivalent photon approach. We set limits on higher-order contributions to the cross section. The e{sup +} and e{sup -} p{sub T} spectra are similar, with no evidence for interference effects due to higher-order diagrams.« less

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

fNL‑gNL mixing in the matter density field at higher orders

NASA Astrophysics Data System (ADS)

Gressel, Hedda A.; Bruni, Marco

2018-06-01

In this paper we examine how primordial non-Gaussianity contributes to nonlinear perturbative orders in the expansion of the density field at large scales in the matter dominated era. General Relativity is an intrinsically nonlinear theory, establishing a nonlinear relation between the metric and the density field. Representing the metric perturbations with the curvature perturbation ζ, it is known that nonlinearity produces effective non-Gaussian terms in the nonlinear perturbations of the matter density field δ, even if the primordial ζ is Gaussian. Here we generalise these results to the case of a non-Gaussian primordial ζ. Using a standard parametrization of primordial non-Gaussianity in ζ in terms of fNL, gNL, hNL\\ldots , we show how at higher order (from third and higher) nonlinearity also produces a mixing of these contributions to the density field at large scales, e.g. both fNL and gNL contribute to the third order in δ. This is the main result of this paper. Our analysis is based on the synergy between a gradient expansion (aka long-wavelength approximation) and standard perturbation theory at higher order. In essence, mathematically the equations for the gradient expansion are equivalent to those of first order perturbation theory, thus first-order results convert into gradient expansion results and, vice versa, the gradient expansion can be used to derive results in perturbation theory at higher order and large scales.

An Efficient Finite Element Framework to Assess Flexibility Performances of SMA Self-Expandable Carotid Artery Stents

PubMed Central

Ferraro, Mauro; Auricchio, Ferdinando; Boatti, Elisa; Scalet, Giulia; Conti, Michele; Morganti, Simone; Reali, Alessandro

2015-01-01

Computer-based simulations are nowadays widely exploited for the prediction of the mechanical behavior of different biomedical devices. In this aspect, structural finite element analyses (FEA) are currently the preferred computational tool to evaluate the stent response under bending. This work aims at developing a computational framework based on linear and higher order FEA to evaluate the flexibility of self-expandable carotid artery stents. In particular, numerical simulations involving large deformations and inelastic shape memory alloy constitutive modeling are performed, and the results suggest that the employment of higher order FEA allows accurately representing the computational domain and getting a better approximation of the solution with a widely-reduced number of degrees of freedom with respect to linear FEA. Moreover, when buckling phenomena occur, higher order FEA presents a superior capability of reproducing the nonlinear local effects related to buckling phenomena. PMID:26184329

Modeling the physisorption of graphene on metals

NASA Astrophysics Data System (ADS)

Tao, Jianmin; Tang, Hong; Patra, Abhirup; Bhattarai, Puskar; Perdew, John P.

2018-04-01

Many processes of technological and fundamental importance occur on surfaces. Adsorption is one of these phenomena that has received the most attention. However, it presents a great challenge to conventional density functional theory. Starting with the Lifshitz-Zaremba-Kohn second-order perturbation theory, here we develop a long-range van der Waals (vdW) correction for physisorption of graphene on metals. The model importantly includes quadrupole-surface interaction and screening effects. The results show that, when the vdW correction is combined with the Perdew-Burke-Enzerhof functional, it yields adsorption energies in good agreement with the random-phase approximation, significantly improving upon other vdW methods. We also find that, compared with the leading-order interaction, the higher-order quadrupole-surface correction accounts for about 25 % of the total vdW correction, suggesting the importance of the higher-order term.

A-posteriori error estimation for the finite point method with applications to compressible flow

NASA Astrophysics Data System (ADS)

Ortega, Enrique; Flores, Roberto; Oñate, Eugenio; Idelsohn, Sergio

2017-08-01

An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

Perturbative Out of Equilibrium Quantum Field Theory beyond the Gradient Approximation and Generalized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Ozaki, H.

2004-01-01

Using the closed-time-path formalism, we construct perturbative frameworks, in terms of quasiparticle picture, for studying quasiuniform relativistic quantum field systems near equilibrium and non-equilibrium quasistationary systems. We employ the derivative expansion and take in up to the second-order term, i.e., one-order higher than the gradient approximation. After constructing self-energy resummed propagator, we formulated two kinds of mutually equivalent perturbative frameworks: The first one is formulated on the basis of the ``bare'' number density function, and the second one is formulated on the basis of ``physical'' number density function. In the course of construction of the second framework, the generalized Boltzmann equations directly come out, which describe the evolution of the system.

B and F Projection Methods for Nearly Incompressible Linear and Nonlinear Elasticity and Plasticity using Higher-order NURBS Elements

DTIC Science & Technology

2007-08-01

Infinite plate with a hole: sequence of meshes produced by h-refinement. The geometry of the coarsest mesh...recalled with an emphasis on k -refinement. In Section 3, the use of high-order NURBS within a projection technique is studied in the geometri - cally linear...case with a B̄ method to investigate the choice of approximation and projection spaces with NURBS.

An algorithm for solving the perturbed gas dynamic equations

NASA Technical Reports Server (NTRS)

Davis, Sanford

1993-01-01

The present application of a compact, higher-order central-difference approximation to the linearized Euler equations illustrates the multimodal character of these equations by means of computations for acoustic, vortical, and entropy waves. Such dissipationless central-difference methods are shown to propagate waves exhibiting excellent phase and amplitude resolution on the basis of relatively large time-steps; they can be applied to wave problems governed by systems of first-order partial differential equations.

Low-frequency approximation for high-order harmonic generation by a bicircular laser field

NASA Astrophysics Data System (ADS)

Milošević, D. B.

2018-01-01

We present low-frequency approximation (LFA) for high-order harmonic generation (HHG) process. LFA represents the lowest-order term of an expansion of the final-state interaction matrix element in powers of the laser-field frequency ω . In this approximation the plane-wave recombination matrix element which appears in the strong-field approximation is replaced by the exact laser-free recombination matrix element calculated for the laser-field dressed electron momenta. First, we have shown that the HHG spectra obtained using the LFA agree with those obtained solving the time-dependent Schrödinger equation. Next, we have applied this LFA to calculate the HHG rate for inert gases exposed to a bicircular field. The bicircular field, which consists of two coplanar counter-rotating fields having different frequencies (usually ω and 2 ω ), is presently an important subject of scientific research since it enables efficient generation of circularly polarized high-order harmonics (coherent soft x rays). Analyzing the photorecombination matrix element we have found that the HHG rate can efficiently be calculated using the angular momentum basis with the states oriented in the direction of the bicircular field components. Our numerical results show that the HHG rate for atoms having p ground state, for higher high-order harmonic energies, is larger for circularly polarized harmonics having the helicity -1 . For lower energies the harmonics having helicity +1 prevails. The transition between these two harmonic energy regions can appear near the Cooper minimum, which, in the case of Ar atoms, makes the selection of high-order harmonics having the same helicity much easier. This is important for applications (for example, for generation of attosecond pulse trains of circularly polarized harmonics).

CMB-lensing beyond the Born approximation

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

Marozzi, Giovanni; Fanizza, Giuseppe; Durrer, Ruth

2016-09-01

We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles ℓ ∼< 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussianmore » nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.« less

Higher-Order Extended Lagrangian Born–Oppenheimer Molecular Dynamics for Classical Polarizable Models

DOE PAGES

Albaugh, Alex; Head-Gordon, Teresa; Niklasson, Anders M. N.

2018-01-09

Generalized extended Lagrangian Born−Oppenheimer molecular dynamics (XLBOMD) methods provide a framework for fast iteration-free simulations of models that normally require expensive electronic ground state optimizations prior to the force evaluations at every time step. XLBOMD uses dynamically driven auxiliary degrees of freedom that fluctuate about a variationally optimized ground state of an approximate “shadow” potential which approximates the true reference potential. While the requirements for such shadow potentials are well understood, constructing such potentials in practice has previously been ad hoc, and in this work, we present a systematic development of XLBOMD shadow potentials that match the reference potential tomore » any order. We also introduce a framework for combining friction-like dissipation for the auxiliary degrees of freedom with general-order integration, a combination that was not previously possible. These developments are demonstrated with a simple fluctuating charge model and point induced dipole polarization models.« less

Higher-Order Extended Lagrangian Born-Oppenheimer Molecular Dynamics for Classical Polarizable Models.

PubMed

Albaugh, Alex; Head-Gordon, Teresa; Niklasson, Anders M N

2018-02-13

Generalized extended Lagrangian Born-Oppenheimer molecular dynamics (XLBOMD) methods provide a framework for fast iteration-free simulations of models that normally require expensive electronic ground state optimizations prior to the force evaluations at every time step. XLBOMD uses dynamically driven auxiliary degrees of freedom that fluctuate about a variationally optimized ground state of an approximate "shadow" potential which approximates the true reference potential. While the requirements for such shadow potentials are well understood, constructing such potentials in practice has previously been ad hoc, and in this work, we present a systematic development of XLBOMD shadow potentials that match the reference potential to any order. We also introduce a framework for combining friction-like dissipation for the auxiliary degrees of freedom with general-order integration, a combination that was not previously possible. These developments are demonstrated with a simple fluctuating charge model and point induced dipole polarization models.

Higher-Order Extended Lagrangian Born–Oppenheimer Molecular Dynamics for Classical Polarizable Models

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

Albaugh, Alex; Head-Gordon, Teresa; Niklasson, Anders M. N.

Generalized extended Lagrangian Born−Oppenheimer molecular dynamics (XLBOMD) methods provide a framework for fast iteration-free simulations of models that normally require expensive electronic ground state optimizations prior to the force evaluations at every time step. XLBOMD uses dynamically driven auxiliary degrees of freedom that fluctuate about a variationally optimized ground state of an approximate “shadow” potential which approximates the true reference potential. While the requirements for such shadow potentials are well understood, constructing such potentials in practice has previously been ad hoc, and in this work, we present a systematic development of XLBOMD shadow potentials that match the reference potential tomore » any order. We also introduce a framework for combining friction-like dissipation for the auxiliary degrees of freedom with general-order integration, a combination that was not previously possible. These developments are demonstrated with a simple fluctuating charge model and point induced dipole polarization models.« less

Higher order temporal finite element methods through mixed formalisms.

PubMed

Kim, Jinkyu

2014-01-01

The extended framework of Hamilton's principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.

Effects of static equilibrium and higher-order nonlinearities on rotor blade stability in hover

NASA Technical Reports Server (NTRS)

Crespodasilva, Marcelo R. M.; Hodges, Dewey H.

1988-01-01

The equilibrium and stability of the coupled elastic lead/lag, flap, and torsion motion of a cantilever rotor blade in hover are addressed, and the influence of several higher-order terms in the equations of motion of the blade is determined for a range of values of collective pitch. The blade is assumed to be untwisted and to have uniform properties along its span. In addition, chordwise offsets between its elastic, tension, mass, and aerodynamic centers are assumed to be negligible for simplicity. The aerodynamic forces acting on the blade are modeled using a quasi-steady, strip-theory approximation.

Target correlation effects on neutron-nucleus total, absorption, and abrasion cross sections

NASA Technical Reports Server (NTRS)

Cucinotta, Francis A.; Townsend, Lawrence W.; Wilson, John W.

1991-01-01

Second order optical model solutions to the elastic scattering amplitude were used to evaluate total, absorption, and abrasion cross sections for neutron nucleus scattering. Improved agreement with experimental data for total and absorption cross sections is found when compared with first order (coherent approximation) solutions, especially below several hundred MeV. At higher energies, the first and second order solutions are similar. There are also large differences in abrasion cross section calculations; these differences indicate a crucial role for cluster knockout in the abrasion step.

Higgs boson production via vector-boson fusion at next-to-next-to-leading order in QCD.

PubMed

Bolzoni, Paolo; Maltoni, Fabio; Moch, Sven-Olaf; Zaro, Marco

2010-07-02

We present the total cross sections at next-to-next-to-leading order in the strong coupling for Higgs boson production via weak-boson fusion. Our results are obtained via the structure function approach, which builds upon the approximate, though very accurate, factorization of the QCD corrections between the two quark lines. The theoretical uncertainty on the total cross sections at the LHC from higher order corrections and the parton distribution uncertainties are estimated at the 2% level each for a wide range of Higgs boson masses.

Analysis of warping deformation modes using higher order ANCF beam element

NASA Astrophysics Data System (ADS)

Orzechowski, Grzegorz; Shabana, Ahmed A.

2016-02-01

Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition. However, in the absolute nodal coordinate formulation (ANCF) continuum-based beams, this assumption can be relaxed allowing for capturing deformation modes that couple the cross-section deformation and beam bending, torsion, and/or elongation. The deformation modes captured by ANCF finite elements depend on the interpolating polynomials used. The most widely used spatial ANCF beam element employs linear approximation in the transverse direction, thereby restricting the cross section deformation and leading to locking problems. The objective of this investigation is to examine the behavior of a higher order ANCF beam element that includes quadratic interpolation in the transverse directions. This higher order element allows capturing warping and non-uniform stretching distribution. Furthermore, this higher order element allows for increasing the degree of continuity at the element interface. It is shown in this paper that the higher order ANCF beam element can be used effectively to capture warping and eliminate Poisson locking that characterizes lower order ANCF finite elements. It is also shown that increasing the degree of continuity requires a special attention in order to have acceptable results. Because higher order elements can be more computationally expensive than the lower order elements, the use of reduced integration for evaluating the stress forces and the use of explicit and implicit numerical integrations to solve the nonlinear dynamic equations of motion are investigated in this paper. It is shown that the use of some of these integration methods can be very effective in reducing the CPU time without adversely affecting the solution accuracy.

Nekton use of intertidal creek edges in low salinity salt marshes of the Yangtze River estuary along a stream-order gradient

NASA Astrophysics Data System (ADS)

Jin, Binsong; Qin, Haiming; Xu, Wang; Wu, Jihua; Zhong, Junsheng; Lei, Guangchun; Chen, Jiakuan; Fu, Cuizhang

2010-07-01

Non-vegetated creek edges were investigated to explore spatial nekton use patterns in a low salinity intertidal salt marsh creek network of the Yangtze River estuary along a stream-order gradient with four creek orders. Non-vegetated creek edges were arbitrarily defined as the approximately 3 m extending from the creek bank (the marsh-creek interface) into open water. Nekton was sampled using seine nets during daytime high slack water during spring tides for two or three days each in May through July 2008. Twenty-three nekton species (16 fishes and 7 crustaceans) were caught during the study. Fishes were dominated by gobies ( Mugilogobius abei, Periophthalmus magnuspinnatus, Periophthalmus modestus, Synechogobius ommaturus), mullets ( Chelon haematocheilus, Liza affinis) and Chinese sea bass ( Lateolabrax maculatus). Crustaceans were dominated by mud crab ( Helice tientsinensis) and white prawn ( Exopalaemon carinicauda). Rank abundance curves revealed higher evenness of nekton assemblages in lower-order creeks compared to higher-order creeks. Fish abundance tended to increase with increasing creek order. Crustacean abundance was higher in the first-third order creeks than in the fourth-order creek. Dominant nekton species displayed various trends in abundance and length-frequency distributions along the stream-order gradient. The spatial separation of nekton assemblages between the first-third order creeks and the fourth-order creek could be attributed to geomorphological factors (distance to mouth and cross-sectional area). These findings indicate that both lower- and higher-order creek edges play important yet different roles for nekton species and life history stages in salt marshes.

Enhanced electron transfer kinetics through hybrid graphene-carbon nanotube films.

PubMed

Henry, Philémon A; Raut, Akshay S; Ubnoske, Stephen M; Parker, Charles B; Glass, Jeffrey T

2014-11-01

We report the first study of the electrochemical reactivity of a graphenated carbon nanotube (g-CNT) film. The electron transfer kinetics of the ferri-ferrocyanide couple were examined for a g-CNT film and compared to the kinetics to standard carbon nanotubes (CNTs). The g-CNT film exhibited much higher catalytic activity, with a heterogeneous electron-transfer rate constant, k 0 , approximately two orders of magnitude higher than for standard CNTs. Scanning electron microscopy and Raman spectroscopy were used to correlate the higher electron transfer kinetics with the higher edge-density of the g-CNT film.

Estimate of higher order ionospheric errors in GNSS positioning

NASA Astrophysics Data System (ADS)

Hoque, M. Mainul; Jakowski, N.

2008-10-01

Precise navigation and positioning using GPS/GLONASS/Galileo require the ionospheric propagation errors to be accurately determined and corrected for. Current dual-frequency method of ionospheric correction ignores higher order ionospheric errors such as the second and third order ionospheric terms in the refractive index formula and errors due to bending of the signal. The total electron content (TEC) is assumed to be same at two GPS frequencies. All these assumptions lead to erroneous estimations and corrections of the ionospheric errors. In this paper a rigorous treatment of these problems is presented. Different approximation formulas have been proposed to correct errors due to excess path length in addition to the free space path length, TEC difference at two GNSS frequencies, and third-order ionospheric term. The GPS dual-frequency residual range errors can be corrected within millimeter level accuracy using the proposed correction formulas.

The consequences of improperly describing oscillator strengths beyond the electric dipole approximation

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

Lestrange, Patrick J.; Egidi, Franco; Li, Xiaosong, E-mail: xsli@uw.edu

2015-12-21

The interaction between a quantum mechanical system and plane wave light is usually modeled within the electric dipole approximation. This assumes that the intensity of the incident field is constant over the length of the system and transition probabilities are described in terms of the electric dipole transition moment. For short wavelength spectroscopies, such as X-ray absorption, the electric dipole approximation often breaks down. Higher order multipoles are then included to describe transition probabilities. The square of the magnetic dipole and electric quadrupole are often included, but this results in an origin-dependent expression for the oscillator strength. The oscillator strengthmore » can be made origin-independent if all terms through the same order in the wave vector are retained. We will show the consequences and potential pitfalls of using either of these two expressions. It is shown that the origin-dependent expression may violate the Thomas-Reiche-Kuhn sum rule and the origin-independent expression can result in negative transition probabilities.« less

The consequences of improperly describing oscillator strengths beyond the electric dipole approximation.

PubMed

Lestrange, Patrick J; Egidi, Franco; Li, Xiaosong

2015-12-21

The interaction between a quantum mechanical system and plane wave light is usually modeled within the electric dipole approximation. This assumes that the intensity of the incident field is constant over the length of the system and transition probabilities are described in terms of the electric dipole transition moment. For short wavelength spectroscopies, such as X-ray absorption, the electric dipole approximation often breaks down. Higher order multipoles are then included to describe transition probabilities. The square of the magnetic dipole and electric quadrupole are often included, but this results in an origin-dependent expression for the oscillator strength. The oscillator strength can be made origin-independent if all terms through the same order in the wave vector are retained. We will show the consequences and potential pitfalls of using either of these two expressions. It is shown that the origin-dependent expression may violate the Thomas-Reiche-Kuhn sum rule and the origin-independent expression can result in negative transition probabilities.

The consequences of improperly describing oscillator strengths beyond the electric dipole approximation

NASA Astrophysics Data System (ADS)

Lestrange, Patrick J.; Egidi, Franco; Li, Xiaosong

2015-12-01

The interaction between a quantum mechanical system and plane wave light is usually modeled within the electric dipole approximation. This assumes that the intensity of the incident field is constant over the length of the system and transition probabilities are described in terms of the electric dipole transition moment. For short wavelength spectroscopies, such as X-ray absorption, the electric dipole approximation often breaks down. Higher order multipoles are then included to describe transition probabilities. The square of the magnetic dipole and electric quadrupole are often included, but this results in an origin-dependent expression for the oscillator strength. The oscillator strength can be made origin-independent if all terms through the same order in the wave vector are retained. We will show the consequences and potential pitfalls of using either of these two expressions. It is shown that the origin-dependent expression may violate the Thomas-Reiche-Kuhn sum rule and the origin-independent expression can result in negative transition probabilities.

Dense grid sibling frames with linear phase filters

NASA Astrophysics Data System (ADS)

Abdelnour, Farras

2013-09-01

We introduce new 5-band dyadic sibling frames with dense time-frequency grid. Given a lowpass filter satisfying certain conditions, the remaining filters are obtained using spectral factorization. The analysis and synthesis filterbanks share the same lowpass and bandpass filters but have different and oversampled highpass filters. This leads to wavelets approximating shift-invariance. The filters are FIR, have linear phase, and the resulting wavelets have vanishing moments. The filters are designed using spectral factorization method. The proposed method leads to smooth limit functions with higher approximation order, and computationally stable filterbanks.

Robust synchronization of master-slave chaotic systems using approximate model: An experimental study.

PubMed

Ahmed, Hafiz; Salgado, Ivan; Ríos, Héctor

2018-02-01

Robust synchronization of master slave chaotic systems are considered in this work. First an approximate model of the error system is obtained using the ultra-local model concept. Then a Continuous Singular Terminal Sliding-Mode (CSTSM) Controller is designed for the purpose of synchronization. The proposed approach is output feedback-based and uses fixed-time higher order sliding-mode (HOSM) differentiator for state estimation. Numerical simulation and experimental results are given to show the effectiveness of the proposed technique. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Divergence of the total cross section for three body rearrangement collisions with coulomb interactions

NASA Technical Reports Server (NTRS)

Omidvar, K.

1972-01-01

Three charged particles 1, 2, 3 collide according to the reaction 1+(2+3) yields (1+3)+2, where (2+3) and (1+3) are hydrogenlike bound states. It is shown when (1+3) is in a highly excited state n, due to the repulsive potential, the cross section in the first Born approximation behaves as 1/n which makes the total cross section to diverge like ln n. The total cross sections in the higher orders of the Born approximation are similarly divergent logarithmically.

"MONSTROUS MOONSHINE" and Physics

NASA Astrophysics Data System (ADS)

Pushkin, A. V.

The report presents some results obtained by the author on the quantum gravitation theory. Algebraic structure of this theory proves to be related to the commutative nonassociative Griess algebra. The theory symmetry is the automorphism group of Griess algebra: "Monster" simple group. Knowledge of the theory symmetry allows to compute observed physical values in the `zero' approximation. The report presents such computed results for values {m_{p}}/{m_{c}} and α, for the latter the `zero' approximation accuracy, controlled by the theory, being one order of magnitude higher than the accuracy of modern measurements.

Time-dependent variational approach in terms of squeezed coherent states: Implication to semi-classical approximation

NASA Technical Reports Server (NTRS)

Tsue, Yasuhiko

1994-01-01

A general framework for time-dependent variational approach in terms of squeezed coherent states is constructed with the aim of describing quantal systems by means of classical mechanics including higher order quantal effects with the aid of canonicity conditions developed in the time-dependent Hartree-Fock theory. The Maslov phase occurring in a semi-classical quantization rule is investigated in this framework. In the limit of a semi-classical approximation in this approach, it is definitely shown that the Maslov phase has a geometric nature analogous to the Berry phase. It is also indicated that this squeezed coherent state approach is a possible way to go beyond the usual WKB approximation.

Born-Oppenheimer approximation for a singular system

NASA Astrophysics Data System (ADS)

Akbas, Haci; Turgut, O. Teoman

2018-01-01

We discuss a simple singular system in one dimension, two heavy particles interacting with a light particle via an attractive contact interaction and not interacting among themselves. It is natural to apply the Born-Oppenheimer approximation to this problem. We present a detailed discussion of this approach; the advantage of this simple model is that one can estimate the error terms self-consistently. Moreover, a Fock space approach to this problem is presented where an expansion can be proposed to get higher order corrections. A slight modification of the same problem in which the light particle is relativistic is discussed in a later section by neglecting pair creation processes. Here, the second quantized description is more challenging, but with some care, one can recover the first order expression exactly.

Upwind methods for the Baer–Nunziato equations and higher-order reconstruction using artificial viscosity

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

Fraysse, F., E-mail: francois.fraysse@rs2n.eu; E. T. S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Madrid; Redondo, C.

This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is appliedmore » to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction.« less

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

DOE PAGES

Grout, Ray; Kolla, Hemanth; Minion, Michael; ...

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering frommore » soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. Here, we demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

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

Grout, Ray; Kolla, Hemanth; Minion, Michael

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited tomore » recovering from soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual on the first correction iteration and changes slowly between successive iterations. We demonstrate the effectiveness of this strategy for both canonical test problems and a comprehen- sive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

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

Grout, Ray; Kolla, Hemanth; Minion, Michael

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering frommore » soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. We demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Breeding for improved potato nutrition: High amylose starch potatoes show promise as fiber source

USDA-ARS?s Scientific Manuscript database

Potato starch is composed of approximately 75% amylopectin and 25% amylose. We are interested in breeding for higher amylose content, which would increase the fiber content of potato and decrease glycemic index. In order to make progress in a breeding program, we have developed a high throughput ass...

75 FR 9196 - Letter From Secretary of Energy Accepting Defense Nuclear Facilities Safety Board (Board...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-03-01

... capability for non- vital laboratory room electrical loads that provides an engineered control to reduce..., approximately two orders of magnitude higher than our evaluation guideline for selecting safety class controls. Approval of the DSA included recognition of weaknesses in the facility's control set and the need to...

General relaxation schemes in multigrid algorithms for higher order singularity methods

NASA Technical Reports Server (NTRS)

Oskam, B.; Fray, J. M. J.

1981-01-01

Relaxation schemes based on approximate and incomplete factorization technique (AF) are described. The AF schemes allow construction of a fast multigrid method for solving integral equations of the second and first kind. The smoothing factors for integral equations of the first kind, and comparison with similar results from the second kind of equations are a novel item. Application of the MD algorithm shows convergence to the level of truncation error of a second order accurate panel method.

Nanosecond-pulse-controlled higher-order sideband comb in a GaAs optomechanical disk resonator in the non-perturbative regime

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

Xiong, Hao, E-mail: haoxiong1217@gmail.com; Si, Liu-Gang, E-mail: siliugang@gmail.com; Lü, Xin-You

2014-10-15

We propose an interesting scheme for tunable high-order sideband comb generation by utilizing ultrastrong optomechanical interaction in a GaAs optomechanical disk resonator beyond the perturbative approximation. We analyze the nonlinear nature of the optomechanical interaction, and give a full description of the non-perturbative effects. It is shown, within the non-perturbative regime, that high-order sideband comb with large intensities can be realized and controlled in a GaAs optomechanical disk resonator with experimentally achievable system parameters, and the non-perturbative regime leads to rich and nontrivial behavior.

Convergence behavior of the random phase approximation renormalized correlation energy

NASA Astrophysics Data System (ADS)

Bates, Jefferson E.; Sensenig, Jonathon; Ruzsinszky, Adrienn

2017-05-01

Based on the random phase approximation (RPA), RPA renormalization [J. E. Bates and F. Furche, J. Chem. Phys. 139, 171103 (2013), 10.1063/1.4827254] is a robust many-body perturbation theory that works for molecules and materials because it does not diverge as the Kohn-Sham gap approaches zero. Additionally, RPA renormalization enables the simultaneous calculation of RPA and beyond-RPA correlation energies since the total correlation energy is the sum of a series of independent contributions. The first-order approximation (RPAr1) yields the dominant beyond-RPA contribution to the correlation energy for a given exchange-correlation kernel, but systematically underestimates the total beyond-RPA correction. For both the homogeneous electron gas model and real systems, we demonstrate numerically that RPA renormalization beyond first order converges monotonically to the infinite-order beyond-RPA correlation energy for several model exchange-correlation kernels and that the rate of convergence is principally determined by the choice of the kernel and spin polarization of the ground state. The monotonic convergence is rationalized from an analysis of the RPA renormalized correlation energy corrections, assuming the exchange-correlation kernel and response functions satisfy some reasonable conditions. For spin-unpolarized atoms, molecules, and bulk solids, we find that RPA renormalization is typically converged to 1 meV error or less by fourth order regardless of the band gap or dimensionality. Most spin-polarized systems converge at a slightly slower rate, with errors on the order of 10 meV at fourth order and typically requiring up to sixth order to reach 1 meV error or less. Slowest to converge, however, open-shell atoms present the most challenging case and require many higher orders to converge.

Probabilistic Reasoning for Plan Robustness

NASA Technical Reports Server (NTRS)

Schaffer, Steve R.; Clement, Bradley J.; Chien, Steve A.

2005-01-01

A planning system must reason about the uncertainty of continuous variables in order to accurately project the possible system state over time. A method is devised for directly reasoning about the uncertainty in continuous activity duration and resource usage for planning problems. By representing random variables as parametric distributions, computing projected system state can be simplified in some cases. Common approximation and novel methods are compared for over-constrained and lightly constrained domains. The system compares a few common approximation methods for an iterative repair planner. Results show improvements in robustness over the conventional non-probabilistic representation by reducing the number of constraint violations witnessed by execution. The improvement is more significant for larger problems and problems with higher resource subscription levels but diminishes as the system is allowed to accept higher risk levels.

A refinement of the combination equations for evaporation

USGS Publications Warehouse

Milly, P.C.D.

1991-01-01

Most combination equations for evaporation rely on a linear expansion of the saturation vapor-pressure curve around the air temperature. Because the temperature at the surface may differ from this temperature by several degrees, and because the saturation vapor-pressure curve is nonlinear, this approximation leads to a certain degree of error in those evaporation equations. It is possible, however, to introduce higher-order polynomial approximations for the saturation vapor-pressure curve and to derive a family of explicit equations for evaporation, having any desired degree of accuracy. Under the linear approximation, the new family of equations for evaporation reduces, in particular cases, to the combination equations of H. L. Penman (Natural evaporation from open water, bare soil and grass, Proc. R. Soc. London, Ser. A193, 120-145, 1948) and of subsequent workers. Comparison of the linear and quadratic approximations leads to a simple approximate expression for the error associated with the linear case. Equations based on the conventional linear approximation consistently underestimate evaporation, sometimes by a substantial amount. ?? 1991 Kluwer Academic Publishers.

3D Higher Order Modeling in the BEM/FEM Hybrid Formulation

NASA Technical Reports Server (NTRS)

Fink, P. W.; Wilton, D. R.

2000-01-01

Higher order divergence- and curl-conforming bases have been shown to provide significant benefits, in both convergence rate and accuracy, in the 2D hybrid finite element/boundary element formulation (P. Fink and D. Wilton, National Radio Science Meeting, Boulder, CO, Jan. 2000). A critical issue in achieving the potential for accuracy of the approach is the accurate evaluation of all matrix elements. These involve products of high order polynomials and, in some instances, singular Green's functions. In the 2D formulation, the use of a generalized Gaussian quadrature method was found to greatly facilitate the computation and to improve the accuracy of the boundary integral equation self-terms. In this paper, a 3D, hybrid electric field formulation employing higher order bases and higher order elements is presented. The improvements in convergence rate and accuracy, compared to those resulting from lower order modeling, are established. Techniques developed to facilitate the computation of the boundary integral self-terms are also shown to improve the accuracy of these terms. Finally, simple preconditioning techniques are used in conjunction with iterative solution procedures to solve the resulting linear system efficiently. In order to handle the boundary integral singularities in the 3D formulation, the parent element- either a triangle or rectangle-is subdivided into a set of sub-triangles with a common vertex at the singularity. The contribution to the integral from each of the sub-triangles is computed using the Duffy transformation to remove the singularity. This method is shown to greatly facilitate t'pe self-term computation when the bases are of higher order. In addition, the sub-triangles can be further divided to achieve near arbitrary accuracy in the self-term computation. An efficient method for subdividing the parent element is presented. The accuracy obtained using higher order bases is compared to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained using higher order bases are compared to those obtained with lower order bases for selected sample

Higher rank ABJM Wilson loops from matrix models

DOE PAGES

Cookmeyer, Jonathan; Liu, James T.; Pando Zayas, Leopoldo A.

2016-11-21

We compute the vacuum expectation values of 1/6 supersymmetric Wilson loops in higher dimensional representations of the gauge group in ABJM theory. We then present results for the m-symmetric and m-antisymmetric representations by exploiting standard matrix model techniques. At leading order, in the saddle point approximation, our expressions reproduce holographic results from both D6 and D2 branes corresponding to the antisymmetric and symmetric representations, respectively. We also compute 1/N corrections to the leading saddle point results.

A critical evaluation of perturbation theories by Monte Carlo simulation of the first four perturbation terms in a Helmholtz energy expansion for the Lennard-Jones fluid

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Gross, Joachim

2017-07-01

The Helmholtz energy of a fluid interacting by a Lennard-Jones pair potential is expanded in a perturbation series. Both the methods of Barker-Henderson (BH) and of Weeks-Chandler-Andersen (WCA) are evaluated for the division of the intermolecular potential into reference and perturbation parts. The first four perturbation terms are evaluated for various densities and temperatures (in the ranges ρ*=0 -1.5 and T*=0.5 -12 ) using Monte Carlo simulations in the canonical ensemble. The simulation results are used to test several approximate theoretical methods for describing perturbation terms or for developing an approximate infinite order perturbation series. Additionally, the simulations serve as a basis for developing fully analytical third order BH and WCA perturbation theories. The development of analytical theories allows (1) a careful comparison between the BH and WCA formalisms, and (2) a systematic examination of the effect of higher-order perturbation terms on calculated thermodynamic properties of fluids. Properties included in the comparison are supercritical thermodynamic properties (pressure, internal energy, and chemical potential), vapor-liquid phase equilibria, second virial coefficients, and heat capacities. For all properties studied, we find a systematically improved description upon using a higher-order perturbation theory. A result of particular relevance is that a third order perturbation theory is capable of providing a quantitative description of second virial coefficients to temperatures as low as the triple-point of the Lennard-Jones fluid. We find no reason to prefer the WCA formalism over the BH formalism.

Treatment of pairing correlations based on the equations of motion for zero-coupled pair operators

NASA Astrophysics Data System (ADS)

Andreozzi, F.; Covello, A.; Gargano, A.; Ye, Liu Jian; Porrino, A.

1985-07-01

The pairing problem is treated by means of the equations of motion for zero-coupled pair operators. Exact equations for the seniority-v states of N particles are derived. These equations can be solved by a step-by-step procedure which consists of progressively adding pairs of particles to a core. The theory can be applied at several levels of approximation depending on the number of core states which are taken into account. Some numerical applications to the treatment of v=0, v=1, and v=2 states in the Ni isotopes are performed. The accuracy of various approximations is tested by comparison with exact results. For the seniority-one and seniority-two problems it turns out that the results obtained from the first-order theory are very accurate, while those of higher order calculations are practically exact. Concerning the seniority-zero problem, a fifth-order calculation reproduces quite well the three lowest states.

Mean field study of a propagation-turnover lattice model for the dynamics of histone marking

NASA Astrophysics Data System (ADS)

Yao, Fan; Li, FangTing; Li, TieJun

2017-02-01

We present a mean field study of a propagation-turnover lattice model, which was proposed by Hodges and Crabtree [Proc. Nat. Acad. Sci. 109, 13296 (2012)] for understanding how posttranslational histone marks modulate gene expression in mammalian cells. The kinetics of the lattice model consists of nucleation, propagation and turnover mechanisms, and exhibits second-order phase transition for the histone marking domain. We showed rigorously that the dynamics essentially depends on a non-dimensional parameter κ = k +/ k -, the ratio between the propagation and turnover rates, which has been observed in the simulations. We then studied the lowest order mean field approximation, and observed the phase transition with an analytically obtained critical parameter. The boundary layer analysis was utilized to investigate the structure of the decay profile of the mark density. We also studied the higher order mean field approximation to achieve sharper estimate of the critical transition parameter and more detailed features. The comparison between the simulation and theoretical results shows the validity of our theory.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017

Description of high-power laser radiation in the paraxial approximation

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

Milant'ev, V P; Karnilovich, S P; Shaar, Ya N

2015-11-30

We consider the feasibility of an adequate description of a laser pulse of arbitrary shape within the framework of the paraxial approximation. In this approximation, using a parabolic equation and an expansion in the small parameter, expressions are obtained for the field of a sufficiently intense laser radiation given in the form of axially symmetric Hermite – Gaussian beams of arbitrary mode and arbitrary polarisation. It is shown that in the case of sufficiently short pulses, corrections to the transverse components of the laser field are the first-order rather than the secondorder quantities in the expansion in the small parameter.more » The peculiarities of the description of higher-mode Hermite – Gaussian beams are outlined. (light wave transformation)« less

Thomas-Fermi approximation for a condensate with higher-order interactions

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

Thoegersen, M.; Jensen, A. S.; Zinner, N. T.

We consider the ground state of a harmonically trapped Bose-Einstein condensate within the Gross-Pitaevskii theory including the effective-range corrections for a two-body zero-range potential. The resulting nonlinear Schroedinger equation is solved analytically in the Thomas-Fermi approximation neglecting the kinetic-energy term. We present results for the chemical potential and the condensate profiles, discuss boundary conditions, and compare to the usual Thomas-Fermi approach. We discuss several ways to increase the influence of effective-range corrections in experiment with magnetically tunable interactions. The level of tuning required could be inside experimental reach in the near future.

Kurtosis Approach for Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation.

The Zeldovich & Adhesion approximations and applications to the local universe

NASA Astrophysics Data System (ADS)

Hidding, Johan; van de Weygaert, Rien; Shandarin, Sergei

2016-10-01

The Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A 3 lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim; Shaw, Leah

2012-02-01

Adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a moment-closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and epidemic spread model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim

2013-03-01

Dynamics of adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a systematic approach to moment closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the mean-field prediction and simulations of the full network system.

Three-Dimensional Navier-Stokes Method with Two-Equation Turbulence Models for Efficient Numerical Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Bardina, J. E.

1994-01-01

A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in complex geometries with good accuracy.

Higher-order correlations for fluctuations in the presence of fields.

PubMed

Boer, A; Dumitru, S

2002-10-01

The higher-order moments of the fluctuations for thermodynamic systems in the presence of fields are investigated in the framework of a theoretical method. The method uses a generalized statistical ensemble consistent with an adequate expression for the internal energy. The applications refer to the case of a system in a magnetoquasistatic field. In the case of linear magnetic media, one finds that, for the description of the magnetic induction fluctuations, the Gaussian approximation is satisfactory. For nonlinear media, the corresponding fluctuations are non-Gaussian, having a non-null asymmetry. Furthermore, the respective fluctuations have characteristics of leptokurtic, mesokurtic and platykurtic type, depending on the value of the magnetic field strength as compared with a scaling factor of the magnetization curve.

Finite element dynamic analysis on CDC STAR-100 computer

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lambiotte, J. J., Jr.

1978-01-01

Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.

Detecting higher-order interactions among the spiking events in a group of neurons.

PubMed

Martignon, L; Von Hasseln, H; Grün, S; Aertsen, A; Palm, G

1995-06-01

We propose a formal framework for the description of interactions among groups of neurons. This framework is not restricted to the common case of pair interactions, but also incorporates higher-order interactions, which cannot be reduced to lower-order ones. We derive quantitative measures to detect the presence of such interactions in experimental data, by statistical analysis of the frequency distribution of higher-order correlations in multiple neuron spike train data. Our first step is to represent a frequency distribution as a Markov field on the minimal graph it induces. We then show the invariance of this graph with regard to changes of state. Clearly, only linear Markov fields can be adequately represented by graphs. Higher-order interdependencies, which are reflected by the energy expansion of the distribution, require more complex graphical schemes, like constellations or assembly diagrams, which we introduce and discuss. The coefficients of the energy expansion not only point to the interactions among neurons but are also a measure of their strength. We investigate the statistical meaning of detected interactions in an information theoretic sense and propose minimum relative entropy approximations as null hypotheses for significance tests. We demonstrate the various steps of our method in the situation of an empirical frequency distribution on six neurons, extracted from data on simultaneous multineuron recordings from the frontal cortex of a behaving monkey and close with a brief outlook on future work.

Silica-coated gold nanorods as saturable absorber for bound-state pulse generation in a fiber laser with near-zero dispersion

NASA Astrophysics Data System (ADS)

Wang, Xude; Luo, Aiping; Luo, Zhichao; Liu, Meng; Zou, Feng; Zhu, Yanfang; Xue, Jianping; Xu, Wencheng

2017-11-01

We presented a bound-state operation in a fiber laser with near-zero anomalous dispersion based on a silica-coated gold nanorods (GNRs@SiO2) saturable absorber (SA). Using a balanced twin detector measurement technique, the modulation depth and nonsaturable loss of the GNRs@SiO2 SA were measured to be approximately 3.5% and 39.3%, respectively. By virtue of the highly nonlinear effect of the GNRs@SiO2 SA, the bound-state pulses could be easily observed. Besides the lower-order bound-state pulses with two, three, and four solitons, the higher-order bound states with up to 12 solitons were also obtained in the laser cavity. The pulse profiles of the higher-order bound states were further reconstructed theoretically. The experimental results would give further insight towards understanding the complex nonlinear dynamics of bound-state pulses in fiber lasers.

Single electron impact ionization of the methane molecule

NASA Astrophysics Data System (ADS)

Bouamoud, Mammar; Sahlaoui, Mohammed; Benmansour, Nour El Houda; Atomic and Molecular Collisions Team

2014-10-01

Triply differential cross sections (TDCS) results of electron-impact ionization of the inner 2a1 molecular orbital of CH4 are presented in the framework of the Second Born Approximation and compared with the experimental data performed in coplanar asymmetric geometry. The cross sections are averaged on the random orientations of the molecular target for accurate comparison with experiments and are compared also with the theoretical calculations of the Three Coulomb wave (3CW) model. Our results are in good agreement with experiments and 3CW results in the binary peak. In contrast the Second Born Approximation yields a significant higher values compared to the 3CW results for the recoil peak and seems to describe suitably the recoil region where higher order effects can occur with the participation of the recoiling ion in the collision process.

Higher-Order Hamiltonian Model for Unidirectional Water Waves

NASA Astrophysics Data System (ADS)

Bona, J. L.; Carvajal, X.; Panthee, M.; Scialom, M.

2018-04-01

Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of these more complex equations is that their solutions corresponding to physically relevant initial perturbations of the rest state may be accurate on a much longer timescale. The initial value problem for the class of equations that emerges from our derivation is then considered. A local well-posedness theory is straightforwardly established by a contraction mapping argument. A subclass of these equations possess a special Hamiltonian structure that implies the local theory can be continued indefinitely.

Effect of initial phase on error in electron energy obtained using paraxial approximation for a focused laser pulse in vacuum

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

Singh, Kunwar Pal, E-mail: k-psingh@yahoo.com; Department of Physics, Shri Venkateshwara University, Gajraula, Amroha, Uttar Pradesh 244236; Arya, Rashmi

2015-09-14

We have investigated the effect of initial phase on error in electron energy obtained using paraxial approximation to study electron acceleration by a focused laser pulse in vacuum using a three dimensional test-particle simulation code. The error is obtained by comparing the energy of the electron for paraxial approximation and seventh-order correction description of the fields of Gaussian laser. The paraxial approximation predicts wrong laser divergence and wrong electron escape time from the pulse which leads to prediction of higher energy. The error shows strong phase dependence for the electrons lying along the axis of the laser for linearly polarizedmore » laser pulse. The relative error may be significant for some specific values of initial phase even at moderate values of laser spot sizes. The error does not show initial phase dependence for a circularly laser pulse.« less

Optimized equation of the state of the square-well fluid of variable range based on a fourth-order free-energy expansion.

PubMed

Espíndola-Heredia, Rodolfo; del Río, Fernando; Malijevsky, Anatol

2009-01-14

The free energy of square-well (SW) systems of hard-core diameter sigma with ranges 1 < or = lambda < or = 3 is expanded in a perturbation series. This interval covers most ranges of interest, from short-ranged SW fluids (lambda approximately 1.2) used in modeling colloids to long ranges (lambda approximately 3) where the van der Waals classic approximation holds. The first four terms are evaluated by means of extensive Monte Carlo simulations. The calculations are corrected for the thermodynamic limit and care is taken to evaluate and to control the various sources of error. The results for the first two terms in the series confirm well-known independent results but have an increased estimated accuracy and cover a wider set of well ranges. The results for the third- and fourth-order terms are novel. The free-energy expansion for systems with short and intermediate ranges, 1 < or = lambda < or = 2, is seen to have properties similar to those of systems with longer ranges, 2 < or = lambda < or = 3. An equation of state (EOS) is built to represent the free-energy data. The thermodynamics given by this EOS, confronted against independent computer simulations, is shown to predict accurately the internal energy, pressure, specific heat, and chemical potential of the SW fluids considered and for densities 0 < or = rho sigma(3) < or = 0.9 including subcritical temperatures. This fourth-order theory is estimated to be accurate except for a small region at high density, rho sigma(3) approximately 0.9, and low temperature where terms of still higher order might be needed.

Generation of higher-order rogue waves from multibreathers by double degeneracy in an optical fiber.

PubMed

Wang, Lihong; He, Jingsong; Xu, Hui; Wang, Ji; Porsezian, Kuppuswamy

2017-04-01

In this paper, we construct a special kind of breather solution of the nonlinear Schrödinger (NLS) equation, the so-called breather-positon (b-positon for short), which can be obtained by taking the limit λ_{j}→λ_{1} of the Lax pair eigenvalues in the order-n periodic solution, which is generated by the n-fold Darboux transformation from a special "seed" solution-plane wave. Further, an order-n b-positon gives an order-n rogue wave under a limit λ_{1}→λ_{0}. Here, λ_{0} is a special eigenvalue in a breather of the NLS equation such that its period goes to infinity. Several analytical plots of order-2 breather confirm visually this double degeneration. The last limit in this double degeneration can be realized approximately in an optical fiber governed by the NLS equation, in which an injected initial ideal pulse is created by a frequency comb system and a programable optical filter (wave shaper) according to the profile of an analytical form of the b-positon at a certain position z_{0}. We also suggest a new way to observe higher-order rogue waves generation in an optical fiber, namely, measure the patterns at the central region of the higher-order b-positon generated by above ideal initial pulses when λ_{1} is very close to the λ_{0}. The excellent agreement between the numerical solutions generated from initial ideal inputs with a low signal-to-noise ratio and analytical solutions of order-2 b-positon supports strongly this way in a realistic optical fiber system. Our results also show the validity of the generating mechanism of a higher-order rogue waves from a multibreathers through the double degeneration.

Homogenization of one-dimensional draining through heterogeneous porous media including higher-order approximations

NASA Astrophysics Data System (ADS)

Anderson, Daniel M.; McLaughlin, Richard M.; Miller, Cass T.

2018-02-01

We examine a mathematical model of one-dimensional draining of a fluid through a periodically-layered porous medium. A porous medium, initially saturated with a fluid of a high density is assumed to drain out the bottom of the porous medium with a second lighter fluid replacing the draining fluid. We assume that the draining layer is sufficiently dense that the dynamics of the lighter fluid can be neglected with respect to the dynamics of the heavier draining fluid and that the height of the draining fluid, represented as a free boundary in the model, evolves in time. In this context, we neglect interfacial tension effects at the boundary between the two fluids. We show that this problem admits an exact solution. Our primary objective is to develop a homogenization theory in which we find not only leading-order, or effective, trends but also capture higher-order corrections to these effective draining rates. The approximate solution obtained by this homogenization theory is compared to the exact solution for two cases: (1) the permeability of the porous medium varies smoothly but rapidly and (2) the permeability varies as a piecewise constant function representing discrete layers of alternating high/low permeability. In both cases we are able to show that the corrections in the homogenization theory accurately predict the position of the free boundary moving through the porous medium.

The refractive index in electron microscopy and the errors of its approximations.

PubMed

Lentzen, M

2017-05-01

In numerical calculations for electron diffraction often a simplified form of the electron-optical refractive index, linear in the electric potential, is used. In recent years improved calculation schemes have been proposed, aiming at higher accuracy by including higher-order terms of the electric potential. These schemes start from the relativistically corrected Schrödinger equation, and use a second simplified form, now for the refractive index squared, being linear in the electric potential. The second and higher-order corrections thus determined have, however, a large error, compared to those derived from the relativistically correct refractive index. The impact of the two simplifications on electron diffraction calculations is assessed through numerical comparison of the refractive index at high-angle Coulomb scattering and of cross-sections for a wide range of scattering angles, kinetic energies, and atomic numbers. Copyright © 2016 Elsevier B.V. All rights reserved.

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

Broda, Jill Terese

The neutron flux across the nuclear reactor core is of interest to reactor designers and others. The diffusion equation, an integro-differential equation in space and energy, is commonly used to determine the flux level. However, the solution of a simplified version of this equation when automated is very time consuming. Since the flux level changes with time, in general, this calculation must be made repeatedly. Therefore solution techniques that speed the calculation while maintaining accuracy are desirable. One factor that contributes to the solution time is the spatial flux shape approximation used. It is common practice to use the samemore » order flux shape approximation in each energy group even though this method may not be the most efficient. The one-dimensional, two-energy group diffusion equation was solved, for the node average flux and core k-effective, using two sets of spatial shape approximations for each of three reactor types. A fourth-order approximation in both energy groups forms the first set of approximations used. The second set used combines a second-order approximation with a fourth-order approximation in energy group two. Comparison of the results from the two approximation sets show that the use of a different order spatial flux shape approximation results in considerable loss in accuracy for the pressurized water reactor modeled. However, the loss in accuracy is small for the heavy water and graphite reactors modeled. The use of different order approximations in each energy group produces mixed results. Further investigation into the accuracy and computing time is required before any quantitative advantage of the use of the second-order approximation in energy group one and the fourth-order approximation in energy group two can be determined.« less

A New Higher-Order Composite Theory for Analysis and Design of High Speed Tilt-Rotor Blades

NASA Technical Reports Server (NTRS)

McCarthy, Thomas Robert

1996-01-01

A higher-order theory is developed to model composite box beams with arbitrary wall thicknesses. The theory, based on a refined displacement field, represents a three-dimensional model which approximates the elasticity solution. Therefore, the cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are automatically included in the formulation. The model accurately captures the transverse shear stresses through the thickness of each wall while satisfying all stress-free boundary conditions. Several numerical results are presented to validate the present theory. The developed theory is then used to model the load carrying member of a tilt-rotor blade which has thick-walled sections. The composite structural analysis is coupled with an aerodynamic analysis to compute the aeroelastic stability of the blade. Finally, a multidisciplinary optimization procedure is developed to improve the aerodynamic, structural and aeroelastic performance of the tilt-rotor aircraft. The Kreisselmeier-Steinhauser function is used to formulate the multiobjective function problem and a hybrid approximate analysis is used to reduce the computational effort. The optimum results are compared with the baseline values and show significant improvements in the overall performance of the tilt-rotor blade.

Anomalies in the 1D Anderson model: Beyond the band-centre and band-edge cases

NASA Astrophysics Data System (ADS)

Tessieri, L.; Izrailev, F. M.

2018-03-01

We consider the one-dimensional Anderson model with weak disorder. Using the Hamiltonian map approach, we analyse the validity of the random-phase approximation for resonant values of the energy, E = 2 cos(πr) , with r a rational number. We expand the invariant measure of the phase variable in powers of the disorder strength and we show that, contrary to what happens at the centre and at the edges of the band, for all other resonant energies the leading term of the invariant measure is uniform. When higher-order terms are taken into account, a modulation of the invariant measure appears for all resonant values of the energy. This implies that, when the localisation length is computed within the second-order approximation in the disorder strength, the Thouless formula is valid everywhere except at the band centre and at the band edges.

A Runge-Kutta discontinuous finite element method for high speed flows

NASA Technical Reports Server (NTRS)

Bey, Kim S.; Oden, J. T.

1991-01-01

A Runge-Kutta discontinuous finite element method is developed for hyperbolic systems of conservation laws in two space variables. The discontinuous Galerkin spatial approximation to the conservation laws results in a system of ordinary differential equations which are marched in time using Runge-Kutta methods. Numerical results for the two-dimensional Burger's equation show that the method is (p+1)-order accurate in time and space, where p is the degree of the polynomial approximation of the solution within an element and is capable of capturing shocks over a single element without oscillations. Results for this problem also show that the accuracy of the solution in smooth regions is unaffected by the local projection and that the accuracy in smooth regions increases as p increases. Numerical results for the Euler equations show that the method captures shocks without oscillations and with higher resolution than a first-order scheme.

For numerical differentiation, dimensionality can be a blessing!

NASA Astrophysics Data System (ADS)

Anderssen, Robert S.; Hegland, Markus

Finite difference methods, such as the mid-point rule, have been applied successfully to the numerical solution of ordinary and partial differential equations. If such formulas are applied to observational data, in order to determine derivatives, the results can be disastrous. The reason for this is that measurement errors, and even rounding errors in computer approximations, are strongly amplified in the differentiation process, especially if small step-sizes are chosen and higher derivatives are required. A number of authors have examined the use of various forms of averaging which allows the stable computation of low order derivatives from observational data. The size of the averaging set acts like a regularization parameter and has to be chosen as a function of the grid size h. In this paper, it is initially shown how first (and higher) order single-variate numerical differentiation of higher dimensional observational data can be stabilized with a reduced loss of accuracy than occurs for the corresponding differentiation of one-dimensional data. The result is then extended to the multivariate differentiation of higher dimensional data. The nature of the trade-off between convergence and stability is explicitly characterized, and the complexity of various implementations is examined.

Real-time approximate optimal guidance laws for the advanced launch system

NASA Technical Reports Server (NTRS)

Speyer, Jason L.; Feeley, Timothy; Hull, David G.

1989-01-01

An approach to optimal ascent guidance for a launch vehicle is developed using an expansion technique. The problem is to maximize the payload put into orbit subject to the equations of motion of a rocket over a rotating spherical earth. It is assumed that the thrust and gravitational forces dominate over the aerodynamic forces. It is shown that these forces can be separated by a small parameter epsilon, where epsilon is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in a series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The zeroth-order problem is that of putting maximum payload into orbit subject to the equations of motion of a rocket in a vacuum over a flat earth. The neglected inertial and aerodynamic terms are included in higher order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only quadrature integrations. These quadrature integrations can be performed rapidly, so that real-time approximate optimization can be used to construct the launch guidance law.

Seismic waves in heterogeneous material: subcell resolution of the discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Castro, Cristóbal E.; Käser, Martin; Brietzke, Gilbert B.

2010-07-01

We present an important extension of the arbitrary high-order discontinuous Galerkin (DG) finite-element method to model 2-D elastic wave propagation in highly heterogeneous material. In this new approach we include space-variable coefficients to describe smooth or discontinuous material variations inside each element using the same numerical approximation strategy as for the velocity-stress variables in the formulation of the elastic wave equation. The combination of the DG method with a time integration scheme based on the solution of arbitrary accuracy derivatives Riemann problems still provides an explicit, one-step scheme which achieves arbitrary high-order accuracy in space and time. Compared to previous formulations the new scheme contains two additional terms in the form of volume integrals. We show that the increasing computational cost per element can be overcompensated due to the improved material representation inside each element as coarser meshes can be used which reduces the total number of elements and therefore computational time to reach a desired error level. We confirm the accuracy of the proposed scheme performing convergence tests and several numerical experiments considering smooth and highly heterogeneous material. As the approximation of the velocity and stress variables in the wave equation and of the material properties in the model can be chosen independently, we investigate the influence of the polynomial material representation on the accuracy of the synthetic seismograms with respect to computational cost. Moreover, we study the behaviour of the new method on strong material discontinuities, in the case where the mesh is not aligned with such a material interface. In this case second-order linear material approximation seems to be the best choice, with higher-order intra-cell approximation leading to potential instable behaviour. For all test cases we validate our solution against the well-established standard fourth-order finite difference and spectral element method.

Aerodynamic prediction techniques for hypersonic configuration design

NASA Technical Reports Server (NTRS)

1981-01-01

An investigation of approximate theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at moderate hypersonic speeds was performed. Emphasis was placed on approaches that would be responsive to preliminary configuration design level of effort. Potential theory was examined in detail to meet this objective. Numerical pilot codes were developed for relatively simple three dimensional geometries to evaluate the capability of the approximate equations of motion considered. Results from the computations indicate good agreement with higher order solutions and experimental results for a variety of wing, body, and wing-body shapes for values of the hypersonic similarity parameter M delta approaching one.

Characterizing reduced sulfur compounds emissions from a swine concentrated animal feeding operation

NASA Astrophysics Data System (ADS)

Rumsey, Ian C.; Aneja, Viney P.; Lonneman, William A.

2014-09-01

Reduced sulfur compounds (RSCs) emissions from concentrated animal feeding operations (CAFOs) have become a potential environmental and human health concern, as a result of changes in livestock production methods. RSC emissions were determined from a swine CAFO in North Carolina. RSC measurements were made over a period of ≈1 week from both the barn and lagoon during each of the four seasonal periods from June 2007 to April 2008. During sampling, meteorological and other environmental parameters were measured continuously. Seasonal hydrogen sulfide (H2S) barn concentrations ranged from 72 to 631 ppb. Seasonal dimethyl sulfide (DMS; CH3SCH3) and dimethyl disulfide (DMDS; CH3S2CH3) concentrations were 2-3 orders of magnitude lower, ranging from 0.18 to 0.89 ppb and 0.47 to 1.02 ppb, respectively. The overall average barn emission rate was 3.3 g day-1 AU-1 (AU (animal unit) = 500 kg of live animal weight) for H2S, which was approximately two orders of magnitude higher than the DMS and DMDS overall average emissions rates, determined as 0.017 g day-1 AU-1 and 0.036 g day-1 AU-1, respectively. The overall average lagoon flux was 1.33 μg m-2 min-1 for H2S, which was approximately an order of magnitude higher than the overall average DMS (0.12 μg m-2 min-1) and DMDS (0.09 μg m-2 min-1) lagoon fluxes. The overall average lagoon emission for H2S (0.038 g day-1 AU-1) was also approximately an order of magnitude higher than the overall average DMS (0.0034 g day-1 AU-1) and DMDS (0.0028 g day-1 AU-1) emissions. H2S, DMS and DMDS have offensive odors and low odor thresholds. Over all four sampling seasons, 77% of 15 min averaged H2S barn concentrations were an order of magnitude above the average odor threshold. During these sampling periods, however, DMS and DMDS concentrations did not exceed their odor thresholds. The overall average barn and lagoon emissions from this study were used to help estimate barn, lagoon and total (barn + lagoon) RSC emissions from swine CAFOs in North Carolina. Total (barn + lagoon) H2S emissions from swine CAFOs in North Carolina were estimated to be 1.22*106 kg yr-1. The barns had significantly higher H2S emissions than the lagoons, contributing ≈98% of total North Carolina H2S swine CAFO emissions. Total (barn + lagoon) emissions for DMS and DMDS were 1-2 orders of magnitude lower, with barns contributing ≈86% and ≈93% of total emissions, respectively. H2S swine CAFO emissions were estimated to contribute ≈18% of North Carolina H2S emissions.

Broadband single-mode operation of standard optical fibers by using a sub-wavelength optical wire filter.

PubMed

Jung, Yongmin; Brambilla, Gilberto; Richardson, David J

2008-09-15

We report the use of a sub-wavelength optical wire (SOW) with a specifically designed transition region as an efficient tool to filter higher-order modes in multimode waveguides. Higher-order modes are effectively suppressed by controlling the transition taper profile and the diameter of the sub-wavelength optical wire. As a practical example, single-mode operation of a standard telecom optical fiber over a broad spectral window (400 approximately 1700 nm) was demonstrated with a 1microm SOW. The ability to obtain robust and stable single-mode operation over a very broad range of wavelengths offers new possibilities for mode control within fiber devices and is relevant to a range of application sectors including high performance fiber lasers, sensors, photolithography, and optical coherence tomography systems.

Substance and Artifact in the Higher-Order Factors of the Big Five

PubMed Central

McCrae, Robert R.; Jang, Kerry L.; Ando, Juko; Ono, Yutaka; Yamagata, Shinji; Riemann, Rainer; Angleitner, Alois; Spinath, Frank M.

2018-01-01

J. M. Digman (1997) proposed that the Big Five personality traits showed a higher-order structure with 2 factors he labeled α and β. These factors have been alternatively interpreted as heritable components of personality or as artifacts of evaluative bias. Using structural equation modeling, the authors reanalyzed data from a cross-national twin study and from American cross-observer studies and analyzed new multimethod data from a German twin study. In all analyses, artifact models outperformed substance models by root-mean-square error of approximation criteria, but models combining both artifact and substance were slightly better. These findings suggest that the search for the biological basis of personality traits may be more profitably focused on the 5 factors themselves and their specific facets, especially in monomethod studies. PMID:18665712

The performance of a reduced-order adaptive controller when used in multi-antenna hyperthermia treatments with nonlinear temperature-dependent perfusion.

PubMed

Cheng, Kung-Shan; Yuan, Yu; Li, Zhen; Stauffer, Paul R; Maccarini, Paolo; Joines, William T; Dewhirst, Mark W; Das, Shiva K

2009-04-07

In large multi-antenna systems, adaptive controllers can aid in steering the heat focus toward the tumor. However, the large number of sources can greatly increase the steering time. Additionally, controller performance can be degraded due to changes in tissue perfusion which vary non-linearly with temperature, as well as with time and spatial position. The current work investigates whether a reduced-order controller with the assumption of piecewise constant perfusion is robust to temperature-dependent perfusion and achieves steering in a shorter time than required by a full-order controller. The reduced-order controller assumes that the optimal heating setting lies in a subspace spanned by the best heating vectors (virtual sources) of an initial, approximate, patient model. An initial, approximate, reduced-order model is iteratively updated by the controller, using feedback thermal images, until convergence of the heat focus to the tumor. Numerical tests were conducted in a patient model with a right lower leg sarcoma, heated in a 10-antenna cylindrical mini-annual phased array applicator operating at 150 MHz. A half-Gaussian model was used to simulate temperature-dependent perfusion. Simulated magnetic resonance temperature images were used as feedback at each iteration step. Robustness was validated for the controller, starting from four approximate initial models: (1) a 'standard' constant perfusion lower leg model ('standard' implies a model that exactly models the patient with the exception that perfusion is considered constant, i.e., not temperature dependent), (2) a model with electrical and thermal tissue properties varied from 50% higher to 50% lower than the standard model, (3) a simplified constant perfusion pure-muscle lower leg model with +/-50% deviated properties and (4) a standard model with the tumor position in the leg shifted by 1.5 cm. Convergence to the desired focus of heating in the tumor was achieved for all four simulated models. The controller accomplished satisfactory therapeutic outcomes: approximately 80% of the tumor was heated to temperatures 43 degrees C and approximately 93% was maintained at temperatures <41 degrees C. Compared to the controller without model reduction, a approximately 9-25 fold reduction in convergence time was accomplished using approximately 2-3 orthonormal virtual sources. In the situations tested, the controller was robust to the presence of temperature-dependent perfusion. The results of this work can help to lay the foundation for real-time thermal control of multi-antenna hyperthermia systems in clinical situations where perfusion can change rapidly with temperature.

Determination of intermediate perturbed orbits of Near-Earth asteroids from range and range rate measurements at three times

NASA Astrophysics Data System (ADS)

Shefer, V. A.

2014-12-01

Two methods that the author developed earlier for finding the intermediate perturbed orbit of a small celestial body from three pairs of range and range rate observations [1, 2] are applied to the determination of orbits of Near-Earth asteroids. The methods are based on using the superosculating orbits with three- and fourth-order tangency. The degrees of approximation of the real motion by the constructed intermediate orbits near the middle measurement time are two and three orders of magnitude higher than by the Keplerian orbit determined with the help of traditional methods. We calculated the orbits of the asteroids 99942 Apophis, 1566 Icarus, 4179 Toutatis, 2007 DN41 and 2012 DA14. For the sake of brevity, we call the method based on the orbit with third-order tangency as Algorithm A1 and the method based on the orbit with fourth-order tangency -- as Algorithm A2. The results of the calculations are compared with the results of the calculations by the version of the methods mentioned that allows us to construct the unperturbed Keplerian orbit. We call this version of the methods as Algorithm A. The observational data were simulated using the nominal trajectories of the selected asteroids. These trajectories were obtained by the numerical integration of the differential equations of motion subject to the perturbations from the eight major planets, Pluto, and the Moon. The integration was carried out with the help of the 15-order Everhart procedure [3]. The main results of the calculations are the following. When the reference time interval is shortened by half (for small sizes of this interval), the errors in the compared algorithms A, A1, A2 decrease approximately by the factors 4, 16, 64 in coordinates and by the factors 2, 8, 16 in velocities, respectively. Such behavior of the errors is most clearly seen with the asteroids 2007 DN41 and 2012 DA14. This leads to a significant increase in the accuracy of the real motion approximation by the intermediate orbits constructed using the A1 and A2 algorithms (2-4 orders of magnitude in coordinates and 4-7 orders of magnitude in velocities higher) compared to the accuracy of the approximation by Keplerian orbits with decreasing the reference arc of the trajectory. Here, the higher is the efficiency of the algorithms A1 and A2, the smaller are the values of the topocentric distances, i.e., the greater are the perturbations caused by the Earth's gravitation. The advantage of Algorithm A2 over Algorithm A1 in accuracy extends approximately one order of magnitude. The minimal methodic errors of the position vector by using the A1 and A2 algorithms range from several meters in the case of the asteroid Apophis to several millimeters in the case of the asteroid 2012 DA14. Hence, the numerical examples analyzed in this work lead us to conclude that the proposed in [1, 2] methods for determination of an intermediate perturbed orbit from range and range rate measurements at three time points allow for significantly raising the accuracy of the calculation of the initial asteroid orbits in comparison with the algorithm based on the finding the unperturbed Keplerian orbit. The shorter is the orbital arc specified by the extreme time points, the greater is the advantage of the algorithms suggested over the algorithms of the traditional approach in the accuracy. The advantage of the algorithms suggested in the accuracy increases with raising the perturbations too, which is especially important for calculation of the initial trajectories of the space objects detected in the Earth's neighbourhood. The work was supported by the Ministry of Education and Science of the Russian Federation, project no. 2014/223(1567).

Multivariate moment closure techniques for stochastic kinetic models

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

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporallymore » evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.« less

An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics

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

Wu, Tong; Shashkov, Mikhail Jurievich; Morgan, Nathaniel Ray

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas dynamics. The new method evolves conserved unknowns in the current configuration, which obviates the Jacobi matrix that maps the element in a reference coordinate system or the initial coordinate system to the current configuration. The density, momentum, and total energy (ρ, ρu, E) are approximated with conservative higher-order Taylor expansions over the element and are limited toward a piecewise constant field near discontinuities using a limiter. Two new limiting methods are presented for enforcing the bounds on the primitive variables of density, velocity, and specific internal energymore » (ρ, u, e). The nodal velocity, and the corresponding forces, are calculated by solving an approximate Riemann problem at the element nodes. An explicit second-order method is used to temporally advance the solution. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. 1D Cartesian coordinates test problem results are presented to demonstrate the accuracy and convergence order of the new DG method with the new limiters.« less

Quadratic canonical transformation theory and higher order density matrices.

PubMed

Neuscamman, Eric; Yanai, Takeshi; Chan, Garnet Kin-Lic

2009-03-28

Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT's accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H(2)O and N(2) binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.

An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics

DOE PAGES

Wu, Tong; Shashkov, Mikhail Jurievich; Morgan, Nathaniel Ray; ...

2018-04-09

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas dynamics. The new method evolves conserved unknowns in the current configuration, which obviates the Jacobi matrix that maps the element in a reference coordinate system or the initial coordinate system to the current configuration. The density, momentum, and total energy (ρ, ρu, E) are approximated with conservative higher-order Taylor expansions over the element and are limited toward a piecewise constant field near discontinuities using a limiter. Two new limiting methods are presented for enforcing the bounds on the primitive variables of density, velocity, and specific internal energymore » (ρ, u, e). The nodal velocity, and the corresponding forces, are calculated by solving an approximate Riemann problem at the element nodes. An explicit second-order method is used to temporally advance the solution. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. 1D Cartesian coordinates test problem results are presented to demonstrate the accuracy and convergence order of the new DG method with the new limiters.« less

A real-time approximate optimal guidance law for flight in a plane

NASA Technical Reports Server (NTRS)

Feeley, Timothy S.; Speyer, Jason L.

1990-01-01

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

Symmetries, invariants and generating functions: higher-order statistics of biased tracers

NASA Astrophysics Data System (ADS)

Munshi, Dipak

2018-01-01

Gravitationally collapsed objects are known to be biased tracers of an underlying density contrast. Using symmetry arguments, generalised biasing schemes have recently been developed to relate the halo density contrast δh with the underlying density contrast δ, divergence of velocity θ and their higher-order derivatives. This is done by constructing invariants such as s, t, ψ,η. We show how the generating function formalism in Eulerian standard perturbation theory (SPT) can be used to show that many of the additional terms based on extended Galilean and Lifshitz symmetry actually do not make any contribution to the higher-order statistics of biased tracers. Other terms can also be drastically simplified allowing us to write the vertices associated with δh in terms of the vertices of δ and θ, the higher-order derivatives and the bias coefficients. We also compute the cumulant correlators (CCs) for two different tracer populations. These perturbative results are valid for tree-level contributions but at an arbitrary order. We also take into account the stochastic nature bias in our analysis. Extending previous results of a local polynomial model of bias, we express the one-point cumulants Script SN and their two-point counterparts, the CCs i.e. Script Cpq, of biased tracers in terms of that of their underlying density contrast counterparts. As a by-product of our calculation we also discuss the results using approximations based on Lagrangian perturbation theory (LPT).

Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance.

PubMed

Richardson, Magnus J E; Gerstner, Wulfram

2005-04-01

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

On a third-order shear deformation theory for laminated composite shells

NASA Technical Reports Server (NTRS)

Liu, C. F.; Reddy, J. N.

1986-01-01

A higher-order theory based on an assumed displacement field in which the surface displacements are expanded in powers of the thickness coordinate up to the third order is presented. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for small strains but moderately large displacements (i.e., von Karman strains). A finite-element model based on independent approximations of the displacements and bending moments (i.e., mixed formulation) is developed. The element is used to analyze cross-ply and angle-ply laminated shells for bending.

Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

NASA Technical Reports Server (NTRS)

Gunderson, R. W.

1975-01-01

A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

Dynamical Conditions of Ice Supersaturation and Ice Nucleation in Convective Systems: A Comparative Analysis Between in Situ Aircraft Observations and WRF Simulations

NASA Technical Reports Server (NTRS)

D’Alessandro, John J.; Diao, Minghui; Wu, Chenglai; Liu, Xiaohong; Chen, Ming; Morrison, Hugh; Eidhammer, Trude; Jensen, Jorgen B.; Bansemer, Aaron; Zondlo, Mark A.;

Evolution of a beam dynamics model for the transport line in a proton therapy facility

NASA Astrophysics Data System (ADS)

Rizzoglio, V.; Adelmann, A.; Baumgarten, C.; Frey, M.; Gerbershagen, A.; Meer, D.; Schippers, J. M.

2017-12-01

During the conceptual design of an accelerator or beamline, first-order beam dynamics models are essential for studying beam properties. However, they can only produce approximate results. During commissioning, these approximate results are compared to measurements, which will rarely coincide if the model does not include the relevant physics. It is therefore essential that this linear model is extended to include higher-order effects. In this paper, the effects of particle-matter interaction have been included in the model of the transport lines in the proton therapy facility at the Paul Scherrer Institut (PSI) in Switzerland. The first-order models of these beamlines provide an approximated estimation of beam size, energy loss and transmission. To improve the performance of the facility, a more precise model was required and has been developed with opal (Object Oriented Parallel Accelerator Library), a multiparticle open source beam dynamics code. In opal, the Monte Carlo simulations of Coulomb scattering and energy loss are performed seamless with the particle tracking. Beside the linear optics, the influence of the passive elements (e.g., degrader, collimators, scattering foils, and air gaps) on the beam emittance and energy spread can be analyzed in the new model. This allows for a significantly improved precision in the prediction of beam transmission and beam properties. The accuracy of the opal model has been confirmed by numerous measurements.

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

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

Du, Qiang, E-mail: jyanghkbu@gmail.com; Yang, Jiang, E-mail: qd2125@columbia.edu

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simplemore » ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.« less

Efficient Reformulation of the Thermoelastic Higher-order Theory for Fgms

NASA Technical Reports Server (NTRS)

Bansal, Yogesh; Pindera, Marek-Jerzy; Arnold, Steven M. (Technical Monitor)

2002-01-01

Functionally graded materials (FGMs) are characterized by spatially variable microstructures which are introduced to satisfy given performance requirements. The microstructural gradation gives rise to continuously or discretely changing material properties which complicate FGM analysis. Various techniques have been developed during the past several decades for analyzing traditional composites and many of these have been adapted for the analysis of FGMs. Most of the available techniques use the so-called uncoupled approach in order to analyze graded structures. These techniques ignore the effect of microstructural gradation by employing specific spatial material property variations that are either assumed or obtained by local homogenization. The higher-order theory for functionally graded materials (HOTFGM) is a coupled approach developed by Aboudi et al. (1999) which takes the effect of microstructural gradation into consideration and does not ignore the local-global interaction of the spatially variable inclusion phase(s). Despite its demonstrated utility, however, the original formulation of the higher-order theory is computationally intensive. Herein, an efficient reformulation of the original higher-order theory for two-dimensional elastic problems is developed and validated. The use of the local-global conductivity and local-global stiffness matrix approach is made in order to reduce the number of equations involved. In this approach, surface-averaged quantities are the primary variables which replace volume-averaged quantities employed in the original formulation. The reformulation decreases the size of the global conductivity and stiffness matrices by approximately sixty percent. Various thermal, mechanical, and combined thermomechanical problems are analyzed in order to validate the accuracy of the reformulated theory through comparison with analytical and finite-element solutions. The presented results illustrate the efficiency of the reformulation and its advantages in analyzing functionally graded materials.

Extension of relativistic dissipative hydrodynamics to third order

NASA Astrophysics Data System (ADS)

El, Andrej; Xu, Zhe; Greiner, Carsten

2010-04-01

Following the procedure introduced by Israel and Stewart, we expand the entropy current up to the third order in the shear stress tensor παβ and derive a novel third-order evolution equation for παβ. This equation is solved for the one-dimensional Bjorken boost-invariant expansion. The scaling solutions for various values of the shear viscosity to the entropy density ratio η/s are shown to be in very good agreement with those obtained from kinetic transport calculations. For the pressure isotropy starting with 1 at τ0=0.4 fm/c, the third-order corrections to Israel-Stewart theory are approximately 10% for η/s=0.2 and more than a factor of 2 for η/s=3. We also estimate all higher-order corrections to Israel-Stewart theory and demonstrate their importance in describing highly viscous matters.

Long Periodic Terms in the Solar System

NASA Technical Reports Server (NTRS)

Bretagnon, P.

1982-01-01

The long period variations of the first eight planets in the solar system are studied. First, the Lagrangian solution is calculated and then the long period terms with fourth order eccentricities and inclinations are introduced into the perturbation function. A second approximation was made taking into account the short period terms' contribution, namely the perturbations of first order with respect to the masses. Special attention was paid to the determination of the integration constants. The relative importance of the different contributions is shown. It is useless, for example, to introduce the long period terms of fifth order if no account has been taken of the short period terms. Meanwhile, the terms that have been neglected would not introduce large changes in the integration constants. Even so, the calculation should be repeated with higher order short period terms and fifth order long periods.

On processed splitting methods and high-order actions in path-integral Monte Carlo simulations.

PubMed

Casas, Fernando

2010-10-21

Processed splitting methods are particularly well adapted to carry out path-integral Monte Carlo (PIMC) simulations: since one is mainly interested in estimating traces of operators, only the kernel of the method is necessary to approximate the thermal density matrix. Unfortunately, they suffer the same drawback as standard, nonprocessed integrators: kernels of effective order greater than two necessarily involve some negative coefficients. This problem can be circumvented, however, by incorporating modified potentials into the composition, thus rendering schemes of higher effective order. In this work we analyze a family of fourth-order schemes recently proposed in the PIMC setting, paying special attention to their linear stability properties, and justify their observed behavior in practice. We also propose a new fourth-order scheme requiring the same computational cost but with an enlarged stability interval.

Power law-based local search in spider monkey optimisation for lower order system modelling

NASA Astrophysics Data System (ADS)

Sharma, Ajay; Sharma, Harish; Bhargava, Annapurna; Sharma, Nirmala

2017-01-01

The nature-inspired algorithms (NIAs) have shown efficiency to solve many complex real-world optimisation problems. The efficiency of NIAs is measured by their ability to find adequate results within a reasonable amount of time, rather than an ability to guarantee the optimal solution. This paper presents a solution for lower order system modelling using spider monkey optimisation (SMO) algorithm to obtain a better approximation for lower order systems and reflects almost original higher order system's characteristics. Further, a local search strategy, namely, power law-based local search is incorporated with SMO. The proposed strategy is named as power law-based local search in SMO (PLSMO). The efficiency, accuracy and reliability of the proposed algorithm is tested over 20 well-known benchmark functions. Then, the PLSMO algorithm is applied to solve the lower order system modelling problem.

Continuum Absorption Coefficient of Atoms and Ions

NASA Technical Reports Server (NTRS)

Armaly, B. F.

1979-01-01

The rate of heat transfer to the heat shield of a Jupiter probe has been estimated to be one order of magnitude higher than any previously experienced in an outer space exploration program. More than one-third of this heat load is due to an emission of continuum radiation from atoms and ions. The existing computer code for calculating the continuum contribution to the total load utilizes a modified version of Biberman's approximate method. The continuum radiation absorption cross sections of a C - H - O - N ablation system were examined in detail. The present computer code was evaluated and updated by being compared with available exact and approximate calculations and correlations of experimental data. A detailed calculation procedure, which can be applied to other atomic species, is presented. The approximate correlations can be made to agree with the available exact and experimental data.

Revisiting the effective medium approximation in all-dielectric subwavelength multilayers: Breakdown and rebuilding

NASA Astrophysics Data System (ADS)

Lei, Xinrui; Mao, Lei; Lu, Yonghua; Wang, Pei

2017-07-01

Here, we present a comprehensive analysis of the effective medium approximation (EMA) breakdown in all-dielectric deep-subwavelength multilayers made of alternating layers by means of the transfer matrix method. We demonstrated that the approximation is invalid at the vicinity of the effective medium's critical angle for total internal reflection and obtained an analytical criterion for the breakdown of the EMA, which depends on the layer thickness, the incident angle, and the permittivity difference between the alternate layers. We rebuilt the EMA by adding higher-order correction onto the traditional effective permittivity. Furthermore, we found that the EMA breakdown that arises from the boundary effect cannot be repaired in the traditional homogenization strategy with only one layer of effective medium. By adding an artificial matched layer after the conventional effective layer, the boundary effect breakdown was neatly removed.

On High-Order Upwind Methods for Advection

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2017-01-01

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom ?? per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2??-1, which is higher than the expected order of ??.

Reliable prediction of three-body intermolecular interactions using dispersion-corrected second-order Møller-Plesset perturbation theory

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

Huang, Yuanhang; Beran, Gregory J. O., E-mail: gregory.beran@ucr.edu

2015-07-28

Three-body and higher intermolecular interactions can play an important role in molecular condensed phases. Recent benchmark calculations found problematic behavior for many widely used density functional approximations in treating 3-body intermolecular interactions. Here, we demonstrate that the combination of second-order Møller-Plesset (MP2) perturbation theory plus short-range damped Axilrod-Teller-Muto (ATM) dispersion accurately describes 3-body interactions with reasonable computational cost. The empirical damping function used in the ATM dispersion term compensates both for the absence of higher-order dispersion contributions beyond the triple-dipole ATM term and non-additive short-range exchange terms which arise in third-order perturbation theory and beyond. Empirical damping enables this simplemore » model to out-perform a non-expanded coupled Kohn-Sham dispersion correction for 3-body intermolecular dispersion. The MP2 plus ATM dispersion model approaches the accuracy of O(N{sup 6}) methods like MP2.5 or even spin-component-scaled coupled cluster models for 3-body intermolecular interactions with only O(N{sup 5}) computational cost.« less

One Century of Tectonic Deformation Along the Sumatran Fault from Triangulation and GPS Surveys

NASA Technical Reports Server (NTRS)

Prawirodirdjo, L.; Bock, Y.; Genrich, J. F.; Puntodewo, S. S. O.; Rais, J.; Subarya, C.; Sutisna, S.

2000-01-01

An analysis combining historical triangulation and recent Global Positioning System (GPS) survey measurements in West and North Sumatra, Indonesia, reveals a detailed slip history along the central part of the Sumatran Fault. The arc-parallel components of the combined velocity field are consistent with slip rates inferred from GPS data, ranging from 23 to 24 mm/yr. Between 1.0 S and 1.3 N the Sumatran Fault appears to be characterized by deep locking depths, on the order of 20 km, and the occurrence of large (M (sub w) approximately 7) earthquakes. The long-term (1883-1993) strains show simple right-lateral shear, with rates similar to GPS-measured, 1989-1993 strain rates. Coseismic deformation due to the 1892 Tapanuli and 1926 Padang Panjang earthquakes, estimated from triangulation measurements taken before and after the events, indicate that the main shocks were significantly larger than previously reported. The 1892 earthquake had a likely magnitude of M (sub w) approximately equal to 7.6, while the 1926 events appear to be comparable in size to the subsequent (M approximately 7) 1943 events, and an order of magnitude higher than previously reported.

Conjugate gradient and cross-correlation based least-square reverse time migration and its application

NASA Astrophysics Data System (ADS)

Sun, Xiao-Dong; Ge, Zhong-Hui; Li, Zhen-Chun

2017-09-01

Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration (LSRTM) (also known as linearized reflectivity inversion) aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional (4D) seismic images compared to traditional RTM and Fourier finite difference (FFD) migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.

Comparison of antioxidant activity of compounds isolated from guava leaves and a stability study of the most active compound.

PubMed

Nantitanon, W; Okonogi, S

2012-02-01

In the present study, quercetin (QT), morin (MR), and quercetin-3-O-glucopyranoside (QG) isolated from guava leaves were comparatively tested for antioxidant activity using DPPH, ABTS, and FRAP methods. QT was the most active among them. The free radical scavenging activity of QT was approximately four times higher than MR and two times higher than QG. The reducing power of QT was eight times higher than MR and two times higher than QG. A mixture of QT with MR or QG showed interesting combination effect. The synergistic antioxidant activity was obtained when QT was mixed with MR whereas the antagonistic effect was found when mixed with QG. The stability study of QT in liquid preparations indicated that the decomposition reaction rate of QT could be explained by a kinetic model assuming a first-order chemical reaction. The aqueous solution of QT was rapidly decomposed with t1/2 of approximately five days whereas QT entrapped in chitosan nanoparticles was five times longer. It was concluded that QT was the most active antioxidant from guava leaves. Entrapment of QT in chitosan nanoparticles could significantly enhance its stability.

Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

NASA Astrophysics Data System (ADS)

Rose, F.; Dupuis, N.

2018-05-01

We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA, the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot-Mendéz-Galain-Wschebor approximation scheme). As an application we consider the two-dimensional quantum O(N ) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the "Higgs" amplitude mode) and the conductivity. In particular, we show how, using Padé approximants to perform the analytic continuation i ωn→ω +i 0+ of imaginary frequency correlation functions χ (i ωn) computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.

Application of low-order potential solutions to higher-order vertical traction boundary problems in an elastic half-space

PubMed Central

Taylor, Adam G.

2018-01-01

New solutions of potential functions for the bilinear vertical traction boundary condition are derived and presented. The discretization and interpolation of higher-order tractions and the superposition of the bilinear solutions provide a method of forming approximate and continuous solutions for the equilibrium state of a homogeneous and isotropic elastic half-space subjected to arbitrary normal surface tractions. Past experimental measurements of contact pressure distributions in granular media are reviewed in conjunction with the application of the proposed solution method to analysis of elastic settlement in shallow foundations. A numerical example is presented for an empirical ‘saddle-shaped’ traction distribution at the contact interface between a rigid square footing and a supporting soil medium. Non-dimensional soil resistance is computed as the reciprocal of normalized surface displacements under this empirical traction boundary condition, and the resulting internal stresses are compared to classical solutions to uniform traction boundary conditions. PMID:29892456

Stability of azimuthal-angle observables under higher order corrections in inclusive three-jet production

NASA Astrophysics Data System (ADS)

Caporale, F.; Celiberto, F. G.; Chachamis, G.; Gómez, D. Gordo; Vera, A. Sabio

2017-04-01

Recently, a new family of observables consisting of azimuthal-angle generalized ratios was proposed in a kinematical setup that resembles the usual Mueller-Navelet jets but with an additional tagged jet in the central region of rapidity. Nontagged minijet activity between the three jets can affect significantly the azimuthal angle orientation of the jets and is accounted for by the introduction of two Balitsky-Fadin-Kuraev- Lipatov (BFKL) gluon Green functions. Here, we calculate the, presumably, most relevant higher order corrections to the observables by now convoluting the three leading order jet vertices with two gluon Green functions at next-to-leading logarithmic approximation. The corrections appear to be mostly moderate, giving us confidence that the recently proposed observables are actually an excellent way to probe the BFKL dynamics at the LHC. Furthermore, we allow for the jets to take values in different rapidity bins in various configurations such that a comparison between our predictions and the experimental data is a straightforward task.

Unveiling the Secrets of Metallicity and Massive Star Formation Using DLAs Along Gamma-Ray Bursts

NASA Technical Reports Server (NTRS)

Cucchiara, A.; Fumagalli, M.; Rafelski, M.; Kocevski, D.; Prochaska, J. X.; Cooke, R. J.; Becker, G. D.

2015-01-01

We present the largest, publicly available, sample of Damped Lyman-alpha systems (DLAs) along Swift discovered Gamma-ray Bursts (GRB) line of sights in order to investigate the environmental properties of long GRB hosts in the z = 1.8 - 6 redshift range. Compared with the most recent quasar DLAs sample (QSO-DLA), our analysis shows that GRB-DLAs probe a more metal enriched environment at z approximately greater than 3, up to [X/H] approximately -0.5. In the z = 2 - 3 redshift range, despite the large number of lower limits, there are hints that the two populations may be more similar (only at 90% significance level) than at higher redshifts. Also, at high-z, the GRB-DLA average metallicity seems to decline at a shallower rate than the QSO-DLAs: GRB-DLA hosts may be polluted with metals at least as far as approximately 2 kpc from the GRB explosion site, probably due to previous star-formation episodes and/or supernovae explosions. This shallow metallicity trend, extended now up to z approximately 5, confirms previous results that GRB hosts are star-forming and have, on average, higher metallicity than the general QSO-DLA population. Finally, our host metallicity measurements are broadly consistent with the predictions derived from the hypothesis of two channels of GRB progenitors, one of which is mildly affected by a metallicity bias, although more data are needed to constrain the models at z approximately greater than 4.

Kerr-like behaviour of second harmonic generation in the far-off resonant regime

NASA Astrophysics Data System (ADS)

Peřinová, Vlasta; Lukš, Antonín; Křepelka, Jaromír; Leoński, Wiesław; Peřina, Jan

2018-05-01

We separate the Kerr-like behaviour of the second-harmonic generation in the far-off resonant regime from the oscillations caused by the time-dependence of the interaction energy. To this purpose, we consider the approximation obtained from the exact dynamics by the method of small rotations. The Floquet-type decomposition of the approximate dynamics comprises the Kerr-like dynamics and oscillations of the same order of magnitude as those assumed for the exact dynamics of the second-harmonic generation. We have found that a superposition of two states of concentrated quantum phase arises in the fundamental mode in the second-harmonic generation in the far-off resonant limit at a later time than a superposition of two coherent states in the corresponding Kerr medium and the difference is larger for higher initial coherent amplitudes. The quantum phase fluctuation is higher for the same initial coherent amplitudes in the fundamental mode in the second-harmonic generation in the far-off resonant limit than in the corresponding Kerr medium and the difference is larger for higher initial coherent amplitudes.

Artificial insemination of Holstein heifers with sex-sorted semen during the hot season in a subtropical region.

PubMed

Chang, Lian-Ben; Chou, Chih-Jen; Shiu, Jia-Shian; Tu, Po-An; Gao, Shi-Xuan; Peng, Shao-Yu; Wu, Shinn-Chih

2017-08-01

Our aim was to investigate insemination techniques in order to improve pregnancy rates of artificial insemination (AI) using sex-sorted semen (sexed AI) in cattle in tropical and subtropical (T/ST) regions. In T/ST regions, the pregnancy rates by sexed AI are reportedly the lowest in the hottest months of the year, with less than 15% in cows and 35-40% in heifers (PMID 24048822). We compared sexed AI by depositing the semen into the uterine body (UB-AI, n = 12) versus the unilateral uterine horn (UUH-AI, n = 14) of pre-ovulation heifers. The ovary and follicle were assessed by rectal ultrasound before AI. After insemination, pregnancy was determined by ultrasound at approximately 40 days and approximately 70 days. In the present study, we demonstrated that high pregnancy rates (>70%) by sexed AI in the hottest season in a subtropical region such as Taiwan can be achieved when heifers with pre-ovulation follicles are used. The overall pregnancy rates were 54% higher in the UUH-AI (71%) group than in the UB-AI (42%) group (P = 0.06), examined on approximately 40 days post-sexed AI. Surprisingly, however, the pregnancy outcome appeared to be higher in the hot season (62%) than in the cool season (46%) although this difference was not statistically significant. Based on the present study, we recommend that cattle breeders perform UUH-AI using sex-sorted semen for heifers with pre-ovulation follicles in order to achieve satisfactory pregnancy outcome in the hot seasons in T/ST regions.

High-Frequency Spin-Based Devices for Nanoscale Signal Processing

DTIC Science & Technology

2009-01-20

feedback on the devices in order to improve their spectral properties . Deliverable: Microwave signals without an Applied Field. We have successfully...additionally have the advantage of higher operating frequencies than the more conventional devices based on NiFe alloys. By combining several of...Output from a Co/Ni based STNO. Corresponds to approximately 20 nW, about 10 times larger than typical NiFe .device. 6 High-Frequency Spin-Based

Trends in Array Antenna Research,

DTIC Science & Technology

1977-06-01

design, because it is possible to record this single mode parameter and still account for all of the subtleties that occur at the array face. 2.5...waveguide field, but did properly account for the full spatial harmonic series (grating lobe series) in the free space half space. Some earlier...described some approximate procedures to account for coupling in large arrays where the numerical evaluation of all the higher order terms would

Research on Nonlinear Dynamical Systems.

DTIC Science & Technology

1983-01-10

Applied Math., to appear. [26] Variational inequalities and flow in porous media, LCDS’Lecture Notes, Brown University #LN 82-1, July 1982. [27] On...approximation schemes for parabolic and hyperbolic systems of partial differential equations, including higher order equations of elasticity based on the...51,58,59,63,64,69]. Finally, stability and bifurcation in parabolic partial differential equations is the focus of [64,65,67,72,73]. In addition to these broad

Analysis of higher order harmonics with holographic reflection gratings

NASA Astrophysics Data System (ADS)

Mas-Abellan, P.; Madrigal, R.; Fimia, A.

2017-05-01

Silver halide emulsions have been considered one of the most energetic sensitive materials for holographic applications. Nonlinear recording effects on holographic reflection gratings recorded on silver halide emulsions have been studied by different authors obtaining excellent experimental results. In this communication specifically we focused our investigation on the effects of refractive index modulation, trying to get high levels of overmodulation that will produce high order harmonics. We studied the influence of the overmodulation and its effects on the transmission spectra for a wide exposure range by use of 9 μm thickness films of ultrafine grain emulsion BB640, exposed to single collimated beams using a red He-Ne laser (wavelength 632.8 nm) with Denisyuk configuration obtaining a spatial frequency of 4990 l/mm recorded on the emulsion. The experimental results show that high overmodulation levels of refractive index produce second order harmonics with high diffraction efficiency (higher than 75%) and a narrow grating bandwidth (12.5 nm). Results also show that overmodulation produce diffraction spectra deformation of the second order harmonic, transforming the spectrum from sinusoidal to approximation of square shape due to very high overmodulation. Increasing the levels of overmodulation of refractive index, we have obtained higher order harmonics, obtaining third order harmonic with diffraction efficiency (up to 23%) and narrowing grating bandwidth (5 nm). This study is the first step to develop a new easy technique to obtain narrow spectral filters based on the use of high index modulation reflection gratings.

The three-point function as a probe of models for large-scale structure

NASA Astrophysics Data System (ADS)

Frieman, Joshua A.; Gaztanaga, Enrique

1994-04-01

We analyze the consequences of models of structure formation for higher order (n-point) galaxy correlation functions in the mildly nonlinear regime. Several variations of the standard Omega = 1 cold dark matter model with scale-invariant primordial perturbations have recently been introduced to obtain more power on large scales, Rp is approximately 20/h Mpc, e.g., low matter-density (nonzero cosmological constant) models, 'tilted' primordial spectra, and scenarios with a mixture of cold and hot dark matter. They also include models with an effective scale-dependent bias, such as the cooperative galaxy formation scenario of Bower et al. We show that higher-order (n-point) galaxy correlation functions can provide a useful test of such models and can discriminate between models with true large-scale power in the density field and those where the galaxy power arises from scale-dependent bias: a bias with rapid scale dependence leads to a dramatic decrease of the the hierarchical amplitudes QJ at large scales, r is greater than or approximately Rp. Current observational constraints on the three-point amplitudes Q3 and S3 can place limits on the bias parameter(s) and appear to disfavor, but not yet rule out, the hypothesis that scale-dependent bias is responsible for the extra power observed on large scales.

A definition of the domains Archaea, Bacteria and Eucarya in terms of small subunit ribosomal RNA characteristics

NASA Technical Reports Server (NTRS)

Winker, S.; Woese, C. R.

1991-01-01

The number of small subunit rRNA sequences is now great enough that the three domains Archaea, Bacteria and Eucarya (Woese et al., 1990) can be reliably defined in terms of their sequence "signatures". Approximately 50 homologous positions (or nucleotide pairs) in the small subunit rRNA characterize and distinguish among the three. In addition, the three can be recognized by a variety of nonhomologous rRNA characters, either individual positions and/or higher-order structural features. The Crenarchaeota and the Euryarchaeota, the two archaeal kingdoms, can also be defined and distinguished by their characteristic compositions at approximately fifteen positions in the small subunit rRNA molecule.

Lithographed Superconducting Resonator Development for Next-Generation Frequency Multiplexing Readout of Transition-Edge Sensors

NASA Astrophysics Data System (ADS)

Faramarzi, F.; De Haan, T.; Kusaka, A.; Lee, A.; Neuhauser, B.; Plambeck, R.; Raum, C.; Suzuki, A.; Westbrook, B.

2018-03-01

Ground-based cosmic microwave background (CMB) experiments are undergoing a period of exponential growth. Current experiments are observing with 1000-10,000 detectors, and the next-generation experiment (CMB stage 4) is proposing to deploy approximately 500,000 detectors. This order of magnitude increase in detector count will require a new approach for readout electronics. We have developed superconducting resonators for next-generation frequency-domain multiplexing (fMUX) readout architecture. Our goal is to reduce the physical size of resonators, such that resonators and detectors can eventually be integrated on a single wafer. To reduce the size of these resonators, we have designed spiral inductors and interdigitated capacitors that resonate around 10-100 MHz, an order of magnitude higher frequency compared to current fMUX readout systems. The higher frequency leads to a wider bandwidth and would enable higher multiplexing factor than the current ˜ 50 detectors per readout channel. We will report on the simulation, fabrication method, characterization technique, and measurement of quality factor of these resonators.

Enhancement of elemental mercury adsorption by silver supported material.

PubMed

Khunphonoi, Rattabal; Khamdahsag, Pummarin; Chiarakorn, Siriluk; Grisdanurak, Nurak; Paerungruang, Adjana; Predapitakkun, Somrudee

2015-06-01

Mercury, generally found in natural gas, is extremely hazardous. Although average mercury levels are relatively low, they are further reduced to comply with future mercury regulations, which are stringent in order to avoid releasing to the environment. Herein, vapor mercury adsorption was therefore investigated using two kinds of supports, granular activated carbon (GAC) and titanium dioxide (TiO2). Both supports were impregnated by silver (5 and 15 wt.%), before testing against a commercial adsorbent (sulfur-impregnated activated carbon, SAC). The adsorption isotherm, kinetics, and its thermodynamics of mercury adsorption were reported. The results revealed that Langmuir isotherm provided a better fit to the experimental data. Pseudo second-order was applicable to describe adsorption kinetics. The higher uniform Ag dispersion was a key factor for the higher mercury uptake. TiO2 supported silver adsorbent showed higher mercury adsorption than the commercial one by approximately 2 times. Chemisorption of mercury onto silver active sites was confirmed by an amalgam formation found in the spent adsorbents. Copyright © 2015. Published by Elsevier B.V.

High-order flux correction/finite difference schemes for strand grids

NASA Astrophysics Data System (ADS)

Katz, Aaron; Work, Dalon

2015-02-01

A novel high-order method combining unstructured flux correction along body surfaces and high-order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids. The flux correction algorithm is applied in each unstructured layer of the strand grid, and the layers are then coupled together via a source term containing derivatives in the strand direction. Strand-direction derivatives are approximated to high-order via summation-by-parts operators for first derivatives and second derivatives with variable coefficients. We show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme. The resulting scheme possesses third-order design accuracy, but often exhibits fourth-order accuracy when higher-order derivatives are employed in the strand direction, especially for highly viscous flows. We prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms. Results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second-order algorithms.

B B ¯ angular correlations at the LHC in the parton Reggeization approach merged with higher-order matrix elements

NASA Astrophysics Data System (ADS)

Karpishkov, A. V.; Nefedov, M. A.; Saleev, V. A.

2017-11-01

We calculate the angular distribution spectra between beauty (B ) and antibeauty (B ¯) mesons in proton-proton collisions in the leading order approximation of the parton Reggeization approach consistently merged with the next-to-leading order corrections from the emission of an additional hard gluon. To describe b-quark hadronization we use the universal scale-dependent parton-to-meson fragmentation functions extracted from the world e+e- annihilation data. We have obtained good agreement between our predictions and data from the CMS Collaboration at the energy √{S }=7 TeV for B B ¯ angular correlations within uncertainties and without free parameters. Predictions for analogous correlation observables at √{S }=13 TeV are provided.

Non-equilibrium many-body influence on mode-locked Vertical External-cavity Surface-emitting Lasers

NASA Astrophysics Data System (ADS)

Kilen, Isak Ragnvald

Vertical external-cavity surface-emitting lasers are ideal testbeds for studying the influence of the non-equilibrium many-body dynamics on mode locking. As we will show in this thesis, ultra short pulse generation involves a marked departure from Fermi carrier distributions assumed in prior theoretical studies. A quantitative model of the mode locking dynamics is presented, where the semiconductor Bloch equations with Maxwell's equation are coupled, in order to study the influences of quantum well carrier scattering on mode locking dynamics. This is the first work where the full model is solved without adiabatically eliminating the microscopic polarizations. In many instances we find that higher order correlation contributions (e.g. polarization dephasing, carrier scattering, and screening) can be represented by rate models, with the effective rates extracted at the level of second Born-Markov approximations. In other circumstances, such as continuous wave multi-wavelength lasing, we are forced to fully include these higher correlation terms. In this thesis we identify the key contributors that control mode locking dynamics, the stability of single pulse mode-locking, and the influence of higher order correlation in sustaining multi-wavelength continuous wave operation.

Parallel Higher-order Finite Element Method for Accurate Field Computations in Wakefield and PIC Simulations

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

Candel, A.; Kabel, A.; Lee, L.

Over the past years, SLAC's Advanced Computations Department (ACD), under SciDAC sponsorship, has developed a suite of 3D (2D) parallel higher-order finite element (FE) codes, T3P (T2P) and Pic3P (Pic2P), aimed at accurate, large-scale simulation of wakefields and particle-field interactions in radio-frequency (RF) cavities of complex shape. The codes are built on the FE infrastructure that supports SLAC's frequency domain codes, Omega3P and S3P, to utilize conformal tetrahedral (triangular)meshes, higher-order basis functions and quadratic geometry approximation. For time integration, they adopt an unconditionally stable implicit scheme. Pic3P (Pic2P) extends T3P (T2P) to treat charged-particle dynamics self-consistently using the PIC (particle-in-cell)more » approach, the first such implementation on a conformal, unstructured grid using Whitney basis functions. Examples from applications to the International Linear Collider (ILC), Positron Electron Project-II (PEP-II), Linac Coherent Light Source (LCLS) and other accelerators will be presented to compare the accuracy and computational efficiency of these codes versus their counterparts using structured grids.« less

Blind motion image deblurring using nonconvex higher-order total variation model

NASA Astrophysics Data System (ADS)

Li, Weihong; Chen, Rui; Xu, Shangwen; Gong, Weiguo

2016-09-01

We propose a nonconvex higher-order total variation (TV) method for blind motion image deblurring. First, we introduce a nonconvex higher-order TV differential operator to define a new model of the blind motion image deblurring, which can effectively eliminate the staircase effect of the deblurred image; meanwhile, we employ an image sparse prior to improve the edge recovery quality. Second, to improve the accuracy of the estimated motion blur kernel, we use L1 norm and H1 norm as the blur kernel regularization term, considering the sparsity and smoothing of the motion blur kernel. Third, because it is difficult to solve the numerically computational complexity problem of the proposed model owing to the intrinsic nonconvexity, we propose a binary iterative strategy, which incorporates a reweighted minimization approximating scheme in the outer iteration, and a split Bregman algorithm in the inner iteration. And we also discuss the convergence of the proposed binary iterative strategy. Last, we conduct extensive experiments on both synthetic and real-world degraded images. The results demonstrate that the proposed method outperforms the previous representative methods in both quality of visual perception and quantitative measurement.

Testing of next-generation nonlinear calibration based non-uniformity correction techniques using SWIR devices

NASA Astrophysics Data System (ADS)

Lovejoy, McKenna R.; Wickert, Mark A.

2017-05-01

A known problem with infrared imaging devices is their non-uniformity. This non-uniformity is the result of dark current, amplifier mismatch as well as the individual photo response of the detectors. To improve performance, non-uniformity correction (NUC) techniques are applied. Standard calibration techniques use linear, or piecewise linear models to approximate the non-uniform gain and off set characteristics as well as the nonlinear response. Piecewise linear models perform better than the one and two-point models, but in many cases require storing an unmanageable number of correction coefficients. Most nonlinear NUC algorithms use a second order polynomial to improve performance and allow for a minimal number of stored coefficients. However, advances in technology now make higher order polynomial NUC algorithms feasible. This study comprehensively tests higher order polynomial NUC algorithms targeted at short wave infrared (SWIR) imagers. Using data collected from actual SWIR cameras, the nonlinear techniques and corresponding performance metrics are compared with current linear methods including the standard one and two-point algorithms. Machine learning, including principal component analysis, is explored for identifying and replacing bad pixels. The data sets are analyzed and the impact of hardware implementation is discussed. Average floating point results show 30% less non-uniformity, in post-corrected data, when using a third order polynomial correction algorithm rather than a second order algorithm. To maximize overall performance, a trade off analysis on polynomial order and coefficient precision is performed. Comprehensive testing, across multiple data sets, provides next generation model validation and performance benchmarks for higher order polynomial NUC methods.

First and second order approximations to stage numbers in multicomponent enrichment cascades

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

Scopatz, A.

2013-07-01

This paper describes closed form, Taylor series approximations to the number product stages in a multicomponent enrichment cascade. Such closed form approximations are required when a symbolic, rather than a numeric, algorithm is used to compute the optimal cascade state. Both first and second order approximations were implemented. The first order solution was found to be grossly incorrect, having the wrong functional form over the entire domain. On the other hand, the second order solution shows excellent agreement with the 'true' solution over the domain of interest. An implementation of the symbolic, second order solver is available in the freemore » and open source PyNE library. (authors)« less

Weak-noise limit of a piecewise-smooth stochastic differential equation.

PubMed

Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram

2013-11-01

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.

Hydrodynamics beyond Navier-Stokes: the slip flow model.

PubMed

Yudistiawan, Wahyu P; Ansumali, Santosh; Karlin, Iliya V

2008-07-01

Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali, Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions--in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.

Extension of relativistic dissipative hydrodynamics to third order

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

El, Andrej; Xu Zhe; Greiner, Carsten

2010-04-15

Following the procedure introduced by Israel and Stewart, we expand the entropy current up to the third order in the shear stress tensor pi{sup a}lpha{sup b}eta and derive a novel third-order evolution equation for pi{sup a}lpha{sup b}eta. This equation is solved for the one-dimensional Bjorken boost-invariant expansion. The scaling solutions for various values of the shear viscosity to the entropy density ratio eta/s are shown to be in very good agreement with those obtained from kinetic transport calculations. For the pressure isotropy starting with 1 at tau{sub 0}=0.4 fm/c, the third-order corrections to Israel-Stewart theory are approximately 10% for eta/s=0.2more » and more than a factor of 2 for eta/s=3. We also estimate all higher-order corrections to Israel-Stewart theory and demonstrate their importance in describing highly viscous matters.« less

The isotropic-nematic phase transition of tangent hard-sphere chain fluids—Pure components

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Oyarzún, Bernardo; Vlugt, Thijs J. H.; Gross, Joachim

2013-07-01

An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under- and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition.

Mapping Tree Density at the Global Scale

NASA Astrophysics Data System (ADS)

Covey, K. R.; Crowther, T. W.; Glick, H.; Bettigole, C.; Bradford, M.

2015-12-01

The global extent and distribution of forest trees is central to our understanding of the terrestrial biosphere. We provide the first spatially continuous map of forest tree density at a global-scale. This map reveals that the global number of trees is approximately 3.04 trillion, an order of magnitude higher than the previous estimate. Of these trees, approximately 1.39 trillion exist in tropical and subtropical regions, with 0.74, and 0.61 trillion in boreal and temperate regions, respectively. Biome-level trends in tree density demonstrate the importance of climate and topography in controlling local tree densities at finer scales, as well as the overwhelming impact of humans across most of the world. Based on our projected tree densities, we estimate that deforestation is currently responsible for removing over 15 billion trees each year, and the global number of trees has fallen by approximately 46% since the start of human civilization.

Mapping tree density at a global scale

NASA Astrophysics Data System (ADS)

Crowther, T. W.; Glick, H. B.; Covey, K. R.; Bettigole, C.; Maynard, D. S.; Thomas, S. M.; Smith, J. R.; Hintler, G.; Duguid, M. C.; Amatulli, G.; Tuanmu, M.-N.; Jetz, W.; Salas, C.; Stam, C.; Piotto, D.; Tavani, R.; Green, S.; Bruce, G.; Williams, S. J.; Wiser, S. K.; Huber, M. O.; Hengeveld, G. M.; Nabuurs, G.-J.; Tikhonova, E.; Borchardt, P.; Li, C.-F.; Powrie, L. W.; Fischer, M.; Hemp, A.; Homeier, J.; Cho, P.; Vibrans, A. C.; Umunay, P. M.; Piao, S. L.; Rowe, C. W.; Ashton, M. S.; Crane, P. R.; Bradford, M. A.

2015-09-01

The global extent and distribution of forest trees is central to our understanding of the terrestrial biosphere. We provide the first spatially continuous map of forest tree density at a global scale. This map reveals that the global number of trees is approximately 3.04 trillion, an order of magnitude higher than the previous estimate. Of these trees, approximately 1.39 trillion exist in tropical and subtropical forests, with 0.74 trillion in boreal regions and 0.61 trillion in temperate regions. Biome-level trends in tree density demonstrate the importance of climate and topography in controlling local tree densities at finer scales, as well as the overwhelming effect of humans across most of the world. Based on our projected tree densities, we estimate that over 15 billion trees are cut down each year, and the global number of trees has fallen by approximately 46% since the start of human civilization.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

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

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2016-08-01

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

Mapping tree density at a global scale.

PubMed

Crowther, T W; Glick, H B; Covey, K R; Bettigole, C; Maynard, D S; Thomas, S M; Smith, J R; Hintler, G; Duguid, M C; Amatulli, G; Tuanmu, M-N; Jetz, W; Salas, C; Stam, C; Piotto, D; Tavani, R; Green, S; Bruce, G; Williams, S J; Wiser, S K; Huber, M O; Hengeveld, G M; Nabuurs, G-J; Tikhonova, E; Borchardt, P; Li, C-F; Powrie, L W; Fischer, M; Hemp, A; Homeier, J; Cho, P; Vibrans, A C; Umunay, P M; Piao, S L; Rowe, C W; Ashton, M S; Crane, P R; Bradford, M A

2015-09-10

The global extent and distribution of forest trees is central to our understanding of the terrestrial biosphere. We provide the first spatially continuous map of forest tree density at a global scale. This map reveals that the global number of trees is approximately 3.04 trillion, an order of magnitude higher than the previous estimate. Of these trees, approximately 1.39 trillion exist in tropical and subtropical forests, with 0.74 trillion in boreal regions and 0.61 trillion in temperate regions. Biome-level trends in tree density demonstrate the importance of climate and topography in controlling local tree densities at finer scales, as well as the overwhelming effect of humans across most of the world. Based on our projected tree densities, we estimate that over 15 billion trees are cut down each year, and the global number of trees has fallen by approximately 46% since the start of human civilization.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory.

PubMed

Faucheaux, Jacob A; Nooijen, Marcel; Hirata, So

2018-02-07

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

NASA Astrophysics Data System (ADS)

Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So

2018-02-01

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Parametric Study of Decay of Homogeneous Isotropic Turbulence Using Large Eddy Simulation

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rumsey, Christopher L.; Rubinstein, Robert; Balakumar, Ponnampalam; Zang, Thomas A.

2012-01-01

Numerical simulations of decaying homogeneous isotropic turbulence are performed with both low-order and high-order spatial discretization schemes. The turbulent Mach and Reynolds numbers for the simulations are 0.2 and 250, respectively. For the low-order schemes we use either second-order central or third-order upwind biased differencing. For higher order approximations we apply weighted essentially non-oscillatory (WENO) schemes, both with linear and nonlinear weights. There are two objectives in this preliminary effort to investigate possible schemes for large eddy simulation (LES). One is to explore the capability of a widely used low-order computational fluid dynamics (CFD) code to perform LES computations. The other is to determine the effect of higher order accuracy (fifth, seventh, and ninth order) achieved with high-order upwind biased WENO-based schemes. Turbulence statistics, such as kinetic energy, dissipation, and skewness, along with the energy spectra from simulations of the decaying turbulence problem are used to assess and compare the various numerical schemes. In addition, results from the best performing schemes are compared with those from a spectral scheme. The effects of grid density, ranging from 32 cubed to 192 cubed, on the computations are also examined. The fifth-order WENO-based scheme is found to be too dissipative, especially on the coarser grids. However, with the seventh-order and ninth-order WENO-based schemes we observe a significant improvement in accuracy relative to the lower order LES schemes, as revealed by the computed peak in the energy dissipation and by the energy spectrum.

Higher-Order Asymptotics and Its Application to Testing the Equality of the Examinee Ability Over Two Sets of Items.

PubMed

Sinharay, Sandip; Jensen, Jens Ledet

2018-06-27

In educational and psychological measurement, researchers and/or practitioners are often interested in examining whether the ability of an examinee is the same over two sets of items. Such problems can arise in measurement of change, detection of cheating on unproctored tests, erasure analysis, detection of item preknowledge, etc. Traditional frequentist approaches that are used in such problems include the Wald test, the likelihood ratio test, and the score test (e.g., Fischer, Appl Psychol Meas 27:3-26, 2003; Finkelman, Weiss, & Kim-Kang, Appl Psychol Meas 34:238-254, 2010; Glas & Dagohoy, Psychometrika 72:159-180, 2007; Guo & Drasgow, Int J Sel Assess 18:351-364, 2010; Klauer & Rettig, Br J Math Stat Psychol 43:193-206, 1990; Sinharay, J Educ Behav Stat 42:46-68, 2017). This paper shows that approaches based on higher-order asymptotics (e.g., Barndorff-Nielsen & Cox, Inference and asymptotics. Springer, London, 1994; Ghosh, Higher order asymptotics. Institute of Mathematical Statistics, Hayward, 1994) can also be used to test for the equality of the examinee ability over two sets of items. The modified signed likelihood ratio test (e.g., Barndorff-Nielsen, Biometrika 73:307-322, 1986) and the Lugannani-Rice approximation (Lugannani & Rice, Adv Appl Prob 12:475-490, 1980), both of which are based on higher-order asymptotics, are shown to provide some improvement over the traditional frequentist approaches in three simulations. Two real data examples are also provided.

Design and simulation of origami structures with smooth folds

PubMed Central

Peraza Hernandez, E. A.; Lagoudas, D. C.

2017-01-01

Origami has enabled new approaches to the fabrication and functionality of multiple structures. Current methods for origami design are restricted to the idealization of folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures of non-negligible fold thickness or maximum curvature at the folds restricted by material limitations. For such structures, folds are not properly represented as creases but rather as bent regions of higher-order geometric continuity. Such fold regions of arbitrary order of continuity are termed as smooth folds. This paper presents a method for solving the following origami design problem: given a goal shape represented as a polygonal mesh (termed as the goal mesh), find the geometry of a single planar sheet, its pattern of smooth folds, and the history of folding motion allowing the sheet to approximate the goal mesh. The parametrization of the planar sheet and the constraints that allow for a valid pattern of smooth folds are presented. The method is tested against various goal meshes having diverse geometries. The results show that every determined sheet approximates its corresponding goal mesh in a known folded configuration having fold angles obtained from the geometry of the goal mesh. PMID:28484322

Design and simulation of origami structures with smooth folds.

PubMed

Peraza Hernandez, E A; Hartl, D J; Lagoudas, D C

2017-04-01

Origami has enabled new approaches to the fabrication and functionality of multiple structures. Current methods for origami design are restricted to the idealization of folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures of non-negligible fold thickness or maximum curvature at the folds restricted by material limitations. For such structures, folds are not properly represented as creases but rather as bent regions of higher-order geometric continuity. Such fold regions of arbitrary order of continuity are termed as smooth folds . This paper presents a method for solving the following origami design problem: given a goal shape represented as a polygonal mesh (termed as the goal mesh ), find the geometry of a single planar sheet, its pattern of smooth folds, and the history of folding motion allowing the sheet to approximate the goal mesh. The parametrization of the planar sheet and the constraints that allow for a valid pattern of smooth folds are presented. The method is tested against various goal meshes having diverse geometries. The results show that every determined sheet approximates its corresponding goal mesh in a known folded configuration having fold angles obtained from the geometry of the goal mesh.

Correlated sequential tunneling through a double barrier for interacting one-dimensional electrons

NASA Astrophysics Data System (ADS)

Thorwart, M.; Egger, R.; Grifoni, M.

2005-07-01

The problem of resonant tunneling through a quantum dot weakly coupled to spinless Tomonaga-Luttinger liquids has been studied. We compute the linear conductance due to sequential tunneling processes upon employing a master equation approach. Besides the previously used lowest-order golden rule rates describing uncorrelated sequential tunneling processes, we systematically include higher-order correlated sequential tunneling (CST) diagrams within the standard Weisskopf-Wigner approximation. We provide estimates for the parameter regions where CST effects can be important. Focusing mainly on the temperature dependence of the peak conductance, we discuss the relation of these findings to previous theoretical and experimental results.

Correlated sequential tunneling in Tomonaga-Luttinger liquid quantum dots

NASA Astrophysics Data System (ADS)

Thorwart, M.; Egger, R.; Grifoni, M.

2005-02-01

We investigate tunneling through a quantum dot formed by two strong impurites in a spinless Tomonaga-Luttinger liquid. Upon employing a Markovian master equation approach, we compute the linear conductance due to sequential tunneling processes. Besides the previously used lowest-order Golden Rule rates describing uncorrelated sequential tunneling (UST) processes, we systematically include higher-order correlated sequential tunneling (CST) diagrams within the standard Weisskopf-Wigner approximation. We provide estimates for the parameter regions where CST effects are shown to dominate over UST. Focusing mainly on the temperature dependence of the conductance maximum, we discuss the relation of our results to previous theoretical and experimental results.

Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme

NASA Astrophysics Data System (ADS)

Mandziuk, Margaret; Schlick, Tamar

1995-05-01

The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- ( Δt) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance ( Δt ≈ 7 fs here) leads to instability, and higher-order resonances ( n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.

Study of weak corrections to Drell-Yan, top-quark pair, and dijet production at high energies with MCFM

DOE PAGES

Campbell, John M.; Wackeroth, Doreen; Zhou, Jia

2016-11-29

Electroweak (EW) corrections can be enhanced at high energies due to the soft or collinear radiation of virtual and real W and Z bosons that result in Sudakov-like corrections of the form αmore » $$l\\atop{W}$$log n(Q 2/M2$$\\atop{W,Z}$$), where α W=α/(4π sin 2θ W) and n ≤ 2l-1. The inclusion of EW corrections in predictions for hadron colliders is, therefore, especially important when searching for signals of possible new physics in distributions probing the kinematic regime Q 2>>M$$2\\atop{V}$$. Next-to-leading order (NLO) EW corrections should also be taken into account when their size [O(α)] is comparable to that of QCD corrections at next-to-next-to-leading order (NNLO) [O(α$$2\\atop{s}$$)]. To this end, we have implemented the NLO weak corrections to the neutral-current Drell-Yan process, top-quark pair production and dijet production in the parton-level Monte Carlo program MCFM. This enables a combined study with the corresponding QCD corrections at NLO and NNLO. We provide both the full NLO weak corrections and their Sudakov approximation since the latter is often used for a fast evaluation of weak effects at high energies and can be extended to higher orders. Finally, with both the exact and approximate results at hand, the validity of the Sudakov approximation can be readily quantified.« less

Limitations of the paraxial Debye approximation.

PubMed

Sheppard, Colin J R

2013-04-01

In the paraxial form of the Debye integral for focusing, higher order defocus terms are ignored, which can result in errors in dealing with aberrations, even for low numerical aperture. These errors can be avoided by using a different integration variable. The aberrations of a glass slab, such as a coverslip, are expanded in terms of the new variable, and expressed in terms of Zernike polynomials to assist with aberration balancing. Tube length error is also discussed.

Plasma Thruster Development: Magnetoplasmadynamic Propulsion, Status and Basic Problems.

DTIC Science & Technology

1986-02-01

34 9 Sublimation Rates vs. Temperature for Typical Electrode Materials 65 10 Time to Reach Melting vs. Surface Heat Load (One-Dimensional, Large Area...Approx.) for Different Electrode Materials and Initial Temperatures 75 V LIST OF TABLES TABLE PAGE I Models of Thruster Types (with approximation (1...much higher specific impulse values than the minimum must be achieved in order to obtain acceptable effi- Sciencies , e.g. for 30% efficiency with argon

Application of finite element approach to transonic flow problems

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C., Jr.

1976-01-01

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, nonrectangular elements, and discontinuous approximation of shock waves are also discussed.

Environmental Impact Analysis Process. Volume 2

DTIC Science & Technology

1987-04-01

in producing stress on a person . Whatever else stress may be, it is certainly multidimensional (produced by an interaction of many factors). Each...dB. According to the National Academy of Sciences’ "Guidelines" referred to above (p. B-6) approximately 12% of the persons exposed to DNL of 60-65...area including highly populated Springfield and Chicopee, the number of persons "highly annoyed" will be substantially higher, possibly by orders of

A higher order conditional random field model for simultaneous classification of land cover and land use

NASA Astrophysics Data System (ADS)

Albert, Lena; Rottensteiner, Franz; Heipke, Christian

2017-08-01

We propose a new approach for the simultaneous classification of land cover and land use considering spatial as well as semantic context. We apply a Conditional Random Fields (CRF) consisting of a land cover and a land use layer. In the land cover layer of the CRF, the nodes represent super-pixels; in the land use layer, the nodes correspond to objects from a geospatial database. Intra-layer edges of the CRF model spatial dependencies between neighbouring image sites. All spatially overlapping sites in both layers are connected by inter-layer edges, which leads to higher order cliques modelling the semantic relation between all land cover and land use sites in the clique. A generic formulation of the higher order potential is proposed. In order to enable efficient inference in the two-layer higher order CRF, we propose an iterative inference procedure in which the two classification tasks mutually influence each other. We integrate contextual relations between land cover and land use in the classification process by using contextual features describing the complex dependencies of all nodes in a higher order clique. These features are incorporated in a discriminative classifier, which approximates the higher order potentials during the inference procedure. The approach is designed for input data based on aerial images. Experiments are carried out on two test sites to evaluate the performance of the proposed method. The experiments show that the classification results are improved compared to the results of a non-contextual classifier. For land cover classification, the result is much more homogeneous and the delineation of land cover segments is improved. For the land use classification, an improvement is mainly achieved for land use objects showing non-typical characteristics or similarities to other land use classes. Furthermore, we have shown that the size of the super-pixels has an influence on the level of detail of the classification result, but also on the degree of smoothing induced by the segmentation method, which is especially beneficial for land cover classes covering large, homogeneous areas.

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Rosen, I. G.

1988-01-01

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Predicting Statistical Response and Extreme Events in Uncertainty Quantification through Reduced-Order Models

NASA Astrophysics Data System (ADS)

Qi, D.; Majda, A.

2017-12-01

A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with distinct statistical structures.

Xanthan gum recovery from fermentation broth using ultrafiltration: Kinetics and process evaluation

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

Lo, Y.M.; Yang, S.T.; Min, D.B.

1995-12-01

Ultrafiltration of xanthan gum solution as an alternative method to alcohol precipitation for xanthan gum recovery from dilute fermentation broth was studied. A polysulfone membrane (with 500,000 MWCO) hollow fiber (106 mil fiber diameter) tubular cartridge was used to concentrate xanthan broth from less than 3 (w/v) % to {approximately}13.5 (w/v) %, with the xanthan recovery yield of {approximately}95 % or higher. During ultrafiltration, the filtrate flux was one order of magnitude lower for xanthan broth than for water, However, the flux remained almost constant for xanthan concentrations up to {approximately}8%. It was then reduced dramatically as the xanthan concentrationmore » increased beyond 8%. The reduced filtrate flux was caused by the reduced pumping (shear) rate and higher viscosities at higher xanthan concentrations. At constant xanthan concentration, the filtrate flux remained almost unchanged for the entire period studied, suggesting that the process is not subject to membrane fouling. In general, the filtrate flux decreased with increasing the xanthan concentration and increased with increasing the pumping (shear) rate and the trans-membrane pressure difference. Changing the solution pH had a slight effect on the viscosity of xanthan solution, but did not affect the filtration performance. Even under high-shear-rate conditions, ultrafiltration did not give any adverse effects on the rheological properties and molecular weight of the xanthan polymer. Thus, ultra filtration can be used to concentrate xanthan broth from fermentation by a factor of four or higher and to reduce the subsequent alcohol recovery costs by at least 75 %.« less

Capturing Structural Heterogeneity in Chromatin Fibers.

PubMed

Ekundayo, Babatunde; Richmond, Timothy J; Schalch, Thomas

2017-10-13

Chromatin fiber organization is implicated in processes such as transcription, DNA repair and chromosome segregation, but how nucleosomes interact to form higher-order structure remains poorly understood. We solved two crystal structures of tetranucleosomes with approximately 11-bp DNA linker length at 5.8 and 6.7 Å resolution. Minimal intramolecular nucleosome-nucleosome interactions result in a fiber model resembling a flat ribbon that is compatible with a two-start helical architecture, and that exposes histone and DNA surfaces to the environment. The differences in the two structures combined with electron microscopy reveal heterogeneous structural states, and we used site-specific chemical crosslinking to assess the diversity of nucleosome-nucleosome interactions through identification of structure-sensitive crosslink sites that provide a means to characterize fibers in solution. The chromatin fiber architectures observed here provide a basis for understanding heterogeneous chromatin higher-order structures as they occur in a genomic context. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Higher-Order Bending Theory for Laminated Composite and Sandwich Beams

NASA Technical Reports Server (NTRS)

Cook, Geoffrey M.

1997-01-01

A higher-order bending theory is derived for laminated composite and sandwich beams. This is accomplished by assuming a special form for the axial and transverse displacement expansions. An independent expansion is also assumed for the transverse normal stress. Appropriate shear correction factors based on energy considerations are used to adjust the shear stiffness. A set of transverse normal correction factors is introduced, leading to significant improvements in the transverse normal strain and stress for laminated composite and sandwich beams. A closed-form solution to the cylindrical elasticity solutions for a wide range of beam aspect ratios and commonly used material systems. Accurate shear stresses for a wide range of laminates, including the challenging unsymmetric composite and sandwich laminates, are obtained using an original corrected integration scheme. For application of the theory to a wider range of problems, guidelines for finite element approximations are presented.

Close-slow analysis for head-on collision of two black holes in higher dimensions: Bowen-York initial data

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

Yoshino, Hirotaka; Graduate School of Science and Engineering, Waseda University, Tokyo 169-8555; Shiromizu, Tetsuya

2006-12-15

Scenarios of large extra dimensions have enhanced the importance for the study of black holes in higher dimensions. In this paper, we analyze an axisymmetric system of two black holes. Specifically, the Bowen-York method is generalized for higher dimensions in order to calculate the initial data for head-on collision of two equal-mass black holes. Then, the initial data are evolved adopting the close-slow approximation to study gravitational waves emitted during the collision. We derive an empirical formula for radiation efficiency, which depends weakly on the dimensionality. Possible implications of our results for the black hole formation in particle colliders aremore » discussed.« less

Cosmological Perturbation Theory and the Spherical Collapse model - I. Gaussian initial conditions

NASA Astrophysics Data System (ADS)

Fosalba, Pablo; Gaztanaga, Enrique

1998-12-01

We present a simple and intuitive approximation for solving the perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for tree-graphs (i.e. at leading order). We find that the non-linear evolution in Lagrangian space is then given by a simple local transformation over the initial conditions, although it is not local in Euler space. This transformation is found to be described by the spherical collapse (SC) dynamics, as it is the exact solution in the shearless (and therefore local) approximation in Lagrangian space. Taking advantage of this property, it is straightforward to derive the one-point cumulants, xi_J, for both the unsmoothed and smoothed density fields to arbitrary order in the perturbative regime. To leading-order this reproduces, and provides us with a simple explanation for, the exact results obtained by Bernardeau. We then show that the SC model leads to accurate estimates for the next corrective terms when compared with the results derived in the exact perturbation theory making use of the loop calculations. The agreement is within a few per cent for the hierarchical ratios S_J=xi_J/xi^J-1_2. We compare our analytic results with N-body simulations, which turn out to be in very good agreement up to scales where sigma~1. A similar treatment is presented to estimate higher order corrections in the Zel'dovich approximation. These results represent a powerful and readily usable tool to produce analytical predictions that describe the gravitational clustering of large-scale structure in the weakly non-linear regime.

Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

NASA Technical Reports Server (NTRS)

Fink, P. W.; Wilton, D. R.; Dobbins, J. A.

2002-01-01

In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required to obtain usable convergence from an iterative solver. The authors have examined the use of an Incomplete LU Threshold (ILUT) preconditioner . to solver linear systems stemming from higher order BEM/FEM formulations in 2D scattering problems. Although the resulting preconditioner provided aD excellent approximation to the system inverse, its size in terms of non-zero entries represented only a modest improvement when compared with the fill-in associated with a sparse direct solver. Furthermore, the fill-in of the preconditioner could not be substantially reduced without the occurrence of instabilities. In addition to the results for these 2D problems, the authors will present iterative solution data from the application of the ILUT preconditioner to 3D problems.

YORP on tumbling asteroids

NASA Astrophysics Data System (ADS)

Rozek, A.; Breiter, S.; Vokrouhlicky, D.

2011-10-01

A semi-analytical model of the Yarkovsky-O'Keefe- Radzievskii-Paddack (YORP) effect on an asteroid spin in non principal axis rotation state is presented. Assuming zero conductivity, the YORP torque is represented by spherical harmonics series with vector coefficients, allowing to use any degree and order of approximation. Within the quadrupole approximation of the illumination function we find the same first integrals involving rotational momentum, obliquity and dynamical inertia that were obtained by Cicaló and Scheeres [1]. The integrals do not exist when higher degree terms of illumination function are included and then the asymptotic states known from Vokrouhlický et al. [2] appear. This resolves an apparent contradiction between earlier results. Averaged equations of motion admit stable and unstable limit cycle solutions that were not detected previously.

Financial incentives do not always work: an example of cesarean sections in Taiwan.

PubMed

Lo, Joan C

2008-10-01

To test the hypothesis that cesarean sections are less likely to be performed after equalizing the fees for vaginal births and cesarean sections. Population-based National Health Insurance inpatient claims in Taiwan are used. Pre-periods and post-periods are identified to investigate the impact of the policy changes. Logistic regressions are employed. The cesarean section rates for the first, second and higher-order births are 29, 37.4 and 39.3%, while the primary cesarean section rates are 29, 11.8 and 12.1%, respectively. After taking into consideration the case-mix and birth order, the second and higher-order births were approximately 60% less likely to be cesarean deliveries compared to the first births and the increase in the VBAC fee had an additional negative effect on them. A fee equalization policy was not found to influence the cesarean delivery. The total cesarean section rate was primarily determined by the cesarean section rate for the first birth. Cesarean section rates are greater for the higher-order births because of the practice "once a cesarean section, always a cesarean section". Against the background of a rapidly declining fertility rate, females play a more important role in the mode of delivery than ever before. As such, financial incentives designed specifically for obstetricians do not have the desired impact. Policies that are aimed at altering behavior should be designed within the social context.

Effects of Alternate Leading Edge Cutback on the Space Shuttle Main Engine Low Pressure Fuel Pump

NASA Technical Reports Server (NTRS)

Mulder, Andrew; Skelley, Stephen

2016-01-01

A higher order cavitation oscillation observed in the SSME low pressure fuel pump has been eliminated in water flow testing of a modified subscale replica of the inducer. The low pressure pump was modified by removing the outboard sections of two opposing blades of the four-bladed inducer, blending the "cutback" regions into the blades at the leading edge and tip, and removing material on the suction sides to decrease the exposed leading edge thickness. The leading edge tips of the cutback blades were moved approximately 25 degrees from their previous locations, thereby increasing one blade to blade spacing, decreasing the second, while simultaneously moving the cutback tips downstream. The test was conducted in MSFC's inducer test loop at scaled operating conditions in degassed and filtered water. In addition to eliminating HOC across the entire scaled operating regime, rotating cavitation was suppressed while the range of both alternate blade and asymmetric cavitation were increased. These latter phenomena, and more significantly, the shifts between these cavitation modes also resulted in significant changes to the head coefficient at low cavitation numbers. Reverse flow was detected at a slightly larger flow coefficient with the cutback inducer and suction capability was reduced by approximately 1 velocity head at and above approximately 90% of the reference flow coefficient. These performance changes along with more intense reverse flow are consistent with poor flow area management and increased incidence in the cutback region. Although the test demonstrated that the inducer modification was successful at eliminating the higher order cavitation across the entire scaled operating regime, different, previously unobserved, cavitation oscillations were introduced and significant performance penalties were imposed.

An approximate viscous shock layer technique for calculating chemically reacting hypersonic flows about blunt-nosed bodies

NASA Technical Reports Server (NTRS)

Cheatwood, F. Mcneil; Dejarnette, Fred R.

1991-01-01

An approximate axisymmetric method was developed which can reliably calculate fully viscous hypersonic flows over blunt nosed bodies. By substituting Maslen's second order pressure expression for the normal momentum equation, a simplified form of the viscous shock layer (VSL) equations is obtained. This approach can solve both the subsonic and supersonic regions of the shock layer without a starting solution for the shock shape. The approach is applicable to perfect gas, equilibrium, and nonequilibrium flowfields. Since the method is fully viscous, the problems associated with a boundary layer solution with an inviscid layer solution are avoided. This procedure is significantly faster than the parabolized Navier-Stokes (PNS) or VSL solvers and would be useful in a preliminary design environment. Problems associated with a previously developed approximate VSL technique are addressed before extending the method to nonequilibrium calculations. Perfect gas (laminar and turbulent), equilibrium, and nonequilibrium solutions were generated for airflows over several analytic body shapes. Surface heat transfer, skin friction, and pressure predictions are comparable to VSL results. In addition, computed heating rates are in good agreement with experimental data. The present technique generates its own shock shape as part of its solution, and therefore could be used to provide more accurate initial shock shapes for higher order procedures which require starting solutions.

Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold

NASA Astrophysics Data System (ADS)

Maliavkin, G. P.; Shmyrov, A. S.; Shmyrov, V. A.

2018-05-01

Vicinities of collinear libration points of the Sun-Earth system are currently quite attractive for the space navigation. Today, various projects on placing of spacecrafts observing the Sun in the L1 libration point and telescopes in L2 have been implemented (e.g. spacecrafts "WIND", "SOHO", "Herschel", "Planck"). Collinear libration points being unstable leads to the problem of stabilization of a spacecraft's motion. Laws of stabilizing motion control in vicinity of L1 point can be constructed using the analytical representation of a stable invariant manifold. Efficiency of these control laws depends on the precision of the representation. Within the model of Hill's approximation of the circular restricted three-body problem in the rotating geocentric coordinate system one can obtain the analytical representation of an invariant manifold filled with bounded trajectories in a form of series in terms of powers of the phase variables. Approximate representations of the orders from the first to the fourth inclusive can be used to construct four laws of stabilizing feedback motion control under which trajectories approach the manifold. By virtue of numerical simulation the comparison can be made: how the precision of the representation of the invariant manifold influences the efficiency of the control, expressed by energy consumptions (characteristic velocity). It shows that using approximations of higher orders in constructing the control laws can significantly reduce the energy consumptions on implementing the control compared to the linear approximation.

Nearly steady flows in GONG prototype data

NASA Technical Reports Server (NTRS)

Hathaway, David H.

1993-01-01

Doppler velocity images obtained with the GONG prototype instrument were analyzed to measure the nearly steady photospheric flows. The data consists of 88 images each of velocity, intensity, and modulation obtained at 20:00 UT on 88 days from July 1992 to February 1994. Each velocity image was temporally filtered to remove the p-mode oscillations, masked to exclude active regions, and then analyzed using spherical harmonics and orthogonal functions as described by Hathaway (1992). The spectral coefficients show very consistent results for the entire time interval with some evidence of year-to-year variations. The rotation profile agrees well with previous results and exhibits a north-south asymmetry that reverses sign during the 20 month interval. The residual rotation velocities exhibit structures with amplitudes of approximately 5 m/s that may be related to torsional oscillations. The meridional circulation is directed from the equator toward the poles with a peak velocity in the photosphere of approximately 50 m/s. The higher order components are very weak but indicate a divergent flow from the mid-latitudes (opposite that found for the June 1989 data). The convective limb shift is well fit by a 3rd order polynomial. The convection spectrum has a prominent peak at spherical harmonic degrees of l approximately 150 with very little signal in the low degree modes. Analysis of this signal shows that there is no evidence for giant cell convection at the level of approximately 10 m/s for all modes up to l = 32.

Second-order singular pertubative theory for gravitational lenses

NASA Astrophysics Data System (ADS)

Alard, C.

2018-03-01

The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second-order expansion is considered as a small correction to the first-order expansion. Using this approach, it is demonstrated that in practice the second-order expansion is reducible to a first order expansion via a re-definition of the first-order pertubative fields. Even if in usual applications the second-order correction is small the reducibility of the second-order expansion to the first-order expansion indicates a potential degeneracy issue. In general, this degeneracy is hard to break. A useful and simple second-order approximation is the thin source approximation, which offers a direct estimation of the correction. The practical application of the corrections derived in this paper is illustrated by using an elliptical NFW lens model. The second-order pertubative expansion provides a noticeable improvement, even for the simplest case of thin source approximation. To conclude, it is clear that for accurate modelization of gravitational lenses using the perturbative method the second-order perturbative expansion should be considered. In particular, an evaluation of the degeneracy due to the second-order term should be performed, for which the thin source approximation is particularly useful.

SURFACE PHONONS IN THE ORDERED c(2 × 2) PHASE OF Pd ON Au(100)

NASA Astrophysics Data System (ADS)

Chadli, R.; Khater, A.; Tigrine, R.

2013-03-01

The vibrational properties of the Au(100)-c(2 × 2)-Pd ordered phase, which is a stable system in the temperature range of 500 K to 600 K, are presented. This surface alloy is formed by depositing Pd atoms onto the Au(100) surface, and annealing at higher temperatures. The equilibrium structural characteristics, phonon dispersions as well as the local density of phonon states are calculated using the matching theory associated with Green's function formalism evaluated in the harmonic approximation. New surface modes have been found on the ordered metallic surface alloy along the three directions of high symmetry /line{Γ X}, /line{XM}, and /line{MΓ }, in comparison with the clean surface Au(100). Three of them are observed above the bulk bands spectrum.

The unitary convolution approximation for heavy ions

NASA Astrophysics Data System (ADS)

Grande, P. L.; Schiwietz, G.

2002-10-01

The convolution approximation for the impact-parameter dependent energy loss is reviewed with emphasis on the determination of the stopping force for heavy projectiles. In this method, the energy loss in different impact-parameter regions is well determined and interpolated smoothly. The physical inputs of the model are the projectile-screening function (in the case of dressed ions), the electron density and oscillators strengths of the target atoms. Moreover, the convolution approximation, in the perturbative mode (called PCA), yields remarkable agreement with full semi-classical-approximation (SCA) results for bare as well as for screened ions at all impact parameters. In the unitary mode (called UCA), the method contains some higher-order effects (yielding in some cases rather good agreement with full coupled-channel calculations) and approaches the classical regime similar as the Bohr model for large perturbations ( Z/ v≫1). The results are then used to compare with experimental values of the non-equilibrium stopping force as a function of the projectile charge as well as with the equilibrium energy loss under non-aligned and channeling conditions.

Swimming of a linear chain with a cargo in an incompressible viscous fluid with inertia

NASA Astrophysics Data System (ADS)

Felderhof, B. U.

2017-01-01

An approximation to the added mass matrix of an assembly of spheres is constructed on the basis of potential flow theory for situations where one sphere is much larger than the others. In the approximation, the flow potential near a small sphere is assumed to be dipolar, but near the large sphere it involves all higher order multipoles. The analysis is based on an exact result for the potential of a magnetic dipole in the presence of a superconducting sphere. Subsequently, the approximate added mass hydrodynamic interactions are used in a calculation of the swimming velocity and rate of dissipation of linear chain structures consisting of a number of small spheres and a single large one, with account also of frictional hydrodynamic interactions. The results derived for periodic swimming on the basis of a kinematic approach are compared with the bilinear theory, valid for small amplitude of stroke, and with the numerical solution of the approximate equations of motion. The calculations interpolate over the whole range of scale number between the friction-dominated Stokes limit and the inertia-dominated regime.

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

A Higher Order Iterative Method for Computing the Drazin Inverse

PubMed Central

Soleymani, F.; Stanimirović, Predrag S.

2013-01-01

A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. PMID:24222747

The three-point function as a probe of models for large-scale structure

NASA Technical Reports Server (NTRS)

Frieman, Joshua A.; Gaztanaga, Enrique

1993-01-01

The consequences of models of structure formation for higher-order (n-point) galaxy correlation functions in the mildly non-linear regime are analyzed. Several variations of the standard Omega = 1 cold dark matter model with scale-invariant primordial perturbations were recently introduced to obtain more power on large scales, R(sub p) is approximately 20 h(sup -1) Mpc, e.g., low-matter-density (non-zero cosmological constant) models, 'tilted' primordial spectra, and scenarios with a mixture of cold and hot dark matter. They also include models with an effective scale-dependent bias, such as the cooperative galaxy formation scenario of Bower, etal. It is shown that higher-order (n-point) galaxy correlation functions can provide a useful test of such models and can discriminate between models with true large-scale power in the density field and those where the galaxy power arises from scale-dependent bias: a bias with rapid scale-dependence leads to a dramatic decrease of the hierarchical amplitudes Q(sub J) at large scales, r is approximately greater than R(sub p). Current observational constraints on the three-point amplitudes Q(sub 3) and S(sub 3) can place limits on the bias parameter(s) and appear to disfavor, but not yet rule out, the hypothesis that scale-dependent bias is responsible for the extra power observed on large scales.

Tritium in well waters, streams and atomic lakes in the East Kazakhstan Oblast of the Semipalatinsk Nuclear Test Site.

PubMed

Mitchell, Peter I; Vintró, Luis León; Omarova, Aigul; Burkitbayev, Mukhambetkali; Nápoles, Humberto Jiménez; Priest, Nicholas D

2005-06-01

The concentration of tritium has been determined in well waters, streams and atomic lakes in the Sarzhal, Tel'kem, Balapan and Degelen Mountains areas of the Semipalatinsk Test Site. The data show that levels of tritium in domestic well waters within the settlement of Sarzhal are extremely low at the present time with a median value of 4.4 Bq dm(-3) (95% confidence interval:4.1-4.7 Bq dm(-3)). These levels are only marginally above the background tritium content in surface waters globally. Levels in the atomic craters at Tel'kem 1 and Tel'kem 2 are between one and two orders of magnitude higher, while the level in Lake Balapan is approximately 12,600 Bq dm(-3). Significantly, levels in streams and test-tunnel waters sourced in the Degelen Mountains, the site of approximately 215 underground nuclear tests, are a further order of magnitude higher, being in the range 133,000--235,500 Bq dm(-3). No evidence was adduced which indicates that domestic wells in Sarzhal are contaminated by tritium-rich waters sourced in the Degelen massif, suggesting that the latter are not connected hydrologically to the near-surface groundwater recharging the Sarzhal wells. Annual doses to humans arising from the ingestion of tritium in these well waters are very low at the present time and are of no radiological significance.

Convergence of the Light-Front Coupled-Cluster Method in Scalar Yukawa Theory

NASA Astrophysics Data System (ADS)

Usselman, Austin

We use Fock-state expansions and the Light-Front Coupled-Cluster (LFCC) method to study mass eigenvalue problems in quantum field theory. Specifically, we study convergence of the method in scalar Yukawa theory. In this theory, a single charged particle is surrounded by a cloud of neutral particles. The charged particle can create or annihilate neutral particles, causing the n-particle state to depend on the n + 1 and n - 1-particle state. Fock state expansion leads to an infinite set of coupled equations where truncation is required. The wave functions for the particle states are expanded in a basis of symmetric polynomials and a generalized eigenvalue problem is solved for the mass eigenvalue. The mass eigenvalue problem is solved for multiple values for the coupling strength while the number of particle states and polynomial basis order are increased. Convergence of the mass eigenvalue solutions is then obtained. Three mass ratios between the charged particle and neutral particles were studied. This includes a massive charged particle, equal masses and massive neutral particles. Relative probability between states can also be explored for more detailed understanding of the process of convergence with respect to the number of Fock sectors. The reliance on higher order particle states depended on how large the mass of the charge particle was. The higher the mass of the charged particle, the more the system depended on higher order particle states. The LFCC method solves this same mass eigenvalue problem using an exponential operator. This exponential operator can then be truncated instead to form a finite system of equations that can be solved using a built in system solver provided in most computational environments, such as MatLab and Mathematica. First approximation in the LFCC method allows for only one particle to be created by the new operator and proved to be not powerful enough to match the Fock state expansion. The second order approximation allowed one and two particles to be created by the new operator and converged to the Fock state expansion results. This showed the LFCC method to be a reliable replacement method for solving quantum field theory problems.

Monte Carlo simulations on marker grouping and ordering.

PubMed

Wu, J; Jenkins, J; Zhu, J; McCarty, J; Watson, C

2003-08-01

Four global algorithms, maximum likelihood (ML), sum of adjacent LOD score (SALOD), sum of adjacent recombinant fractions (SARF) and product of adjacent recombinant fraction (PARF), and one approximation algorithm, seriation (SER), were used to compare the marker ordering efficiencies for correctly given linkage groups based on doubled haploid (DH) populations. The Monte Carlo simulation results indicated the marker ordering powers for the five methods were almost identical. High correlation coefficients were greater than 0.99 between grouping power and ordering power, indicating that all these methods for marker ordering were reliable. Therefore, the main problem for linkage analysis was how to improve the grouping power. Since the SER approach provided the advantage of speed without losing ordering power, this approach was used for detailed simulations. For more generality, multiple linkage groups were employed, and population size, linkage cutoff criterion, marker spacing pattern (even or uneven), and marker spacing distance (close or loose) were considered for obtaining acceptable grouping powers. Simulation results indicated that the grouping power was related to population size, marker spacing distance, and cutoff criterion. Generally, a large population size provided higher grouping power than small population size, and closely linked markers provided higher grouping power than loosely linked markers. The cutoff criterion range for achieving acceptable grouping power and ordering power differed for varying cases; however, combining all situations in this study, a cutoff criterion ranging from 50 cM to 60 cM was recommended for achieving acceptable grouping power and ordering power for different cases.

Integration of the Rotation of an Earth-like Body as a Perturbed Spherical Rotor

NASA Astrophysics Data System (ADS)

Ferrer, Sebastián; Lara, Martin

2010-05-01

For rigid bodies close to a sphere, we propose an analytical solution that is free from elliptic integrals and functions, and can be fundamental for application to perturbed problems. After reordering the Hamiltonian as a perturbed spherical rotor, the Lie-series solution is generated up to an arbitrary order. Using the inertia parameters of different solar system bodies, the comparison of the approximate series solution with the exact analytical one shows that the precision reached with relatively low orders is at the same level of the observational accuracy for the Earth and Mars. Thus, for instance, the periodic errors of the mathematical solution are confined to the microarcsecond level with a simple second-order truncation for the Earth. On the contrary, higher orders are required for the mathematical solution to reach a precision at the expected level of accuracy of proposed new theories for the rotational dynamics of the Moon.

Secular motion around synchronously orbiting planetary satellites.

PubMed

Lara, Martin; San-Juan, Juan F; Ferrer, Sebastián

2005-12-01

We investigate the secular motion of a spacecraft around the natural satellite of a planet. The satellite rotates synchronously with its mean motion around the planet. Our model takes into account the gravitational potential of the satellite up to the second order, and the third-body perturbation in Hill's approximation. Close to the satellite, the ratio of rotation rate of the satellite to mean motion of the orbiter is small. When considering this ratio as a small parameter, the Coriolis effect is a first-order perturbation, while the third-body tidal attraction, the ellipticity effect, and the oblateness perturbation remain at higher orders. Then, we apply perturbation theory and find that a third-order approach is enough to show the influence of the satellite's ellipticity in the pericenter dynamics. Finally, we discuss the averaged system in the three-dimensional parametric space, and provide a global description of the flow.

A Method for Calculating Viscosity and Thermal Conductivity of a Helium-Xenon Gas Mixture

NASA Technical Reports Server (NTRS)

Johnson, Paul K.

2006-01-01

A method for calculating viscosity and thermal conductivity of a helium-xenon (He-Xe) gas mixture was employed, and results were compared to AiResearch (part of Honeywell) analytical data. The method of choice was that presented by Hirschfelder with Singh's third-order correction factor applied to thermal conductivity. Values for viscosity and thermal conductivity were calculated over a temperature range of 400 to 1200 K for He-Xe gas mixture molecular weights of 20.183, 39.94, and 83.8 kg/kmol. First-order values for both transport properties were in good agreement with AiResearch analytical data. Third-order-corrected thermal conductivity values were all greater than AiResearch data, but were considered to be a better approximation of thermal conductivity because higher-order effects of mass and temperature were taken into consideration. Viscosity, conductivity, and Prandtl number were then compared to experimental data presented by Taylor.

Combination of the pair density approximation and the Takahashi–Imada approximation for path integral Monte Carlo simulations

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

Zillich, Robert E., E-mail: robert.zillich@jku.at

2015-11-15

We construct an accurate imaginary time propagator for path integral Monte Carlo simulations for heterogeneous systems consisting of a mixture of atoms and molecules. We combine the pair density approximation, which is highly accurate but feasible only for the isotropic interactions between atoms, with the Takahashi–Imada approximation for general interactions. We present finite temperature simulations results for energy and structure of molecules–helium clusters X{sup 4}He{sub 20} (X=HCCH and LiH) which show a marked improvement over the Trotter approximation which has a 2nd-order time step bias. We show that the 4th-order corrections of the Takahashi–Imada approximation can also be applied perturbativelymore » to a 2nd-order simulation.« less

An approximation technique for predicting the transient response of a second order nonlinear equation

NASA Technical Reports Server (NTRS)

Laurenson, R. M.; Baumgarten, J. R.

1975-01-01

An approximation technique has been developed for determining the transient response of a nonlinear dynamic system. The nonlinearities in the system which has been considered appear in the system's dissipation function. This function was expressed as a second order polynomial in the system's velocity. The developed approximation is an extension of the classic Kryloff-Bogoliuboff technique. Two examples of the developed approximation are presented for comparative purposes with other approximation methods.

A higher-order theory for geometrically nonlinear analysis of composite laminates

NASA Technical Reports Server (NTRS)

Reddy, J. N.; Liu, C. F.

1987-01-01

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

On the calculation of charge transfer transitions with standard density functionals using constrained variational density functional theory.

PubMed

Ziegler, Tom; Krykunov, Mykhaylo

2010-08-21

It is well known that time-dependent density functional theory (TD-DFT) based on standard gradient corrected functionals affords both a quantitative and qualitative incorrect picture of charge transfer transitions between two spatially separated regions. It is shown here that the well known failure can be traced back to the use of linear response theory. Further, it is demonstrated that the inclusion of higher order terms readily affords a qualitatively correct picture even for simple functionals based on the local density approximation. The inclusion of these terms is done within the framework of a newly developed variational approach to excitation energies called constrained variational density functional theory (CV-DFT). To second order [CV(2)-DFT] this theory is identical to adiabatic TD-DFT within the Tamm-Dancoff approximation. With inclusion of fourth order corrections [CV(4)-DFT] it affords a qualitative correct description of charge transfer transitions. It is finally demonstrated that the relaxation of the ground state Kohn-Sham orbitals to first order in response to the change in density on excitation together with CV(4)-DFT affords charge transfer excitations in good agreement with experiment. The new relaxed theory is termed R-CV(4)-DFT. The relaxed scheme represents an effective way in which to introduce double replacements into the description of single electron excitations, something that would otherwise require a frequency dependent kernel.

A higher order numerical method for time fractional partial differential equations with nonsmooth data

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

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

Cui, Xia, E-mail: cui_xia@iapcm.ac.cn; Yuan, Guang-wei; Shen, Zhi-jun

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-ordermore » accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.« less

Resonant oscillations in open axisymmetric tubes

NASA Astrophysics Data System (ADS)

Amundsen, D. E.; Mortell, M. P.; Seymour, B. R.

2017-12-01

We study the behaviour of the isentropic flow of a gas in both a straight tube of constant cross section and a cone, open at one end and forced at or near resonance at the other. A continuous transition between these configurations is provided through the introduction of a geometric parameter k associated with the opening angle of the cone where the tube corresponds to k=0. The primary objective is to find long-time resonant and near-resonant approximate solutions for the open tube, i.e. k→ 0. Detailed analysis for both the tube and cone in the limit of small forcing (O(ɛ 3)) is carried out, where ɛ 3 is the Mach number of the forcing function and the resulting flow has Mach number O(ɛ ). The resulting approximate solutions are compared with full numerical simulations. Interesting distinctions between the cone and the tube emerge. Depending on the damping and detuning, the responses for the tube are continuous and of O(ɛ ). In the case of the cone, the resonant response involves an amplification of the fundamental resonant mode, usually called the dominant first-mode approximation. However, higher modes must be included for the tube to account for the nonlinear generation of higher-order resonances. Bridging these distinct solution behaviours is a transition layer of O(ɛ 2) in k. It is found that an appropriately truncated set of modes provides the requisite modal approximation, again comparing well to numerical simulations.

Are non-linearity effects of absorption important for MAX-DOAS observations?

NASA Astrophysics Data System (ADS)

Pukite, Janis; Wang, Yang; Wagner, Thomas

2017-04-01

For scattered light observations the absorption optical depth depends non-linearly on the trace gas concentrations if their absorption is strong. This is the case because the Beer-Lambert law is generally not applicable for scattered light measurements due to many (i.e. more than one) light paths contributing to the measurement. While in many cases a linear approximation can be made, for scenarios with strong absorption non-linear effects cannot always be neglected. This is especially the case for observation geometries with spatially extended and diffuse light paths, especially in satellite limb geometry but also for nadir measurements as well. Fortunately the effects of non-linear effects can be quantified by means of expanding the radiative transfer equation in a Taylor series with respect to the trace gas absorption coefficients. Herewith if necessary (1) the higher order absorption structures can be described as separate fit parameters in the DOAS fit and (2) the algorithm constraints of retrievals of VCDs and profiles can be improved by considering higher order sensitivity parameters. In this study we investigate the contribution of the higher order absorption structures for MAX-DOAS observation geometry for different atmospheric and ground properties (cloud and aerosol effects, trace gas amount, albedo) and geometry (different Sun and viewing angles).

Three-dimensional organization of otolith-ocular reflexes in rhesus monkeys. III. Responses To translation

NASA Technical Reports Server (NTRS)

Angelaki, D. E.

1998-01-01

The three-dimensional (3-D) properties of the translational vestibulo-ocular reflexes (translational VORs) during lateral and fore-aft oscillations in complete darkness were studied in rhesus monkeys at frequencies between 0.16 and 25 Hz. In addition, constant velocity off-vertical axis rotations extended the frequency range to 0.02 Hz. During lateral motion, horizontal responses were in phase with linear velocity in the frequency range of 2-10 Hz. At both lower and higher frequencies, phase lags were introduced. Torsional response phase changed more than 180 degrees in the tested frequency range such that torsional eye movements, which could be regarded as compensatory to "an apparent roll tilt" at the lowest frequencies, became anticompensatory at all frequencies above approximately 1 Hz. These results suggest two functionally different frequency bandwidths for the translational VORs. In the low-frequency spectrum (<<0.5 Hz), horizontal responses compensatory to translation are small and high-pass-filtered whereas torsional response sensitivity is relatively frequency independent. At higher frequencies however, both horizontal and torsional response sensitivity and phase exhibit a similar frequency dependence, suggesting a common role during head translation. During up-down motion, vertical responses were in phase with translational velocity at 3-5 Hz but phase leads progressively increased for lower frequencies (>90 degrees at frequencies <0.2 Hz). No consistent dependence on static head orientation was observed for the vertical response components during up-down motion and the horizontal and torsional response components during lateral translation. The frequency response characteristics of the translational VORs were fitted by "periphery/brain stem" functions that related the linear acceleration input, transduced by primary otolith afferents, to the velocity signals providing the input to the velocity-to-position neural integrator and the oculomotor plant. The lowest-order, best-fit periphery/brain stem model that approximated the frequency dependence of the data consisted of a second order transfer function with two alternating poles (at 0.4 and 7.2 Hz) and zeros (at 0.035 and 3.4 Hz). In addition to clearly differentiator dynamics at low frequencies (less than approximately 0.5 Hz), there was no frequency bandwidth where the periphery/brain stem function could be approximated by an integrator, as previously suggested. In this scheme, the oculomotor plant dynamics are assumed to perform the necessary high-frequency integration as required by the reflex. The detailed frequency dependence of the data could only be precisely described by higher order functions with nonminimum phase characteristics that preclude simple filtering of afferent inputs and might be suggestive of distributed spatiotemporal processing of otolith signals in the translational VORs.

Nonlinear Aeroelastic Equations of Motion of Twisted, Nonuniform, Flexible Horizontal-Axis Wind Turbine Blades

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.

1980-01-01

The second-degree nonlinear equations of motion for a flexible, twisted, nonuniform, horizontal axis wind turbine blade were developed using Hamilton's principle. A mathematical ordering scheme which was consistent with the assumption of a slender beam was used to discard some higher-order elastic and inertial terms in the second-degree nonlinear equations. The blade aerodynamic loading which was employed accounted for both wind shear and tower shadow and was obtained from strip theory based on a quasi-steady approximation of two-dimensional, incompressible, unsteady, airfoil theory. The resulting equations had periodic coefficients and were suitable for determining the aeroelastic stability and response of large horizontal-axis wind turbine blades.

Merging NLO multi-jet calculations with improved unitarization

NASA Astrophysics Data System (ADS)

Bellm, Johannes; Gieseke, Stefan; Plätzer, Simon

2018-03-01

We present an algorithm to combine multiple matrix elements at LO and NLO with a parton shower. We build on the unitarized merging paradigm. The inclusion of higher orders and multiplicities reduce the scale uncertainties for observables sensitive to hard emissions, while preserving the features of inclusive quantities. The combination allows further soft and collinear emissions to be predicted by the all-order parton-shower approximation. We inspect the impact of terms that are formally but not parametrically negligible. We present results for a number of collider observables where multiple jets are observed, either on their own or in the presence of additional uncoloured particles. The algorithm is implemented in the event generator Herwig.

Three-Point Bending Fracture Behavior of Single Oriented Crossed-Lamellar Structure in Scapharca broughtonii Shell

PubMed Central

Ji, Hong-Mei; Zhang, Wen-Qian; Wang, Xu; Li, Xiao-Wu

2015-01-01

The three-point bending strength and fracture behavior of single oriented crossed-lamellar structure in Scapharca broughtonii shell were investigated. The samples for bending tests were prepared with two different orientations perpendicular and parallel to the radial ribs of the shell, which corresponds to the tiled and stacked directions of the first-order lamellae, respectively. The bending strength in the tiled direction is approximately 60% higher than that in the stacked direction, primarily because the regularly staggered arrangement of the second-order lamellae in the tiled direction can effectively hinder the crack propagation, whereas the cracks can easily propagate along the interfaces between lamellae in the stacked direction. PMID:28793557

AN EFFICIENT HIGHER-ORDER FAST MULTIPOLE BOUNDARY ELEMENT SOLUTION FOR POISSON-BOLTZMANN BASED MOLECULAR ELECTROSTATICS

PubMed Central

Bajaj, Chandrajit; Chen, Shun-Chuan; Rand, Alexander

2011-01-01

In order to compute polarization energy of biomolecules, we describe a boundary element approach to solving the linearized Poisson-Boltzmann equation. Our approach combines several important features including the derivative boundary formulation of the problem and a smooth approximation of the molecular surface based on the algebraic spline molecular surface. State of the art software for numerical linear algebra and the kernel independent fast multipole method is used for both simplicity and efficiency of our implementation. We perform a variety of computational experiments, testing our method on a number of actual proteins involved in molecular docking and demonstrating the effectiveness of our solver for computing molecular polarization energy. PMID:21660123

Modeling tracer transport in randomly heterogeneous porous media by nonlocal moment equations: Anomalous transport

NASA Astrophysics Data System (ADS)

Morales-Casique, E.; Lezama-Campos, J. L.; Guadagnini, A.; Neuman, S. P.

2013-05-01

Modeling tracer transport in geologic porous media suffers from the corrupt characterization of the spatial distribution of hydrogeologic properties of the system and the incomplete knowledge of processes governing transport at multiple scales. Representations of transport dynamics based on a Fickian model of the kind considered in the advection-dispersion equation (ADE) fail to capture (a) the temporal variation associated with the rate of spreading of a tracer, and (b) the distribution of early and late arrival times which are often observed in field and/or laboratory scenarios and are considered as the signature of anomalous transport. Elsewhere we have presented exact stochastic moment equations to model tracer transport in randomly heterogeneous aquifers. We have also developed a closure scheme which enables one to provide numerical solutions of such moment equations at different orders of approximations. The resulting (ensemble) average and variance of concentration fields were found to display a good agreement against Monte Carlo - based simulation results for mildly heterogeneous (or well-conditioned strongly heterogeneous) media. Here we explore the ability of the moment equations approach to describe the distribution of early arrival times and late time tailing effects which can be observed in Monte-Carlo based breakthrough curves (BTCs) of the (ensemble) mean concentration. We show that BTCs of mean resident concentration calculated at a fixed space location through higher-order approximations of moment equations display long tailing features of the kind which is typically associated with anomalous transport behavior and are not represented by an ADE model with constant dispersive parameter, such as the zero-order approximation.

Resummed memory kernels in generalized system-bath master equations

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

Mavros, Michael G.; Van Voorhis, Troy, E-mail: tvan@mit.edu

2014-08-07

Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between themore » two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the “Landau-Zener resummation” of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.« less

Sensitivity of gravitational wave searches to the full signal of intermediate-mass black hole binaries during the first observing run of Advanced LIGO

NASA Astrophysics Data System (ADS)

Calderón Bustillo, Juan; Salemi, Francesco; Dal Canton, Tito; Jani, Karan P.

2018-01-01

The sensitivity of gravitational wave searches for binary black holes is estimated via the injection and posterior recovery of simulated gravitational wave signals in the detector data streams. When a search reports no detections, the estimated sensitivity is then used to place upper limits on the coalescence rate of the target source. In order to obtain correct sensitivity and rate estimates, the injected waveforms must be faithful representations of the real signals. Up to date, however, injected waveforms have neglected radiation modes of order higher than the quadrupole, potentially biasing sensitivity and coalescence rate estimates. In particular, higher-order modes are known to have a large impact in the gravitational waves emitted by intermediate-mass black holes binaries. In this work, we evaluate the impact of this approximation in the context of two search algorithms run by the LIGO Scientific Collaboration in their search for intermediate-mass black hole binaries in the O1 LIGO Science Run data: a matched filter-based pipeline and a coherent unmodeled one. To this end, we estimate the sensitivity of both searches to simulated signals for nonspinning binaries including and omitting higher-order modes. We find that omission of higher-order modes leads to biases in the sensitivity estimates which depend on the masses of the binary, the search algorithm, and the required level of significance for detection. In addition, we compare the sensitivity of the two search algorithms across the studied parameter space. We conclude that the most recent LIGO-Virgo upper limits on the rate of coalescence of intermediate-mass black hole binaries are conservative for the case of highly asymmetric binaries. However, the tightest upper limits, placed for nearly equal-mass sources, remain unchanged due to the small contribution of higher modes to the corresponding sources.

Nuclear recoil effect on the binding energies in highly charged He-like ions

NASA Astrophysics Data System (ADS)

Malyshev, A. V.; Popov, R. V.; Shabaev, V. M.; Zubova, N. A.

2018-04-01

The most precise to-date evaluation of the nuclear recoil effect on the n = 1 and n = 2 energy levels of He-like ions is presented in the range Z = 12–100. The one-electron recoil contribution is calculated within the framework of the rigorous quantum electrodynamics approach to first order in the electron-to-nucleus mass ratio m/M and to all orders in the parameter αZ. The two-electron m/M recoil term is calculated employing the 1/Z perturbation theory. The recoil contribution of the zeroth order in 1/Z is evaluated to all orders in αZ, while the 1/Z term is calculated using the Breit approximation. The recoil corrections of the second and higher orders in 1/Z are taken into account within the nonrelativistic approach. The obtained results are compared with the previous evaluation of this effect (Artemyev et al 2005 Phys. Rev. A 71 062104).

Relativistic corrections to the ground state of H2 calculated without using the Born-Oppenheimer approximation

NASA Astrophysics Data System (ADS)

Wang, L. M.; Yan, Z.-C.

2018-06-01

The Schrödinger equation for the ground state of the hydrogen molecule H2 is solved by applying the Rayleigh-Ritz variational method in Hylleraas coordinates without using the Born-Oppenheimer approximation. The nonrelativistic energy eigenvalue is converged to -1.164 025 030 880 (7 ) atomic units. The leading-order relativistic corrections, including the mass-velocity, Darwin, orbit-orbit, spin-spin, and relativistic recoil terms, are evaluated perturbatively. Together with the higher-order relativistic and quantum electrodynamic corrections obtained by Puchalski et al. [Phys. Rev. Lett. 117, 263002 (2016), 10.1103/PhysRevLett.117.263002], we determine the dissociation energy of the hydrogen molecule, D0=36 118.069 71 (33 ) cm-1 , which agrees with the two recent experimental results of Liu et al. [J. Chem. Phys. 130, 174306 (2009), 10.1063/1.3120443], 36 118.069 62 (37 ) cm-1 , and Altmann et al. [Phys. Rev. Lett. 120, 043204 (2018), 10.1103/PhysRevLett.120.043204], 36 118.069 45 (31 ) cm-1 .

An efficient higher order family of root finders

NASA Astrophysics Data System (ADS)

Petkovic, Ljiljana D.; Rancic, Lidija; Petkovic, Miodrag S.

2008-06-01

A one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial, based on a cubically convergent Hansen-Patrick's family, is studied. We show that the convergence of the basic family of the fourth order can be increased to five and six using Newton's and Halley's corrections, respectively. Since these corrections use the already calculated values, the computational efficiency of the accelerated methods is significantly increased. Further acceleration is achieved by applying the Gauss-Seidel approach (single-step mode). One of the most important problems in solving nonlinear equations, the construction of initial conditions which provide both the guaranteed and fast convergence, is considered for the proposed accelerated family. These conditions are computationally verifiable; they depend only on the polynomial coefficients, its degree and initial approximations, which is of practical importance. Some modifications of the considered family, providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions, are also studied. Numerical examples demonstrate the convergence properties of the presented family of root-finding methods.

Yarkovsky-O'Keefe-Radzievskii-Paddack effect on tumbling objects

NASA Astrophysics Data System (ADS)

Breiter, S.; Rożek, A.; Vokrouhlický, D.

2011-11-01

A semi-analytical model of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect on an asteroid spin in a non-principal axis rotation state is developed. The model describes the spin-state evolution in Deprit-Elipe variables, first-order averaged with respect to rotation and Keplerian orbital motion. Assuming zero conductivity, the YORP torque is represented by spherical harmonic series with vectorial coefficients, allowing us to use any degree and order of approximation. Within the quadrupole approximation of the illumination function we find the same first integrals involving rotational momentum, obliquity and dynamical inertia that were obtained by Cicaló & Scheeres. The integrals do not exist when higher degree terms of the illumination function are included, and then the asymptotic states known from Vokrouhlický et al. appear. This resolves an apparent contradiction between earlier results. Averaged equations of motion admit stable and unstable limit cycle solutions that were not previously detected. Non-averaged numerical integration by the Taylor series method for an exemplary shape of 3103 Eger is in good agreement with the semi-analytical theory.

A Simple Method for High-Lift Propeller Conceptual Design

NASA Technical Reports Server (NTRS)

Patterson, Michael; Borer, Nick; German, Brian

2016-01-01

In this paper, we present a simple method for designing propellers that are placed upstream of the leading edge of a wing in order to augment lift. Because the primary purpose of these "high-lift propellers" is to increase lift rather than produce thrust, these props are best viewed as a form of high-lift device; consequently, they should be designed differently than traditional propellers. We present a theory that describes how these props can be designed to provide a relatively uniform axial velocity increase, which is hypothesized to be advantageous for lift augmentation based on a literature survey. Computational modeling indicates that such propellers can generate the same average induced axial velocity while consuming less power and producing less thrust than conventional propeller designs. For an example problem based on specifications for NASA's Scalable Convergent Electric Propulsion Technology and Operations Research (SCEPTOR) flight demonstrator, a propeller designed with the new method requires approximately 15% less power and produces approximately 11% less thrust than one designed for minimum induced loss. Higher-order modeling and/or wind tunnel testing are needed to verify the predicted performance.

Effect of hydrostatic pressure, temperature, and solvent on the rate of the Diels-Alder reaction between 9,10-anthracenedimethanol and maleic anhydride

NASA Astrophysics Data System (ADS)

Kiselev, V. D.; Kornilov, D. A.; Anikin, O. V.; Latypova, L. I.; Konovalov, A. I.

2017-03-01

The rate of the reaction between 9,10-anthracenedimethanol and maleic anhydride in 1,4-dioxane, acetonitrile, trichloromethane, and toluene is studied at 25, 35, 45°C in the pressure range of 1-1772 bar. The rate constants, enthalpies, entropies and activation volumes are determined. It is shown that the rate of reaction with 9,10-anthracenedimethanol is approximately one order of magnitude higher than with 9-anthracenemethanol.

Stopping relativistic Xe, Ho, Au, and U nuclei in nuclear emulsions

NASA Technical Reports Server (NTRS)

Waddington, C. J.; Fixsen, D. J.; Freier, P. S.

1985-01-01

Nuclei of Xe-54, Ho-67, Au-79 and U-92 accelerated at the Bevalac to energies between 1200 and 900 MeV/n were stopped in nuclear emulsions. The observed residual ranges were compared with those calculated from various models of energy loss and shown to be most consistent with a calculation that includes those higher order correction terms proposed previously to describe the energy loss of highly changed particles, for which the first Born approximation is not valid.

Stopping relativistic Xe, Ho, Au and U nuclei in nuclear emulsions

NASA Technical Reports Server (NTRS)

Waddington, C. J.; Fixsen, D. J.; Freier, P. S.

1985-01-01

Nuclei of Xe-54, Ho-67, Au-79 and U-92 accelerated at the Bevalac to energies between 1200 and 900 MeV/n were stopped in nuclear emulsions. The observed residual ranges were compared with those calculated from various models of energy loss and shown to be most consistent with a calculation that includes those higher order correction terms proposed previously to describe the energy loss of highly charged particles, for which the first Born approximation is not valid.

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

PubMed

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

2007-03-23

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

A technique for increasing the accuracy of the numerical inversion of the Laplace transform with applications

NASA Technical Reports Server (NTRS)

Berger, B. S.; Duangudom, S.

1973-01-01

A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.

Error analysis of finite element method for Poisson–Nernst–Planck equations

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

Sun, Yuzhou; Sun, Pengtao; Zheng, Bin

A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.

Derivation of the density functional theory from the cluster expansion.

PubMed

Hsu, J Y

2003-09-26

The density functional theory is derived from a cluster expansion by truncating the higher-order correlations in one and only one term in the kinetic energy. The formulation allows self-consistent calculation of the exchange correlation effect without imposing additional assumptions to generalize the local density approximation. The pair correlation is described as a two-body collision of bound-state electrons, and modifies the electron- electron interaction energy as well as the kinetic energy. The theory admits excited states, and has no self-interaction energy.

Highly soluble [1]benzothieno[3,2-b]benzothiophene (BTBT) derivatives for high-performance, solution-processed organic field-effect transistors.

PubMed

Ebata, Hideaki; Izawa, Takafumi; Miyazaki, Eigo; Takimiya, Kazuo; Ikeda, Masaaki; Kuwabara, Hirokazu; Yui, Tatsuto

2007-12-26

2,7-Dialkyl[1]benzothieno[3,2-b]benzothiophenes were tested as solution-processible molecular semiconductors. Thin films of the organic semiconductors deposited on Si/SiO2 substrates by spin coating have well-ordered structures as confirmed by XRD analysis. Evaluations of the devices under ambient conditions showed typical p-channel FET responses with the field-effect mobility higher than 1.0 cm2 V-1 s-1 and Ion/Ioff of approximately 10(7).

Renormalization scheme dependence of high-order perturbative QCD predictions

NASA Astrophysics Data System (ADS)

Ma, Yang; Wu, Xing-Gang

2018-02-01

Conventionally, one adopts typical momentum flow of a physical observable as the renormalization scale for its perturbative QCD (pQCD) approximant. This simple treatment leads to renormalization scheme-and-scale ambiguities due to the renormalization scheme and scale dependence of the strong coupling and the perturbative coefficients do not exactly cancel at any fixed order. It is believed that those ambiguities will be softened by including more higher-order terms. In the paper, to show how the renormalization scheme dependence changes when more loop terms have been included, we discuss the sensitivity of pQCD prediction on the scheme parameters by using the scheme-dependent {βm ≥2}-terms. We adopt two four-loop examples, e+e-→hadrons and τ decays into hadrons, for detailed analysis. Our results show that under the conventional scale setting, by including more-and-more loop terms, the scheme dependence of the pQCD prediction cannot be reduced as efficiently as that of the scale dependence. Thus a proper scale-setting approach should be important to reduce the scheme dependence. We observe that the principle of minimum sensitivity could be such a scale-setting approach, which provides a practical way to achieve optimal scheme and scale by requiring the pQCD approximate be independent to the "unphysical" theoretical conventions.

Propagation of coherent light pulses with PHASE

NASA Astrophysics Data System (ADS)

Bahrdt, J.; Flechsig, U.; Grizzoli, W.; Siewert, F.

2014-09-01

The current status of the software package PHASE for the propagation of coherent light pulses along a synchrotron radiation beamline is presented. PHASE is based on an asymptotic expansion of the Fresnel-Kirchhoff integral (stationary phase approximation) which is usually truncated at the 2nd order. The limits of this approximation as well as possible extensions to higher orders are discussed. The accuracy is benchmarked against a direct integration of the Fresnel-Kirchhoff integral. Long range slope errors of optical elements can be included by means of 8th order polynomials in the optical element coordinates w and l. Only recently, a method for the description of short range slope errors has been implemented. The accuracy of this method is evaluated and examples for realistic slope errors are given. PHASE can be run either from a built-in graphical user interface or from any script language. The latter method provides substantial flexibility. Optical elements including apertures can be combined. Complete wave packages can be propagated, as well. Fourier propagators are included in the package, thus, the user may choose between a variety of propagators. Several means to speed up the computation time were tested - among them are the parallelization in a multi core environment and the parallelization on a cluster.

Fabrication of low-temperature solid oxide fuel cells with a nanothin protective layer by atomic layer deposition

PubMed Central

2013-01-01

Anode aluminum oxide-supported thin-film fuel cells having a sub-500-nm-thick bilayered electrolyte comprising a gadolinium-doped ceria (GDC) layer and an yttria-stabilized zirconia (YSZ) layer were fabricated and electrochemically characterized in order to investigate the effect of the YSZ protective layer. The highly dense and thin YSZ layer acted as a blockage against electron and oxygen permeation between the anode and GDC electrolyte. Dense GDC and YSZ thin films were fabricated using radio frequency sputtering and atomic layer deposition techniques, respectively. The resulting bilayered thin-film fuel cell generated a significantly higher open circuit voltage of approximately 1.07 V compared with a thin-film fuel cell with a single-layered GDC electrolyte (approximately 0.3 V). PMID:23342963

A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

Efremenko, Dmitry S.; Molina García, Víctor; Gimeno García, Sebastián; Doicu, Adrian

2017-07-01

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.

A soil catena on schist in northwestern California

USGS Publications Warehouse

Marron, D.C.; Popenoe, J.H.

1986-01-01

Soil characteristics in a small steepland watershed underlain by schist in a rainy, tectonically active area in northwestern California show close associations with drainage-basin position and slope characteristics. Five soil-topography units based on these associations are defined in the study watershed. Spatial relationships of soil series, and patterns of soil development as indicated by B-horizon clay content and redness, reflect interactions between pedogenesis and erosion. General soil-topography patterns include: (1) decreases in soil-development moving from low-order to higher-order stream vallyes; and (2) more developed soils on north-facing as opposed to south-facing slopes. Decreases in soil-profile development moving from slopes near low-order streams to slopes near higher-order streams approximately correlate with increases in gradient, vertical relief, and drainage density, and reflect a more vigorous stripping of regolith by erosion on the slopes near the higher-order streams. The larger percentage of area covered by the more developed soils on north-facing as opposed to south-facing slopes appears to reflect a contrast in the way dominant erosional processes interact with pedogenic processes. Roadcuts on middle and upper slopes show soil discontinuities indicative of disturbance by block slides or slumps or both. Roadcuts on lower slopes show disrupted soils in small bedrock hollows that could have been created by rapid, shallow landslides or by the pulled-up root wads of toppled trees. Soil-profile characteristics and soil-topography patterns in the study area demonstrate that both erosional and pedogenic processes need to be considered when interpreting characteristics of hillslope soils. ?? 1986.

Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

NASA Technical Reports Server (NTRS)

Putko, Michele M.; Taylor, Arthur C., III; Newman, Perry A.; Green, Lawrence L.

2002-01-01

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Harmonic generation beyond the Strong-Field Approximation: the physics behind the short-wave-infrared scaling laws.

PubMed

Pérez-Hernández, J A; Roso, L; Plaja, L

2009-06-08

The physics of laser-mater interactions beyond the perturbative limit configures the field of extreme non-linear optics. Although most experiments have been done in the near infrared ( lambda

Pure quasi-P-wave calculation in transversely isotropic media using a hybrid method

NASA Astrophysics Data System (ADS)

Wu, Zedong; Liu, Hongwei; Alkhalifah, Tariq

2018-07-01

The acoustic approximation for anisotropic media is widely used in current industry imaging and inversion algorithms mainly because Pwaves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulae tend to be simpler, resulting in more efficient implementations, and depend on fewer medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from shear wave artefacts. Thus, we derive a new acoustic wave equation for wave propagation in transversely isotropic (TI) media, which is based on a partially separable approximation of the dispersion relation for TI media and free of shear wave artefacts. Even though our resulting equation is not a partial differential equation, it is still a linear equation. Thus, we propose to implement this equation efficiently by combining the finite difference approximation with spectral evaluation of the space-independent parts. The resulting algorithm provides solutions without the constraint ɛ ≥ δ. Numerical tests demonstrate the effectiveness of the approach.

Modeling the global positioning system signal propagation through the ionosphere

NASA Technical Reports Server (NTRS)

Bassiri, S.; Hajj, G. A.

1992-01-01

Based on realistic modeling of the electron density of the ionosphere and using a dipole moment approximation for the Earth's magnetic field, one is able to estimate the effect of the ionosphere on the Global Positioning System (GPS) signal for a ground user. The lowest order effect, which is on the order of 0.1-100 m of group delay, is subtracted out by forming a linear combination of the dual frequencies of the GPS signal. One is left with second- and third-order effects that are estimated typically to be approximately 0-2 cm and approximately 0-2 mm at zenith, respectively, depending on the geographical location, the time of day, the time of year, the solar cycle, and the relative geometry of the magnetic field and the line of sight. Given the total electron content along a line of sight, the authors derive an approximation to the second-order term which is accurate to approximately 90 percent within the magnetic dipole moment model; this approximation can be used to reduce the second-order term to the millimeter level, thus potentially improving precise positioning in space and on the ground. The induced group delay, or phase advance, due to second- and third-order effects is examined for two ground receivers located at equatorial and mid-latitude regions tracking several GPS satellites.

Effect of preparation technique on the properties and in vivo efficacy of benzocaine-loaded ethosomes.

PubMed

Maestrelli, Francesca; Capasso, Gaetano; González-Rodríguez, Maria L; Rabasco, Antonio M; Ghelardini, Carla; Mura, Paola

2009-01-01

This study aimed to investigate the influence of the preparation conditions on the performance of an ethosomal formulation for topical delivery of the local anesthetic agent, benzocaine (BZC). Ethosomes were prepared with different techniques, such as thin-layer evaporation, freezing and thawing, reverse-phase evaporation, extrusion and sonication, obtaining, respectively, multilayer vesicles (MLVs), frozen and thawed MLV (FATMLV), large unilamellar vesicles (LUVs), and small unilamellar vesicles (SUVs). The obtained vesicles were characterized for morphology, size, zeta potential, and entrapment efficiency (EE%), and their stability was monitored during storage at 4 degrees C. In vitro permeation properties from gels incorporating drug ethosomal dispersions were evaluated in vitro by using artificial lipophilic membranes, while their anesthetic effect was determined in vivo on rabbits. The results suggested that the vesicle preparation method plays an important role in affecting the properties and effectiveness of ethosomal formulations. MLVs and LUVs exhibited higher drug EE% and better stability than FATMLV and SUV vesicles. The In vitro drug permeation rate was directly related to the vesicle EE% and varied in the order MLV>LUV approximately FATMLV>SUV. The therapeutic efficacy of BZC ethosomal formulations was significantly improved with respect to the corresponding BZC solution. The best results, in terms of enhanced intensity of anesthetic effect, were given by formulations containing MLVs and LUVs, and the order of effectiveness was MLV approximately LUV>FATMLV approximately SUV, rather similar to that found in permeation studies. On the contrary, unexpectedly, the effectiveness order in increasing the duration of drug action was SUV> or =MLV>LUV approximately FATMLV. The highest efficacy of SUVs was probably due to the more intimate contact with the epithelium due to their greatest surface area, which allowed the longest extension of drug therapeutic action. The overall results suggest that a suitably developed ethosomal formulation of BZC can be of actual value for improving its clinical effectiveness in topical anesthesia.

An Extension of the Krieger-Li-Iafrate Approximation to the Optimized-Effective-Potential Method

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

Wilson, B.G.

1999-11-11

The Krieger-Li-Iafrate approximation can be expressed as the zeroth order result of an unstable iterative method for solving the integral equation form of the optimized-effective-potential method. By pre-conditioning the iterate a first order correction can be obtained which recovers the bulk of quantal oscillations missing in the zeroth order approximation. A comparison of calculated total energies are given with Krieger-Li-Iafrate, Local Density Functional, and Hyper-Hartree-Fock results for non-relativistic atoms and ions.

Effect of boundary representation on viscous, separated flows in a discontinuous-Galerkin Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Nelson, Daniel A.; Jacobs, Gustaaf B.; Kopriva, David A.

2016-08-01

The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier-Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.

An analytical technique for approximating unsteady aerodynamics in the time domain

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1980-01-01

An analytical technique is presented for approximating unsteady aerodynamic forces in the time domain. The order of elements of a matrix Pade approximation was postulated, and the resulting polynomial coefficients were determined through a combination of least squares estimates for the numerator coefficients and a constrained gradient search for the denominator coefficients which insures stable approximating functions. The number of differential equations required to represent the aerodynamic forces to a given accuracy tends to be smaller than that employed in certain existing techniques where the denominator coefficients are chosen a priori. Results are shown for an aeroelastic, cantilevered, semispan wing which indicate a good fit to the aerodynamic forces for oscillatory motion can be achieved with a matrix Pade approximation having fourth order numerator and second order denominator polynomials.

The use of fractional orders in the determination of birefringence of highly dispersive materials by the channelled spectrum method

NASA Astrophysics Data System (ADS)

Nagarajan, K.; Shashidharan Nair, C. K.

2007-07-01

The channelled spectrum employing polarized light interference is a very convenient method for the study of dispersion of birefringence. However, while using this method, the absolute order of the polarized light interference fringes cannot be determined easily. Approximate methods are therefore used to estimate the order. One of the approximations is that the dispersion of birefringence across neighbouring integer order fringes is negligible. In this paper, we show how this approximation can cause errors. A modification is reported whereby the error in the determination of absolute fringe order can be reduced using fractional orders instead of integer orders. The theoretical background for this method supported with computer simulation is presented. An experimental arrangement implementing these modifications is described. This method uses a Constant Deviation Spectrometer (CDS) and a Soleil Babinet Compensator (SBC).

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Pseudospectral collocation methods for fourth order differential equations

NASA Technical Reports Server (NTRS)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

An Additive to Improve the Wear Characteristics of Perfluoropolyether Based Greases

NASA Technical Reports Server (NTRS)

Jones, David G. V.; Fowzy, Mahmoud A.; Landry, James F.; Jones, William R., Jr.; Shogrin, Bradley A.; Nguyen, QuynhGiao

1999-01-01

The friction and wear characteristics of two formulated perfluoropolyether based greases were compared to their non-additive base greases. One grease was developed for the electronics industry (designated as GXL-296A) while the other is for space applications (designated as GXL-320A). The formulated greases (GXL-296B and GXL-320B) contained a proprietary antiwear additive at an optimized concentration. Tests were conducted using a vacuum four-ball tribometer. AISI 52100 steel specimens were used for all GXL-296 tests. Both AISI 52100 steel and 440C stainless steel were tested with the GXL-320 greases. Test conditions included: a pressure less than 6.7 x 10(exp )-4 Pa, a 200N load, a sliding velocity of 28.8 mm/sec (100 rpm) and room temperature (approximately equal to 23 C). Wear rates for each grease were determined from the slope of the wear volume as a function of sliding distance. Both non-additive base greases yielded relatively high wear rates on the order of 10(exp -8) cu mm using AISI 52100 steel specimens. Formulated grease GXL-296B yielded a reduction in wear rate by a factor of approximately 21, while grease GXL-320B had a reduction of approximately 12 times. Lower wear rates (-50%) were observed with both GXL-320 greases using 440C stainless steel. Mean friction coefficients were slightly higher for both formulated greases compared to their base greases. The GXL-296 series (higher base oil viscosity) yielded much higher friction coefficients compared to their GXL-320 series (lower base oil viscosity) counterparts.

The p-version of the finite element method in incremental elasto-plastic analysis

NASA Technical Reports Server (NTRS)

Holzer, Stefan M.; Yosibash, Zohar

1993-01-01

Whereas the higher-order versions of the finite elements method (the p- and hp-version) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. Aspects of incremental elasto-plastic finite element analysis which are particularly amenable to improvements by the p-version is discussed. These theoretical considerations are supported by several numerical experiments. First, an example for which an analytical solution is available is studied. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared to the traditional h-version but also in respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-worked lug - is presented which demonstrates how the modeling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.

The NuSTAR Extragalactic Survey: A First Sensitive Look at the High-Energy Cosmic X-Ray Background Population

NASA Technical Reports Server (NTRS)

Alexander, D. M.; Stern, D.; DelMoro, A.; Lansbury, G. B.; Assef, R. J.; Aird, J.; Ajello, M.; Ballantyne, D. R.; Bauer, F. E.; Boggs, S. E.;

First-order symmetry-adapted perturbation theory for multiplet splittings.

PubMed

Patkowski, Konrad; Żuchowski, Piotr S; Smith, Daniel G A

2018-04-28

We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S 2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S 2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

First-order symmetry-adapted perturbation theory for multiplet splittings

NASA Astrophysics Data System (ADS)

Patkowski, Konrad; Żuchowski, Piotr S.; Smith, Daniel G. A.

2018-04-01

We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

Self-force as a cosmic censor in the Kerr overspinning problem

NASA Astrophysics Data System (ADS)

Colleoni, Marta; Barack, Leor; Shah, Abhay G.; van de Meent, Maarten

2015-10-01

It is known that a near-extremal Kerr black hole can be spun up beyond its extremal limit by capturing a test particle. Here we show that overspinning is always averted once backreaction from the particle's own gravity is properly taken into account. We focus on nonspinning, uncharged, massive particles thrown in along the equatorial plane and work in the first-order self-force approximation (i.e., we include all relevant corrections to the particle's acceleration through linear order in the ratio, assumed small, between the particle's energy and the black hole's mass). Our calculation is a numerical implementation of a recent analysis by two of us [Phys. Rev. D 91, 104024 (2015)], in which a necessary and sufficient "censorship" condition was formulated for the capture scenario, involving certain self-force quantities calculated on the one-parameter family of unstable circular geodesics in the extremal limit. The self-force information accounts both for radiative losses and for the finite-mass correction to the critical value of the impact parameter. Here we obtain the required self-force data and present strong evidence to suggest that captured particles never drive the black hole beyond its extremal limit. We show, however, that, within our first-order self-force approximation, it is possible to reach the extremal limit with a suitable choice of initial orbital parameters. To rule out such a possibility would require (currently unavailable) information about higher-order self-force corrections.

Analytical Debye-Huckel model for electrostatic potentials around dissolved DNA.

PubMed

Wagner, K; Keyes, E; Kephart, T W; Edwards, G

1997-07-01

We present an analytical, Green-function-based model for the electric potential of DNA in solution, treating the surrounding solvent with the Debye-Huckel approximation. The partial charge of each atom is accounted for by modeling DNA as linear distributions of atoms on concentric cylindrical surfaces. The condensed ions of the solvent are treated with the Debye-Huckel approximation. The resultant leading term of the potential is that of a continuous shielded line charge, and the higher order terms account for the helical structure. Within several angstroms of the surface there is sufficient information in the electric potential to distinguish features and symmetries of DNA. Plots of the potential and equipotential surfaces, dominated by the phosphate charges, reflect the structural differences between the A, B, and Z conformations and, to a smaller extent, the difference between base sequences. As the distances from the helices increase, the magnitudes of the potentials decrease. However, the bases and sugars account for a larger fraction of the double helix potential with increasing distance. We have found that when the solvent is treated with the Debye-Huckel approximation, the potential decays more rapidly in every direction from the surface than it did in the concentric dielectric cylinder approximation.

Uniformly high-order accurate non-oscillatory schemes, 1

NASA Technical Reports Server (NTRS)

Harten, A.; Osher, S.

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Coexistence of ΘI I-loop-current order with checkerboard d -wave CDW/PDW order in a hot-spot model for cuprate superconductors

NASA Astrophysics Data System (ADS)

de Carvalho, Vanuildo S.; Pépin, Catherine; Freire, Hermann

2016-03-01

We investigate the strong influence of the ΘI I-loop-current order on both unidirectional and bidirectional d -wave charge-density-wave/pair-density-wave (CDW/PDW) composite orders along axial momenta (±Q0,0 ) and (0 ,±Q0) that emerge in an effective hot-spot model departing from the three-band Emery model relevant to the phenomenology of the cuprate superconductors. This study is motivated by the compelling evidence that the ΘI I-loop-current order described by this model may explain groundbreaking experiments such as spin-polarized neutron scattering performed in these materials. Here, we demonstrate, within a saddle-point approximation, that the ΘI I-loop-current order clearly coexists with bidirectional (i.e., checkerboard) d -wave CDW and PDW orders along axial momenta, but is visibly detrimental to the unidirectional (i.e., stripe) case. This result has potentially far-reaching implications for the physics of the cuprates and agrees well with very recent x-ray experiments on YBCO that indicate that at higher dopings the CDW order has indeed a tendency to be bidirectional.

Antiferromagnetic order and the structural order-disorder transition in the Cd6Ho quasicrystal approximant

NASA Astrophysics Data System (ADS)

Kreyssig, Andreas; Beutier, Guillaume; Hiroto, Takanobu; Kim, Min Gyu; Tucker, Gregory S.; de Boissieu, Marc; Tamura, Ryuji; Goldman, Alan I.

2013-09-01

It has generally been accepted that the orientational ordering of the Cd4 tetrahedron within the Cd6 R quasicrystal approximants is kinetically inhibited for R = Ho, Er, Tm and Lu by steric constraints. Our high-resolution X-ray scattering measurements of the Cd6Ho quasicrystal approximant, however, reveal an abrupt (first-order) transition to a monoclinic structure below T S = 178 K for samples that have 'aged' at room temperature for approximately one year, reopening this question. Using X-ray resonant magnetic scattering at the Ho L 3-edge we have elucidated the nature of the antiferromagnetic ordering below T N = 8.5 K in Cd6Ho. The magnetic Bragg peaks are found at the charge forbidden H + K + L = 2n + 1 positions, referenced to the high-temperature body-centred cubic structure. In general terms, this corresponds to antiferromagnetic arrangements of the Ho moments on adjacent clusters in the unit cell as previously found for Cd6Tb.

Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

NASA Technical Reports Server (NTRS)

Putko, Michele M.; Newman, Perry A.; Taylor, Arthur C., III; Green, Lawrence L.

2001-01-01

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Thermoelectrics in Coulomb-coupled quantum dots: Cotunneling and energy-dependent lead couplings

NASA Astrophysics Data System (ADS)

Walldorf, Nicklas; Jauho, Antti-Pekka; Kaasbjerg, Kristen

2017-09-01

We study thermoelectric effects in Coulomb-coupled quantum-dot (CCQD) systems beyond lowest-order tunneling processes and the often applied wide-band approximation. To this end, we present a master-equation (ME) approach based on a perturbative T -matrix calculation of the charge and heat tunneling rates and transport currents. Applying the method to transport through a noninteracting single-level QD, we demonstrate excellent agreement with the Landauer-Büttiker theory when higher-order (cotunneling) processes are included in the ME. Next, we study the effect of cotunneling and energy-dependent lead couplings on the heat currents in a system of two CCQDs. We find that cotunneling processes (i) can dominate the off-resonant heat currents at low temperature and bias compared to the interdot interaction, and (ii) give rise to a pronounced reduction of the cooling power achievable with the recently demonstrated Maxwell's demon cooling mechanism. Furthermore, we demonstrate that the cooling power can be boosted significantly by carefully engineering the energy dependence of the lead couplings to filter out undesired transport processes. Our findings emphasize the importance of higher-order cotunneling processes as well as engineered energy-dependent lead couplings in the optimization of the thermoelectric performance of CCQD systems.

Considering Horn's Parallel Analysis from a Random Matrix Theory Point of View.

PubMed

Saccenti, Edoardo; Timmerman, Marieke E

2017-03-01

Horn's parallel analysis is a widely used method for assessing the number of principal components and common factors. We discuss the theoretical foundations of parallel analysis for principal components based on a covariance matrix by making use of arguments from random matrix theory. In particular, we show that (i) for the first component, parallel analysis is an inferential method equivalent to the Tracy-Widom test, (ii) its use to test high-order eigenvalues is equivalent to the use of the joint distribution of the eigenvalues, and thus should be discouraged, and (iii) a formal test for higher-order components can be obtained based on a Tracy-Widom approximation. We illustrate the performance of the two testing procedures using simulated data generated under both a principal component model and a common factors model. For the principal component model, the Tracy-Widom test performs consistently in all conditions, while parallel analysis shows unpredictable behavior for higher-order components. For the common factor model, including major and minor factors, both procedures are heuristic approaches, with variable performance. We conclude that the Tracy-Widom procedure is preferred over parallel analysis for statistically testing the number of principal components based on a covariance matrix.

Connectivity strategies for higher-order neural networks applied to pattern recognition

NASA Technical Reports Server (NTRS)

Spirkovska, Lilly; Reid, Max B.

1990-01-01

Different strategies for non-fully connected HONNs (higher-order neural networks) are discussed, showing that by using such strategies an input field of 128 x 128 pixels can be attained while still achieving in-plane rotation and translation-invariant recognition. These techniques allow HONNs to be used with the larger input scenes required for practical pattern-recognition applications. The number of interconnections that must be stored has been reduced by a factor of approximately 200,000 in a T/C case and about 2000 in a Space Shuttle/F-18 case by using regional connectivity. Third-order networks have been simulated using several connection strategies. The method found to work best is regional connectivity. The main advantages of this strategy are the following: (1) it considers features of various scales within the image and thus gets a better sample of what the image looks like; (2) it is invariant to shape-preserving geometric transformations, such as translation and rotation; (3) the connections are predetermined so that no extra computations are necessary during run time; and (4) it does not require any extra storage for recording which connections were formed.

Discretization analysis of bifurcation based nonlinear amplifiers

NASA Astrophysics Data System (ADS)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2017-09-01

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

Low rank approach to computing first and higher order derivatives using automatic differentiation

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

Reed, J. A.; Abdel-Khalik, H. S.; Utke, J.

2012-07-01

This manuscript outlines a new approach for increasing the efficiency of applying automatic differentiation (AD) to large scale computational models. By using the principles of the Efficient Subspace Method (ESM), low rank approximations of the derivatives for first and higher orders can be calculated using minimized computational resources. The output obtained from nuclear reactor calculations typically has a much smaller numerical rank compared to the number of inputs and outputs. This rank deficiency can be exploited to reduce the number of derivatives that need to be calculated using AD. The effective rank can be determined according to ESM by computingmore » derivatives with AD at random inputs. Reduced or pseudo variables are then defined and new derivatives are calculated with respect to the pseudo variables. Two different AD packages are used: OpenAD and Rapsodia. OpenAD is used to determine the effective rank and the subspace that contains the derivatives. Rapsodia is then used to calculate derivatives with respect to the pseudo variables for the desired order. The overall approach is applied to two simple problems and to MATWS, a safety code for sodium cooled reactors. (authors)« less

Higher order parametric excitation modes for spaceborne quadrupole mass spectrometers

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

Gershman, D. J.; Block, B. P.; Rubin, M.

This paper describes a technique to significantly improve upon the mass peak shape and mass resolution of spaceborne quadrupole mass spectrometers (QMSs) through higher order auxiliary excitation of the quadrupole field. Using a novel multiresonant tank circuit, additional frequency components can be used to drive modulating voltages on the quadrupole rods in a practical manner, suitable for both improved commercial applications and spaceflight instruments. Auxiliary excitation at frequencies near twice that of the fundamental quadrupole RF frequency provides the advantages of previously studied parametric excitation techniques, but with the added benefit of increased sensed excitation amplitude dynamic range and themore » ability to operate voltage scan lines through the center of upper stability islands. Using a field programmable gate array, the amplitudes and frequencies of all QMS signals are digitally generated and managed, providing a robust and stable voltage control system. These techniques are experimentally verified through an interface with a commercial Pfeiffer QMG422 quadrupole rod system. When operating through the center of a stability island formed from higher order auxiliary excitation, approximately 50% and 400% improvements in 1% mass resolution and peak stability were measured, respectively, when compared with traditional QMS operation. Although tested with a circular rod system, the presented techniques have the potential to improve the performance of both circular and hyperbolic rod geometry QMS sensors.« less

Local Higher-Order Graph Clustering

PubMed Central

Yin, Hao; Benson, Austin R.; Leskovec, Jure; Gleich, David F.

2018-01-01

Local graph clustering methods aim to find a cluster of nodes by exploring a small region of the graph. These methods are attractive because they enable targeted clustering around a given seed node and are faster than traditional global graph clustering methods because their runtime does not depend on the size of the input graph. However, current local graph partitioning methods are not designed to account for the higher-order structures crucial to the network, nor can they effectively handle directed networks. Here we introduce a new class of local graph clustering methods that address these issues by incorporating higher-order network information captured by small subgraphs, also called network motifs. We develop the Motif-based Approximate Personalized PageRank (MAPPR) algorithm that finds clusters containing a seed node with minimal motif conductance, a generalization of the conductance metric for network motifs. We generalize existing theory to prove the fast running time (independent of the size of the graph) and obtain theoretical guarantees on the cluster quality (in terms of motif conductance). We also develop a theory of node neighborhoods for finding sets that have small motif conductance, and apply these results to the case of finding good seed nodes to use as input to the MAPPR algorithm. Experimental validation on community detection tasks in both synthetic and real-world networks, shows that our new framework MAPPR outperforms the current edge-based personalized PageRank methodology. PMID:29770258

An intermediate orbit calculated from three position vectors: accuracy of approximation of a perturbed motion. (Russian Title: Промежуточная орбита, вычисленная по трем векторам положения: точность аппроксимации возмущенного движения)

NASA Astrophysics Data System (ADS)

Shefer, V. A.

2015-12-01

We examine intermediate perturbed orbit proposed by the author previously, defined from the three position vectors of a small celestial body. It is shown theoretically, that at a small reference time interval covering the body positions the approximation accuracy of real motion by this orbit corresponds approximately to the fourth order of tangency. The smaller reference interval of time, the better this correspondence. Laws of variation of the methodical errors in constructing intermediate orbit subject to the length of reference time interval are deduced. According to these laws, the convergence rate of the method to the exact solution (upon reducing the reference interval of time) in the general case is higher by three orders of magnitude than in the case of conventional methods using Keplerian unperturbed orbit. The considered orbit is among the most accurate in set of orbits of their class determined by the order of tangency. The theoretical results are validated by numerical examples. The work was supported by the Ministry of Education and Science of the Russian Federation, project no. 2014/223(1567).

Lessons from an evolving rRNA: 16S and 23S rRNA structures from a comparative perspective

NASA Technical Reports Server (NTRS)

Gutell, R. R.; Larsen, N.; Woese, C. R.

1994-01-01

The 16S and 23S rRNA higher-order structures inferred from comparative analysis are now quite refined. The models presented here differ from their immediate predecessors only in minor detail. Thus, it is safe to assert that all of the standard secondary-structure elements in (prokaryotic) rRNAs have been identified, with approximately 90% of the individual base pairs in each molecule having independent comparative support, and that at least some of the tertiary interactions have been revealed. It is interesting to compare the rRNAs in this respect with tRNA, whose higher-order structure is known in detail from its crystal structure (36) (Table 2). It can be seen that rRNAs have as great a fraction of their sequence in established secondary-structure elements as does tRNA. However, the fact that the former show a much lower fraction of identified tertiary interactions and a greater fraction of unpaired nucleotides than the latter implies that many of the rRNA tertiary interactions remain to be located. (Alternatively, the ribosome might involve protein-rRNA rather than intramolecular rRNA interactions to stabilize three-dimensional structure.) Experimental studies on rRNA are consistent to a first approximation with the structures proposed here, confirming the basic assumption of comparative analysis, i.e., that bases whose compositions strictly covary are physically interacting. In the exhaustive study of Moazed et al. (45) on protection of the bases in the small-subunit rRNA against chemical modification, the vast majority of bases inferred to pair by covariation are found to be protected from chemical modification, both in isolated small-subunit rRNA and in the 30S subunit. The majority of the tertiary interactions are reflected in the chemical protection data as well (45). On the other hand, many of the bases not shown as paired in Fig. 1 are accessible to chemical attack (45). However, in this case a sizeable fraction of them are also protected against chemical modification (in the isolated rRNA), which suggests that considerable higher-order structure remains to be found (although all of it may not involve base-base interactions and so may not be detectable by comparative analysis). The agreement between the higher-order structure of the small-subunit rRNA and protection against chemical modification is not perfect, however; some bases shown to covary canonically are accessible to chemical modification (45).(ABSTRACT TRUNCATED AT 400 WORDS).

N-point statistics of large-scale structure in the Zel'dovich approximation

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

Tassev, Svetlin, E-mail: tassev@astro.princeton.edu

2014-06-01

Motivated by the results presented in a companion paper, here we give a simple analytical expression for the matter n-point functions in the Zel'dovich approximation (ZA) both in real and in redshift space (including the angular case). We present numerical results for the 2-dimensional redshift-space correlation function, as well as for the equilateral configuration for the real-space 3-point function. We compare those to the tree-level results. Our analysis is easily extendable to include Lagrangian bias, as well as higher-order perturbative corrections to the ZA. The results should be especially useful for modelling probes of large-scale structure in the linear regime,more » such as the Baryon Acoustic Oscillations. We make the numerical code used in this paper freely available.« less

Stability of Dirac Liquids with Strong Coulomb Interaction.

PubMed

Tupitsyn, Igor S; Prokof'ev, Nikolay V

2017-01-13

We develop and apply the diagrammatic Monte Carlo technique to address the problem of the stability of the Dirac liquid state (in a graphene-type system) against the strong long-range part of the Coulomb interaction. So far, all attempts to deal with this problem in the field-theoretical framework were limited either to perturbative or random phase approximation and functional renormalization group treatments, with diametrically opposite conclusions. Our calculations aim at the approximation-free solution with controlled accuracy by computing vertex corrections from higher-order skeleton diagrams and establishing the renormalization group flow of the effective Coulomb coupling constant. We unambiguously show that with increasing the system size L (up to ln(L)∼40), the coupling constant always flows towards zero; i.e., the two-dimensional Dirac liquid is an asymptotically free T=0 state with divergent Fermi velocity.

Deposition of conductive TiN shells on SiO2 nanoparticles with a fluidized bed ALD reactor

NASA Astrophysics Data System (ADS)

Didden, Arjen; Hillebrand, Philipp; Wollgarten, Markus; Dam, Bernard; van de Krol, Roel

2016-02-01

Conductive TiN shells have been deposited on SiO2 nanoparticles (10-20 nm primary particle size) with fluidized bed atomic layer deposition using TDMAT and NH3 as precursors. Analysis of the powders confirms that shell growth saturates at approximately 0.4 nm/cycle at TDMAT doses of >1.2 mmol/g of powder. TEM and XPS analysis showed that all particles were coated with homogeneous shells containing titanium. Due to the large specific surface area of the nanoparticles, the TiN shells rapidly oxidize upon exposure to air. Electrical measurements show that the partially oxidized shells are conducting, with apparent resistivity of approximately 11 kΩ cm. The resistivity of the powders is strongly influenced by the NH3 dose, with a smaller dose giving an order-of-magnitude higher resistivity.

Chemical association in simple models of molecular and ionic fluids. III. The cavity function

NASA Astrophysics Data System (ADS)

Zhou, Yaoqi; Stell, George

1992-01-01

Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ``linear'' approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier's principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data.

Properties of quantum systems via diagonalization of transition amplitudes. II. Systematic improvements of short-time propagation

NASA Astrophysics Data System (ADS)

Vidanović, Ivana; Bogojević, Aleksandar; Balaž, Antun; Belić, Aleksandar

2009-12-01

In this paper, building on a previous analysis [I. Vidanović, A. Bogojević, and A. Belić, preceding paper, Phys. Rev. E 80, 066705 (2009)] of exact diagonalization of the space-discretized evolution operator for the study of properties of nonrelativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one- and two-dimensional models. The quality of numerically calculated higher-order eigenstates is assessed by comparison with semiclassical cumulative density of states.

Superconducting Hot-Electron Submillimeter-Wave Detector

NASA Technical Reports Server (NTRS)

Karasik, Boris; McGrath, William; Leduc, Henry

2009-01-01

A superconducting hot-electron bolometer has been built and tested as a prototype of high-sensitivity, rapid-response detectors of submillimeter-wavelength radiation. There are diverse potential applications for such detectors, a few examples being submillimeter spectroscopy for scientific research; detection of leaking gases; detection of explosive, chemical, and biological weapons; and medical imaging. This detector is a superconducting-transition- edge device. Like other such devices, it includes a superconducting bridge that has a low heat capacity and is maintained at a critical temperature (T(sub c)) at the lower end of its superconducting-transition temperature range. Incident photons cause transient increases in electron temperature through the superconducting-transition range, thereby yielding measurable increases in electrical resistance. In this case, T(sub c) = 6 K, which is approximately the upper limit of the operating-temperature range of silicon-based bolometers heretofore used routinely in many laboratories. However, whereas the response speed of a typical silicon- based laboratory bolometer is characterized by a frequency of the order of a kilohertz, the response speed of the present device is much higher characterized by a frequency of the order of 100 MHz. For this or any bolometer, a useful figure of merit that one seeks to minimize is (NEP)(tau exp 1/2), where NEP denotes the noise-equivalent power (NEP) and the response time. This figure of merit depends primarily on the heat capacity and, for a given heat capacity, is approximately invariant. As a consequence of this approximate invariance, in designing a device having a given heat capacity to be more sensitive (to have lower NEP), one must accept longer response time (slower response) or, conversely, in designing it to respond faster, one must accept lower sensitivity. Hence, further, in order to increase both the speed of response and the sensitivity, one must make the device very small in order to make its heat capacity very small; this is the approach followed in developing the present device.

Atmospheric Turbulence Modeling for Aerospace Vehicles: Fractional Order Fit

NASA Technical Reports Server (NTRS)

Kopasakis, George (Inventor)

2015-01-01

An improved model for simulating atmospheric disturbances is disclosed. A scale Kolmogorov spectral may be scaled to convert the Kolmogorov spectral into a finite energy von Karman spectral and a fractional order pole-zero transfer function (TF) may be derived from the von Karman spectral. Fractional order atmospheric turbulence may be approximated with an integer order pole-zero TF fit, and the approximation may be stored in memory.

Quantitative analysis of neuronal response properties in primary and higher-order auditory cortical fields of awake house mice (Mus musculus)

PubMed Central

Joachimsthaler, Bettina; Uhlmann, Michaela; Miller, Frank; Ehret, Günter; Kurt, Simone

2014-01-01

Because of its great genetic potential, the mouse (Mus musculus) has become a popular model species for studies on hearing and sound processing along the auditory pathways. Here, we present the first comparative study on the representation of neuronal response parameters to tones in primary and higher-order auditory cortical fields of awake mice. We quantified 12 neuronal properties of tone processing in order to estimate similarities and differences of function between the fields, and to discuss how far auditory cortex (AC) function in the mouse is comparable to that in awake monkeys and cats. Extracellular recordings were made from 1400 small clusters of neurons from cortical layers III/IV in the primary fields AI (primary auditory field) and AAF (anterior auditory field), and the higher-order fields AII (second auditory field) and DP (dorsoposterior field). Field specificity was shown with regard to spontaneous activity, correlation between spontaneous and evoked activity, tone response latency, sharpness of frequency tuning, temporal response patterns (occurrence of phasic responses, phasic-tonic responses, tonic responses, and off-responses), and degree of variation between the characteristic frequency (CF) and the best frequency (BF) (CF–BF relationship). Field similarities were noted as significant correlations between CFs and BFs, V-shaped frequency tuning curves, similar minimum response thresholds and non-monotonic rate-level functions in approximately two-thirds of the neurons. Comparative and quantitative analyses showed that the measured response characteristics were, to various degrees, susceptible to influences of anesthetics. Therefore, studies of neuronal responses in the awake AC are important in order to establish adequate relationships between neuronal data and auditory perception and acoustic response behavior. PMID:24506843

Magnetic quantum tunneling: key insights from multi-dimensional high-field EPR.

PubMed

Lawrence, J; Yang, E-C; Hendrickson, D N; Hill, S

2009-08-21

Multi-dimensional high-field/frequency electron paramagnetic resonance (HFEPR) spectroscopy is performed on single-crystals of the high-symmetry spin S = 4 tetranuclear single-molecule magnet (SMM) [Ni(hmp)(dmb)Cl](4), where hmp(-) is the anion of 2-hydroxymethylpyridine and dmb is 3,3-dimethyl-1-butanol. Measurements performed as a function of the applied magnetic field strength and its orientation within the hard-plane reveal the four-fold behavior associated with the fourth order transverse zero-field splitting (ZFS) interaction, (1/2)B(S + S), within the framework of a rigid spin approximation (with S = 4). This ZFS interaction mixes the m(s) = +/-4 ground states in second order of perturbation, generating a sizeable (12 MHz) tunnel splitting, which explains the fast magnetic quantum tunneling in this SMM. Meanwhile, multi-frequency measurements performed with the field parallel to the easy-axis reveal HFEPR transitions associated with excited spin multiplets (S < 4). Analysis of the temperature dependence of the intensities of these transitions enables determination of the isotropic Heisenberg exchange constant, J = -6.0 cm(-1), which couples the four spin s = 1 Ni(II) ions within the cluster, as well as a characterization of the ZFS within excited states. The combined experimental studies support recent work indicating that the fourth order anisotropy associated with the S = 4 state originates from second order ZFS interactions associated with the individual Ni(II) centers, but only as a result of higher-order processes that occur via S-mixing between the ground state and higher-lying (S < 4) spin multiplets. We argue that this S-mixing plays an important role in the low-temperature quantum dynamics associated with many other well known SMMs.

Representation of the exact relativistic electronic Hamiltonian within the regular approximation

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2003-12-01

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

Simulations of phase space distributions of storm time proton ring current

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Lyons, Larry R.; Schulz, Michael

1994-01-01

We use results of guiding-center simulations of ion transport to map phase space densities of the stormtime proton ring current. We model a storm as a sequence of substorm-associated enhancements in the convection electric field. Our pre-storm phase space distribution is an analytical solution to a steady-state transport model in which quiet-time radial diffusion balances charge exchange. This pre-storm phase space spectra at L approximately 2 to 4 reproduce many of the features found in observed quiet-time spectra. Using results from simulations of ion transport during model storms having main phases of 3, 6, and 12 hr, we map phase space distributions from the pre-storm distribution in accordance with Liouville's theorem. We find stormtime enhancements in the phase space densities at energies E approximately 30-160 keV for L approximately 2.5 to 4. These enhancements agree well with the observed stormtime ring current. For storms with shorter main phases (approximately 3 hr), the enhancements are caused mainly by the trapping of ions injected from open night side trajectories, and diffusive transport of higher-energy (greater than or approximately 160 keV) ions contributes little to the stormtime ring current. However, the stormtime ring current is augmented also by the diffusive transport of higher-energy ions (E greater than or approximately 160 keV) durinng stroms having longer main phases (greater than or approximately 6 hr). In order to account for the increase in Dst associated with the formation of the stormtime ring current, we estimate the enhancement in particle-energy content that results from stormtime ion transport in the equatorial magnetosphere. We find that transport alone cannot account for the entire increase in absolute value of Dst typical of a major storm. However, we can account for the entire increase in absolute value of Dst by realistically increasing the stormtime outer boundary value of the phase space density relative to the quiet-time value. We compute the magnetic field produced by the ring current itself and find that radial profiles of the magnetic field depression resemble those obtained from observational data.

Interpretation of electron diffraction patterns from amorphous and fullerene-like carbon allotropes.

PubMed

Czigány, Zsolt; Hultman, Lars

2010-06-01

The short range order in amorphous and fullerene-like carbon compounds has been characterized by selected area electron diffraction (SAED) patterns and compared with simulations of model nanoclusters. Broad rings in SAED pattern from fullerene-like CN(x) at approximately 1.2, approximately 2, and approximately 3.5A indicate short-range order similar to that in graphite, but peak shifts indicate sheet curvature in agreement with high-resolution transmission electron microscopy images. Fullerene-like CP(x) exhibits rings at approximately 1.6 and 2.6A, which can be explained if it consists of fragments with short-range order and high curvature similar to that of C(20). Copyright 2010 Elsevier B.V. All rights reserved.

Effect of the interconnected network structure on the epidemic threshold.

PubMed

Wang, Huijuan; Li, Qian; D'Agostino, Gregorio; Havlin, Shlomo; Stanley, H Eugene; Van Mieghem, Piet

2013-08-01

Most real-world networks are not isolated. In order to function fully, they are interconnected with other networks, and this interconnection influences their dynamic processes. For example, when the spread of a disease involves two species, the dynamics of the spread within each species (the contact network) differs from that of the spread between the two species (the interconnected network). We model two generic interconnected networks using two adjacency matrices, A and B, in which A is a 2N×2N matrix that depicts the connectivity within each of two networks of size N, and B a 2N×2N matrix that depicts the interconnections between the two. Using an N-intertwined mean-field approximation, we determine that a critical susceptible-infected-susceptible (SIS) epidemic threshold in two interconnected networks is 1/λ(1)(A+αB), where the infection rate is β within each of the two individual networks and αβ in the interconnected links between the two networks and λ(1)(A+αB) is the largest eigenvalue of the matrix A+αB. In order to determine how the epidemic threshold is dependent upon the structure of interconnected networks, we analytically derive λ(1)(A+αB) using a perturbation approximation for small and large α, the lower and upper bound for any α as a function of the adjacency matrix of the two individual networks, and the interconnections between the two and their largest eigenvalues and eigenvectors. We verify these approximation and boundary values for λ(1)(A+αB) using numerical simulations, and determine how component network features affect λ(1)(A+αB). We note that, given two isolated networks G(1) and G(2) with principal eigenvectors x and y, respectively, λ(1)(A+αB) tends to be higher when nodes i and j with a higher eigenvector component product x(i)y(j) are interconnected. This finding suggests essential insights into ways of designing interconnected networks to be robust against epidemics.

Effect of the interconnected network structure on the epidemic threshold

NASA Astrophysics Data System (ADS)

Wang, Huijuan; Li, Qian; D'Agostino, Gregorio; Havlin, Shlomo; Stanley, H. Eugene; Van Mieghem, Piet

2013-08-01

Most real-world networks are not isolated. In order to function fully, they are interconnected with other networks, and this interconnection influences their dynamic processes. For example, when the spread of a disease involves two species, the dynamics of the spread within each species (the contact network) differs from that of the spread between the two species (the interconnected network). We model two generic interconnected networks using two adjacency matrices, A and B, in which A is a 2N×2N matrix that depicts the connectivity within each of two networks of size N, and B a 2N×2N matrix that depicts the interconnections between the two. Using an N-intertwined mean-field approximation, we determine that a critical susceptible-infected-susceptible (SIS) epidemic threshold in two interconnected networks is 1/λ1(A+αB), where the infection rate is β within each of the two individual networks and αβ in the interconnected links between the two networks and λ1(A+αB) is the largest eigenvalue of the matrix A+αB. In order to determine how the epidemic threshold is dependent upon the structure of interconnected networks, we analytically derive λ1(A+αB) using a perturbation approximation for small and large α, the lower and upper bound for any α as a function of the adjacency matrix of the two individual networks, and the interconnections between the two and their largest eigenvalues and eigenvectors. We verify these approximation and boundary values for λ1(A+αB) using numerical simulations, and determine how component network features affect λ1(A+αB). We note that, given two isolated networks G1 and G2 with principal eigenvectors x and y, respectively, λ1(A+αB) tends to be higher when nodes i and j with a higher eigenvector component product xiyj are interconnected. This finding suggests essential insights into ways of designing interconnected networks to be robust against epidemics.

Evidence for Black Hole Growth in Local Analogs to Lyman Break Galaxies

NASA Technical Reports Server (NTRS)

Jia, Jianjun; Ptak, Andrew; Heckman, Timothy M.; Overzier, Roderik A.; Hornschemeier, Ann; LaMassa, Stephanie M.

2011-01-01

We have used XMM-Newton to observe six Lyman break analogs (LBAs): members of the rare population of local galaxies that have properties that are very similar to distant Lyman break galaxies. Our six targets were specifically selected because they have optical emission-line properties that are intermediate between starbursts and Type 2 (obscured) active galactic nuclei (AGNs). Our new X-ray data provide an important diagnostic of the presence of an AGN. We find X-ray luminosities of order 10(sup 42) erg per second and ratios of X-ray to far-IR lummositles that are higher than values in pure starburst galaxies by factors ranging from approximately 3 to 30. This strongly suggests the presence of an AGN in at least some of the galaxies. The ratios of the luminosities of the hard (2-10 keV) X-ray to [O III] emission line are low by about an order of magnitude compared with Type 1 AGN, but are consistent with the broad range seen in Type 2 AGN. Either the AGN hard X-rays are significantly obscured or the [O III] emission is dominated by the starburst. We searched for an iron emission line at approximately 6.4 ke V, which is a key feature of obscured AGNs, but only detected emission at the approximately 2sigma level. Finally, we find that the ratios of the mid-infrared (24 micrometer) continuum to [O III]lambda 5007 luminosities in these LBAs are higher than the values for Type 2 AGN by an average of 0.8 dex. Combining all these clues, we conclude that an AGN is likely to be present, but that the bolometric luminosity is produced primarily by an intense starburst. If these black holes are radiating at the Eddington limit, their masses would lie in the range of 10(sup 5) - 10(sup 6) solar mass. These objects may offer ideal local laboratories to investigate the processes by which black holes grew in the early universe.

Self-focusing of ultraintense femtosecond optical vortices in air.

PubMed

Polynkin, P; Ament, C; Moloney, J V

2013-07-12

Our experiments show that the critical power for self-focusing collapse of femtosecond vortex beams in air is significantly higher than that of a flattop beam and grows approximately linearly with the vortex order. With less than 10% of initial transverse intensity modulation of the beam profiles, the dominant mode of self-focusing collapse is the azimuthal breakup of the vortex rings into individual filaments, the number of which grows with the input beam power. The generated bottlelike distributions of plasma filaments rotate on propagation in the direction determined by the sense of vorticity.

Supercomputer modeling of flow past hypersonic flight vehicles

NASA Astrophysics Data System (ADS)

Ermakov, M. K.; Kryukov, I. A.

2017-02-01

A software platform for MPI-based parallel solution of the Navier-Stokes (Euler) equations for viscous heat-conductive compressible perfect gas on 3-D unstructured meshes is developed. The discretization and solution of the Navier-Stokes equations are constructed on generalized S.K. Godunov’s method and the second order approximation in space and time. Developed software platform allows to carry out effectively flow past hypersonic flight vehicles simulations for the Mach numbers 6 and higher, and numerical meshes with up to 1 billion numerical cells and with up to 128 processors.

A root-mean-square pressure fluctuations model for internal flow applications

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1985-01-01

A transport equation for the root-mean-square pressure fluctuations of turbulent flow is derived from the time-dependent momentum equation for incompressible flow. Approximate modeling of this transport equation is included to relate terms with higher order correlations to the mean quantities of turbulent flow. Three empirical constants are introduced in the model. Two of the empirical constants are estimated from homogeneous turbulence data and wall pressure fluctuations measurements. The third constant is determined by comparing the results of large eddy simulations for a plane channel flow and an annulus flow.

Justification and refinement of Winkler–Fuss hypothesis

NASA Astrophysics Data System (ADS)

Kaplunov, J.; Prikazchikov, D.; Sultanova, L.

2018-06-01

Two-parametric asymptotic analysis of the equilibrium of an elastic half-space coated by a thin soft layer is developed. The initial scaling is motivated by the exact solution of the plane problem for a vertical harmonic load. It is established that the Winkler-Fuss hypothesis is valid only for a sufficiently high contrast in the stiffnesses of the layer and the half-space. As an alternative, a uniformly valid non-local approximation is proposed. Higher-order corrections to the Winkler-Fuss formulation, such as the Pasternak model, are also studied.

Spectral function from Reduced Density Matrix Functional Theory

NASA Astrophysics Data System (ADS)

Romaniello, Pina; di Sabatino, Stefano; Berger, Jan A.; Reining, Lucia

2015-03-01

In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.

Numerical solution for weight reduction model due to health campaigns in Spain

NASA Astrophysics Data System (ADS)

Mohammed, Maha A.; Noor, Noor Fadiya Mohd; Siri, Zailan; Ibrahim, Adriana Irawati Nur

2015-10-01

Transition model between three subpopulations based on Body Mass Index of Valencia community in Spain is considered. No changes in population nutritional habits and public health strategies on weight reduction until 2030 are assumed. The system of ordinary differential equations is solved using Runge-Kutta method of higher order. The numerical results obtained are compared with the predicted values of subpopulation proportion based on statistical estimation in 2013, 2015 and 2030. Relative approximate error is calculated. The consistency of the Runge-Kutta method in solving the model is discussed.

Multipole Plasmon Resonances in Gold Nanorods

PubMed Central

Payne, Emma Kathryn; Shuford, Kevin L.; Park, Sungho; Schatz, George C.

2011-01-01

The optical properties of gold rods electrochemically deposited in anodic aluminum oxide templates have been investigated. Homogeneous suspensions of rods with average diameter of 85 nm and varying lengths of 96, 186, 321, 465, 495, 578, 641, 735, and 1175 nm were fabricated. The purity and dimensions of these rod nanostructures allowed us to observe higher order multipole resonances for the first time in a colloidal suspension. The experimental optical spectra agree with discrete dipole approximation calculations that have been modeled from the dimensions of the gold nanorods. PMID:16471797

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Fourth-order numerical solutions of diffusion equation by using SOR method with Crank-Nicolson approach

NASA Astrophysics Data System (ADS)

Muhiddin, F. A.; Sulaiman, J.

2017-09-01

The aim of this paper is to investigate the effectiveness of the Successive Over-Relaxation (SOR) iterative method by using the fourth-order Crank-Nicolson (CN) discretization scheme to derive a five-point Crank-Nicolson approximation equation in order to solve diffusion equation. From this approximation equation, clearly, it can be shown that corresponding system of five-point approximation equations can be generated and then solved iteratively. In order to access the performance results of the proposed iterative method with the fourth-order CN scheme, another point iterative method which is Gauss-Seidel (GS), also presented as a reference method. Finally the numerical results obtained from the use of the fourth-order CN discretization scheme, it can be pointed out that the SOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.

Signatures of pair-density wave order via measurement of the current-phase relation in La2-xBaxCuO4 Josephson junctions

NASA Astrophysics Data System (ADS)

Hamilton, David; Weis, Adam; Gu, Genda; van Harlingen, Dale

La2-xBaxCuO4 (LBCO) exhibits a sharp drop in the transition temperature near x = 1 / 8 doping. In this regime, charge, spin and superconducting orders are intertwined and superconductivity is believed to exist in a pair-density wave (PDW) state, an ordered stripe phase characterized by sign changes in the superconducting order parameter between adjacent stripes. We present direct measurements of the current-phase relation (CPR) of Josephson junctions patterned onto crystals of LBCO at x = 1 / 8 and x = 0 . 155 (optimal doping) using a phase-sensitive Josephson interferometry technique. In contrast to the approximately sinusoidal CPR observed at optimal doping, we find the proportion of higher harmonics in the CPR increases at x = 1 / 8 doping, consistent with the formation of a PDW state. In parallel, we are carrying out measurements of the resistance noise in thin films of LBCO of various doping levels to identify features that signify the onset of charge order and changes in the dynamics of charge stripes.

Biaxial order parameter in the homologous series of orthogonal bent-core smectic liquid crystals

NASA Astrophysics Data System (ADS)

Sreenilayam, S.; Panarin, Y. P.; Vij, J. K.; Osipov, M.; Lehmann, A.; Tschierske, C.

2013-07-01

The fundamental parameter of the uniaxial liquid crystalline state that governs nearly all of its physical properties is the primary orientational order parameter (S) for the long axes of molecules with respect to the director. The biaxial liquid crystals (LCs) possess biaxial order parameters depending on the phase symmetry of the system. In this paper we show that in the first approximation a biaxial orthogonal smectic phase can be described by two primary order parameters: S for the long axes and C for the ordering of the short axes of molecules. The temperature dependencies of S and C are obtained by the Haller's extrapolation technique through measurements of the optical birefringence and biaxiality on a nontilted polar antiferroelectric (Sm-APA) phase of a homologous series of LCs built from the bent-core achiral molecules. For such a biaxial smectic phase both S and C, particularly the temperature dependency of the latter, are being experimentally determined. Results show that S in the orthogonal smectic phase composed of bent cores is higher than in Sm-A calamatic LCs and C is also significantly large.

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

Buckley, Andy; /Edinburgh U.; Butterworth, Jonathan

We review the physics basis, main features and use of general-purpose Monte Carlo event generators for the simulation of proton-proton collisions at the Large Hadron Collider. Topics included are: the generation of hard-scattering matrix elements for processes of interest, at both leading and next-to-leading QCD perturbative order; their matching to approximate treatments of higher orders based on the showering approximation; the parton and dipole shower formulations; parton distribution functions for event generators; non-perturbative aspects such as soft QCD collisions, the underlying event and diffractive processes; the string and cluster models for hadron formation; the treatment of hadron and tau decays;more » the inclusion of QED radiation and beyond-Standard-Model processes. We describe the principal features of the Ariadne, Herwig++, Pythia 8 and Sherpa generators, together with the Rivet and Professor validation and tuning tools, and discuss the physics philosophy behind the proper use of these generators and tools. This review is aimed at phenomenologists wishing to understand better how parton-level predictions are translated into hadron-level events as well as experimentalists wanting a deeper insight into the tools available for signal and background simulation at the LHC.« less

Higher Order Modulation Intersymbol Interference Caused by Traveling-wave Tube Amplifiers

NASA Technical Reports Server (NTRS)

Kory, Carol L.; Andro, Monty; Williams, W. D. (Technical Monitor)

2002-01-01

For the first time, a time-dependent, physics-based computational model has been used to provide a direct description of the effects of the traveling wave tube amplifier (TWTA) on modulated digital signals. The TWT model comprehensively takes into account the effects of frequency dependent AM/AM and AM/PM conversion; gain and phase ripple; drive-induced oscillations; harmonic generation; intermodulation products; and backward waves, Thus, signal integrity can be investigated in the presence of these sources of potential distortion as a function of the physical geometry and operating characteristics of the high power amplifier and the operational digital signal. This method promises superior predictive fidelity compared to methods using TWT models based on swept-amplitude and/or swept-frequency data. First, the TWT model using the three dimensional (3D) electromagnetic code MAFIA is presented. Then, this comprehensive model is used to investigate approximations made in conventional TWT black-box models used in communication system level simulations, To quantitatively demonstrate the effects these approximations have on digital signal performance predictions, including intersymbol interference (ISI), the MAFIA results are compared to the system level analysis tool, Signal Processing, Workstation (SPW), using high order modulation schemes including 16 and 64-QAM.

Rocksalt or cesium chloride: Investigating the relative stability of the cesium halide structures with random phase approximation based methods

NASA Astrophysics Data System (ADS)

Nepal, Niraj K.; Ruzsinszky, Adrienn; Bates, Jefferson E.

2018-03-01

The ground state structural and energetic properties for rocksalt and cesium chloride phases of the cesium halides were explored using the random phase approximation (RPA) and beyond-RPA methods to benchmark the nonempirical SCAN meta-GGA and its empirical dispersion corrections. The importance of nonadditivity and higher-order multipole moments of dispersion in these systems is discussed. RPA generally predicts the equilibrium volume for these halides within 2.4% of the experimental value, while beyond-RPA methods utilizing the renormalized adiabatic LDA (rALDA) exchange-correlation kernel are typically within 1.8%. The zero-point vibrational energy is small and shows that the stability of these halides is purely due to electronic correlation effects. The rAPBE kernel as a correction to RPA overestimates the equilibrium volume and could not predict the correct phase ordering in the case of cesium chloride, while the rALDA kernel consistently predicted results in agreement with the experiment for all of the halides. However, due to its reasonable accuracy with lower computational cost, SCAN+rVV10 proved to be a good alternative to the RPA-like methods for describing the properties of these ionic solids.

Virial Coefficients and Equations of State for Hard Polyhedron Fluids.

PubMed

Irrgang, M Eric; Engel, Michael; Schultz, Andrew J; Kofke, David A; Glotzer, Sharon C

2017-10-24

Hard polyhedra are a natural extension of the hard sphere model for simple fluids, but there is no general scheme for predicting the effect of shape on thermodynamic properties, even in moderate-density fluids. Only the second virial coefficient is known analytically for general convex shapes, so higher-order equations of state have been elusive. Here we investigate high-precision state functions in the fluid phase of 14 representative polyhedra with different assembly behaviors. We discuss historic efforts in analytically approximating virial coefficients up to B 4 and numerically evaluating them to B 8 . Using virial coefficients as inputs, we show the convergence properties for four equations of state for hard convex bodies. In particular, the exponential approximant of Barlow et al. (J. Chem. Phys. 2012, 137, 204102) is found to be useful up to the first ordering transition for most polyhedra. The convergence behavior we explore can guide choices in expending additional resources for improved estimates. Fluids of arbitrary hard convex bodies are too complicated to be described in a general way at high densities, so the high-precision state data we provide can serve as a reference for future work in calculating state data or as a basis for thermodynamic integration.

Estimating amplitude ratios in boundary layer stability theory: a comparison between two approaches

NASA Astrophysics Data System (ADS)

Govindarajan, Rama; Narasimha, R.

2001-07-01

We first demonstrate that, if the contributions of higher-order mean flow are ignored, the parabolized stability equations (Bertolotti et al. 1992) and the ‘full’ non-parallel equation of Govindarajan & Narasimha (1995, hereafter GN95) are both equivalent to order R[minus sign]1 in the local Reynolds number R to Gaster's (1974) equation for the stability of spatially developing boundary layers. It is therefore of some concern that a detailed comparison between Gaster (1974) and GN95 reveals a small difference in the computed amplitude ratios. Although this difference is not significant in practical terms in Blasius flow, it is traced here to the approximation, in Gaster's method, of neglecting the change in eigenfunction shape due to flow non-parallelism. This approximation is not justified in the critical and the wall layers, where the neglected term is respectively O(R[minus sign]2/3) and O(R[minus sign]1) compared to the largest term. The excellent agreement of GN95 with exact numerical simulations, on the other hand, suggests that the effect of change in eigenfunction is accurately taken into account in that paper.

Theoretical Investigation of Anharmonic Effects Observed in the Infrared Spectra of the Formaldehyde Cation and its Hydroxymethylene Isomer

NASA Astrophysics Data System (ADS)

Madison, Lindsey R.; Mosley, Jonathan; Mauney, Daniel; Duncan, Michael A.; McCoy, Anne B.

2016-06-01

Formaldehyde is the smallest organic molecule and is a prime candidate for a thorough investigation regarding the anharmonic approximations made in computationally modeling its infrared spectrum. Mass-selected ion spectroscopy was used to detect mass 30 cations which include of HCOH^+ and CH_2O^+. In order to elucidate the differences between the structures of these isomers, infrared spectroscopy was performed on the mass 30 cations using Ar predissociation. Interestingly, several additional spectral features are observed that cannot be explained by the fundamental OH and CH stretch vibrations alone. By including anharmonic coupling between OH and CH stretching and various overtones and combination bands involving lower frequency vibrations, we are able to identify how specific modes couple and lead to the experimentally observed spectral features. We combine straight-forward, ab initio calculations of the anharmonic frequencies of the mass 30 cations with higher order, adiabatic approximations and Fermi resonance models. By including anharmonic effects we are able to confirm that the isomers of the CH_2O^+\\cdotAr system have substantially different, and thus distinguishable, IR spectra and that many of the features can only be explained with anharmonic treatments.

Absence of B1-B2 structural transition in lithium halides under hydrostatic pressure

NASA Astrophysics Data System (ADS)

de Coss, Romeo; Murrieta, Gabriel

2005-03-01

We have investigated the B1-B2 structural transition in LiF, LiCl, LiBr, and LiI under hydrostatic pressure by means of first-principles total-energy calculations using the Full- Potential LAPW method. In order to analyze the gradient effects, we have performed calculations using the local density approximation (LDA) and the generalized gradient approximation (GGA), for the exchange and correlation potential. In agreement with the experimental observations, we find that even for pressures higher than 100 GPa, the Li halides do not present the B1-B2 structural transition. In order to understand this behavior, we have calculated the distribution of the electron densities. From the analysis of the distribution of electron densities for the Li halides in the B1 and B2 phases, we find that for this group of ionic compounds the B1 phase have a distribution of electron densities more homogeneous than in the B2 phase, preventing the B1-B2 structural transition. This work was partially supported by Consejo Nacional de Ciencia y Tecnolog'ia (CONACYT, M'exico) under Grant No. 43830-F.

Efficient High-Order Accurate Methods using Unstructured Grids for Hydrodynamics and Acoustics

DTIC Science & Technology

2007-08-31

Leer. On upstream differencing and godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25(1):35-61, 1983. [46] F . Eleuterio Toro ...early stage [4-61. The basic idea can be surmised from simple approximation theory. If a continuous function f is to be approximated over a set of...a2f 4h4 a4ff(x+eh) = f (x)+-- + _ •-+• e +0 +... (1) where 0 < e < 1 for approximations inside the interval of width h. For a second-order approximation

On singlet s-wave electron-hydrogen scattering.

NASA Technical Reports Server (NTRS)

Madan, R. N.

1973-01-01

Discussion of various zeroth-order approximations to s-wave scattering of electrons by hydrogen atoms below the first excitation threshold. The formalism previously developed by the author (1967, 1968) is applied to Feshbach operators to derive integro-differential equations, with the optical-potential set equal to zero, for the singlet and triplet cases. Phase shifts of s-wave scattering are computed in the zeroth-order approximation of the Feshbach operator method and in the static-exchange approximation. It is found that the convergence of numerical computations is faster in the former approximation than in the latter.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

Asymptotic safety of quantum gravity beyond Ricci scalars

NASA Astrophysics Data System (ADS)

Falls, Kevin; King, Callum R.; Litim, Daniel F.; Nikolakopoulos, Kostas; Rahmede, Christoph

2018-04-01

We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalization with high order polynomial approximations and full numerical integration we derive the renormalization group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterized by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilize the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from f (R ) -type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.

Seabird guano is an efficient conveyer of persistent organic pollutants (POPs) to Arctic lake ecosystems.

PubMed

Evenset, A; Carroll, J; Christensen, G N; Kallenborn, R; Gregor, D; Gabrielsen, G W

2007-02-15

Migratory seabirds have been linked to localized "hotspots" of contamination in remote Arctic lakes. One of these lakes is Lake Ellasjøen on Bjørnøya in the Barents Sea. Here we provide quantitative evidence demonstrating that even relatively small populations of certain seabird species can lead to major impacts for ecosystems. In the present example, seabird guano accounts for approximately 14% of the contaminant inventory of the Lake Ellasjøen catchment area, approximately 80% of the contaminant inventory of the lake itself, and is approximately thirty times more efficient as a contaminant transport pathway compared to atmospheric long-range transport. We have further shown that this biological transport mechanism is an important contaminant exposure route for ecosystems, responsible for POPs levels in freshwater fish that are an order of magnitude higher than those in Arctic top predators. Given the worldwide presence of seabird colonies in coastal marine areas where resources are also harvested by humans, this biological transport pathway may be a greater source of dietary contamination than is currently recognized with consequent risks for human health.

An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case

NASA Technical Reports Server (NTRS)

Goodrich, John W.

1995-01-01

Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

Natural distribution of environmental radon daughters in the different brain areas of an Alzheimer disease victim.

PubMed

Momcilović, Berislav; Lykken, Glenn I; Cooley, Marvin

2006-09-11

Radon is a ubiquitous noble gas in the environment and a primary source of harmful radiation exposure for humans; it decays in a cascade of daughters (RAD) by releasing the cell damaging high energy alpha particles. We studied natural distribution of RAD 210Po and 210Bi in the different parts of the postmortem brain of 86-year-old woman who had suffered from Alzheimer's disease (AD). A distinct brain map emerged, since RAD distribution was different among the analyzed brain areas. The highest RAD irradiation (mSv x year(-1)) occurred in the decreasing order of magnitude: amygdala (Amy) > hippocampus (Hip) > temporal lobe (Tem) approximately = frontal lobe (Fro) > occipital lobe (Occ) approximately = parietal lobe (Par) > substantia nigra (SN) > locus ceruleus (LC) approximately = nucleus basalis (NB); generally more RAD accumulated in the proteins than lipids of gray and white (gray > white) brain matter. Amy and Hip are particularly vulnerable brain structure targets to significant RAD internal radiation damage in AD (5.98 and 1.82 mSv x year(-1), respectively). Next, naturally occurring RAD radiation for Tem and Fro, then Occ and Par, and SN was an order of magnitude higher than that in LC and NB; the later was within RAD we observed previously in the healthy control brains. Naturally occurring environmental RAD exposure may dramatically enhance AD deterioration by selectively targeting brain areas of emotions (Amy) and memory (Hip).

A unified stochastic formulation of dissipative quantum dynamics. II. Beyond linear response of spin baths

NASA Astrophysics Data System (ADS)

Hsieh, Chang-Yu; Cao, Jianshu

2018-01-01

We use the "generalized hierarchical equation of motion" proposed in Paper I [C.-Y. Hsieh and J. Cao, J. Chem. Phys. 148, 014103 (2018)] to study decoherence in a system coupled to a spin bath. The present methodology allows a systematic incorporation of higher-order anharmonic effects of the bath in dynamical calculations. We investigate the leading order corrections to the linear response approximations for spin bath models. Two kinds of spin-based environments are considered: (1) a bath of spins discretized from a continuous spectral density and (2) a bath of localized nuclear or electron spins. The main difference resides with how the bath frequency and the system-bath coupling parameters are distributed in an environment. When discretized from a continuous spectral density, the system-bath coupling typically scales as ˜1 /√{NB } where NB is the number of bath spins. This scaling suppresses the non-Gaussian characteristics of the spin bath and justifies the linear response approximations in the thermodynamic limit. For the nuclear/electron spin bath models, system-bath couplings are directly deduced from spin-spin interactions and do not necessarily obey the 1 /√{NB } scaling. It is not always possible to justify the linear response approximations in this case. Furthermore, if the spin-spin Hamiltonian is highly symmetrical, there exist additional constraints that generate highly non-Markovian and persistent dynamics that is beyond the linear response treatments.

A novel toll-like receptor from Mytilus coruscus is induced in response to stress.

PubMed

Xu, Mengshan; Wu, Jiong; Ge, Delong; Wu, Changwen; Changfeng Chi; Lv, Zhenming; Liao, Zhi; Liu, Huihui

2018-07-01

Toll-like receptor (TLR) is considered to be an evolutionarily conserved transmembrane protein which promotes the Toll signal pathway to active the expression of transcription factors in the innate immunity of the organism. In this study, a full length of TLR homologue of 2525bp in Mytilus coruscus (named as McTLR-a, GenBank accession no: KY940571) was characterized. Its ORF was 1815 bp with a 5'untranslated region (UTR) of 128 bp and a 3'UTR of 582 bp, encoding 602 amino acid residues with a calculated molecular weight of 70.870 kDa (pI = 6.10). BLASTn analysis and phylogenetic relationship strongly suggested that this cDNA sequence was a member of TLR family. Quantitative real time RT-PCR showed that constitutive expression of McTLR-a was occurred, with increasing order in hemocyte, gonad, mantle, adducter, gill and hepatopancreas. Bacterial infection and heavy metals stimulation up-regulated the expression of McTLR-a mRNA in hepatopancreas with time-dependent manners. The maximum expression appeared at 12 h after pathogenic bacteria injection, with approximately 22-fold in Aeromonas hydrophila and 17-fold in Vibrio parahemolyticus higher than that of the blank group. In heavy metals stress group, they all reached peaks at 3d, while the diverse concentration caused the maximum expression were different. The highest expression reached approximately 7-fold higher than the blank in low concentration of Pb 2+ exposure. In Cu 2+ treated group, it reached the peak (approximately 12-fold higher than the blank)in middle concentration. These results indicated that McTLR-a might be involved in the defense response and had a significant role in mediating the environmental stress. Copyright © 2018 Elsevier Ltd. All rights reserved.

The integrated bispectrum and beyond

NASA Astrophysics Data System (ADS)

Munshi, Dipak; Coles, Peter

2017-02-01

The position-dependent power spectrum has been recently proposed as a descriptor of gravitationally induced non-Gaussianity in galaxy clustering, as it is sensitive to the "soft limit" of the bispectrum (i.e. when one of the wave number tends to zero). We generalise this concept to higher order and clarify their relationship to other known statistics such as the skew-spectrum, the kurt-spectra and their real-space counterparts the cumulants correlators. Using the Hierarchical Ansatz (HA) as a toy model for the higher order correlation hierarchy, we show how in the soft limit, polyspectra at a given order can be identified with lower order polyspectra with the same geometrical dependence but with renormalised amplitudes expressed in terms of amplitudes of the original polyspectra. We extend the concept of position-dependent bispectrum to bispectrum of the divergence of the velocity field Θ and mixed multispectra involving δ and Θ in the 3D perturbative regime. To quantify the effects of transients in numerical simulations, we also present results for lowest order in Lagrangian perturbation theory (LPT) or the Zel'dovich approximation (ZA). Finally, we discuss how to extend the position-dependent spectrum concept to encompass cross-spectra. And finally study the application of this concept to two dimensions (2D), for projected galaxy maps, convergence κ maps from weak-lensing surveys or maps of CMB secondaries e.g. the frequency cleaned y-parameter maps of thermal Sunyaev-Zel'dovich (tSZ) effect from CMB surveys.

Electroencephalography in ellipsoidal geometry with fourth-order harmonics.

PubMed

Alcocer-Sosa, M; Gutierrez, D

2016-08-01

We present a solution to the electroencephalographs (EEG) forward problem of computing the scalp electric potentials for the case when the head's geometry is modeled using a four-shell ellipsoidal geometry and the brain sources with an equivalent current dipole (ECD). The proposed solution includes terms up to the fourth-order ellipsoidal harmonics and we compare this new approximation against those that only considered up to second- and third-order harmonics. Our comparisons use as reference a solution in which a tessellated volume approximates the head and the forward problem is solved through the boundary element method (BEM). We also assess the solution to the inverse problem of estimating the magnitude of an ECD through different harmonic approximations. Our results show that the fourth-order solution provides a better estimate of the ECD in comparison to lesser order ones.

The 4th order GISS model of the global atmosphere

NASA Technical Reports Server (NTRS)

Kalnay-Rivas, E.; Bayliss, A.; Storch, J.

1977-01-01

The new GISS 4th order model of the global atmosphere is described. It is based on 4th order quadratically conservative differences with the periodic application of a 16th order filter on the sea level pressure and potential temperature equations, a combination which is approximately enstrophy conserving. Several short range forecasts indicate a significant improvement over 2nd order forecasts with the same resolution (approximately 400 km). However the 4th order forecasts are somewhat inferior to 2nd order forecasts with double resolution. This is probably due to the presence of short waves in the range between 1000 km and 2000 km, which are computed more accurately by the 2nd order high resolution model. An operation count of the schemes indicates that with similar code optimization, the 4th order model will require approximately the same amount of computer time as the 2nd order model with the same resolution. It is estimated that the 4th order model with a grid size of 200 km provides enough accuracy to make horizontal truncation errors negligible over a period of a week for all synoptic scales (waves longer than 1000 km).

Raman scattering of IrTe2

NASA Astrophysics Data System (ADS)

Lee, Alexander; Thorsmolle, Verner; Artyukhin, Sergey; Yang, Jun; Cheong, Sang-Wook; Blumberg, Girsh

2014-03-01

IrTe2 presents a layered compound with a triangular lattice. It is known to exhibit a first order structural phase transition at approximately 260 K which is of a first order, corresponding to a formation of a superstructure with a period of five unit cells. Using polarized Raman spectroscopy we have studied the temperature dependence of 14 observed Raman allowed phononic modes. These phonons couple strongly to this transition and one additional first order transition at approximately 170 K. In the high-temperature phase only 3 modes are observed, while below approximately 280 K all 14 modes become visible. Below approximately 170 K only 11 modes are observed. Our results shed light on the possible mechanism driving the transitions. ACL, VKT and GB acknowledge support by NSF DMR-1104884.

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Diverse trends of electron correlation effects for properties with different radial and angular factors in an atomic system: a case study in Ca+

NASA Astrophysics Data System (ADS)

Kumar, Pradeep; Li, Cheng-Bin; Sahoo, B. K.

2018-03-01

Dependencies of electron correlation effects with the rank and radial behavior of spectroscopic properties are analyzed in the singly charged calcium ion (Ca+). To demonstrate these trends, we have determined field shift constants, magnetic dipole and electric quadrupole hyperfine structure constants, Landé g J factors, and electric quadrupole moments that are described by electronic operators with different radial and angular factors. Radial dependencies are investigated by comparing correlation trends among the properties that have similar angular factors and vice versa. To highlight these observations, we present results from the mean-field approach to all-orders along with intermediate contributions. Contributions from higher relativistic corrections are also given. These findings suggest that sometime lower-order approximations can give results agreeing with the experimental results, but inclusion of some of higher-order correlation effects can cause large disagreement with the experimental values. Therefore, validity of a method for accurate evaluation of atomic properties can be tested by performing calculations of several properties simultaneously that have diverse dependencies on the angular and radial factors and comparing with the available experimental results. Nevertheless, it is imperative to include full triple and quadrupole excitations in the all-order many-body methods for high-precision calculations that are yet to be developed adopting spherical coordinate system for atomic studies.

Enhancement of high-order harmonic generation by a two-color field: Influence of propagation effects

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

Schiessl, K.; Persson, E.; Burgdoerfer, J.

2006-11-15

Recent calculations of the response of a single atom subjected to a two-color laser pulse with the higher frequency being resonant with an excitation of the target atom revealed a significant enhancement of photoionization as well as high-order harmonic generation [K. Ishikawa, Phy. Rev. Lett. 91, 043002 (2003)]. We investigate the problem in the framework a fully quantum-mechanical pulse propagation algorithm and perform calculations for rare gases in the single-active-electron approximation. The enhancement of harmonic output compared to the corresponding one-color pulse remains intact for short propagation lengths, promising the feasibility of experimental realization. We also study weak second colorsmore » resonant via a two-photon transition where significant enhancements in harmonic yields can be observed as well.« less

Steady-state phase error for a phase-locked loop subjected to periodic Doppler inputs

NASA Technical Reports Server (NTRS)

Chen, C.-C.; Win, M. Z.

1991-01-01

The performance of a carrier phase locked loop (PLL) driven by a periodic Doppler input is studied. By expanding the Doppler input into a Fourier series and applying the linearized PLL approximations, it is easy to show that, for periodic frequency disturbances, the resulting steady state phase error is also periodic. Compared to the method of expanding frequency excursion into a power series, the Fourier expansion method can be used to predict the maximum phase error excursion for a periodic Doppler input. For systems with a large Doppler rate fluctuation, such as an optical transponder aboard an Earth orbiting spacecraft, the method can be applied to test whether a lower order tracking loop can provide satisfactory tracking and thereby save the effect of a higher order loop design.

Two-peak structure in the K-edge RIXS spectra of a spatially frustrated Heisenberg antiferromagnet

NASA Astrophysics Data System (ADS)

Datta, Trinanjan; Luo, Cheng; Yao, Dao-Xin

2014-03-01

Quantum fluctuations due to spatial anisotropy and strong magnetic frustration lead to the formation of a two-peak structure in the K-edge bimagnon RIXS intensity spectra of a Jx-Jy-J2 Heisenberg model on a square lattice. We compute the RIXS intensity, including up to first order 1/S spin wave expansion correction, using the Bethe-Salpeter equation within the ladder approximation scheme. The two-peak feature occurs in both the antiferromagnetic phase and the collinear antiferromagnetic phase. A knowledge of the peak splitting energy from both magnetically ordered regime can provide experimentalists with an alternative means to measure and study the effects of local microscopic exchange constants. Cottrell Research Corporation, NSFC-11074310, NSFC-11275279, Specialized Research Fund for the Doctoral Program of Higher Education.

Deterministic diffusion in flower-shaped billiards.

PubMed

Harayama, Takahisa; Klages, Rainer; Gaspard, Pierre

2002-08-01

We propose a flower-shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles in the shape of a flower, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes, all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent.

Quantum search algorithms on a regular lattice

NASA Astrophysics Data System (ADS)

Hein, Birgit; Tanner, Gregor

2010-07-01

Quantum algorithms for searching for one or more marked items on a d-dimensional lattice provide an extension of Grover’s search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behavior for the search time and the localization probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.

Ordered Nanostructures Made Using Chaperonin Polypeptides

NASA Technical Reports Server (NTRS)

Trent, Jonathan; McMillan, Robert; Paavola, Chad; Mogul, Rakesh; Kagawa, Hiromi

2004-01-01

A recently invented method of fabricating periodic or otherwise ordered nanostructures involves the use of chaperonin polypeptides. The method is intended to serve as a potentially superior and less expensive alternative to conventional lithographic methods for use in the patterning steps of the fabrication of diverse objects characterized by features of the order of nanometers. Typical examples of such objects include arrays of quantum dots that would serve as the functional building blocks of future advanced electronic and photonic devices. A chaperonin is a double-ring protein structure having a molecular weight of about 60 plus or minus 5 kilodaltons. In nature, chaperonins are ubiquitous, essential, subcellular structures. Each natural chaperonin molecule comprises 14, 16, or 18 protein subunits, arranged as two stacked rings approximately 16 to 18 nm tall by approximately 15 to 17 nm wide, the exact dimensions depending on the biological species in which it originates. The natural role of chaperonins is unknown, but they are believed to aid in the correct folding of other proteins, by enclosing unfolded proteins and preventing nonspecific aggregation during assembly. What makes chaperonins useful for the purpose of the present method is that under the proper conditions, chaperonin rings assemble themselves into higher-order structures. This method exploits such higher-order structures to define nanoscale devices. The higher-order structures are tailored partly by choice of chemical and physical conditions for assembly and partly by using chaperonins that have been mutated. The mutations are made by established biochemical techniques. The assembly of chaperonin polypeptides into such structures as rings, tubes, filaments, and sheets (two-dimensional crystals) can be regulated chemically. Rings, tubes, and filaments of some chaperonin polypeptides can, for example, function as nano vessels if they are able to absorb, retain, protect, and release gases or chemical reagents, including reagents of medical or pharmaceutical interest. Chemical reagents can be bound in, or released from, such structures under suitable controlled conditions. In an example of a contemplated application, a two-dimensional crystal of chaperonin polypeptides would be formed on a surface of an inorganic substrate and used to form a planar array of nanoparticles or quantum dots. Through genetic engineering of the organisms used to manufacture the chaperonins, specific sites on the chaperonin molecules and, thus, on the two-dimensional crystals can be chemically modified to react in a specific manner so as to favor the deposition of the material of the desired nanoparticles or quantum dots. A mutation that introduces a cysteine residue at the desired sites on a chaperonin of Sulfolobus shibatae was used to form planar arrays of gold nanoparticles (see figure).

Biomedical aspects of natural and manufactured environmental radioactivity

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

Hodge, V.

1996-12-31

While weapons testing has altered natural radioactivity background, manufactured radioactivity in most parts of the world constitutes but a very small fraction of the total alpha, beta, and gamma radioactivity in soil, air, water, and the biota. For example, in the early 1970s, we found what appeared to be the highest natural concentration of radioactivity ever reported in fish while attempting to measure the manufactured plutonium ({sup 239}Pu and {sup 240}Pu) in organs of oceanic tuna. The natural alpha emitter polonium ({sup 210}Po) was discovered in the same organs at orders of magnitude higher concentrations. In particular, the caecum, whichmore » is a digestive organ composed of many small closed-ended sacs, contained concentrations of polonium as high as 79 pCi/g of wet tissue and lesser amounts of two manufactured isotopes: 0.0001 pCi/g of plutonium and 0.01 pCi/g of radiocesium ({sup 137}Cs). This equates to {approximately}80 rem/yr of radiation dose to this organ, overwhelmingly from the natural polonium, or {approximately}5000 times higher than is found in the human liver, the highest polonium concentration in man. The average background radiation for humans, for comparison, is {approximately}0.2 rem/yr, but the dose for Japanese, whose diet is high in seafood, is {approximately}15 rem/yr. The question arose: {open_quotes}Are these high concentrations of natural polonium limited to oceanic fish?{close_quotes} To answer this question, polonium was determined in the organs of striped bass and catfish from Lake Mead. In a related study, the plutonium and radiocesium ({sup 137}Cs) distributions in soils were determined to ascertain the impact of weapons testing on the natural background radioactivity of soils.« less

Single embryo transfer and IVF/ICSI outcome: a balanced appraisal.

PubMed

Gerris, Jan M R

2005-01-01

This review considers the value of single embryo transfer (SET) to prevent multiple pregnancies (MP) after IVF/ICSI. The incidence of MP (twins and higher order pregnancies) after IVF/ICSI is much higher (approximately 30%) than after natural conception (approximately 1%). Approximately half of all the neonates are multiples. The obstetric, neonatal and long-term consequences for the health of these children are enormous and costs incurred extremely high. Judicious SET is the only method to decrease this epidemic of iatrogenic multiple gestations. Clinical trials have shown that programmes with >50% of SET maintain high overall ongoing pregnancy rates ( approximately 30% per started cycle) while reducing the MP rate to <10%. Experience with SET remains largely European although the need to reduce MP is accepted worldwide. An important issue is how to select patients suitable for SET and embryos with a high putative implantation potential. The typical patient suitable for SET is young (aged <36 years) and in her first or second IVF/ICSI trial. Embryo selection is performed using one or a combination of embryo characteristics. Available evidence suggests that, for the overall population, day 3 and day 5 selection yield similar results but better than zygote selection results. Prospective studies correlating embryo characteristics with documented implantation potential, utilizing databases of individual embryos, are needed. The application of SET should be supported by other measures: reimbursement of IVF/ICSI (earned back by reducing costs), optimized cryopreservation to augment cumulative pregnancy rates per oocyte harvest and a standardized format for reporting results. To make SET the standard of care in the appropriate target group, there is a need for more clinical studies, for intensive counselling of patients, and for an increased sense of responsibility in patients, health care providers and health insurers.

Second order nonlinear QED processes in ultra-strong laser fields

NASA Astrophysics Data System (ADS)

Mackenroth, Felix

2017-10-01

In the interaction of ultra-intense laser fields with matter the ever increasing peak laser intensities render nonlinear QED effects ever more important. For long, ultra-intense laser pulses scattering large systems, like a macroscopic plasma, the interaction time can be longer than the scattering time, leading to multiple scatterings. These are usually approximated as incoherent cascades of single-vertex processes. Under certain conditions, however, this common cascade approximation may be insufficient, as it disregards several effects such as coherent processes, quantum interferences or pulse shape effects. Quantifying deviations of the full amplitude of multiple scatterings from the commonly employed cascade approximations is a formidable, yet unaccomplished task. In this talk we are going to discuss how to compute second order nonlinear QED amplitudes and relate them to the conventional cascade approximation. We present examples for typical second order processes and benchmark the full result against common approximations. We demonstrate that the approximation of multiple nonlinear QED scatterings as a cascade of single interactions has certain limitations and discuss these limits in light of upcoming experimental tests.

Minimal-Approximation-Based Distributed Consensus Tracking of a Class of Uncertain Nonlinear Multiagent Systems With Unknown Control Directions.

PubMed

Choi, Yun Ho; Yoo, Sung Jin

2017-03-28

A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.

Kinetic studies of a doubly bound red cell antigen-antibody system.

PubMed

Oberhardt, B J; Miller, I F

1972-08-01

The Polybrene method for detection of red cell antibodies which utilizes continuous flow equipment was modified so that kinetic studies could be performed on red cell antibodies doubly bound between adjacent red cells. In the anti-Rh(o)-Rh(o) erythrocyte system, deaggregation by temperature was studied over an antibody concentration range of from approximately 1 to 500 antibody molecules per erythrocyte, a residence time range of approximately eightfold, and a temperature range of from 10 to 55 degrees C. The rate of dissociation of antigen-antibody complex, as determined from deaggregation of antibody-dependent red cell aggregates, was found to be of apparent zero order. The apparent activation energy for the antigen-antibody reaction under the experimental conditions was determined and found to be higher than would be expected for singly bound antigen-antibody systems. Possible explanations are considered for these findings in terms of an antigen-antibody bond-breaking model.

Pushing the glass transition towards random close packing using self-propelled hard spheres

NASA Astrophysics Data System (ADS)

Ni, Ran; Stuart, Martien A. Cohen; Dijkstra, Marjolein

2013-10-01

Although the concept of random close packing with an almost universal packing fraction of approximately 0.64 for hard spheres was introduced more than half a century ago, there are still ongoing debates. The main difficulty in searching the densest packing is that states with packing fractions beyond the glass transition at approximately 0.58 are inherently non-equilibrium systems, where the dynamics slows down with a structural relaxation time diverging with density; hence, the random close packing is inaccessible. Here we perform simulations of self-propelled hard spheres, and we find that with increasing activity the relaxation dynamics can be sped up by orders of magnitude. The glass transition shifts to higher packing fractions upon increasing the activity, allowing the study of sphere packings with fluid-like dynamics at packing fractions close to RCP. Our study opens new possibilities of investigating dense packings and the glass transition in systems of hard particles.

Born distorted-wave approximation applied to the H+ + He collisions at intermediate and high energies

NASA Astrophysics Data System (ADS)

Rahmanian, M.; Fathi, R.; Shojaei, F.

2017-11-01

The single-charge transfer process in collision of protons with helium atoms in their ground states is investigated. The model utilizes the second-order three-body Born distorted-wave approximation (BDW-3B) with correct Coulomb boundary conditions to calculate the differential and total cross sections at intermediate and high energies. The role of the passive electrons and electron-electron correlations are studied by comparing our results and the BDW-4B calculations with the complete perturbation potential. The present results are also compared with other theories, and the Thomas scattering mechanism is investigated. The obtained results are also compared with the recent experimental measurements. For the prior differential cross sections, the comparisons show better agreement with the experiments at smaller scattering angles. The agreement between the total cross sections and the BDW-4B results as well as the experimental data is good at higher impact energies.

Mitochondrial phylogenomics of Hemiptera reveals adaptive innovations driving the diversification of true bugs

PubMed Central

Li, Hu; Leavengood, John M.; Chapman, Eric G.; Burkhardt, Daniel; Song, Fan; Jiang, Pei; Liu, Jinpeng; Cai, Wanzhi

2017-01-01

Hemiptera, the largest non-holometabolous order of insects, represents approximately 7% of metazoan diversity. With extraordinary life histories and highly specialized morphological adaptations, hemipterans have exploited diverse habitats and food sources through approximately 300 Myr of evolution. To elucidate the phylogeny and evolutionary history of Hemiptera, we carried out the most comprehensive mitogenomics analysis on the richest taxon sampling to date covering all the suborders and infraorders, including 34 newly sequenced and 94 published mitogenomes. With optimized branch length and sequence heterogeneity, Bayesian analyses using a site-heterogeneous mixture model resolved the higher-level hemipteran phylogeny as (Sternorrhyncha, (Auchenorrhyncha, (Coleorrhyncha, Heteroptera))). Ancestral character state reconstruction and divergence time estimation suggest that the success of true bugs (Heteroptera) is probably due to angiosperm coevolution, but key adaptive innovations (e.g. prognathous mouthpart, predatory behaviour, and haemelytron) facilitated multiple independent shifts among diverse feeding habits and multiple independent colonizations of aquatic habitats. PMID:28878063

Errors in the estimation of approximate entropy and other recurrence-plot-derived indices due to the finite resolution of RR time series.

PubMed

García-González, Miguel A; Fernández-Chimeno, Mireya; Ramos-Castro, Juan

2009-02-01

An analysis of the errors due to the finite resolution of RR time series in the estimation of the approximate entropy (ApEn) is described. The quantification errors in the discrete RR time series produce considerable errors in the ApEn estimation (bias and variance) when the signal variability or the sampling frequency is low. Similar errors can be found in indices related to the quantification of recurrence plots. An easy way to calculate a figure of merit [the signal to resolution of the neighborhood ratio (SRN)] is proposed in order to predict when the bias in the indices could be high. When SRN is close to an integer value n, the bias is higher than when near n - 1/2 or n + 1/2. Moreover, if SRN is close to an integer value, the lower this value, the greater the bias is.

Diagnostics of seeded RF plasmas: An experimental study related to the gaseous core reactor

NASA Technical Reports Server (NTRS)

Thompson, S. D.; Clement, J. D.; Williams, J. R.

1974-01-01

Measurements of the temperature profiles in an RF argon plasma were made over magnetic field intensities ranging from 20 amp turns/cm to 80 amp turns/cm. The results were compared with a one-dimensional numerical treatment of the governing equations and with an approximate closed form analytical solution that neglected radiation losses. The average measured temperatures in the plasma compared well with the numerical treatment, though the experimental profile showed less of an off center temperature peak than predicted by theory. This may be a result of the complex turbulent flow pattern present in the experimental torch and not modeled in the numerical treatment. The radiation term cannot be neglected for argon at the power levels investigated. The closed form analytical approximation that neglected radiation led to temperature predictions on the order of 1000 K to 2000 K higher than measured or predicted by the numerical treatment which considered radiation losses.

Final state interactions and the transverse structure of the pion using non-perturbative eikonal methods

DOE PAGES

Gamberg, Leonard; Schlegel, Marc

2010-01-18

In the factorized picture of semi-inclusive hadronic processes the naive time reversal-odd parton distributions exist by virtue of the gauge link which renders it color gauge invariant. The link characterizes the dynamical effect of initial/final-state interactions of the active parton due soft gluon exchanges with the target remnant. Though these interactions are non-perturbative, studies of final-state interaction have been approximated by perturbative one-gluon approximation in Abelian models. We include higher-order contributions by applying non-perturbative eikonal methods incorporating color degrees of freedom in a calculation of the Boer-Mulders function of the pion. Lastly, using this framework we explore under what conditionsmore » the Boer Mulders function can be described in terms of factorization of final state interactions and a spatial distribution in impact parameter space.« less

An accurate analytic description of neutrino oscillations in matter

NASA Astrophysics Data System (ADS)

Akhmedov, E. Kh.; Niro, Viviana

2008-12-01

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

Identifying and reducing error in cluster-expansion approximations of protein energies.

PubMed

Hahn, Seungsoo; Ashenberg, Orr; Grigoryan, Gevorg; Keating, Amy E

2010-12-01

Protein design involves searching a vast space for sequences that are compatible with a defined structure. This can pose significant computational challenges. Cluster expansion is a technique that can accelerate the evaluation of protein energies by generating a simple functional relationship between sequence and energy. The method consists of several steps. First, for a given protein structure, a training set of sequences with known energies is generated. Next, this training set is used to expand energy as a function of clusters consisting of single residues, residue pairs, and higher order terms, if required. The accuracy of the sequence-based expansion is monitored and improved using cross-validation testing and iterative inclusion of additional clusters. As a trade-off for evaluation speed, the cluster-expansion approximation causes prediction errors, which can be reduced by including more training sequences, including higher order terms in the expansion, and/or reducing the sequence space described by the cluster expansion. This article analyzes the sources of error and introduces a method whereby accuracy can be improved by judiciously reducing the described sequence space. The method is applied to describe the sequence-stability relationship for several protein structures: coiled-coil dimers and trimers, a PDZ domain, and T4 lysozyme as examples with computationally derived energies, and SH3 domains in amphiphysin-1 and endophilin-1 as examples where the expanded pseudo-energies are obtained from experiments. Our open-source software package Cluster Expansion Version 1.0 allows users to expand their own energy function of interest and thereby apply cluster expansion to custom problems in protein design. © 2010 Wiley Periodicals, Inc.

Investigations on the heat transport capability of a cryogenic oscillating heat pipe and its application in achieving ultra-fast cooling rates for cell vitrification cryopreservation.

PubMed

Han, Xu; Ma, Hongbin; Jiao, Anjun; Critser, John K

2008-06-01

Theoretically, direct vitrification of cell suspensions with relatively low concentrations ( approximately 1 M) of permeating cryoprotective agents (CPA) is suitable for cryopreservation of almost all cell types and can be accomplished by ultra-fast cooling rates that are on the order of 10(6-7) K/min. However, the methods and devices currently available for cell cryopreservation cannot achieve such high cooling rates. In this study, we constructed a novel cryogenic oscillating heat pipe (COHP) using liquid nitrogen as its working fluid and investigated its heat transport capability to assess its application for achieving ultra-fast cooling rates for cell cryopreservation. The experimental results showed that the apparent heat transfer coefficient of the COHP can reach 2 x 10(5) W/m(2).K, which is two orders of the magnitude higher than traditional heat pipes. Theoretical analyzes showed that the average local heat transfer coefficient in the thin film evaporation region of the COHP can reach 1.2 x 10(6) W/m(2).K, which is approximately 10(3) times higher than that achievable with standard pool-boiling approaches. Based on these results, a novel device design applying the COHP and microfabrication techniques is proposed and its efficiency for cell vitrification is demonstrated through numerical simulation. The estimated average cooling rates achieved through this approach is 10(6-7)K/min, which is much faster than the currently available methods and sufficient for achieving vitrification with relatively low concentrations of CPA.

Enhanced sensitivity for Os isotope ratios by magnetic sector ICP-MS with a capacitive decoupling Pt guard electrode.

PubMed

Townsend, A T

2000-08-01

A magnetic sector ICP-MS with enhanced sensitivity was used to measure Os isotope ratios in solutions of low Os concentration (approximately 1 ng g(-1) or less). Ratios with 192Os as the basis were determined, while the geologically useful 187Os/188Os ratio was also measured. Sample introduction was via the traditional nebuliser-spray chamber method. A capacitive decoupling Pt shield torch was developed "in-house" and was found to increase Os signals by approximately 5 x under "moderate" plasma conditions (1050 W) over that found during normal operation (1250 W). Sensitivity using the guard electrode for 192Os was approximately 250-350,000 counts s(-1) per ng g(-1) Os. For a I ng g(-1) Os solution with no guard electrode, precisions of the order of 0.2-0.3% (189Os/192Os and 190Os/192Os) to approximately 1% or greater (186Os/192Os, 187Os/192Os and 187Os/188Os) were found (values as 1 sigma for n = 10). With the guard electrode in use, ratio precisions were found to improve to 0.2 to 0.8%. The total amount of Os used in the acquisition of this data was approximately 2.5 ng per measurement per replicate. At the higher concentration of 10 ng g(-1), precisions of the order of 0.15-0.3% were measured (for all ratios), irrespective of whether the shield torch was used. Ratio accuracy was confirmed by comparison with independently obtained NTIMS data. For both Os concentrations considered, the improvement in precision offered by the guard electrode (if any) was small in comparison to calculated theoretical values based on Poisson counting statistics, suggesting noise contributions from other sources (such as the sample introduction system, plasma flicker etc). At lower Os concentrations (to 100 pg g(-1)) no appreciable loss of ratio accuracy was observed, although as expected based on counting statistics, poorer precisions of the order of 0.45-3% (1 sigma, n = 5) were noted. Re was found to have a detrimental effect on the precision of Os ratios involving 187Os, indicating that separation of Re and Os samples is a necessary pre-requisite for highly accurate and precise Os isotope ratio measurements.

Absolute phase estimation: adaptive local denoising and global unwrapping.

PubMed

Bioucas-Dias, Jose; Katkovnik, Vladimir; Astola, Jaakko; Egiazarian, Karen

2008-10-10

The paper attacks absolute phase estimation with a two-step approach: the first step applies an adaptive local denoising scheme to the modulo-2 pi noisy phase; the second step applies a robust phase unwrapping algorithm to the denoised modulo-2 pi phase obtained in the first step. The adaptive local modulo-2 pi phase denoising is a new algorithm based on local polynomial approximations. The zero-order and the first-order approximations of the phase are calculated in sliding windows of varying size. The zero-order approximation is used for pointwise adaptive window size selection, whereas the first-order approximation is used to filter the phase in the obtained windows. For phase unwrapping, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [IEEE Trans. Image Process.16, 698 (2007)] to the denoised wrapped phase. Simulations give evidence that the proposed algorithm yields state-of-the-art performance, enabling strong noise attenuation while preserving image details. (c) 2008 Optical Society of America

Orbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: theory and test calculations of second order approximation.

PubMed

Chen, Zhenhua; Hoffmann, Mark R

2012-07-07

A unitary wave operator, exp (G), G(+) = -G, is considered to transform a multiconfigurational reference wave function Φ to the potentially exact, within basis set limit, wave function Ψ = exp (G)Φ. To obtain a useful approximation, the Hausdorff expansion of the similarity transformed effective Hamiltonian, exp (-G)Hexp (G), is truncated at second order and the excitation manifold is limited; an additional separate perturbation approximation can also be made. In the perturbation approximation, which we refer to as multireference unitary second-order perturbation theory (MRUPT2), the Hamiltonian operator in the highest order commutator is approximated by a Mo̸ller-Plesset-type one-body zero-order Hamiltonian. If a complete active space self-consistent field wave function is used as reference, then the energy is invariant under orbital rotations within the inactive, active, and virtual orbital subspaces for both the second-order unitary coupled cluster method and its perturbative approximation. Furthermore, the redundancies of the excitation operators are addressed in a novel way, which is potentially more efficient compared to the usual full diagonalization of the metric of the excited configurations. Despite the loss of rigorous size-extensivity possibly due to the use of a variational approach rather than a projective one in the solution of the amplitudes, test calculations show that the size-extensivity errors are very small. Compared to other internally contracted multireference perturbation theories, MRUPT2 only needs reduced density matrices up to three-body even with a non-complete active space reference wave function when two-body excitations within the active orbital subspace are involved in the wave operator, exp (G). Both the coupled cluster and perturbation theory variants are amenable to large, incomplete model spaces. Applications to some widely studied model systems that can be problematic because of geometry dependent quasidegeneracy, H4, P4, and BeH(2), are performed in order to test the new methods on problems where full configuration interaction results are available.

Analytical Debye-Huckel model for electrostatic potentials around dissolved DNA.

PubMed Central

Wagner, K; Keyes, E; Kephart, T W; Edwards, G

1997-01-01

We present an analytical, Green-function-based model for the electric potential of DNA in solution, treating the surrounding solvent with the Debye-Huckel approximation. The partial charge of each atom is accounted for by modeling DNA as linear distributions of atoms on concentric cylindrical surfaces. The condensed ions of the solvent are treated with the Debye-Huckel approximation. The resultant leading term of the potential is that of a continuous shielded line charge, and the higher order terms account for the helical structure. Within several angstroms of the surface there is sufficient information in the electric potential to distinguish features and symmetries of DNA. Plots of the potential and equipotential surfaces, dominated by the phosphate charges, reflect the structural differences between the A, B, and Z conformations and, to a smaller extent, the difference between base sequences. As the distances from the helices increase, the magnitudes of the potentials decrease. However, the bases and sugars account for a larger fraction of the double helix potential with increasing distance. We have found that when the solvent is treated with the Debye-Huckel approximation, the potential decays more rapidly in every direction from the surface than it did in the concentric dielectric cylinder approximation. Images FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 7 PMID:9199767

Uranium-series constraints on radionuclide transport and groundwater flow at the Nopal I uranium deposit, Sierra Pena Blanca, Mexico.

PubMed

Goldstein, Steven J; Abdel-Fattah, Amr I; Murrell, Michael T; Dobson, Patrick F; Norman, Deborah E; Amato, Ronald S; Nunn, Andrew J

2010-03-01

Uranium-series data for groundwater samples from the Nopal I uranium ore deposit were obtained to place constraints on radionuclide transport and hydrologic processes for a nuclear waste repository located in fractured, unsaturated volcanic tuff. Decreasing uranium concentrations for wells drilled in 2003 are consistent with a simple physical mixing model that indicates that groundwater velocities are low ( approximately 10 m/y). Uranium isotopic constraints, well productivities, and radon systematics also suggest limited groundwater mixing and slow flow in the saturated zone. Uranium isotopic systematics for seepage water collected in the mine adit show a spatial dependence which is consistent with longer water-rock interaction times and higher uranium dissolution inputs at the front adit where the deposit is located. Uranium-series disequilibria measurements for mostly unsaturated zone samples indicate that (230)Th/(238)U activity ratios range from 0.005 to 0.48 and (226)Ra/(238)U activity ratios range from 0.006 to 113. (239)Pu/(238)U mass ratios for the saturated zone are <2 x 10(-14), and Pu mobility in the saturated zone is >1000 times lower than the U mobility. Saturated zone mobility decreases in the order (238)U approximately (226)Ra > (230)Th approximately (239)Pu. Radium and thorium appear to have higher mobility in the unsaturated zone based on U-series data from fractures and seepage water near the deposit.

Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

NASA Technical Reports Server (NTRS)

Melott, A. L.; Buchert, T.; Weib, A. G.

1995-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

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

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

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

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

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

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

Swept sine testing of rotor-bearing system for damping estimation

NASA Astrophysics Data System (ADS)

Chandra, N. Harish; Sekhar, A. S.

2014-01-01

Many types of rotating components commonly operate above the first or second critical speed and they are subjected to run-ups and shutdowns frequently. The present study focuses on developing FRF of rotor bearing systems for damping estimation from swept-sine excitation. The principle of active vibration control states that with increase in angular acceleration, the amplitude of vibration due to unbalance will reduce and the FRF envelope will shift towards the right (or higher frequency). The frequency response function (FRF) estimated by tracking filters or Co-Quad analyzers was proved to induce an error into the FRF estimate. Using Fast Fourier Transform (FFT) algorithm and stationary wavelet transform (SWT) decomposition FRF distortion can be reduced. To obtain a theoretical clarity, the shifting of FRF envelope phenomenon is incorporated into conventional FRF expressions and validation is performed with the FRF estimated using the Fourier Transform approach. The half-power bandwidth method is employed to extract damping ratios from the FRF estimates. While deriving half-power points for both types of responses (acceleration and displacement), damping ratio (ζ) is estimated with different approximations like classical definition (neglecting damping ratio of order higher than 2), third order (neglecting damping ratios with order higher than 4) and exact (no assumptions on damping ratio). The use of stationary wavelet transform to denoise the noise corrupted FRF data is explained. Finally, experiments are performed on a test rotor excited with different sweep rates to estimate the damping ratio.

Prevalence and Predictors of Herbal Medicine Use Among Adults in the United States.

PubMed

Rashrash, Mohamed; Schommer, Jon C; Brown, Lawrence M

2017-09-01

To describe the prevalence of herbal medicine use among US adults and to assess factors associated with and predictors of herbal use. The data for herbal products use were collected from the 2015 National Consumer Survey on the Medication Experience and Pharmacists' Roles. Chi-square test was used to analyz factors associated with herbal use, and predictors of herbal use were assessed with logistic regression analysis. Factors associated with herbal supplement use include age older than 70, having a higher than high school education, using prescription medications or over-the-counter (OTC) medications, and using a mail-order pharmacy." All Disease state associated significantly with herbal use. Approximately thirty-eight percent of those who used herbals used prescription medications and 42% of those who used herbals also used an OTC medication. The most frequent conditions associated with herbal supplement use were a stroke (48.7%), cancer (43.1%), and arthritis (43.0%). Among herbal product users, factors that predicted use included having higher than school education, using OTC medications, using mail-order pharmacy, stroke, obesity, arthritis, and breathing problems. More than one-third of respondents reported using herbal supplements. Older age and higher education were associated with a higher use of herbal supplements. People with chronic diseases are more likely to use herbal medicines than others. OTC drug users and patients with stroke are more likely to use herbal medicines than others.

Effects of gestational length, gender, postnatal age, and birth order on visual contrast sensitivity in infants.

PubMed

Dobkins, Karen R; Bosworth, Rain G; McCleery, Joseph P

2009-09-30

To investigate effects of visual experience versus preprogrammed mechanisms on visual development, we used multiple regression analysis to determine the extent to which a variety of variables (that differ in the extent to which they are tied to visual experience) predict luminance and chromatic (red/green) contrast sensitivity (CS), which are mediated by the magnocellular (M) and parvocellular (P) subcortical pathways, respectively. Our variables included gestational length (GL), birth weight (BW), gender, postnatal age (PNA), and birth order (BO). Two-month-olds (n = 60) and 6-month-olds (n = 122) were tested. Results revealed that (1) at 2 months, infants with longer GL have higher luminance CS; (2) at both ages, CS significantly increases over a approximately 21-day range of PNA, but this effect is stronger in 2- than 6-month-olds and stronger for chromatic than luminance CS; (3) at 2 months, boys have higher luminance CS than girls; and (4) at 2 months, firstborn infants have higher CS, while at 6 months, non-firstborn infants have higher CS. The results for PNA/GL are consistent with the possibility that P pathway development is more influenced by variables tied to visual experience (PNA), while M pathway development is more influenced by variables unrelated to visual experience (GL). Other variables, including prenatal environment, are also discussed.

Nonlinear Binormal Flow of Vortex Filaments

NASA Astrophysics Data System (ADS)

Strong, Scott; Carr, Lincoln

2015-11-01

With the current advances in vortex imaging of Bose-Einstein condensates occurring at the Universities of Arizona, São Paulo and Cambridge, interest in vortex filament dynamics is experiencing a resurgence. Recent simulations, Salman (2013), depict dissipative mechanisms resulting from vortex ring emissions and Kelvin wave generation associated with vortex self-intersections. As the local induction approximation fails to capture reconnection events, it lacks a similar dissipative mechanism. On the other hand, Strong&Carr (2012) showed that the exact representation of the velocity field induced by a curved segment of vortex contains higher-order corrections expressed in powers of curvature. This nonlinear binormal flow can be transformed, Hasimoto (1972), into a fully nonlinear equation of Schrödinger type. Continued transformation, Madelung (1926), reveals that the filament's square curvature obeys a quasilinear scalar conservation law with source term. This implies a broader range of filament dynamics than is possible with the integrable linear binormal flow. In this talk we show the affect higher-order corrections have on filament dynamics and discuss physical scales for which they may be witnessed in future experiments. Partially supported by NSF.

Sensitivity of an Antarctic Ice Sheet Model to Sub-Ice-Shelf Melting

NASA Astrophysics Data System (ADS)

Lipscomb, W. H.; Leguy, G.; Urban, N. M.; Berdahl, M.

2017-12-01

Theory and observations suggest that marine-based sectors of the Antarctic ice sheet could retreat rapidly under ocean warming and increased melting beneath ice shelves. Numerical models of marine ice sheets vary widely in sensitivity, depending on grid resolution and the parameterization of key processes (e.g., calving and hydrofracture). Here we study the sensitivity of the Antarctic ice sheet to ocean warming and sub-shelf melting in standalone simulations of the Community Ice Sheet Model (CISM). Melt rates either are prescribed based on observations and high-resolution ocean model output, or are derived from a plume model forced by idealized ocean temperature profiles. In CISM, we vary the model resolution (between 1 and 8 km), Stokes approximation (shallow-shelf, depth-integrated higher-order, or 3D higher-order) and calving scheme to create an ensemble of plausible responses to sub-shelf melting. This work supports a broader goal of building statistical and reduced models that can translate large-scale Earth-system model projections to changes in Antarctic ocean temperatures and ice sheet discharge, thus better quantifying uncertainty in Antarctic-sourced sea-level rise.

Higher-Order Systematic Effects in the Muon Beam-Spin Dynamics for Muon g-2

NASA Astrophysics Data System (ADS)

Crnkovic, Jason; Brown, Hugh; Krouppa, Brandon; Metodiev, Eric; Morse, William; Semertzidis, Yannis; Tishchenko, Vladimir

2016-03-01

The BNL Muon g-2 Experiment (E821) produced a precision measurement of the muon anomalous magnetic moment, where as the Fermilab Muon g-2 Experiment (E989) is an upgraded version of E821 that has a goal of producing a measurement with approximately 4 times more precision. Improving the precision requires a more detailed understanding of the experimental systematic effects, and so three higher-order systematic effects in the muon beam-spin dynamics have recently been found and estimated for E821. The beamline systematic effect originates from muon production in beamline spectrometers, as well as from muons traversing beamline bending magnets. The kicker systematic effect comes from a combination of the variation in time spent inside the muon storage ring across a muon bunch and the temporal structure of the storage ring kicker waveform. Finally, the detector systematic effect arises from a combination of the energy dependent muon equilibrium orbit in the storage ring, muon decay electron drift time, and decay electron detector acceptance effects. Brookhaven Natl Lab.

Self-Phase-Matched Second-Harmonic and White-Light Generation in a Biaxial Zinc Tungstate Single Crystal

PubMed Central

Osewski, Pawel; Belardini, Alessandro; Petronijevic, Emilija; Centini, Marco; Leahu, Grigore; Diduszko, Ryszard; Pawlak, Dorota A.; Sibilia, Concita

2017-01-01

Second-order nonlinear optical materials are used to generate new frequencies by exploiting second-harmonic generation (SHG), a phenomenon where a nonlinear material generates light at double the optical frequency of the input beam. Maximum SHG is achieved when the pump and the generated waves are in phase, for example through birefringence in uniaxial crystals. However, applying these materials usually requires a complicated cutting procedure to yield a crystal with a particular orientation. Here we demonstrate the first example of phase matching under the normal incidence of SHG in a biaxial monoclinic single crystal of zinc tungstate. The crystal was grown by the micro-pulling-down method with the (102) plane perpendicular to the growth direction. Additionally, at the same time white light was generated as a result of stimulated Raman scattering and multiphoton luminescence induced by higher-order effects such as three-photon luminescence enhanced by cascaded third-harmonic generation. The annealed crystal offers SHG intensities approximately four times larger than the as grown one; optimized growth and annealing conditions may lead to much higher SHG intensities. PMID:28338074

Self-Phase-Matched Second-Harmonic and White-Light Generation in a Biaxial Zinc Tungstate Single Crystal

NASA Astrophysics Data System (ADS)

Osewski, Pawel; Belardini, Alessandro; Petronijevic, Emilija; Centini, Marco; Leahu, Grigore; Diduszko, Ryszard; Pawlak, Dorota A.; Sibilia, Concita

2017-03-01

Second-order nonlinear optical materials are used to generate new frequencies by exploiting second-harmonic generation (SHG), a phenomenon where a nonlinear material generates light at double the optical frequency of the input beam. Maximum SHG is achieved when the pump and the generated waves are in phase, for example through birefringence in uniaxial crystals. However, applying these materials usually requires a complicated cutting procedure to yield a crystal with a particular orientation. Here we demonstrate the first example of phase matching under the normal incidence of SHG in a biaxial monoclinic single crystal of zinc tungstate. The crystal was grown by the micro-pulling-down method with the (102) plane perpendicular to the growth direction. Additionally, at the same time white light was generated as a result of stimulated Raman scattering and multiphoton luminescence induced by higher-order effects such as three-photon luminescence enhanced by cascaded third-harmonic generation. The annealed crystal offers SHG intensities approximately four times larger than the as grown one; optimized growth and annealing conditions may lead to much higher SHG intensities.

Serum albumin and the haloperidol pharmacokinectics. A study using a computational model

NASA Astrophysics Data System (ADS)

de Morais e Coura, Carla Patrícia; Paulino, Erica Tex; Cortez, Celia Martins; da Silva Fragoso, Viviane Muniz

2016-12-01

Here we are studying the binding of haloperidol with human and bovine sera albumins applying a computational model, based on spectrofluorimetry, statistical and mathematical knowledge. Haloperidol is one of the oldest antipsychotic drug in use for therapy of patients with acute and chronic schizophrenia. It was found that the fluorescence of HSA was quenched in 18.0 (± 0.2)% and for BSA it was 24.0 (± 0.9)%, for a ratio of 1/1000 of haloperidol/albumin. Results suggested that the primary binding site is located in the subdomain IB. Quenching constants of the albumin fluorescence by haloperidol were in the order of 107, approximately 100-fold higher than that found for risperidone, and about 1000-fold higher than that estimated for chlorpromazine and sulpiride.

A Second-Order Phase Transition as a Limit of the First-Order Phase Transitions —Coherent Anomalies and Critical Phenomena in the Potts Models—

NASA Astrophysics Data System (ADS)

Katori, Makoto

1988-12-01

A new scheme of the coherent-anomaly method (CAM) is proposed to study critical phenomena in the models for which a mean-field description gives spurious first-order phase transition. A canonical series of mean-field-type approximations are constructed so that the spurious discontinuity should vanish asymptotically as the approximate critical temperature approachs the true value. The true value of the critical exponents β and γ are related to the coherent-anomaly exponents defined among the classical approximations. The formulation is demonstrated in the two-dimensional q-state Potts models for q{=}3 and 4. The result shows that the present method enables us to estimate the critical exponents with high accuracy by using the date of the cluster-mean-field approximations.

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

NASA Technical Reports Server (NTRS)

Grossman, Bernard

1999-01-01

The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing.

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Fabrication of Ordered Blue Nanostructure by Anodization of an Aluminum Plate

NASA Astrophysics Data System (ADS)

Kurashima, Yuichi; Yokota, Yoshihiko; Miyamoto, Iwao; Itatani, Taro

2007-03-01

Colors in organisms are created by chemical interactions of molecular pigments and by optical interactions of incident light with biological nanostructures. The latter classes are called structural colors and form an important component of the phenotypes of many animals and even some plants. In this paper, we report on the fabrication of an ordered blue nanostructure by the anodization of an Al plate. In the fabrication of such an ordered nanostructure by the anodization of an Al plate, ordered nanostructures with a pitch and an alumina thickness of approximately 100 nm were produced on the Al plate. The ordered nanostructures on the Al plate showed no colors. However, an ordered nanostructure deposited with a Pt thin film with a thickness of approximately 10 nm showed a blue reflection with a peak reflectivity of approximately 370 nm. We conclude that this blue nanostructure on the Al plate is caused by an interference between the Al surface and the Pt surface.

Confidence Intervals for Error Rates Observed in Coded Communications Systems

NASA Astrophysics Data System (ADS)

Hamkins, J.

2015-05-01

We present methods to compute confidence intervals for the codeword error rate (CWER) and bit error rate (BER) of a coded communications link. We review several methods to compute exact and approximate confidence intervals for the CWER, and specifically consider the situation in which the true CWER is so low that only a handful, if any, codeword errors are able to be simulated. In doing so, we answer the question of how long an error-free simulation must be run in order to certify that a given CWER requirement is met with a given level of confidence, and discuss the bias introduced by aborting a simulation after observing the first codeword error. Next, we turn to the lesser studied problem of determining confidence intervals for the BER of coded systems. Since bit errors in systems that use coding or higher-order modulation do not occur independently, blind application of a method that assumes independence leads to inappropriately narrow confidence intervals. We present a new method to compute the confidence interval properly, using the first and second sample moments of the number of bit errors per codeword. This is the first method we know of to compute a confidence interval for the BER of a coded or higher-order modulation system.

Centrality dependence of chemical freeze-out parameters from net-proton and net-charge fluctuations using a hadron resonance gas model

NASA Astrophysics Data System (ADS)

Adak, Rama Prasad; Das, Supriya; Ghosh, Sanjay K.; Ray, Rajarshi; Samanta, Subhasis

2017-07-01

We estimate chemical freeze-out parameters in Hadron Resonance Gas (HRG) and Excluded Volume HRG (EVHRG) models by fitting the experimental information of net-proton and net-charge fluctuations measured in Au + Au collisions by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider (RHIC). We observe that chemical freeze-out parameters obtained from lower and higher order fluctuations are almost the same for √{sNN}>27 GeV, but tend to deviate from each other at lower √{sNN}. Moreover, these separations increase with decrease of √{sNN}, and for a fixed √{sNN} increase towards central collisions. Furthermore, we observe an approximate scaling behavior of (μB/T ) /(μB/T)central with (Npart) /(Npart)central for the parameters estimated from lower order fluctuations for 11.5 ≤√{sNN}≤200 GeV. Scaling is violated for the parameters estimated from higher order fluctuations for √{sNN}=11.5 and 19.6 GeV. It is observed that the chemical freeze-out parameter, which can describe σ2/M of net protons very well in all energies and centralities, cannot describe the s σ equally well, and vice versa.

Efficient electronic structure theory via hierarchical scale-adaptive coupled-cluster formalism: I. Theory and computational complexity analysis

NASA Astrophysics Data System (ADS)

Lyakh, Dmitry I.

2018-03-01

A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalisation group approach, H/H2-matrix algebra and fast multipole method, the computational scaling reduction in our formalism is achieved via coarsening of quantum many-body interactions at larger interaction scales, thus imposing a hierarchical structure on many-body tensors of coupled-cluster theory. In our approach, the interaction scale can be defined on any appropriate Euclidean domain (spatial domain, momentum-space domain, energy domain, etc.). We show that the hierarchically resolved many-body tensors can reduce the storage requirements to O(N), where N is the number of simulated quantum particles. Subsequently, we prove that any connected many-body diagram consisting of a finite number of arbitrary-order tensors, e.g. an arbitrary coupled-cluster diagram, can be evaluated in O(NlogN) floating-point operations. On top of that, we suggest an additional approximation to further reduce the computational complexity of higher order coupled-cluster equations, i.e. equations involving higher than double excitations, which otherwise would introduce a large prefactor into formal O(NlogN) scaling.

Inference of higher-order relationships in the cycads from a large chloroplast data set.

PubMed

Rai, Hardeep S; O'Brien, Heath E; Reeves, Patrick A; Olmstead, Richard G; Graham, Sean W

2003-11-01

We investigated higher-order relationships in the cycads, an ancient group of seed-bearing plants, by examining a large portion of the chloroplast genome from seven species chosen to exemplify our current understanding of taxonomic diversity in the order. The regions considered span approximately 13.5 kb of unaligned data per taxon, and comprise a diverse range of coding sequences, introns and intergenic spacers dispersed throughout the plastid genome. Our results provide substantial support for most of the inferred backbone of cycad phylogeny, and weak evidence that the sister-group of the cycads among living seed plants is Ginkgo biloba. Cycas (representing Cycadaceae) is the sister-group of the remaining cycads; Dioon is part of the next most basal split. Two of the three commonly recognized families of cycads (Zamiaceae and Stangeriaceae) are not monophyletic; Stangeria is embedded within Zamiaceae, close to Zamia and Ceratozamia, and not closely allied to the other genus of Stangeriaceae, Bowenia. In contrast to the other seed plants, cycad chloroplast genomes share two features with Ginkgo: a reduced rate of evolution and an elevated transition:transversion ratio. We demonstrate that the latter aspect of their molecular evolution is unlikely to have affected inference of cycad relationships in the context of seed-plant wide analyses.

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Slack, David C.; Whitaker, D. L.; Walters, Robert W.

1994-01-01

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Simulated Reentry Heating by Torching

NASA Technical Reports Server (NTRS)

Harvey, Gale A.

2008-01-01

The two first order reentry heating parameters are peak heating flux (W/cm2) and peak heat load (kJ/cm2). Peak heating flux (and deceleration, gs) is higher for a ballistic reentry and peak heat load is higher for a lifting reentry. Manned vehicle reentries are generally lifting reentries at nominal 1-5 gs so that personnel will not be crushed by high deceleration force. A few off-nominal manned reentries have experienced 8 or more gs with corresponding high heating flux (but below nominal heat load). The Shuttle Orbiter reentries provide about an order of magnitude difference in peak heating flux at mid-bottom (TPS tiles, approximately 6 W/cm2 or 5 BTU/ft2- sec) and leading edge (RCC, approximately 60 W/cm2 or 50 BTU/ft2- sec). Orion lunar return and Mars sample lander are of the same order of magnitude as orbiter leading edge peak heat loads. Flight temperature measurements are available for some orbiter TPS tile and RCC locations. Return-to-Flight on-orbit tile-repair-candidate-material-heating performance was evaluated by matching propane torch heating of candidate-materials temperatures at several depths to orbiter TPS tile flight-temperatures. Char and ash characteristics, heat expansion, and temperature histories at several depths of the cure-in-place ablator were some of the TPS repair material performance characteristics measured. The final char surface was above the initial surface for the primary candidate (silicone based) material, in contrast to a receded surface for the Apollo-type ablative heat shield material. Candidate TPS materials for Orion CEV (LEO and lunar return), and for Mars sample lander are now being evaluated. Torching of a candidate ablator material, PICA, was performed to match the ablation experienced by the STARDUST PICA heat shield. Torching showed that the carbon fiberform skeleton in a sample of PICA was inhomogeneous in that sample, and allowed measurements (of the clumps and voids) of the inhomogeneity. Additional reentry heating-performance characterizations of high temperature insulation materials were performed.

A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks accounting for matrix to fracture flow

NASA Astrophysics Data System (ADS)

Nœtinger, B.

2015-02-01

Modeling natural Discrete Fracture Networks (DFN) receives more and more attention in applied geosciences, from oil and gas industry, to geothermal recovery and aquifer management. The fractures may be either natural, or artificial in case of well stimulation. Accounting for the flow inside the fracture network, and accounting for the transfers between the matrix and the fractures, with the same level of accuracy is an important issue for calibrating the well architecture and for setting up optimal resources recovery strategies. Recently, we proposed an original method allowing to model transient pressure diffusion in the fracture network only [1]. The matrix was assumed to be impervious. A systematic approximation scheme was built, allowing to model the initial DFN by a set of N unknowns located at each identified intersection between fractures. The higher N, the higher the accuracy of the model. The main assumption was using a quasi steady state hypothesis, that states that the characteristic diffusion time over one single fracture is negligible compared with the characteristic time of the macroscopic problem, e.g. change of boundary conditions. In that context, the lowest order approximation N = 1 has the form of solving a transient problem in a resistor/capacitor network, a so-called pipe network. Its topology is the same as the network of geometrical intersections between fractures. In this paper, we generalize this approach in order to account for fluxes from matrix to fractures. The quasi steady state hypothesis at the fracture level is still kept. Then, we show that in the case of well separated time scales between matrix and fractures, the preceding model needs only to be slightly modified in order to incorporate these fluxes. The additional knowledge of the so-called matrix to fracture transfer function allows to modify the mass matrix that becomes a time convolution operator. This is reminiscent of existing space averaged transient dual porosity models.

How reliable is the linear noise approximation of gene regulatory networks?

PubMed Central

2013-01-01

Background The linear noise approximation (LNA) is commonly used to predict how noise is regulated and exploited at the cellular level. These predictions are exact for reaction networks composed exclusively of first order reactions or for networks involving bimolecular reactions and large numbers of molecules. It is however well known that gene regulation involves bimolecular interactions with molecule numbers as small as a single copy of a particular gene. It is therefore questionable how reliable are the LNA predictions for these systems. Results We implement in the software package intrinsic Noise Analyzer (iNA), a system size expansion based method which calculates the mean concentrations and the variances of the fluctuations to an order of accuracy higher than the LNA. We then use iNA to explore the parametric dependence of the Fano factors and of the coefficients of variation of the mRNA and protein fluctuations in models of genetic networks involving nonlinear protein degradation, post-transcriptional, post-translational and negative feedback regulation. We find that the LNA can significantly underestimate the amplitude and period of noise-induced oscillations in genetic oscillators. We also identify cases where the LNA predicts that noise levels can be optimized by tuning a bimolecular rate constant whereas our method shows that no such regulation is possible. All our results are confirmed by stochastic simulations. Conclusion The software iNA allows the investigation of parameter regimes where the LNA fares well and where it does not. We have shown that the parametric dependence of the coefficients of variation and Fano factors for common gene regulatory networks is better described by including terms of higher order than LNA in the system size expansion. This analysis is considerably faster than stochastic simulations due to the extensive ensemble averaging needed to obtain statistically meaningful results. Hence iNA is well suited for performing computationally efficient and quantitative studies of intrinsic noise in gene regulatory networks. PMID:24266939

APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER*

PubMed Central

BARMPOUTIS, ANGELOS; JEFFREY, HO; VEMURI, BABA C.

2012-01-01

Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space P02m of 2mth-order symmetric positive semi-definite tensors is known to be a convex cone, enforcing positivity constraint directly on P02m is usually not straightforward computationally because there is no known analytic description of P02m for m > 1. In this paper, we propose a novel approach for enforcing the positivity constraint on even-order tensors by approximating the cone P02m for the cases 0 < m < 3, and presenting an explicit characterization of the approximation Σ2m ⊂ Ω2m for m ≥ 1, using the subset Ω2m⊂P02m of semi-definite tensors that can be written as a sum of squares of tensors of order m. Furthermore, we show that this approximation leads to a non-negative linear least-squares (NNLS) optimization problem with the complexity that equals the number of generators in Σ2m. Finally, we experimentally validate the proposed approach and we present an application for computing 2mth-order diffusion tensors from Diffusion Weighted Magnetic Resonance Images. PMID:23285313

Connection between the regular approximation and the normalized elimination of the small component in relativistic quantum theory

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2005-02-01

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac-Hartree-Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5×10-9hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.

Periodic response of nonlinear systems

NASA Technical Reports Server (NTRS)

Nataraj, C.; Nelson, H. D.

1988-01-01

A procedure is developed to determine approximate periodic solutions of autonomous and non-autonomous systems. The trignometric collocation method (TCM) is formalized to allow for the analysis of relatively small order systems directly in physical coordinates. The TCM is extended to large order systems by utilizing modal analysis in a component mode synthesis strategy. The procedure was coded and verified by several check cases. Numerical results for two small order mechanical systems and one large order rotor dynamic system are presented. The method allows for the possibility of approximating periodic responses for large order forced and self-excited nonlinear systems.

Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

NASA Astrophysics Data System (ADS)

Terasaki, J.; Smetana, A.; Šimkovic, F.; Krivoruchenko, M. I.

2017-10-01

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number N = 2 and numerically for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation.

Extracellular distribution volumes of hydrophilic solutes used to measure the glomerular filtration rate: comparison between chromium-51-EDTA and iohexol.

PubMed

Bird, Nicholas J; Peters, Christina; Michell, A Robert; Peters, A Michael

2007-02-01

Extracellular fluid volume (ECV) is larger when measured with Tc-99m-DTPA ( approximately 500 Da) than inulin (6 kDa). As part of an assessment of the suitability of the non-radioactive marker, iohexol, against the gold standard tracer, Cr-51-EDTA, for measurement of the glomerular filtration rate (GFR) based on a postal service, we took the opportunity to determine if this volume dependence is present for diffusible markers less disparate in size than inulin and Tc-99m-DTPA. Cr-51-EDTA ( approximately 400 Da) and iohexol ( approximately 900 Da) were administered into the opposite arms of 20 normal volunteers (fasting and non-fasting) and 60 patients (non-fasting), including 36 diabetics, 10 cancer patients and 13 dermatology patients. Blood was obtained from both arms 20, 40, 60, 120, 180 and 240 min after injection and assayed for a marker injected contra-laterally. The glomerular filtration rate (GFR) and mean indicator transit time, T, were measured from the bi-exponential clearance curves. ECV, the product of GFR and T, was subdivided into V(1) (administered indicator divided by the sum of zero-time intercepts of the two exponentials) and V(2) (the difference between V(1) and ECV). Variables were scaled to 1.73 m(2). For all 100 studies, the mean GFR from Cr-51-EDTA was 3 ml min(-1) higher than iohexol (p < 0.01). ECV was 0.41 L higher (p < 0.02) and V(1) 0.65 L higher (p < 0.001) from Cr-51-EDTA but V(2) was 0.33 L lower (p < 0.02). V(1)/ECV was 0.031 higher from Cr-51-EDTA (p < 0.01). ECV and V(2) from Cr-51-EDTA were both higher in diabetics (15.1 [1.7] and 5.0 [0.095] L, respectively) compared with normal non-fasting subjects (13.7 [1.5] and 4.3 [1.0]; p < 0.01). ECV and the volumes of its sub-compartments are different between markers that are less than an order of magnitude different in size.

Nitrogen retention in rivers: Model development and application to watersheds in the northeastern U.S.A.

USGS Publications Warehouse

Seitzinger, S.P.; Styles, R.V.; Boyer, E.W.; Alexander, R.B.; Billen, G.; Howarth, R.W.; Mayer, B.; Van Breemen, N.

2002-01-01

A regression model (RivR-N) was developed that predicts the proportion of N removed from streams and reservoirs as an inverse function of the water displacement time of the water body (ratio of water body depth to water time of travel). When applied to 16 drainage networks in the eastern U.S., the RivR-N model predicted that 37% to 76% of N input to these rivers is removed during transport through the river networks. Approximately half of that is removed in 1st through 4th order streams which account for 90% of the total stream length. The other half is removed in 5th order and higher rivers which account for only about 10% of the total stream length. Most N removed in these higher orders is predicted to originate from watershed loading to small and intermediate sized streams. The proportion of N removed from all streams in the watersheds (37-76%) is considerably higher than the proportion of N input to an individual reach that is removed in that reach (generally <20%) because of the cumulative effect of continued nitrogen removal along the entire flow path in downstream reaches. This generally has not been recognized in previous studies, but is critical to an evaluation of the total amount of N removed within a river network. At the river network scale, reservoirs were predicted to have a minimal effect on N removal. A fairly modest decrease (<10 percentage points) in the N removed at the river network scale was predicted when a third of the direct watershed loading was to the two highest orders compared to a uniform loading.

Sensor Properties of Field-Effect Transistors Based on Graphene Oxide and Nafion Films with Proton Conductivity

NASA Astrophysics Data System (ADS)

Smirnov, V. A.; Mokrushin, A. D.; Denisov, N. N.; Dobrovolsky, Yu. A.

2018-07-01

The proton conductivity of graphene oxide (GO) and Nafion films was studied depending on the humidity and voltage on electrodes. The electric properties of the films were similar, but the mobility of positive charges in Nafion was approximately two orders of magnitude higher than in GO. In GO films, the negative ion current with a positive voltage bias was up to 10% of the proton current, while in Nafion films it was almost absent (<1%). The sensors based on GO and Nafion films were most effective at humidity (RH) in the range 20-80%.

Wide band cryogenic ultra-high vacuum microwave absorber

DOEpatents

Campisi, I.E.

1992-05-12

An absorber waveguide assembly for absorbing higher order modes of microwave energy under cryogenic ultra-high vacuum conditions, that absorbs wide-band multi-mode energy. The absorber is of a special triangular shape, made from flat tiles of silicon carbide and aluminum nitride. The leading sharp end of the absorber is located in a corner of the waveguide and tapers to a larger cross-sectional area whose center is located approximately in the center of the wave guide. The absorber is relatively short, being of less height than the maximum width of the waveguide. 11 figs.

Wide band cryogenic ultra-high vacuum microwave absorber

DOEpatents

Campisi, Isidoro E.

1992-01-01

An absorber wave guide assembly for absorbing higher order modes of microwave energy under cryogenic ultra-high vacuum conditions, that absorbs wide-band multi-mode energy. The absorber is of a special triangular shape, made from flat tiles of silicon carbide and aluminum nitride. The leading sharp end of the absorber is located in a corner of the wave guide and tapers to a larger cross-sectional area whose center is located approximately in the center of the wave guide. The absorber is relatively short, being of less height than the maximum width of the wave guide.

Balloon borne Antarctic frost point measurements and their impact on polar stratospheric cloud theories

NASA Technical Reports Server (NTRS)

Rosen, James M.; Hofmann, D. J.; Carpenter, J. R.; Harder, J. W.; Oltsmans, S. J.

1988-01-01

Balloon-borne frost point measurements were performed over Antarctica during September-October 1987 as part of the NOZE II effort at McMurdo. The results show water mixing ratios on the order of 2 ppmv in the 20 km region, suggesting that models of the springtime Antarctic stratosphere should be based on approximately 2 ppmv water vapor. Evidence indicating that some PSCs form at temperatures higher than the frost point in the 15 to 20 km region is discussed. This supports the binary HNO3-H2O theory of PSC composition.

Summation by parts, projections, and stability

NASA Technical Reports Server (NTRS)

Olsson, Pelle

1993-01-01

We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By slightly rearranging the analytic equations, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield strict stability on curvilinear non-smooth domains in two space dimensions. Finally, we show how to incorporate inhomogeneous boundary data while retaining strict stability. Using the same procedure one can prove strict stability in higher dimensions as well.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim S.; Shaw, Leah B.

2013-11-01

Adaptive social networks, in which nodes and network structure coevolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher-order topological structures. We propose a new approach to moment closure based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 1.1)

NASA Technical Reports Server (NTRS)

Magnus, A. E.; Epton, M. A.

1981-01-01

Panel aerodynamics (PAN AIR) is a system of computer programs designed to analyze subsonic and supersonic inviscid flows about arbitrary configurations. A panel method is a program which solves a linear partial differential equation by approximating the configuration surface by a set of panels. An overview of the theory of potential flow in general and PAN AIR in particular is given along with detailed mathematical formulations. Fluid dynamics, the Navier-Stokes equation, and the theory of panel methods were also discussed.

Higher-order Fourier analysis over finite fields and applications

NASA Astrophysics Data System (ADS)

Hatami, Pooya

Higher-order Fourier analysis is a powerful tool in the study of problems in additive and extremal combinatorics, for instance the study of arithmetic progressions in primes, where the traditional Fourier analysis comes short. In recent years, higher-order Fourier analysis has found multiple applications in computer science in fields such as property testing and coding theory. In this thesis, we develop new tools within this theory with several new applications such as a characterization theorem in algebraic property testing. One of our main contributions is a strong near-equidistribution result for regular collections of polynomials. The densities of small linear structures in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by approximating the indicator function of a subset by a function of bounded number of polynomials. Then, to approximate the average, it suffices to know the joint distribution of the polynomials applied to the linear forms. We prove a near-equidistribution theorem that describes these distributions for the group F(n/p) when p is a fixed prime. This fundamental fact was previously known only under various extra assumptions about the linear forms or the field size. We use this near-equidistribution theorem to settle a conjecture of Gowers and Wolf on the true complexity of systems of linear forms. Our next application is towards a characterization of testable algebraic properties. We prove that every locally characterized affine-invariant property of functions f : F(n/p) → R with n∈ N, is testable. In fact, we prove that any such property P is proximity-obliviously testable. More generally, we show that any affine-invariant property that is closed under subspace restrictions and has "bounded complexity" is testable. We also prove that any property that can be described as the property of decomposing into a known structure of low-degree polynomials is locally characterized and is, hence, testable. We discuss several notions of regularity which allow us to deduce algorithmic versions of various regularity lemmas for polynomials by Green and Tao and by Kaufman and Lovett. We show that our algorithmic regularity lemmas for polynomials imply algorithmic versions of several results relying on regularity, such as decoding Reed-Muller codes beyond the list decoding radius (for certain structured errors), and prescribed polynomial decompositions. Finally, motivated by the definition of Gowers norms, we investigate norms defined by different systems of linear forms. We give necessary conditions on the structure of systems of linear forms that define norms. We prove that such norms can be one of only two types, and assuming that |F p| is sufficiently large, they essentially are equivalent to either a Gowers norm or Lp norms.

Effective potentials in nonlinear polycrystals and quadrature formulae

NASA Astrophysics Data System (ADS)

Michel, Jean-Claude; Suquet, Pierre

2017-08-01

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471, 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

f and g series solutions to a post-Newtonian two-body problem with parameters β and γ

NASA Astrophysics Data System (ADS)

Qin, Song-He; Liu, Jing-Xi; Zhong, Ze-Hao; Xie, Yi

2016-01-01

Classical Newtonian f and g series for a Keplerian two-body problem are extended for the case of a post-Newtonian two-body problem with parameters β and γ. These two parameters are introduced to parameterize the post-Newtonian approximation of alternative theories of gravity and they are both equal to 1 in general relativity. Up to the order of 30, we obtain all of the coefficients of the series in their exact forms without any cutoff for significant figures. The f and g series for the post-Newtonian two-body problem are also compared with a Runge-Kutta order 7 integrator. Although the f and g series have no superiority in terms of accuracy or efficiency at the order of 7, the discrepancy in the performances of these two methods is not quite distinct. However, the f and g series have the advantage of flexibility for going to higher orders. Some examples of relativistic advance of periastron are given and the effect of gravitational radiation on the scheme of f and g series is evaluated.

The role of higher-order terms in perturbation approaches to the monomer and\\xA0bonding contributions in a SAFT-type equation of state for square-well chain\\xA0fluids

NASA Astrophysics Data System (ADS)

Solana, J. R.; Akhouri, B. P.

2018-07-01

A perturbation theory for square-well chain fluids is developed within the scheme of the (generalised) Wertheim thermodynamic perturbation theory. The theory is based on the Pavlyukhin parametrisations [Y. T. Pavlyukhin, J. Struct. Chem. 53, 476 (2012)] of their simulation data for the first four perturbation terms in the high temperature expansion of the Helmholtz free energy of square-well monomer fluids combined with a second-order perturbation theory for the contact value of the radial distribution function of the square-well monomer fluid that enters into bonding contribution. To obtain the latter perturbation terms, we have performed computer simulations in the hard-sphere reference system. The importance of the perturbation terms beyond the second-order one for the monomer fluid and of the approximations of different orders in the bonding contribution for the chain fluids in the predicted equation of state, excess energy and liquid-vapour coexistence densities is analysed.

Effective potentials in nonlinear polycrystals and quadrature formulae.

PubMed

Michel, Jean-Claude; Suquet, Pierre

2017-08-01

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471 , 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

Groupwise Registration and Atlas Construction of 4th-Order Tensor Fields Using the ℝ+ Riemannian Metric*

PubMed Central

Barmpoutis, Angelos

2010-01-01

Registration of Diffusion-Weighted MR Images (DW-MRI) can be achieved by registering the corresponding 2nd-order Diffusion Tensor Images (DTI). However, it has been shown that higher-order diffusion tensors (e.g. order-4) outperform the traditional DTI in approximating complex fiber structures such as fiber crossings. In this paper we present a novel method for unbiased group-wise non-rigid registration and atlas construction of 4th-order diffusion tensor fields. To the best of our knowledge there is no other existing method to achieve this task. First we define a metric on the space of positive-valued functions based on the Riemannian metric of real positive numbers (denoted by ℝ+). Then, we use this metric in a novel functional minimization method for non-rigid 4th-order tensor field registration. We define a cost function that accounts for the 4th-order tensor re-orientation during the registration process and has analytic derivatives with respect to the transformation parameters. Finally, the tensor field atlas is computed as the minimizer of the variance defined using the Riemannian metric. We quantitatively compare the proposed method with other techniques that register scalar-valued or diffusion tensor (rank-2) representations of the DWMRI. PMID:20436782

Renormalization group methods for the Reynolds stress transport equations

NASA Technical Reports Server (NTRS)

Rubinstein, R.

1992-01-01

The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

High Altitude Supersonic Decelerator Test Vehicle

NASA Technical Reports Server (NTRS)

Cook, Brant T.; Blando, Guillermo; Kennett, Andrew; Von Der Heydt, Max; Wolff, John Luke; Yerdon, Mark

2013-01-01

The Low Density Supersonic Decelerator (LDSD) project is tasked by NASA's Office of the Chief Technologist (OCT) to advance the state of the art in Mars entry and descent technology in order to allow for larger payloads to be delivered to Mars at higher altitudes with better accuracy. The project will develop a 33.5 m Do Supersonic Ringsail (SSRS) parachute, 6m attached torus, robotic class Supersonic Inflatable Aerodynamic Decelerator (SIAD-R), and an 8 m attached isotensoid, exploration class Supersonic Inflatable Aerodynamic Decelerator (SIAD-E). The SSRS and SIAD-R should be brought to TRL-6, while the SIAD-E should be brought to TRL-5. As part of the qualification and development program, LDSD must perform a Mach-scaled Supersonic Flight Dynamics Test (SFDT) in order to demonstrate successful free flight dynamic deployments at Mars equivalent altitude, of all three technologies. In order to perform these tests, LDSD must design and build a test vehicle to deliver all technologies to approximately 180,000 ft and Mach 4, deploy a SIAD, free fly to approximately Mach 2, deploy the SSRS, record high-speed and high-resolution imagery of both deployments, as well as record data from an instrumentation suite capable of characterizing the technology induced vehicle dynamics. The vehicle must also be recoverable after splashdown into the ocean under a nominal flight, while guaranteeing forensic data protection in an off nominal catastrophic failure of a test article that could result in a terminal velocity, tumbling water impact.

Convergence of the strong-potential-Born approximation in Z/sub less-than//Z/sub greater-than/

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

McGuire, J.H.; Sil, N.C.

1986-01-01

Convergence of the strong-potential Born (SPB) approximation as a function of the charges of the projectile and target is studied numerically. Time-reversal invariance (or detailed balance) is satisfied at sufficiently high velocities even when the charges are asymmetric. This demonstarates that the SPB approximation converges to the correct result even when the charge of the ''weak'' potential, which is kept to first order, is larger than the charge of the ''strong'' potential, which is retained to all orders. Consequently, the SPB approximation is valid for systems of arbitrary charge symmetry (including symmetric systems) at sufficiently high velocities.

Non-hard sphere thermodynamic perturbation theory.

PubMed

Zhou, Shiqi

2011-08-21

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established. © 2011 American Institute of Physics

Quantification and parametrization of non-linearity effects by higher-order sensitivity terms in scattered light differential optical absorption spectroscopy

NASA Astrophysics Data System (ADS)

Puķīte, Jānis; Wagner, Thomas

2016-05-01

We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on temperature and scattering processes.

Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials

NASA Astrophysics Data System (ADS)

Throckmorton, Robert E.; Hofmann, Johannes; Barnes, Edwin; Das Sarma, S.

2015-09-01

We develop a theory for electron-electron interaction-induced many-body effects in three-dimensional Weyl or Dirac semimetals, including interaction corrections to the polarizability, electron self-energy, and vertex function, up to second order in the effective fine-structure constant of the Dirac material. These results are used to derive the higher-order ultraviolet renormalization of the Fermi velocity, effective coupling, and quasiparticle residue, revealing that the corrections to the renormalization group flows of both the velocity and coupling counteract the leading-order tendencies of velocity enhancement and coupling suppression at low energies. This in turn leads to the emergence of a critical coupling above which the interaction strength grows with decreasing energy scale. In addition, we identify a range of coupling strengths below the critical point in which the Fermi velocity varies nonmonotonically as the low-energy, noninteracting fixed point is approached. Furthermore, we find that while the higher-order correction to the flow of the coupling is generally small compared to the leading order, the corresponding correction to the velocity flow carries an additional factor of the Dirac cone flavor number (the multiplicity of electron species, e.g. ground-state valley degeneracy arising from the band structure) relative to the leading-order result. Thus, for materials with a larger multiplicity, the regime of velocity nonmonotonicity is reached for modest values of the coupling strength. This is in stark contrast to an approach based on a large-N expansion or the random phase approximation (RPA), where higher-order corrections are strongly suppressed for larger values of the Dirac cone multiplicity. This suggests that perturbation theory in the coupling constant (i.e., the loop expansion) and the RPA/large-N expansion are complementary in the sense that they are applicable in different parameter regimes of the theory. We show how our results for the ultraviolet renormalization of quasiparticle properties can be tested experimentally through measurements of quantities such as the optical conductivity or dielectric function (with carrier density or temperature acting as the scale being varied to induce the running coupling). Although experiments typically access the finite-density regime, we show that our zero-density results still capture clear many-body signatures that should be visible at higher temperatures even in real systems with disorder and finite doping.

Structure and thermodynamics of a simple fluid

NASA Astrophysics Data System (ADS)

Stell, G.; Weis, J. J.

1980-02-01

Monte Carlo results are found for a simple fluid with a pair potential consisting of a hard-sphere core and a Lennard-Jones attractive tail. They are compared with several of the most promising recent theoretical treatments of simple fluids, all of which involve the decomposition of the pair potential into a hard-sphere-core term and an attractive-tail term. This direct comparison avoids the use of a second perturbation scheme associated with softening the core, which would introduce an ambiguity in the significance of the differences found between the theoretical and Monte Carlo results. The study includes the optimized random-phase approximation (ORPA) and exponential (EXP) approximations of Andersen and Chandler, an extension of the latter approximation to nodal order three (the N3 approximation), the linear-plus-square (LIN + SQ) approximation of Høye and Stell, the renormalized hypernetted chain (RHNC) approximation of Lado, and the quadratic (QUAD) approximation suggested by second-order self-consistent Γ ordering, the lowest order of which is identical to the ORPA. As anticipated on the basis of earlier studies, it is found that the EXP approximation yields radial distribution functions and structure factors of excellent overall accuracy in the liquid state, where the RHNC results are also excellent and the EXP, QUAD, and LIN + SQ results prove to be virtually indistinguishable from one another. For all the approximations, however, the thermodynamics from the compressibility relation are poor and the virial-theorem results are not uniformly reliable. Somewhat more surprisingly, it is found that the EXP results yield a negative structure factor S(k) for very small k in the liquid state and poor radial distribution functions at low densities. The RHNC results are nowhere worse than the EXP results and in some states (e.g., at low densities) much better. In contrast, the N3 results are better in some respects than the EXP results but worse in others. The authors briefly comment on the RHNC and EXP approximations applied to the full Lennard-Jones potential, for which the EXP approximation appears somewhat improved in the liquid state as a result of the softening of the potential core.

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Karpel, Mordechay

1989-01-01

Various control analysis, design, and simulation techniques for aeroelastic applications require the equations of motion to be cast in a linear time-invariant state-space form. Unsteady aerodynamics forces have to be approximated as rational functions of the Laplace variable in order to put them in this framework. For the minimum-state method, the number of denominator roots in the rational approximation. Results are shown of applying various approximation enhancements (including optimization, frequency dependent weighting of the tabular data, and constraint selection) with the minimum-state formulation to the active flexible wing wind-tunnel model. The results demonstrate that good models can be developed which have an order of magnitude fewer augmenting aerodynamic equations more than traditional approaches. This reduction facilitates the design of lower order control systems, analysis of control system performance, and near real-time simulation of aeroservoelastic phenomena.

High-Precision Differential Predictions for Top-Quark Pairs at the LHC

NASA Astrophysics Data System (ADS)

Czakon, Michal; Heymes, David; Mitov, Alexander

2016-02-01

We present the first complete next-to-next-to-leading order (NNLO) QCD predictions for differential distributions in the top-quark pair production process at the LHC. Our results are derived from a fully differential partonic Monte Carlo calculation with stable top quarks which involves no approximations beyond the fixed-order truncation of the perturbation series. The NNLO corrections improve the agreement between existing LHC measurements [V. Khachatryan et al. (CMS Collaboration), Eur. Phys. J. C 75, 542 (2015)] and standard model predictions for the top-quark transverse momentum distribution, thus helping alleviate one long-standing discrepancy. The shape of the top-quark pair invariant mass distribution turns out to be stable with respect to radiative corrections beyond NLO which increases the value of this observable as a place to search for physics beyond the standard model. The results presented here provide essential input for parton distribution function fits, implementation of higher-order effects in Monte Carlo generators, as well as top-quark mass and strong coupling determination.

High-Precision Differential Predictions for Top-Quark Pairs at the LHC.

PubMed

Czakon, Michal; Heymes, David; Mitov, Alexander

2016-02-26

We present the first complete next-to-next-to-leading order (NNLO) QCD predictions for differential distributions in the top-quark pair production process at the LHC. Our results are derived from a fully differential partonic Monte Carlo calculation with stable top quarks which involves no approximations beyond the fixed-order truncation of the perturbation series. The NNLO corrections improve the agreement between existing LHC measurements [V. Khachatryan et al. (CMS Collaboration), Eur. Phys. J. C 75, 542 (2015)] and standard model predictions for the top-quark transverse momentum distribution, thus helping alleviate one long-standing discrepancy. The shape of the top-quark pair invariant mass distribution turns out to be stable with respect to radiative corrections beyond NLO which increases the value of this observable as a place to search for physics beyond the standard model. The results presented here provide essential input for parton distribution function fits, implementation of higher-order effects in Monte Carlo generators, as well as top-quark mass and strong coupling determination.

Effects of high-order correlations on personalized recommendations for bipartite networks

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Zhou, Tao; Che, Hong-An; Wang, Bing-Hong; Zhang, Yi-Cheng

2010-02-01

In this paper, we introduce a modified collaborative filtering (MCF) algorithm, which has remarkably higher accuracy than the standard collaborative filtering. In the MCF, instead of the cosine similarity index, the user-user correlations are obtained by a diffusion process. Furthermore, by considering the second-order correlations, we design an effective algorithm that depresses the influence of mainstream preferences. Simulation results show that the algorithmic accuracy, measured by the average ranking score, is further improved by 20.45% and 33.25% in the optimal cases of MovieLens and Netflix data. More importantly, the optimal value λ depends approximately monotonously on the sparsity of the training set. Given a real system, we could estimate the optimal parameter according to the data sparsity, which makes this algorithm easy to be applied. In addition, two significant criteria of algorithmic performance, diversity and popularity, are also taken into account. Numerical results show that as the sparsity increases, the algorithm considering the second-order correlation can outperform the MCF simultaneously in all three criteria.

The distribution of cosmic rays in the galaxy and their dynamics as deduced from recent gamma-ray observations. [X-ray intensity variations with galactocentric distance

NASA Technical Reports Server (NTRS)

Puget, J. L.; Stecker, F. W.

1974-01-01

Recent data from SAS-2 on the galactic gamma ray line flux as a function of longitude reveal a broad maximum in the gamma ray intensity in the region absolute value of l approximately smaller than 30 deg. These data imply that the low energy galactic cosmic ray flux varies with galactocentric distance and is about an order of magnitude higher than the local value in a toroidal region between 4 and 5 kpc from the galactic center. This enhancement can be plausibly accounted for by first order Fermi acceleration, compression and trapping of cosmic rays consistent with present ideas of galactic dynamics and galactic structure theory. Calculations indicate that cosmic rays in the 4 to 5 kpc region are trapped and accelerated over a mean time of the order of a few million years or about 2 to 4 times the assumed trapping time in the solar region of the galaxy.

Tunable d-Limonene Permeability in Starch-Based Nanocomposite Films Reinforced by Cellulose Nanocrystals.

PubMed

Liu, Siyuan; Li, Xiaoxi; Chen, Ling; Li, Lin; Li, Bing; Zhu, Jie

2018-01-31

In order to control d-limonene permeability, cellulose nanocrystals (CNC) were used to regulate starch-based film multiscale structures. The effect of sphere-like cellulose nanocrystal (CS) and rod-like cellulose nanocrystal (CR) on starch molecular interaction, short-range molecular conformation, crystalline structure, and micro-ordered aggregated region structure were systematically discussed. CNC aspect ratio and content were proved to be independent variables to control d-limonene permeability via film-structure regulation. New hydrogen bonding formation and increased hydroxypropyl starch (HPS) relative crystallinity could be the reason for the lower d-limonene permeability compared with tortuous path model approximation. More hydrogen bonding formation, higher HPS relative crystallinity and larger size of micro-ordered aggregated region in CS0.5 and CR2 could explain the lower d-limonene permeability than CS2 and CR0.5, respectively. This study provided new insight for the control of the flavor release from starch-based films, which favored its application in biodegradable food packaging and flavor encapsulation.

A regularized vortex-particle mesh method for large eddy simulation

NASA Astrophysics Data System (ADS)

Spietz, H. J.; Walther, J. H.; Hejlesen, M. M.

2017-11-01

We present recent developments of the remeshed vortex particle-mesh method for simulating incompressible fluid flow. The presented method relies on a parallel higher-order FFT based solver for the Poisson equation. Arbitrary high order is achieved through regularization of singular Green's function solutions to the Poisson equation and recently we have derived novel high order solutions for a mixture of open and periodic domains. With this approach the simulated variables may formally be viewed as the approximate solution to the filtered Navier Stokes equations, hence we use the method for Large Eddy Simulation by including a dynamic subfilter-scale model based on test-filters compatible with the aforementioned regularization functions. Further the subfilter-scale model uses Lagrangian averaging, which is a natural candidate in light of the Lagrangian nature of vortex particle methods. A multiresolution variation of the method is applied to simulate the benchmark problem of the flow past a square cylinder at Re = 22000 and the obtained results are compared to results from the literature.

Impact sensitivity of materials in contact with liquid and gaseous oxygen at high pressure

NASA Technical Reports Server (NTRS)

Schwinghamer, R. J.

1972-01-01

As a result of the Apollo 13 incident, increased emphasis is being placed on materials compatibility in a high pressure GOX environment. It is known that in addition to impact sensitivity of materials, approximately adiabatic compression conditions can contrive to induce materials reactivity. Test runs at high pressure using the ABMA tester indicate the following: (1) The materials used in the tests showed an inverse relationship between thickness and impact sensitivity. (2) Several materials tested exhibited greater impact sensitivity in GOX than in LOX. (3) The impact sensitivity of the materials tested in GOX, at the pressures tested, showed enhanced impact sensitivity with higher pressure. (4) The rank ordering of the materials tested in LOX up to 1000 psia is the same as the rank ordering resulting from tests in LOX at 14.7 psia.

Pure-quartic solitons

PubMed Central

Blanco-Redondo, Andrea; Martijn, de Sterke C.; Sipe, J.E.; Krauss, Thomas F.; Eggleton, Benjamin J.; Husko, Chad

2016-01-01

Temporal optical solitons have been the subject of intense research due to their intriguing physics and applications in ultrafast optics and supercontinuum generation. Conventional bright optical solitons result from the interaction of anomalous group-velocity dispersion and self-phase modulation. Here we experimentally demonstrate a class of bright soliton arising purely from the interaction of negative fourth-order dispersion and self-phase modulation, which can occur even for normal group-velocity dispersion. We provide experimental and numerical evidence of shape-preserving propagation and flat temporal phase for the fundamental pure-quartic soliton and periodically modulated propagation for the higher-order pure-quartic solitons. We derive the approximate shape of the fundamental pure-quartic soliton and discover that is surprisingly Gaussian, exhibiting excellent agreement with our experimental observations. Our discovery, enabled by precise dispersion engineering, could find applications in communications, frequency combs and ultrafast lasers. PMID:26822758

Adaptive Discrete Hypergraph Matching.

PubMed

Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao

2018-02-01

This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.

Nonlinear evolution of Benjamin-Feir wave group based on third order solution of Benjamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Zahnur; Halfiani, Vera; Salmawaty; Tulus; Ramli, Marwan

2018-01-01

This study concerns on the evolution of trichromatic wave group. It has been known that the trichromatic wave group undergoes an instability during its propagation, which results wave deformation and amplification on the waves amplitude. The previous results on the KdV wave group showed that the nonlinear effect will deform the wave and lead to large wave whose amplitude is higher than the initial input. In this study we consider the Benjamin-Bona-Mahony equation and the theory of third order side band approximation to investigate the peaking and splitting phenomena of the wave groups which is initially in trichromatic signal. The wave amplitude amplification and the maximum position will be observed through a quantity called Maximal Temporal Amplitude (MTA) which measures the maximum amplitude of the waves over time.

A comprehensive comparison between thermodynamic perturbation theory and first-order mean spherical approximation: Based on discrete potentials with hard core

NASA Astrophysics Data System (ADS)

Zhou, Shiqi; Zhou, Run

2017-08-01

Using the TL (Tang and Lu, 1993) method, Ornstein-Zernike integral equation is solved perturbatively under the mean spherical approximation (MSA) for fluid with potential consisting of a hard sphere plus square-well plus square-shoulder (HS + SW + SS) to obtain first-order analytic expressions of radial distribution function (RDF), second-order direct correlation function, and semi-analytic expressions for common thermodynamic properties. A comprehensive comparison between the first-order MSA and high temperature series expansion (HTSE) to third-, fifth- and seventh-order is performed over a wide parameter range for both a HS + SW and the HS + SW + SS model fluids by using corresponding ;exact; Monte Carlo results as a reference; although the HTSE is carried out up to seventh-order, and not to the first order as the first-order MSA the comparison is considered fair from a calculation complexity perspective. It is found that the performance of the first-order MSA is dramatically model-dependent: as target potentials go from the HS + SW to the HS + SW + SS, (i) there is a dramatic dropping of performance of the first-order MSA expressions in calculating the thermodynamic properties, especially both the excess internal energy and constant volume excess heat capacity of the HS + SW + SS model cannot be predicted even qualitatively correctly. (ii) One tendency is noticed that the first-order MSA gets more reliable with increasing temperatures in dealing with the pressure, excess Helmholtz free energy, excess enthalpy and excess chemical potential. (iii) Concerning the RDF, the first-order MSA is not as disappointing as it displays in the cases of thermodynamics. (iv) In the case of the HS + SW model, the first-order MSA solution is shown to be quantitatively correct in calculating the pressure and excess chemical potential even if the reduced temperatures are as low as 0.8. On the other hand, the seventh-order HTSE is less model-dependent; in most cases of the HS + SW and the HS + SW + SS models, the seventh-order HTSE improves the fifth- and third-order HTSE in both thermodynamic properties and RDF, and the improvements are very demonstrable in both the excess internal energy and constant volume excess heat capacity; for very limited cases, the seventh-order HTSE improves the fifth-order HTSE only within lower density domain and even shows a bit of inadaptation over higher density domain.

The Approximation of Two-Mode Proximity Matrices by Sums of Order-Constrained Matrices.

ERIC Educational Resources Information Center

Hubert, Lawrence; Arabie, Phipps

1995-01-01

A least-squares strategy is proposed for representing a two-mode proximity matrix as an approximate sum of a small number of matrices that satisfy certain simple order constraints on their entries. The primary class of constraints considered defines Q-forms for particular conditions in a two-mode matrix. (SLD)

Thermal desorption of CO and H2 from degassed 304 and 347 stainless steel

NASA Technical Reports Server (NTRS)

Rezaie-Serej, S.; Outlaw, R. A.

1994-01-01

Thermal desorption spectroscopy (TDS), along with Auger electron spectroscopy, was used to study the desorption of H2 and CO from baked 304 and 347 stainless-steel samples exposed only to residual gases. Both 347 and 304 samples gave identical TDS spectra. The spectra for CO contained a sharp leading peak centered in the temperature range 410-440C and an exponentially increasing part for temperatures higher than 500C, with a small peak around 600C appearing as a shoulder. The leading peak followed a second-order desorption behavior with an activation energy of 28+/-2 kcal/mol, suggesting that the rate-limiting step for this peak is most likely a surface reaction that produces the CO molecules in the surface layer. The amount of desorbed CO corresponding to this peak was approximately 0.5X10(exp 14) molecules/cm(exp 2) . The exponentially rising part of the CO spectrum appeared to originate from a bulk diffusion process. The TDS spectrum for H2 consisted of a main peak centered also in the temperature range 410-440C, with two small peaks appearing as shoulders at approximately 500 and 650C. The main peak in this case also displayed a second-order behavior with an activation energy of 14+/-2 kcal/mol. The amount of desorbed H2, approximately 1.9X 10(exp 15) molecules/cm(exp 2) , appeared to be independent of the concentration of hydrogen in the bulk, indicating that the majority of the desorbed H2 originated from the surface layer.

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

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

1997-01-01

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

Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering

NASA Astrophysics Data System (ADS)

Atalay, Bora; Berker, A. Nihat

2018-05-01

Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states q =3 ,4 in d dimensions. We use renormalization-group theory that is exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all d >1 and all noninfinite temperatures, the system eventually renormalizes to a random single state, thus signaling q ×q degenerate ordering. Note that this is the maximally degenerate ordering. For high-temperature initial conditions, the system crosses over to this highly degenerate ordering only after spending many renormalization-group iterations near the disordered (infinite-temperature) fixed point. Thus, a temperature range of short-range disorder in the presence of long-range order is identified, as previously seen in underfrustrated Ising spin-glass systems. The entropy is calculated for all temperatures, behaves similarly for ferromagnetic and antiferromagnetic interactions, and shows a derivative maximum at the short-range disordering temperature. With a sharp immediate contrast of infinitesimally higher dimension 1 +ɛ , the system is as expected disordered at all temperatures for d =1 .

Breathers and rogue waves in a Heisenberg ferromagnetic spin chain or an alpha helical protein

NASA Astrophysics Data System (ADS)

Yang, Jin-Wei; Gao, Yi-Tian; Su, Chuan-Qi; Wang, Qi-Min; Lan, Zhong-Zhou

2017-07-01

In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation for a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain or an alpha helical protein has been investigated. Breathers and rogue waves are constructed via the Darboux transformation and generalized Darboux transformation, respectively. Results of the breathers and rogue waves are presented: (1) The first- and second-order Akhmediev breathers and Kuznetsov-Ma solitons are presented with different values of variable coefficients which are related to the energy transfer or higher-order excitations and interactions in the helical protein, or related to the spin excitations resulting from the lowest order continuum approximation and octupole-dipole interaction in a Heisenberg ferromagnetic spin chain, and the nonlinear periodic breathers resulting from the Akhmediev breathers are studied as well; (2) For the first- and second-order rogue waves, we find that they can be split into many similar components when the variable coefficients are polynomial functions of time; (3) Rogue waves can also be split when the variable coefficients are hyperbolic secant functions of time, but the profile of each component in such a case is different.

Combined temperature and density series for fluid-phase properties. I. Square-well spheres

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

Elliott, J. Richard; Schultz, Andrew J.; Kofke, David A.

Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B{sub 2}(β) η + B{sub 3}(β) η{sup 2} + B{sub 4}(β) η{sup 3} + ⋯, where Z is the compressibility factor, η is the packing fraction, and the B{sub i}(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the B{sub i} coefficients can be expressed in closed form asmore » a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the B{sub i} coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.« less

Well-Balanced Second-Order Approximation of the Shallow Water Equations With Friction via Continuous Galerkin Finite Elements

NASA Astrophysics Data System (ADS)

Quezada de Luna, M.; Farthing, M.; Guermond, J. L.; Kees, C. E.; Popov, B.

2017-12-01

The Shallow Water Equations (SWEs) are popular for modeling non-dispersive incompressible water waves where the horizontal wavelength is much larger than the vertical scales. They can be derived from the incompressible Navier-Stokes equations assuming a constant vertical velocity. The SWEs are important in Geophysical Fluid Dynamics for modeling surface gravity waves in shallow regimes; e.g., in the deep ocean. Some common geophysical applications are the evolution of tsunamis, river flooding and dam breaks, storm surge simulations, atmospheric flows and others. This work is concerned with the approximation of the time-dependent Shallow Water Equations with friction using explicit time stepping and continuous finite elements. The objective is to construct a method that is at least second-order accurate in space and third or higher-order accurate in time, positivity preserving, well-balanced with respect to rest states, well-balanced with respect to steady sliding solutions on inclined planes and robust with respect to dry states. Methods fulfilling the desired goals are common within the finite volume literature. However, to the best of our knowledge, schemes with the above properties are not well developed in the context of continuous finite elements. We start this work based on a finite element method that is second-order accurate in space, positivity preserving and well-balanced with respect to rest states. We extend it by: modifying the artificial viscosity (via the entropy viscosity method) to deal with issues of loss of accuracy around local extrema, considering a singular Manning friction term handled via an explicit discretization under the usual CFL condition, considering a water height regularization that depends on the mesh size and is consistent with the polynomial approximation, reducing dispersive errors introduced by lumping the mass matrix and others. After presenting the details of the method we show numerical tests that demonstrate the well-balanced nature of the scheme and its convergence properties. We conclude with well-known benchmark problems including the Malpasset dam break (see the attached figure). All numerical experiments are performed and available in the Proteus toolkit, which is an open source python package for modeling continuum mechanical processes and fluid flow.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

DEMNUni: massive neutrinos and the bispectrum of large scale structures

NASA Astrophysics Data System (ADS)

Ruggeri, Rossana; Castorina, Emanuele; Carbone, Carmelita; Sefusatti, Emiliano

2018-03-01

The main effect of massive neutrinos on the large-scale structure consists in a few percent suppression of matter perturbations on all scales below their free-streaming scale. Such effect is of particular importance as it allows to constraint the value of the sum of neutrino masses from measurements of the galaxy power spectrum. In this work, we present the first measurements of the next higher-order correlation function, the bispectrum, from N-body simulations that include massive neutrinos as particles. This is the simplest statistics characterising the non-Gaussian properties of the matter and dark matter halos distributions. We investigate, in the first place, the suppression due to massive neutrinos on the matter bispectrum, comparing our measurements with the simplest perturbation theory predictions, finding the approximation of neutrinos contributing at quadratic order in perturbation theory to provide a good fit to the measurements in the simulations. On the other hand, as expected, a linear approximation for neutrino perturbations would lead to Script O(fν) errors on the total matter bispectrum at large scales. We then attempt an extension of previous results on the universality of linear halo bias in neutrino cosmologies, to non-linear and non-local corrections finding consistent results with the power spectrum analysis.

Oligomerization affects the kinetics and thermodynamics of the interaction of a Bowman-Birk inhibitor with proteases.

PubMed

Brand, G D; Pires, D A T; Furtado, J R; Cooper, A; Freitas, S M; Bloch, C

2017-03-15

The black-eyed pea trypsin/chymotrypsin inhibitor (BTCI) forms concentration dependent homomultimers, as previously demonstrated by Light scattering and Atomic Force Microscopy. Considering that these self-aggregates might influence their binding to cognate enzymes, we investigated the interaction of BTCI at picomolar concentrations using surface immobilized Chymotrypsin (α-CT) and Trypsin (T) by Surface Plasmon Resonance. Our results indicate that BTCI has subnanomolar affinity to both immobilized enzymes, which is approximately two orders of magnitude higher than previously reported. Moreover, we probed the influence of temperature on protein binding equilibria in order to investigate their interaction energetics. While the BTCI/T interaction concurs with the canonical entropy-driven mechanism described for BBI interactions with serine proteinases, the BTCI/α-CT interaction does not. Our measurements indicate that bimolecular BTCI/α-CT complexes form with a negative enthalpy change and a moderate entropic increase. Direct calorimetric evaluation is in accord with the van't Hoff approximation obtained by SPR. We demonstrate that as protein concentrations increase to the micromolar range, secondary endothermic events become prevalent and affect both the kinetics and thermodynamics of protein associations. Our study reinforces that BBI interactions with serine proteinases should be studied in dilute solutions to abridge often neglected secondary interactions. Copyright © 2017 Elsevier Inc. All rights reserved.

Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

NASA Astrophysics Data System (ADS)

Kim, SungKun; Lee, Hunpyo

2017-06-01

Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

Approximate analysis for repeated eigenvalue problems with applications to controls-structure integrated design

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Hou, Gene J. W.

1994-01-01

A method for eigenvalue and eigenvector approximate analysis for the case of repeated eigenvalues with distinct first derivatives is presented. The approximate analysis method developed involves a reparameterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations to changes in the eigenvalues and the eigenvectors associated with the repeated eigenvalue problem. This work also presents a numerical technique that facilitates the definition of an eigenvector derivative for the case of repeated eigenvalues with repeated eigenvalue derivatives (of all orders). Examples are given which demonstrate the application of such equations for sensitivity and approximate analysis. Emphasis is placed on the application of sensitivity analysis to large-scale structural and controls-structures optimization problems.

Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.; Korte, John J.; Mauery, Timothy M.; Mistree, Farrokh

1998-01-01

In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

Mechanisms of time-based figure-ground segregation.

PubMed

Kandil, Farid I; Fahle, Manfred

2003-11-01

Figure-ground segregation can rely on purely temporal information, that is, on short temporal delays between positional changes of elements in figure and ground (Kandil, F.I. & Fahle, M. (2001) Eur. J. Neurosci., 13, 2004-2008). Here, we investigate the underlying mechanisms by measuring temporal segregation thresholds for various kinds of motion cues. Segregation can rely on monocular first-order motion (based on luminance modulation) and second-order motion cues (contrast modulation) with a high temporal resolution of approximately 20 ms. The mechanism can also use isoluminant motion with a reduced temporal resolution of 60 ms. Figure-ground segregation can be achieved even at presentation frequencies too high for human subjects to inspect successive frames individually. In contrast, when stimuli are presented dichoptically, i.e. separately to both eyes, subjects are unable to perceive any segregation, irrespective of temporal frequency. We propose that segregation in these displays is detected by a mechanism consisting of at least two stages. On the first level, standard motion or flicker detectors signal local positional changes (flips). On the second level, a segregation mechanism combines the local activities of the low-level detectors with high temporal precision. Our findings suggest that the segregation mechanism can rely on monocular detectors but not on binocular mechanisms. Moreover, the results oppose the idea that segregation in these displays is achieved by motion detectors of a higher order (motion-from-motion), but favour mechanisms sensitive to short temporal delays even without activation of higher-order motion detectors.

The integrated bispectrum and beyond

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

Munshi, Dipak; Coles, Peter, E-mail: D.Munshi@sussex.ac.uk, E-mail: P.Coles@sussex.ac.uk

2017-02-01

The position-dependent power spectrum has been recently proposed as a descriptor of gravitationally induced non-Gaussianity in galaxy clustering, as it is sensitive to the 'soft limit' of the bispectrum (i.e. when one of the wave number tends to zero). We generalise this concept to higher order and clarify their relationship to other known statistics such as the skew-spectrum, the kurt-spectra and their real-space counterparts the cumulants correlators. Using the Hierarchical Ansatz (HA) as a toy model for the higher order correlation hierarchy, we show how in the soft limit, polyspectra at a given order can be identified with lower ordermore » polyspectra with the same geometrical dependence but with renormalised amplitudes expressed in terms of amplitudes of the original polyspectra. We extend the concept of position-dependent bispectrum to bispectrum of the divergence of the velocity field Θ and mixed multispectra involving δ and Θ in the 3D perturbative regime. To quantify the effects of transients in numerical simulations, we also present results for lowest order in Lagrangian perturbation theory (LPT) or the Zel'dovich approximation (ZA). Finally, we discuss how to extend the position-dependent spectrum concept to encompass cross-spectra. And finally study the application of this concept to two dimensions (2D), for projected galaxy maps, convergence κ maps from weak-lensing surveys or maps of CMB secondaries e.g. the frequency cleaned y -parameter maps of thermal Sunyaev-Zel'dovich (tSZ) effect from CMB surveys.« less

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Improving fast generation of halo catalogues with higher order Lagrangian perturbation theory

NASA Astrophysics Data System (ADS)

Munari, Emiliano; Monaco, Pierluigi; Sefusatti, Emiliano; Castorina, Emanuele; Mohammad, Faizan G.; Anselmi, Stefano; Borgani, Stefano

2017-03-01

We present the latest version of PINOCCHIO, a code that generates catalogues of dark matter haloes in an approximate but fast way with respect to an N-body simulation. This code version implements a new on-the-fly production of halo catalogue on the past light cone with continuous time sampling, and the computation of particle and halo displacements are extended up to third-order Lagrangian perturbation theory (LPT), in contrast with previous versions that used Zel'dovich approximation. We run PINOCCHIO on the same initial configuration of a reference N-body simulation, so that the comparison extends to the object-by-object level. We consider haloes at redshifts 0 and 1, using different LPT orders either for halo construction or to compute halo final positions. We compare the clustering properties of PINOCCHIO haloes with those from the simulation by computing the power spectrum and two-point correlation function in real and redshift space (monopole and quadrupole), the bispectrum and the phase difference of halo distributions. We find that 2LPT and 3LPT give noticeable improvement. 3LPT provides the best agreement with N-body when it is used to displace haloes, while 2LPT gives better results for constructing haloes. At the highest orders, linear bias is typically recovered at a few per cent level. In Fourier space and using 3LPT for halo displacements, the halo power spectrum is recovered to within 10 per cent up to kmax ∼ 0.5 h Mpc-1. The results presented in this paper have interesting implications for the generation of large ensemble of mock surveys for the scientific exploitation of data from big surveys.

Selenite sorption by carbonate substituted apatite

DOE PAGES

Moore, Robert C.; Rigali, Mark J.; Brady, Patrick

2016-08-31

The sorption of selenite, SeO 3 2–, by carbonate substituted hydroxylapatite was investigated using batch kinetic and equilibrium experiments. The carbonate substituted hydroxylapatite was prepared by a precipitation method and characterized by SEM, XRD, FT-IR, TGA, BET and solubility measurements. The material is poorly crystalline, contains approximately 9.4% carbonate by weight and has a surface area of 210.2 m 2/g. Uptake of selenite by the carbonated hydroxylapatite was approximately an order of magnitude higher than the uptake by uncarbonated hydroxylapatite reported in the literature. Distribution coefficients, K d, determined for the carbonated apatite in this work ranged from approximately 4200more » to over 14,000 L/kg. A comparison of the results from kinetic experiments performed in this work and literature kinetic data indicates the carbonated apatite synthesized in this study sorbed selenite 23 times faster than uncarbonated hydroxylapatite based on values normalized to the surface area of each material. Furthermore, the results indicate carbonated apatite is a potential candidate for use as a sorbent for pump-and-treat technologies, soil amendments or for use in permeable reactive barriers for the remediation of selenium contaminated sediments and groundwaters.« less

Application of ab initio many-body perturbation theory with Gaussian basis sets to the singlet and triplet excitations of organic molecules

NASA Astrophysics Data System (ADS)

Hamed, Samia; Rangel, Tonatiuh; Bruneval, Fabien; Neaton, Jeffrey B.

Quantitative understanding of charged and neutral excitations of organic molecules is critical in diverse areas of study that include astrophysics and the development of energy technologies that are clean and efficient. The recent use of local basis sets with ab initio many-body perturbation theory in the GW approximation and the Bethe-Saltpeter equation approach (BSE), methods traditionally applied to periodic condensed phases with a plane-wave basis, has opened the door to detailed study of such excitations for molecules, as well as accurate numerical benchmarks. Here, through a series of systematic benchmarks with a Gaussian basis, we report on the extent to which the predictive power and utility of this approach depend critically on interdependent underlying approximations and choices for molecules, including the mean-field starting point (eg optimally-tuned range separated hybrids, pure DFT functionals, and untuned hybrids), the GW scheme, and the Tamm Dancoff approximation. We demonstrate the effects of these choices in the context of Thiels' set while drawing analogies to linear-response time-dependent DFT and making comparisons to best theoretical estimates from higher-order wavefunction-based theories.

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

NASA Astrophysics Data System (ADS)

Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José

2017-05-01

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required.

Fast Electron Correlation Methods for Molecular Clusters without Basis Set Superposition Errors

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

Kamiya, Muneaki; Hirata, So; Valiev, Marat

2008-02-19

Two critical extensions to our fast, accurate, and easy-to-implement binary or ternary interaction method for weakly-interacting molecular clusters [Hirata et al. Mol. Phys. 103, 2255 (2005)] have been proposed, implemented, and applied to water hexamers, hydrogen fluoride chains and rings, and neutral and zwitterionic glycine–water clusters with an excellent result for an initial performance assessment. Our original method included up to two- or three-body Coulomb, exchange, and correlation energies exactly and higher-order Coulomb energies in the dipole–dipole approximation. In this work, the dipole moments are replaced by atom-centered point charges determined so that they reproduce the electrostatic potentials of themore » cluster subunits as closely as possible and also self-consistently with one another in the cluster environment. They have been shown to lead to dramatic improvement in the description of short-range electrostatic potentials not only of large, charge-separated subunits like zwitterionic glycine but also of small subunits. Furthermore, basis set superposition errors (BSSE) known to plague direct evaluation of weak interactions have been eliminated by com-bining the Valiron–Mayer function counterpoise (VMFC) correction with our binary or ternary interaction method in an economical fashion (quadratic scaling n2 with respect to the number of subunits n when n is small and linear scaling when n is large). A new variant of VMFC has also been proposed in which three-body and all higher-order Coulomb effects on BSSE are estimated approximately. The BSSE-corrected ternary interaction method with atom-centered point charges reproduces the VMFC-corrected results of conventional electron correlation calculations within 0.1 kcal/mol. The proposed method is significantly more accurate and also efficient than conventional correlation methods uncorrected of BSSE.« less

Pre/post-closure assessment of groundwater pharmaceutical fate in a wastewater-facility-impacted stream reach.

PubMed

Bradley, Paul M; Barber, Larry B; Clark, Jimmy M; Duris, Joseph W; Foreman, William T; Furlong, Edward T; Givens, Carrie E; Hubbard, Laura E; Hutchinson, Kasey J; Journey, Celeste A; Keefe, Steffanie H; Kolpin, Dana W

2016-10-15

Pharmaceutical contamination of contiguous groundwater is a substantial concern in wastewater-impacted streams, due to ubiquity in effluent, high aqueous mobility, designed bioactivity, and to effluent-driven hydraulic gradients. Wastewater treatment facility (WWTF) closures are rare environmental remediation events; offering unique insights into contaminant persistence, long-term wastewater impacts, and ecosystem recovery processes. The USGS conducted a combined pre/post-closure groundwater assessment adjacent to an effluent-impacted reach of Fourmile Creek, Ankeny, Iowa, USA. Higher surface-water concentrations, consistent surface-water to groundwater concentration gradients, and sustained groundwater detections tens of meters from the stream bank demonstrated the importance of WWTF effluent as the source of groundwater pharmaceuticals as well as the persistence of these contaminants under effluent-driven, pre-closure conditions. The number of analytes (110 total) detected in surface water decreased from 69 prior to closure down to 8 in the first post-closure sampling event approximately 30 d later, with a corresponding 2 order of magnitude decrease in the cumulative concentration of detected analytes. Post-closure cumulative concentrations of detected analytes were approximately 5 times higher in proximal groundwater than in surface water. About 40% of the 21 contaminants detected in a downstream groundwater transect immediately before WWTF closure exhibited rapid attenuation with estimated half-lives on the order of a few days; however, a comparable number exhibited no consistent attenuation during the year-long post-closure assessment. The results demonstrate the potential for effluent-impacted shallow groundwater systems to accumulate pharmaceutical contaminants and serve as long-term residual sources, further increasing the risk of adverse ecological effects in groundwater and the near-stream ecosystem. Published by Elsevier B.V.

The Copernicus Complexio: a high-resolution view of the small-scale Universe

NASA Astrophysics Data System (ADS)

Hellwing, Wojciech A.; Frenk, Carlos S.; Cautun, Marius; Bose, Sownak; Helly, John; Jenkins, Adrian; Sawala, Till; Cytowski, Maciej

2016-04-01

We introduce Copernicus Complexio (COCO), a high-resolution cosmological N-body simulation of structure formation in the ΛCDM model. COCO follows an approximately spherical region of radius ˜17.4 h-1 Mpc embedded in a much larger periodic cube that is followed at lower resolution. The high-resolution volume has a particle mass of 1.135 × 105 h-1 M⊙ (60 times higher than the Millennium-II simulation). COCO gives the dark matter halo mass function over eight orders of magnitude in halo mass; it forms ˜60 haloes of galactic size, each resolved with about 10 million particles. We confirm the power-law character of the subhalo mass function, overline{N}(>μ )∝ μ ^{-s}, down to a reduced subhalo mass Msub/M200 ≡ μ = 10-6, with a best-fitting power-law index, s = 0.94, for hosts of mass = 1012 h-1 M⊙. The concentration-mass relation of COCO haloes deviates from a single power law for masses M200 < afew × 108 h-1 M⊙, where it flattens, in agreement with results by Sanchez-Conde et al. The host mass invariance of the reduced maximum circular velocity function of subhaloes, ν ≡ Vmax/V200, hinted at in previous simulations, is clearly demonstrated over five orders of magnitude in host mass. Similarly, we find that the average, normalized radial distribution of subhaloes is approximately universal (I.e. independent of subhalo mass), as previously suggested by the Aquarius simulations of individual haloes. Finally, we find that at fixed physical subhalo size, subhaloes in lower mass hosts typically have lower central densities than those in higher mass hosts.

Pre/post-closure assessment of groundwater pharmaceutical fate in a wastewater‑facility-impacted stream reach

USGS Publications Warehouse

Bradley, Paul M.; Barber, Larry B.; Clark, Jimmy M.; Duris, Joseph W.; Foreman, William T.; Furlong, Edward T.; Givens, Carrie E.; Hubbard, Laura E.; Hutchinson, Kasey J.; Journey, Celeste A.; Keefe, Steffanie H.; Kolpin, Dana W.

2016-01-01

Pharmaceutical contamination of contiguous groundwater is a substantial concern in wastewater-impacted streams, due to ubiquity in effluent, high aqueous mobility, designed bioactivity, and to effluent-driven hydraulic gradients. Wastewater treatment facility (WWTF) closures are rare environmental remediation events; offering unique insights into contaminant persistence, long-term wastewater impacts, and ecosystem recovery processes. The USGS conducted a combined pre/post-closure groundwater assessment adjacent to an effluent-impacted reach of Fourmile Creek, Ankeny, Iowa, USA. Higher surface-water concentrations, consistent surface-water to groundwater concentration gradients, and sustained groundwater detections tens of meters from the stream bank demonstrated the importance of WWTF effluent as the source of groundwater pharmaceuticals as well as the persistence of these contaminants under effluent-driven, pre-closure conditions. The number of analytes (110 total) detected in surface water decreased from 69 prior to closure down to 8 in the first post-closure sampling event approximately 30 d later, with a corresponding 2 order of magnitude decrease in the cumulative concentration of detected analytes. Post-closure cumulative concentrations of detected analytes were approximately 5 times higher in proximal groundwater than in surface water. About 40% of the 21 contaminants detected in a downstream groundwater transect immediately before WWTF closure exhibited rapid attenuation with estimated half-lives on the order of a few days; however, a comparable number exhibited no consistent attenuation during the year-long post-closure assessment. The results demonstrate the potential for effluent-impacted shallow groundwater systems to accumulate pharmaceutical contaminants and serve as long-term residual sources, further increasing the risk of adverse ecological effects in groundwater and the near-stream ecosystem.

Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid.

PubMed

Mercier Franco, Luís Fernando; Castier, Marcelo; Economou, Ioannis G

2017-12-07

We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.

Numerical solution of the unsteady Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Osher, Stanley J.; Engquist, Bjoern

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Physical Applications of a Simple Approximation of Bessel Functions of Integer Order

ERIC Educational Resources Information Center

Barsan, V.; Cojocaru, S.

2007-01-01

Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…

The arbitrary order mixed mimetic finite difference method for the diffusion equation

DOE PAGES

Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

2016-05-01

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less

On the convergence of difference approximations to scalar conservation laws

NASA Technical Reports Server (NTRS)

Osher, S.; Tadmor, E.

1985-01-01

A unified treatment of explicit in time, two level, second order resolution, total variation diminishing, approximations to scalar conservation laws are presented. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced and results in terms of the latter are obtained. The existence of a cell entropy inequality is discussed and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first order accurate in general. Convergence for total variation diminishing-second order resolution schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

Relaxation approximations to second-order traffic flow models by high-resolution schemes

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

Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.

2015-03-10

A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reportedmore » demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.« less

Possible mechanism to enhance spin-fluctuation-mediated superconductivity in two-dimensional organic conductor

NASA Astrophysics Data System (ADS)

Nonoyama, Yoshito; Maekawa, Yukiko; Kobayashi, Akito; Suzumura, Yoshikazu; Yamada, Jun-ichi

2008-10-01

Mechanisms of superconductivity in quasi-two-dimensional organic conductors have been investigated using an extended Hubbard model by using the transfer energies between BDA-TTP molecules for β-(BDA-TTP)2I3 based on the X-ray experiment data and the extended Hückel calculation. We obtain several mean-field solutions with charge orderings which may represent short-range orderings or low-energy fluctuations in the low-dimensional electronic system. In the pressure-temperature phase diagram, a charge ordered metal state almost degenerates with a normal metal state between an insulating phase with charge ordering and the normal metal phase. Using the random phase approximation (RPA) and the linearized gap equation, the transition temperature of the superconducting state is estimated for the charge-ordered metal state and the normal metal state. It is found that transition temperature of the superconductivity induced by spin fluctuations in the charge-ordered metal state is much higher than that of the normal metal state and that the superconductivity in the charge-ordered metal state is the gapless d-wave. This suggests that the short range charge ordering may also contribute to an enhancement of spin-fluctuation-mediated superconductivity. The difference in the superconducting states between β-(BDA-TTP)2I3 and β-(BDA-TTP)2SbF6 are briefly discussed.