Sample records for accurate analytical approximation

  1. 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.

  2. An Accurate Analytic Approximation for Light Scattering by Non-absorbing Spherical Aerosol Particles

    NASA Astrophysics Data System (ADS)

    Lewis, E. R.

    2017-12-01

    The scattering of light by particles in the atmosphere is a ubiquitous and important phenomenon, with applications to numerous fields of science and technology. The problem of scattering of electromagnetic radiation by a uniform spherical particle can be solved by the method of Mie and Debye as a series of terms depending on the size parameter, x=2πr/λ, and the complex index of refraction, m. However, this solution does not provide insight into the dependence of the scattering on the radius of the particle, the wavelength, or the index of refraction, or how the scattering varies with relative humidity. Van de Hulst demonstrated that the scattering efficiency (the scattering cross section divided by the geometric cross section) of a non-absorbing sphere, over a wide range of particle sizes of atmospheric importance, depends not on x and m separately, but on the quantity 2x(m-1); this is the basis for the anomalous diffraction approximation. Here an analytic approximation for the scattering efficiency of a non-absorbing spherical particle is presented in terms of this new quantity that is accurate over a wide range of particle sizes of atmospheric importance and which readily displays the dependences of the scattering efficiency on particle radius, index of refraction, and wavelength. For an aerosol for which the particle size distribution is parameterized as a gamma function, this approximation also yields analytical results for the scattering coefficient and for the Ångström exponent, with the dependences of scattering properties on wavelength and index of refraction clearly displayed. This approximation provides insight into the dependence of light scattering properties on factors such as relative humidity, readily enables conversion of scattering from one index of refraction to another, and demonstrates the conditions under which the aerosol index (the product of the aerosol optical depth and the Ångström exponent) is a useful proxy for the number of cloud

  3. Partially Coherent Scattering in Stellar Chromospheres. Part 4; Analytic Wing Approximations

    NASA Technical Reports Server (NTRS)

    Gayley, K. G.

    1993-01-01

    Simple analytic expressions are derived to understand resonance-line wings in stellar chromospheres and similar astrophysical plasmas. The results are approximate, but compare well with accurate numerical simulations. The redistribution is modeled using an extension of the partially coherent scattering approximation (PCS) which we term the comoving-frame partially coherent scattering approximation (CPCS). The distinction is made here because Doppler diffusion is included in the coherent/noncoherent decomposition, in a form slightly improved from the earlier papers in this series.

  4. Rapid perfusion quantification using Welch-Satterthwaite approximation and analytical spectral filtering

    NASA Astrophysics Data System (ADS)

    Krishnan, Karthik; Reddy, Kasireddy V.; Ajani, Bhavya; Yalavarthy, Phaneendra K.

    2017-02-01

    CT and MR perfusion weighted imaging (PWI) enable quantification of perfusion parameters in stroke studies. These parameters are calculated from the residual impulse response function (IRF) based on a physiological model for tissue perfusion. The standard approach for estimating the IRF is deconvolution using oscillatory-limited singular value decomposition (oSVD) or Frequency Domain Deconvolution (FDD). FDD is widely recognized as the fastest approach currently available for deconvolution of CT Perfusion/MR PWI. In this work, three faster methods are proposed. The first is a direct (model based) crude approximation to the final perfusion quantities (Blood flow, Blood volume, Mean Transit Time and Delay) using the Welch-Satterthwaite approximation for gamma fitted concentration time curves (CTC). The second method is a fast accurate deconvolution method, we call Analytical Fourier Filtering (AFF). The third is another fast accurate deconvolution technique using Showalter's method, we call Analytical Showalter's Spectral Filtering (ASSF). Through systematic evaluation on phantom and clinical data, the proposed methods are shown to be computationally more than twice as fast as FDD. The two deconvolution based methods, AFF and ASSF, are also shown to be quantitatively accurate compared to FDD and oSVD.

  5. Development and application of accurate analytical models for single active electron potentials

    NASA Astrophysics Data System (ADS)

    Miller, Michelle; Jaron-Becker, Agnieszka; Becker, Andreas

    2015-05-01

    The single active electron (SAE) approximation is a theoretical model frequently employed to study scenarios in which inner-shell electrons may productively be treated as frozen spectators to a physical process of interest, and accurate analytical approximations for these potentials are sought as a useful simulation tool. Density function theory is often used to construct a SAE potential, requiring that a further approximation for the exchange correlation functional be enacted. In this study, we employ the Krieger, Li, and Iafrate (KLI) modification to the optimized-effective-potential (OEP) method to reduce the complexity of the problem to the straightforward solution of a system of linear equations through simple arguments regarding the behavior of the exchange-correlation potential in regions where a single orbital dominates. We employ this method for the solution of atomic and molecular potentials, and use the resultant curve to devise a systematic construction for highly accurate and useful analytical approximations for several systems. Supported by the U.S. Department of Energy (Grant No. DE-FG02-09ER16103), and the U.S. National Science Foundation (Graduate Research Fellowship, Grants No. PHY-1125844 and No. PHY-1068706).

  6. Differential equation based method for accurate approximations in optimization

    NASA Technical Reports Server (NTRS)

    Pritchard, Jocelyn I.; Adelman, Howard M.

    1990-01-01

    This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.

  7. Differential equation based method for accurate approximations in optimization

    NASA Technical Reports Server (NTRS)

    Pritchard, Jocelyn I.; Adelman, Howard M.

    1990-01-01

    A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.

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

    NASA Astrophysics Data System (ADS)

    Turkyilmazoglu, Mustafa

    2016-05-01

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

  9. Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

    NASA Astrophysics Data System (ADS)

    Huo, Mingying; Mengali, Giovanni; Quarta, Alessandro A.

    2018-05-01

    Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.

  10. Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies

    NASA Technical Reports Server (NTRS)

    Mirels, Harold

    1959-01-01

    Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

  11. Comparing numerical and analytic approximate gravitational waveforms

    NASA Astrophysics Data System (ADS)

    Afshari, Nousha; Lovelace, Geoffrey; SXS Collaboration

    2016-03-01

    A direct observation of gravitational waves will test Einstein's theory of general relativity under the most extreme conditions. The Laser Interferometer Gravitational-Wave Observatory, or LIGO, began searching for gravitational waves in September 2015 with three times the sensitivity of initial LIGO. To help Advanced LIGO detect as many gravitational waves as possible, a major research effort is underway to accurately predict the expected waves. In this poster, I will explore how the gravitational waveform produced by a long binary-black-hole inspiral, merger, and ringdown is affected by how fast the larger black hole spins. In particular, I will present results from simulations of merging black holes, completed using the Spectral Einstein Code (black-holes.org/SpEC.html), including some new, long simulations designed to mimic black hole-neutron star mergers. I will present comparisons of the numerical waveforms with analytic approximations.

  12. Analytical approximations to the dynamics of an array of coupled DC SQUIDs

    NASA Astrophysics Data System (ADS)

    Berggren, Susan; Palacios, Antonio

    2014-04-01

    Coupled dynamical systems that operate near the onset of a bifurcation can lead, under certain conditions, to strong signal amplification effects. Over the past years we have studied this generic feature on a wide range of systems, including: magnetic and electric fields sensors, gyroscopic devices, and arrays of loops of superconducting quantum interference devices, also known as SQUIDs. In this work, we consider an array of SQUID loops connected in series as a case study to derive asymptotic analytical approximations to the exact solutions through perturbation analysis. Two approaches are considered. First, a straightforward expansion in which the non-linear parameter related to the inductance of the DC SQUID is treated as the small perturbation parameter. Second, a more accurate procedure that considers the SQUID phase dynamics as non-uniform motion on a circle. This second procedure is readily extended to the series array and it could serve as a mathematical framework to find approximate solutions to related complex systems with high-dimensionality. To the best of our knowledge, an approximate analytical solutions to an array of SQUIDs has not been reported yet in the literature.

  13. How accurate is the Pearson r-from-Z approximation? A Monte Carlo simulation study.

    PubMed

    Hittner, James B; May, Kim

    2012-01-01

    The Pearson r-from-Z approximation estimates the sample correlation (as an effect size measure) from the ratio of two quantities: the standard normal deviate equivalent (Z-score) corresponding to a one-tailed p-value divided by the square root of the total (pooled) sample size. The formula has utility in meta-analytic work when reports of research contain minimal statistical information. Although simple to implement, the accuracy of the Pearson r-from-Z approximation has not been empirically evaluated. To address this omission, we performed a series of Monte Carlo simulations. Results indicated that in some cases the formula did accurately estimate the sample correlation. However, when sample size was very small (N = 10) and effect sizes were small to small-moderate (ds of 0.1 and 0.3), the Pearson r-from-Z approximation was very inaccurate. Detailed figures that provide guidance as to when the Pearson r-from-Z formula will likely yield valid inferences are presented.

  14. Analytical approximations for spiral waves

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

    Löber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald

    2013-12-15

    We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +}more » with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.« less

  15. Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

    NASA Astrophysics Data System (ADS)

    Bervillier, C.; Boisseau, B.; Giacomini, H.

    2008-02-01

    The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).

  16. A Mathematica program for the approximate analytical solution to a nonlinear undamped Duffing equation by a new approximate approach

    NASA Astrophysics Data System (ADS)

    Wu, Dongmei; Wang, Zhongcheng

    2006-03-01

    , we present a new iteration algorithm to calculate the coefficients of the Fourier series. By using this new method, the iteration procedure starts with a(x)cos(ωx)+b(x)sin(ωx), and the accuracy may be improved gradually by determining new coefficients a,a,… will be produced automatically in an one-by-one manner. In all the stage of calculation, we need only to solve a cubic equation. Using this new algorithm, we develop a Mathematica program, which demonstrates following main advantages over the previous HB method: (1) it avoids solving a set of associate nonlinear equations; (2) it is easier to be implemented into a computer program, and produces a highly accurate solution with analytical expression efficiently. It is interesting to find that, generally, for a given set of parameters, a nonlinear Duffing equation can have three independent oscillation modes. For some sets of the parameters, it can have two modes with complex displacement and one with real displacement. But in some cases, it can have three modes, all of them having real displacement. Therefore, we can divide the parameters into two classes, according to the solution property: there is only one mode with real displacement and there are three modes with real displacement. This program should be useful to study the dynamically periodic behavior of a Duffing oscillator and can provide an approximate analytical solution with high-accuracy for testing the error behavior of newly developed numerical methods with a wide range of parameters. Program summaryTitle of program:AnalyDuffing.nb Catalogue identifier:ADWR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWR_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Computer for which the program is designed and others on which it has been tested:the program has been designed for a microcomputer and been tested on the microcomputer. Computers:IBM PC Installations:the address

  17. Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: Analytical approximation

    NASA Astrophysics Data System (ADS)

    Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

    2017-09-01

    Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. Lü, A. Perkins, C. Pope, and K. Stelle [Phys. Rev. Lett. 114, 171601 (2015), 10.1103/PhysRevLett.114.171601] found a numerical solution describing a spherically symmetric non-Schwarzschild asymptotically flat black hole in Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent this numerical solution in the analytical form, which is accurate not only near the event horizon or far from the black hole, but in the whole space. Thereby, the obtained analytical form of the metric allows one to study easily all the further properties of the black hole, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representation can serve in the same way as an exact solution.

  18. Approximated analytical solution to an Ebola optimal control problem

    NASA Astrophysics Data System (ADS)

    Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.

    2016-11-01

    An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.

  19. Approximate analytic expression for the Skyrmions crystal

    NASA Astrophysics Data System (ADS)

    Grandi, Nicolás; Sturla, Mauricio

    2018-01-01

    We find approximate solutions for the two-dimensional nonlinear Σ-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

  20. 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.

  1. Analytical approximations to seawater optical phase functions of scattering

    NASA Astrophysics Data System (ADS)

    Haltrin, Vladimir I.

    2004-11-01

    This paper proposes a number of analytical approximations to the classic and recently measured seawater light scattering phase functions. The three types of analytical phase functions are derived: individual representations for 15 Petzold, 41 Mankovsky, and 91 Gulf of Mexico phase functions; collective fits to Petzold phase functions; and analytical representations that take into account dependencies between inherent optical properties of seawater. The proposed phase functions may be used for problems of radiative transfer, remote sensing, visibility and image propagation in natural waters of various turbidity.

  2. Analytical Derivation and Experimental Evaluation of Short-Bearing Approximation for Full Journal Bearing

    NASA Technical Reports Server (NTRS)

    Dubois, George B; Ocvirk, Fred W

    1953-01-01

    An approximate analytical solution including the effect of end leakage from the oil film of short plain bearings is presented because of the importance of endwise flow in sleeve bearings of the short lengths commonly used. The analytical approximation is supported by experimental data, resulting in charts which facilitate analysis of short plain bearings. The analytical approximation includes the endwise flow and that part of the circumferential flow which is related to surface velocity and film thickness but neglects the effect of film pressure on the circumferential flow. In practical use, this approximation applies best to bearings having a length-diameter ratio up to 1, and the effects of elastic deflection, inlet oil pressure, and changes of clearance with temperature minimize the relative importance of the neglected term. The analytical approximation was found to be an extension of a little-known pressure-distribution function originally proposed by Michell and Cardullo.

  3. General properties and analytical approximations of photorefractive solitons

    NASA Astrophysics Data System (ADS)

    Geisler, A.; Homann, F.; Schmidt, H.-J.

    2004-08-01

    We investigate general properties of spatial 1-dimensional bright photorefractive solitons and discuss various analytical approximations for the soliton profile and the half width, both depending on an intensity parameter r. The case of dark solitons is also briefly addressed.

  4. Accurate mass measurements and their appropriate use for reliable analyte identification.

    PubMed

    Godfrey, A Ruth; Brenton, A Gareth

    2012-09-01

    Accurate mass instrumentation is becoming increasingly available to non-expert users. This data can be mis-used, particularly for analyte identification. Current best practice in assigning potential elemental formula for reliable analyte identification has been described with modern informatic approaches to analyte elucidation, including chemometric characterisation, data processing and searching using facilities such as the Chemical Abstracts Service (CAS) Registry and Chemspider.

  5. Analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric

    NASA Astrophysics Data System (ADS)

    Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

    2017-09-01

    We construct an analytical approximation for the numerical black hole metric of P. Kanti et al. [Phys. Rev. D 54, 5049 (1996), 10.1103/PhysRevD.54.5049] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a compactified radial coordinate, used here, converges slowly when the dilaton coupling approaches its extremal values, but for a black hole far from the extremal state, the analytical formula has a maximal relative error of a fraction of one percent already within the third order of the continued fraction expansion. The suggested analytical representation of the numerical black hole metric is relatively compact and a good approximation in the whole space outside the black hole event horizon. Therefore, it can serve in the same way as an exact solution when analyzing particles' motion, perturbations, quasinormal modes, Hawking radiation, accreting disks, and many other problems in the vicinity of a black hole. In addition, we construct the approximate analytical expression for the dilaton field.

  6. Testing approximations for non-linear gravitational clustering

    NASA Technical Reports Server (NTRS)

    Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.

    1993-01-01

    The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

  7. An analytic, approximate method for modeling steady, three-dimensional flow to partially penetrating wells

    NASA Astrophysics Data System (ADS)

    Bakker, Mark

    2001-05-01

    An analytic, approximate solution is derived for the modeling of three-dimensional flow to partially penetrating wells. The solution is written in terms of a correction on the solution for a fully penetrating well and is obtained by dividing the aquifer up, locally, in a number of aquifer layers. The resulting system of differential equations is solved by application of the theory for multiaquifer flow. The presented approach has three major benefits. First, the solution may be applied to any groundwater model that can simulate flow to a fully penetrating well; the solution may be superimposed onto the solution for the fully penetrating well to simulate the local three-dimensional drawdown and flow field. Second, the approach is applicable to isotropic, anisotropic, and stratified aquifers and to both confined and unconfined flow. Third, the solution extends over a small area around the well only; outside this area the three-dimensional effect of the partially penetrating well is negligible, and no correction to the fully penetrating well is needed. A number of comparisons are made to existing three-dimensional, analytic solutions, including radial confined and unconfined flow and a well in a uniform flow field. It is shown that a subdivision in three layers is accurate for many practical cases; very accurate solutions are obtained with more layers.

  8. An approximate analytical solution for interlaminar stresses in angle-ply laminates

    NASA Technical Reports Server (NTRS)

    Rose, Cheryl A.; Herakovich, Carl T.

    1991-01-01

    An improved approximate analytical solution for interlaminar stresses in finite width, symmetric, angle-ply laminated coupons subjected to axial loading is presented. The solution is based upon statically admissible stress fields which take into consideration local property mismatch effects and global equilibrium requirements. Unknown constants in the admissible stress states are determined through minimization of the complementary energy. Typical results are presented for through-the-thickness and interlaminar stress distributions for angle-ply laminates. It is shown that the results represent an improved approximate analytical solution for interlaminar stresses.

  9. Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

    NASA Astrophysics Data System (ADS)

    Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad

    2017-12-01

    A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

  10. Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

    NASA Astrophysics Data System (ADS)

    Lau, Chun Sing

    This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in

  11. Fast and Accurate Approximation to Significance Tests in Genome-Wide Association Studies

    PubMed Central

    Zhang, Yu; Liu, Jun S.

    2011-01-01

    Genome-wide association studies commonly involve simultaneous tests of millions of single nucleotide polymorphisms (SNP) for disease association. The SNPs in nearby genomic regions, however, are often highly correlated due to linkage disequilibrium (LD, a genetic term for correlation). Simple Bonferonni correction for multiple comparisons is therefore too conservative. Permutation tests, which are often employed in practice, are both computationally expensive for genome-wide studies and limited in their scopes. We present an accurate and computationally efficient method, based on Poisson de-clumping heuristics, for approximating genome-wide significance of SNP associations. Compared with permutation tests and other multiple comparison adjustment approaches, our method computes the most accurate and robust p-value adjustments for millions of correlated comparisons within seconds. We demonstrate analytically that the accuracy and the efficiency of our method are nearly independent of the sample size, the number of SNPs, and the scale of p-values to be adjusted. In addition, our method can be easily adopted to estimate false discovery rate. When applied to genome-wide SNP datasets, we observed highly variable p-value adjustment results evaluated from different genomic regions. The variation in adjustments along the genome, however, are well conserved between the European and the African populations. The p-value adjustments are significantly correlated with LD among SNPs, recombination rates, and SNP densities. Given the large variability of sequence features in the genome, we further discuss a novel approach of using SNP-specific (local) thresholds to detect genome-wide significant associations. This article has supplementary material online. PMID:22140288

  12. Analytic approximations to the modon dispersion relation. [in oceanography

    NASA Technical Reports Server (NTRS)

    Boyd, J. P.

    1981-01-01

    Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

  13. Accurate analytical modeling of junctionless DG-MOSFET by green's function approach

    NASA Astrophysics Data System (ADS)

    Nandi, Ashutosh; Pandey, Nilesh

    2017-11-01

    An accurate analytical model of Junctionless double gate MOSFET (JL-DG-MOSFET) in the subthreshold regime of operation is developed in this work using green's function approach. The approach considers 2-D mixed boundary conditions and multi-zone techniques to provide an exact analytical solution to 2-D Poisson's equation. The Fourier coefficients are calculated correctly to derive the potential equations that are further used to model the channel current and subthreshold slope of the device. The threshold voltage roll-off is computed from parallel shifts of Ids-Vgs curves between the long channel and short-channel devices. It is observed that the green's function approach of solving 2-D Poisson's equation in both oxide and silicon region can accurately predict channel potential, subthreshold current (Isub), threshold voltage (Vt) roll-off and subthreshold slope (SS) of both long & short channel devices designed with different doping concentrations and higher as well as lower tsi/tox ratio. All the analytical model results are verified through comparisons with TCAD Sentaurus simulation results. It is observed that the model matches quite well with TCAD device simulations.

  14. Approximate analytical modeling of leptospirosis infection

    NASA Astrophysics Data System (ADS)

    Ismail, Nur Atikah; Azmi, Amirah; Yusof, Fauzi Mohamed; Ismail, Ahmad Izani

    2017-11-01

    Leptospirosis is an infectious disease carried by rodents which can cause death in humans. The disease spreads directly through contact with feces, urine or through bites of infected rodents and indirectly via water contaminated with urine and droppings from them. Significant increase in the number of leptospirosis cases in Malaysia caused by the recent severe floods were recorded during heavy rainfall season. Therefore, to understand the dynamics of leptospirosis infection, a mathematical model based on fractional differential equations have been developed and analyzed. In this paper an approximate analytical method, the multi-step Laplace Adomian decomposition method, has been used to conduct numerical simulations so as to gain insight on the spread of leptospirosis infection.

  15. Precise analytic approximations for the Bessel function J1 (x)

    NASA Astrophysics Data System (ADS)

    Maass, Fernando; Martin, Pablo

    2018-03-01

    Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.

  16. Petermann I and II spot size: Accurate semi analytical description involving Nelder-Mead method of nonlinear unconstrained optimization and three parameter fundamental modal field

    NASA Astrophysics Data System (ADS)

    Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal

    2013-01-01

    A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.

  17. Analytical approximation of the InGaZnO thin-film transistors surface potential

    NASA Astrophysics Data System (ADS)

    Colalongo, Luigi

    2016-10-01

    Surface-potential-based mathematical models are among the most accurate and physically based compact models of thin-film transistors, and in turn of indium gallium zinc oxide TFTs, available today. However, the need of iterative computations of the surface potential limits their computational efficiency and diffusion in CAD applications. The existing closed-form approximations of the surface potential are based on regional approximations and empirical smoothing functions that could result not accurate enough in particular to model transconductances and transcapacitances. In this work we present an extremely accurate (in the range of nV) and computationally efficient non-iterative approximation of the surface potential that can serve as a basis for advanced surface-potential-based indium gallium zinc oxide TFTs models.

  18. Analytical approximate solutions for a general class of nonlinear delay differential equations.

    PubMed

    Căruntu, Bogdan; Bota, Constantin

    2014-01-01

    We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

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

    NASA Astrophysics Data System (ADS)

    Poirier, M.

    2015-06-01

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

  20. Approximate analytical solution for induction heating of solid cylinders

    DOE PAGES

    Jankowski, Todd Andrew; Pawley, Norma Helen; Gonzales, Lindsey Michal; ...

    2015-10-20

    An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit, and formore » the frequency response of a variable frequency power supply driving the tank circuit. The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. In conclusion, the expressions developed here provide physical insight into observations made during load signature analysis of induction heating.« less

  1. Analytical approximations to the Hotelling trace for digital x-ray detectors

    NASA Astrophysics Data System (ADS)

    Clarkson, Eric; Pineda, Angel R.; Barrett, Harrison H.

    2001-06-01

    The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

  2. Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models

    NASA Astrophysics Data System (ADS)

    Luther, K.; Haitjema, H. M.

    2000-04-01

    We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.

  3. 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.

  4. 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.

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

    NASA Astrophysics Data System (ADS)

    Kassem, Ayman Hamdy

    1998-09-01

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

  6. An analytic model for accurate spring constant calibration of rectangular atomic force microscope cantilevers.

    PubMed

    Li, Rui; Ye, Hongfei; Zhang, Weisheng; Ma, Guojun; Su, Yewang

    2015-10-29

    Spring constant calibration of the atomic force microscope (AFM) cantilever is of fundamental importance for quantifying the force between the AFM cantilever tip and the sample. The calibration within the framework of thin plate theory undoubtedly has a higher accuracy and broader scope than that within the well-established beam theory. However, thin plate theory-based accurate analytic determination of the constant has been perceived as an extremely difficult issue. In this paper, we implement the thin plate theory-based analytic modeling for the static behavior of rectangular AFM cantilevers, which reveals that the three-dimensional effect and Poisson effect play important roles in accurate determination of the spring constants. A quantitative scaling law is found that the normalized spring constant depends only on the Poisson's ratio, normalized dimension and normalized load coordinate. Both the literature and our refined finite element model validate the present results. The developed model is expected to serve as the benchmark for accurate calibration of rectangular AFM cantilevers.

  7. 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.

  8. Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

    NASA Astrophysics Data System (ADS)

    Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

    2017-10-01

    Over the recent decades, a number of fast approximate solutions of Lippmann-Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

  9. Algorithms and analytical solutions for rapidly approximating long-term dispersion from line and area sources

    NASA Astrophysics Data System (ADS)

    Barrett, Steven R. H.; Britter, Rex E.

    Predicting long-term mean pollutant concentrations in the vicinity of airports, roads and other industrial sources are frequently of concern in regulatory and public health contexts. Many emissions are represented geometrically as ground-level line or area sources. Well developed modelling tools such as AERMOD and ADMS are able to model dispersion from finite (i.e. non-point) sources with considerable accuracy, drawing upon an up-to-date understanding of boundary layer behaviour. Due to mathematical difficulties associated with line and area sources, computationally expensive numerical integration schemes have been developed. For example, some models decompose area sources into a large number of line sources orthogonal to the mean wind direction, for which an analytical (Gaussian) solution exists. Models also employ a time-series approach, which involves computing mean pollutant concentrations for every hour over one or more years of meteorological data. This can give rise to computer runtimes of several days for assessment of a site. While this may be acceptable for assessment of a single industrial complex, airport, etc., this level of computational cost precludes national or international policy assessments at the level of detail available with dispersion modelling. In this paper, we extend previous work [S.R.H. Barrett, R.E. Britter, 2008. Development of algorithms and approximations for rapid operational air quality modelling. Atmospheric Environment 42 (2008) 8105-8111] to line and area sources. We introduce approximations which allow for the development of new analytical solutions for long-term mean dispersion from line and area sources, based on hypergeometric functions. We describe how these solutions can be parameterized from a single point source run from an existing advanced dispersion model, thereby accounting for all processes modelled in the more costly algorithms. The parameterization method combined with the analytical solutions for long-term mean

  10. Radiative transfer in falling snow: A two-stream approximation

    NASA Astrophysics Data System (ADS)

    Koh, Gary

    1989-04-01

    Light transmission measurements through falling snow have produced results unexplainable by single scattering arguments. A two-stream approximation to radiative transfer is used to derive an analytical expression that describes the effects of multiple scattering as a function of the snow optical depth and the snow asymmetry parameter. The approximate solution is simple and it may be as accurate as the exact solution for describing the transmission measurements within the limits of experimental uncertainties.

  11. An approximate analytical solution for describing surface runoff and sediment transport over hillslope

    NASA Astrophysics Data System (ADS)

    Tao, Wanghai; Wang, Quanjiu; Lin, Henry

    2018-03-01

    Soil and water loss from farmland causes land degradation and water pollution, thus continued efforts are needed to establish mathematical model for quantitative analysis of relevant processes and mechanisms. In this study, an approximate analytical solution has been developed for overland flow model and sediment transport model, offering a simple and effective means to predict overland flow and erosion under natural rainfall conditions. In the overland flow model, the flow regime was considered to be transitional with the value of parameter β (in the kinematic wave model) approximately two. The change rate of unit discharge with distance was assumed to be constant and equal to the runoff rate at the outlet of the plane. The excess rainfall was considered to be constant under uniform rainfall conditions. The overland flow model developed can be further applied to natural rainfall conditions by treating excess rainfall intensity as constant over a small time interval. For the sediment model, the recommended values of the runoff erosion calibration constant (cr) and the splash erosion calibration constant (cf) have been given in this study so that it is easier to use the model. These recommended values are 0.15 and 0.12, respectively. Comparisons with observed results were carried out to validate the proposed analytical solution. The results showed that the approximate analytical solution developed in this paper closely matches the observed data, thus providing an alternative method of predicting runoff generation and sediment yield, and offering a more convenient method of analyzing the quantitative relationships between variables. Furthermore, the model developed in this study can be used as a theoretical basis for developing runoff and erosion control methods.

  12. An improved thin film approximation to accurately determine the optical conductivity of graphene from infrared transmittance

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

    Weber, J. W.; Bol, A. A.; Sanden, M. C. M. van de

    2014-07-07

    This work presents an improved thin film approximation to extract the optical conductivity from infrared transmittance in a simple yet accurate way. This approximation takes into account the incoherent reflections from the backside of the substrate. These reflections are shown to have a significant effect on the extracted optical conductivity and hence on derived parameters as carrier mobility and density. By excluding the backside reflections, the error for these parameters for typical chemical vapor deposited (CVD) graphene on a silicon substrate can be as high as 17% and 45% for the carrier mobility and density, respectively. For the mid- andmore » near-infrared, the approximation can be simplified such that the real part of the optical conductivity is extracted without the need for a parameterization of the optical conductivity. This direct extraction is shown for Fourier transform infrared (FTIR) transmittance measurements of CVD graphene on silicon in the photon energy range of 370–7000 cm{sup −1}. From the real part of the optical conductivity, the carrier density, mobility, and number of graphene layers are determined but also residue, originating from the graphene transfer, is detected. FTIR transmittance analyzed with the improved thin film approximation is shown to be a non-invasive, easy, and accurate measurement and analysis method for assessing the quality of graphene and can be used for other 2-D materials.« less

  13. Direct application of Padé approximant for solving nonlinear differential equations.

    PubMed

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

    2014-01-01

    This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

  14. Approximate analytical description of the elastic strain field due to an inclusion in a continuous medium with cubic anisotropy

    NASA Astrophysics Data System (ADS)

    Nenashev, A. V.; Koshkarev, A. A.; Dvurechenskii, A. V.

    2018-03-01

    We suggest an approach to the analytical calculation of the strain distribution due to an inclusion in elastically anisotropic media for the case of cubic anisotropy. The idea consists in the approximate reduction of the anisotropic problem to a (simpler) isotropic problem. This gives, for typical semiconductors, an improvement in accuracy by an order of magnitude, compared to the isotropic approximation. Our method allows using, in the case of elastically anisotropic media, analytical solutions obtained for isotropic media only, such as analytical formulas for the strain due to polyhedral inclusions. The present work substantially extends the applicability of analytical results, making them more suitable for describing real systems, such as epitaxial quantum dots.

  15. 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

  16. 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.

  17. A fast algorithm for determining bounds and accurate approximate p-values of the rank product statistic for replicate experiments.

    PubMed

    Heskes, Tom; Eisinga, Rob; Breitling, Rainer

    2014-11-21

    The rank product method is a powerful statistical technique for identifying differentially expressed molecules in replicated experiments. A critical issue in molecule selection is accurate calculation of the p-value of the rank product statistic to adequately address multiple testing. Both exact calculation and permutation and gamma approximations have been proposed to determine molecule-level significance. These current approaches have serious drawbacks as they are either computationally burdensome or provide inaccurate estimates in the tail of the p-value distribution. We derive strict lower and upper bounds to the exact p-value along with an accurate approximation that can be used to assess the significance of the rank product statistic in a computationally fast manner. The bounds and the proposed approximation are shown to provide far better accuracy over existing approximate methods in determining tail probabilities, with the slightly conservative upper bound protecting against false positives. We illustrate the proposed method in the context of a recently published analysis on transcriptomic profiling performed in blood. We provide a method to determine upper bounds and accurate approximate p-values of the rank product statistic. The proposed algorithm provides an order of magnitude increase in throughput as compared with current approaches and offers the opportunity to explore new application domains with even larger multiple testing issue. The R code is published in one of the Additional files and is available at http://www.ru.nl/publish/pages/726696/rankprodbounds.zip .

  18. Approximate analytic solutions to coupled nonlinear Dirac equations

    DOE PAGES

    Khare, Avinash; Cooper, Fred; Saxena, Avadh

    2017-01-30

    Here, we consider the coupled nonlinear Dirac equations (NLDEs) in 1+11+1 dimensions with scalar–scalar self-interactions g 1 2/2(more » $$\\bar{ψ}$$ψ) 2 + g 2 2/2($$\\bar{Φ}$$Φ) 2 + g 2 3($$\\bar{ψ}$$ψ)($$\\bar{Φ}$$Φ) as well as vector–vector interactions g 1 2/2($$\\bar{ψ}$$γμψ)($$\\bar{ψ}$$γμψ) + g 2 2/2($$\\bar{Φ}$$γμΦ)($$\\bar{Φ}$$γμΦ) + g 2 3($$\\bar{ψ}$$γμψ)($$\\bar{Φ}$$γμΦ). Writing the two components of the assumed rest frame solution of the coupled NLDE equations in the form ψ=e –iω1tR 1cosθ,R 1sinθΦ=e –iω2tR 2cosη,R 2sinη, and assuming that θ(x),η(x) have the same functional form they had when g3 = 0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri(x) which are valid for small values of g 3 2/g 2 2 and g 3 2/g 1 2. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ±∞.« less

  19. Approximate analytic solutions to coupled nonlinear Dirac equations

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

    Khare, Avinash; Cooper, Fred; Saxena, Avadh

    Here, we consider the coupled nonlinear Dirac equations (NLDEs) in 1+11+1 dimensions with scalar–scalar self-interactions g 1 2/2(more » $$\\bar{ψ}$$ψ) 2 + g 2 2/2($$\\bar{Φ}$$Φ) 2 + g 2 3($$\\bar{ψ}$$ψ)($$\\bar{Φ}$$Φ) as well as vector–vector interactions g 1 2/2($$\\bar{ψ}$$γμψ)($$\\bar{ψ}$$γμψ) + g 2 2/2($$\\bar{Φ}$$γμΦ)($$\\bar{Φ}$$γμΦ) + g 2 3($$\\bar{ψ}$$γμψ)($$\\bar{Φ}$$γμΦ). Writing the two components of the assumed rest frame solution of the coupled NLDE equations in the form ψ=e –iω1tR 1cosθ,R 1sinθΦ=e –iω2tR 2cosη,R 2sinη, and assuming that θ(x),η(x) have the same functional form they had when g3 = 0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri(x) which are valid for small values of g 3 2/g 2 2 and g 3 2/g 1 2. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ±∞.« less

  20. Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

    NASA Astrophysics Data System (ADS)

    Poungthong, P.; Saengow, C.; Giacomin, A. J.; Kolitawong, C.; Merger, D.; Wilhelm, M.

    2018-04-01

    Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the inexact form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. The recent advent of exact solutions in LAOS presents an opportunity to identify accurate and useful Padé approximants. For this identification, we replace the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We uncover the most accurate and useful approximant, the [3,4] approximant, and then test its accuracy against the exact solution [C. Saengow and A. J. Giacomin, "Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow," Phys. Fluids 29, 121601 (2017)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map it onto the Pipkin space. Our two applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene and on dissolved polyisobutylene in isobutylene oligomer.

  1. 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.

  2. Realistic Analytical Polyhedral MRI Phantoms

    PubMed Central

    Ngo, Tri M.; Fung, George S. K.; Han, Shuo; Chen, Min; Prince, Jerry L.; Tsui, Benjamin M. W.; McVeigh, Elliot R.; Herzka, Daniel A.

    2015-01-01

    Purpose Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing 3D analytical phantoms are unable to accurately model shapes of biomedical interest. It is demonstrated that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedical shapes. Theory The derivations of the Fourier transform of a polygon and polyhedron are presented. Methods The Fourier transform of a polyhedron was implemented and its accuracy in representing faceted and smooth surfaces was characterized. Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D/2D MRI acquisitions was described. Results Using polyhedra, the Fourier transform of faceted shapes can be computed to within machine precision. Smooth surfaces can be approximated with increasing accuracy by increasing the number of facets in the polyhedron; the additional accumulated numerical imprecision of the Fourier transform of polyhedra with many faces remained small. Simulations of 3D/2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing as compared to equivalent voxelized/rasterized phantoms. Conclusion Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. PMID:26479724

  3. APPROXIMATE AND ANALYTICAL SOLUTIONS FOR SOLUTE TRANSPORT FROM AN INJECTION WELL INTO A SINGLE FRACTURE

    EPA Science Inventory

    In dealing with problems related to land-based nuclear waste management, a number of analytical and approximate solutions were developed to quantify radionuclide transport through fractures contained in the porous formation. t has been reported that by treating the radioactive de...

  4. Communication: Analytic continuation of the virial series through the critical point using parametric approximants.

    PubMed

    Barlow, Nathaniel S; Schultz, Andrew J; Weinstein, Steven J; Kofke, David A

    2015-08-21

    The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.

  5. Approximate analytical solutions in the analysis of thin elastic plates

    NASA Astrophysics Data System (ADS)

    Goloskokov, Dmitriy P.; Matrosov, Alexander V.

    2018-05-01

    Two approaches to the construction of approximate analytical solutions for bending of a rectangular thin plate are presented: the superposition method based on the method of initial functions (MIF) and the one built using the Green's function in the form of orthogonal series. Comparison of two approaches is carried out by analyzing a square plate clamped along its contour. Behavior of the moment and the shear force in the neighborhood of the corner points is discussed. It is shown that both solutions give identical results at all points of the plate except for the neighborhoods of the corner points. There are differences in the values of bending moments and generalized shearing forces in the neighborhoods of the corner points.

  6. Analytical approximations for effective relative permeability in the capillary limit

    NASA Astrophysics Data System (ADS)

    Rabinovich, Avinoam; Li, Boxiao; Durlofsky, Louis J.

    2016-10-01

    We present an analytical method for calculating two-phase effective relative permeability, krjeff, where j designates phase (here CO2 and water), under steady state and capillary-limit assumptions. These effective relative permeabilities may be applied in experimental settings and for upscaling in the context of numerical flow simulations, e.g., for CO2 storage. An exact solution for effective absolute permeability, keff, in two-dimensional log-normally distributed isotropic permeability (k) fields is the geometric mean. We show that this does not hold for krjeff since log normality is not maintained in the capillary-limit phase permeability field (Kj=k·krj) when capillary pressure, and thus the saturation field, is varied. Nevertheless, the geometric mean is still shown to be suitable for approximating krjeff when the variance of ln⁡k is low. For high-variance cases, we apply a correction to the geometric average gas effective relative permeability using a Winsorized mean, which neglects large and small Kj values symmetrically. The analytical method is extended to anisotropically correlated log-normal permeability fields using power law averaging. In these cases, the Winsorized mean treatment is applied to the gas curves for cases described by negative power law exponents (flow across incomplete layers). The accuracy of our analytical expressions for krjeff is demonstrated through extensive numerical tests, using low-variance and high-variance permeability realizations with a range of correlation structures. We also present integral expressions for geometric-mean and power law average krjeff for the systems considered, which enable derivation of closed-form series solutions for krjeff without generating permeability realizations.

  7. Analytical approximation of a distorted reflector surface defined by a discrete set of points

    NASA Technical Reports Server (NTRS)

    Acosta, Roberto J.; Zaman, Afroz A.

    1988-01-01

    Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

  8. Branch and bound algorithm for accurate estimation of analytical isotropic bidirectional reflectance distribution function models.

    PubMed

    Yu, Chanki; Lee, Sang Wook

    2016-05-20

    We present a reliable and accurate global optimization framework for estimating parameters of isotropic analytical bidirectional reflectance distribution function (BRDF) models. This approach is based on a branch and bound strategy with linear programming and interval analysis. Conventional local optimization is often very inefficient for BRDF estimation since its fitting quality is highly dependent on initial guesses due to the nonlinearity of analytical BRDF models. The algorithm presented in this paper employs L1-norm error minimization to estimate BRDF parameters in a globally optimal way and interval arithmetic to derive our feasibility problem and lower bounding function. Our method is developed for the Cook-Torrance model but with several normal distribution functions such as the Beckmann, Berry, and GGX functions. Experiments have been carried out to validate the presented method using 100 isotropic materials from the MERL BRDF database, and our experimental results demonstrate that the L1-norm minimization provides a more accurate and reliable solution than the L2-norm minimization.

  9. Using radiance predicted by the P3 approximation in a spherical geometry to predict tissue optical properties

    NASA Astrophysics Data System (ADS)

    Dickey, Dwayne J.; Moore, Ronald B.; Tulip, John

    2001-01-01

    For photodynamic therapy of solid tumors, such as prostatic carcinoma, to be achieved, an accurate model to predict tissue parameters and light dose must be found. Presently, most analytical light dosimetry models are fluence based and are not clinically viable for tissue characterization. Other methods of predicting optical properties, such as Monet Carlo, are accurate but far too time consuming for clinical application. However, radiance predicted by the P3-Approximation, an anaylitical solution to the transport equation, may be a viable and accurate alternative. The P3-Approximation accurately predicts optical parameters in intralipid/methylene blue based phantoms in a spherical geometry. The optical parameters furnished by the radiance, when introduced into fluence predicted by both P3- Approximation and Grosjean Theory, correlate well with experimental data. The P3-Approximation also predicts the optical properties of prostate tissue, agreeing with documented optical parameters. The P3-Approximation could be the clinical tool necessary to facilitate PDT of solid tumors because of the limited number of invasive measurements required and the speed in which accurate calculations can be performed.

  10. Beyond mean-field approximations for accurate and computationally efficient models of on-lattice chemical kinetics

    NASA Astrophysics Data System (ADS)

    Pineda, M.; Stamatakis, M.

    2017-07-01

    Modeling the kinetics of surface catalyzed reactions is essential for the design of reactors and chemical processes. The majority of microkinetic models employ mean-field approximations, which lead to an approximate description of catalytic kinetics by assuming spatially uncorrelated adsorbates. On the other hand, kinetic Monte Carlo (KMC) methods provide a discrete-space continuous-time stochastic formulation that enables an accurate treatment of spatial correlations in the adlayer, but at a significant computation cost. In this work, we use the so-called cluster mean-field approach to develop higher order approximations that systematically increase the accuracy of kinetic models by treating spatial correlations at a progressively higher level of detail. We further demonstrate our approach on a reduced model for NO oxidation incorporating first nearest-neighbor lateral interactions and construct a sequence of approximations of increasingly higher accuracy, which we compare with KMC and mean-field. The latter is found to perform rather poorly, overestimating the turnover frequency by several orders of magnitude for this system. On the other hand, our approximations, while more computationally intense than the traditional mean-field treatment, still achieve tremendous computational savings compared to KMC simulations, thereby opening the way for employing them in multiscale modeling frameworks.

  11. Spline methods for approximating quantile functions and generating random samples

    NASA Technical Reports Server (NTRS)

    Schiess, J. R.; Matthews, C. G.

    1985-01-01

    Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.

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

    PubMed

    Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning

    2016-11-21

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

  13. A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices

    NASA Astrophysics Data System (ADS)

    AlQurashi, Ahmed; Selvakumar, C. R.

    2018-06-01

    There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices.

  14. 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

  15. Construction and accuracy of partial differential equation approximations to the chemical master equation.

    PubMed

    Grima, Ramon

    2011-11-01

    The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

  16. Double power series method for approximating cosmological perturbations

    NASA Astrophysics Data System (ADS)

    Wren, Andrew J.; Malik, Karim A.

    2017-04-01

    We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

  17. Analytical mass formula and nuclear surface properties in the ETF approximation. Part I: symmetric nuclei

    NASA Astrophysics Data System (ADS)

    Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

    2016-08-01

    The problem of determination of nuclear surface energy is addressed within the framework of the extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. In this first paper, we consider the case of symmetric nuclei. In this situation, the ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed and it is shown that they cannot be deduced simply from the local part of the functional, as it was suggested in previous works.

  18. Analytic model for the long-term evolution of circular Earth satellite orbits including lunar node regression

    NASA Astrophysics Data System (ADS)

    Zhu, Ting-Lei; Zhao, Chang-Yin; Zhang, Ming-Jiang

    2017-04-01

    This paper aims to obtain an analytic approximation to the evolution of circular orbits governed by the Earth's J2 and the luni-solar gravitational perturbations. Assuming that the lunar orbital plane coincides with the ecliptic plane, Allan and Cook (Proc. R. Soc. A, Math. Phys. Eng. Sci. 280(1380):97, 1964) derived an analytic solution to the orbital plane evolution of circular orbits. Using their result as an intermediate solution, we establish an approximate analytic model with lunar orbital inclination and its node regression be taken into account. Finally, an approximate analytic expression is derived, which is accurate compared to the numerical results except for the resonant cases when the period of the reference orbit approximately equals the integer multiples (especially 1 or 2 times) of lunar node regression period.

  19. Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

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

    Bonatsos, Dennis; Karampagia, S.; Casten, R. F.

    2011-05-15

    Using a contraction of the SU(3) algebra to the algebra of the rigid rotator in the large-boson-number limit of the interacting boson approximation (IBA) model, a line is found inside the symmetry triangle of the IBA, along which the SU(3) symmetry is preserved. The line extends from the SU(3) vertex to near the critical line of the first-order shape/phase transition separating the spherical and prolate deformed phases, and it lies within the Alhassid-Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices in the midst of chaotic regions. In addition to providing an explanation formore » the existence of the arc of regularity, the present line represents an example of an analytically determined approximate symmetry in the interior of the symmetry triangle of the IBA. The method is applicable to algebraic models possessing subalgebras amenable to contraction. This condition is equivalent to algebras in which the equilibrium ground state and its rotational band become energetically isolated from intrinsic excitations, as typified by deformed solutions to the IBA for large numbers of valence nucleons.« less

  20. 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.

  1. Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

    NASA Technical Reports Server (NTRS)

    Gnoffo, Peter A.

    2006-01-01

    Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

  2. An improved 3D MoF method based on analytical partial derivatives

    NASA Astrophysics Data System (ADS)

    Chen, Xiang; Zhang, Xiong

    2016-12-01

    MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

  3. 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

  4. Compressible Flow in Front of an Axisymmetric Blunt Object: Analytic Approximation and Astrophysical Implications

    NASA Astrophysics Data System (ADS)

    Keshet, Uri; Naor, Yossi

    2016-10-01

    Compressible flows around blunt objects have diverse applications, but current analytic treatments are inaccurate and limited to narrow parameter regimes. We show that the gas-dynamic flow in front of an axisymmetric blunt body is accurately derived analytically using a low order expansion of the perpendicular gradients in terms of the parallel velocity. This reproduces both subsonic and supersonic flows measured and simulated for a sphere, including the transonic regime and the bow shock properties. Some astrophysical implications are outlined, in particular for planets in the solar wind and for clumps and bubbles in the intergalactic medium. The bow shock standoff distance normalized by the obstacle curvature is ∼ 2/(3g) in the strong shock limit, where g is the compression ratio. For a subsonic Mach number M approaching unity, the thickness δ of an initially weak, draped magnetic layer is a few times larger than in the incompressible limit, with amplification ∼ (1+1.3{M}2.6)/(3δ ).

  5. An analytic performance model of disk arrays and its application

    NASA Technical Reports Server (NTRS)

    Lee, Edward K.; Katz, Randy H.

    1991-01-01

    As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

  6. Uniform analytic approximation of Wigner rotation matrices

    NASA Astrophysics Data System (ADS)

    Hoffmann, Scott E.

    2018-02-01

    We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

  7. A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

    NASA Astrophysics Data System (ADS)

    Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

    2014-02-01

    This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

  8. Accurate expressions for solar cell fill factors including series and shunt resistances

    NASA Astrophysics Data System (ADS)

    Green, Martin A.

    2016-02-01

    Together with open-circuit voltage and short-circuit current, fill factor is a key solar cell parameter. In their classic paper on limiting efficiency, Shockley and Queisser first investigated this factor's analytical properties showing, for ideal cells, it could be expressed implicitly in terms of the maximum power point voltage. Subsequently, fill factors usually have been calculated iteratively from such implicit expressions or from analytical approximations. In the absence of detrimental series and shunt resistances, analytical fill factor expressions have recently been published in terms of the Lambert W function available in most mathematical computing software. Using a recently identified perturbative relationship, exact expressions in terms of this function are derived in technically interesting cases when both series and shunt resistances are present but have limited impact, allowing a better understanding of their effect individually and in combination. Approximate expressions for arbitrary shunt and series resistances are then deduced, which are significantly more accurate than any previously published. A method based on the insights developed is also reported for deducing one-diode fits to experimental data.

  9. Approximate analytical solutions of a pair of coupled anharmonic oscillators

    NASA Astrophysics Data System (ADS)

    Alam, Nasir; Mandal, Swapan; Öhberg, Patrik

    2015-02-01

    The Hamiltonian and the corresponding equations of motion involving the field operators of two quartic anharmonic oscillators indirectly coupled via a linear oscillator are constructed. The approximate analytical solutions of the coupled differential equations involving the non-commuting field operators are solved up to the second order in the anharmonic coupling. In the absence of nonlinearity these solutions are used to calculate the second order variances and hence the squeezing in pure and in mixed modes. The higher order quadrature squeezing and the amplitude squared squeezing of various field modes are also investigated where the squeezing in pure and in mixed modes are found to be suppressed. Moreover, the absence of a nonlinearity prohibits the higher order quadrature and higher ordered amplitude squeezing of the input coherent states. It is established that the mere coupling of two oscillators through a third one is unable to produce any squeezing effects of input coherent light, but the presence of a nonlinear interaction may provide squeezed states and other nonclassical phenomena.

  10. Approximate Solutions for Ideal Dam-Break Sediment-Laden Flows on Uniform Slopes

    NASA Astrophysics Data System (ADS)

    Ni, Yufang; Cao, Zhixian; Borthwick, Alistair; Liu, Qingquan

    2018-04-01

    Shallow water hydro-sediment-morphodynamic (SHSM) models have been applied increasingly widely in hydraulic engineering and geomorphological studies over the past few decades. Analytical and approximate solutions are usually sought to verify such models and therefore confirm their credibility. Dam-break flows are often evoked because such flows normally feature shock waves and contact discontinuities that warrant refined numerical schemes to solve. While analytical and approximate solutions to clear-water dam-break flows have been available for some time, such solutions are rare for sediment transport in dam-break flows. Here we aim to derive approximate solutions for ideal dam-break sediment-laden flows resulting from the sudden release of a finite volume of frictionless, incompressible water-sediment mixture on a uniform slope. The approximate solutions are presented for three typical sediment transport scenarios, i.e., pure advection, pure sedimentation, and concurrent entrainment and deposition. Although the cases considered in this paper are not real, the approximate solutions derived facilitate suitable benchmark tests for evaluating SHSM models, especially presently when shock waves can be numerically resolved accurately with a suite of finite volume methods, while the accuracy of the numerical solutions of contact discontinuities in sediment transport remains generally poorer.

  11. 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.

  12. Linear Power Spectra in Cold+Hot Dark Matter Models: Analytical Approximations and Applications

    NASA Astrophysics Data System (ADS)

    Ma, Chung-Pei

    1996-11-01

    This paper presents simple analytic approximations to the linear power spectra, linear growth rates, and rms mass fluctuations for both components in a family of cold + hot dark matter (CDM + HDM) models that are of current cosmological interest. The formulas are valid for a wide range of wavenumbers, neutrino fractions, redshifts, and Hubble constants: k ≤ 1O h Mpc-1, 0.05 ≤ Ωv le; 0.3 0 ≤ z ≤ 15, and 0.5 ≤ h ≤ 0.8. A new, redshift-dependent shape parameter, Γv = a½Ωvh2, is introduced to simplify the multidimensional parameter space and to characterize the effect of massive neutrinos on the power spectrum. The physical origin of Γv lies in the neutrino free-streaming process, and the analytic approximations can be simplified to depend only on this variable and Ωv. Linear calculations with these power spectra as input are performed to compare the predictions of Ωv ≤ 0.3 models with observational constraints from the reconstructed linear power spectrum and cluster abundance. The usual assumption of an exact scale-invariant primordial power spectrum is relaxed to allow a spectral index of 0.8 ≤ n ≤ 1. It is found that a slight tilt of n = 0.9 (no tensor mode) or n = 0.95 (with tensor mode) in 0.t-0.2 CDM + HDM models gives a power spectrum similar to that of an open CDM model with a shape parameter Γ = 0.25, providing good agreement with the power spectrum reconstructed by Peacock & Dodds and the observed cluster abundance at low redshifts. Late galaxy formation at high redshifts, however, will be a more severe problem in tilted models.

  13. Approximate Bayesian evaluations of measurement uncertainty

    NASA Astrophysics Data System (ADS)

    Possolo, Antonio; Bodnar, Olha

    2018-04-01

    The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

  14. Padé Approximant and Minimax Rational Approximation in Standard Cosmology

    NASA Astrophysics Data System (ADS)

    Zaninetti, Lorenzo

    2016-02-01

    The luminosity distance in the standard cosmology as given by $\\Lambda$CDM and consequently the distance modulus for supernovae can be defined by the Pad\\'e approximant. A comparison with a known analytical solution shows that the Pad\\'e approximant for the luminosity distance has an error of $4\\%$ at redshift $= 10$. A similar procedure for the Taylor expansion of the luminosity distance gives an error of $4\\%$ at redshift $=0.7 $; this means that for the luminosity distance, the Pad\\'e approximation is superior to the Taylor series. The availability of an analytical expression for the distance modulus allows applying the Levenberg--Marquardt method to derive the fundamental parameters from the available compilations for supernovae. A new luminosity function for galaxies derived from the truncated gamma probability density function models the observed luminosity function for galaxies when the observed range in absolute magnitude is modeled by the Pad\\'e approximant. A comparison of $\\Lambda$CDM with other cosmologies is done adopting a statistical point of view.

  15. Accurate analytical periodic solution of the elliptical Kepler equation using the Adomian decomposition method

    NASA Astrophysics Data System (ADS)

    Alshaery, Aisha; Ebaid, Abdelhalim

    2017-11-01

    Kepler's equation is one of the fundamental equations in orbital mechanics. It is a transcendental equation in terms of the eccentric anomaly of a planet which orbits the Sun. Determining the position of a planet in its orbit around the Sun at a given time depends upon the solution of Kepler's equation, which we will solve in this paper by the Adomian decomposition method (ADM). Several properties of the periodicity of the obtained approximate solutions have been proved in lemmas. Our calculations demonstrated a rapid convergence of the obtained approximate solutions which are displayed in tables and graphs. Also, it has been shown in this paper that only a few terms of the Adomian decomposition series are sufficient to achieve highly accurate numerical results for any number of revolutions of the Earth around the Sun as a consequence of the periodicity property. Numerically, the four-term approximate solution coincides with the Bessel-Fourier series solution in the literature up to seven decimal places at some values of the time parameter and nine decimal places at other values. Moreover, the absolute error approaches zero using the nine term approximate Adomian solution. In addition, the approximate Adomian solutions for the eccentric anomaly have been used to show the convergence of the approximate radial distances of the Earth from the Sun for any number of revolutions. The minimal distance (perihelion) and maximal distance (aphelion) approach 147 million kilometers and 152.505 million kilometers, respectively, and these coincide with the well known results in astronomical physics. Therefore, the Adomian decomposition method is validated as an effective tool to solve Kepler's equation for elliptical orbits.

  16. Exponentially accurate approximations to piece-wise smooth periodic functions

    NASA Technical Reports Server (NTRS)

    Greer, James; Banerjee, Saheb

    1995-01-01

    A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.

  17. Application of the weighted-density approximation to the accurate description of electron-positron correlation effects in materials

    NASA Astrophysics Data System (ADS)

    Callewaert, Vincent; Saniz, Rolando; Barbiellini, Bernardo; Bansil, Arun; Partoens, Bart

    2017-08-01

    We discuss positron-annihilation lifetimes for a set of illustrative bulk materials within the framework of the weighted-density approximation (WDA). The WDA can correctly describe electron-positron correlations in strongly inhomogeneous systems, such as surfaces, where the applicability of (semi-)local approximations is limited. We analyze the WDA in detail and show that the electrons which cannot screen external charges efficiently, such as the core electrons, cannot be treated accurately via the pair correlation of the homogeneous electron gas. We discuss how this problem can be addressed by reducing the screening in the homogeneous electron gas by adding terms depending on the gradient of the electron density. Further improvements are obtained when core electrons are treated within the LDA and the valence electron using the WDA. Finally, we discuss a semiempirical WDA-based approach in which a sum rule is imposed to reproduce the experimental lifetimes.

  18. On the Accuracy of Double Scattering Approximation for Atmospheric Polarization Computations

    NASA Technical Reports Server (NTRS)

    Korkin, Sergey V.; Lyapustin, Alexei I.; Marshak, Alexander L.

    2011-01-01

    Interpretation of multi-angle spectro-polarimetric data in remote sensing of atmospheric aerosols require fast and accurate methods of solving the vector radiative transfer equation (VRTE). The single and double scattering approximations could provide an analytical framework for the inversion algorithms and are relatively fast, however accuracy assessments of these approximations for the aerosol atmospheres in the atmospheric window channels have been missing. This paper provides such analysis for a vertically homogeneous aerosol atmosphere with weak and strong asymmetry of scattering. In both cases, the double scattering approximation gives a high accuracy result (relative error approximately 0.2%) only for the low optical path - 10(sup -2) As the error rapidly grows with optical thickness, a full VRTE solution is required for the practical remote sensing analysis. It is shown that the scattering anisotropy is not important at low optical thicknesses neither for reflected nor for transmitted polarization components of radiation.

  19. Analytic Approximation of Carbon Condensation Issues in Type ii Supernovae

    NASA Astrophysics Data System (ADS)

    Clayton, Donald D.

    2013-01-01

    I present analytic approximations for some issues related to condensation of graphite, TiC, and silicon carbide in oxygen-rich cores of supernovae of Type II. Increased understanding, which mathematical analysis can support, renders researchers more receptive to condensation in O-rich supernova gases. Taking SN 1987A as typical, my first analysis shows why the abundance of CO molecules reaches an early maximum in which free carbon remains more abundant than CO. This analysis clarifies why O-rich gas cannot oxidize C if 56Co radioactivity is as strong as in SN 1987A. My next analysis shows that the CO abundance could be regarded as being in chemical equilibrium if the CO molecule is given an effective binding energy rather than its laboratory dissociation energy. The effective binding energy makes the thermal dissociation rate of CO equal to its radioactive dissociation rate. This preserves possible relevance for the concept of chemical equilibrium. My next analysis shows that the observed abundances of CO and SiO molecules in SN 1987A rule out frequent suggestions that equilibrium condensation of SUNOCONs has occurred following atomic mixing of the He-burning shell with more central zones in such a way as to reproduce roughly the observed spectrum of isotopes in SUNOCONs while preserving C/O > 1. He atoms admixed along with the excess carbon would destroy CO and SiO molecules, leaving their observed abundances unexplained. The final analysis argues that a chemical quasiequilibrium among grains (but not gas) may exist approximately during condensation, so that its computational use is partially justified as a guide to which mineral phases would be stable against reactions with gas. I illustrate this point with quasiequilibrium calculations by Ebel & Grossman that have shown that graphite is stable even when O/C >1 if prominent molecules are justifiably excluded from the calculation of chemical equilibrium.

  20. Analytical Model For Fluid Dynamics In A Microgravity Environment

    NASA Technical Reports Server (NTRS)

    Naumann, Robert J.

    1995-01-01

    Report presents analytical approximation methodology for providing coupled fluid-flow, heat, and mass-transfer equations in microgravity environment. Experimental engineering estimates accurate to within factor of 2 made quickly and easily, eliminating need for time-consuming and costly numerical modeling. Any proposed experiment reviewed to see how it would perform in microgravity environment. Model applied in commercial setting for preliminary design of low-Grashoff/Rayleigh-number experiments.

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

    PubMed

    Gai, Litao; Bilige, Sudao; Jie, Yingmo

    2016-01-01

    In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

  2. Two-dimensional analytic weighting functions for limb scattering

    NASA Astrophysics Data System (ADS)

    Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.

    2017-10-01

    Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.

  3. AN ANALYTIC MODEL OF DUSTY, STRATIFIED, SPHERICAL H ii REGIONS

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

    Rodríguez-Ramírez, J. C.; Raga, A. C.; Lora, V.

    2016-12-20

    We study analytically the effect of radiation pressure (associated with photoionization processes and with dust absorption) on spherical, hydrostatic H ii regions. We consider two basic equations, one for the hydrostatic balance between the radiation-pressure components and the gas pressure, and another for the balance among the recombination rate, the dust absorption, and the ionizing photon rate. Based on appropriate mathematical approximations, we find a simple analytic solution for the density stratification of the nebula, which is defined by specifying the radius of the external boundary, the cross section of dust absorption, and the luminosity of the central star. Wemore » compare the analytic solution with numerical integrations of the model equations of Draine, and find a wide range of the physical parameters for which the analytic solution is accurate.« less

  4. Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)

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

    Peskin, M

    2004-04-22

    I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.

  5. Using Stochastic Approximation Techniques to Efficiently Construct Confidence Intervals for Heritability.

    PubMed

    Schweiger, Regev; Fisher, Eyal; Rahmani, Elior; Shenhav, Liat; Rosset, Saharon; Halperin, Eran

    2018-06-22

    Estimation of heritability is an important task in genetics. The use of linear mixed models (LMMs) to determine narrow-sense single-nucleotide polymorphism (SNP)-heritability and related quantities has received much recent attention, due of its ability to account for variants with small effect sizes. Typically, heritability estimation under LMMs uses the restricted maximum likelihood (REML) approach. The common way to report the uncertainty in REML estimation uses standard errors (SEs), which rely on asymptotic properties. However, these assumptions are often violated because of the bounded parameter space, statistical dependencies, and limited sample size, leading to biased estimates and inflated or deflated confidence intervals (CIs). In addition, for larger data sets (e.g., tens of thousands of individuals), the construction of SEs itself may require considerable time, as it requires expensive matrix inversions and multiplications. Here, we present FIESTA (Fast confidence IntErvals using STochastic Approximation), a method for constructing accurate CIs. FIESTA is based on parametric bootstrap sampling, and, therefore, avoids unjustified assumptions on the distribution of the heritability estimator. FIESTA uses stochastic approximation techniques, which accelerate the construction of CIs by several orders of magnitude, compared with previous approaches as well as to the analytical approximation used by SEs. FIESTA builds accurate CIs rapidly, for example, requiring only several seconds for data sets of tens of thousands of individuals, making FIESTA a very fast solution to the problem of building accurate CIs for heritability for all data set sizes.

  6. Analytic Interatomic Forces in the Random Phase Approximation

    NASA Astrophysics Data System (ADS)

    Ramberger, Benjamin; Schäfer, Tobias; Kresse, Georg

    2017-03-01

    We discuss that in the random phase approximation (RPA) the first derivative of the energy with respect to the Green's function is the self-energy in the G W approximation. This relationship allows us to derive compact equations for the RPA interatomic forces. We also show that position dependent overlap operators are elegantly incorporated in the present framework. The RPA force equations have been implemented in the projector augmented wave formalism, and we present illustrative applications, including ab initio molecular dynamics simulations, the calculation of phonon dispersion relations for diamond and graphite, as well as structural relaxations for water on boron nitride. The present derivation establishes a concise framework for forces within perturbative approaches and is also applicable to more involved approximations for the correlation energy.

  7. Analytic barrage attack model. Final report, January 1986-January 1989

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

    St Ledger, J.W.; Naegeli, R.E.; Dowden, N.A.

    An analytic model is developed for a nuclear barrage attack, assuming weapons with no aiming error and a cookie-cutter damage function. The model is then extended with approximations for the effects of aiming error and distance damage sigma. The final result is a fast running model which calculates probability of damage for a barrage attack. The probability of damage is accurate to within seven percent or better, for weapon reliabilities of 50 to 100 percent, distance damage sigmas of 0.5 or less, and zero to very large circular error probabilities. FORTRAN 77 coding is included in the report for themore » analytic model and for a numerical model used to check the analytic results.« less

  8. Thermodynamics of Gas Turbine Cycles with Analytic Derivatives in OpenMDAO

    NASA Technical Reports Server (NTRS)

    Gray, Justin; Chin, Jeffrey; Hearn, Tristan; Hendricks, Eric; Lavelle, Thomas; Martins, Joaquim R. R. A.

    2016-01-01

    A new equilibrium thermodynamics analysis tool was built based on the CEA method using the OpenMDAO framework. The new tool provides forward and adjoint analytic derivatives for use with gradient based optimization algorithms. The new tool was validated against the original CEA code to ensure an accurate analysis and the analytic derivatives were validated against finite-difference approximations. Performance comparisons between analytic and finite difference methods showed a significant speed advantage for the analytic methods. To further test the new analysis tool, a sample optimization was performed to find the optimal air-fuel equivalence ratio, , maximizing combustion temperature for a range of different pressures. Collectively, the results demonstrate the viability of the new tool to serve as the thermodynamic backbone for future work on a full propulsion modeling tool.

  9. SU-F-T-144: Analytical Closed Form Approximation for Carbon Ion Bragg Curves in Water

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

    Tuomanen, S; Moskvin, V; Farr, J

    2016-06-15

    Purpose: Semi-empirical modeling is a powerful computational method in radiation dosimetry. A set of approximations exist for proton ion depth dose distribution (DDD) in water. However, the modeling is more complicated for carbon ions due to fragmentation. This study addresses this by providing and evaluating a new methodology for DDD modeling of carbon ions in water. Methods: The FLUKA, Monte Carlo (MC) general-purpose transport code was used for simulation of carbon DDDs for energies of 100–400 MeV in water as reference data model benchmarking. Based on Thomas Bortfeld’s closed form equation approximating proton Bragg Curves as a basis, we derivedmore » the critical constants for a beam of Carbon ions by applying models of radiation transport by Lee et. al. and Geiger to our simulated Carbon curves. We hypothesized that including a new exponential (κ) residual distance parameter to Bortfeld’s fluence reduction relation would improve DDD modeling for carbon ions. We are introducing an additional term to be added to Bortfeld’s equation to describe fragmentation tail. This term accounts for the pre-peak dose from nuclear fragments (NF). In the post peak region, the NF transport will be treated as new beams utilizing the Glauber model for interaction cross sections and the Abrasion- Ablation fragmentation model. Results: The carbon beam specific constants in the developed model were determined to be : p= 1.75, β=0.008 cm-1, γ=0.6, α=0.0007 cm MeV, σmono=0.08, and the new exponential parameter κ=0.55. This produced a close match for the plateau part of the curve (max deviation 6.37%). Conclusion: The derived semi-empirical model provides an accurate approximation of the MC simulated clinical carbon DDDs. This is the first direct semi-empirical simulation for the dosimetry of therapeutic carbon ions. The accurate modeling of the NF tail in the carbon DDD will provide key insight into distal edge dose deposition formation.« less

  10. Analytic approximation for random muffin-tin alloys

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

    Mills, R.; Gray, L.J.; Kaplan, T.

    1983-03-15

    The methods introduced in a previous paper under the name of ''traveling-cluster approximation'' (TCA) are applied, in a multiple-scattering approach, to the case of a random muffin-tin substitutional alloy. This permits the iterative part of a self-consistent calculation to be carried out entirely in terms of on-the-energy-shell scattering amplitudes. Off-shell components of the mean resolvent, needed for the calculation of spectral functions, are obtained by standard methods involving single-site scattering wave functions. The single-site TCA is just the usual coherent-potential approximation, expressed in a form particularly suited for iteration. A fixed-point theorem is proved for the general t-matrix TCA, ensuringmore » convergence upon iteration to a unique self-consistent solution with the physically essential Herglotz properties.« less

  11. H2+, HeH and H2: Approximating potential curves, calculating rovibrational states

    NASA Astrophysics Data System (ADS)

    Olivares-Pilón, Horacio; Turbiner, Alexander V.

    2018-06-01

    Analytic consideration of the Bohr-Oppenheimer (BO) potential curves for diatomic molecules is proposed: accurate analytic interpolation for a potential curve consistent with its rovibrational spectra is found. It is shown that in the BO approximation for four lowest electronic states 1 sσg and 2 pσu, 2 pπu and 3 dπg of H2+, the ground state X2Σ+ of HeH and the two lowest states 1 Σg+ and 3 Σu+ of H2, the potential curves can be analytically interpolated in full range of internuclear distances R with not less than 4-5-6 s.d. Approximation based on matching the Laurant-type expansion at small R and a combination of the multipole expansion with one-instanton type contribution at large distances R is given by two-point Padé approximant. The position of minimum, when exists, is predicted within 1% or better. For the molecular ion H2+ in the Lagrange mesh method, the spectra of vibrational, rotational and rovibrational states (ν , L) associated with 1 sσg and 2 pσu, 2 pπu and 3 dπg potential curves are calculated. In general, it coincides with spectra found via numerical solution of the Schrödinger equation (when available) within six s.d. It is shown that 1 sσg curve contains 19 vibrational states (ν , 0) , while 2 pσu curve contains a single one (0 , 0) and 2 pπu state contains 12 vibrational states (ν , 0) . In general, 1 sσg electronic curve contains 420 rovibrational states, which increases up to 423 when we are beyond BO approximation. For the state 2 pσu the total number of rovibrational states (all with ν = 0) is equal to 3, within or beyond Bohr-Oppenheimer approximation. As for the state 2 pπu within the Bohr-Oppenheimer approximation the total number of the rovibrational bound states is equal to 284. The state 3 dπg is repulsive, no rovibrational state is found. It is confirmed in Lagrange mesh formalism the statement that the ground state potential curve of the heteronuclear molecule HeH does not support rovibrational states. Accurate

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

    NASA Technical Reports Server (NTRS)

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

    1984-01-01

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

  13. Approximation of Failure Probability Using Conditional Sampling

    NASA Technical Reports Server (NTRS)

    Giesy. Daniel P.; Crespo, Luis G.; Kenney, Sean P.

    2008-01-01

    In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.

  14. Analytic saddlepoint approximation for ionization energy loss distributions

    DOE PAGES

    Sjue, Sky K. L.; George, Jr., Richard Neal; Mathews, David Gregory

    2017-07-27

    Here, we present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v/c < 1, provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal’s distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov’s κ approaches 1.

  15. Analytic saddlepoint approximation for ionization energy loss distributions

    NASA Astrophysics Data System (ADS)

    Sjue, S. K. L.; George, R. N.; Mathews, D. G.

    2017-09-01

    We present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v / c < 1 , provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal's distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov's κ approaches 1.

  16. Analytic saddlepoint approximation for ionization energy loss distributions

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

    Sjue, Sky K. L.; George, Jr., Richard Neal; Mathews, David Gregory

    Here, we present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v/c < 1, provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal’s distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov’s κ approaches 1.

  17. Numerical integration for ab initio many-electron self energy calculations within the GW approximation

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

    Liu, Fang, E-mail: fliu@lsec.cc.ac.cn; Lin, Lin, E-mail: linlin@math.berkeley.edu; Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

    We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit ofmore » using different self energy expressions to perform the numerical convolution at different frequencies.« less

  18. On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

    NASA Technical Reports Server (NTRS)

    Gottlieb, David; Shu, Chi-Wang

    1994-01-01

    The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

  19. A useful approximation for the flat surface impulse response

    NASA Technical Reports Server (NTRS)

    Brown, Gary S.

    1989-01-01

    The flat surface impulse response (FSIR) is a very useful quantity in computing the mean return power for near-nadir-oriented short-pulse radar altimeters. However, for very small antenna beamwidths and relatively large pointing angles, previous analytical descriptions become very difficult to compute accurately. An asymptotic approximation is developed to overcome these computational problems. Since accuracy is of key importance, a condition is developed under which this solution is within 2 percent of the exact answer. The asymptotic solution is shown to be in functional agreement with a conventional clutter power result and gives a 1.25-dB correction to this formula to account properly for the antenna-pattern variation over the illuminated area.

  20. Approximate analytic method for high-apogee twelve-hour orbits of artificial Earth's satellites

    NASA Astrophysics Data System (ADS)

    Vashkovyaka, M. A.; Zaslavskii, G. S.

    2016-09-01

    We propose an approach to the study of the evolution of high-apogee twelve-hour orbits of artificial Earth's satellites. We describe parameters of the motion model used for the artificial Earth's satellite such that the principal gravitational perturbations of the Moon and Sun, nonsphericity of the Earth, and perturbations from the light pressure force are approximately taken into account. To solve the system of averaged equations describing the evolution of the orbit parameters of an artificial satellite, we use both numeric and analytic methods. To select initial parameters of the twelve-hour orbit, we assume that the path of the satellite along the surface of the Earth is stable. Results obtained by the analytic method and by the numerical integration of the evolving system are compared. For intervals of several years, we obtain estimates of oscillation periods and amplitudes for orbital elements. To verify the results and estimate the precision of the method, we use the numerical integration of rigorous (not averaged) equations of motion of the artificial satellite: they take into account forces acting on the satellite substantially more completely and precisely. The described method can be applied not only to the investigation of orbit evolutions of artificial satellites of the Earth; it can be applied to the investigation of the orbit evolution for other planets of the Solar system provided that the corresponding research problem will arise in the future and the considered special class of resonance orbits of satellites will be used for that purpose.

  1. Accurate quantification of PGE2 in the polyposis in rat colon (Pirc) model by surrogate analyte-based UPLC-MS/MS.

    PubMed

    Yun, Changhong; Dashwood, Wan-Mohaiza; Kwong, Lawrence N; Gao, Song; Yin, Taijun; Ling, Qinglan; Singh, Rashim; Dashwood, Roderick H; Hu, Ming

    2018-01-30

    An accurate and reliable UPLC-MS/MS method is reported for the quantification of endogenous Prostaglandin E2 (PGE 2 ) in rat colonic mucosa and polyps. This method adopted the "surrogate analyte plus authentic bio-matrix" approach, using two different stable isotopic labeled analogs - PGE 2 -d9 as the surrogate analyte and PGE 2 -d4 as the internal standard. A quantitative standard curve was constructed with the surrogate analyte in colonic mucosa homogenate, and the method was successfully validated with the authentic bio-matrix. Concentrations of endogenous PGE 2 in both normal and inflammatory tissue homogenates were back-calculated based on the regression equation. Because of no endogenous interference on the surrogate analyte determination, the specificity was particularly good. By using authentic bio-matrix for validation, the matrix effect and exaction recovery are identically same for the quantitative standard curve and actual samples - this notably increased the assay accuracy. The method is easy, fast, robust and reliable for colon PGE 2 determination. This "surrogate analyte" approach was applied to measure the Pirc (an Apc-mutant rat kindred that models human FAP) mucosa and polyps PGE 2 , one of the strong biomarkers of colorectal cancer. A similar concept could be applied to endogenous biomarkers in other tissues. Copyright © 2017 Elsevier B.V. All rights reserved.

  2. Electrolyte diodes with weak acids and bases. I. Theory and an approximate analytical solution.

    PubMed

    Iván, Kristóf; Simon, Péter L; Wittmann, Mária; Noszticzius, Zoltán

    2005-10-22

    Until now acid-base diodes and transistors applied strong mineral acids and bases exclusively. In this work properties of electrolyte diodes with weak electrolytes are studied and compared with those of diodes with strong ones to show the advantages of weak acids and bases in these applications. The theoretical model is a one dimensional piece of gel containing fixed ionizable groups and connecting reservoirs of an acid and a base. The electric current flowing through the gel is measured as a function of the applied voltage. The steady-state current-voltage characteristic (CVC) of such a gel looks like that of a diode under these conditions. Results of our theoretical, numerical, and experimental investigations are reported in two parts. In this first, theoretical part governing equations necessary to calculate the steady-state CVC of a reverse-biased electrolyte diode are presented together with an approximate analytical solution of this reaction-diffusion-ionic migration problem. The applied approximations are quasielectroneutrality and quasiequilibrium. It is shown that the gel can be divided into an alkaline and an acidic zone separated by a middle weakly acidic region. As a further approximation it is assumed that the ionization of the fixed acidic groups is complete in the alkaline zone and that it is completely suppressed in the acidic one. The general solution given here describes the CVC and the potential and ionic concentration profiles of diodes applying either strong or weak electrolytes. It is proven that previous formulas valid for a strong acid-strong base diode can be regarded as a special case of the more general formulas presented here.

  3. Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method.

    PubMed

    Graf, Daniel; Beuerle, Matthias; Schurkus, Henry F; Luenser, Arne; Savasci, Gökcen; Ochsenfeld, Christian

    2018-05-08

    An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.

  4. Exact PDF equations and closure approximations for advective-reactive transport

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

    Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

    2013-06-01

    Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less

  5. Development of highly accurate approximate scheme for computing the charge transfer integral

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

    Pershin, Anton; Szalay, Péter G.

    The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, itmore » was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the “exact” scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the “exact” calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature.« less

  6. Analytical approximation and numerical simulations for periodic travelling water waves

    NASA Astrophysics Data System (ADS)

    Kalimeris, Konstantinos

    2017-12-01

    We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity. This article is part of the theme issue 'Nonlinear water waves'.

  7. Assessment of the analytical capabilities of inductively coupled plasma-mass spectrometry

    USGS Publications Warehouse

    Taylor, Howard E.; Garbarino, John R.

    1988-01-01

    A thorough assessment of the analytical capabilities of inductively coupled plasma-mass spectrometry was conducted for selected analytes of importance in water quality applications and hydrologic research. A multielement calibration curve technique was designed to produce accurate and precise results in analysis times of approximately one minute. The suite of elements included Al, As, B, Ba, Be, Cd, Co, Cr, Cu, Hg, Li, Mn, Mo, Ni, Pb, Se, Sr, V, and Zn. The effects of sample matrix composition on the accuracy of the determinations showed that matrix elements (such as Na, Ca, Mg, and K) that may be present in natural water samples at concentration levels greater than 50 mg/L resulted in as much as a 10% suppression in ion current for analyte elements. Operational detection limits are presented.

  8. Spacing of bending-induced fractures at saturation: Numerical models and approximate analytical solution

    NASA Astrophysics Data System (ADS)

    Schöpfer, Martin; Lehner, Florian; Grasemann, Bernhard; Kaserer, Klemens; Hinsch, Ralph

    2017-04-01

    analytical solution is derived for the critical fracture spacing, i.e. the spacing below which the maximum tensile stress cannot reach the layer strength. The model results are consistent with an approximate analytical solution, and illustrate that the spacing of bending-induced fractures is proportional to layer thickness and a square root function of the ratio of layer tensile strength to confining pressure. Although highly idealised, models and analysis presented in this study offer an explanation for fracture saturation during folding and point towards certain key factors that may control fracture spacing in natural systems.

  9. Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

    PubMed

    Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

    2016-01-01

    Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

  10. Analytic approximations of Von Kármán plate under arbitrary uniform pressure—equations in integral form

    NASA Astrophysics Data System (ADS)

    Zhong, XiaoXu; Liao, ShiJun

    2018-01-01

    Analytic approximations of the Von Kármán's plate equations in integral form for a circular plate under external uniform pressure to arbitrary magnitude are successfully obtained by means of the homotopy analysis method (HAM), an analytic approximation technique for highly nonlinear problems. Two HAM-based approaches are proposed for either a given external uniform pressure Q or a given central deflection, respectively. Both of them are valid for uniform pressure to arbitrary magnitude by choosing proper values of the so-called convergence-control parameters c 1 and c 2 in the frame of the HAM. Besides, it is found that the HAM-based iteration approaches generally converge much faster than the interpolation iterative method. Furthermore, we prove that the interpolation iterative method is a special case of the first-order HAM iteration approach for a given external uniform pressure Q when c 1 = - θ and c 2 = -1, where θ denotes the interpolation iterative parameter. Therefore, according to the convergence theorem of Zheng and Zhou about the interpolation iterative method, the HAM-based approaches are valid for uniform pressure to arbitrary magnitude at least in the special case c 1 = - θ and c 2 = -1. In addition, we prove that the HAM approach for the Von Kármán's plate equations in differential form is just a special case of the HAM for the Von Kármán's plate equations in integral form mentioned in this paper. All of these illustrate the validity and great potential of the HAM for highly nonlinear problems, and its superiority over perturbation techniques.

  11. Super-sample covariance approximations and partial sky coverage

    NASA Astrophysics Data System (ADS)

    Lacasa, Fabien; Lima, Marcos; Aguena, Michel

    2018-04-01

    Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample variance, which is particularly useful for the self-calibration of the cluster observable-mass relation; our approach can similarly be applied to other observables, such as galaxy clustering and lensing shear. We first examined the accuracy of two analytical approximations proposed in the literature for the flat sky limit, finding that they are accurate at the 15% and 30-35% level, respectively, for covariances of counts in the same redshift bin. We then developed a harmonic expansion formalism that allows for the prediction of SSC in an arbitrary survey mask geometry, such as large sky areas of current and future surveys. We show analytically and numerically that this formalism recovers the full sky and flat sky limits present in the literature. We then present an efficient numerical implementation of the formalism, which allows fast and easy runs of covariance predictions when the survey mask is modified. We applied our method to a mask that is broadly similar to the Dark Energy Survey footprint, finding a non-negligible negative cross-z covariance, i.e. redshift bins are anti-correlated. We also examined the case of data removal from holes due to, for example bright stars, quality cuts, or systematic removals, and find that this does not have noticeable effects on the structure of the SSC matrix, only rescaling its amplitude by the effective survey area. These advances enable analytical covariances of LSS observables to be computed for current and future galaxy surveys, which cover large areas of the sky where the flat sky approximation fails.

  12. Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Abd-Elhameed, W. M.

    2005-09-01

    We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

  13. A cubic spline approximation for problems in fluid mechanics

    NASA Technical Reports Server (NTRS)

    Rubin, S. G.; Graves, R. A., Jr.

    1975-01-01

    A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

  14. An asymptotically consistent approximant method with application to soft- and hard-sphere fluids.

    PubMed

    Barlow, N S; Schultz, A J; Weinstein, S J; Kofke, D A

    2012-11-28

    A modified Padé approximant is used to construct an equation of state, which has the same large-density asymptotic behavior as the model fluid being described, while still retaining the low-density behavior of the virial equation of state (virial series). Within this framework, all sequences of rational functions that are analytic in the physical domain converge to the correct behavior at the same rate, eliminating the ambiguity of choosing the correct form of Padé approximant. The method is applied to fluids composed of "soft" spherical particles with separation distance r interacting through an inverse-power pair potential, φ = ε(σ∕r)(n), where ε and σ are model parameters and n is the "hardness" of the spheres. For n < 9, the approximants provide a significant improvement over the 8-term virial series, when compared against molecular simulation data. For n ≥ 9, both the approximants and the 8-term virial series give an accurate description of the fluid behavior, when compared with simulation data. When taking the limit as n → ∞, an equation of state for hard spheres is obtained, which is closer to simulation data than the 10-term virial series for hard spheres, and is comparable in accuracy to other recently proposed equations of state. By applying a least square fit to the approximants, we obtain a general and accurate soft-sphere equation of state as a function of n, valid over the full range of density in the fluid phase.

  15. Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary

    PubMed Central

    Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

    2016-01-01

    Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations. PMID:27031232

  16. A non-grey analytical model for irradiated atmospheres. II. Analytical vs. numerical solutions

    NASA Astrophysics Data System (ADS)

    Parmentier, Vivien; Guillot, Tristan; Fortney, Jonathan J.; Marley, Mark S.

    2015-02-01

    Context. The recent discovery and characterization of the diversity of the atmospheres of exoplanets and brown dwarfs calls for the development of fast and accurate analytical models. Aims: We wish to assess the goodness of the different approximations used to solve the radiative transfer problem in irradiated atmospheres analytically, and we aim to provide a useful tool for a fast computation of analytical temperature profiles that remains correct over a wide range of atmospheric characteristics. Methods: We quantify the accuracy of the analytical solution derived in paper I for an irradiated, non-grey atmosphere by comparing it to a state-of-the-art radiative transfer model. Then, using a grid of numerical models, we calibrate the different coefficients of our analytical model for irradiated solar-composition atmospheres of giant exoplanets and brown dwarfs. Results: We show that the so-called Eddington approximation used to solve the angular dependency of the radiation field leads to relative errors of up to ~5% on the temperature profile. For grey or semi-grey atmospheres (i.e., when the visible and thermal opacities, respectively, can be considered independent of wavelength), we show that the presence of a convective zone has a limited effect on the radiative atmosphere above it and leads to modifications of the radiative temperature profile of approximately ~2%. However, for realistic non-grey planetary atmospheres, the presence of a convective zone that extends to optical depths smaller than unity can lead to changes in the radiative temperature profile on the order of 20% or more. When the convective zone is located at deeper levels (such as for strongly irradiated hot Jupiters), its effect on the radiative atmosphere is again on the same order (~2%) as in the semi-grey case. We show that the temperature inversion induced by a strong absorber in the optical, such as TiO or VO is mainly due to non-grey thermal effects reducing the ability of the upper

  17. Mutual capture of dipolar molecules at low and very low energies. I. Approximate analytical treatment.

    PubMed

    Nikitin, E E; Troe, J

    2010-09-16

    Approximate analytical expressions are derived for the low-energy rate coefficients of capture of two identical dipolar polarizable rigid rotors in their lowest nonresonant (j(1) = 0 and j(2) = 0) and resonant (j(1) = 0,1 and j(2) = 1,0) states. The considered range extends from the quantum, ultralow energy regime, characterized by s-wave capture, to the classical regime described within fly wheel and adiabatic channel approaches, respectively. This is illustrated by the table of contents graphic (available on the Web) that shows the scaled rate coefficients for the mutual capture of rotors in the resonant state versus the reduced wave vector between the Bethe zero-energy (left arrows) and classical high-energy (right arrow) limits for different ratios δ of the dipole-dipole to dispersion interaction.

  18. Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation.

    PubMed

    Franssens, G; De Maziére, M; Fonteyn, D

    2000-08-20

    A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz's model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.

  19. 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

  20. Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.

    PubMed

    Chao, Fa-An; Byrd, R Andrew

    2017-04-01

    The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C α , H α , etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain. Published by Elsevier Inc.

  1. Quo vadis, analytical chemistry?

    PubMed

    Valcárcel, Miguel

    2016-01-01

    This paper presents an open, personal, fresh approach to the future of Analytical Chemistry in the context of the deep changes Science and Technology are anticipated to experience. Its main aim is to challenge young analytical chemists because the future of our scientific discipline is in their hands. A description of not completely accurate overall conceptions of our discipline, both past and present, to be avoided is followed by a flexible, integral definition of Analytical Chemistry and its cornerstones (viz., aims and objectives, quality trade-offs, the third basic analytical reference, the information hierarchy, social responsibility, independent research, transfer of knowledge and technology, interfaces to other scientific-technical disciplines, and well-oriented education). Obsolete paradigms, and more accurate general and specific that can be expected to provide the framework for our discipline in the coming years are described. Finally, the three possible responses of analytical chemists to the proposed changes in our discipline are discussed.

  2. Analytical method for the accurate determination of tricothecenes in grains using LC-MS/MS: a comparison between MRM transition and MS3 quantitation.

    PubMed

    Lim, Chee Wei; Tai, Siew Hoon; Lee, Lin Min; Chan, Sheot Harn

    2012-07-01

    The current food crisis demands unambiguous determination of mycotoxin contamination in staple foods to achieve safer food for consumption. This paper describes the first accurate LC-MS/MS method developed to analyze tricothecenes in grains by applying multiple reaction monitoring (MRM) transition and MS(3) quantitation strategies in tandem. The tricothecenes are nivalenol, deoxynivalenol, deoxynivalenol-3-glucoside, fusarenon X, 3-acetyl-deoxynivalenol, 15-acetyldeoxynivalenol, diacetoxyscirpenol, and HT-2 and T-2 toxins. Acetic acid and ammonium acetate were used to convert the analytes into their respective acetate adducts and ammonium adducts under negative and positive MS polarity conditions, respectively. The mycotoxins were separated by reversed-phase LC in a 13.5-min run, ionized using electrospray ionization, and detected by tandem mass spectrometry. Analyte-specific mass-to-charge (m/z) ratios were used to perform quantitation under MRM transition and MS(3) (linear ion trap) modes. Three experiments were made for each quantitation mode and matrix in batches over 6 days for recovery studies. The matrix effect was investigated at concentration levels of 20, 40, 80, 120, 160, and 200 μg kg(-1) (n = 3) in 5 g corn flour and rice flour. Extraction with acetonitrile provided a good overall recovery range of 90-108% (n = 3) at three levels of spiking concentration of 40, 80, and 120 μg kg(-1). A quantitation limit of 2-6 μg kg(-1) was achieved by applying an MRM transition quantitation strategy. Under MS(3) mode, a quantitation limit of 4-10 μg kg(-1) was achieved. Relative standard deviations of 2-10% and 2-11% were reported for MRM transition and MS(3) quantitation, respectively. The successful utilization of MS(3) enabled accurate analyte fragmentation pattern matching and its quantitation, leading to the development of analytical methods in fields that demand both analyte specificity and fragmentation fingerprint-matching capabilities that are

  3. Two approximations for the geometric model of signal amplification in an electron-multiplying charge-coupled device detector

    PubMed Central

    Chao, Jerry; Ram, Sripad; Ward, E. Sally; Ober, Raimund J.

    2014-01-01

    The extraction of information from images acquired under low light conditions represents a common task in diverse disciplines. In single molecule microscopy, for example, techniques for superresolution image reconstruction depend on the accurate estimation of the locations of individual particles from generally low light images. In order to estimate a quantity of interest with high accuracy, however, an appropriate model for the image data is needed. To this end, we previously introduced a data model for an image that is acquired using the electron-multiplying charge-coupled device (EMCCD) detector, a technology of choice for low light imaging due to its ability to amplify weak signals significantly above its readout noise floor. Specifically, we proposed the use of a geometrically multiplied branching process to model the EMCCD detector’s stochastic signal amplification. Geometric multiplication, however, can be computationally expensive and challenging to work with analytically. We therefore describe here two approximations for geometric multiplication that can be used instead. The high gain approximation is appropriate when a high level of signal amplification is used, a scenario which corresponds to the typical usage of an EMCCD detector. It is an accurate approximation that is computationally more efficient, and can be used to perform maximum likelihood estimation on EMCCD image data. In contrast, the Gaussian approximation is applicable at all levels of signal amplification, but is only accurate when the initial signal to be amplified is relatively large. As we demonstrate, it can importantly facilitate the analysis of an information-theoretic quantity called the noise coefficient. PMID:25075263

  4. Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization.

    PubMed

    Petrenko, Taras; Kossmann, Simone; Neese, Frank

    2011-02-07

    In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The

  5. A test of the adhesion approximation for gravitational clustering

    NASA Technical Reports Server (NTRS)

    Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.

    1993-01-01

    We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

  6. A test of the adhesion approximation for gravitational clustering

    NASA Technical Reports Server (NTRS)

    Melott, Adrian L.; Shandarin, Sergei F.; Weinberg, David H.

    1994-01-01

    We quantitatively compare a particle implementation of the adhesion approximation to fully nonlinear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

  7. An Analytic Approximation to Very High Specific Impulse and Specific Power Interplanetary Space Mission Analysis

    NASA Technical Reports Server (NTRS)

    Williams, Craig Hamilton

    1995-01-01

    A simple, analytic approximation is derived to calculate trip time and performance for propulsion systems of very high specific impulse (50,000 to 200,000 seconds) and very high specific power (10 to 1000 kW/kg) for human interplanetary space missions. The approach assumed field-free space, constant thrust/constant specific power, and near straight line (radial) trajectories between the planets. Closed form, one dimensional equations of motion for two-burn rendezvous and four-burn round trip missions are derived as a function of specific impulse, specific power, and propellant mass ratio. The equations are coupled to an optimizing parameter that maximizes performance and minimizes trip time. Data generated for hypothetical one-way and round trip human missions to Jupiter were found to be within 1% and 6% accuracy of integrated solutions respectively, verifying that for these systems, credible analysis does not require computationally intensive numerical techniques.

  8. Novel approximation of misalignment fading modeled by Beckmann distribution on free-space optical links.

    PubMed

    Boluda-Ruiz, Rubén; García-Zambrana, Antonio; Castillo-Vázquez, Carmen; Castillo-Vázquez, Beatriz

    2016-10-03

    A novel accurate and useful approximation of the well-known Beckmann distribution is presented here, which is used to model generalized pointing errors in the context of free-space optical (FSO) communication systems. We derive an approximate closed-form probability density function (PDF) for the composite gamma-gamma (GG) atmospheric turbulence with the pointing error model using the proposed approximation of the Beckmann distribution, which is valid for most practical terrestrial FSO links. This approximation takes into account the effect of the beam width, different jitters for the elevation and the horizontal displacement and the simultaneous effect of nonzero boresight errors for each axis at the receiver plane. Additionally, the proposed approximation allows us to delimit two different FSO scenarios. The first of them is when atmospheric turbulence is the dominant effect in relation to generalized pointing errors, and the second one when generalized pointing error is the dominant effect in relation to atmospheric turbulence. The second FSO scenario has not been studied in-depth by the research community. Moreover, the accuracy of the method is measured both visually and quantitatively using curve-fitting metrics. Simulation results are further included to confirm the analytical results.

  9. Low-frequency sound propagation modeling over a locally-reacting boundary using the parabolic approximation

    NASA Technical Reports Server (NTRS)

    Robertson, J. S.; Siegman, W. L.; Jacobson, M. J.

    1989-01-01

    There is substantial interest in the analytical and numerical modeling of low-frequency, long-range atmospheric acoustic propagation. Ray-based models, because of frequency limitations, do not always give an adequate prediction of quantities such as sound pressure or intensity levels. However, the parabolic approximation method, widely used in ocean acoustics, and often more accurate than ray models for lower frequencies of interest, can be applied to acoustic propagation in the atmosphere. Modifications of an existing implicit finite-difference implementation for computing solutions to the parabolic approximation are discussed. A locally-reacting boundary is used together with a one-parameter impedance model. Intensity calculations are performed for a number of flow resistivity values in both quiescent and windy atmospheres. Variations in the value of this parameter are shown to have substantial effects on the spatial variation of the acoustic signal.

  10. Binary collision approximations for the memory function for density fluctuations in equilibrium atomic liquids

    NASA Astrophysics Data System (ADS)

    Noah, Joyce E.

    Time correlation functions of density fluctuations of liquids at equilibrium can be used to relate the microscopic dynamics of a liquid to its macroscopic transport properties. Time correlation functions are especially useful since they can be generated in a variety of ways, from scattering experiments to computer simulation to analytic theory. The kinetic theory of fluctuations in equilibrium liquids is an analytic theory for calculating correlation functions using memory functions. In this work, we use a diagrammatic formulation of the kinetic theory to develop a series of binary collision approximations for the collisional part of the memory function. We define binary collisions as collisions between two distinct density fluctuations whose identities are fixed during the duration of a collsion. R approximations are for the short time part of the memory function, and build upon the work of Ranganathan and Andersen. These approximations have purely repulsive interactions between the fluctuations. The second type of approximation, RA approximations, is for the longer time part of the memory function, where the density fluctuations now interact via repulsive and attractive forces. Although RA approximations are a natural extension of R approximations, they permit two density fluctuations to become trapped in the wells of the interaction potential, leading to long-lived oscillatory behavior, which is unphysical. Therefore we consider S approximations which describe binary particles which experience the random effect of the surroundings while interacting via repulsive or repulsive and attractive interactions. For each of these approximations for the memory function we numerically solve the kinetic equation to generate correlation functions. These results are compared to molecular dynamics results for the correlation functions. Comparing the successes and failures of the different approximations, we conclude that R approximations give more accurate intermediate and

  11. An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations for marginally unstable systems

    NASA Technical Reports Server (NTRS)

    Hinata, S.

    1989-01-01

    An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations is obtained. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field is incorporated into the model. To single out the effect of the Lorentz force on the omega-effect, the effect of the Lorentz force on the alpha-effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo number N. The amplitude is proportional to N - 1, while the period is almost exactly the same as the dissipation time of the unstable mode (proportional to N).

  12. Accurate modelling of unsteady flows in collapsible tubes.

    PubMed

    Marchandise, Emilie; Flaud, Patrice

    2010-01-01

    The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.

  13. Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions

    NASA Astrophysics Data System (ADS)

    Nguyen, Thuong T.; Székely, Eszter; Imbalzano, Giulio; Behler, Jörg; Csányi, Gábor; Ceriotti, Michele; Götz, Andreas W.; Paesani, Francesco

    2018-06-01

    The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.

  14. Approximate Analytical Time-Dependent Solutions to Describe Large-Amplitude Local Calcium Transients in the Presence of Buffers

    PubMed Central

    Mironova, Lidia A.; Mironov, Sergej L.

    2008-01-01

    Local Ca2+ signaling controls many neuronal functions, which is often achieved through spatial localization of Ca2+ signals. These nanodomains are formed due to combined effects of Ca2+ diffusion and binding to the cytoplasmic buffers. In this article we derived simple analytical expressions to describe Ca2+ diffusion in the presence of mobile and immobile buffers. A nonlinear character of the reaction-diffusion problem was circumvented by introducing a logarithmic approximation of the concentration term. The obtained formulas reproduce free Ca2+ levels up to 50 μM and their changes in the millisecond range. Derived equations can be useful to predict spatiotemporal profiles of large-amplitude [Ca2+] transients, which participate in various physiological processes. PMID:17872951

  15. Analytic double product integrals for all-frequency relighting.

    PubMed

    Wang, Rui; Pan, Minghao; Chen, Weifeng; Ren, Zhong; Zhou, Kun; Hua, Wei; Bao, Hujun

    2013-07-01

    This paper presents a new technique for real-time relighting of static scenes with all-frequency shadows from complex lighting and highly specular reflections from spatially varying BRDFs. The key idea is to depict the boundaries of visible regions using piecewise linear functions, and convert the shading computation into double product integrals—the integral of the product of lighting and BRDF on visible regions. By representing lighting and BRDF with spherical Gaussians and approximating their product using Legendre polynomials locally in visible regions, we show that such double product integrals can be evaluated in an analytic form. Given the precomputed visibility, our technique computes the visibility boundaries on the fly at each shading point, and performs the analytic integral to evaluate the shading color. The result is a real-time all-frequency relighting technique for static scenes with dynamic, spatially varying BRDFs, which can generate more accurate shadows than the state-of-the-art real-time PRT methods.

  16. Analytical approximations for the collapse of an empty spherical bubble.

    PubMed

    Obreschkow, D; Bruderer, M; Farhat, M

    2012-06-01

    The Rayleigh equation 3/2R+RR+pρ(-1)=0 with initial conditions R(0)=R(0), R(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and density ρ. The solution for r≡R/R(0) as a function of time t≡T/T(c), where R(T(c))≡0, is independent of R(0), p, and ρ. While no closed-form expression for r(t) is known, we find that r(0)(t)=(1-t(2))(2/5) approximates r(t) with an error below 1%. A systematic development in orders of t(2) further yields the 0.001% approximation r(*)(t)=r(0)(t)[1-a(1)Li(2.21)(t(2))], where a(1)≈-0.01832099 is a constant and Li is the polylogarithm. The usefulness of these approximations is demonstrated by comparison to high-precision cavitation data obtained in microgravity.

  17. Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation

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

    Bozkaya, Uğur, E-mail: ugur.bozkaya@hacettepe.edu.tr; Department of Chemistry, Atatürk University, Erzurum 25240; Sherrill, C. David

    2016-05-07

    An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the “gradient terms”: computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbitalmore » (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C{sub 10}H{sub 22}), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.« less

  18. Covariance approximation for fast and accurate computation of channelized Hotelling observer statistics

    NASA Astrophysics Data System (ADS)

    Bonetto, P.; Qi, Jinyi; Leahy, R. M.

    2000-08-01

    Describes a method for computing linear observer statistics for maximum a posteriori (MAP) reconstructions of PET images. The method is based on a theoretical approximation for the mean and covariance of MAP reconstructions. In particular, the authors derive here a closed form for the channelized Hotelling observer (CHO) statistic applied to 2D MAP images. The theoretical analysis models both the Poission statistics of PET data and the inhomogeneity of tracer uptake. The authors show reasonably good correspondence between these theoretical results and Monte Carlo studies. The accuracy and low computational cost of the approximation allow the authors to analyze the observer performance over a wide range of operating conditions and parameter settings for the MAP reconstruction algorithm.

  19. An approximate analytical methodology for the concentration CDF and corresponding adverse health effects in 3D heterogeneous aquifers

    NASA Astrophysics Data System (ADS)

    Zarlenga, Antonio; de Barros, Felipe; Fiori, Aldo

    2017-04-01

    Predicting solutes displacement in ecosystems is a complex task because of heterogeneity of hydrogeological properties and limited financial resources for characterization. As a consequence, solute transport model predictions are subject to uncertainty and probabilistic methods are invoked. Despite the significant theoretical advances in subsurface hydrology, there is a compelling need to transfer those specialized know-hows into an easy-to-use practical tool. The deterministic approach is able to capture some features of the transport behavior but its adoption in practical applications (e.g. remediation strategies or health risk assessment) is often inadequate because of its inability to accurately model the phenomena triggered by the spatial heterogeneity. The rigorous evaluation of the local contaminant concentration in natural aquifers requires an accurate estimate of the domain properties and huge computational times; those aspects limit the adoption of fully 3D numerical models. In this presentation, we illustrate a physically-based methodology to analytically estimate of the statistics of the solute concentration in natural aquifers and the related health risk. Our methodology aims to provide a simple tool for a quick assessment of the contamination level in aquifers, as function of a few relevant, physically based parameters such as the log conductivity variance, the mean flow velocity, the Péclet number. Solutions of the 3D analytical model adopt the results of previous works: transport model is based on the solutions proposed by Zarlenga and Fiori (2013, 2014) where semi-analytical relations for the statics of local contaminant concentration are carry out through a Lagrangian first-order model. As suggested in de Barros and Fiori (2014), the Beta distribution is assumed for the concentration cumulative density function (CDF). We illustrate the use of the closed-form equations for the probability of local contaminant concentration and health risk in a

  20. Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation

    NASA Astrophysics Data System (ADS)

    Salajegheh, Maral; Nejad, S. Mohammad Moosavi; Khanpour, Hamzeh; Tehrani, S. Atashbar

    2018-05-01

    In this paper, we present SMKA18 analysis, which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton g1p(x ,Q2) , neutron g1n(x ,Q2) , and deuteron g1d(x ,Q2) spin-dependent structure functions data set including the most recent high-precision measurements from COMPASS16 experiments at CERN, which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard Hessian error propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering data set and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of x .

  1. The need for accurate total cholesterol measurement. Recommended analytical goals, current state of reliability, and guidelines for better determinations.

    PubMed

    Naito, H K

    1989-03-01

    We have approached a dawn of a new era in detection, evaluation, treatment, and monitoring of individuals with elevated blood cholesterol levels who are at increased risk for CHD. The NHLBI's National Cholesterol Education Program will be the major force underlying this national awareness program, which is dependent on the clinical laboratories providing reliable data. Precision or reproducibility of results is not a problem for most of the laboratories, but accuracy is a major concern. Both the manufacturers and laboratorians need to standardize the measurement for cholesterol so that the accuracy base is traceable to the NCCLS NRS/CHOL. The manufacturers need to adopt a uniform policy that will ensure that the values assigned to calibration, quality control, and quality assurance or survey materials are accurate and traceable to the NCCLS/CHOL. Since, at present, there are some limitations of these materials caused by matrix effects, laboratories are encouraged to use the CDC-NHLBI National Reference Laboratory Network to evaluate and monitor their ability to measure patient blood cholesterol levels accurately. Major areas of analytical problems are identified and general, as well as specific, recommendations are provided to help ensure reliable measurement of cholesterol in patient specimens.

  2. Robust Accurate Non-Invasive Analyte Monitor

    DOEpatents

    Robinson, Mark R.

    1998-11-03

    An improved method and apparatus for determining noninvasively and in vivo one or more unknown values of a known characteristic, particularly the concentration of an analyte in human tissue. The method includes: (1) irradiating the tissue with infrared energy (400 nm-2400 nm) having at least several wavelengths in a given range of wavelengths so that there is differential absorption of at least some of the wavelengths by the tissue as a function of the wavelengths and the known characteristic, the differential absorption causeing intensity variations of the wavelengths incident from the tissue; (2) providing a first path through the tissue; (3) optimizing the first path for a first sub-region of the range of wavelengths to maximize the differential absorption by at least some of the wavelengths in the first sub-region; (4) providing a second path through the tissue; and (5) optimizing the second path for a second sub-region of the range, to maximize the differential absorption by at least some of the wavelengths in the second sub-region. In the preferred embodiment a third path through the tissue is provided for, which path is optimized for a third sub-region of the range. With this arrangement, spectral variations which are the result of tissue differences (e.g., melanin and temperature) can be reduced. At least one of the paths represents a partial transmission path through the tissue. This partial transmission path may pass through the nail of a finger once and, preferably, twice. Also included are apparatus for: (1) reducing the arterial pulsations within the tissue; and (2) maximizing the blood content i the tissue.

  3. On the dynamics of approximating schemes for dissipative nonlinear equations

    NASA Technical Reports Server (NTRS)

    Jones, Donald A.

    1993-01-01

    Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

  4. Analytical Validation of a Highly Quantitative, Sensitive, Accurate, and Reproducible Assay (HERmark) for the Measurement of HER2 Total Protein and HER2 Homodimers in FFPE Breast Cancer Tumor Specimens.

    PubMed

    Larson, Jeffrey S; Goodman, Laurie J; Tan, Yuping; Defazio-Eli, Lisa; Paquet, Agnes C; Cook, Jennifer W; Rivera, Amber; Frankson, Kristi; Bose, Jolly; Chen, Lili; Cheung, Judy; Shi, Yining; Irwin, Sarah; Kiss, Linda D B; Huang, Weidong; Utter, Shannon; Sherwood, Thomas; Bates, Michael; Weidler, Jodi; Parry, Gordon; Winslow, John; Petropoulos, Christos J; Whitcomb, Jeannette M

    2010-06-28

    We report here the results of the analytical validation of assays that measure HER2 total protein (H2T) and HER2 homodimer (H2D) expression in Formalin Fixed Paraffin Embedded (FFPE) breast cancer tumors as well as cell line controls. The assays are based on the VeraTag technology platform and are commercially available through a central CAP-accredited clinical reference laboratory. The accuracy of H2T measurements spans a broad dynamic range (2-3 logs) as evaluated by comparison with cross-validating technologies. The measurement of H2T expression demonstrates a sensitivity that is approximately 7-10 times greater than conventional immunohistochemistry (IHC) (HercepTest). The HERmark assay is a quantitative assay that sensitively and reproducibly measures continuous H2T and H2D protein expression levels and therefore may have the potential to stratify patients more accurately with respect to response to HER2-targeted therapies than current methods which rely on semiquantitative protein measurements (IHC) or on indirect assessments of gene amplification (FISH).

  5. Targeted Analyte Detection by Standard Addition Improves Detection Limits in MALDI Mass Spectrometry

    PubMed Central

    Eshghi, Shadi Toghi; Li, Xingde; Zhang, Hui

    2014-01-01

    Matrix-assisted laser desorption/ionization has proven an effective tool for fast and accurate determination of many molecules. However, the detector sensitivity and chemical noise compromise the detection of many invaluable low-abundance molecules from biological and clinical samples. To challenge this limitation, we developed a targeted analyte detection (TAD) technique. In TAD, the target analyte is selectively elevated by spiking a known amount of that analyte into the sample, thereby raising its concentration above the noise level, where we take advantage of the improved sensitivity to detect the presence of the endogenous analyte in the sample. We assessed TAD on three peptides in simple and complex background solutions with various exogenous analyte concentrations in two MALDI matrices. TAD successfully improved the limit of detection (LOD) of target analytes when the target peptides were added to the sample in a concentration close to optimum concentration. The optimum exogenous concentration was estimated through a quantitative method to be approximately equal to the original LOD for each target. Also, we showed that TAD could achieve LOD improvements on an average of 3-fold in a simple and 2-fold in a complex sample. TAD provides a straightforward assay to improve the LOD of generic target analytes without the need for costly hardware modifications. PMID:22877355

  6. Use of the thin sheath approximation for obtaining ion temperatures from the ISEE 1 limited aperture RPA. [for magnetosphere

    NASA Technical Reports Server (NTRS)

    Comfort, R. H.; Baugher, C. R.; Chappell, C. R.

    1982-01-01

    A procedure for analyzing low-energy (less than approximately 100 eV) ion data from the plasma composition experiment on ISEE 1 is set forth. The method is based on a derived analytic expression for particle flux to a limited aperture retarding potential analyzer (RPA) in the thin sheath approximation, which makes allowance for some effects of a charged spacecraft on plasma particle trajectories. Calculations using simulated data are employed in testing the efficacy and accuracy of the technique. On the basis of an analysis of these calculation results and the mathematical model, the method is seen as being able to provide accurate ion temperatures from all good plasmaspheric RPA data. It is noted that corresponding densities and spacecraft potentials should be accurate when spacecraft potentials are negative but that they are subject to error for positive spacecraft potentials, particularly when ion Mach numbers are much less than 1. An analysis of data from a representative ISEE 1 pass produces a plasmasphere temperature profile that is consistent in overall structure with previous observations.

  7. Finding accurate frontiers: A knowledge-intensive approach to relational learning

    NASA Technical Reports Server (NTRS)

    Pazzani, Michael; Brunk, Clifford

    1994-01-01

    An approach to analytic learning is described that searches for accurate entailments of a Horn Clause domain theory. A hill-climbing search, guided by an information based evaluation function, is performed by applying a set of operators that derive frontiers from domain theories. The analytic learning system is one component of a multi-strategy relational learning system. We compare the accuracy of concepts learned with this analytic strategy to concepts learned with an analytic strategy that operationalizes the domain theory.

  8. Testing validity of the Kirkwood approximation using an extended Sznajd model

    NASA Astrophysics Data System (ADS)

    Timpanaro, André M.; Galam, Serge

    2015-12-01

    We revisit the deduction of the exit probability of the one-dimensional Sznajd model through the Kirkwood approximation [F. Slanina et al., Europhys. Lett. 82, 18006 (2008), 10.1209/0295-5075/82/18006]. This approximation is peculiar in that, in spite of the agreement with simulation results [F. Slanina et al., Europhys. Lett. 82, 18006 (2008), 10.1209/0295-5075/82/18006; R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008), 10.1209/0295-5075/82/18007; A. M. Timpanaro and C. P. C. Prado, Phys. Rev. E 89, 052808 (2014), 10.1103/PhysRevE.89.052808], the hypothesis about the correlation lengths behind it are inconsistent and fixing these inconsistencies leads to the same results as a simple mean field. We use an extended version of the Sznajd model to test the Kirkwood approximation in a wider context. This model includes the voter, Sznajd, and "United we stand, divided we fall" models [R. A. Holley and T. M. Liggett, Ann. Prob. 3, 643 (1975), 10.1214/aop/1176996306; K. Sznajd-Weron and J. Sznajd, Int. J. Mod. Phys. C 11, 1157 (2000), 10.1142/S0129183100000936] as different parameter combinations, meaning that some analytical results from these models can be used to evaluate the performance of the Kirkwood approximation. We also compare the predicted exit probability with simulation results for networks with 103 sites. The results show clearly the regions in parameter space where the approximation gives accurate predictions, as well as where it starts failing, leading to a better understanding of its reliability.

  9. Analytical Validation of a Highly Quantitative, Sensitive, Accurate, and Reproducible Assay (HERmark®) for the Measurement of HER2 Total Protein and HER2 Homodimers in FFPE Breast Cancer Tumor Specimens

    PubMed Central

    Larson, Jeffrey S.; Goodman, Laurie J.; Tan, Yuping; Defazio-Eli, Lisa; Paquet, Agnes C.; Cook, Jennifer W.; Rivera, Amber; Frankson, Kristi; Bose, Jolly; Chen, Lili; Cheung, Judy; Shi, Yining; Irwin, Sarah; Kiss, Linda D. B.; Huang, Weidong; Utter, Shannon; Sherwood, Thomas; Bates, Michael; Weidler, Jodi; Parry, Gordon; Winslow, John; Petropoulos, Christos J.; Whitcomb, Jeannette M.

    2010-01-01

    We report here the results of the analytical validation of assays that measure HER2 total protein (H2T) and HER2 homodimer (H2D) expression in Formalin Fixed Paraffin Embedded (FFPE) breast cancer tumors as well as cell line controls. The assays are based on the VeraTag technology platform and are commercially available through a central CAP-accredited clinical reference laboratory. The accuracy of H2T measurements spans a broad dynamic range (2-3 logs) as evaluated by comparison with cross-validating technologies. The measurement of H2T expression demonstrates a sensitivity that is approximately 7–10 times greater than conventional immunohistochemistry (IHC) (HercepTest). The HERmark assay is a quantitative assay that sensitively and reproducibly measures continuous H2T and H2D protein expression levels and therefore may have the potential to stratify patients more accurately with respect to response to HER2-targeted therapies than current methods which rely on semiquantitative protein measurements (IHC) or on indirect assessments of gene amplification (FISH). PMID:21151530

  10. Interpretation of plasma impurity deposition probes. Analytic approximation

    NASA Astrophysics Data System (ADS)

    Stangeby, P. C.

    1987-10-01

    Insertion of a probe into the plasma induces a high speed flow of the hydrogenic plasma to the probe which, by friction, accelerates the impurity ions to velocities approaching the hydrogenic ion acoustic speed, i.e., higher than the impurity ion thermal speed. A simple analytic theory based on this effect provides a relation between impurity fluxes to the probe Γimp and the undisturbed impurity ion density nimp, with the hydrogenic temperature and density as input parameters. Probe size also influences the collection process and large probes are found to attract a higher flux density than small probes in the same plasma. The quantity actually measured, cimp, the impurity atom surface density (m-2) net-deposited on the probe, is related to Γimp and thus to nimp by taking into account the partial removal of deposited material caused by sputtering and the redeposition process.

  11. Effectiveness of “Thin-Layer” and “Effective Medium” Approximations in Numerical Simulation of Dielectric Spectra of Biological Cell Suspensions

    NASA Astrophysics Data System (ADS)

    Asami, Koji

    2010-12-01

    There are a few concerns in dielectric modeling of biological cells by the finite-element method (FEM) to simulate their dielectric spectra. Cells possess thin plasma membranes and membrane-bound intracellular organelles, requiring extra fine meshes and considerable computational tasks in the simulation. To solve the problems, the “thin-layer” approximation (TLA) and the “effective medium” approximation (EMA) were adopted. TLA deals with the membrane as an interface of the specific membrane impedance, and therefore it is not necessary to divide the membrane region. EMA regards the composite cytoplasm as an effective homogeneous phase whose dielectric properties are calculated separately. It was proved that TLA and EMA were both useful for greatly reducing computational tasks while accurately coinciding with analytical solutions.

  12. Cosmological applications of Padé approximant

    NASA Astrophysics Data System (ADS)

    Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

    2014-01-01

    As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

  13. Fluorescence polarization immunoassays for rapid, accurate, and sensitive determination of mycotoxins

    USDA-ARS?s Scientific Manuscript database

    Analytical methods for the determination of mycotoxins in foods are commonly based on chromatographic techniques (GC, HPLC or LC-MS). Although these methods permit a sensitive and accurate determination of the analyte, they require skilled personnel and are time-consuming, expensive, and unsuitable ...

  14. Approximate analytical solutions in the analysis of elastic structures of complex geometry

    NASA Astrophysics Data System (ADS)

    Goloskokov, Dmitriy P.; Matrosov, Alexander V.

    2018-05-01

    A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

  15. Legendre-tau approximations for functional differential equations

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1986-01-01

    The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

  16. Legendre-Tau approximations for functional differential equations

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1983-01-01

    The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

  17. Visual analytics of brain networks.

    PubMed

    Li, Kaiming; Guo, Lei; Faraco, Carlos; Zhu, Dajiang; Chen, Hanbo; Yuan, Yixuan; Lv, Jinglei; Deng, Fan; Jiang, Xi; Zhang, Tuo; Hu, Xintao; Zhang, Degang; Miller, L Stephen; Liu, Tianming

    2012-05-15

    Identification of regions of interest (ROIs) is a fundamental issue in brain network construction and analysis. Recent studies demonstrate that multimodal neuroimaging approaches and joint analysis strategies are crucial for accurate, reliable and individualized identification of brain ROIs. In this paper, we present a novel approach of visual analytics and its open-source software for ROI definition and brain network construction. By combining neuroscience knowledge and computational intelligence capabilities, visual analytics can generate accurate, reliable and individualized ROIs for brain networks via joint modeling of multimodal neuroimaging data and an intuitive and real-time visual analytics interface. Furthermore, it can be used as a functional ROI optimization and prediction solution when fMRI data is unavailable or inadequate. We have applied this approach to an operation span working memory fMRI/DTI dataset, a schizophrenia DTI/resting state fMRI (R-fMRI) dataset, and a mild cognitive impairment DTI/R-fMRI dataset, in order to demonstrate the effectiveness of visual analytics. Our experimental results are encouraging. Copyright © 2012 Elsevier Inc. All rights reserved.

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

    NASA Astrophysics Data System (ADS)

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

    2013-11-01

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

  19. An analytical model for scanning electron microscope Type I magnetic contrast with energy filtering

    NASA Astrophysics Data System (ADS)

    Chim, W. K.

    1994-02-01

    In this article, a theoretical model for type I magnetic contrast calculations in the scanning electron microscope with energy filtering is presented. This model uses an approximate form of the secondary electron (SE) energy distribution by Chung and Everhart [M. S. Chung and T. E. Everhart, J. Appl. Phys. 45, 707 (1974). Closed form analytical expressions for the contrast and quality factors, which take into consideration the work function and field-distance integral of the material being studied, are obtained. This analytical model is compared with that of a more accurate numerical model. Results showed that the contrast and quality factors for the analytical model differed by not more than 20% from the numerical model, with the actual difference depending on the range of filtered SE energies considered. This model has also been extended to the situation of a two-detector (i.e., detector A and B) configuration, in which enhanced magnetic contrast and quality factor can be obtained by operating in the ``A-B'' mode.

  20. Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis

    NASA Technical Reports Server (NTRS)

    Sobieszczanski-Sobieski, Jaroslaw; Kim, Hongman; Ragon, Scott; Soremekun, Grant; Malone, Brett

    2004-01-01

    Bi-Level Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.

  1. Approximate Model of Zone Sedimentation

    NASA Astrophysics Data System (ADS)

    Dzianik, František

    2011-12-01

    The process of zone sedimentation is affected by many factors that are not possible to express analytically. For this reason, the zone settling is evaluated in practice experimentally or by application of an empirical mathematical description of the process. The paper presents the development of approximate model of zone settling, i.e. the general function which should properly approximate the behaviour of the settling process within its entire range and at the various conditions. Furthermore, the specification of the model parameters by the regression analysis of settling test results is shown. The suitability of the model is reviewed by graphical dependencies and by statistical coefficients of correlation. The approximate model could by also useful on the simplification of process design of continual settling tanks and thickeners.

  2. Analytical Method of Approximating the Motion of a Spinning Vehicle with Variable Mass and Inertia Properties Acted Upon by Several Disturbing Parameters

    NASA Technical Reports Server (NTRS)

    Buglia, James J.; Young, George R.; Timmons, Jesse D.; Brinkworth, Helen S.

    1961-01-01

    An analytical method has been developed which approximates the dispersion of a spinning symmetrical body in a vacuum, with time-varying mass and inertia characteristics, under the action of several external disturbances-initial pitching rate, thrust misalignment, and dynamic unbalance. The ratio of the roll inertia to the pitch or yaw inertia is assumed constant. Spin was found to be very effective in reducing the dispersion due to an initial pitch rate or thrust misalignment, but was completely Ineffective in reducing the dispersion of a dynamically unbalanced body.

  3. Second derivatives for approximate spin projection methods

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

    Thompson, Lee M.; Hratchian, Hrant P., E-mail: hhratchian@ucmerced.edu

    2015-02-07

    The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical secondmore » derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.« less

  4. Algorithmic implementation of particle-particle ladder diagram approximation to study strongly-correlated metals and semiconductors

    NASA Astrophysics Data System (ADS)

    Prayogi, A.; Majidi, M. A.

    2017-07-01

    In condensed-matter physics, strongly-correlated systems refer to materials that exhibit variety of fascinating properties and ordered phases, depending on temperature, doping, and other factors. Such unique properties most notably arise due to strong electron-electron interactions, and in some cases due to interactions involving other quasiparticles as well. Electronic correlation effects are non-trivial that one may need a sufficiently accurate approximation technique with quite heavy computation, such as Quantum Monte-Carlo, in order to capture particular material properties arising from such effects. Meanwhile, less accurate techniques may come with lower numerical cost, but the ability to capture particular properties may highly depend on the choice of approximation. Among the many-body techniques derivable from Feynman diagrams, we aim to formulate algorithmic implementation of the Ladder Diagram approximation to capture the effects of electron-electron interactions. We wish to investigate how these correlation effects influence the temperature-dependent properties of strongly-correlated metals and semiconductors. As we are interested to study the temperature-dependent properties of the system, the Ladder diagram method needs to be applied in Matsubara frequency domain to obtain the self-consistent self-energy. However, at the end we would also need to compute the dynamical properties like density of states (DOS) and optical conductivity that are defined in the real frequency domain. For this purpose, we need to perform the analytic continuation procedure. At the end of this study, we will test the technique by observing the occurrence of metal-insulator transition in strongly-correlated metals, and renormalization of the band gap in strongly-correlated semiconductors.

  5. Coestimation of recombination, substitution and molecular adaptation rates by approximate Bayesian computation.

    PubMed

    Lopes, J S; Arenas, M; Posada, D; Beaumont, M A

    2014-03-01

    The estimation of parameters in molecular evolution may be biased when some processes are not considered. For example, the estimation of selection at the molecular level using codon-substitution models can have an upward bias when recombination is ignored. Here we address the joint estimation of recombination, molecular adaptation and substitution rates from coding sequences using approximate Bayesian computation (ABC). We describe the implementation of a regression-based strategy for choosing subsets of summary statistics for coding data, and show that this approach can accurately infer recombination allowing for intracodon recombination breakpoints, molecular adaptation and codon substitution rates. We demonstrate that our ABC approach can outperform other analytical methods under a variety of evolutionary scenarios. We also show that although the choice of the codon-substitution model is important, our inferences are robust to a moderate degree of model misspecification. In addition, we demonstrate that our approach can accurately choose the evolutionary model that best fits the data, providing an alternative for when the use of full-likelihood methods is impracticable. Finally, we applied our ABC method to co-estimate recombination, substitution and molecular adaptation rates from 24 published human immunodeficiency virus 1 coding data sets.

  6. Analytical model of diffuse reflectance spectrum of skin tissue

    NASA Astrophysics Data System (ADS)

    Lisenko, S. A.; Kugeiko, M. M.; Firago, V. A.; Sobchuk, A. N.

    2014-01-01

    We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions.

  7. Accurate and Efficient Approximation to the Optimized Effective Potential for Exchange

    NASA Astrophysics Data System (ADS)

    Ryabinkin, Ilya G.; Kananenka, Alexei A.; Staroverov, Viktor N.

    2013-07-01

    We devise an efficient practical method for computing the Kohn-Sham exchange-correlation potential corresponding to a Hartree-Fock electron density. This potential is almost indistinguishable from the exact-exchange optimized effective potential (OEP) and, when used as an approximation to the OEP, is vastly better than all existing models. Using our method one can obtain unambiguous, nearly exact OEPs for any reasonable finite one-electron basis set at the same low cost as the Krieger-Li-Iafrate and Becke-Johnson potentials. For all practical purposes, this solves the long-standing problem of black-box construction of OEPs in exact-exchange calculations.

  8. Self-consistent approximation beyond the CPA: Part II

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

    Kaplan, T.; Gray, L.J.

    1981-08-01

    In Part I, Professor Leath has described the substantial efforts to generalize the CPA. In this second part, a particular self-consistent approximation for random alloys developed by Kaplan, Leath, Gray, and Diehl is described. This approximation is applicable to diagonal, off-diagonal and environmental disorder, includes cluster scattering, and yields a translationally invariant and analytic (Herglotz) average Green's function. Furthermore Gray and Kaplan have shown that an approximation for alloys with short-range order can be constructed from this theory.

  9. An Approximate Approach to Automatic Kernel Selection.

    PubMed

    Ding, Lizhong; Liao, Shizhong

    2016-02-02

    Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

  10. Combining Graphical and Analytical Methods with Molecular Simulations To Analyze Time-Resolved FRET Measurements of Labeled Macromolecules Accurately

    PubMed Central

    2017-01-01

    Förster resonance energy transfer (FRET) measurements from a donor, D, to an acceptor, A, fluorophore are frequently used in vitro and in live cells to reveal information on the structure and dynamics of DA labeled macromolecules. Accurate descriptions of FRET measurements by molecular models are complicated because the fluorophores are usually coupled to the macromolecule via flexible long linkers allowing for diffusional exchange between multiple states with different fluorescence properties caused by distinct environmental quenching, dye mobilities, and variable DA distances. It is often assumed for the analysis of fluorescence intensity decays that DA distances and D quenching are uncorrelated (homogeneous quenching by FRET) and that the exchange between distinct fluorophore states is slow (quasistatic). This allows us to introduce the FRET-induced donor decay, εD(t), a function solely depending on the species fraction distribution of the rate constants of energy transfer by FRET, for a convenient joint analysis of fluorescence decays of FRET and reference samples by integrated graphical and analytical procedures. Additionally, we developed a simulation toolkit to model dye diffusion, fluorescence quenching by the protein surface, and FRET. A benchmark study with simulated fluorescence decays of 500 protein structures demonstrates that the quasistatic homogeneous model works very well and recovers for single conformations the average DA distances with an accuracy of < 2%. For more complex cases, where proteins adopt multiple conformations with significantly different dye environments (heterogeneous case), we introduce a general analysis framework and evaluate its power in resolving heterogeneities in DA distances. The developed fast simulation methods, relying on Brownian dynamics of a coarse-grained dye in its sterically accessible volume, allow us to incorporate structural information in the decay analysis for heterogeneous cases by relating dye states

  11. An efficient method for the calculation of mean extinction. I - The analyticity of the complex extinction efficiency of homogeneous spheres

    NASA Astrophysics Data System (ADS)

    Xing, Zhang-Fan; Greenberg, J. M.

    1992-11-01

    Results of an investigation of the analyticity of the complex extinction efficiency Q-tilde(ext) in different parameter domains are presented. In the size parameter domain, x = omega(a/c), numerical Hilbert transforms are used to study the analyticity properties of Q-tilde(ext) for homogeneous spheres. Q-tilde(ext) is found to be analytic in the entire lower complex x-tilde-plane when the refractive index, m, is fixed as a real constant (pure scattering) or infinity (perfect conductor); poles, however, appear in the left side of the lower complex x-tilde-plane as m becomes complex. The computation of the mean extinction produced by an extended size distribution of particles may be conveniently and accurately approximated using only a few values of the complex extinction evaluated in the complex plane.

  12. Distribution of Steps with Finite-Range Interactions: Analytic Approximations and Numerical Results

    NASA Astrophysics Data System (ADS)

    GonzáLez, Diego Luis; Jaramillo, Diego Felipe; TéLlez, Gabriel; Einstein, T. L.

    2013-03-01

    While most Monte Carlo simulations assume only nearest-neighbor steps interact elastically, most analytic frameworks (especially the generalized Wigner distribution) posit that each step elastically repels all others. In addition to the elastic repulsions, we allow for possible surface-state-mediated interactions. We investigate analytically and numerically how next-nearest neighbor (NNN) interactions and, more generally, interactions out to q'th nearest neighbor alter the form of the terrace-width distribution and of pair correlation functions (i.e. the sum over n'th neighbor distribution functions, which we investigated recently.[2] For physically plausible interactions, we find modest changes when NNN interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

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

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

    Lewis, E.R.; Schwartz, S.

    2010-03-15

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

  14. Accurate thermoelastic tensor and acoustic velocities of NaCl

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

    Marcondes, Michel L., E-mail: michel@if.usp.br; Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455; Shukla, Gaurav, E-mail: shukla@physics.umn.edu

    Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor bymore » using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.« less

  15. Universal analytical scattering form factor for shell-, core-shell, or homogeneous particles with continuously variable density profile shape.

    PubMed

    Foster, Tobias

    2011-09-01

    A novel analytical and continuous density distribution function with a widely variable shape is reported and used to derive an analytical scattering form factor that allows us to universally describe the scattering from particles with the radial density profile of homogeneous spheres, shells, or core-shell particles. Composed by the sum of two Fermi-Dirac distribution functions, the shape of the density profile can be altered continuously from step-like via Gaussian-like or parabolic to asymptotically hyperbolic by varying a single "shape parameter", d. Using this density profile, the scattering form factor can be calculated numerically. An analytical form factor can be derived using an approximate expression for the original Fermi-Dirac distribution function. This approximation is accurate for sufficiently small rescaled shape parameters, d/R (R being the particle radius), up to values of d/R ≈ 0.1, and thus captures step-like, Gaussian-like, and parabolic as well as asymptotically hyperbolic profile shapes. It is expected that this form factor is particularly useful in a model-dependent analysis of small-angle scattering data since the applied continuous and analytical function for the particle density profile can be compared directly with the density profile extracted from the data by model-free approaches like the generalized inverse Fourier transform method. © 2011 American Chemical Society

  16. Approximate analytical solution for non-Darcian flow toward a partially penetrating well in a confined aquifer

    NASA Astrophysics Data System (ADS)

    Wen, Zhang; Liu, Kai; Chen, Xiaolian

    2013-08-01

    In this study, non-Darcian flow to a partially penetrating well in a confined aquifer was investigated. The flow in the horizontal direction was assumed to be non-Darcian, while the flow in the vertical direction was assumed to be Darcian. The Izbash equation was employed to describe the non-Darcian flow in the horizontal direction of the aquifer. We used a linearization procedure to approximate the non-linear term in the governing equation enabling the mathematical model to be solved using a combination of Laplace and Fourier cosine transforms. Approximate analytical solutions for the drawdown were obtained and the impacts of different parameters on the drawdown were analyzed. The results indicated that a larger power index n in the Izbash equation leads to a larger drawdown at early times, while a larger n results in a smaller drawdown at late times. The drawdowns along the vertical direction z are symmetric if the well screen is located in the center of the aquifer, and the drawdown at the center of the aquifer is the largest along the vertical direction for this case. The length of the well screen w has little impact on the drawdown at early times, while a larger length of the well screen results in a smaller drawdown at late times. The drawdown increases with Kr at early times, while it decreases as Kr increases at late times, in which Kr is the apparent radial hydraulic conductivity. A sensitivity analysis of the parameters, i.e., the specific storage Ss, w, n and Kr, indicated that the drawdown is not sensitive to them at early times, while it is very sensitive to these parameters at late times especially to the power index n.

  17. Simple, accurate formula for the average bit error probability of multiple-input multiple-output free-space optical links over negative exponential turbulence channels.

    PubMed

    Peppas, Kostas P; Lazarakis, Fotis; Alexandridis, Antonis; Dangakis, Kostas

    2012-08-01

    In this Letter we investigate the error performance of multiple-input multiple-output free-space optical communication systems employing intensity modulation/direct detection and operating over strong atmospheric turbulence channels. Atmospheric-induced strong turbulence fading is modeled using the negative exponential distribution. For the considered system, an approximate yet accurate analytical expression for the average bit error probability is derived and an efficient method for its numerical evaluation is proposed. Numerically evaluated and computer simulation results are further provided to demonstrate the validity of the proposed mathematical analysis.

  18. Targeted analyte detection by standard addition improves detection limits in matrix-assisted laser desorption/ionization mass spectrometry.

    PubMed

    Toghi Eshghi, Shadi; Li, Xingde; Zhang, Hui

    2012-09-18

    Matrix-assisted laser desorption/ionization (MALDI) has proven an effective tool for fast and accurate determination of many molecules. However, the detector sensitivity and chemical noise compromise the detection of many invaluable low-abundance molecules from biological and clinical samples. To challenge this limitation, we developed a targeted analyte detection (TAD) technique. In TAD, the target analyte is selectively elevated by spiking a known amount of that analyte into the sample, thereby raising its concentration above the noise level, where we take advantage of the improved sensitivity to detect the presence of the endogenous analyte in the sample. We assessed TAD on three peptides in simple and complex background solutions with various exogenous analyte concentrations in two MALDI matrices. TAD successfully improved the limit of detection (LOD) of target analytes when the target peptides were added to the sample in a concentration close to optimum concentration. The optimum exogenous concentration was estimated through a quantitative method to be approximately equal to the original LOD for each target. Also, we showed that TAD could achieve LOD improvements on an average of 3-fold in a simple and 2-fold in a complex sample. TAD provides a straightforward assay to improve the LOD of generic target analytes without the need for costly hardware modifications.

  19. Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation

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

    Zhang, Du; Yang, Weitao

    An efficient method for calculating excitation energies based on the particle-particle random phase approximation (ppRPA) is presented. Neglecting the contributions from the high-lying virtual states and the low-lying core states leads to the significantly smaller active-space ppRPA matrix while keeping the error to within 0.05 eV from the corresponding full ppRPA excitation energies. The resulting computational cost is significantly reduced and becomes less than the construction of the non-local Fock exchange potential matrix in the self-consistent-field (SCF) procedure. With only a modest number of active orbitals, the original ppRPA singlet-triplet (ST) gaps as well as the low-lying single and doublemore » excitation energies can be accurately reproduced at much reduced computational costs, up to 100 times faster than the iterative Davidson diagonalization of the original full ppRPA matrix. For high-lying Rydberg excitations where the Davidson algorithm fails, the computational savings of active-space ppRPA with respect to the direct diagonalization is even more dramatic. The virtues of the underlying full ppRPA combined with the significantly lower computational cost of the active-space approach will significantly expand the applicability of the ppRPA method to calculate excitation energies at a cost of O(K^{4}), with a prefactor much smaller than a single SCF Hartree-Fock (HF)/hybrid functional calculation, thus opening up new possibilities for the quantum mechanical study of excited state electronic structure of large systems.« less

  20. Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation

    DOE PAGES

    Zhang, Du; Yang, Weitao

    2016-10-13

    An efficient method for calculating excitation energies based on the particle-particle random phase approximation (ppRPA) is presented. Neglecting the contributions from the high-lying virtual states and the low-lying core states leads to the significantly smaller active-space ppRPA matrix while keeping the error to within 0.05 eV from the corresponding full ppRPA excitation energies. The resulting computational cost is significantly reduced and becomes less than the construction of the non-local Fock exchange potential matrix in the self-consistent-field (SCF) procedure. With only a modest number of active orbitals, the original ppRPA singlet-triplet (ST) gaps as well as the low-lying single and doublemore » excitation energies can be accurately reproduced at much reduced computational costs, up to 100 times faster than the iterative Davidson diagonalization of the original full ppRPA matrix. For high-lying Rydberg excitations where the Davidson algorithm fails, the computational savings of active-space ppRPA with respect to the direct diagonalization is even more dramatic. The virtues of the underlying full ppRPA combined with the significantly lower computational cost of the active-space approach will significantly expand the applicability of the ppRPA method to calculate excitation energies at a cost of O(K^{4}), with a prefactor much smaller than a single SCF Hartree-Fock (HF)/hybrid functional calculation, thus opening up new possibilities for the quantum mechanical study of excited state electronic structure of large systems.« less

  1. Conservative Analytical Collision Probabilities for Orbital Formation Flying

    NASA Technical Reports Server (NTRS)

    Carpenter, J. Russell

    2004-01-01

    The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

  2. 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.

  3. Quasistatic limit of the strong-field approximation describing atoms in intense laser fields: Circular polarization

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

    Bauer, Jaroslaw H.

    2011-03-15

    In the recent work of Vanne and Saenz [Phys. Rev. A 75, 063403 (2007)] the quasistatic limit of the velocity gauge strong-field approximation describing the ionization rate of atomic or molecular systems exposed to linearly polarized laser fields was derived. It was shown that in the low-frequency limit the ionization rate is proportional to the laser frequency {omega} (for a constant intensity of the laser field). In the present work I show that for circularly polarized laser fields the ionization rate is proportional to {omega}{sup 4} for H(1s) and H(2s) atoms, to {omega}{sup 6} for H(2p{sub x}) and H(2p{sub y})more » atoms, and to {omega}{sup 8} for H(2p{sub z}) atoms. The analytical expressions for asymptotic ionization rates (which become nearly accurate in the limit {omega}{yields}0) contain no summations over multiphoton contributions. For very low laser frequencies (optical or infrared) these expressions usually remain with an order-of-magnitude agreement with the velocity gauge strong-field approximation.« less

  4. Insight solutions are correct more often than analytic solutions

    PubMed Central

    Salvi, Carola; Bricolo, Emanuela; Kounios, John; Bowden, Edward; Beeman, Mark

    2016-01-01

    How accurate are insights compared to analytical solutions? In four experiments, we investigated how participants’ solving strategies influenced their solution accuracies across different types of problems, including one that was linguistic, one that was visual and two that were mixed visual-linguistic. In each experiment, participants’ self-judged insight solutions were, on average, more accurate than their analytic ones. We hypothesised that insight solutions have superior accuracy because they emerge into consciousness in an all-or-nothing fashion when the unconscious solving process is complete, whereas analytic solutions can be guesses based on conscious, prematurely terminated, processing. This hypothesis is supported by the finding that participants’ analytic solutions included relatively more incorrect responses (i.e., errors of commission) than timeouts (i.e., errors of omission) compared to their insight responses. PMID:27667960

  5. A general analytical platform and strategy in search for illegal drugs.

    PubMed

    Johansson, Monika; Fransson, Dick; Rundlöf, Torgny; Huynh, Ngoc-Hang; Arvidsson, Torbjörn

    2014-11-01

    An effective screening procedure to identify and quantify active pharmaceutical substances in suspected illegal medicinal products is described. The analytical platform, consisting of accurate mass determination with liquid chromatography time-of-flight mass spectrometry (LC-QTOF-MS) in combination with nuclear magnetic resonance (NMR) spectroscopy provides an excellent analytical tool to screen for unknowns in medicinal products, food supplements and herbal formulations. This analytical approach has been successfully applied to analyze thousands of samples. The general screening method usually starts with a methanol extraction of tablets/capsules followed by liquid chromatographic separation on a Halo Phenyl-Hexyl column (2.7μm; 100mm×2.1mm) using an acetonitrile/0.1% formic acid gradient as eluent. The accurate mass of peaks of interest was recorded and a search made against an in-house database containing approximately 4200 substances, mostly pharmaceutical compounds. The search could be general or tailored against different classes of compounds. Hits were confirmed by analyzing a reference substance and/or by NMR. Quantification was normally performed with quantitative NMR (qNMR) spectroscopy. Applications for weight-loss substances like sibutramine and orlistat, sexual potency enhancement (PDE-5 inhibitors), and analgesic drugs are presented in this study. We have also identified prostaglandin analogues in eyelash growth serum, exemplified by isopropyl cloprostenate and bimatoprost. For creams and ointments, matrix solid-phase dispersion (MSPD) was found to give a clean extracts with high recovery prior to LC-MS analyses. The structural elucidation of cetilistat, a new weight-loss substance recently found in illegal medicines purchased over the Internet, is also presented. Copyright © 2014 Elsevier B.V. All rights reserved.

  6. Approximation methods in gravitational-radiation theory

    NASA Technical Reports Server (NTRS)

    Will, C. M.

    1986-01-01

    The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.

  7. Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk.

    PubMed

    Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias

    2018-01-22

    Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

  8. Accurate approximation method for prediction of class I MHC affinities for peptides of length 8, 10 and 11 using prediction tools trained on 9mers.

    PubMed

    Lundegaard, Claus; Lund, Ole; Nielsen, Morten

    2008-06-01

    Several accurate prediction systems have been developed for prediction of class I major histocompatibility complex (MHC):peptide binding. Most of these are trained on binding affinity data of primarily 9mer peptides. Here, we show how prediction methods trained on 9mer data can be used for accurate binding affinity prediction of peptides of length 8, 10 and 11. The method gives the opportunity to predict peptides with a different length than nine for MHC alleles where no such peptides have been measured. As validation, the performance of this approach is compared to predictors trained on peptides of the peptide length in question. In this validation, the approximation method has an accuracy that is comparable to or better than methods trained on a peptide length identical to the predicted peptides. The algorithm has been implemented in the web-accessible servers NetMHC-3.0: http://www.cbs.dtu.dk/services/NetMHC-3.0, and NetMHCpan-1.1: http://www.cbs.dtu.dk/services/NetMHCpan-1.1

  9. New realisation of Preisach model using adaptive polynomial approximation

    NASA Astrophysics Data System (ADS)

    Liu, Van-Tsai; Lin, Chun-Liang; Wing, Home-Young

    2012-09-01

    Modelling system with hysteresis has received considerable attention recently due to the increasing accurate requirement in engineering applications. The classical Preisach model (CPM) is the most popular model to demonstrate hysteresis which can be represented by infinite but countable first-order reversal curves (FORCs). The usage of look-up tables is one way to approach the CPM in actual practice. The data in those tables correspond with the samples of a finite number of FORCs. This approach, however, faces two major problems: firstly, it requires a large amount of memory space to obtain an accurate prediction of hysteresis; secondly, it is difficult to derive efficient ways to modify the data table to reflect the timing effect of elements with hysteresis. To overcome, this article proposes the idea of using a set of polynomials to emulate the CPM instead of table look-up. The polynomial approximation requires less memory space for data storage. Furthermore, the polynomial coefficients can be obtained accurately by using the least-square approximation or adaptive identification algorithm, such as the possibility of accurate tracking of hysteresis model parameters.

  10. Arbitrarily accurate twin composite π -pulse sequences

    NASA Astrophysics Data System (ADS)

    Torosov, Boyan T.; Vitanov, Nikolay V.

    2018-04-01

    We present three classes of symmetric broadband composite pulse sequences. The composite phases are given by analytic formulas (rational fractions of π ) valid for any number of constituent pulses. The transition probability is expressed by simple analytic formulas and the order of pulse area error compensation grows linearly with the number of pulses. Therefore, any desired compensation order can be produced by an appropriate composite sequence; in this sense, they are arbitrarily accurate. These composite pulses perform equally well as or better than previously published ones. Moreover, the current sequences are more flexible as they allow total pulse areas of arbitrary integer multiples of π .

  11. Recognition of computerized facial approximations by familiar assessors.

    PubMed

    Richard, Adam H; Monson, Keith L

    2017-11-01

    Studies testing the effectiveness of facial approximations typically involve groups of participants who are unfamiliar with the approximated individual(s). This limitation requires the use of photograph arrays including a picture of the subject for comparison to the facial approximation. While this practice is often necessary due to the difficulty in obtaining a group of assessors who are familiar with the approximated subject, it may not accurately simulate the thought process of the target audience (friends and family members) in comparing a mental image of the approximated subject to the facial approximation. As part of a larger process to evaluate the effectiveness and best implementation of the ReFace facial approximation software program, the rare opportunity arose to conduct a recognition study using assessors who were personally acquainted with the subjects of the approximations. ReFace facial approximations were generated based on preexisting medical scans, and co-workers of the scan donors were tested on whether they could accurately pick out the approximation of their colleague from arrays of facial approximations. Results from the study demonstrated an overall poor recognition performance (i.e., where a single choice within a pool is not enforced) for individuals who were familiar with the approximated subjects. Out of 220 recognition tests only 10.5% resulted in the assessor selecting the correct approximation (or correctly choosing not to make a selection when the array consisted only of foils), an outcome that was not significantly different from the 9% random chance rate. When allowed to select multiple approximations the assessors felt resembled the target individual, the overall sensitivity for ReFace approximations was 16.0% and the overall specificity was 81.8%. These results differ markedly from the results of a previous study using assessors who were unfamiliar with the approximated subjects. Some possible explanations for this disparity in

  12. Contextual classification of multispectral image data: Approximate algorithm

    NASA Technical Reports Server (NTRS)

    Tilton, J. C. (Principal Investigator)

    1980-01-01

    An approximation to a classification algorithm incorporating spatial context information in a general, statistical manner is presented which is computationally less intensive. Classifications that are nearly as accurate are produced.

  13. Assessing the Clinical Impact of Approximations in Analytical Dose Calculations for Proton Therapy

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

    Schuemann, Jan, E-mail: jschuemann@mgh.harvard.edu; Giantsoudi, Drosoula; Grassberger, Clemens

    2015-08-01

    Purpose: To assess the impact of approximations in current analytical dose calculation methods (ADCs) on tumor control probability (TCP) in proton therapy. Methods: Dose distributions planned with ADC were compared with delivered dose distributions as determined by Monte Carlo simulations. A total of 50 patients were investigated in this analysis with 10 patients per site for 5 treatment sites (head and neck, lung, breast, prostate, liver). Differences were evaluated using dosimetric indices based on a dose-volume histogram analysis, a γ-index analysis, and estimations of TCP. Results: We found that ADC overestimated the target doses on average by 1% to 2%more » for all patients considered. The mean dose, D95, D50, and D02 (the dose value covering 95%, 50% and 2% of the target volume, respectively) were predicted within 5% of the delivered dose. The γ-index passing rate for target volumes was above 96% for a 3%/3 mm criterion. Differences in TCP were up to 2%, 2.5%, 6%, 6.5%, and 11% for liver and breast, prostate, head and neck, and lung patients, respectively. Differences in normal tissue complication probabilities for bladder and anterior rectum of prostate patients were less than 3%. Conclusion: Our results indicate that current dose calculation algorithms lead to underdosage of the target by as much as 5%, resulting in differences in TCP of up to 11%. To ensure full target coverage, advanced dose calculation methods like Monte Carlo simulations may be necessary in proton therapy. Monte Carlo simulations may also be required to avoid biases resulting from systematic discrepancies in calculated dose distributions for clinical trials comparing proton therapy with conventional radiation therapy.« less

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

    PubMed

    Theodorakis, Stavros

    2003-06-01

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

  15. Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas

    NASA Astrophysics Data System (ADS)

    Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.

    2010-03-01

    infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

  16. Analytic energy gradients for orbital-optimized MP3 and MP2.5 with the density-fitting approximation: An efficient implementation.

    PubMed

    Bozkaya, Uğur

    2018-03-15

    Efficient implementations of analytic gradients for the orbital-optimized MP3 and MP2.5 and their standard versions with the density-fitting approximation, which are denoted as DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5, are presented. The DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5 methods are applied to a set of alkanes and noncovalent interaction complexes to compare the computational cost with the conventional MP3, MP2.5, OMP3, and OMP2.5. Our results demonstrate that density-fitted perturbation theory (DF-MP) methods considered substantially reduce the computational cost compared to conventional MP methods. The efficiency of our DF-MP methods arise from the reduced input/output (I/O) time and the acceleration of gradient related terms, such as computations of particle density and generalized Fock matrices (PDMs and GFM), solution of the Z-vector equation, back-transformations of PDMs and GFM, and evaluation of analytic gradients in the atomic orbital basis. Further, application results show that errors introduced by the DF approach are negligible. Mean absolute errors for bond lengths of a molecular set, with the cc-pCVQZ basis set, is 0.0001-0.0002 Å. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  17. A hybrid analytical model for open-circuit field calculation of multilayer interior permanent magnet machines

    NASA Astrophysics Data System (ADS)

    Zhang, Zhen; Xia, Changliang; Yan, Yan; Geng, Qiang; Shi, Tingna

    2017-08-01

    Due to the complicated rotor structure and nonlinear saturation of rotor bridges, it is difficult to build a fast and accurate analytical field calculation model for multilayer interior permanent magnet (IPM) machines. In this paper, a hybrid analytical model suitable for the open-circuit field calculation of multilayer IPM machines is proposed by coupling the magnetic equivalent circuit (MEC) method and the subdomain technique. In the proposed analytical model, the rotor magnetic field is calculated by the MEC method based on the Kirchhoff's law, while the field in the stator slot, slot opening and air-gap is calculated by subdomain technique based on the Maxwell's equation. To solve the whole field distribution of the multilayer IPM machines, the coupled boundary conditions on the rotor surface are deduced for the coupling of the rotor MEC and the analytical field distribution of the stator slot, slot opening and air-gap. The hybrid analytical model can be used to calculate the open-circuit air-gap field distribution, back electromotive force (EMF) and cogging torque of multilayer IPM machines. Compared with finite element analysis (FEA), it has the advantages of faster modeling, less computation source occupying and shorter time consuming, and meanwhile achieves the approximate accuracy. The analytical model is helpful and applicable for the open-circuit field calculation of multilayer IPM machines with any size and pole/slot number combination.

  18. The Analytical Limits of Modeling Short Diffusion Timescales

    NASA Astrophysics Data System (ADS)

    Bradshaw, R. W.; Kent, A. J.

    2016-12-01

    Chemical and isotopic zoning in minerals is widely used to constrain the timescales of magmatic processes such as magma mixing and crystal residence, etc. via diffusion modeling. Forward modeling of diffusion relies on fitting diffusion profiles to measured compositional gradients. However, an individual measurement is essentially an average composition for a segment of the gradient defined by the spatial resolution of the analysis. Thus there is the potential for the analytical spatial resolution to limit the timescales that can be determined for an element of given diffusivity, particularly where the scale of the gradient approaches that of the measurement. Here we use a probabilistic modeling approach to investigate the effect of analytical spatial resolution on estimated timescales from diffusion modeling. Our method investigates how accurately the age of a synthetic diffusion profile can be obtained by modeling an "unknown" profile derived from discrete sampling of the synthetic compositional gradient at a given spatial resolution. We also include the effects of analytical uncertainty and the position of measurements relative to the diffusion gradient. We apply this method to the spatial resolutions of common microanalytical techniques (LA-ICP-MS, SIMS, EMP, NanoSIMS). Our results confirm that for a given diffusivity, higher spatial resolution gives access to shorter timescales, and that each analytical spacing has a minimum timescale, below which it overestimates the timescale. For example, for Ba diffusion in plagioclase at 750 °C timescales are accurate (within 20%) above 10, 100, 2,600, and 71,000 years at 0.3, 1, 5, and 25 mm spatial resolution, respectively. For Sr diffusion in plagioclase at 750 °C, timescales are accurate above 0.02, 0.2, 4, and 120 years at the same spatial resolutions. Our results highlight the importance of selecting appropriate analytical techniques to estimate accurate diffusion-based timescales.

  19. Minimax rational approximation of the Fermi-Dirac distribution.

    PubMed

    Moussa, Jonathan E

    2016-10-28

    Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ -1 )) poles to achieve an error tolerance ϵ at temperature β -1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δ occ , the occupied energy interval. This is particularly beneficial when Δ ≫ Δ occ , such as in electronic structure calculations that use a large basis set.

  20. Minimax rational approximation of the Fermi-Dirac distribution

    NASA Astrophysics Data System (ADS)

    Moussa, Jonathan E.

    2016-10-01

    Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ɛ-1)) poles to achieve an error tolerance ɛ at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.

  1. Approximation methods for combined thermal/structural design

    NASA Technical Reports Server (NTRS)

    Haftka, R. T.; Shore, C. P.

    1979-01-01

    Two approximation concepts for combined thermal/structural design are evaluated. The first concept is an approximate thermal analysis based on the first derivatives of structural temperatures with respect to design variables. Two commonly used first-order Taylor series expansions are examined. The direct and reciprocal expansions are special members of a general family of approximations, and for some conditions other members of that family of approximations are more accurate. Several examples are used to compare the accuracy of the different expansions. The second approximation concept is the use of critical time points for combined thermal and stress analyses of structures with transient loading conditions. Significant time savings are realized by identifying critical time points and performing the stress analysis for those points only. The design of an insulated panel which is exposed to transient heating conditions is discussed.

  2. Conservative Analytical Collision Probability for Design of Orbital Formations

    NASA Technical Reports Server (NTRS)

    Carpenter, J. Russell

    2004-01-01

    The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

  3. pyJac: Analytical Jacobian generator for chemical kinetics

    NASA Astrophysics Data System (ADS)

    Niemeyer, Kyle E.; Curtis, Nicholas J.; Sung, Chih-Jen

    2017-06-01

    Accurate simulations of combustion phenomena require the use of detailed chemical kinetics in order to capture limit phenomena such as ignition and extinction as well as predict pollutant formation. However, the chemical kinetic models for hydrocarbon fuels of practical interest typically have large numbers of species and reactions and exhibit high levels of mathematical stiffness in the governing differential equations, particularly for larger fuel molecules. In order to integrate the stiff equations governing chemical kinetics, generally reactive-flow simulations rely on implicit algorithms that require frequent Jacobian matrix evaluations. Some in situ and a posteriori computational diagnostics methods also require accurate Jacobian matrices, including computational singular perturbation and chemical explosive mode analysis. Typically, finite differences numerically approximate these, but for larger chemical kinetic models this poses significant computational demands since the number of chemical source term evaluations scales with the square of species count. Furthermore, existing analytical Jacobian tools do not optimize evaluations or support emerging SIMD processors such as GPUs. Here we introduce pyJac, a Python-based open-source program that generates analytical Jacobian matrices for use in chemical kinetics modeling and analysis. In addition to producing the necessary customized source code for evaluating reaction rates (including all modern reaction rate formulations), the chemical source terms, and the Jacobian matrix, pyJac uses an optimized evaluation order to minimize computational and memory operations. As a demonstration, we first establish the correctness of the Jacobian matrices for kinetic models of hydrogen, methane, ethylene, and isopentanol oxidation (number of species ranging 13-360) by showing agreement within 0.001% of matrices obtained via automatic differentiation. We then demonstrate the performance achievable on CPUs and GPUs using py

  4. Approximate Evaluation of Reliability and Availability via Perturbation Analysis.

    DTIC Science & Technology

    1986-12-01

    generating the dxact answers to which the results of the approximation will be compared are discussed:." - 87 7" 2 04 2LOISTRIGUTIONIAVAILASILITYI OF...appropriately, constructing the Markov process that approximately governs interclass behavior from the result above (this is called the enlarged... compared to a numerical or analytical computation of the aame quantities. This work and its continuation represents our progress so far on Goal 3. 2.4I

  5. Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

    NASA Astrophysics Data System (ADS)

    Cummings, Patrick

    We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

  6. A generic analytical foot rollover model for predicting translational ankle kinematics in gait simulation studies.

    PubMed

    Ren, Lei; Howard, David; Ren, Luquan; Nester, Chris; Tian, Limei

    2010-01-19

    The objective of this paper is to develop an analytical framework to representing the ankle-foot kinematics by modelling the foot as a rollover rocker, which cannot only be used as a generic tool for general gait simulation but also allows for case-specific modelling if required. Previously, the rollover models used in gait simulation have often been based on specific functions that have usually been of a simple form. In contrast, the analytical model described here is in a general form that the effective foot rollover shape can be represented by any polar function rho=rho(phi). Furthermore, a normalized generic foot rollover model has been established based on a normative foot rollover shape dataset of 12 normal healthy subjects. To evaluate model accuracy, the predicted ankle motions and the centre of pressure (CoP) were compared with measurement data for both subject-specific and general cases. The results demonstrated that the ankle joint motions in both vertical and horizontal directions (relative RMSE approximately 10%) and CoP (relative RMSE approximately 15% for most of the subjects) are accurately predicted over most of the stance phase (from 10% to 90% of stance). However, we found that the foot cannot be very accurately represented by a rollover model just after heel strike (HS) and just before toe off (TO), probably due to shear deformation of foot plantar tissues (ankle motion can occur without any foot rotation). The proposed foot rollover model can be used in both inverse and forward dynamics gait simulation studies and may also find applications in rehabilitation engineering. Copyright 2009 Elsevier Ltd. All rights reserved.

  7. Analytical solution for a class of network dynamics with mechanical and financial applications

    NASA Astrophysics Data System (ADS)

    Krejčí, P.; Lamba, H.; Melnik, S.; Rachinskii, D.

    2014-09-01

    We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks. As illustrative applications, we introduce a quasistatic mechanical model with objects interacting via frictional forces and a financial market model with avalanches and critical behavior that are generated by momentum trading strategies.

  8. Scaling in situ cosmogenic nuclide production rates using analytical approximations to atmospheric cosmic-ray fluxes

    NASA Astrophysics Data System (ADS)

    Lifton, Nathaniel; Sato, Tatsuhiko; Dunai, Tibor J.

    2014-01-01

    Several models have been proposed for scaling in situ cosmogenic nuclide production rates from the relatively few sites where they have been measured to other sites of interest. Two main types of models are recognized: (1) those based on data from nuclear disintegrations in photographic emulsions combined with various neutron detectors, and (2) those based largely on neutron monitor data. However, stubborn discrepancies between these model types have led to frequent confusion when calculating surface exposure ages from production rates derived from the models. To help resolve these discrepancies and identify the sources of potential biases in each model, we have developed a new scaling model based on analytical approximations to modeled fluxes of the main atmospheric cosmic-ray particles responsible for in situ cosmogenic nuclide production. Both the analytical formulations and the Monte Carlo model fluxes on which they are based agree well with measured atmospheric fluxes of neutrons, protons, and muons, indicating they can serve as a robust estimate of the atmospheric cosmic-ray flux based on first principles. We are also using updated records for quantifying temporal and spatial variability in geomagnetic and solar modulation effects on the fluxes. A key advantage of this new model (herein termed LSD) over previous Monte Carlo models of cosmogenic nuclide production is that it allows for faster estimation of scaling factors based on time-varying geomagnetic and solar inputs. Comparing scaling predictions derived from the LSD model with those of previously published models suggest potential sources of bias in the latter can be largely attributed to two factors: different energy responses of the secondary neutron detectors used in developing the models, and different geomagnetic parameterizations. Given that the LSD model generates flux spectra for each cosmic-ray particle of interest, it is also relatively straightforward to generate nuclide-specific scaling

  9. Approximate Computing Techniques for Iterative Graph Algorithms

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

    Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh

    Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with lowmore » impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.« less

  10. Minimax rational approximation of the Fermi-Dirac distribution

    DOE PAGES

    Moussa, Jonathan E.

    2016-10-27

    Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ –1)) poles to achieve an error tolerance ϵ at temperature β –1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δ occ, the occupied energy interval. Furthermore, this is particularly beneficial when Δ >> Δ occ, such as in electronic structure calculations that use a large basis set.

  11. Substrate mass transfer: analytical approach for immobilized enzyme reactions

    NASA Astrophysics Data System (ADS)

    Senthamarai, R.; Saibavani, T. N.

    2018-04-01

    In this paper, the boundary value problem in immobilized enzyme reactions is formulated and approximate expression for substrate concentration without external mass transfer resistance is presented. He’s variational iteration method is used to give approximate and analytical solutions of non-linear differential equation containing a non linear term related to enzymatic reaction. The relevant analytical solution for the dimensionless substrate concentration profile is discussed in terms of dimensionless reaction parameters α and β.

  12. Recent advances in approximation concepts for optimum structural design

    NASA Technical Reports Server (NTRS)

    Barthelemy, Jean-Francois M.; Haftka, Raphael T.

    1991-01-01

    The basic approximation concepts used in structural optimization are reviewed. Some of the most recent developments in that area since the introduction of the concept in the mid-seventies are discussed. The paper distinguishes between local, medium-range, and global approximations; it covers functions approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It also appears that some new methodologies are emerging which could greatly benefit from the introduction of new computer architecture.

  13. Hydraulic modeling of riverbank filtration systems with curved boundaries using analytic elements and series solutions

    NASA Astrophysics Data System (ADS)

    Bakker, Mark

    2010-08-01

    A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases.

  14. High accurate interpolation of NURBS tool path for CNC machine tools

    NASA Astrophysics Data System (ADS)

    Liu, Qiang; Liu, Huan; Yuan, Songmei

    2016-09-01

    Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level without sacrificing the computing efficiency at present. In order to solve this problem, a high accurate interpolation method for NURBS tool path is proposed. The proposed method can efficiently reduce the feedrate fluctuation by forming a quartic equation with respect to the curve parameter increment, which can be efficiently solved by analytic methods in real-time. Theoretically, the proposed method can totally eliminate the feedrate fluctuation for any 2nd degree NURBS curves and can interpolate 3rd degree NURBS curves with minimal feedrate fluctuation. Moreover, a smooth feedrate planning algorithm is also proposed to generate smooth tool motion with considering multiple constraints and scheduling errors by an efficient planning strategy. Experiments are conducted to verify the feasibility and applicability of the proposed method. This research presents a novel NURBS interpolation method with not only high accuracy but also satisfying computing efficiency.

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

    NASA Technical Reports Server (NTRS)

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

    1979-01-01

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

  16. Modern analytical chemistry in the contemporary world

    NASA Astrophysics Data System (ADS)

    Šíma, Jan

    2016-12-01

    Students not familiar with chemistry tend to misinterpret analytical chemistry as some kind of the sorcery where analytical chemists working as modern wizards handle magical black boxes able to provide fascinating results. However, this approach is evidently improper and misleading. Therefore, the position of modern analytical chemistry among sciences and in the contemporary world is discussed. Its interdisciplinary character and the necessity of the collaboration between analytical chemists and other experts in order to effectively solve the actual problems of the human society and the environment are emphasized. The importance of the analytical method validation in order to obtain the accurate and precise results is highlighted. The invalid results are not only useless; they can often be even fatal (e.g., in clinical laboratories). The curriculum of analytical chemistry at schools and universities is discussed. It is referred to be much broader than traditional equilibrium chemistry coupled with a simple description of individual analytical methods. Actually, the schooling of analytical chemistry should closely connect theory and practice.

  17. Low-dimensional, morphologically accurate models of subthreshold membrane potential

    PubMed Central

    Kellems, Anthony R.; Roos, Derrick; Xiao, Nan; Cox, Steven J.

    2009-01-01

    The accurate simulation of a neuron’s ability to integrate distributed synaptic input typically requires the simultaneous solution of tens of thousands of ordinary differential equations. For, in order to understand how a cell distinguishes between input patterns we apparently need a model that is biophysically accurate down to the space scale of a single spine, i.e., 1 μm. We argue here that one can retain this highly detailed input structure while dramatically reducing the overall system dimension if one is content to accurately reproduce the associated membrane potential at a small number of places, e.g., at the site of action potential initiation, under subthreshold stimulation. The latter hypothesis permits us to approximate the active cell model with an associated quasi-active model, which in turn we reduce by both time-domain (Balanced Truncation) and frequency-domain (ℋ2 approximation of the transfer function) methods. We apply and contrast these methods on a suite of typical cells, achieving up to four orders of magnitude in dimension reduction and an associated speed-up in the simulation of dendritic democratization and resonance. We also append a threshold mechanism and indicate that this reduction has the potential to deliver an accurate quasi-integrate and fire model. PMID:19172386

  18. Green-Ampt approximations: A comprehensive analysis

    NASA Astrophysics Data System (ADS)

    Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K.

    2016-04-01

    Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems.

  19. Estimating ice particle scattering properties using a modified Rayleigh-Gans approximation

    NASA Astrophysics Data System (ADS)

    Lu, Yinghui; Clothiaux, Eugene E.; Aydin, Kültegin; Verlinde, Johannes

    2014-09-01

    A modification to the Rayleigh-Gans approximation is made that includes self-interactions between different parts of an ice crystal, which both improves the accuracy of the Rayleigh-Gans approximation and extends its applicability to polarization-dependent parameters. This modified Rayleigh-Gans approximation is both efficient and reasonably accurate for particles with at least one dimension much smaller than the wavelength (e.g., dendrites at millimeter or longer wavelengths) or particles with sparse structures (e.g., low-density aggregates). Relative to the Generalized Multiparticle Mie method, backscattering reflectivities at horizontal transmit and receive polarization (HH) (ZHH) computed with this modified Rayleigh-Gans approach are about 3 dB more accurate than with the traditional Rayleigh-Gans approximation. For realistic particle size distributions and pristine ice crystals the modified Rayleigh-Gans approach agrees with the Generalized Multiparticle Mie method to within 0.5 dB for ZHH whereas for the polarimetric radar observables differential reflectivity (ZDR) and specific differential phase (KDP) agreement is generally within 0.7 dB and 13%, respectively. Compared to the A-DDA code, the modified Rayleigh-Gans approximation is several to tens of times faster if scattering properties for different incident angles and particle orientations are calculated. These accuracies and computational efficiencies are sufficient to make this modified Rayleigh-Gans approach a viable alternative to the Rayleigh-Gans approximation in some applications such as millimeter to centimeter wavelength radars and to other methods that assume simpler, less accurate shapes for ice crystals. This method should not be used on materials with dielectric properties much different from ice and on compact particles much larger than the wavelength.

  20. Stable computations with flat radial basis functions using vector-valued rational approximations

    NASA Astrophysics Data System (ADS)

    Wright, Grady B.; Fornberg, Bengt

    2017-02-01

    One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are 'flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vector-valued analytic functions with the property that all components of the vector share the same singularities. This new algorithm (RBF-RA) is more accurate, robust, and easier to implement than the Contour-Padé method, which is similarly based on vector-valued rational approximation. In contrast to the stable RBF-QR and RBF-GA algorithms, which are based on finding a better conditioned base in the same RBF-space, the new algorithm can be used with any type of smooth radial kernel, and it is also applicable to a wider range of tasks (including calculating Hermite type implicit RBF-FD stencils). We present a series of numerical experiments demonstrating the effectiveness of this new method for computing RBF interpolants in the flat regime. We also demonstrate the flexibility of the method by using it to compute implicit RBF-FD formulas in the flat regime and then using these for solving Poisson's equation in a 3-D spherical shell.

  1. A semi-analytical bearing model considering outer race flexibility for model based bearing load monitoring

    NASA Astrophysics Data System (ADS)

    Kerst, Stijn; Shyrokau, Barys; Holweg, Edward

    2018-05-01

    This paper proposes a novel semi-analytical bearing model addressing flexibility of the bearing outer race structure. It furthermore presents the application of this model in a bearing load condition monitoring approach. The bearing model is developed as current computational low cost bearing models fail to provide an accurate description of the more and more common flexible size and weight optimized bearing designs due to their assumptions of rigidity. In the proposed bearing model raceway flexibility is described by the use of static deformation shapes. The excitation of the deformation shapes is calculated based on the modelled rolling element loads and a Fourier series based compliance approximation. The resulting model is computational low cost and provides an accurate description of the rolling element loads for flexible outer raceway structures. The latter is validated by a simulation-based comparison study with a well-established bearing simulation software tool. An experimental study finally shows the potential of the proposed model in a bearing load monitoring approach.

  2. NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

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

    Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.

    The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, ourmore » FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.« less

  3. PyVCI: A flexible open-source code for calculating accurate molecular infrared spectra

    NASA Astrophysics Data System (ADS)

    Sibaev, Marat; Crittenden, Deborah L.

    2016-06-01

    The PyVCI program package is a general purpose open-source code for simulating accurate molecular spectra, based upon force field expansions of the potential energy surface in normal mode coordinates. It includes harmonic normal coordinate analysis and vibrational configuration interaction (VCI) algorithms, implemented primarily in Python for accessibility but with time-consuming routines written in C. Coriolis coupling terms may be optionally included in the vibrational Hamiltonian. Non-negligible VCI matrix elements are stored in sparse matrix format to alleviate the diagonalization problem. CPU and memory requirements may be further controlled by algorithmic choices and/or numerical screening procedures, and recommended values are established by benchmarking using a test set of 44 molecules for which accurate analytical potential energy surfaces are available. Force fields in normal mode coordinates are obtained from the PyPES library of high quality analytical potential energy surfaces (to 6th order) or by numerical differentiation of analytic second derivatives generated using the GAMESS quantum chemical program package (to 4th order).

  4. Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory.

    PubMed

    Bardhan, Jaydeep P

    2008-10-14

    The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement

  5. Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

    NASA Technical Reports Server (NTRS)

    Warming, Robert F.; Beam, Richard M.

    1988-01-01

    Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

  6. Collaborative Visual Analytics: A Health Analytics Approach to Injury Prevention

    PubMed Central

    Fisher, Brian; Smith, Jennifer; Pike, Ian

    2017-01-01

    Background: Accurate understanding of complex health data is critical in order to deal with wicked health problems and make timely decisions. Wicked problems refer to ill-structured and dynamic problems that combine multidimensional elements, which often preclude the conventional problem solving approach. This pilot study introduces visual analytics (VA) methods to multi-stakeholder decision-making sessions about child injury prevention; Methods: Inspired by the Delphi method, we introduced a novel methodology—group analytics (GA). GA was pilot-tested to evaluate the impact of collaborative visual analytics on facilitating problem solving and supporting decision-making. We conducted two GA sessions. Collected data included stakeholders’ observations, audio and video recordings, questionnaires, and follow up interviews. The GA sessions were analyzed using the Joint Activity Theory protocol analysis methods; Results: The GA methodology triggered the emergence of ‘common ground’ among stakeholders. This common ground evolved throughout the sessions to enhance stakeholders’ verbal and non-verbal communication, as well as coordination of joint activities and ultimately collaboration on problem solving and decision-making; Conclusions: Understanding complex health data is necessary for informed decisions. Equally important, in this case, is the use of the group analytics methodology to achieve ‘common ground’ among diverse stakeholders about health data and their implications. PMID:28895928

  7. Collaborative Visual Analytics: A Health Analytics Approach to Injury Prevention.

    PubMed

    Al-Hajj, Samar; Fisher, Brian; Smith, Jennifer; Pike, Ian

    2017-09-12

    Background : Accurate understanding of complex health data is critical in order to deal with wicked health problems and make timely decisions. Wicked problems refer to ill-structured and dynamic problems that combine multidimensional elements, which often preclude the conventional problem solving approach. This pilot study introduces visual analytics (VA) methods to multi-stakeholder decision-making sessions about child injury prevention; Methods : Inspired by the Delphi method, we introduced a novel methodology-group analytics (GA). GA was pilot-tested to evaluate the impact of collaborative visual analytics on facilitating problem solving and supporting decision-making. We conducted two GA sessions. Collected data included stakeholders' observations, audio and video recordings, questionnaires, and follow up interviews. The GA sessions were analyzed using the Joint Activity Theory protocol analysis methods; Results : The GA methodology triggered the emergence of ' common g round ' among stakeholders. This common ground evolved throughout the sessions to enhance stakeholders' verbal and non-verbal communication, as well as coordination of joint activities and ultimately collaboration on problem solving and decision-making; Conclusion s : Understanding complex health data is necessary for informed decisions. Equally important, in this case, is the use of the group analytics methodology to achieve ' common ground' among diverse stakeholders about health data and their implications.

  8. Transverse signal decay under the weak field approximation: Theory and validation.

    PubMed

    Berman, Avery J L; Pike, G Bruce

    2018-07-01

    To derive an expression for the transverse signal time course from systems in the motional narrowing regime, such as water diffusing in blood. This was validated in silico and experimentally with ex vivo blood samples. A closed-form solution (CFS) for transverse signal decay under any train of refocusing pulses was derived using the weak field approximation. The CFS was validated via simulations of water molecules diffusing in the presence of spherical perturbers, with a range of sizes and under various pulse sequences. The CFS was compared with more conventional fits assuming monoexponential decay, including chemical exchange, using ex vivo blood Carr-Purcell-Meiboom-Gill data. From simulations, the CFS was shown to be valid in the motional narrowing regime and partially into the intermediate dephasing regime, with increased accuracy with increasing Carr-Purcell-Meiboom-Gill refocusing rate. In theoretical calculations of the CFS, fitting for the transverse relaxation rate (R 2 ) gave excellent agreement with the weak field approximation expression for R 2 for Carr-Purcell-Meiboom-Gill sequences, but diverged for free induction decay. These same results were confirmed in the ex vivo analysis. Transverse signal decay in the motional narrowing regime can be accurately described analytically. This theory has applications in areas such as tissue iron imaging, relaxometry of blood, and contrast agent imaging. Magn Reson Med 80:341-350, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

  9. Accurate upwind methods for the Euler equations

    NASA Technical Reports Server (NTRS)

    Huynh, Hung T.

    1993-01-01

    A new class of piecewise linear methods for the numerical solution of the one-dimensional Euler equations of gas dynamics is presented. These methods are uniformly second-order accurate, and can be considered as extensions of Godunov's scheme. With an appropriate definition of monotonicity preservation for the case of linear convection, it can be shown that they preserve monotonicity. Similar to Van Leer's MUSCL scheme, they consist of two key steps: a reconstruction step followed by an upwind step. For the reconstruction step, a monotonicity constraint that preserves uniform second-order accuracy is introduced. Computational efficiency is enhanced by devising a criterion that detects the 'smooth' part of the data where the constraint is redundant. The concept and coding of the constraint are simplified by the use of the median function. A slope steepening technique, which has no effect at smooth regions and can resolve a contact discontinuity in four cells, is described. As for the upwind step, existing and new methods are applied in a manner slightly different from those in the literature. These methods are derived by approximating the Euler equations via linearization and diagonalization. At a 'smooth' interface, Harten, Lax, and Van Leer's one intermediate state model is employed. A modification for this model that can resolve contact discontinuities is presented. Near a discontinuity, either this modified model or a more accurate one, namely, Roe's flux-difference splitting. is used. The current presentation of Roe's method, via the conceptually simple flux-vector splitting, not only establishes a connection between the two splittings, but also leads to an admissibility correction with no conditional statement, and an efficient approximation to Osher's approximate Riemann solver. These reconstruction and upwind steps result in schemes that are uniformly second-order accurate and economical at smooth regions, and yield high resolution at discontinuities.

  10. Analytical phase diagrams for colloids and non-adsorbing polymer.

    PubMed

    Fleer, Gerard J; Tuinier, Remco

    2008-11-04

    We review the free-volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett. 20 (1992) 559] for the phase behavior of colloids in the presence of non-adsorbing polymer and we extend this theory in several aspects: (i) We take the solvent into account as a separate component and show that the natural thermodynamic parameter for the polymer properties is the insertion work Pi(v), where Pi is the osmotic pressure of the (external) polymer solution and v the volume of a colloid particle. (ii) Curvature effects are included along the lines of Aarts et al. [J. Phys.: Condens. Matt. 14 (2002) 7551] but we find accurate simple power laws which simplify the mathematical procedure considerably. (iii) We find analytical forms for the first, second, and third derivatives of the grand potential, needed for the calculation of the colloid chemical potential, the pressure, gas-liquid critical points and the critical endpoint (cep), where the (stable) critical line ends and then coincides with the triple point. This cep determines the boundary condition for a stable liquid. We first apply these modifications to the so-called colloid limit, where the size ratio q(R)=R/a between the radius of gyration R of the polymer and the particle radius a is small. In this limit the binodal polymer concentrations are below overlap: the depletion thickness delta is nearly equal to R, and Pi can be approximated by the ideal (van't Hoff) law Pi=Pi(0)=phi/N, where phi is the polymer volume fraction and N the number of segments per chain. The results are close to those of the original Lekkerkerker theory. However, our analysis enables very simple analytical expressions for the polymer and colloid concentrations in the critical and triple points and along the binodals as a function of q(R). Also the position of the cep is found analytically. In order to make the model applicable to higher size ratio's q(R) (including the so-called protein limit where q(R)>1) further extensions are needed. We

  11. Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation.

    PubMed

    Liu, Jian; Miller, William H

    2008-09-28

    The maximum entropy analytic continuation (MEAC) method is used to extend the range of accuracy of the linearized semiclassical initial value representation (LSC-IVR)/classical Wigner approximation for real time correlation functions. LSC-IVR provides a very effective "prior" for the MEAC procedure since it is very good for short times, exact for all time and temperature for harmonic potentials (even for correlation functions of nonlinear operators), and becomes exact in the classical high temperature limit. This combined MEAC+LSC/IVR approach is applied here to two highly nonlinear dynamical systems, a pure quartic potential in one dimensional and liquid para-hydrogen at two thermal state points (25 and 14 K under nearly zero external pressure). The former example shows the MEAC procedure to be a very significant enhancement of the LSC-IVR for correlation functions of both linear and nonlinear operators, and especially at low temperature where semiclassical approximations are least accurate. For liquid para-hydrogen, the LSC-IVR is seen already to be excellent at T=25 K, but the MEAC procedure produces a significant correction at the lower temperature (T=14 K). Comparisons are also made as to how the MEAC procedure is able to provide corrections for other trajectory-based dynamical approximations when used as priors.

  12. Approximate solutions to Mathieu's equation

    NASA Astrophysics Data System (ADS)

    Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

    2018-06-01

    Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

  13. Interacting steps with finite-range interactions: Analytical approximation and numerical results

    NASA Astrophysics Data System (ADS)

    Jaramillo, Diego Felipe; Téllez, Gabriel; González, Diego Luis; Einstein, T. L.

    2013-05-01

    We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions q on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

  14. Rational approximations from power series of vector-valued meromorphic functions

    NASA Technical Reports Server (NTRS)

    Sidi, Avram

    1992-01-01

    Let F(z) be a vector-valued function, F: C yields C(sup N), which is analytic at z = 0 and meromorphic in a neighborhood of z = 0, and let its Maclaurin series be given. In this work we developed vector-valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyzed some of the algebraic and analytic properties of the rational approximations thus obtained, and showed that they were akin to Pade approximations. In particular, we proved a Koenig type theorem concerning their poles and a de Montessus type theorem concerning their uniform convergence. We showed how optical approximations to multiple poles and to Laurent expansions about these poles can be constructed. Extensions of the procedures above and the accompanying theoretical results to functions defined in arbitrary linear spaces was also considered. One of the most interesting and immediate applications of the results of this work is to the matrix eigenvalue problem. In a forthcoming paper we exploited the developments of the present work to devise bona fide generalizations of the classical power method that are especially suitable for very large and sparse matrices. These generalizations can be used to approximate simultaneously several of the largest distinct eigenvalues and corresponding eigenvectors and invariant subspaces of arbitrary matrices which may or may not be diagonalizable, and are very closely related with known Krylov subspace methods.

  15. Analytic Regularity and Polynomial Approximation of Parametric and Stochastic Elliptic PDEs

    DTIC Science & Technology

    2010-05-31

    Todor : Finite elements for elliptic problems with stochastic coefficients Comp. Meth. Appl. Mech. Engg. 194 (2005) 205-228. [14] R. Ghanem and P. Spanos...for elliptic partial differential equations with random input data SIAM J. Num. Anal. 46(2008), 2411–2442. [20] R. Todor , Robust eigenvalue computation...for smoothing operators, SIAM J. Num. Anal. 44(2006), 865– 878. [21] Ch. Schwab and R.A. Todor , Karhúnen-Loève Approximation of Random Fields by

  16. An Approximate Solution to the Equation of Motion for Large-Angle Oscillations of the Simple Pendulum with Initial Velocity

    ERIC Educational Resources Information Center

    Johannessen, Kim

    2010-01-01

    An analytic approximation of the solution to the differential equation describing the oscillations of a simple pendulum at large angles and with initial velocity is discussed. In the derivation, a sinusoidal approximation has been applied, and an analytic formula for the large-angle period of the simple pendulum is obtained, which also includes…

  17. New analytical model for the ozone electronic ground state potential surface and accurate ab initio vibrational predictions at high energy range.

    PubMed

    Tyuterev, Vladimir G; Kochanov, Roman V; Tashkun, Sergey A; Holka, Filip; Szalay, Péter G

    2013-10-07

    An accurate description of the complicated shape of the potential energy surface (PES) and that of the highly excited vibration states is of crucial importance for various unsolved issues in the spectroscopy and dynamics of ozone and remains a challenge for the theory. In this work a new analytical representation is proposed for the PES of the ground electronic state of the ozone molecule in the range covering the main potential well and the transition state towards the dissociation. This model accounts for particular features specific to the ozone PES for large variations of nuclear displacements along the minimum energy path. The impact of the shape of the PES near the transition state (existence of the "reef structure") on vibration energy levels was studied for the first time. The major purpose of this work was to provide accurate theoretical predictions for ozone vibrational band centres at the energy range near the dissociation threshold, which would be helpful for understanding the very complicated high-resolution spectra and its analyses currently in progress. Extended ab initio electronic structure calculations were carried out enabling the determination of the parameters of a minimum energy path PES model resulting in a new set of theoretical vibrational levels of ozone. A comparison with recent high-resolution spectroscopic data on the vibrational levels gives the root-mean-square deviations below 1 cm(-1) for ozone band centres up to 90% of the dissociation energy. New ab initio vibrational predictions represent a significant improvement with respect to all previously available calculations.

  18. Temporal Learning Analytics for Adaptive Assessment

    ERIC Educational Resources Information Center

    Papamitsiou, Zacharoula; Economides, Anastasios A.

    2014-01-01

    Accurate and early predictions of student performance could significantly affect interventions during teaching and assessment, which gradually could lead to improved learning outcomes. In our research, we seek to identify and formalize temporal parameters as predictors of performance ("temporal learning analytics" or TLA) and examine…

  19. Detection efficiency calculation for photons, electrons and positrons in a well detector. Part I: Analytical model

    NASA Astrophysics Data System (ADS)

    Pommé, S.

    2009-06-01

    An analytical model is presented to calculate the total detection efficiency of a well-type radiation detector for photons, electrons and positrons emitted from a radioactive source at an arbitrary position inside the well. The model is well suited to treat a typical set-up with a point source or cylindrical source and vial inside a NaI well detector, with or without lead shield surrounding it. It allows for fast absolute or relative total efficiency calibrations for a wide variety of geometrical configurations and also provides accurate input for the calculation of coincidence summing effects. Depending on its accuracy, it may even be applied in 4π-γ counting, a primary standardisation method for activity. Besides an accurate account of photon interactions, precautions are taken to simulate the special case of 511 keV annihilation quanta and to include realistic approximations for the range of (conversion) electrons and β -- and β +-particles.

  20. The Investigation of Optimal Discrete Approximations for Real Time Flight Simulations

    NASA Technical Reports Server (NTRS)

    Parrish, E. A.; Mcvey, E. S.; Cook, G.; Henderson, K. C.

    1976-01-01

    The results are presented of an investigation of discrete approximations for real time flight simulation. Major topics discussed include: (1) consideration of the particular problem of approximation of continuous autopilots by digital autopilots; (2) use of Bode plots and synthesis of transfer functions by asymptotic fits in a warped frequency domain; (3) an investigation of the various substitution formulas, including the effects of nonlinearities; (4) use of pade approximation to the solution of the matrix exponential arising from the discrete state equations; and (5) an analytical integration of the state equation using interpolated input.

  1. Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description

    NASA Astrophysics Data System (ADS)

    Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

    2014-03-01

    We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ɛ(r) is close to one everywhere inside the protein. The Gaussian widths σi of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σi. A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by

  2. Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description.

    PubMed

    Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

    2014-03-14

    We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ(i) of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ(i). A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by

  3. Extracting Time-Accurate Acceleration Vectors From Nontrivial Accelerometer Arrangements.

    PubMed

    Franck, Jennifer A; Blume, Janet; Crisco, Joseph J; Franck, Christian

    2015-09-01

    Sports-related concussions are of significant concern in many impact sports, and their detection relies on accurate measurements of the head kinematics during impact. Among the most prevalent recording technologies are videography, and more recently, the use of single-axis accelerometers mounted in a helmet, such as the HIT system. Successful extraction of the linear and angular impact accelerations depends on an accurate analysis methodology governed by the equations of motion. Current algorithms are able to estimate the magnitude of acceleration and hit location, but make assumptions about the hit orientation and are often limited in the position and/or orientation of the accelerometers. The newly formulated algorithm presented in this manuscript accurately extracts the full linear and rotational acceleration vectors from a broad arrangement of six single-axis accelerometers directly from the governing set of kinematic equations. The new formulation linearizes the nonlinear centripetal acceleration term with a finite-difference approximation and provides a fast and accurate solution for all six components of acceleration over long time periods (>250 ms). The approximation of the nonlinear centripetal acceleration term provides an accurate computation of the rotational velocity as a function of time and allows for reconstruction of a multiple-impact signal. Furthermore, the algorithm determines the impact location and orientation and can distinguish between glancing, high rotational velocity impacts, or direct impacts through the center of mass. Results are shown for ten simulated impact locations on a headform geometry computed with three different accelerometer configurations in varying degrees of signal noise. Since the algorithm does not require simplifications of the actual impacted geometry, the impact vector, or a specific arrangement of accelerometer orientations, it can be easily applied to many impact investigations in which accurate kinematics need

  4. A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

    NASA Astrophysics Data System (ADS)

    Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

    2018-03-01

    Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

  5. Determination of immersion factors for radiance sensors in marine and inland waters: a semi-analytical approach using refractive index approximation

    NASA Astrophysics Data System (ADS)

    Dev, Pravin J.; Shanmugam, P.

    2016-05-01

    Underwater radiometers are generally calibrated in air using a standard source. The immersion factors are required for these radiometers to account for the change in the in-water measurements with respect to in-air due to the different refractive index of the medium. The immersion factors previously determined for RAMSES series of commercial radiometers manufactured by TriOS are applicable to clear oceanic waters. In typical inland and turbid productive coastal waters, these experimentally determined immersion factors yield significantly large errors in water-leaving radiances (Lw) and hence remote sensing reflectances (Rrs). To overcome this limitation, a semi-analytical method with based on the refractive index approximation is proposed in this study, with the aim of obtaining reliable Lw and Rrs from RAMSES radiometers for turbid and productive waters within coastal and inland water environments. We also briefly show the variation of pure water immersion factors (Ifw) and newly derived If on Lw and Rrs for clear and turbid waters. The remnant problems other than the immersion factor coefficients such as transmission, air-water and water-air Fresnel's reflectances are also discussed.

  6. Variational Gaussian approximation for Poisson data

    NASA Astrophysics Data System (ADS)

    Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

    2018-02-01

    The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

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

    NASA Astrophysics Data System (ADS)

    Parise, M.

    2018-01-01

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

  8. A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

    PubMed

    Asgharzadeh, Hafez; Borazjani, Iman

    2017-02-15

    diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

  9. A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

    PubMed Central

    Asgharzadeh, Hafez; Borazjani, Iman

    2016-01-01

    diagonal of the Jacobian further improves the performance by 42 – 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future. PMID:28042172

  10. A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

    NASA Astrophysics Data System (ADS)

    Asgharzadeh, Hafez; Borazjani, Iman

    2017-02-01

    diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

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

    NASA Astrophysics Data System (ADS)

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

    2016-10-01

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

  12. Infinite order sudden approximation for rotational energy transfer in gaseous mixtures

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

    Goldflam, R.; Green, S.; Kouri, D.J.

    1977-11-01

    Rotational energy transfer in gaseous mixtures has been considered within the framework of the infinite order sudden (IOS) approximation. A new derivation of the IOS from the coupled states Lippmann--Schwinger equation is given. This approach shows the relation between the IOS and CS T matrices and also shows in a rather transparent fashion Sencrest's result that the IOS method does not truncate closed channels but rather employs a closure relation to sum over all rotor states. The general CS effective cross section formula for relaxation processes is used, along with the IOS approximation to the CS T matrix, to derivemore » the general IOS effctive cross section.Factorization permits one to calculate other types of cross sections if any one type of cross section has been obtained by some procedure. The functional form can also be used to compact data. This formalism has been applied to calculate pressure broadening for the systems HD--He, HCl--He, CO--He, HCN--He, HCl--Ar, and CO/sub 2/--Ar. To test the IOS approximation, comparisons have been made to the CS results, which are known to be accurate for all these systems. The IOS approximation is found to be very accurate whenever the rotor spacings are small compared to the kinetic energy, provided closed channels do not play too great a role. For the systems CO--He, HCN--He, and CO/sub 2/--Ar, these conditions are well satisfied and the IOS is found to yield results accurate to within 10%--15%.« less

  13. Fast and accurate computation of projected two-point functions

    NASA Astrophysics Data System (ADS)

    Grasshorn Gebhardt, Henry S.; Jeong, Donghui

    2018-01-01

    We present the two-point function from the fast and accurate spherical Bessel transformation (2-FAST) algorithmOur code is available at https://github.com/hsgg/twoFAST. for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when projecting the galaxy power spectrum P (k ) onto the configuration space, ξℓν(r ), or spherical harmonic space, Cℓ(χ ,χ'). First, we employ the FFTLog transformation of the power spectrum to divide the calculation into P (k )-dependent coefficients and P (k )-independent integrations of basis functions multiplied by spherical Bessel functions. We find analytical expressions for the latter integrals in terms of special functions, for which recursion provides a fast and accurate evaluation. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.

  14. Creating analytically divergence-free velocity fields from grid-based data

    NASA Astrophysics Data System (ADS)

    Ravu, Bharath; Rudman, Murray; Metcalfe, Guy; Lester, Daniel R.; Khakhar, Devang V.

    2016-10-01

    We present a method, based on B-splines, to calculate a C2 continuous analytic vector potential from discrete 3D velocity data on a regular grid. A continuous analytically divergence-free velocity field can then be obtained from the curl of the potential. This field can be used to robustly and accurately integrate particle trajectories in incompressible flow fields. Based on the method of Finn and Chacon (2005) [10] this new method ensures that the analytic velocity field matches the grid values almost everywhere, with errors that are two to four orders of magnitude lower than those of existing methods. We demonstrate its application to three different problems (each in a different coordinate system) and provide details of the specifics required in each case. We show how the additional accuracy of the method results in qualitatively and quantitatively superior trajectories that results in more accurate identification of Lagrangian coherent structures.

  15. Building pit dewatering: application of transient analytic elements.

    PubMed

    Zaadnoordijk, Willem J

    2006-01-01

    Analytic elements are well suited for the design of building pit dewatering. Wells and drains can be modeled accurately by analytic elements, both nearby to determine the pumping level and at some distance to verify the targeted drawdown at the building site and to estimate the consequences in the vicinity. The ability to shift locations of wells or drains easily makes the design process very flexible. The temporary pumping has transient effects, for which transient analytic elements may be used. This is illustrated using the free, open-source, object-oriented analytic element simulator Tim(SL) for the design of a building pit dewatering near a canal. Steady calculations are complemented with transient calculations. Finally, the bandwidths of the results are estimated using linear variance analysis.

  16. 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.

  17. Loglinear Approximate Solutions to Real-Business-Cycle Models: Some Observations

    ERIC Educational Resources Information Center

    Lau, Sau-Him Paul; Ng, Philip Hoi-Tak

    2007-01-01

    Following the analytical approach suggested in Campbell, the authors consider a baseline real-business-cycle (RBC) model with endogenous labor supply. They observe that the coefficients in the loglinear approximation of the dynamic equations characterizing the equilibrium are related to the fundamental parameters in a relatively simple manner.…

  18. A simple approximation for the current-voltage characteristics of high-power, relativistic diodes

    DOE PAGES

    Ekdahl, Carl

    2016-06-10

    A simple approximation for the current-voltage characteristics of a relativistic electron diode is presented. The approximation is accurate from non-relativistic through relativistic electron energies. Although it is empirically developed, it has many of the fundamental properties of the exact diode solutions. Lastly, the approximation is simple enough to be remembered and worked on almost any pocket calculator, so it has proven to be quite useful on the laboratory floor.

  19. A Gaussian Approximation Potential for Silicon

    NASA Astrophysics Data System (ADS)

    Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor

    We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.

  20. Efficient solution of parabolic equations by Krylov approximation methods

    NASA Technical Reports Server (NTRS)

    Gallopoulos, E.; Saad, Y.

    1990-01-01

    Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

  1. Integral approximations to classical diffusion and smoothed particle hydrodynamics

    DOE PAGES

    Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

    2014-12-31

    The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

  2. Semigroup theory and numerical approximation for equations in linear viscoelasticity

    NASA Technical Reports Server (NTRS)

    Fabiano, R. H.; Ito, K.

    1990-01-01

    A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

  3. Analytic studies of the hard dumbell fluid

    NASA Astrophysics Data System (ADS)

    Morriss, G. P.; Cummings, P. T.

    A closed form analytic theory for the structure of the hard dumbell fluid is introduced and evaluated. It is found to be comparable in accuracy to the reference interaction site approximation (RISA) of Chandler and Andersen.

  4. Approximate Single-Diode Photovoltaic Model for Efficient I-V Characteristics Estimation

    PubMed Central

    Ting, T. O.; Zhang, Nan; Guan, Sheng-Uei; Wong, Prudence W. H.

    2013-01-01

    Precise photovoltaic (PV) behavior models are normally described by nonlinear analytical equations. To solve such equations, it is necessary to use iterative procedures. Aiming to make the computation easier, this paper proposes an approximate single-diode PV model that enables high-speed predictions for the electrical characteristics of commercial PV modules. Based on the experimental data, statistical analysis is conducted to validate the approximate model. Simulation results show that the calculated current-voltage (I-V) characteristics fit the measured data with high accuracy. Furthermore, compared with the existing modeling methods, the proposed model reduces the simulation time by approximately 30% in this work. PMID:24298205

  5. An efficient and accurate molecular alignment and docking technique using ab initio quality scoring

    PubMed Central

    Füsti-Molnár, László; Merz, Kenneth M.

    2008-01-01

    An accurate and efficient molecular alignment technique is presented based on first principle electronic structure calculations. This new scheme maximizes quantum similarity matrices in the relative orientation of the molecules and uses Fourier transform techniques for two purposes. First, building up the numerical representation of true ab initio electronic densities and their Coulomb potentials is accelerated by the previously described Fourier transform Coulomb method. Second, the Fourier convolution technique is applied for accelerating optimizations in the translational coordinates. In order to avoid any interpolation error, the necessary analytical formulas are derived for the transformation of the ab initio wavefunctions in rotational coordinates. The results of our first implementation for a small test set are analyzed in detail and compared with published results of the literature. A new way of refinement of existing shape based alignments is also proposed by using Fourier convolutions of ab initio or other approximate electron densities. This new alignment technique is generally applicable for overlap, Coulomb, kinetic energy, etc., quantum similarity measures and can be extended to a genuine docking solution with ab initio scoring. PMID:18624561

  6. Piezoresistive Cantilever Performance—Part I: Analytical Model for Sensitivity

    PubMed Central

    Park, Sung-Jin; Doll, Joseph C.; Pruitt, Beth L.

    2010-01-01

    An accurate analytical model for the change in resistance of a piezoresistor is necessary for the design of silicon piezoresistive transducers. Ion implantation requires a high-temperature oxidation or annealing process to activate the dopant atoms, and this treatment results in a distorted dopant profile due to diffusion. Existing analytical models do not account for the concentration dependence of piezoresistance and are not accurate for nonuniform dopant profiles. We extend previous analytical work by introducing two nondimensional factors, namely, the efficiency and geometry factors. A practical benefit of this efficiency factor is that it separates the process parameters from the design parameters; thus, designers may address requirements for cantilever geometry and fabrication process independently. To facilitate the design process, we provide a lookup table for the efficiency factor over an extensive range of process conditions. The model was validated by comparing simulation results with the experimentally determined sensitivities of piezoresistive cantilevers. We performed 9200 TSUPREM4 simulations and fabricated 50 devices from six unique process flows; we systematically explored the design space relating process parameters and cantilever sensitivity. Our treatment focuses on piezoresistive cantilevers, but the analytical sensitivity model is extensible to other piezoresistive transducers such as membrane pressure sensors. PMID:20336183

  7. Piezoresistive Cantilever Performance-Part I: Analytical Model for Sensitivity.

    PubMed

    Park, Sung-Jin; Doll, Joseph C; Pruitt, Beth L

    2010-02-01

    An accurate analytical model for the change in resistance of a piezoresistor is necessary for the design of silicon piezoresistive transducers. Ion implantation requires a high-temperature oxidation or annealing process to activate the dopant atoms, and this treatment results in a distorted dopant profile due to diffusion. Existing analytical models do not account for the concentration dependence of piezoresistance and are not accurate for nonuniform dopant profiles. We extend previous analytical work by introducing two nondimensional factors, namely, the efficiency and geometry factors. A practical benefit of this efficiency factor is that it separates the process parameters from the design parameters; thus, designers may address requirements for cantilever geometry and fabrication process independently. To facilitate the design process, we provide a lookup table for the efficiency factor over an extensive range of process conditions. The model was validated by comparing simulation results with the experimentally determined sensitivities of piezoresistive cantilevers. We performed 9200 TSUPREM4 simulations and fabricated 50 devices from six unique process flows; we systematically explored the design space relating process parameters and cantilever sensitivity. Our treatment focuses on piezoresistive cantilevers, but the analytical sensitivity model is extensible to other piezoresistive transducers such as membrane pressure sensors.

  8. Analytic Neutrino Oscillation Probabilities in Matter: Revisited

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

    Parke, Stephen J.; Denton, Peter B.; Minakata, Hisakazu

    2018-01-02

    We summarize our recent paper on neutrino oscillation probabilities in matter, explaining the importance, relevance and need for simple, highly accurate approximations to the neutrino oscillation probabilities in matter.

  9. Accurate Sloshing Modes Modeling: A New Analytical Solution and its Consequences on Control

    NASA Astrophysics Data System (ADS)

    Gonidou, Luc-Olivier; Desmariaux, Jean

    2014-06-01

    This study addresses the issue of sloshing modes modeling for GNC analyses purposes. On European launchers, equivalent mechanical systems are commonly used for modeling sloshing effects on launcher dynamics. The representativeness of such a methodology is discussed here. First an exact analytical formulation of the launcher dynamics fitted with sloshing modes is proposed and discrepancies with equivalent mechanical system approach are emphasized. Then preliminary comparative GNC analyses are performed using the different models of dynamics in order to evaluate the impact of the aforementioned discrepancies from GNC standpoint. Special attention is paid to system stability.

  10. Dipole Approximation to Predict the Resonances of Dimers Composed of Dielectric Resonators for Directional Emission: Dielectric Dimers Dipole Approximation

    DOE PAGES

    Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.

    2017-09-29

    In this paper we develop a fully-retarded, dipole approximation model to estimate the effective polarizabilities of a dimer made of dielectric resonators. They are computed from the polarizabilities of the two resonators composing the dimer. We analyze the situation of full-cubes as well as split-cubes, which have been shown to exhibit overlapping electric and magnetic resonances. We compare the effective dimer polarizabilities to ones retrieved via full-wave simulations as well as ones computed via a quasi-static, dipole approximation. We observe good agreement between the fully-retarded solution and the full-wave results, whereas the quasi-static approximation is less accurate for the problemmore » at hand. The developed model can be used to predict the electric and magnetic resonances of a dimer under parallel or orthogonal (to the dimer axis) excitation. This is particularly helpful when interested in locating frequencies at which the dimer will emit directional radiation.« less

  11. Capricorn-A Web-Based Automatic Case Log and Volume Analytics for Diagnostic Radiology Residents.

    PubMed

    Chen, Po-Hao; Chen, Yin Jie; Cook, Tessa S

    2015-10-01

    On-service clinical learning is a mainstay of radiology education. However, an accurate and timely case log is difficult to keep, especially in the absence of software tools tailored to resident education. Furthermore, volume-related feedback from the residency program sometimes occurs months after a rotation ends, limiting the opportunity for meaningful intervention. We surveyed the residents of a single academic institution to evaluate the current state of and the existing need for tracking interpretation volume. Using the results of the survey, we created an open-source automated case log software. Finally, we evaluated the effect of the software tool on the residency in a 1-month, postimplementation survey. Before implementation of the system, 89% of respondents stated that volume is an important component of training, but 71% stated that volume data was inconvenient to obtain. Although the residency program provides semiannual reviews, 90% preferred reviewing interpretation volumes at least once monthly. After implementation, 95% of the respondents stated that the software is convenient to access, 75% found it useful, and 88% stated they would use the software at least once a month. The included analytics module, which benchmarks the user using historical aggregate average volumes, is the most often used feature of the software. Server log demonstrates that, on average, residents use the system approximately twice a week. An automated case log software system may fulfill a previously unmet need in diagnostic radiology training, making accurate and timely review of volume-related performance analytics a convenient process. Copyright © 2015 AUR. Published by Elsevier Inc. All rights reserved.

  12. Importance of accurate measurements in nutrition research: dietary flavonoids as a case study

    USDA-ARS?s Scientific Manuscript database

    Accurate measurements of the secondary metabolites in natural products and plant foods are critical to establishing diet/health relationships. There are as many as 50,000 secondary metabolites which may influence human health. Their structural and chemical diversity present a challenge to analytic...

  13. Calculating Resonance Positions and Widths Using the Siegert Approximation Method

    ERIC Educational Resources Information Center

    Rapedius, Kevin

    2011-01-01

    Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…

  14. The Analytic Hierarchy Process and Participatory Decisionmaking

    Treesearch

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

    1995-01-01

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

  15. Analytical Expressions for Deformation from an Arbitrarily Oriented Spheroid in a Half-Space

    NASA Astrophysics Data System (ADS)

    Cervelli, P. F.

    2013-12-01

    Deformation from magma chambers can be modeled by an elastic half-space with an embedded cavity subject to uniform pressure change along its interior surface. For a small number of cavity shapes, such as a sphere or a prolate spheroid, closed-form, analytical expressions for deformation have been derived, although these only approximate the uniform-pressure-change boundary condition, with the approximation becoming more accurate as the ratio of source depth to source dimension increases. Using the method of Elshelby [1957] and Yang [1988], which consists of a distribution of double forces and centers of dilatation along the vertical axis, I have derived expressions for displacement from a finite spheroid of arbitrary orientation and aspect ratio that are exact in an infinite elastic medium and approximate in a half-space. The approximation, like those for other cavity shapes, becomes increasingly accurate as the depth to source ratio grows larger, and is accurate to within a few percent in most real-world cases. I have also derived expressions for the deformation-gradient tensor, i.e., the derivatives of each component of displacement with respect to each coordinate direction. These can be transformed easily into the strain and stress tensors. The expressions give deformation both at the surface and at any point within the half-space, and include conditional statements that account for limiting cases that would otherwise prove singular. I have developed MATLAB code for these expressions (and their derivatives), which I use to demonstrate the accuracy of the approximation by showing how well the uniform-pressure-change boundary condition is satisfied in a variety of cases. I also show that a vertical, oblate spheroid with a zero-length vertical axis is equivalent to the penny-shaped crack of Fialko [2001] in an infinite medium and an excellent approximation in a half-space. Finally, because, in many cases, volume change is more tangible than pressure change, I have

  16. Effects of a finite aperture on the Inverse Born Approximation

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

    Kogan, V.G.; Rose, J.H.

    1983-01-01

    One of the most important effects of complex part geometry is that the available entrance and exit angles for ultrasound are limited. We will present a study of the Inverse Born approximation in which we have data for incident (and exit) directions confined to a conical aperture. Modeling the direct problem by the Born Approximation, we obtained analytical results for (1) a weak spherical inclusion, and (2) a penny shaped crack (modeled by an oblate spheroid). General results are: (a) the value of the characteristic function ..gamma.. is constant in the interior of the flaw, but reduced in value; (b)more » the discontinuity at the boundary of the flaw occurs over the lighted portion of the flaw; (c) this discontinuity is contrasted by a region where ..gamma.. is negative; and (d) new non-physical discontinuities and non-analyticities appear in the reconstructed characteristic function. These general features also appear in numerical calculations which use as input strong scattering data from a spherical void and a flat penny shaped crack in Titanium. The numerical results can be straightforwardly interpreted in terms of the analytical calculation mentioned above, indicating that they will be useful in the study of realistic flaws. We conclude by discussing the stabilization of the aperture limited inversion problem and the removal of non-physical features in the reconstruction.« less

  17. Scaling laws and accurate small-amplitude stationary solution for the motion of a planar vortex filament in the Cartesian form of the local induction approximation.

    PubMed

    Van Gorder, Robert A

    2013-04-01

    We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrödinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely.

  18. Evaluation of an Approximate Method for Synthesizing Covariance Matrices for Use in Meta-Analytic SEM

    ERIC Educational Resources Information Center

    Beretvas, S. Natasha; Furlow, Carolyn F.

    2006-01-01

    Meta-analytic structural equation modeling (MA-SEM) is increasingly being used to assess model-fit for variables' interrelations synthesized across studies. MA-SEM researchers have analyzed synthesized correlation matrices using structural equation modeling (SEM) estimation that is designed for covariance matrices. This can produce incorrect…

  19. Distribution of curvature of 3D nonrotational surfaces approximating the corneal topography

    NASA Astrophysics Data System (ADS)

    Kasprzak, Henryk T.

    1998-10-01

    The first part of the paper presents the analytical curves used to approximate the corneal profile. Next, some definition of 3D surfaces curvature, like main normal sections, main radii of curvature and their orientations are given. The examples of four nonrotational 3D surfaces such as: ellipsoidal, surface based on hyperbolic cosine function, sphero-cylindrical and toroidal, approximating the corneal topography are proposed. The 3D surface and the contour plots of main radii of curvature and their orientation for four nonrotational approximation of the cornea are shown. Results of calculations are discussed from the point of view of videokeratometric images.

  20. Numerical modeling and analytical evaluation of light absorption by gold nanostars

    NASA Astrophysics Data System (ADS)

    Zarkov, Sergey; Akchurin, Georgy; Yakunin, Alexander; Avetisyan, Yuri; Akchurin, Garif; Tuchin, Valery

    2018-04-01

    In this paper, the regularity of local light absorption by gold nanostars (AuNSts) model is studied by method of numerical simulation. The mutual diffraction influence of individual geometric fragments of AuNSts is analyzed. A comparison is made with an approximate analytical approach for estimating the average bulk density of absorbed power and total absorbed power by individual geometric fragments of AuNSts. It is shown that the results of the approximate analytical estimate are in qualitative agreement with the numerical calculations of the light absorption by AuNSts.

  1. Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

    PubMed Central

    Orio, Patricio; Soudry, Daniel

    2012-01-01

    Background The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled gating particles, while the DA was modeled using uncoupled gating particles. Implementations of DA with coupled particles, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. Main Contributions We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable – allowing an easy, transparent and efficient DA implementation, avoiding unnecessary approximations. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods, except when

  2. Optimal approximation of harmonic growth clusters by orthogonal polynomials

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

    Teodorescu, Razvan

    2008-01-01

    Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoreticaI model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of Hele-Shaw flows), to the granular dynamics of hard spheres, and even diffusion-limited aggregation. Although a complete solution for the continuum case exists, efficient approximations of the boundary evolution are very useful due to their practical applications. In this article, the approximation scheme based on orthogonal polynomials with a deformed Gaussian kernel is discussed, as well as relations to potential theory.

  3. Cold pasta phase in the extended Thomas-Fermi approximation

    NASA Astrophysics Data System (ADS)

    Avancini, S. S.; Bertolino, B. P.

    2015-10-01

    In this paper, we aim to obtain more accurate values for the transition density to the homogenous phase in the nuclear pasta that occurs in the inner crust of neutron stars. To that end, we use the nonlinear Walecka model at zero temperature and an approach based on the extended Thomas-Fermi (ETF) approximation.

  4. Slow-roll approximation in loop quantum cosmology

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

    Luc, Joanna; Mielczarek, Jakub, E-mail: joanna.luc@uj.edu.pl, E-mail: jakub.mielczarek@uj.edu.pl

    The slow-roll approximation is an analytical approach to study dynamical properties of the inflationary universe. In this article, systematic construction of the slow-roll expansion for effective loop quantum cosmology is presented. The analysis is performed up to the fourth order in both slow-roll parameters and the parameter controlling the strength of deviation from the classical case. The expansion is performed for three types of the slow-roll parameters: Hubble slow-roll parameters, Hubble flow parameters and potential slow-roll parameters. An accuracy of the approximation is verified by comparison with the numerical phase space trajectories for the case with a massive potential term.more » The results obtained in this article may be helpful in the search for the subtle quantum gravitational effects with use of the cosmological data.« less

  5. Toward more accurate loss tangent measurements in reentrant cavities

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

    Moyer, R. D.

    1980-05-01

    Karpova has described an absolute method for measurement of dielectric properties of a solid in a coaxial reentrant cavity. His cavity resonance equation yields very accurate results for dielectric constants. However, he presented only approximate expressions for the loss tangent. This report presents more exact expressions for that quantity and summarizes some experimental results.

  6. A numerical approximation to the elastic properties of sphere-reinforced composites

    NASA Astrophysics Data System (ADS)

    Segurado, J.; Llorca, J.

    2002-10-01

    Three-dimensional cubic unit cells containing 30 non-overlapping identical spheres randomly distributed were generated using a new, modified random sequential adsortion algorithm suitable for particle volume fractions of up to 50%. The elastic constants of the ensemble of spheres embedded in a continuous and isotropic elastic matrix were computed through the finite element analysis of the three-dimensional periodic unit cells, whose size was chosen as a compromise between the minimum size required to obtain accurate results in the statistical sense and the maximum one imposed by the computational cost. Three types of materials were studied: rigid spheres and spherical voids in an elastic matrix and a typical composite made up of glass spheres in an epoxy resin. The moduli obtained for different unit cells showed very little scatter, and the average values obtained from the analysis of four unit cells could be considered very close to the "exact" solution to the problem, in agreement with the results of Drugan and Willis (J. Mech. Phys. Solids 44 (1996) 497) referring to the size of the representative volume element for elastic composites. They were used to assess the accuracy of three classical analytical models: the Mori-Tanaka mean-field analysis, the generalized self-consistent method, and Torquato's third-order approximation.

  7. Correction for isotopic interferences between analyte and internal standard in quantitative mass spectrometry by a nonlinear calibration function.

    PubMed

    Rule, Geoffrey S; Clark, Zlatuse D; Yue, Bingfang; Rockwood, Alan L

    2013-04-16

    Stable isotope-labeled internal standards are of great utility in providing accurate quantitation in mass spectrometry (MS). An implicit assumption has been that there is no "cross talk" between signals of the internal standard and the target analyte. In some cases, however, naturally occurring isotopes of the analyte do contribute to the signal of the internal standard. This phenomenon becomes more pronounced for isotopically rich compounds, such as those containing sulfur, chlorine, or bromine, higher molecular weight compounds, and those at high analyte/internal standard concentration ratio. This can create nonlinear calibration behavior that may bias quantitative results. Here, we propose the use of a nonlinear but more accurate fitting of data for these situations that incorporates one or two constants determined experimentally for each analyte/internal standard combination and an adjustable calibration parameter. This fitting provides more accurate quantitation in MS-based assays where contributions from analyte to stable labeled internal standard signal exist. It can also correct for the reverse situation where an analyte is present in the internal standard as an impurity. The practical utility of this approach is described, and by using experimental data, the approach is compared to alternative fits.

  8. On the accuracy of the 'decoupled l-dominant' approximation for atom-molecule scattering

    NASA Technical Reports Server (NTRS)

    Green, S.

    1976-01-01

    Cross sections for rotational excitation and spectral pressure broadening of HD, HCl, CO, and HCN due to collisions with low energy He atoms have been computed within the 'decoupled l-dominant' (DLD) approximation and are compared with accurate close coupling results and also with two similar approximations, the effective potential of Rabitz and the coupled states of McGuire and Kouri. DLD predictions of state-to-state cross sections are rather good, being only slightly less accurate than coupled states results. DLD is far superior to either the coupled states or effective potential methods for pressure broadening calculations, although it may not be uniformly of the quantitative accuracy desirable for obtaining intermolecular potentials from experimental data.

  9. Note: Model identification and analysis of bivalent analyte surface plasmon resonance data.

    PubMed

    Tiwari, Purushottam Babu; Üren, Aykut; He, Jin; Darici, Yesim; Wang, Xuewen

    2015-10-01

    Surface plasmon resonance (SPR) is a widely used, affinity based, label-free biophysical technique to investigate biomolecular interactions. The extraction of rate constants requires accurate identification of the particular binding model. The bivalent analyte model involves coupled non-linear differential equations. No clear procedure to identify the bivalent analyte mechanism has been established. In this report, we propose a unique signature for the bivalent analyte model. This signature can be used to distinguish the bivalent analyte model from other biphasic models. The proposed method is demonstrated using experimentally measured SPR sensorgrams.

  10. Approximate Solution of Time-Fractional Advection-Dispersion Equation via Fractional Variational Iteration Method

    PubMed Central

    İbiş, Birol

    2014-01-01

    This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie's modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs. PMID:24578662

  11. Biological Matrix Effects in Quantitative Tandem Mass Spectrometry-Based Analytical Methods: Advancing Biomonitoring

    PubMed Central

    Panuwet, Parinya; Hunter, Ronald E.; D’Souza, Priya E.; Chen, Xianyu; Radford, Samantha A.; Cohen, Jordan R.; Marder, M. Elizabeth; Kartavenka, Kostya; Ryan, P. Barry; Barr, Dana Boyd

    2015-01-01

    The ability to quantify levels of target analytes in biological samples accurately and precisely, in biomonitoring, involves the use of highly sensitive and selective instrumentation such as tandem mass spectrometers and a thorough understanding of highly variable matrix effects. Typically, matrix effects are caused by co-eluting matrix components that alter the ionization of target analytes as well as the chromatographic response of target analytes, leading to reduced or increased sensitivity of the analysis. Thus, before the desired accuracy and precision standards of laboratory data are achieved, these effects must be characterized and controlled. Here we present our review and observations of matrix effects encountered during the validation and implementation of tandem mass spectrometry-based analytical methods. We also provide systematic, comprehensive laboratory strategies needed to control challenges posed by matrix effects in order to ensure delivery of the most accurate data for biomonitoring studies assessing exposure to environmental toxicants. PMID:25562585

  12. An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions.

    PubMed

    Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E

    2018-03-14

    We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

  13. An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions

    NASA Astrophysics Data System (ADS)

    Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.

    2018-03-01

    We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

  14. service line analytics in the new era.

    PubMed

    Spence, Jay; Seargeant, Dan

    2015-08-01

    To succeed under the value-based business model, hospitals and health systems require effective service line analytics that combine inpatient and outpatient data and that incorporate quality metrics for evaluating clinical operations. When developing a framework for collection, analysis, and dissemination of service line data, healthcare organizations should focus on five key aspects of effective service line analytics: Updated service line definitions. Ability to analyze and trend service line net patient revenues by payment source. Access to accurate service line cost information across multiple dimensions with drill-through capabilities. Ability to redesign key reports based on changing requirements. Clear assignment of accountability.

  15. Analytical quality goals derived from the total deviation from patients' homeostatic set points, with a margin for analytical errors.

    PubMed

    Bolann, B J; Asberg, A

    2004-01-01

    The deviation of test results from patients' homeostatic set points in steady-state conditions may complicate interpretation of the results and the comparison of results with clinical decision limits. In this study the total deviation from the homeostatic set point is defined as the maximum absolute deviation for 95% of measurements, and we present analytical quality requirements that prevent analytical error from increasing this deviation to more than about 12% above the value caused by biology alone. These quality requirements are: 1) The stable systematic error should be approximately 0, and 2) a systematic error that will be detected by the control program with 90% probability, should not be larger than half the value of the combined analytical and intra-individual standard deviation. As a result, when the most common control rules are used, the analytical standard deviation may be up to 0.15 times the intra-individual standard deviation. Analytical improvements beyond these requirements have little impact on the interpretability of measurement results.

  16. Approximate Solutions for Flow with a Stretching Boundary due to Partial Slip

    PubMed Central

    Filobello-Nino, U.; Vazquez-Leal, H.; Sarmiento-Reyes, A.; Benhammouda, B.; Jimenez-Fernandez, V. M.; Pereyra-Diaz, D.; Perez-Sesma, A.; Cervantes-Perez, J.; Huerta-Chua, J.; Sanchez-Orea, J.; Contreras-Hernandez, A. D.

    2014-01-01

    The homotopy perturbation method (HPM) is coupled with versions of Laplace-Padé and Padé methods to provide an approximate solution to the nonlinear differential equation that describes the behaviour of a flow with a stretching flat boundary due to partial slip. Comparing results between approximate and numerical solutions, we concluded that our results are capable of providing an accurate solution and are extremely efficient. PMID:27433526

  17. Intermediate boundary conditions for LOD, ADI and approximate factorization methods

    NASA Technical Reports Server (NTRS)

    Leveque, R. J.

    1985-01-01

    A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.

  18. Boundary Approximation Methods for Sloving Elliptic Problems on Unbounded Domains

    NASA Astrophysics Data System (ADS)

    Li, Zi-Cai; Mathon, Rudolf

    1990-08-01

    Boundary approximation methods with partial solutions are presented for solving a complicated problem on an unbounded domain, with both a crack singularity and a corner singularity. Also an analysis of partial solutions near the singular points is provided. These methods are easy to apply, have good stability properties, and lead to highly accurate solutions. Hence, boundary approximation methods with partial solutions are recommended for the treatment of elliptic problems on unbounded domains provided that piecewise solution expansions, in particular, asymptotic solutions near the singularities and infinity, can be found.

  19. Analytical estimation of ultrasound properties, thermal diffusivity, and perfusion using magnetic resonance-guided focused ultrasound temperature data

    PubMed Central

    Dillon, C R; Borasi, G; Payne, A

    2016-01-01

    For thermal modeling to play a significant role in treatment planning, monitoring, and control of magnetic resonance-guided focused ultrasound (MRgFUS) thermal therapies, accurate knowledge of ultrasound and thermal properties is essential. This study develops a new analytical solution for the temperature change observed in MRgFUS which can be used with experimental MR temperature data to provide estimates of the ultrasound initial heating rate, Gaussian beam variance, tissue thermal diffusivity, and Pennes perfusion parameter. Simulations demonstrate that this technique provides accurate and robust property estimates that are independent of the beam size, thermal diffusivity, and perfusion levels in the presence of realistic MR noise. The technique is also demonstrated in vivo using MRgFUS heating data in rabbit back muscle. Errors in property estimates are kept less than 5% by applying a third order Taylor series approximation of the perfusion term and ensuring the ratio of the fitting time (the duration of experimental data utilized for optimization) to the perfusion time constant remains less than one. PMID:26741344

  20. Karhunen Loève approximation of random fields by generalized fast multipole methods

    NASA Astrophysics Data System (ADS)

    Schwab, Christoph; Todor, Radu Alexandru

    2006-09-01

    KL approximation of a possibly instationary random field a( ω, x) ∈ L2( Ω, d P; L∞( D)) subject to prescribed meanfield Ea(x)=∫a(ω,x) dP(ω) and covariance Va(x,x')=∫(a(ω,x)-Ea(x))(a(ω,x')-Ea(x')) dP(ω) in a polyhedral domain D⊂Rd is analyzed. We show how for stationary covariances Va( x, x') = ga(| x - x'|) with ga( z) analytic outside of z = 0, an M-term approximate KL-expansion aM( ω, x) of a( ω, x) can be computed in log-linear complexity. The approach applies in arbitrary domains D and for nonseparable covariances Ca. It involves Galerkin approximation of the KL eigenvalue problem by discontinuous finite elements of degree p ⩾ 0 on a quasiuniform, possibly unstructured mesh of width h in D, plus a generalized fast multipole accelerated Krylov-Eigensolver. The approximate KL-expansion aM( x, ω) of a( x, ω) has accuracy O(exp(- bM1/ d)) if ga is analytic at z = 0 and accuracy O( M- k/ d) if ga is Ck at zero. It is obtained in O( MN(log N) b) operations where N = O( h- d).

  1. Strong shock implosion, approximate solution

    NASA Astrophysics Data System (ADS)

    Fujimoto, Y.; Mishkin, E. A.; Alejaldre, C.

    1983-01-01

    The self-similar, center-bound motion of a strong spherical, or cylindrical, shock wave moving through an ideal gas with a constant, γ= cp/ cv, is considered and a linearized, approximate solution is derived. An X, Y phase plane of the self-similar solution is defined and the representative curved of the system behind the shock front is replaced by a straight line connecting the mappings of the shock front with that of its tail. The reduced pressure P(ξ), density R(ξ) and velocity U1(ξ) are found in closed, quite accurate, form. Comparison with numerically obtained results, for γ= {5}/{3} and γ= {7}/{5}, is shown.

  2. Comparison between numeric and approximate analytic solutions for the prediction of soil metal uptake by roots. Example of cadmium.

    PubMed

    Schneider, André; Lin, Zhongbing; Sterckeman, Thibault; Nguyen, Christophe

    2018-04-01

    The dissociation of metal complexes in the soil solution can increase the availability of metals for root uptake. When it is accounted for in models of bioavailability of soil metals, the number of partial differential equations (PDEs) increases and the computation time to numerically solve these equations may be problematic when a large number of simulations are required, for example for sensitivity analyses or when considering root architecture. This work presents analytical solutions for the set of PDEs describing the bioavailability of soil metals including the kinetics of complexation for three scenarios where the metal complex in solution was fully inert, fully labile, or partially labile. The analytical solutions are only valid i) at steady-state when the PDEs become ordinary differential equations, the transient phase being not covered, ii) when diffusion is the major mechanism of transport and therefore, when convection is negligible, iii) when there is no between-root competition. The formulation of the analytical solutions is for cylindrical geometry but the solutions rely on the spread of the depletion profile around the root, which was modelled assuming a planar geometry. The analytical solutions were evaluated by comparison with the corresponding PDEs for cadmium in the case of the French agricultural soils. Provided that convection was much lower than diffusion (Péclet's number<0.02), the cumulative uptakes calculated from the analytic solutions were in very good agreement with those calculated from the PDEs, even in the case of a partially labile complex. The analytic solutions can be used instead of the PDEs to predict root uptake of metals. The analytic solutions were also used to build an indicator of the contribution of a complex to the uptake of the metal by roots, which can be helpful to predict the effect of soluble organic matter on the bioavailability of soil metals. Copyright © 2017 Elsevier B.V. All rights reserved.

  3. Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum.

    PubMed

    Shahbazi, Mohammad; Saranlı, Uluç; Babuška, Robert; Lopes, Gabriel A D

    2016-12-05

    This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of non-negligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.

  4. The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions

    PubMed Central

    2012-01-01

    Background It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. Results We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. Conclusions A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a

  5. A parallel offline CFD and closed-form approximation strategy for computationally efficient analysis of complex fluid flows

    NASA Astrophysics Data System (ADS)

    Allphin, Devin

    Computational fluid dynamics (CFD) solution approximations for complex fluid flow problems have become a common and powerful engineering analysis technique. These tools, though qualitatively useful, remain limited in practice by their underlying inverse relationship between simulation accuracy and overall computational expense. While a great volume of research has focused on remedying these issues inherent to CFD, one traditionally overlooked area of resource reduction for engineering analysis concerns the basic definition and determination of functional relationships for the studied fluid flow variables. This artificial relationship-building technique, called meta-modeling or surrogate/offline approximation, uses design of experiments (DOE) theory to efficiently approximate non-physical coupling between the variables of interest in a fluid flow analysis problem. By mathematically approximating these variables, DOE methods can effectively reduce the required quantity of CFD simulations, freeing computational resources for other analytical focuses. An idealized interpretation of a fluid flow problem can also be employed to create suitably accurate approximations of fluid flow variables for the purposes of engineering analysis. When used in parallel with a meta-modeling approximation, a closed-form approximation can provide useful feedback concerning proper construction, suitability, or even necessity of an offline approximation tool. It also provides a short-circuit pathway for further reducing the overall computational demands of a fluid flow analysis, again freeing resources for otherwise unsuitable resource expenditures. To validate these inferences, a design optimization problem was presented requiring the inexpensive estimation of aerodynamic forces applied to a valve operating on a simulated piston-cylinder heat engine. The determination of these forces was to be found using parallel surrogate and exact approximation methods, thus evidencing the comparative

  6. Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

    DOE PAGES

    Song, Chenchen; Martinez, Todd J.

    2017-08-29

    Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less

  7. Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

    NASA Astrophysics Data System (ADS)

    Song, Chenchen; Martínez, Todd J.

    2017-10-01

    Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. The resulting energy conservation in micro-canonical AIMD demonstrates that the implementation provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.

  8. Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

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

    Song, Chenchen; Martinez, Todd J.

    Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less

  9. Swiss-cheese models and the Dyer-Roeder approximation

    NASA Astrophysics Data System (ADS)

    Fleury, Pierre

    2014-06-01

    In view of interpreting the cosmological observations precisely, especially when they involve narrow light beams, it is crucial to understand how light propagates in our statistically homogeneous, clumpy, Universe. Among the various approaches to tackle this issue, Swiss-cheese models propose an inhomogeneous spacetime geometry which is an exact solution of Einstein's equation, while the Dyer-Roeder approximation deals with inhomogeneity in an effective way. In this article, we demonstrate that the distance-redshift relation of a certain class of Swiss-cheese models is the same as the one predicted by the Dyer-Roeder approach, at a well-controlled level of approximation. Both methods are therefore equivalent when applied to the interpretation of, e.g., supernova obervations. The proof relies on completely analytical arguments, and is illustrated by numerical results.

  10. Pre-analytical and analytical variation of drug determination in segmented hair using ultra-performance liquid chromatography-tandem mass spectrometry.

    PubMed

    Nielsen, Marie Katrine Klose; Johansen, Sys Stybe; Linnet, Kristian

    2014-01-01

    Assessment of total uncertainty of analytical methods for the measurements of drugs in human hair has mainly been derived from the analytical variation. However, in hair analysis several other sources of uncertainty will contribute to the total uncertainty. Particularly, in segmental hair analysis pre-analytical variations associated with the sampling and segmentation may be significant factors in the assessment of the total uncertainty budget. The aim of this study was to develop and validate a method for the analysis of 31 common drugs in hair using ultra-performance liquid chromatography-tandem mass spectrometry (UHPLC-MS/MS) with focus on the assessment of both the analytical and pre-analytical sampling variations. The validated method was specific, accurate (80-120%), and precise (CV≤20%) across a wide linear concentration range from 0.025-25 ng/mg for most compounds. The analytical variation was estimated to be less than 15% for almost all compounds. The method was successfully applied to 25 segmented hair specimens from deceased drug addicts showing a broad pattern of poly-drug use. The pre-analytical sampling variation was estimated from the genuine duplicate measurements of two bundles of hair collected from each subject after subtraction of the analytical component. For the most frequently detected analytes, the pre-analytical variation was estimated to be 26-69%. Thus, the pre-analytical variation was 3-7 folds larger than the analytical variation (7-13%) and hence the dominant component in the total variation (29-70%). The present study demonstrated the importance of including the pre-analytical variation in the assessment of the total uncertainty budget and in the setting of the 95%-uncertainty interval (±2CVT). Excluding the pre-analytical sampling variation could significantly affect the interpretation of results from segmental hair analysis. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

  11. Plasma Physics Approximations in Ares

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

    Managan, R. A.

    Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, F n( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζmore » ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ)F 1/2(μ/θ), F 1/2'/F 1/2, F c α, and F c β. In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.« less

  12. Tungsten devices in analytical atomic spectrometry

    NASA Astrophysics Data System (ADS)

    Hou, Xiandeng; Jones, Bradley T.

    2002-04-01

    Tungsten devices have been employed in analytical atomic spectrometry for approximately 30 years. Most of these atomizers can be electrically heated up to 3000 °C at very high heating rates, with a simple power supply. Usually, a tungsten device is employed in one of two modes: as an electrothermal atomizer with which the sample vapor is probed directly, or as an electrothermal vaporizer, which produces a sample aerosol that is then carried to a separate atomizer for analysis. Tungsten devices may take various physical shapes: tubes, cups, boats, ribbons, wires, filaments, coils and loops. Most of these orientations have been applied to many analytical techniques, such as atomic absorption spectrometry, atomic emission spectrometry, atomic fluorescence spectrometry, laser excited atomic fluorescence spectrometry, metastable transfer emission spectroscopy, inductively coupled plasma optical emission spectrometry, inductively coupled plasma mass spectrometry and microwave plasma atomic spectrometry. The analytical figures of merit and the practical applications reported for these techniques are reviewed. Atomization mechanisms reported for tungsten atomizers are also briefly summarized. In addition, less common applications of tungsten devices are discussed, including analyte preconcentration by adsorption or electrodeposition and electrothermal separation of analytes prior to analysis. Tungsten atomization devices continue to provide simple, versatile alternatives for analytical atomic spectrometry.

  13. Traveling-cluster approximation for uncorrelated amorphous systems

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

    Sen, A.K.; Mills, R.; Kaplan, T.

    1984-11-15

    We have developed a formalism for including cluster effects in the one-electron Green's function for a positionally disordered (liquid or amorphous) system without any correlation among the scattering sites. This method is an extension of the technique known as the traveling-cluster approximation (TCA) originally obtained and applied to a substitutional alloy by Mills and Ratanavararaksa. We have also proved the appropriate fixed-point theorem, which guarantees, for a bounded local potential, that the self-consistent equations always converge upon iteration to a unique, Herglotz solution. To our knowledge, this is the only analytic theory for considering cluster effects. Furthermore, we have performedmore » some computer calculations in the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results have been compared with ''exact calculations'' (which, in principle, take into account all cluster effects) and with the coherent-potential approximation (CPA), which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA and yet, apparently, the pair approximation distorts some of the features of the exact results.« less

  14. Approximate Dispersion Relations for Waves on Arbitrary Shear Flows

    NASA Astrophysics Data System (ADS)

    Ellingsen, S. À.; Li, Y.

    2017-12-01

    An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3-D generalization of the much used approximation by Skop (1987), developed further by Kirby and Chen (1989), but is shown to be more robust, succeeding in situations where the Kirby and Chen model fails. The two approximations incur the same numerical cost and difficulty. While the Kirby and Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability. A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding second-order expression proposed by Kirby and Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our second-order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby and Chen.Plain Language SummaryIn order to answer key questions such as how the ocean surface affects the climate, erodes the coastline and transports nutrients, we must understand how waves move. This is not so easy when depth varying currents are present, as they often are in coastal waters. We have developed a modeling tool for <span class="hlt">accurately</span> predicting wave properties in such situations, ready for use, for example, in the</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018MPLB...3250159L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018MPLB...3250159L"><span>Convergence and <span class="hlt">approximate</span> calculation of average degree under different network sizes for decreasing random birth-and-death networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Long, Yin; Zhang, Xiao-Jun; Wang, Kui</p> <p>2018-05-01</p> <p>In this paper, convergence and <span class="hlt">approximate</span> calculation of average degree under different network sizes for decreasing random birth-and-death networks (RBDNs) are studied. First, we find and demonstrate that the average degree is convergent in the form of power law. Meanwhile, we discover that the ratios of the back items to front items of convergent reminder are independent of network link number for large network size, and we theoretically prove that the limit of the ratio is a constant. Moreover, since it is difficult to calculate the <span class="hlt">analytical</span> solution of the average degree for large network sizes, we adopt numerical method to obtain <span class="hlt">approximate</span> expression of the average degree to <span class="hlt">approximate</span> its <span class="hlt">analytical</span> solution. Finally, simulations are presented to verify our theoretical results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19800006556','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19800006556"><span><span class="hlt">Approximate</span> and exact numerical integration of the gas dynamic equations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lewis, T. S.; Sirovich, L.</p> <p>1979-01-01</p> <p>A highly <span class="hlt">accurate</span> <span class="hlt">approximation</span> and a rapidly convergent numerical procedure are developed for two dimensional steady supersonic flow over an airfoil. Examples are given for a symmetric airfoil over a range of Mach numbers. Several interesting features are found in the calculation of the tail shock and the flow behind the airfoil.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20000025072&hterms=mule&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dmule','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20000025072&hterms=mule&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dmule"><span>Photogrammetrically Measured Distortions of Composite Structure Microwave Reflectors at <span class="hlt">Approximately</span> 90 K</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Mule, Peter; Hill, Michael D.; Sampler, Henry P.</p> <p>2000-01-01</p> <p>The Microwave Anisotropy Probe (MAP) Observatory, scheduled for a fall 2000 launch, is designed to measure temperature fluctuations (anisotropy) and produce a high sensitivity and high spatial resolution (better than 0.3 deg.) map of the cosmic microwave background (CMB) radiation over the entire sky between 22 and 90 GHz. MAP utilizes back-to-back composite Gregorian telescopes supported on a composite truss structure to focus the microwave signals into 10 differential microwave receivers. Proper position and shape of the telescope reflectors at the operating temperature of <span class="hlt">approximately</span> 90 K is a critical element to ensuring mission success. We describe the methods and analysis used to validate the in-flight position and shape predictions for the reflectors based on photogrammetric (PG) metrology data taken under vacuum with the reflectors at <span class="hlt">approximately</span> 90 K. Contour maps showing reflector distortion <span class="hlt">analytical</span> extrapolations were generated. The resulting reflector distortion data are shown to be crucial to the <span class="hlt">analytical</span> assessment of the MAP instrument's microwave system in-flight performance.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3477701','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3477701"><span>Finite element modeling of mitral leaflet tissue using a layered shell <span class="hlt">approximation</span></span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Ratcliffe, Mark B.; Guccione, Julius M.</p> <p>2012-01-01</p> <p>The current study presents a finite element model of mitral leaflet tissue, which incorporates the anisotropic material response and <span class="hlt">approximates</span> the layered structure. First, continuum mechanics and the theory of layered composites are used to develop an <span class="hlt">analytical</span> representation of membrane stress in the leaflet material. This is done with an existing anisotropic constitutive law from literature. Then, the concept is implemented in a finite element (FE) model by overlapping and merging two layers of transversely isotropic membrane elements in LS-DYNA, which homogenizes the response. The FE model is then used to simulate various biaxial extension tests and out-of-plane pressure loading. Both the <span class="hlt">analytical</span> and FE model show good agreement with experimental biaxial extension data, and show good mutual agreement. This confirms that the layered composite <span class="hlt">approximation</span> presented in the current study is able to capture the exponential stiffening seen in both the circumferential and radial directions of mitral leaflets. PMID:22971896</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19820046619&hterms=kernel&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dkernel','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19820046619&hterms=kernel&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dkernel"><span>An <span class="hlt">accurate</span> and efficient method for evaluating the kernel of the integral equation relating pressure to normalwash in unsteady potential flow</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Desmarais, R. N.</p> <p>1982-01-01</p> <p>This paper describes an <span class="hlt">accurate</span> economical method for generating <span class="hlt">approximations</span> to the kernel of the integral equation relating unsteady pressure to normalwash in nonplanar flow. The method is capable of generating <span class="hlt">approximations</span> of arbitrary accuracy. It is based on <span class="hlt">approximating</span> the algebraic part of the non elementary integrals in the kernel by exponential <span class="hlt">approximations</span> and then integrating termwise. The exponent spacing in the <span class="hlt">approximation</span> is a geometric sequence. The coefficients and exponent multiplier of the exponential <span class="hlt">approximation</span> are computed by least squares so the method is completely automated. Exponential <span class="hlt">approximates</span> generated in this manner are two orders of magnitude more <span class="hlt">accurate</span> than the exponential <span class="hlt">approximation</span> that is currently most often used for this purpose. Coefficients for 8, 12, 24, and 72 term <span class="hlt">approximations</span> are tabulated in the report. Also, since the method is automated, it can be used to generate <span class="hlt">approximations</span> to attain any desired trade-off between accuracy and computing cost.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26170553','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26170553"><span>Fast and <span class="hlt">accurate</span> Monte Carlo modeling of a kilovoltage X-ray therapy unit using a photon-source <span class="hlt">approximation</span> for treatment planning in complex media.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Zeinali-Rafsanjani, B; Mosleh-Shirazi, M A; Faghihi, R; Karbasi, S; Mosalaei, A</p> <p>2015-01-01</p> <p>To <span class="hlt">accurately</span> recompute dose distributions in chest-wall radiotherapy with 120 kVp kilovoltage X-rays, an MCNP4C Monte Carlo model is presented using a fast method that obviates the need to fully model the tube components. To validate the model, half-value layer (HVL), percentage depth doses (PDDs) and beam profiles were measured. Dose measurements were performed for a more complex situation using thermoluminescence dosimeters (TLDs) placed within a Rando phantom. The measured and computed first and second HVLs were 3.8, 10.3 mm Al and 3.8, 10.6 mm Al, respectively. The differences between measured and calculated PDDs and beam profiles in water were within 2 mm/2% for all data points. In the Rando phantom, differences for majority of data points were within 2%. The proposed model offered an <span class="hlt">approximately</span> 9500-fold reduced run time compared to the conventional full simulation. The acceptable agreement, based on international criteria, between the simulations and the measurements validates the accuracy of the model for its use in treatment planning and radiobiological modeling studies of superficial therapies including chest-wall irradiation using kilovoltage beam.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li class="active"><span>17</span></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_17 --> <div id="page_18" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li class="active"><span>18</span></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="341"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890015825','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890015825"><span>An <span class="hlt">approximation</span> function for frequency constrained structural optimization</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Canfield, R. A.</p> <p>1989-01-01</p> <p>The purpose is to examine a function for <span class="hlt">approximating</span> natural frequency constraints during structural optimization. The nonlinearity of frequencies has posed a barrier to constructing <span class="hlt">approximations</span> for frequency constraints of high enough quality to facilitate efficient solutions. A new function to represent frequency constraints, called the Rayleigh Quotient <span class="hlt">Approximation</span> (RQA), is presented. Its ability to represent the actual frequency constraint results in stable convergence with effectively no move limits. The objective of the optimization problem is to minimize structural weight subject to some minimum (or maximum) allowable frequency and perhaps subject to other constraints such as stress, displacement, and gage size, as well. A reason for constraining natural frequencies during design might be to avoid potential resonant frequencies due to machinery or actuators on the structure. Another reason might be to satisy requirements of an aircraft or spacecraft's control law. Whatever the structure supports may be sensitive to a frequency band that must be avoided. Any of these situations or others may require the designer to insure the satisfaction of frequency constraints. A further motivation for considering <span class="hlt">accurate</span> <span class="hlt">approximations</span> of natural frequencies is that they are fundamental to dynamic response constraints.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/782843','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/782843"><span>Statistically Qualified Neuro-<span class="hlt">Analytic</span> system and Method for Process Monitoring</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Vilim, Richard B.; Garcia, Humberto E.; Chen, Frederick W.</p> <p>1998-11-04</p> <p>An apparatus and method for monitoring a process involves development and application of a statistically qualified neuro-<span class="hlt">analytic</span> (SQNA) model to <span class="hlt">accurately</span> and reliably identify process change. The development of the SQNA model is accomplished in two steps: deterministic model adaption and stochastic model adaptation. Deterministic model adaption involves formulating an <span class="hlt">analytic</span> model of the process representing known process characteristics,augmenting the <span class="hlt">analytic</span> model with a neural network that captures unknown process characteristics, and training the resulting neuro-<span class="hlt">analytic</span> model by adjusting the neural network weights according to a unique scaled equation emor minimization technique. Stochastic model adaptation involves qualifying any remaining uncertaintymore » in the trained neuro-<span class="hlt">analytic</span> model by formulating a likelihood function, given an error propagation equation, for computing the probability that the neuro-<span class="hlt">analytic</span> model generates measured process output. Preferably, the developed SQNA model is validated using known sequential probability ratio tests and applied to the process as an on-line monitoring system.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/969042','DOE-PATENT-XML'); return false;" href="https://www.osti.gov/servlets/purl/969042"><span>Statistically qualified neuro-<span class="hlt">analytic</span> failure detection method and system</span></a></p> <p><a target="_blank" href="http://www.osti.gov/doepatents">DOEpatents</a></p> <p>Vilim, Richard B.; Garcia, Humberto E.; Chen, Frederick W.</p> <p>2002-03-02</p> <p>An apparatus and method for monitoring a process involve development and application of a statistically qualified neuro-<span class="hlt">analytic</span> (SQNA) model to <span class="hlt">accurately</span> and reliably identify process change. The development of the SQNA model is accomplished in two stages: deterministic model adaption and stochastic model modification of the deterministic model adaptation. Deterministic model adaption involves formulating an <span class="hlt">analytic</span> model of the process representing known process characteristics, augmenting the <span class="hlt">analytic</span> model with a neural network that captures unknown process characteristics, and training the resulting neuro-<span class="hlt">analytic</span> model by adjusting the neural network weights according to a unique scaled equation error minimization technique. Stochastic model modification involves qualifying any remaining uncertainty in the trained neuro-<span class="hlt">analytic</span> model by formulating a likelihood function, given an error propagation equation, for computing the probability that the neuro-<span class="hlt">analytic</span> model generates measured process output. Preferably, the developed SQNA model is validated using known sequential probability ratio tests and applied to the process as an on-line monitoring system. Illustrative of the method and apparatus, the method is applied to a peristaltic pump system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JAMES..10..826P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JAMES..10..826P"><span>An Economical <span class="hlt">Analytical</span> Equation for the Integrated Vertical Overlap of Cumulus and Stratus</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Park, Sungsu</p> <p>2018-03-01</p> <p>By extending the previously proposed heuristic parameterization, the author derived an <span class="hlt">analytical</span> equation computing the overlap areas between the precipitation (or radiation) areas and the cloud areas in a cloud system consisting of cumulus and stratus. The new <span class="hlt">analytical</span> equation is <span class="hlt">accurate</span> and much more efficient than the previous heuristic equation, which suffers from the truncation error in association with the digitalization of the overlap areas. Global test simulations with the new <span class="hlt">analytical</span> formula in an offline mode showed that the maximum cumulus overlap simulates more surface precipitation flux than the random cumulus overlap. On the other hand, the maximum stratus overlap simulates less surface precipitation flux than random stratus overlap, which is due to the increase in the evaporation rate of convective precipitation from the random to maximum stratus overlap. The independent precipitation <span class="hlt">approximation</span> (IPA) marginally decreases the surface precipitation flux, implying that IPA works well with other parameterizations. In contrast to the net production rate of precipitation and surface precipitation flux that increase when the cumulus and stratus are maximally and randomly overlapped, respectively, the global mean net radiative cooling and longwave cloud radiative forcing (LWCF) increase when the cumulus and stratus are randomly overlapped. On the global average, the vertical cloud overlap exerts larger impacts on the precipitation flux than on the radiation flux. The radiation scheme taking the subgrid variability of water vapor between the cloud and clear portions into account substantially increases the global mean LWCF in tropical deep convection and midlatitude storm track regions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://eric.ed.gov/?q=Physics%3a+AND+Motion+AND+Forces&pg=6&id=EJ882152','ERIC'); return false;" href="https://eric.ed.gov/?q=Physics%3a+AND+Motion+AND+Forces&pg=6&id=EJ882152"><span><span class="hlt">Approximate</span> Formula for the Vertical Asymptote of Projectile Motion in Midair</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Chudinov, Peter Sergey</p> <p>2010-01-01</p> <p>The classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. An <span class="hlt">analytical</span> approach is used for the investigation. An <span class="hlt">approximate</span> formula is obtained for one of the characteristics of the motion--the vertical…</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20120011949','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20120011949"><span>An <span class="hlt">Analytical</span> Solution for Transient Thermal Response of an Insulated Structure</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Blosser, Max L.</p> <p>2012-01-01</p> <p>An <span class="hlt">analytical</span> solution was derived for the transient response of an insulated aerospace vehicle structure subjected to a simplified heat pulse. This simplified problem <span class="hlt">approximates</span> the thermal response of a thermal protection system of an atmospheric entry vehicle. The exact <span class="hlt">analytical</span> solution is solely a function of two non-dimensional parameters. A simpler function of these two parameters was developed to <span class="hlt">approximate</span> the maximum structural temperature over a wide range of parameter values. Techniques were developed to choose constant, effective properties to represent the relevant temperature and pressure-dependent properties for the insulator and structure. A technique was also developed to map a time-varying surface temperature history to an equivalent square heat pulse. Using these techniques, the maximum structural temperature rise was calculated using the <span class="hlt">analytical</span> solutions and shown to typically agree with finite element simulations within 10 to 20 percent over the relevant range of parameters studied.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JSV...386..407X','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JSV...386..407X"><span><span class="hlt">Analytical</span> estimation on divergence and flutter vibrations of symmetrical three-phase induction stator via field-synchronous coordinates</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Xia, Ying; Wang, Shiyu; Sun, Wenjia; Xiu, Jie</p> <p>2017-01-01</p> <p>The electromagnetically induced parametric vibration of the symmetrical three-phase induction stator is examined. While it can be analyzed by an <span class="hlt">approximate</span> <span class="hlt">analytical</span> or numerical method, more <span class="hlt">accurate</span> and simple <span class="hlt">analytical</span> method is desirable. This work proposes a new method based on the field-synchronous coordinates. A mechanical-electromagnetic coupling model is developed under this frame such that a time-invariant governing equation with gyroscopic term can be developed. With the general vibration theory, the eigenvalue is formulated; the transition curves between the stable and unstable regions, and response are all determined as closed-form expressions of basic mechanical-electromagnetic parameters. The dependence of these parameters on the instability behaviors is demonstrated. The results imply that the divergence and flutter instabilities can occur even for symmetrical motors with balanced, constant amplitude and sinusoidal voltage. To verify the <span class="hlt">analytical</span> predictions, this work also builds up a time-variant model of the same system under the conventional inertial frame. The Floquét theory is employed to predict the parametric instability and the numerical integration is used to obtain the parametric response. The parametric instability and response are both well compared against those under the field-synchronous coordinates. The proposed field-synchronous coordinates allows a quick estimation on the electromagnetically induced vibration. The convenience offered by the body-fixed coordinates is discussed across various fields.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018RvMP...90a5008H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018RvMP...90a5008H"><span>High precision <span class="hlt">analytical</span> description of the allowed β spectrum shape</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hayen, Leendert; Severijns, Nathal; Bodek, Kazimierz; Rozpedzik, Dagmara; Mougeot, Xavier</p> <p>2018-01-01</p> <p>A fully <span class="hlt">analytical</span> description of the allowed β spectrum shape is given in view of ongoing and planned measurements. Its study forms an invaluable tool in the search for physics beyond the standard electroweak model and the weak magnetism recoil term. Contributions stemming from finite size corrections, mass effects, and radiative corrections are reviewed. Particular focus is placed on atomic and chemical effects, where the existing description is extended and <span class="hlt">analytically</span> provided. The effects of QCD-induced recoil terms are discussed, and cross-checks were performed for different theoretical formalisms. Special attention was given to a comparison of the treatment of nuclear structure effects in different formalisms. Corrections were derived for both Fermi and Gamow-Teller transitions, and methods of <span class="hlt">analytical</span> evaluation thoroughly discussed. In its integrated form, calculated f values were in agreement with the most precise numerical results within the aimed for precision. The need for an <span class="hlt">accurate</span> evaluation of weak magnetism contributions was stressed, and the possible significance of the oft-neglected induced pseudoscalar interaction was noted. Together with improved atomic corrections, an <span class="hlt">analytical</span> description was presented of the allowed β spectrum shape <span class="hlt">accurate</span> to a few parts in 10-4 down to 1 keV for low to medium Z nuclei, thereby extending the work by previous authors by nearly an order of magnitude.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23440770','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23440770"><span>Spiral trajectory design: a flexible numerical algorithm and base <span class="hlt">analytical</span> equations.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Pipe, James G; Zwart, Nicholas R</p> <p>2014-01-01</p> <p>Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several <span class="hlt">analytical</span> expressions for charactering the base (critically sampled) class of these trajectories. Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. <span class="hlt">Analytical</span> expressions <span class="hlt">approximating</span> the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with <span class="hlt">analytically</span> obtained results. Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and <span class="hlt">analytical</span> approaches are in good agreement. A versatile numerical algorithm was developed, and was written in publicly available code. <span class="hlt">Approximate</span> <span class="hlt">analytical</span> formulas are given that help characterize spiral trajectories. Copyright © 2013 Wiley Periodicals, Inc.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19970041606','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19970041606"><span>Exponential <span class="hlt">Approximations</span> Using Fourier Series Partial Sums</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Banerjee, Nana S.; Geer, James F.</p> <p>1997-01-01</p> <p>The problem of <span class="hlt">accurately</span> reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to <span class="hlt">approximate</span> the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are <span class="hlt">approximated</span> to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is <span class="hlt">approximated</span> to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of <span class="hlt">approximations</span> to f. Each of these new <span class="hlt">approximations</span> is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new <span class="hlt">approximations</span>, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23485274','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23485274"><span>Extension of the KLI <span class="hlt">approximation</span> toward the exact optimized effective potential.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Iafrate, G J; Krieger, J B</p> <p>2013-03-07</p> <p> determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit <span class="hlt">analytic</span> results are provided to illustrate the first order iterative correction beyond the KLI <span class="hlt">approximation</span>. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as <span class="hlt">accurately</span> as desired.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JChPh.138i4104I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JChPh.138i4104I"><span>Extension of the KLI <span class="hlt">approximation</span> toward the exact optimized effective potential</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Iafrate, G. J.; Krieger, J. B.</p> <p>2013-03-01</p> <p> determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit <span class="hlt">analytic</span> results are provided to illustrate the first order iterative correction beyond the KLI <span class="hlt">approximation</span>. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as <span class="hlt">accurately</span> as desired.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870020664','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870020664"><span>UNAERO: A package of FORTRAN subroutines for <span class="hlt">approximating</span> unsteady aerodynamics in the time domain</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Dunn, H. J.</p> <p>1985-01-01</p> <p>This report serves as an instruction and maintenance manual for a collection of CDC CYBER FORTRAN IV subroutines for <span class="hlt">approximating</span> the unsteady aerodynamic forces in the time domain. The result is a set of constant-coefficient first-order differential equations that <span class="hlt">approximate</span> the dynamics of the vehicle. Provisions are included for adjusting the number of modes used for calculating the <span class="hlt">approximations</span> so that an <span class="hlt">accurate</span> <span class="hlt">approximation</span> is generated. The number of data points at different values of reduced frequency can also be varied to adjust the accuracy of the <span class="hlt">approximation</span> over the reduced-frequency range. The denominator coefficients of the <span class="hlt">approximation</span> may be calculated by means of a gradient method or a least-squares <span class="hlt">approximation</span> technique. Both the <span class="hlt">approximation</span> methods use weights on the residual error. A new set of system equations, at a different dynamic pressure, can be generated without the <span class="hlt">approximations</span> being recalculated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992JChPh..96.6654Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992JChPh..96.6654Z"><span>An <span class="hlt">approximate</span> classical unimolecular reaction rate theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhao, Meishan; Rice, Stuart A.</p> <p>1992-05-01</p> <p>We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying <span class="hlt">approximations</span>. These <span class="hlt">approximations</span> concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which <span class="hlt">approximation</span> is similar to but extends and improves the <span class="hlt">approximations</span> for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an <span class="hlt">analytic</span> representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25045677','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25045677"><span>Big data <span class="hlt">analytics</span> in immunology: a knowledge-based approach.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Zhang, Guang Lan; Sun, Jing; Chitkushev, Lou; Brusic, Vladimir</p> <p>2014-01-01</p> <p>With the vast amount of immunological data available, immunology research is entering the big data era. These data vary in granularity, quality, and complexity and are stored in various formats, including publications, technical reports, and databases. The challenge is to make the transition from data to actionable knowledge and wisdom and bridge the knowledge gap and application gap. We report a knowledge-based approach based on a framework called KB-builder that facilitates data mining by enabling fast development and deployment of web-accessible immunological data knowledge warehouses. Immunological knowledge discovery relies heavily on both the availability of <span class="hlt">accurate</span>, up-to-date, and well-organized data and the proper <span class="hlt">analytics</span> tools. We propose the use of knowledge-based approaches by developing knowledgebases combining well-annotated data with specialized <span class="hlt">analytical</span> tools and integrating them into <span class="hlt">analytical</span> workflow. A set of well-defined workflow types with rich summarization and visualization capacity facilitates the transformation from data to critical information and knowledge. By using KB-builder, we enabled streamlining of normally time-consuming processes of database development. The knowledgebases built using KB-builder will speed up rational vaccine design by providing <span class="hlt">accurate</span> and well-annotated data coupled with tailored computational analysis tools and workflow.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28538985','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28538985"><span>Numerical <span class="hlt">Approximation</span> of Elasticity Tensor Associated With Green-Naghdi Rate.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Liu, Haofei; Sun, Wei</p> <p>2017-08-01</p> <p>Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an <span class="hlt">approximation</span> method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the <span class="hlt">approximation</span> method and the closed-form <span class="hlt">analytical</span> method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the <span class="hlt">approximation</span> method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CNSNS..27..206L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CNSNS..27..206L"><span>Semi-<span class="hlt">analytic</span> valuation of stock loans with finite maturity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lu, Xiaoping; Putri, Endah R. M.</p> <p>2015-10-01</p> <p>In this paper we study stock loans of finite maturity with different dividend distributions semi-<span class="hlt">analytically</span> using the <span class="hlt">analytical</span> <span class="hlt">approximation</span> method in Zhu (2006). Stock loan partial differential equations (PDEs) are established under Black-Scholes framework. Laplace transform method is used to solve the PDEs. Optimal exit price and stock loan value are obtained in Laplace space. Values in the original time space are recovered by numerical Laplace inversion. To demonstrate the efficiency and accuracy of our semi-<span class="hlt">analytic</span> method several examples are presented, the results are compared with those calculated using existing methods. We also present a calculation of fair service fee charged by the lender for different loan parameters.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1364064-small-asymptotics-quark-helicity-distribution-analytic-results','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1364064-small-asymptotics-quark-helicity-distribution-analytic-results"><span>Small-x asymptotics of the quark helicity distribution: <span class="hlt">Analytic</span> results</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.</p> <p>2017-06-15</p> <p>In this Letter, we <span class="hlt">analytically</span> solve the evolution equations for the small-x asymptotic behavior of the (flavor singlet) quark helicity distribution in the large- N c limit. Here, these evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This <span class="hlt">approximate</span> numerical solution, however, revealed simplifying properties of the small-x asymptotics, which we exploit here to obtain an <span class="hlt">analytic</span> solution.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JSV...417..359L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JSV...417..359L"><span>An efficient <span class="hlt">analytical</span> model for baffled, multi-celled membrane-type acoustic metamaterial panels</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Langfeldt, F.; Gleine, W.; von Estorff, O.</p> <p>2018-03-01</p> <p>A new <span class="hlt">analytical</span> model for the oblique incidence sound transmission loss prediction of baffled panels with multiple subwavelength sized membrane-type acoustic metamaterial (MAM) unit cells is proposed. The model employs a novel approach via the concept of the effective surface mass density and <span class="hlt">approximates</span> the unit cell vibrations in the form of piston-like displacements. This yields a coupled system of linear equations that can be solved efficiently using well-known solution procedures. A comparison with results from finite element model simulations for both normal and diffuse field incidence shows that the <span class="hlt">analytical</span> model delivers <span class="hlt">accurate</span> results as long as the edge length of the MAM unit cells is smaller than half the acoustic wavelength. The computation times for the <span class="hlt">analytical</span> calculations are 100 times smaller than for the numerical simulations. In addition to that, the effect of flexible MAM unit cell edges compared to the fixed edges assumed in the <span class="hlt">analytical</span> model is studied numerically. It is shown that the compliance of the edges has only a small impact on the transmission loss of the panel, except at very low frequencies in the stiffness-controlled regime. The proposed <span class="hlt">analytical</span> model is applied to investigate the effect of variations of the membrane prestress, added mass, and mass eccentricity on the diffuse transmission loss of a MAM panel with 120 unit cells. Unlike most previous investigations of MAMs, these results provide a better understanding of the acoustic performance of MAMs under more realistic conditions. For example, it is shown that by varying these parameters deliberately in a checkerboard pattern, a new anti-resonance with large transmission loss values can be introduced. A random variation of these parameters, on the other hand, is shown to have only little influence on the diffuse transmission loss, as long as the standard deviation is not too large. For very large random variations, it is shown that the peak transmission loss</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018CPL...698..176Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018CPL...698..176Z"><span>An <span class="hlt">accurate</span> computational method for the diffusion regime verification</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhokh, Alexey A.; Strizhak, Peter E.</p> <p>2018-04-01</p> <p>The diffusion regime (sub-diffusive, standard, or super-diffusive) is defined by the order of the derivative in the corresponding transport equation. We develop an <span class="hlt">accurate</span> computational method for the direct estimation of the diffusion regime. The method is based on the derivative order estimation using the asymptotic <span class="hlt">analytic</span> solutions of the diffusion equation with the integer order and the time-fractional derivatives. The robustness and the computational cheapness of the proposed method are verified using the experimental methane and methyl alcohol transport kinetics through the catalyst pellet.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li class="active"><span>18</span></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_18 --> <div id="page_19" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li class="active"><span>19</span></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="361"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29041301','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29041301"><span><span class="hlt">Analytical</span> modeling of light transport in scattering materials with strong absorption.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Meretska, M L; Uppu, R; Vissenberg, G; Lagendijk, A; Ijzerman, W L; Vos, W L</p> <p>2017-10-02</p> <p>We have investigated the transport of light through slabs that both scatter and strongly absorb, a situation that occurs in diverse application fields ranging from biomedical optics, powder technology, to solid-state lighting. In particular, we study the transport of light in the visible wavelength range between 420 and 700 nm through silicone plates filled with YAG:Ce 3+ phosphor particles, that even re-emit absorbed light at different wavelengths. We measure the total transmission, the total reflection, and the ballistic transmission of light through these plates. We obtain average single particle properties namely the scattering cross-section σ s , the absorption cross-section σ a , and the anisotropy factor µ using an <span class="hlt">analytical</span> approach, namely the P3 <span class="hlt">approximation</span> to the radiative transfer equation. We verify the extracted transport parameters using Monte-Carlo simulations of the light transport. Our approach fully describes the light propagation in phosphor diffuser plates that are used in white LEDs and that reveal a strong absorption (L/l a > 1) up to L/l a = 4, where L is the slab thickness, l a is the absorption mean free path. In contrast, the widely used diffusion theory fails to describe this parameter range. Our approach is a suitable <span class="hlt">analytical</span> tool for industry, since it provides a fast yet <span class="hlt">accurate</span> determination of key transport parameters, and since it introduces predictive power into the design process of white light emitting diodes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22255061-double-hybrid-density-functional-theory-meta-generalized-gradient-approximations','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22255061-double-hybrid-density-functional-theory-meta-generalized-gradient-approximations"><span>Double-hybrid density-functional theory with meta-generalized-gradient <span class="hlt">approximations</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Souvi, Sidi M. O., E-mail: sidi.souvi@irsn.fr; Sharkas, Kamal; Toulouse, Julien, E-mail: julien.toulouse@upmc.fr</p> <p>2014-02-28</p> <p>We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-<span class="hlt">approximation</span> (meta-GGA) exchange-correlation density functionals. We construct several variants of one-parameter double-hybrid <span class="hlt">approximations</span> using the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional and test them on test sets of atomization energies and reaction barrier heights. The most <span class="hlt">accurate</span> variant uses the uniform coordinate scaling of the density and of the kinetic energy density in the correlation functional, and improves over both standard Kohn-Sham TPSS and second-order Møller-Plesset calculations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24320422','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24320422"><span>A new concept of pencil beam dose calculation for 40-200 keV photons using <span class="hlt">analytical</span> dose kernels.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Bartzsch, Stefan; Oelfke, Uwe</p> <p>2013-11-01</p> <p>The advent of widespread kV-cone beam computer tomography in image guided radiation therapy and special therapeutic application of keV photons, e.g., in microbeam radiation therapy (MRT) require <span class="hlt">accurate</span> and fast dose calculations for photon beams with energies between 40 and 200 keV. Multiple photon scattering originating from Compton scattering and the strong dependence of the photoelectric cross section on the atomic number of the interacting tissue render these dose calculations by far more challenging than the ones established for corresponding MeV beams. That is why so far developed <span class="hlt">analytical</span> models of kV photon dose calculations fail to provide the required accuracy and one has to rely on time consuming Monte Carlo simulation techniques. In this paper, the authors introduce a novel <span class="hlt">analytical</span> approach for kV photon dose calculations with an accuracy that is almost comparable to the one of Monte Carlo simulations. First, <span class="hlt">analytical</span> point dose and pencil beam kernels are derived for homogeneous media and compared to Monte Carlo simulations performed with the Geant4 toolkit. The dose contributions are systematically separated into contributions from the relevant orders of multiple photon scattering. Moreover, <span class="hlt">approximate</span> scaling laws for the extension of the algorithm to inhomogeneous media are derived. The comparison of the <span class="hlt">analytically</span> derived dose kernels in water showed an excellent agreement with the Monte Carlo method. Calculated values deviate less than 5% from Monte Carlo derived dose values, for doses above 1% of the maximum dose. The <span class="hlt">analytical</span> structure of the kernels allows adaption to arbitrary materials and photon spectra in the given energy range of 40-200 keV. The presented <span class="hlt">analytical</span> methods can be employed in a fast treatment planning system for MRT. In convolution based algorithms dose calculation times can be reduced to a few minutes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27006884','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27006884"><span>Laplace transform homotopy perturbation method for the <span class="hlt">approximation</span> of variational problems.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R</p> <p>2016-01-01</p> <p>This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find <span class="hlt">analytical</span> <span class="hlt">approximate</span> solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the <span class="hlt">approximate</span> solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25637925','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25637925"><span><span class="hlt">Approximating</span> high-dimensional dynamics by barycentric coordinates with linear programming.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma</p> <p>2015-01-01</p> <p>The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for <span class="hlt">accurate</span> modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to <span class="hlt">accurately</span> model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the <span class="hlt">approximation</span> errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more <span class="hlt">accurately</span> than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012REDS..167..841R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012REDS..167..841R"><span><span class="hlt">Accurate</span> monoenergetic electron parameters of laser wakefield in a bubble model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Raheli, A.; Rahmatallahpur, S. H.</p> <p>2012-11-01</p> <p>A reliable <span class="hlt">analytical</span> expression for the potential of plasma waves with phase velocities near the speed of light is derived. The presented spheroid cavity model is more consistent than the previous spherical and ellipsoidal model and it explains the mono-energetic electron trajectory more <span class="hlt">accurately</span>, especially at the relativistic region. As a result, the quasi-mono-energetic electrons output beam interacting with the laser plasma can be more appropriately described with this model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JAP...123q4304C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JAP...123q4304C"><span>Comparison of <span class="hlt">approximate</span> solutions to the phonon Boltzmann transport equation with the relaxation time <span class="hlt">approximation</span>: Spherical harmonics expansions and the discrete ordinates method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Christenson, J. G.; Austin, R. A.; Phillips, R. J.</p> <p>2018-05-01</p> <p>The phonon Boltzmann transport equation is used to analyze model problems in one and two spatial dimensions, under transient and steady-state conditions. New, explicit solutions are obtained by using the P1 and P3 <span class="hlt">approximations</span>, based on expansions in spherical harmonics, and are compared with solutions from the discrete ordinates method. For steady-state energy transfer, it is shown that <span class="hlt">analytic</span> expressions derived using the P1 and P3 <span class="hlt">approximations</span> agree quantitatively with the discrete ordinates method, in some cases for large Knudsen numbers, and always for Knudsen numbers less than unity. However, for time-dependent energy transfer, the PN solutions differ qualitatively from converged solutions obtained by the discrete ordinates method. Although they correctly capture the wave-like behavior of energy transfer at short times, the P1 and P3 <span class="hlt">approximations</span> rely on one or two wave velocities, respectively, yielding abrupt, step-changes in temperature profiles that are absent when the angular dependence of the phonon velocities is captured more completely. It is shown that, with the gray <span class="hlt">approximation</span>, the P1 <span class="hlt">approximation</span> is formally equivalent to the so-called "hyperbolic heat equation." Overall, these results support the use of the PN <span class="hlt">approximation</span> to find solutions to the phonon Boltzmann transport equation for steady-state conditions. Such solutions can be useful in the design and analysis of devices that involve heat transfer at nanometer length scales, where continuum-scale approaches become inaccurate.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018AJ....155..253S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018AJ....155..253S"><span>A Fast and <span class="hlt">Accurate</span> Method of Radiation Hydrodynamics Calculation in Spherical Symmetry</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Stamer, Torsten; Inutsuka, Shu-ichiro</p> <p>2018-06-01</p> <p>We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion <span class="hlt">approximation</span>, and it is <span class="hlt">accurate</span> for optically thin, thick, and intermediate systems. In the limit of a homogeneously distributed extinction coefficient, our method is very <span class="hlt">accurate</span> and exceptionally fast. We combine this fast method with a slower but more generally applicable method to describe realistic problems. We perform various test calculations, including a simplified protostellar collapse simulation. We also discuss possible future improvements.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26597159','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26597159"><span>The relationship between stochastic and deterministic quasi-steady state <span class="hlt">approximations</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R</p> <p>2015-11-23</p> <p>The quasi steady-state <span class="hlt">approximation</span> (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is <span class="hlt">accurate</span>. However, a number of recent examples show that this is not necessarily the case. Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is <span class="hlt">accurate</span> whenever its deterministic counterpart provides an <span class="hlt">accurate</span> <span class="hlt">approximation</span> over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations. The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are <span class="hlt">accurate</span>. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1379693-stabilizing-potentials-bound-state-analytic-continuation-methods-electronic-resonances-polyatomic-molecules','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1379693-stabilizing-potentials-bound-state-analytic-continuation-methods-electronic-resonances-polyatomic-molecules"><span>Stabilizing potentials in bound state <span class="hlt">analytic</span> continuation methods for electronic resonances in polyatomic molecules</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>White, Alec F.; Head-Gordon, Martin; McCurdy, C. William</p> <p>2017-01-30</p> <p>The computation of Siegert energies by <span class="hlt">analytic</span> continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. Here, we critically evaluate a recently proposed <span class="hlt">analytic</span> continuation method based on low order (type III) Padé <span class="hlt">approximants</span> as well as an <span class="hlt">analytic</span> continuation method based on high order (type II) Padé <span class="hlt">approximants</span>. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2Π g shape resonance of N 2 - whichmore » has been studied extensively by other methods. Both the choice of stabilizing potential and method of <span class="hlt">analytic</span> continuation prove to be important to the accuracy of the results. We then conclude that an attenuated Coulomb potential is the most effective of the three for bound state <span class="hlt">analytic</span> continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1379693','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1379693"><span>Stabilizing potentials in bound state <span class="hlt">analytic</span> continuation methods for electronic resonances in polyatomic molecules</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>White, Alec F.; Head-Gordon, Martin; McCurdy, C. William</p> <p></p> <p>The computation of Siegert energies by <span class="hlt">analytic</span> continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. Here, we critically evaluate a recently proposed <span class="hlt">analytic</span> continuation method based on low order (type III) Padé <span class="hlt">approximants</span> as well as an <span class="hlt">analytic</span> continuation method based on high order (type II) Padé <span class="hlt">approximants</span>. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2Π g shape resonance of N 2 - whichmore » has been studied extensively by other methods. Both the choice of stabilizing potential and method of <span class="hlt">analytic</span> continuation prove to be important to the accuracy of the results. We then conclude that an attenuated Coulomb potential is the most effective of the three for bound state <span class="hlt">analytic</span> continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JPhB...50x5007S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JPhB...50x5007S"><span><span class="hlt">Analytic</span> model of a multi-electron atom</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Skoromnik, O. D.; Feranchuk, I. D.; Leonau, A. U.; Keitel, C. H.</p> <p>2017-12-01</p> <p>A fully <span class="hlt">analytical</span> <span class="hlt">approximation</span> for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully <span class="hlt">analytical</span> zeroth-order <span class="hlt">approximation</span> describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22375874-strong-washout-approximation-resonant-leptogenesis','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22375874-strong-washout-approximation-resonant-leptogenesis"><span>Strong washout <span class="hlt">approximation</span> to resonant leptogenesis</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Garbrecht, Björn; Gautier, Florian; Klaric, Juraj, E-mail: garbrecht@tum.de, E-mail: florian.gautier@tum.de, E-mail: juraj.klaric@tum.de</p> <p></p> <p>We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be <span class="hlt">approximated</span> by its late-time limit ε=Xsin(2φ)/(X{sup 2}+sin{sup 2}φ), where X=8πΔ/(|Y{sub 1}|{sup 2}+|Y{sub 2}|{sup 2}), Δ=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), φ=arg(Y{sub 2}/Y{sub 1}), and M{sub 1,2}, Y{sub 1,2} are the masses and Yukawa couplings of the sterile neutrinos. This <span class="hlt">approximation</span> in particular extends to parametric regions where |Y{sub 1,2}|{sup 2}>> Δ, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to themore » case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish <span class="hlt">analytic</span> criteria for the validity of the late-time <span class="hlt">approximation</span> for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvD..97i1502A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvD..97i1502A"><span><span class="hlt">Analytic</span> representation of FK/Fπ in two loop chiral perturbation theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ananthanarayan, B.; Bijnens, Johan; Friot, Samuel; Ghosh, Shayan</p> <p>2018-05-01</p> <p>We present an <span class="hlt">analytic</span> representation of FK/Fπ as calculated in three-flavor two-loop chiral perturbation theory, which involves expressing three mass scale sunsets in terms of Kampé de Fériet series. We demonstrate how <span class="hlt">approximations</span> may be made to obtain relatively compact <span class="hlt">analytic</span> representations. An illustrative set of fits using lattice data is also presented, which shows good agreement with existing fits.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AGUFM.C53F..05P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AGUFM.C53F..05P"><span><span class="hlt">Accurate</span> numerical forward model for optimal retracking of SIRAL2 SAR echoes over open ocean</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Phalippou, L.; Demeestere, F.</p> <p>2011-12-01</p> <p>The SAR mode of SIRAL-2 on board Cryosat-2 has been designed to measure primarily sea-ice and continental ice (Wingham et al. 2005). In 2005, K. Raney (KR, 2005) pointed out the improvements brought by SAR altimeter for open ocean. KR results were mostly based on 'rule of thumb' considerations on speckle noise reduction due to the higher PRF and to speckle decorrelation after SAR processing. In 2007, Phalippou and Enjolras (PE,2007) provided the theoretical background for optimal retracking of SAR echoes over ocean with a focus on the forward modelling of the power-waveforms. The accuracies of geophysical parameters (range, significant wave heights, and backscattering coefficient) retrieved from SAR altimeter data were derived accounting for SAR echo shape and speckle noise <span class="hlt">accurate</span> modelling. The step forward to optimal retracking using numerical forward model (NFM) was also pointed out. NFM of the power waveform avoids <span class="hlt">analytical</span> <span class="hlt">approximation</span>, a warranty to minimise the geophysical dependent biases in the retrieval. NFM have been used for many years, in operational meteorology in particular, for retrieving temperature and humidity profiles from IR and microwave radiometers as the radiative transfer function is complex (Eyre, 1989). So far this technique was not used in the field of ocean conventional altimetry as <span class="hlt">analytical</span> models (e.g. Brown's model for instance) were found to give sufficient accuracy. However, although NFM seems desirable even for conventional nadir altimetry, it becomes inevitable if one wish to process SAR altimeter data as the transfer function is too complex to be <span class="hlt">approximated</span> by a simple <span class="hlt">analytical</span> function. This was clearly demonstrated in PE 2007. The paper describes the background to SAR data retracking over open ocean. Since PE 2007 improvements have been brought to the forward model and it is shown that the altimeter on-ground and in flight characterisation (e.g antenna pattern range impulse response, azimuth impulse response</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EL....11458002T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EL....11458002T"><span><span class="hlt">Approximating</span> natural connectivity of scale-free networks based on largest eigenvalue</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tan, S.-Y.; Wu, J.; Li, M.-J.; Lu, X.</p> <p>2016-06-01</p> <p>It has been recently proposed that natural connectivity can be used to efficiently characterize the robustness of complex networks. The natural connectivity has an intuitive physical meaning and a simple mathematical formulation, which corresponds to an average eigenvalue calculated from the graph spectrum. However, as a network model close to the real-world system that widely exists, the scale-free network is found difficult to obtain its spectrum <span class="hlt">analytically</span>. In this article, we investigate the <span class="hlt">approximation</span> of natural connectivity based on the largest eigenvalue in both random and correlated scale-free networks. It is demonstrated that the natural connectivity of scale-free networks can be dominated by the largest eigenvalue, which can be expressed asymptotically and <span class="hlt">analytically</span> to <span class="hlt">approximate</span> natural connectivity with small errors. Then we show that the natural connectivity of random scale-free networks increases linearly with the average degree given the scaling exponent and decreases monotonically with the scaling exponent given the average degree. Moreover, it is found that, given the degree distribution, the more assortative a scale-free network is, the more robust it is. Experiments in real networks validate our methods and results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4497482','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4497482"><span><span class="hlt">Analytic</span> expressions for ULF wave radiation belt radial diffusion coefficients</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Ozeke, Louis G; Mann, Ian R; Murphy, Kyle R; Jonathan Rae, I; Milling, David K</p> <p>2014-01-01</p> <p>We present <span class="hlt">analytic</span> expressions for ULF wave-derived radiation belt radial diffusion coefficients, as a function of L and Kp, which can easily be incorporated into global radiation belt transport models. The diffusion coefficients are derived from statistical representations of ULF wave power, electric field power mapped from ground magnetometer data, and compressional magnetic field power from in situ measurements. We show that the overall electric and magnetic diffusion coefficients are to a good <span class="hlt">approximation</span> both independent of energy. We present example 1-D radial diffusion results from simulations driven by CRRES-observed time-dependent energy spectra at the outer boundary, under the action of radial diffusion driven by the new ULF wave radial diffusion coefficients and with empirical chorus wave loss terms (as a function of energy, Kp and L). There is excellent agreement between the differential flux produced by the 1-D, Kp-driven, radial diffusion model and CRRES observations of differential electron flux at 0.976 MeV—even though the model does not include the effects of local internal acceleration sources. Our results highlight not only the importance of correct specification of radial diffusion coefficients for developing <span class="hlt">accurate</span> models but also show significant promise for belt specification based on relatively simple models driven by solar wind parameters such as solar wind speed or geomagnetic indices such as Kp. Key Points <span class="hlt">Analytic</span> expressions for the radial diffusion coefficients are presented The coefficients do not dependent on energy or wave m value The electric field diffusion coefficient dominates over the magnetic PMID:26167440</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002PhRvB..66u4206G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002PhRvB..66u4206G"><span>Phonons in random alloys: The itinerant coherent-potential <span class="hlt">approximation</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ghosh, Subhradip; Leath, P. L.; Cohen, Morrel H.</p> <p>2002-12-01</p> <p>We present the itinerant coherent-potential <span class="hlt">approximation</span> (ICPA), an <span class="hlt">analytic</span>, translationally invariant, and tractable form of augmented-space-based multiple-scattering theory18 in a single-site <span class="hlt">approximation</span> for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for Ni55Pd45 and Ni50Pt50 alloys which serve as test cases, the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential <span class="hlt">approximation</span> (CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20170000232','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20170000232"><span>Optimization of Turbine Engine Cycle Analysis with <span class="hlt">Analytic</span> Derivatives</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.</p> <p>2016-01-01</p> <p>A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides <span class="hlt">analytic</span> derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative <span class="hlt">approximation</span> methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference <span class="hlt">approximated</span> derivatives.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CNSNS..52..165D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CNSNS..52..165D"><span><span class="hlt">Analytical</span> solutions for coupling fractional partial differential equations with Dirichlet boundary conditions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ding, Xiao-Li; Nieto, Juan J.</p> <p>2017-11-01</p> <p>In this paper, we consider the <span class="hlt">analytical</span> solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive <span class="hlt">approximations</span> is used to obtain the <span class="hlt">analytical</span> solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained <span class="hlt">analytical</span> solutions to the resulting multi-term time fractional ordinary differential equations, the desired <span class="hlt">analytical</span> solutions of the coupling FPDEs are given. Our results are applied to derive the <span class="hlt">analytical</span> solutions of some special cases to demonstrate their applicability.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li class="active"><span>19</span></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_19 --> <div id="page_20" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li class="active"><span>20</span></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="381"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1055452','DOE-PATENT-XML'); return false;" href="https://www.osti.gov/servlets/purl/1055452"><span><span class="hlt">Analytical</span> effective tensor for flow-through composites</span></a></p> <p><a target="_blank" href="http://www.osti.gov/doepatents">DOEpatents</a></p> <p>Sviercoski, Rosangela De Fatima [Los Alamos, NM</p> <p>2012-06-19</p> <p>A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an <span class="hlt">analytical</span> calculation of an effective tensor K.sup.a suitable for use with a variety of media. The <span class="hlt">analytical</span> calculation corresponds to an <span class="hlt">approximation</span> to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28654275','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28654275"><span><span class="hlt">Accurate</span> Quasiparticle Spectra from the T-Matrix Self-Energy and the Particle-Particle Random Phase <span class="hlt">Approximation</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Zhang, Du; Su, Neil Qiang; Yang, Weitao</p> <p>2017-07-20</p> <p>The GW self-energy, especially G 0 W 0 based on the particle-hole random phase <span class="hlt">approximation</span> (phRPA), is widely used to study quasiparticle (QP) energies. Motivated by the desirable features of the particle-particle (pp) RPA compared to the conventional phRPA, we explore the pp counterpart of GW, that is, the T-matrix self-energy, formulated with the eigenvectors and eigenvalues of the ppRPA matrix. We demonstrate the accuracy of the T-matrix method for molecular QP energies, highlighting the importance of the pp channel for calculating QP spectra.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EntIS..11..434Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EntIS..11..434Z"><span>Identification of <span class="hlt">approximately</span> duplicate material records in ERP systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zong, Wei; Wu, Feng; Chu, Lap-Keung; Sculli, Domenic</p> <p>2017-03-01</p> <p>The quality of master data is crucial for the <span class="hlt">accurate</span> functioning of the various modules of an enterprise resource planning (ERP) system. This study addresses specific data problems arising from the generation of <span class="hlt">approximately</span> duplicate material records in ERP databases. Such problems are mainly due to the firm's lack of unique and global identifiers for the material records, and to the arbitrary assignment of alternative names for the same material by various users. Traditional duplicate detection methods are ineffective in identifying such <span class="hlt">approximately</span> duplicate material records because these methods typically rely on string comparisons of each field. To address this problem, a machine learning-based framework is developed to recognise semantic similarity between strings and to further identify and reunify <span class="hlt">approximately</span> duplicate material records - a process referred to as de-duplication in this article. First, the keywords of the material records are extracted to form vectors of discriminating words. Second, a machine learning method using a probabilistic neural network is applied to determine the semantic similarity between these material records. The approach was evaluated using data from a real case study. The test results indicate that the proposed method outperforms traditional algorithms in identifying <span class="hlt">approximately</span> duplicate material records.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..MARF52013Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..MARF52013Y"><span>Charge noise in quantum dot qubits: beyond the Markovian <span class="hlt">approximation</span>.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yang, Yuan-Chi; Friesen, Mark; Coppersmith, S. N.</p> <p></p> <p>Charge noise is a limiting factor in the performance of semiconductor quantum dot qubits, including both spin and charge qubits. In this work, we develop an <span class="hlt">analytical</span> formalism for treating semiclassical noise beyond the Markovian <span class="hlt">approximation</span>, which allows us to investigate noise models relevant for quantum dots, such as 1 / f noise. We apply our methods to both charge qubits and quantum dot hybrid qubits, and study the effects of charge noise on single-qubit rotations in these systems. The formalism is also directly applicable to the case of strong microwave driving, for which the rotating wave <span class="hlt">approximation</span> breaks down. This work was supported in part by ARO (W911NF-12-0607) and ONR (N00014-15-1-0029), and the University of Wisconsin-Madison.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26920854','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26920854"><span><span class="hlt">Analytical</span> performance of a bronchial genomic classifier.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hu, Zhanzhi; Whitney, Duncan; Anderson, Jessica R; Cao, Manqiu; Ho, Christine; Choi, Yoonha; Huang, Jing; Frink, Robert; Smith, Kate Porta; Monroe, Robert; Kennedy, Giulia C; Walsh, P Sean</p> <p>2016-02-26</p> <p>The current standard practice of lung lesion diagnosis often leads to inconclusive results, requiring additional diagnostic follow up procedures that are invasive and often unnecessary due to the high benign rate in such lesions (Chest 143:e78S-e92, 2013). The Percepta bronchial genomic classifier was developed and clinically validated to provide more <span class="hlt">accurate</span> classification of lung nodules and lesions that are inconclusive by bronchoscopy, using bronchial brushing specimens (N Engl J Med 373:243-51, 2015, BMC Med Genomics 8:18, 2015). The <span class="hlt">analytical</span> performance of the Percepta test is reported here. <span class="hlt">Analytical</span> performance studies were designed to characterize the stability of RNA in bronchial brushing specimens during collection and shipment; <span class="hlt">analytical</span> sensitivity defined as input RNA mass; <span class="hlt">analytical</span> specificity (i.e. potentially interfering substances) as tested on blood and genomic DNA; and assay performance studies including intra-run, inter-run, and inter-laboratory reproducibility. RNA content within bronchial brushing specimens preserved in RNAprotect is stable for up to 20 days at 4 °C with no changes in RNA yield or integrity. <span class="hlt">Analytical</span> sensitivity studies demonstrated tolerance to variation in RNA input (157 ng to 243 ng). <span class="hlt">Analytical</span> specificity studies utilizing cancer positive and cancer negative samples mixed with either blood (up to 10 % input mass) or genomic DNA (up to 10 % input mass) demonstrated no assay interference. The test is reproducible from RNA extraction through to Percepta test result, including variation across operators, runs, reagent lots, and laboratories (standard deviation of 0.26 for scores on > 6 unit scale). <span class="hlt">Analytical</span> sensitivity, <span class="hlt">analytical</span> specificity and robustness of the Percepta test were successfully verified, supporting its suitability for clinical use.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29526444','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29526444"><span>Healthcare predictive <span class="hlt">analytics</span>: An overview with a focus on Saudi Arabia.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Alharthi, Hana</p> <p>2018-03-08</p> <p>Despite a newfound wealth of data and information, the healthcare sector is lacking in actionable knowledge. This is largely because healthcare data, though plentiful, tends to be inherently complex and fragmented. Health data <span class="hlt">analytics</span>, with an emphasis on predictive <span class="hlt">analytics</span>, is emerging as a transformative tool that can enable more proactive and preventative treatment options. This review considers the ways in which predictive <span class="hlt">analytics</span> has been applied in the for-profit business sector to generate well-timed and <span class="hlt">accurate</span> predictions of key outcomes, with a focus on key features that may be applicable to healthcare-specific applications. Published medical research presenting assessments of predictive <span class="hlt">analytics</span> technology in medical applications are reviewed, with particular emphasis on how hospitals have integrated predictive <span class="hlt">analytics</span> into their day-to-day healthcare services to improve quality of care. This review also highlights the numerous challenges of implementing predictive <span class="hlt">analytics</span> in healthcare settings and concludes with a discussion of current efforts to implement healthcare data <span class="hlt">analytics</span> in the developing country, Saudi Arabia. Copyright © 2018 The Author. Published by Elsevier Ltd.. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..95j4054G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..95j4054G"><span>Deriving <span class="hlt">analytic</span> solutions for compact binary inspirals without recourse to adiabatic <span class="hlt">approximations</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Galley, Chad R.; Rothstein, Ira Z.</p> <p>2017-05-01</p> <p>We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is v5ν Ω (t -t0) where t0 is the initial time, t is the time elapsed, and Ω and v are the angular orbital frequency and initial speed, respectively. ν is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second-order corrections of the leading radiation reaction force, which involves highly nontrivial checks of the formalism (i.e., its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging, we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find <span class="hlt">analytic</span> solutions to the spin equations of motion that are valid over long times.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22617041-numerical-approximation-framework-stochastic-linear-quadratic-regulator-hilbert-spaces','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22617041-numerical-approximation-framework-stochastic-linear-quadratic-regulator-hilbert-spaces"><span>A Numerical <span class="hlt">Approximation</span> Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu</p> <p></p> <p>We present an <span class="hlt">approximation</span> framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our <span class="hlt">approximation</span> framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially <span class="hlt">analytic</span> generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the <span class="hlt">approximate</span> finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the <span class="hlt">approximate</span> finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008JPhB...41u5206K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008JPhB...41u5206K"><span>Born Hartree Bethe <span class="hlt">approximation</span> in the theory of inelastic electron molecule scattering</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kretinin, I. Yu; Krisilov, A. V.; Zon, B. A.</p> <p>2008-11-01</p> <p>We propose a new <span class="hlt">approximation</span> in the theory of inelastic electron atom and electron molecule scattering. Taking into account the completeness property of atomic and molecular wavefunctions, considered in the Hartree <span class="hlt">approximation</span>, and using Bethe's parametrization for electronic excitations during inelastic collisions via the mean excitation energy, we show that the calculation of the inelastic total integral cross-sections (TICS), in the framework of the first Born <span class="hlt">approximation</span>, involves only the ground-state wavefunction. The final <span class="hlt">analytical</span> formula obtained for the TICS, i.e. for the sum of elastic and inelastic ones, contains no adjusting parameters. Calculated TICS for electron scattering by light atoms and molecules (He, Ne, and H2) are in good agreement within the experimental data; results show asymptotic coincidence for heavier ones (Ar, Kr, Xe and N2).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002AcSpe..57.1277K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002AcSpe..57.1277K"><span><span class="hlt">Analytical</span> procedures for the determination of selected trace elements in peat and plant samples by inductively coupled plasma mass spectrometry</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Krachler, Michael; Mohl, Carola; Emons, Hendrik; Shotyk, William</p> <p>2002-08-01</p> <p>A simple, robust and reliable <span class="hlt">analytical</span> procedure for the determination of 15 elements, namely Ca, V, Cr, Mn, Co, Ni, Cu, Zn, Rb, Ag, Cd, Ba, Tl, Th and U in peat and plant materials by inductively coupled plasma-quadrupole mass spectrometry (ICP-QMS) was developed. Powdered sample aliquots of <span class="hlt">approximately</span> 220 mg were dissolved with various acid mixtures in a microwave heated high-pressure autoclave capable to digest 40 samples simultaneously. The selection of appropriate amounts of digestion acids (nitric acid, hydrofluoric acid or tetrafluoroboric acid) was crucial to obtain <span class="hlt">accurate</span> results. The optimized acid mixture for digestion of plant and peat samples consisted of 3 ml HNO 3 and 0.1 ml HBF 4. An ultrasonic nebulizer with an additional membrane desolvation unit was found beneficial for the determination of Co, Ni, Ag, Tl, Th and U, allowing to aspirate a dry sample aerosol into the ICP-QMS. A pneumatic cross flow nebulizer served as sample introduction device for the other elements. Internal standardization was achieved with 103Rh for all elements, except for Th whose ICP-QMS signals were corrected by 103Rh and 185Re. Quality control was ascertained by analysis of the certified plant reference material GBW 07602 Bush Branches and Leaves. In almost all cases HNO 3 alone could not fully liberate the <span class="hlt">analytes</span> of interest from the peat or plant matrix, probably because of the silicates present. After adding small amounts (0.05-0.1 ml) of either HF or HBF 4 to the digestion mixture, concentrations quantified by ICP-QMS generally increased significantly, in the case of Rb up to 80%. Further increasing the volumes of HF or HBF 4 in turn, resulted in a loss of recoveries of almost all elements, some of which amounted to <span class="hlt">approximately</span> 60%. The successful <span class="hlt">analytical</span> procedures were applied to the determination of two bulk peat materials. In general, good agreement between the found concentrations and results from an inter-laboratory trial or from instrumental</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22403372-approximating-high-dimensional-dynamics-barycentric-coordinates-linear-programming','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22403372-approximating-high-dimensional-dynamics-barycentric-coordinates-linear-programming"><span><span class="hlt">Approximating</span> high-dimensional dynamics by barycentric coordinates with linear programming</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki</p> <p></p> <p>The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for <span class="hlt">accurate</span> modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to <span class="hlt">accurately</span> model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the <span class="hlt">approximation</span> errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics ofmore » the underlying attractors more <span class="hlt">accurately</span> than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/21550238-analytical-ground-state-jaynes-cummings-model-ultrastrong-coupling','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/21550238-analytical-ground-state-jaynes-cummings-model-ultrastrong-coupling"><span><span class="hlt">Analytical</span> ground state for the Jaynes-Cummings model with ultrastrong coupling</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Zhang Yuanwei; Institute of Theoretical Physics, Shanxi University, Taiyuan 030006; Chen Gang</p> <p>2011-06-15</p> <p>We present a generalized variational method to <span class="hlt">analytically</span> obtain the ground-state properties of the Jaynes-Cummings model with the ultrastrong coupling. An explicit expression for the ground-state energy, which agrees well with the numerical simulation in a wide range of the experimental parameters, is given. In particular, the introduced method can successfully solve this Jaynes-Cummings model with the positive detuning (the atomic resonant level is larger than the photon frequency), which cannot be treated in the adiabatical <span class="hlt">approximation</span> and the generalized rotating-wave <span class="hlt">approximation</span>. Finally, we also demonstrate <span class="hlt">analytically</span> how to control the mean photon number by means of the current experimentalmore » parameters including the photon frequency, the coupling strength, and especially the atomic resonant level.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20180001595','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20180001595"><span>The Quantum <span class="hlt">Approximation</span> Optimization Algorithm for MaxCut: A Fermionic View</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang; Rieffel, Eleanor G.</p> <p>2017-01-01</p> <p>Farhi et al. recently proposed a class of quantum algorithms, the Quantum <span class="hlt">Approximate</span> Optimization Algorithm (QAOA), for <span class="hlt">approximately</span> solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we <span class="hlt">analytically</span> and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an <span class="hlt">analytical</span> expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain <span class="hlt">analytical</span> expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27501105','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27501105"><span>High-Resolution Metabolomics Assessment of Military Personnel: Evaluating <span class="hlt">Analytical</span> Strategies for Chemical Detection.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Liu, Ken H; Walker, Douglas I; Uppal, Karan; Tran, ViLinh; Rohrbeck, Patricia; Mallon, Timothy M; Jones, Dean P</p> <p>2016-08-01</p> <p>The aim of this study was to maximize detection of serum metabolites with high-resolution metabolomics (HRM). Department of Defense Serum Repository (DoDSR) samples were analyzed using ultrahigh resolution mass spectrometry with three complementary chromatographic phases and four ionization modes. Chemical coverage was evaluated by number of ions detected and <span class="hlt">accurate</span> mass matches to a human metabolomics database. Individual HRM platforms provided <span class="hlt">accurate</span> mass matches for up to 58% of the KEGG metabolite database. Combining two <span class="hlt">analytical</span> methods increased matches to 72% and included metabolites in most major human metabolic pathways and chemical classes. Detection and feature quality varied by <span class="hlt">analytical</span> configuration. Dual chromatography HRM with positive and negative electrospray ionization provides an effective generalized method for metabolic assessment of military personnel.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4978147','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4978147"><span>High-resolution metabolomics assessment of military personnel: Evaluating <span class="hlt">analytical</span> strategies for chemical detection</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Liu, Ken H.; Walker, Douglas I.; Uppal, Karan; Tran, ViLinh; Rohrbeck, Patricia; Mallon, Timothy M.; Jones, Dean P.</p> <p>2016-01-01</p> <p>Objective To maximize detection of serum metabolites with high-resolution metabolomics (HRM). Methods Department of Defense Serum Repository (DoDSR) samples were analyzed using ultra-high resolution mass spectrometry with three complementary chromatographic phases and four ionization modes. Chemical coverage was evaluated by number of ions detected and <span class="hlt">accurate</span> mass matches to a human metabolomics database. Results Individual HRM platforms provided <span class="hlt">accurate</span> mass matches for up to 58% of the KEGG metabolite database. Combining two <span class="hlt">analytical</span> methods increased matches to 72%, and included metabolites in most major human metabolic pathways and chemical classes. Detection and feature quality varied by <span class="hlt">analytical</span> configuration. Conclusions Dual chromatography HRM with positive and negative electrospray ionization provides an effective generalized method for metabolic assessment of military personnel. PMID:27501105</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018EPJWC.17508006B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018EPJWC.17508006B"><span>Real-time dynamics of matrix quantum mechanics beyond the classical <span class="hlt">approximation</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas</p> <p>2018-03-01</p> <p>We describe a numerical method which allows to go beyond the classical <span class="hlt">approximation</span> for the real-time dynamics of many-body systems by <span class="hlt">approximating</span> the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state <span class="hlt">approximation</span> is <span class="hlt">accurate</span> for significantly smaller field strengths and longer times than the classical one. Applying this <span class="hlt">approximation</span> to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27066108','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27066108"><span>Evaluation of <span class="hlt">Analytical</span> Modeling Functions for the Phonation Onset Process.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael</p> <p>2016-01-01</p> <p>The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different <span class="hlt">analytical</span> approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six <span class="hlt">analytical</span> functions were tested that <span class="hlt">approximate</span> the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct <span class="hlt">approximation</span> of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the <span class="hlt">approximation</span> of VO. The results suggest the computation of VOT by a fourth-order polynomial <span class="hlt">approximation</span> in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19850022413','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19850022413"><span>On the convergence of difference <span class="hlt">approximations</span> to scalar conservation laws</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Osher, S.; Tadmor, E.</p> <p>1985-01-01</p> <p>A unified treatment of explicit in time, two level, second order resolution, total variation diminishing, <span class="hlt">approximations</span> 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 <span class="hlt">accurate</span> in general. Convergence for total variation diminishing-second order resolution schemes <span class="hlt">approximating</span> convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19880037825&hterms=levels+law&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3DA%2Blevels%2Blaw','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19880037825&hterms=levels+law&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3DA%2Blevels%2Blaw"><span>On the convergence of difference <span class="hlt">approximations</span> to scalar conservation laws</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Osher, Stanley; Tadmor, Eitan</p> <p>1988-01-01</p> <p>A unified treatment is given for time-explicit, two-level, second-order-resolution (SOR), total-variation-diminishing (TVD) <span class="hlt">approximations</span> to scalar conservation laws. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced to obtain results in terms of the latter. 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 <span class="hlt">accurate</span> in general. Convergence for TVD-SOR schemes <span class="hlt">approximating</span> convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1379538-low-rank-approximation-g0w0-calculations','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1379538-low-rank-approximation-g0w0-calculations"><span>Low rank <span class="hlt">approximation</span> in G 0W 0 calculations</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Shao, MeiYue; Lin, Lin; Yang, Chao; ...</p> <p>2016-06-04</p> <p>The single particle energies obtained in a Kohn-Sham density functional theory (DFT) calculation are generally known to be poor <span class="hlt">approximations</span> to electron excitation energies that are measured in tr ansport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green’s function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is <span class="hlt">approximated</span>. The G 0W 0 <span class="hlt">approximation</span> is a widely used techniquemore » in which the self energy is expressed as the convolution of a noninteracting Green’s function (G 0) and a screened Coulomb interaction (W 0) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating W 0 at multiple frequencies. In this paper, we discuss how the cost of G 0W 0 calculation can be reduced by constructing a low rank <span class="hlt">approximation</span> to the frequency dependent part of W 0 . In particular, we examine the effect of such a low rank <span class="hlt">approximation</span> on the accuracy of the G 0W 0 <span class="hlt">approximation</span>. We also discuss how the numerical convolution of G 0 and W 0 can be evaluated efficiently and <span class="hlt">accurately</span> by using a contour deformation technique with an appropriate choice of the contour.« less</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li class="active"><span>20</span></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_20 --> <div id="page_21" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li class="active"><span>21</span></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="401"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24018780','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24018780"><span><span class="hlt">Accurate</span> and efficient modeling of the detector response in small animal multi-head PET systems.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cecchetti, Matteo; Moehrs, Sascha; Belcari, Nicola; Del Guerra, Alberto</p> <p>2013-10-07</p> <p>In fully three-dimensional PET imaging, iterative image reconstruction techniques usually outperform <span class="hlt">analytical</span> algorithms in terms of image quality provided that an appropriate system model is used. In this study we concentrate on the calculation of an <span class="hlt">accurate</span> system model for the YAP-(S)PET II small animal scanner, with the aim to obtain fully resolution- and contrast-recovered images at low levels of image roughness. For this purpose we calculate the system model by decomposing it into a product of five matrices: (1) a detector response component obtained via Monte Carlo simulations, (2) a geometric component which describes the scanner geometry and which is calculated via a multi-ray method, (3) a detector normalization component derived from the acquisition of a planar source, (4) a photon attenuation component calculated from x-ray computed tomography data, and finally, (5) a positron range component is formally included. This system model factorization allows the optimization of each component in terms of computation time, storage requirements and accuracy. The main contribution of this work is a new, efficient way to calculate the detector response component for rotating, planar detectors, that consists of a GEANT4 based simulation of a subset of lines of flight (LOFs) for a single detector head whereas the missing LOFs are obtained by using intrinsic detector symmetries. Additionally, we introduce and analyze a probability threshold for matrix elements of the detector component to optimize the trade-off between the matrix size in terms of non-zero elements and the resulting quality of the reconstructed images. In order to evaluate our proposed system model we reconstructed various images of objects, acquired according to the NEMA NU 4-2008 standard, and we compared them to the images reconstructed with two other system models: a model that does not include any detector response component and a model that <span class="hlt">approximates</span> <span class="hlt">analytically</span> the depth of interaction</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013PMB....58.6713C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013PMB....58.6713C"><span><span class="hlt">Accurate</span> and efficient modeling of the detector response in small animal multi-head PET systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cecchetti, Matteo; Moehrs, Sascha; Belcari, Nicola; Del Guerra, Alberto</p> <p>2013-10-01</p> <p>In fully three-dimensional PET imaging, iterative image reconstruction techniques usually outperform <span class="hlt">analytical</span> algorithms in terms of image quality provided that an appropriate system model is used. In this study we concentrate on the calculation of an <span class="hlt">accurate</span> system model for the YAP-(S)PET II small animal scanner, with the aim to obtain fully resolution- and contrast-recovered images at low levels of image roughness. For this purpose we calculate the system model by decomposing it into a product of five matrices: (1) a detector response component obtained via Monte Carlo simulations, (2) a geometric component which describes the scanner geometry and which is calculated via a multi-ray method, (3) a detector normalization component derived from the acquisition of a planar source, (4) a photon attenuation component calculated from x-ray computed tomography data, and finally, (5) a positron range component is formally included. This system model factorization allows the optimization of each component in terms of computation time, storage requirements and accuracy. The main contribution of this work is a new, efficient way to calculate the detector response component for rotating, planar detectors, that consists of a GEANT4 based simulation of a subset of lines of flight (LOFs) for a single detector head whereas the missing LOFs are obtained by using intrinsic detector symmetries. Additionally, we introduce and analyze a probability threshold for matrix elements of the detector component to optimize the trade-off between the matrix size in terms of non-zero elements and the resulting quality of the reconstructed images. In order to evaluate our proposed system model we reconstructed various images of objects, acquired according to the NEMA NU 4-2008 standard, and we compared them to the images reconstructed with two other system models: a model that does not include any detector response component and a model that <span class="hlt">approximates</span> <span class="hlt">analytically</span> the depth of interaction</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1194163-rayleigh-approximation-ground-state-bose-coulomb-glasses','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1194163-rayleigh-approximation-ground-state-bose-coulomb-glasses"><span>Rayleigh <span class="hlt">approximation</span> to ground state of the Bose and Coulomb glasses</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Ryan, S. D.; Mityushev, V.; Vinokur, V. M.; ...</p> <p>2015-01-16</p> <p>Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an <span class="hlt">analytical</span> approach based on the method of functional equations that allows us to construct the Rayleigh <span class="hlt">approximation</span> to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Ourmore » findings break ground for <span class="hlt">analytical</span> studies of glassy systems, marking an important step towards understanding their properties.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4296301','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4296301"><span>Rayleigh <span class="hlt">approximation</span> to ground state of the Bose and Coulomb glasses</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Ryan, S. D.; Mityushev, V.; Vinokur, V. M.; Berlyand, L.</p> <p>2015-01-01</p> <p>Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an <span class="hlt">analytical</span> approach based on the method of functional equations that allows us to construct the Rayleigh <span class="hlt">approximation</span> to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for <span class="hlt">analytical</span> studies of glassy systems, marking an important step towards understanding their properties. PMID:25592417</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/19044628','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19044628"><span>Compact, <span class="hlt">accurate</span> description of diagnostic neutral beam propagation and attenuation in a high temperature plasma for charge exchange recombination spectroscopy analysis.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Bespamyatnov, Igor O; Rowan, William L; Granetz, Robert S</p> <p>2008-10-01</p> <p>Charge exchange recombination spectroscopy on Alcator C-Mod relies on the use of the diagnostic neutral beam injector as a source of neutral particles which penetrate deep into the plasma. It employs the emission resulting from the interaction of the beam atoms with fully ionized impurity ions. To interpret the emission from a given point in the plasma as the density of emitting impurity ions, the density of beam atoms must be known. Here, an analysis of beam propagation is described which yields the beam density profile throughout the beam trajectory from the neutral beam injector to the core of the plasma. The analysis includes the effects of beam formation, attenuation in the neutral gas surrounding the plasma, and attenuation in the plasma. In the course of this work, a numerical simulation and an <span class="hlt">analytical</span> <span class="hlt">approximation</span> for beam divergence are developed. The description is made sufficiently compact to yield <span class="hlt">accurate</span> results in a time consistent with between-shot analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010ChPhB..19l0503G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010ChPhB..19l0503G"><span>S-curve networks and an <span class="hlt">approximate</span> method for estimating degree distributions of complex networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Guo, Jin-Li</p> <p>2010-12-01</p> <p>In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 (Internet Protocol version 4) addresses, this paper proposes a forecasting model by using S curve (logistic curve). The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the <span class="hlt">analytic</span> method based on uniform distributions (i.e., Barabási-Albert method) is not suitable for the network. It develops an <span class="hlt">approximate</span> method to predict the growth dynamics of the individual nodes, and uses this to calculate <span class="hlt">analytically</span> the degree distribution and the scaling exponents. The <span class="hlt">analytical</span> result agrees with the simulation well, obeying an <span class="hlt">approximately</span> power-law form. This method can overcome a shortcoming of Barabási-Albert method commonly used in current network research.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JPhD...46H5202Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JPhD...46H5202Y"><span>A semi-<span class="hlt">analytical</span> study of positive corona discharge in wire-plane electrode configuration</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yanallah, K.; Pontiga, F.; Chen, J. H.</p> <p>2013-08-01</p> <p>Wire-to-plane positive corona discharge in air has been studied using an <span class="hlt">analytical</span> model of two species (electrons and positive ions). The spatial distributions of electric field and charged species are obtained by integrating Gauss's law and the continuity equations of species along the Laplacian field lines. The experimental values of corona current intensity and applied voltage, together with Warburg's law, have been used to formulate the boundary condition for the electron density on the corona wire. To test the accuracy of the model, the <span class="hlt">approximate</span> electric field distribution has been compared with the exact numerical solution obtained from a finite element analysis. A parametrical study of wire-to-plane corona discharge has then been undertaken using the <span class="hlt">approximate</span> semi-<span class="hlt">analytical</span> solutions. Thus, the spatial distributions of electric field and charged particles have been computed for different values of the gas pressure, wire radius and electrode separation. Also, the two dimensional distribution of ozone density has been obtained using a simplified plasma chemistry model. The <span class="hlt">approximate</span> semi-<span class="hlt">analytical</span> solutions can be evaluated in a negligible computational time, yet provide precise estimates of corona discharge variables.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/15783645','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/15783645"><span>Hamiltonian chaos acts like a finite energy reservoir: accuracy of the Fokker-Planck <span class="hlt">approximation</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Riegert, Anja; Baba, Nilüfer; Gelfert, Katrin; Just, Wolfram; Kantz, Holger</p> <p>2005-02-11</p> <p>The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov <span class="hlt">approximation</span>, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and <span class="hlt">analytical</span> analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic <span class="hlt">approximation</span> on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012APS..MARB54007S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012APS..MARB54007S"><span>Asymptotically inspired moment-closure <span class="hlt">approximation</span> for adaptive networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Shkarayev, Maxim; Shaw, Leah</p> <p>2012-02-01</p> <p>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 <span class="hlt">approximation</span> based on the <span class="hlt">analytical</span> 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.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013APS..MARZ29005S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013APS..MARZ29005S"><span>Asymptotically inspired moment-closure <span class="hlt">approximation</span> for adaptive networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Shkarayev, Maxim</p> <p>2013-03-01</p> <p>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 <span class="hlt">approximation</span> based on the <span class="hlt">analytical</span> 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.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015NatSR...5E8756Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015NatSR...5E8756Z"><span><span class="hlt">Analytical</span> Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhang, Guofeng; Zhu, Hanjie</p> <p>2015-03-01</p> <p>The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms <span class="hlt">approximately</span> and obtain the <span class="hlt">analytical</span> energy spectrums and wavefunctions. These <span class="hlt">analytical</span> results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave <span class="hlt">approximation</span> on the assumption of near-resonance and relatively weak coupling. Moreover, the <span class="hlt">analytical</span> expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25736827','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25736827"><span><span class="hlt">Analytical</span> solution for the anisotropic Rabi model: effects of counter-rotating terms.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Zhang, Guofeng; Zhu, Hanjie</p> <p>2015-03-04</p> <p>The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms <span class="hlt">approximately</span> and obtain the <span class="hlt">analytical</span> energy spectrums and wavefunctions. These <span class="hlt">analytical</span> results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave <span class="hlt">approximation</span> on the assumption of near-resonance and relatively weak coupling. Moreover, the <span class="hlt">analytical</span> expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19860020297','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19860020297"><span>An experimental and <span class="hlt">analytical</span> method for <span class="hlt">approximate</span> determination of the tilt rotor research aircraft rotor/wing download</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Jordon, D. E.; Patterson, W.; Sandlin, D. R.</p> <p>1985-01-01</p> <p>The XV-15 Tilt Rotor Research Aircraft download phenomenon was analyzed. This phenomenon is a direct result of the two rotor wakes impinging on the wing upper surface when the aircraft is in the hover configuration. For this study the analysis proceeded along tow lines. First was a method whereby results from actual hover tests of the XV-15 aircraft were combined with drag coefficient results from wind tunnel tests of a wing that was representative of the aircraft wing. Second, an <span class="hlt">analytical</span> method was used that modeled that airflow caused gy the two rotors. Formulas were developed in such a way that acomputer program could be used to calculate the axial velocities were then used in conjunction with the aforementioned wind tunnel drag coefficinet results to produce download values. An attempt was made to validate the <span class="hlt">analytical</span> results by modeling a model rotor system for which direct download values were determinrd..</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/377088-singular-values-imbedding-operators-some-classes-analytic-functions-several-variables','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/377088-singular-values-imbedding-operators-some-classes-analytic-functions-several-variables"><span>The singular values of the imbedding operators of some classes of <span class="hlt">analytic</span> functions of several variables</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Parfenov, O.G.</p> <p>1994-12-25</p> <p>We discuss three results. The first exhibits the order of decrease of the s-values as a function of the CR-dimension of a compact set on which we <span class="hlt">approximate</span> the class of <span class="hlt">analytic</span> functions being studied. The second is an asymptotic formula for the case when the domain of <span class="hlt">analyticity</span> and the compact set are Reinhart domains. The third is the computation of the s-values of a special operator that is of interest for <span class="hlt">approximation</span> theory on one-dimensional manifolds.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5084694','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5084694"><span><span class="hlt">Analytic</span> TOF PET reconstruction algorithm within DIRECT data partitioning framework</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Matej, Samuel; Daube-Witherspoon, Margaret E.; Karp, Joel S.</p> <p>2016-01-01</p> <p>Iterative reconstruction algorithms are routinely used for clinical practice; however, <span class="hlt">analytic</span> algorithms are relevant candidates for quantitative research studies due to their linear behavior. While iterative algorithms also benefit from the inclusion of <span class="hlt">accurate</span> data and noise models the widespread use of TOF scanners with less sensitivity to noise and data imperfections make <span class="hlt">analytic</span> algorithms even more promising. In our previous work we have developed a novel iterative reconstruction approach (Direct Image Reconstruction for TOF) providing convenient TOF data partitioning framework and leading to very efficient reconstructions. In this work we have expanded DIRECT to include an <span class="hlt">analytic</span> TOF algorithm with confidence weighting incorporating models of both TOF and spatial resolution kernels. Feasibility studies using simulated and measured data demonstrate that <span class="hlt">analytic</span>-DIRECT with appropriate resolution and regularization filters is able to provide matched bias vs. variance performance to iterative TOF reconstruction with a matched resolution model. PMID:27032968</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PMB....61.3365M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PMB....61.3365M"><span><span class="hlt">Analytic</span> TOF PET reconstruction algorithm within DIRECT data partitioning framework</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Matej, Samuel; Daube-Witherspoon, Margaret E.; Karp, Joel S.</p> <p>2016-05-01</p> <p>Iterative reconstruction algorithms are routinely used for clinical practice; however, <span class="hlt">analytic</span> algorithms are relevant candidates for quantitative research studies due to their linear behavior. While iterative algorithms also benefit from the inclusion of <span class="hlt">accurate</span> data and noise models the widespread use of time-of-flight (TOF) scanners with less sensitivity to noise and data imperfections make <span class="hlt">analytic</span> algorithms even more promising. In our previous work we have developed a novel iterative reconstruction approach (DIRECT: direct image reconstruction for TOF) providing convenient TOF data partitioning framework and leading to very efficient reconstructions. In this work we have expanded DIRECT to include an <span class="hlt">analytic</span> TOF algorithm with confidence weighting incorporating models of both TOF and spatial resolution kernels. Feasibility studies using simulated and measured data demonstrate that <span class="hlt">analytic</span>-DIRECT with appropriate resolution and regularization filters is able to provide matched bias versus variance performance to iterative TOF reconstruction with a matched resolution model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4506829','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4506829"><span>Recent Developments in the Speciation and Determination of Mercury Using Various <span class="hlt">Analytical</span> Techniques</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Suvarapu, Lakshmi Narayana; Baek, Sung-Ok</p> <p>2015-01-01</p> <p>This paper reviews the speciation and determination of mercury by various <span class="hlt">analytical</span> techniques such as atomic absorption spectrometry, voltammetry, inductively coupled plasma techniques, spectrophotometry, spectrofluorometry, high performance liquid chromatography, and gas chromatography. <span class="hlt">Approximately</span> 126 research papers on the speciation and determination of mercury by various <span class="hlt">analytical</span> techniques published in international journals since 2013 are reviewed. PMID:26236539</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25882725','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25882725"><span>Fast <span class="hlt">analytical</span> scatter estimation using graphics processing units.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ingleby, Harry; Lippuner, Jonas; Rickey, Daniel W; Li, Yue; Elbakri, Idris</p> <p>2015-01-01</p> <p>To develop a fast patient-specific <span class="hlt">analytical</span> estimator of first-order Compton and Rayleigh scatter in cone-beam computed tomography, implemented using graphics processing units. The authors developed an <span class="hlt">analytical</span> estimator for first-order Compton and Rayleigh scatter in a cone-beam computed tomography geometry. The estimator was coded using NVIDIA's CUDA environment for execution on an NVIDIA graphics processing unit. Performance of the <span class="hlt">analytical</span> estimator was validated by comparison with high-count Monte Carlo simulations for two different numerical phantoms. Monoenergetic <span class="hlt">analytical</span> simulations were compared with monoenergetic and polyenergetic Monte Carlo simulations. <span class="hlt">Analytical</span> and Monte Carlo scatter estimates were compared both qualitatively, from visual inspection of images and profiles, and quantitatively, using a scaled root-mean-square difference metric. Reconstruction of simulated cone-beam projection data of an anthropomorphic breast phantom illustrated the potential of this method as a component of a scatter correction algorithm. The monoenergetic <span class="hlt">analytical</span> and Monte Carlo scatter estimates showed very good agreement. The monoenergetic <span class="hlt">analytical</span> estimates showed good agreement for Compton single scatter and reasonable agreement for Rayleigh single scatter when compared with polyenergetic Monte Carlo estimates. For a voxelized phantom with dimensions 128 × 128 × 128 voxels and a detector with 256 × 256 pixels, the <span class="hlt">analytical</span> estimator required 669 seconds for a single projection, using a single NVIDIA 9800 GX2 video card. Accounting for first order scatter in cone-beam image reconstruction improves the contrast to noise ratio of the reconstructed images. The <span class="hlt">analytical</span> scatter estimator, implemented using graphics processing units, provides rapid and <span class="hlt">accurate</span> estimates of single scatter and with further acceleration and a method to account for multiple scatter may be useful for practical scatter correction schemes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26574370','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26574370"><span>Molecular Excitation Energies from Time-Dependent Density Functional Theory Employing Random-Phase <span class="hlt">Approximation</span> Hessians with Exact Exchange.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Heßelmann, Andreas</p> <p>2015-04-14</p> <p>Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase <span class="hlt">approximation</span> Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly <span class="hlt">accurate</span> local valence excitations if combined with <span class="hlt">accurate</span> asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates <span class="hlt">accurate</span> reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional <span class="hlt">approximations</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27415227','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27415227"><span>Radial distribution function for hard spheres in fractal dimensions: A heuristic <span class="hlt">approximation</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Santos, Andrés; de Haro, Mariano López</p> <p>2016-06-01</p> <p><span class="hlt">Analytic</span> <span class="hlt">approximations</span> for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such <span class="hlt">approximate</span> results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li class="active"><span>21</span></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_21 --> <div id="page_22" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li class="active"><span>22</span></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="421"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhRvA..92f3815S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhRvA..92f3815S"><span><span class="hlt">Analytic</span> solution and pulse area theorem for three-level atoms</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Shchedrin, Gavriil; O'Brien, Chris; Rostovtsev, Yuri; Scully, Marlan O.</p> <p>2015-12-01</p> <p>We report an <span class="hlt">analytic</span> solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our <span class="hlt">analytic</span> result and the numerical simulations. We use our solution to derive a pulse area theorem for three-level V and Λ systems without making the rotating wave <span class="hlt">approximation</span>. Formulated as an energy conservation law, this pulse area theorem can be used to understand pulse propagation through three-level media.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22679883-effect-limber-flat-sky-approximations-galaxy-weak-lensing','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22679883-effect-limber-flat-sky-approximations-galaxy-weak-lensing"><span>The effect of Limber and flat-sky <span class="hlt">approximations</span> on galaxy weak lensing</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Lemos, Pablo; Challinor, Anthony; Efstathiou, George, E-mail: pl411@cam.ac.uk, E-mail: a.d.challinor@ast.cam.ac.uk, E-mail: gpe@ast.cam.ac.uk</p> <p></p> <p>We review the effect of the commonly-used Limber and flat-sky <span class="hlt">approximations</span> on the calculation of shear power spectra and correlation functions for galaxy weak lensing. These <span class="hlt">approximations</span> are <span class="hlt">accurate</span> at small scales, but it has been claimed recently that their impact on low multipoles could lead to an increase in the amplitude of the mass fluctuations inferred from surveys such as CFHTLenS, reducing the tension between galaxy weak lensing and the amplitude determined by Planck from observations of the cosmic microwave background. Here, we explore the impact of these <span class="hlt">approximations</span> on cosmological parameters derived from weak lensing surveys, using themore » CFHTLenS data as a test case. We conclude that the use of small-angle <span class="hlt">approximations</span> for cosmological parameter estimation is negligible for current data, and does not contribute to the tension between current weak lensing surveys and Planck.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900003821','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900003821"><span>An Eigenvalue Analysis of finite-difference <span class="hlt">approximations</span> for hyperbolic IBVPs</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Warming, Robert F.; Beam, Richard M.</p> <p>1989-01-01</p> <p>The eigenvalue spectrum associated with a linear finite-difference <span class="hlt">approximation</span> plays a crucial role in the stability analysis and in the actual computational performance of the discrete <span class="hlt">approximation</span>. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is <span class="hlt">analytically</span> intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22375830-thermal-effects-sudden-decay-approximation-curvaton-scenario','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22375830-thermal-effects-sudden-decay-approximation-curvaton-scenario"><span>Thermal effects and sudden decay <span class="hlt">approximation</span> in the curvaton scenario</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Kitajima, Naoya; Takesako, Tomohiro; Yokoyama, Shuichiro</p> <p>2014-10-01</p> <p>We study the impact of a temperature-dependent curvaton decay rate on the primordial curvature perturbation generated in the curvaton scenario. Using the familiar sudden decay <span class="hlt">approximation</span>, we obtain an <span class="hlt">analytical</span> expression for the curvature perturbation after the decay of the curvaton. We then investigate numerically the evolution of the background and of the perturbations during the decay. We first show that the instantaneous transfer coefficient, related to the curvaton energy fraction at the decay, can be extended into a more general parameter, which depends on the net transfer of the curvaton energy into radiation energy or, equivalently, on the totalmore » entropy ratio after the complete curvaton decay. We then compute the curvature perturbation and compare this result with the sudden decay <span class="hlt">approximation</span> prediction.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003JChPh.11911526F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003JChPh.11911526F"><span>Representation of the exact relativistic electronic Hamiltonian within the regular <span class="hlt">approximation</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Filatov, Michael; Cremer, Dieter</p> <p>2003-12-01</p> <p>The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular <span class="hlt">approximation</span>. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular <span class="hlt">approximation</span> (IORA) rather than the zeroth-order regular <span class="hlt">approximation</span> 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 <span class="hlt">accurate</span> 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.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25828436','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25828436"><span>Characterization of gold nanoparticles with different hydrophilic coatings via capillary electrophoresis and Taylor dispersion analysis. Part I: determination of the zeta potential employing a modified <span class="hlt">analytic</span> <span class="hlt">approximation</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Pyell, Ute; Jalil, Alaa H; Pfeiffer, Christian; Pelaz, Beatriz; Parak, Wolfgang J</p> <p>2015-07-15</p> <p>Taking gold nanoparticles with different hydrophilic coatings as an example, it is investigated whether capillary electrophoresis in combination with Taylor dispersion analysis allows for the precise determination of mean electrophoretic mobilities, electrophoretic mobility distributions, and zeta potentials in a matrix of exactly known composition and the calibration-free determination of number-weighted mean hydrodynamic radii. Our experimental data confirm that the calculation of the zeta potential for colloidal nanoparticles with ζ>25 mV requires to take the relaxation effect into account. Because of the requirement to avoid particle-wall interactions, a solution of disodiumtetraborate decahydrate (borax) in deionized water had been selected as suitable electrolyte. Measurements of the electrophoretic mobility at different ionic strength and application of the <span class="hlt">analytic</span> <span class="hlt">approximation</span> developed by Ohshima show that in the present case of a buffered solution with a weak electrolyte co-ion and a strong electrolyte counterion, the effective ionic drag coefficient should be <span class="hlt">approximated</span> with the ionic drag coefficient of the counterion. The obtained results are in good agreement with theoretical expectations regarding the dependence of the zeta potential and the electrokinetic surface charge density on the ionic strength. We also show that Taylor dispersion analysis (besides estimation of the number-weighted mean hydrodynamic radius) provides additional information on the type and width of the number-weighted particle distribution. Copyright © 2015 Elsevier Inc. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23554899','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23554899"><span>DendroBLAST: <span class="hlt">approximate</span> phylogenetic trees in the absence of multiple sequence alignments.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kelly, Steven; Maini, Philip K</p> <p>2013-01-01</p> <p>The rapidly growing availability of genome information has created considerable demand for both fast and <span class="hlt">accurate</span> phylogenetic inference algorithms. We present a novel method called DendroBLAST for reconstructing phylogenetic dendrograms/trees from protein sequences using BLAST. This method differs from other methods by incorporating a simple model of sequence evolution to test the effect of introducing sequence changes on the reliability of the bipartitions in the inferred tree. Using realistic simulated sequence data we demonstrate that this method produces phylogenetic trees that are more <span class="hlt">accurate</span> than other commonly-used distance based methods though not as <span class="hlt">accurate</span> as maximum likelihood methods from good quality multiple sequence alignments. In addition to tests on simulated data, we use DendroBLAST to generate input trees for a supertree reconstruction of the phylogeny of the Archaea. This independent analysis produces an <span class="hlt">approximate</span> phylogeny of the Archaea that has both high precision and recall when compared to previously published analysis of the same dataset using conventional methods. Taken together these results demonstrate that <span class="hlt">approximate</span> phylogenetic trees can be produced in the absence of multiple sequence alignments, and we propose that these trees will provide a platform for improving and informing downstream bioinformatic analysis. A web implementation of the DendroBLAST method is freely available for use at http://www.dendroblast.com/.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AIPC.1894b0025T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AIPC.1894b0025T"><span>Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase <span class="hlt">approximation</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Terasaki, J.; Smetana, A.; Šimkovic, F.; Krivoruchenko, M. I.</p> <p>2017-10-01</p> <p>It is shown that the random-phase <span class="hlt">approximation</span> (RPA) method with its nonlinear higher generalization, which was previously considered as <span class="hlt">approximation</span> 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 <span class="hlt">analytically</span> 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.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20050188486','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20050188486"><span>A More <span class="hlt">Accurate</span> and Efficient Technique Developed for Using Computational Methods to Obtain Helical Traveling-Wave Tube Interaction Impedance</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kory, Carol L.</p> <p>1999-01-01</p> <p>The phenomenal growth of commercial communications has created a great demand for traveling-wave tube (TWT) amplifiers. Although the helix slow-wave circuit remains the mainstay of the TWT industry because of its exceptionally wide bandwidth, until recently it has been impossible to <span class="hlt">accurately</span> analyze a helical TWT using its exact dimensions because of the complexity of its geometrical structure. For the first time, an <span class="hlt">accurate</span> three-dimensional helical model was developed that allows <span class="hlt">accurate</span> prediction of TWT cold-test characteristics including operating frequency, interaction impedance, and attenuation. This computational model, which was developed at the NASA Lewis Research Center, allows TWT designers to obtain a more <span class="hlt">accurate</span> value of interaction impedance than is possible using experimental methods. Obtaining helical slow-wave circuit interaction impedance is an important part of the design process for a TWT because it is related to the gain and efficiency of the tube. This impedance cannot be measured directly; thus, conventional methods involve perturbing a helical circuit with a cylindrical dielectric rod placed on the central axis of the circuit and obtaining the difference in resonant frequency between the perturbed and unperturbed circuits. A mathematical relationship has been derived between this frequency difference and the interaction impedance (ref. 1). However, because of the complex configuration of the helical circuit, deriving this relationship involves several <span class="hlt">approximations</span>. In addition, this experimental procedure is time-consuming and expensive, but until recently it was widely accepted as the most <span class="hlt">accurate</span> means of determining interaction impedance. The advent of an <span class="hlt">accurate</span> three-dimensional helical circuit model (ref. 2) made it possible for Lewis researchers to fully investigate standard <span class="hlt">approximations</span> made in deriving the relationship between measured perturbation data and interaction impedance. The most prominent <span class="hlt">approximations</span> made</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5045300','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5045300"><span>The <span class="hlt">analytical</span> validation of the Oncotype DX Recurrence Score assay</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Baehner, Frederick L</p> <p>2016-01-01</p> <p>In vitro diagnostic multivariate index assays are highly complex molecular assays that can provide clinically actionable information regarding the underlying tumour biology and facilitate personalised treatment. These assays are only useful in clinical practice if all of the following are established: <span class="hlt">analytical</span> validation (i.e., how <span class="hlt">accurately</span>/reliably the assay measures the molecular characteristics), clinical validation (i.e., how consistently/<span class="hlt">accurately</span> the test detects/predicts the outcomes of interest), and clinical utility (i.e., how likely the test is to significantly improve patient outcomes). In considering the use of these assays, clinicians often focus primarily on the clinical validity/utility; however, the <span class="hlt">analytical</span> validity of an assay (e.g., its accuracy, reproducibility, and standardisation) should also be evaluated and carefully considered. This review focuses on the rigorous <span class="hlt">analytical</span> validation and performance of the Oncotype DX® Breast Cancer Assay, which is performed at the Central Clinical Reference Laboratory of Genomic Health, Inc. The assay process includes tumour tissue enrichment (if needed), RNA extraction, gene expression quantitation (using a gene panel consisting of 16 cancer genes plus 5 reference genes and quantitative real-time RT-PCR), and an automated computer algorithm to produce a Recurrence Score® result (scale: 0–100). This review presents evidence showing that the Recurrence Score result reported for each patient falls within a tight clinically relevant confidence interval. Specifically, the review discusses how the development of the assay was designed to optimise assay performance, presents data supporting its <span class="hlt">analytical</span> validity, and describes the quality control and assurance programmes that ensure optimal test performance over time. PMID:27729940</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27729940','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27729940"><span>The <span class="hlt">analytical</span> validation of the Oncotype DX Recurrence Score assay.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Baehner, Frederick L</p> <p>2016-01-01</p> <p>In vitro diagnostic multivariate index assays are highly complex molecular assays that can provide clinically actionable information regarding the underlying tumour biology and facilitate personalised treatment. These assays are only useful in clinical practice if all of the following are established: <span class="hlt">analytical</span> validation (i.e., how <span class="hlt">accurately</span>/reliably the assay measures the molecular characteristics), clinical validation (i.e., how consistently/<span class="hlt">accurately</span> the test detects/predicts the outcomes of interest), and clinical utility (i.e., how likely the test is to significantly improve patient outcomes). In considering the use of these assays, clinicians often focus primarily on the clinical validity/utility; however, the <span class="hlt">analytical</span> validity of an assay (e.g., its accuracy, reproducibility, and standardisation) should also be evaluated and carefully considered. This review focuses on the rigorous <span class="hlt">analytical</span> validation and performance of the Oncotype DX ® Breast Cancer Assay, which is performed at the Central Clinical Reference Laboratory of Genomic Health, Inc. The assay process includes tumour tissue enrichment (if needed), RNA extraction, gene expression quantitation (using a gene panel consisting of 16 cancer genes plus 5 reference genes and quantitative real-time RT-PCR), and an automated computer algorithm to produce a Recurrence Score ® result (scale: 0-100). This review presents evidence showing that the Recurrence Score result reported for each patient falls within a tight clinically relevant confidence interval. Specifically, the review discusses how the development of the assay was designed to optimise assay performance, presents data supporting its <span class="hlt">analytical</span> validity, and describes the quality control and assurance programmes that ensure optimal test performance over time.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4892255','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4892255"><span><span class="hlt">Analytical</span> <span class="hlt">approximations</span> for spatial stochastic gene expression in single cells and tissues</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Smith, Stephen; Cianci, Claudia; Grima, Ramon</p> <p>2016-01-01</p> <p>Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the <span class="hlt">approximate</span> steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhDT.......103N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhDT.......103N"><span><span class="hlt">Approximation</span> methods in relativistic eigenvalue perturbation theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Noble, Jonathan Howard</p> <p></p> <p>In this dissertation, three questions, concerning <span class="hlt">approximation</span> methods for the eigenvalues of quantum mechanical systems, are investigated: (i) What is a pseudo--Hermitian Hamiltonian, and how can its eigenvalues be <span class="hlt">approximated</span> via numerical calculations? This is a fairly broad topic, and the scope of the investigation is narrowed by focusing on a subgroup of pseudo--Hermitian operators, namely, PT--symmetric operators. Within a numerical approach, one projects a PT--symmetric Hamiltonian onto an appropriate basis, and uses a straightforward two--step algorithm to diagonalize the resulting matrix, leading to numerically <span class="hlt">approximated</span> eigenvalues. (ii) Within an <span class="hlt">analytic</span> ansatz, how can a relativistic Dirac Hamiltonian be decoupled into particle and antiparticle degrees of freedom, in appropriate kinematic limits? One possible answer is the Foldy--Wouthuysen transform; however, there are alter- native methods which seem to have some advantages over the time--tested approach. One such method is investigated by applying both the traditional Foldy--Wouthuysen transform and the "chiral" Foldy--Wouthuysen transform to a number of Dirac Hamiltonians, including the central-field Hamiltonian for a gravitationally bound system; namely, the Dirac-(Einstein-)Schwarzschild Hamiltonian, which requires the formal- ism of general relativity. (iii) Are there are pseudo--Hermitian variants of Dirac Hamiltonians that can be <span class="hlt">approximated</span> using a decoupling transformation? The tachyonic Dirac Hamiltonian, which describes faster-than-light spin-1/2 particles, is gamma5--Hermitian, i.e., pseudo-Hermitian. Superluminal particles remain faster than light upon a Lorentz transformation, and hence, the Foldy--Wouthuysen program is unsuited for this case. Thus, inspired by the Foldy--Wouthuysen program, a decoupling transform in the ultrarelativistic limit is proposed, which is applicable to both sub- and superluminal particles.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/17497141','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/17497141"><span><span class="hlt">Analytical</span> procedures for water-soluble vitamins in foods and dietary supplements: a review.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Blake, Christopher J</p> <p>2007-09-01</p> <p>Water-soluble vitamins include the B-group vitamins and vitamin C. In order to correctly monitor water-soluble vitamin content in fortified foods for compliance monitoring as well as to establish <span class="hlt">accurate</span> data banks, an <span class="hlt">accurate</span> and precise <span class="hlt">analytical</span> method is a prerequisite. For many years microbiological assays have been used for analysis of B vitamins. However they are no longer considered to be the gold standard in vitamins analysis as many studies have shown up their deficiencies. This review describes the current status of <span class="hlt">analytical</span> methods, including microbiological assays and spectrophotometric, biosensor and chromatographic techniques. In particular it describes the current status of the official methods and highlights some new developments in chromatographic procedures and detection methods. An overview is made of multivitamin extractions and analyses for foods and supplements.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://eric.ed.gov/?q=Pendulum&pg=3&id=EJ901519','ERIC'); return false;" href="https://eric.ed.gov/?q=Pendulum&pg=3&id=EJ901519"><span>Improvements in the <span class="hlt">Approximate</span> Formulae for the Period of the Simple Pendulum</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Turkyilmazoglu, M.</p> <p>2010-01-01</p> <p>This paper is concerned with improvements in some exact formulae for the period of the simple pendulum problem. Two recently presented formulae are re-examined and refined rationally, yielding more <span class="hlt">accurate</span> <span class="hlt">approximate</span> periods. Based on the improved expressions here, a particular new formula is proposed for the period. It is shown that the derived…</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006APS..MARW24004P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006APS..MARW24004P"><span>Simple <span class="hlt">Analytic</span> Model for Nanowire Array Polarizers</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pelletier, Vincent; Asakawa, Koji; Wu, Mingshaw; Register, Richard; Chaikin, Paul</p> <p>2006-03-01</p> <p>Cylinder-forming diblock copolymers can be used to pattern nanowire arrays on a transparent substrate to be used as a polarizer, as described by Koji Asakawa in a complementary talk at this meeting. With a 33nm period, these wire arrays can polarize UV radiation, which is of great interest in lithography, astronomy and other areas. One can gain an <span class="hlt">analytical</span> understanding of such an array made of non-perfectly conducting material of finite thickness using a model with an appropriately averaged complex dielectric function in an infinite wavelength <span class="hlt">approximation</span>. This analysis predicts that the grid can go from an E-polarizer to an H-polarizer as the wavelength decreases below a cross-over wavelength, and experimental data confirm this cross-over. The overall response of the polarizing grid depends primarily on the plasma frequency of the metal used and the volume fraction of the nanowires, as well as the grid thickness. A numerical approach is also used to confirm the <span class="hlt">analytical</span> model and assess departure from infinite wavelength effects. For our array dimensions, the polarization is only slightly different from this <span class="hlt">approximation</span> for wavelengths down to 150nm.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22488899-approximation-solution-schrodinger-equation-deformed-rosen-morse-using-supersymmetry-quantum-mechanics-susy-qm','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22488899-approximation-solution-schrodinger-equation-deformed-rosen-morse-using-supersymmetry-quantum-mechanics-susy-qm"><span><span class="hlt">Approximation</span> solution of Schrodinger equation for Q-deformed Rosen-Morse using supersymmetry quantum mechanics (SUSY QM)</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Alemgadmi, Khaled I. K., E-mail: azozkied@yahoo.com; Suparmi; Cari</p> <p>2015-09-30</p> <p>The <span class="hlt">approximate</span> <span class="hlt">analytical</span> solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The <span class="hlt">approximate</span> bound state energy is given in the closed form and the corresponding <span class="hlt">approximate</span> wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900019364','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900019364"><span><span class="hlt">Accurate</span> quantum chemical calculations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.; Taylor, Peter R.</p> <p>1989-01-01</p> <p>An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently <span class="hlt">accurate</span> result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark <span class="hlt">approximate</span> techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems; to transition metals; and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform <span class="hlt">accurate</span> calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JAP...114o3712B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JAP...114o3712B"><span>Modeling of phonon scattering in n-type nanowire transistors using one-shot <span class="hlt">analytic</span> continuation technique</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bescond, Marc; Li, Changsheng; Mera, Hector; Cavassilas, Nicolas; Lannoo, Michel</p> <p>2013-10-01</p> <p>We present a one-shot current-conserving approach to model the influence of electron-phonon scattering in nano-transistors using the non-equilibrium Green's function formalism. The approach is based on the lowest order <span class="hlt">approximation</span> (LOA) to the current and its simplest <span class="hlt">analytic</span> continuation (LOA+AC). By means of a scaling argument, we show how both LOA and LOA+AC can be easily obtained from the first iteration of the usual self-consistent Born <span class="hlt">approximation</span> (SCBA) algorithm. Both LOA and LOA+AC are then applied to model n-type silicon nanowire field-effect-transistors and are compared to SCBA current characteristics. In this system, the LOA fails to describe electron-phonon scattering, mainly because of the interactions with acoustic phonons at the band edges. In contrast, the LOA+AC still well <span class="hlt">approximates</span> the SCBA current characteristics, thus demonstrating the power of <span class="hlt">analytic</span> continuation techniques. The limits of validity of LOA+AC are also discussed, and more sophisticated and general <span class="hlt">analytic</span> continuation techniques are suggested for more demanding cases.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2894168','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2894168"><span><span class="hlt">Accurate</span> Computation of Electric Field Enhancement Factors for Metallic Nanoparticles Using the Discrete Dipole <span class="hlt">Approximation</span></span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p></p> <p>2010-01-01</p> <p>We model the response of nanoscale Ag prolate spheroids to an external uniform static electric field using simulations based on the discrete dipole <span class="hlt">approximation</span>, in which the spheroid is represented as a collection of polarizable subunits. We compare the results of simulations that employ subunit polarizabilities derived from the Clausius–Mossotti relation with those of simulations that employ polarizabilities that include a local environmental correction for subunits near the spheroid’s surface [Rahmani et al. Opt Lett 27: 2118 (2002)]. The simulations that employ corrected polarizabilities give predictions in very good agreement with exact results obtained by solving Laplace’s equation. In contrast, simulations that employ uncorrected Clausius–Mossotti polarizabilities substantially underestimate the extent of the electric field “hot spot” near the spheroid’s sharp tip, and give predictions for the field enhancement factor near the tip that are 30 to 50% too small. PMID:20672062</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li class="active"><span>22</span></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_22 --> <div id="page_23" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li class="active"><span>23</span></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="441"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940012611','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940012611"><span><span class="hlt">Approximate</span> Green's function methods for HZE transport in multilayered materials</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Wilson, John W.; Badavi, Francis F.; Shinn, Judy L.; Costen, Robert C.</p> <p>1993-01-01</p> <p>A nonperturbative <span class="hlt">analytic</span> solution of the high charge and energy (HZE) Green's function is used to implement a computer code for laboratory ion beam transport in multilayered materials. The code is established to operate on the Langley nuclear fragmentation model used in engineering applications. Computational procedures are established to generate linear energy transfer (LET) distributions for a specified ion beam and target for comparison with experimental measurements. The code was found to be highly efficient and compared well with the perturbation <span class="hlt">approximation</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920039514&hterms=john+maxwell&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Djohn%2Bmaxwell','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920039514&hterms=john+maxwell&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Djohn%2Bmaxwell"><span>Pulsed plane wave <span class="hlt">analytic</span> solutions for generic shapes and the validation of Maxwell's equations solvers</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Yarrow, Maurice; Vastano, John A.; Lomax, Harvard</p> <p>1992-01-01</p> <p>Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined <span class="hlt">analytically</span>. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order <span class="hlt">accurate</span> in space and fourth-order <span class="hlt">accurate</span> in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the <span class="hlt">analytic</span> solutions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhRvE..91b2813A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhRvE..91b2813A"><span>Mean-field <span class="hlt">approximation</span> for the Sznajd model in complex networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Araújo, Maycon S.; Vannucchi, Fabio S.; Timpanaro, André M.; Prado, Carmen P. C.</p> <p>2015-02-01</p> <p>This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field <span class="hlt">approximation</span>. Although quite simple, this <span class="hlt">approximation</span> allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The <span class="hlt">analytical</span> prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong <span class="hlt">approximations</span> involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950012948','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950012948"><span>Comparison of dynamical <span class="hlt">approximation</span> schemes for non-linear gravitational clustering</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Melott, Adrian L.</p> <p>1994-01-01</p> <p>We have recently conducted a controlled comparison of a number of <span class="hlt">approximations</span> for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion <span class="hlt">approximation</span>, the frozen-flow <span class="hlt">approximation</span>, the Zel'dovich <span class="hlt">approximation</span> (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of <span class="hlt">approximation</span> by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to <span class="hlt">approximation</span> schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich <span class="hlt">approximation</span>, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) 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. All other schemes, including those proposed as generalizations of the Zel'dovich <span class="hlt">approximation</span> created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion <span class="hlt">approximation</span> produced the most <span class="hlt">accurate</span> nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich <span class="hlt">approximation</span>, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25903880','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25903880"><span>Subsystem density functional theory with meta-generalized gradient <span class="hlt">approximation</span> exchange-correlation functionals.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio</p> <p>2015-04-21</p> <p>We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient <span class="hlt">approximation</span> (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level <span class="hlt">approximation</span> to the KED which overcomes this limitation and provides a simple and <span class="hlt">accurate</span> way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the <span class="hlt">approximations</span> in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27138343','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27138343"><span>Improving the <span class="hlt">analytical</span> performance and versatility of paper spray mass spectrometry via paper microfluidics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Murray, Ian; Walker, Glenn; Bereman, Michael S</p> <p>2016-06-20</p> <p>Two paper-based microfluidic techniques, photolithography and wax patterning, were investigated for their potential to improve upon the sensitivity, reproducibility, and versatility of paper spray mass spectrometry. The main limitation of photolithography was the significant signal (<span class="hlt">approximately</span> three orders of magnitude) above background which was attributed to the chemicals used in the photoresist process. Hydrophobic barriers created via wax patterning were discovered to have <span class="hlt">approximately</span> 2 orders of magnitude less background signal compared to analogous barriers created using photolithography. A minimum printed wax barrier thickness of <span class="hlt">approximately</span> 0.3 mm was necessary to consistently retain commonly used paper spray solvents (1 : 1 water : acetonitrile/methanol) and avoid leakage. Constricting capillary flow via wax-printed channels yielded both a significant increase in signal and detection time for detection of model <span class="hlt">analytes</span>. This signal increase, which was attributed to restricting the radial flow of <span class="hlt">analyte</span>/solvent on paper (i.e., a concentrating effect), afforded a significant increase in sensitivity (p ≪ 0.05) for the detection of pesticides spiked into residential tap water using a five-point calibration curve. Finally, unique mixing designs using wax patterning can be envisioned to perform on-paper <span class="hlt">analyte</span> derivatization.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20170002541','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20170002541"><span>Optimization of Turbine Engine Cycle Analysis with <span class="hlt">Analytic</span> Derivatives</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.</p> <p>2016-01-01</p> <p>A new engine cycle analysis tool, called Pycycle, was recently built using the OpenMDAO framework. This tool uses equilibrium chemistry based thermodynamics, and provides <span class="hlt">analytic</span> derivatives. This allows for stable and efficient use of gradient-based optimization and sensitivity analysis methods on engine cycle models, without requiring the use of finite difference derivative <span class="hlt">approximation</span> methods. To demonstrate this, a gradient-based design optimization was performed on a multi-point turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference <span class="hlt">approximated</span> derivatives.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22611442-multi-level-methods-approximating-distribution-functions','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22611442-multi-level-methods-approximating-distribution-functions"><span>Multi-level methods and <span class="hlt">approximating</span> distribution functions</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Wilson, D., E-mail: daniel.wilson@dtc.ox.ac.uk; Baker, R. E.</p> <p>2016-07-15</p> <p>Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated <span class="hlt">analytically</span> and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore <span class="hlt">approximate</span> stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparablemore » to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely <span class="hlt">approximating</span> required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to <span class="hlt">approximate</span> entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24288668','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24288668"><span>Selecting summary statistics in <span class="hlt">approximate</span> Bayesian computation for calibrating stochastic models.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Burr, Tom; Skurikhin, Alexei</p> <p>2013-01-01</p> <p><span class="hlt">Approximate</span> Bayesian computation (ABC) is an approach for using measurement data to calibrate stochastic computer models, which are common in biology applications. ABC is becoming the "go-to" option when the data and/or parameter dimension is large because it relies on user-chosen summary statistics rather than the full data and is therefore computationally feasible. One technical challenge with ABC is that the quality of the <span class="hlt">approximation</span> to the posterior distribution of model parameters depends on the user-chosen summary statistics. In this paper, the user requirement to choose effective summary statistics in order to <span class="hlt">accurately</span> estimate the posterior distribution of model parameters is investigated and illustrated by example, using a model and corresponding real data of mitochondrial DNA population dynamics. We show that for some choices of summary statistics, the posterior distribution of model parameters is closely <span class="hlt">approximated</span> and for other choices of summary statistics, the posterior distribution is not closely <span class="hlt">approximated</span>. A strategy to choose effective summary statistics is suggested in cases where the stochastic computer model can be run at many trial parameter settings, as in the example.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19820015320','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19820015320"><span>An <span class="hlt">accurate</span> method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Desmarais, R. N.</p> <p>1982-01-01</p> <p>The method is capable of generating <span class="hlt">approximations</span> of arbitrary accuracy. It is based on <span class="hlt">approximating</span> the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the <span class="hlt">approximation</span> is a geometric sequence. The coefficients and exponent multiplier of the exponential <span class="hlt">approximation</span> are computed by least squares so the method is completely automated. Exponential <span class="hlt">approximates</span> generated in this manner are two orders of magnitude more <span class="hlt">accurate</span> than the exponential <span class="hlt">approximation</span> that is currently most often used for this purpose. The method can be used to generate <span class="hlt">approximations</span> to attain any desired trade-off between accuracy and computing cost.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25920871','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25920871"><span>A comparison of finite element and <span class="hlt">analytic</span> models of acoustic scattering from rough poroelastic interfaces.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Bonomo, Anthony L; Isakson, Marcia J; Chotiros, Nicholas P</p> <p>2015-04-01</p> <p>The finite element method is used to model acoustic scattering from rough poroelastic surfaces. Both monostatic and bistatic scattering strengths are calculated and compared with three <span class="hlt">analytic</span> models: Perturbation theory, the Kirchhoff <span class="hlt">approximation</span>, and the small-slope <span class="hlt">approximation</span>. It is found that the small-slope <span class="hlt">approximation</span> is in very close agreement with the finite element results for all cases studied and that perturbation theory and the Kirchhoff <span class="hlt">approximation</span> can be considered valid in those instances where their predictions match those given by the small-slope <span class="hlt">approximation</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/6637686-approximate-stoichiometry-rich-hydrocarbon-mixtures','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/6637686-approximate-stoichiometry-rich-hydrocarbon-mixtures"><span><span class="hlt">Approximate</span> stoichiometry for rich hydrocarbon mixtures</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Beans, E.W.</p> <p>1993-03-01</p> <p>The stoichiometry of lean mixtures can readily and <span class="hlt">accurately</span> be determined from the assumption that all the carbon oxidizes to carbon dioxide and all the hydrogen oxidizes to water. This assumption is valid up to an equivalence ratio ([sigma]) of 0.8 and can be used with little error up to [sigma] = 1. The composition of the products of a hydrocarbon burnt in air under the foregoing assumption can be obtained from simple carbon, hydrogen, oxygen and nitrogen balances. Given the composition, one can determine the energy released and/or the adiabatic flame temperature. For rich mixtures, the foregoing assumption, ofmore » course, is not valid. Hence, there is no easy way to determine the stoichiometry of the products of a rich mixture. The objective of this note is to present an equation' which will allow one to readily determine the composition of the products of rich hydrocarbon mixtures. The equation is based on equilibrium composition calculations and some assumptions regarding the characteristics of hydrocarbons. The equation gives <span class="hlt">approximate</span> results. However, the results are sufficiently <span class="hlt">accurate</span> for many situations. If more accuracy is wanted, one should use an equilibrium combustion program like the one by Gordon and McBride.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24323015','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24323015"><span>Analysis of the impacts of horizontal translation and scaling on wavefront <span class="hlt">approximation</span> coefficients with rectangular pupils for Chebyshev and Legendre polynomials.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Sun, Wenqing; Chen, Lei; Tuya, Wulan; He, Yong; Zhu, Rihong</p> <p>2013-12-01</p> <p>Chebyshev and Legendre polynomials are frequently used in rectangular pupils for wavefront <span class="hlt">approximation</span>. Ideally, the dataset completely fits with the polynomial basis, which provides the full-pupil <span class="hlt">approximation</span> coefficients and the corresponding geometric aberrations. However, if there are horizontal translation and scaling, the terms in the original polynomials will become the linear combinations of the coefficients of the other terms. This paper introduces <span class="hlt">analytical</span> expressions for two typical situations after translation and scaling. With a small translation, first-order Taylor expansion could be used to simplify the computation. Several representative terms could be selected as inputs to compute the coefficient changes before and after translation and scaling. Results show that the outcomes of the <span class="hlt">analytical</span> solutions and the <span class="hlt">approximated</span> values under discrete sampling are consistent. With the computation of a group of randomly generated coefficients, we contrasted the changes under different translation and scaling conditions. The larger ratios correlate the larger deviation from the <span class="hlt">approximated</span> values to the original ones. Finally, we analyzed the peak-to-valley (PV) and root mean square (RMS) deviations from the uses of the first-order <span class="hlt">approximation</span> and the direct expansion under different translation values. The results show that when the translation is less than 4%, the most deviated 5th term in the first-order 1D-Legendre expansion has a PV deviation less than 7% and an RMS deviation less than 2%. The <span class="hlt">analytical</span> expressions and the computed results under discrete sampling given in this paper for the multiple typical function basis during translation and scaling in the rectangular areas could be applied in wavefront <span class="hlt">approximation</span> and analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19790005954&hterms=singularities&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsingularities','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19790005954&hterms=singularities&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsingularities"><span>A singularity free <span class="hlt">analytical</span> solution of artificial satellite motion with drag</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Mueller, A.</p> <p>1978-01-01</p> <p>An <span class="hlt">analytical</span> satellite theory based on the regular, canonical Poincare-Similar (PS phi) elements is described along with an <span class="hlt">accurate</span> density model which can be implemented into the drag theory. A computationally efficient manner in which to expand the equations of motion into a fourier series is discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27140125','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27140125"><span><span class="hlt">Analytical</span> model of the optical vortex microscope.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Płocinniczak, Łukasz; Popiołek-Masajada, Agnieszka; Masajada, Jan; Szatkowski, Mateusz</p> <p>2016-04-20</p> <p>This paper presents an <span class="hlt">analytical</span> model of the optical vortex scanning microscope. In this microscope the Gaussian beam with an embedded optical vortex is focused into the sample plane. Additionally, the optical vortex can be moved inside the beam, which allows fine scanning of the sample. We provide an <span class="hlt">analytical</span> solution of the whole path of the beam in the system (within paraxial <span class="hlt">approximation</span>)-from the vortex lens to the observation plane situated on the CCD camera. The calculations are performed step by step from one optical element to the next. We show that at each step, the expression for light complex amplitude has the same form with only four coefficients modified. We also derive a simple expression for the vortex trajectory of small vortex displacements.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JAG...152..100L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JAG...152..100L"><span>Arrival-time picking method based on <span class="hlt">approximate</span> negentropy for microseismic data</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Li, Yue; Ni, Zhuo; Tian, Yanan</p> <p>2018-05-01</p> <p><span class="hlt">Accurate</span> and dependable picking of the first arrival time for microseismic data is an important part in microseismic monitoring, which directly affects analysis results of post-processing. This paper presents a new method based on <span class="hlt">approximate</span> negentropy (AN) theory for microseismic arrival time picking in condition of much lower signal-to-noise ratio (SNR). According to the differences in information characteristics between microseismic data and random noise, an appropriate <span class="hlt">approximation</span> of negentropy function is selected to minimize the effect of SNR. At the same time, a weighted function of the differences between maximum and minimum value of AN spectrum curve is designed to obtain a proper threshold function. In this way, the region of signal and noise is distinguished to pick the first arrival time <span class="hlt">accurately</span>. To demonstrate the effectiveness of AN method, we make many experiments on a series of synthetic data with different SNR from -1 dB to -12 dB and compare it with previously published Akaike information criterion (AIC) and short/long time average ratio (STA/LTA) methods. Experimental results indicate that these three methods can achieve well picking effect when SNR is from -1 dB to -8 dB. However, when SNR is as low as -8 dB to -12 dB, the proposed AN method yields more <span class="hlt">accurate</span> and stable picking result than AIC and STA/LTA methods. Furthermore, the application results of real three-component microseismic data also show that the new method is superior to the other two methods in accuracy and stability.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://eric.ed.gov/?q=time+AND+travel&pg=2&id=EJ985438','ERIC'); return false;" href="https://eric.ed.gov/?q=time+AND+travel&pg=2&id=EJ985438"><span>Fall with Linear Drag and Wien's Displacement Law: <span class="hlt">Approximate</span> Solution and Lambert Function</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Vial, Alexandre</p> <p>2012-01-01</p> <p>We present an <span class="hlt">approximate</span> solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-<span class="hlt">analytical</span> solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for…</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19910045449&hterms=feedforward+control&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dfeedforward%2Bcontrol','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19910045449&hterms=feedforward+control&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dfeedforward%2Bcontrol"><span>Neural networks for function <span class="hlt">approximation</span> in nonlinear control</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Linse, Dennis J.; Stengel, Robert F.</p> <p>1990-01-01</p> <p>Two neural network architectures are compared with a classical spline interpolation technique for the <span class="hlt">approximation</span> of functions useful in a nonlinear control system. A standard back-propagation feedforward neural network and a cerebellar model articulation controller (CMAC) neural network are presented, and their results are compared with a B-spline interpolation procedure that is updated using recursive least-squares parameter identification. Each method is able to <span class="hlt">accurately</span> represent a one-dimensional test function. Tradeoffs between size requirements, speed of operation, and speed of learning indicate that neural networks may be practical for identification and adaptation in a nonlinear control environment.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1326627-approximate-maximum-likelihood-localization-solver','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1326627-approximate-maximum-likelihood-localization-solver"><span>A 3D <span class="hlt">approximate</span> maximum likelihood localization solver</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p></p> <p>2016-09-23</p> <p>A robust three-dimensional solver was needed to <span class="hlt">accurately</span> and efficiently estimate the time sequence of locations of fish tagged with acoustic transmitters and vocalizing marine mammals to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives and support Marine Renewable Energy. An <span class="hlt">approximate</span> maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4348629','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4348629"><span><span class="hlt">Analytical</span> Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Zhang, Guofeng; Zhu, Hanjie</p> <p>2015-01-01</p> <p>The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms <span class="hlt">approximately</span> and obtain the <span class="hlt">analytical</span> energy spectrums and wavefunctions. These <span class="hlt">analytical</span> results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave <span class="hlt">approximation</span> on the assumption of near-resonance and relatively weak coupling. Moreover, the <span class="hlt">analytical</span> expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model. PMID:25736827</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li class="active"><span>23</span></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_23 --> <div id="page_24" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li class="active"><span>24</span></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="461"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018MNRAS.tmp.1361N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018MNRAS.tmp.1361N"><span>The Excursion set approach: Stratonovich <span class="hlt">approximation</span> and Cholesky decomposition</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nikakhtar, Farnik; Ayromlou, Mohammadreza; Baghram, Shant; Rahvar, Sohrab; Tabar, M. Reza Rahimi; Sheth, Ravi K.</p> <p>2018-05-01</p> <p>The excursion set approach is a framework for estimating how the number density of nonlinear structures in the cosmic web depends on the expansion history of the universe and the nature of gravity. A key part of the approach is the estimation of the first crossing distribution of a suitably chosen barrier by random walks having correlated steps: The shape of the barrier is determined by the physics of nonlinear collapse, and the correlations between steps by the nature of the initial density fluctuation field. We describe <span class="hlt">analytic</span> and numerical methods for calculating such first up-crossing distributions. While the exact solution can be written formally as an infinite series, we show how to <span class="hlt">approximate</span> it efficiently using the Stratonovich <span class="hlt">approximation</span>. We demonstrate its accuracy using Monte-Carlo realizations of the walks, which we generate using a novel Cholesky-decomposition based algorithm, which is significantly faster than the algorithm that is currently in the literature.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018EL....12110007N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018EL....12110007N"><span>Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov <span class="hlt">approximation</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Napiórkowski, M.; Reuvers, R.; Solovej, J. P.</p> <p>2018-01-01</p> <p>Following an earlier calculation in 3D, we calculate the 2D critical temperature of a dilute, translation-invariant Bose gas using a variational formulation of the Bogoliubov <span class="hlt">approximation</span> introduced by Critchley and Solomon in 1976. This provides the first <span class="hlt">analytical</span> calculation of the Kosterlitz-Thouless transition temperature that includes the constant in the logarithm.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1393610-approximate-solutions-diffusive-fracture-matrix-transfer-application-storage-dissolved-co2-fractured-rocks','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1393610-approximate-solutions-diffusive-fracture-matrix-transfer-application-storage-dissolved-co2-fractured-rocks"><span><span class="hlt">Approximate</span> solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO 2 in fractured rocks</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Zhou, Quanlin; Oldenburg, Curtis M.; Spangler, Lee H.; ...</p> <p>2017-01-05</p> <p><span class="hlt">Analytical</span> solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form <span class="hlt">approximate</span> solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined <span class="hlt">analytically</span> for isotropic blocks (e.g., spheresmore » and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative <span class="hlt">approximation</span> error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These <span class="hlt">approximate</span> solutions are building blocks for development of <span class="hlt">analytical</span> and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930007473','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930007473"><span><span class="hlt">Approximation</span> methods for stochastic petri nets</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Jungnitz, Hauke Joerg</p> <p>1992-01-01</p> <p>Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done <span class="hlt">analytically</span>. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, <span class="hlt">approximation</span> techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time <span class="hlt">approximation</span> technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time <span class="hlt">approximation</span> converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time <span class="hlt">approximation</span> converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890016300','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890016300"><span><span class="hlt">Analytic</span> theory for the selection of 2-D needle crystal at arbitrary Peclet number</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Tanveer, Saleh</p> <p>1989-01-01</p> <p>An <span class="hlt">accurate</span> <span class="hlt">analytic</span> theory is presented for the velocity selection of a two-dimensional needle crystal for arbitrary Peclet number for small values of the surface tension parameter. The velocity selection is caused by the effect of transcendentally small terms which are determined by <span class="hlt">analytic</span> continuation to the complex plane and analysis of nonlinear equations. The work supports the general conclusion of previous small Peclet number <span class="hlt">analytical</span> results of other investigators, though there are some discrepancies in details. It also addresses questions raised on the validity of selection theory owing to assumptions made on shape corrections at large distances from the tip.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA180863','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA180863"><span>An <span class="hlt">Analytical</span> Study of Icing Similitude for Aircraft Engine Testing. Revision</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>1987-02-01</p> <p>MODELING GEOMETRIES Component Cowl Spinner Fan Blade Fan Stator Exit Vane Probe <span class="hlt">Approximating</span> Geometry NACA 0012 Airfoil Sphere NACA 0012...DOT/FAA/CT·86/35 AEDC·TR·86·26 An <span class="hlt">Analytical</span> Study of Icing Similitude for Aircraft Engine Testing c. Scott Bartlett Sverdrup Technology, Inc...8217~,feCa.ORI A n <span class="hlt">AnalYtical</span> Study )f Icin~ Similitude for Aircraft Engine Tes t tu~ 12. PERSONAL AUTHOR/S) B a r t l e t t , C. Scot t , Sverdrup</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014CeMDA.118...99B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CeMDA.118...99B"><span><span class="hlt">Analytical</span> formulation of impulsive collision avoidance dynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bombardelli, Claudio</p> <p>2014-02-01</p> <p>The paper deals with the problem of impulsive collision avoidance between two colliding objects in three dimensions and assuming elliptical Keplerian orbits. Closed-form <span class="hlt">analytical</span> expressions are provided that <span class="hlt">accurately</span> predict the relative dynamics of the two bodies in the encounter b-plane following an impulsive delta-V manoeuvre performed by one object at a given orbit location prior to the impact and with a generic three-dimensional orientation. After verifying the accuracy of the <span class="hlt">analytical</span> expressions for different orbital eccentricities and encounter geometries the manoeuvre direction that maximises the miss distance is obtained numerically as a function of the arc length separation between the manoeuvre point and the predicted collision point. The provided formulas can be used for high-accuracy instantaneous estimation of the outcome of a generic impulsive collision avoidance manoeuvre and its optimisation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3977112','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3977112"><span>Determination of Slope Safety Factor with <span class="hlt">Analytical</span> Solution and Searching Critical Slip Surface with Genetic-Traversal Random Method</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p></p> <p>2014-01-01</p> <p>In the current practice, to determine the safety factor of a slope with two-dimensional circular potential failure surface, one of the searching methods for the critical slip surface is Genetic Algorithm (GA), while the method to calculate the slope safety factor is Fellenius' slices method. However GA needs to be validated with more numeric tests, while Fellenius' slices method is just an <span class="hlt">approximate</span> method like finite element method. This paper proposed a new method to determine the minimum slope safety factor which is the determination of slope safety factor with <span class="hlt">analytical</span> solution and searching critical slip surface with Genetic-Traversal Random Method. The <span class="hlt">analytical</span> solution is more <span class="hlt">accurate</span> than Fellenius' slices method. The Genetic-Traversal Random Method uses random pick to utilize mutation. A computer automatic search program is developed for the Genetic-Traversal Random Method. After comparison with other methods like slope/w software, results indicate that the Genetic-Traversal Random Search Method can give very low safety factor which is about half of the other methods. However the obtained minimum safety factor with Genetic-Traversal Random Search Method is very close to the lower bound solutions of slope safety factor given by the Ansys software. PMID:24782679</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19770052661&hterms=fair+value&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dfair%2Bvalue','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19770052661&hterms=fair+value&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dfair%2Bvalue"><span>An <span class="hlt">analytical</span> theory of planetary rotation rates</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Harris, A. W.</p> <p>1977-01-01</p> <p>An <span class="hlt">approximate</span> <span class="hlt">analytical</span> theory is derived for the rate of rotation acquired by a planet as it grows from the solar nebula. This theory was motivated by a numerical study by Giuli, and yields fair agreement with his results. The periods of planetary rotation obtained are proportional to planetesimal encounter velocity, and appear to suggest lower values of this velocity than are commonly assumed to have existed during planetary formation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/15283574','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/15283574"><span>Discordance between net <span class="hlt">analyte</span> signal theory and practical multivariate calibration.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Brown, Christopher D</p> <p>2004-08-01</p> <p>Lorber's concept of net <span class="hlt">analyte</span> signal is reviewed in the context of classical and inverse least-squares approaches to multivariate calibration. It is shown that, in the presence of device measurement error, the classical and inverse calibration procedures have radically different theoretical prediction objectives, and the assertion that the popular inverse least-squares procedures (including partial least squares, principal components regression) <span class="hlt">approximate</span> Lorber's net <span class="hlt">analyte</span> signal vector in the limit is disproved. Exact theoretical expressions for the prediction error bias, variance, and mean-squared error are given under general measurement error conditions, which reinforce the very discrepant behavior between these two predictive approaches, and Lorber's net <span class="hlt">analyte</span> signal theory. Implications for multivariate figures of merit and numerous recently proposed preprocessing treatments involving orthogonal projections are also discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1998CoPhC.112....1W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1998CoPhC.112....1W"><span>Wavelets and distributed <span class="hlt">approximating</span> functionals</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wei, G. W.; Kouri, D. J.; Hoffman, D. K.</p> <p>1998-07-01</p> <p>A general procedure is proposed for constructing father and mother wavelets that have excellent time-frequency localization and can be used to generate entire wavelet families for use as wavelet transforms. One interesting feature of our father wavelets (scaling functions) is that they belong to a class of generalized delta sequences, which we refer to as distributed <span class="hlt">approximating</span> functionals (DAFs). We indicate this by the notation wavelet-DAFs. Correspondingly, the mother wavelets generated from these wavelet-DAFs are appropriately called DAF-wavelets. Wavelet-DAFs can be regarded as providing a pointwise (localized) spectral method, which furnishes a bridge between the traditional global methods and local methods for solving partial differential equations. They are shown to provide extremely <span class="hlt">accurate</span> numerical solutions for a number of nonlinear partial differential equations, including the Korteweg-de Vries (KdV) equation, for which a previous method has encountered difficulties (J. Comput. Phys. 132 (1997) 233).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006JPhCS..46..200C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006JPhCS..46..200C"><span>Petascale self-consistent electromagnetic computations using scalable and <span class="hlt">accurate</span> algorithms for complex structures</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cary, John R.; Abell, D.; Amundson, J.; Bruhwiler, D. L.; Busby, R.; Carlsson, J. A.; Dimitrov, D. A.; Kashdan, E.; Messmer, P.; Nieter, C.; Smithe, D. N.; Spentzouris, P.; Stoltz, P.; Trines, R. M.; Wang, H.; Werner, G. R.</p> <p>2006-09-01</p> <p>As the size and cost of particle accelerators escalate, high-performance computing plays an increasingly important role; optimization through <span class="hlt">accurate</span>, detailed computermodeling increases performance and reduces costs. But consequently, computer simulations face enormous challenges. Early <span class="hlt">approximation</span> methods, such as expansions in distance from the design orbit, were unable to supply detailed <span class="hlt">accurate</span> results, such as in the computation of wake fields in complex cavities. Since the advent of message-passing supercomputers with thousands of processors, earlier <span class="hlt">approximations</span> are no longer necessary, and it is now possible to compute wake fields, the effects of dampers, and self-consistent dynamics in cavities <span class="hlt">accurately</span>. In this environment, the focus has shifted towards the development and implementation of algorithms that scale to large numbers of processors. So-called charge-conserving algorithms evolve the electromagnetic fields without the need for any global solves (which are difficult to scale up to many processors). Using cut-cell (or embedded) boundaries, these algorithms can simulate the fields in complex accelerator cavities with curved walls. New implicit algorithms, which are stable for any time-step, conserve charge as well, allowing faster simulation of structures with details small compared to the characteristic wavelength. These algorithmic and computational advances have been implemented in the VORPAL7 Framework, a flexible, object-oriented, massively parallel computational application that allows run-time assembly of algorithms and objects, thus composing an application on the fly.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28268545','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28268545"><span>Fast <span class="hlt">analytical</span> spectral filtering methods for magnetic resonance perfusion quantification.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Reddy, Kasireddy V; Mitra, Abhishek; Yalavarthy, Phaneendra K</p> <p>2016-08-01</p> <p>The deconvolution in the perfusion weighted imaging (PWI) plays an important role in quantifying the MR perfusion parameters. The PWI application to stroke and brain tumor studies has become a standard clinical practice. The standard approach for this deconvolution is oscillatory-limited singular value decomposition (oSVD) and frequency domain deconvolution (FDD). The FDD is widely recognized as the fastest approach currently available for deconvolution of MR perfusion data. In this work, two fast deconvolution methods (namely <span class="hlt">analytical</span> fourier filtering and <span class="hlt">analytical</span> showalter spectral filtering) are proposed. Through systematic evaluation, the proposed methods are shown to be computationally efficient and quantitatively <span class="hlt">accurate</span> compared to FDD and oSVD.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19840048909&hterms=Berman&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3DS.%2BS.%2BBerman','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19840048909&hterms=Berman&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3DS.%2BS.%2BBerman"><span>System identification of <span class="hlt">analytical</span> models of damped structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Fuh, J.-S.; Chen, S.-Y.; Berman, A.</p> <p>1984-01-01</p> <p>A procedure is presented for identifying linear nonproportionally damped system. The system damping is assumed to be representable by a real symmetric matrix. <span class="hlt">Analytical</span> mass, stiffness and damping matrices which constitute an <span class="hlt">approximate</span> representation of the system are assumed to be available. Given also are an incomplete set of measured natural frequencies, damping ratios and complex mode shapes of the structure, normally obtained from test data. A method is developed to find the smallest changes in the <span class="hlt">analytical</span> model so that the improved model can exactly predict the measured modal parameters. The present method uses the orthogonality relationship to improve mass and damping matrices and the dynamic equation to find the improved stiffness matrix.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JEI....27a3011L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JEI....27a3011L"><span>Local facet <span class="hlt">approximation</span> for image stitching</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Li, Jing; Lai, Shiming; Liu, Yu; Wang, Zhengming; Zhang, Maojun</p> <p>2018-01-01</p> <p>Image stitching aims at eliminating multiview parallax and generating a seamless panorama given a set of input images. This paper proposes a local adaptive stitching method, which could achieve both <span class="hlt">accurate</span> and robust image alignments across the whole panorama. A transformation estimation model is introduced by <span class="hlt">approximating</span> the scene as a combination of neighboring facets. Then, the local adaptive stitching field is constructed using a series of linear systems of the facet parameters, which enables the parallax handling in three-dimensional space. We also provide a concise but effective global projectivity preserving technique that smoothly varies the transformations from local adaptive to global planar. The proposed model is capable of stitching both normal images and fisheye images. The efficiency of our method is quantitatively demonstrated in the comparative experiments on several challenging cases.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhFl...29j3606L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhFl...29j3606L"><span>Exact and <span class="hlt">approximate</span> solutions for transient squeezing flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lang, Ji; Santhanam, Sridhar; Wu, Qianhong</p> <p>2017-10-01</p> <p>In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An <span class="hlt">approximate</span> solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the <span class="hlt">analytical</span> and the numerical solutions is obtained, indicating the validity of the <span class="hlt">analytical</span> approaches. The study presented herein fills the gap in the literature and will have a broad impact on industrial and biomedical applications.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012EPJB...85..323S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012EPJB...85..323S"><span>Quantitative molecular orbital energies within a G0W0 <span class="hlt">approximation</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sharifzadeh, S.; Tamblyn, I.; Doak, P.; Darancet, P. T.; Neaton, J. B.</p> <p>2012-09-01</p> <p>Using many-body perturbation theory within a G 0 W 0 <span class="hlt">approximation</span>, with a plane wave basis set and using a starting point based on density functional theory within the generalized gradient <span class="hlt">approximation</span>, we explore routes for computing the ionization potential (IP), electron affinity (EA), and fundamental gap of three gas-phase molecules — benzene, thiophene, and (1,4) diamino-benzene — and compare with experiments. We examine the dependence of the IP and fundamental gap on the number of unoccupied states used to represent the dielectric function and the self energy, as well as the dielectric function plane-wave cutoff. We find that with an effective completion strategy for <span class="hlt">approximating</span> the unoccupied subspace, and a well converged dielectric function kinetic energy cutoff, the computed IPs and EAs are in excellent quantitative agreement with available experiment (within 0.2 eV), indicating that a one-shot G 0 W 0 approach can be very <span class="hlt">accurate</span> for calculating addition/removal energies of small organic molecules.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/956522','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/956522"><span><span class="hlt">Approximate</span> inference on planar graphs using loop calculus and belief progagation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Chertkov, Michael; Gomez, Vicenc; Kappen, Hilbert</p> <p></p> <p>We introduce novel results for <span class="hlt">approximate</span> inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006b) allows to express the exact partition function Z of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in Chertkov et al. (2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyzemore » in detail both the loop series and the Pfaffian series for models with binary variables and pairwise interactions, and show that the first term of the Pfaffian series can provide very <span class="hlt">accurate</span> <span class="hlt">approximations</span>. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state-of-the-art methods for <span class="hlt">approximate</span> inference.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20160013222','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20160013222"><span>Optics of Water Microdroplets with Soot Inclusions: Exact Versus <span class="hlt">Approximate</span> Results</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liu, Li; Mishchenko, Michael I.</p> <p>2016-01-01</p> <p>We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with <span class="hlt">approximate</span> ones obtained using the Maxwell-Garnett effective-medium <span class="hlt">approximation</span> (MGA) and the Monte Carlo ray-tracing <span class="hlt">approximation</span> (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while <span class="hlt">accurate</span> MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4848050','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4848050"><span>Health Informatics for Neonatal Intensive Care Units: An <span class="hlt">Analytical</span> Modeling Perspective</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Mench-Bressan, Nadja; McGregor, Carolyn; Pugh, James Edward</p> <p>2015-01-01</p> <p>The effective use of data within intensive care units (ICUs) has great potential to create new cloud-based health <span class="hlt">analytics</span> solutions for disease prevention or earlier condition onset detection. The Artemis project aims to achieve the above goals in the area of neonatal ICUs (NICU). In this paper, we proposed an <span class="hlt">analytical</span> model for the Artemis cloud project which will be deployed at McMaster Children’s Hospital in Hamilton. We collect not only physiological data but also the infusion pumps data that are attached to NICU beds. Using the proposed <span class="hlt">analytical</span> model, we predict the amount of storage, memory, and computation power required for the system. Capacity planning and tradeoff analysis would be more <span class="hlt">accurate</span> and systematic by applying the proposed <span class="hlt">analytical</span> model in this paper. Numerical results are obtained using real inputs acquired from McMaster Children’s Hospital and a pilot deployment of the system at The Hospital for Sick Children (SickKids) in Toronto. PMID:27170907</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li class="active"><span>24</span></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_24 --> <div id="page_25" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li class="active"><span>25</span></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="481"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4450587','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4450587"><span>Continuous Metabolic Monitoring Based on Multi-<span class="hlt">Analyte</span> Biomarkers to Predict Exhaustion</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Kastellorizios, Michail; Burgess, Diane J.</p> <p>2015-01-01</p> <p>This work introduces the concept of multi-<span class="hlt">analyte</span> biomarkers for continuous metabolic monitoring. The importance of using more than one marker lies in the ability to obtain a holistic understanding of the metabolism. This is showcased for the detection and prediction of exhaustion during intense physical exercise. The findings presented here indicate that when glucose and lactate changes over time are combined into multi-<span class="hlt">analyte</span> biomarkers, their monitoring trends are more sensitive in the subcutaneous tissue, an implantation-friendly peripheral tissue, compared to the blood. This unexpected observation was confirmed in normal as well as type 1 diabetic rats. This study was designed to be of direct value to continuous monitoring biosensor research, where single <span class="hlt">analytes</span> are typically monitored. These findings can be implemented in new multi-<span class="hlt">analyte</span> continuous monitoring technologies for more <span class="hlt">accurate</span> insulin dosing, as well as for exhaustion prediction studies based on objective data rather than the subject’s perception. PMID:26028477</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26028477','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26028477"><span>Continuous metabolic monitoring based on multi-<span class="hlt">analyte</span> biomarkers to predict exhaustion.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kastellorizios, Michail; Burgess, Diane J</p> <p>2015-06-01</p> <p>This work introduces the concept of multi-<span class="hlt">analyte</span> biomarkers for continuous metabolic monitoring. The importance of using more than one marker lies in the ability to obtain a holistic understanding of the metabolism. This is showcased for the detection and prediction of exhaustion during intense physical exercise. The findings presented here indicate that when glucose and lactate changes over time are combined into multi-<span class="hlt">analyte</span> biomarkers, their monitoring trends are more sensitive in the subcutaneous tissue, an implantation-friendly peripheral tissue, compared to the blood. This unexpected observation was confirmed in normal as well as type 1 diabetic rats. This study was designed to be of direct value to continuous monitoring biosensor research, where single <span class="hlt">analytes</span> are typically monitored. These findings can be implemented in new multi-<span class="hlt">analyte</span> continuous monitoring technologies for more <span class="hlt">accurate</span> insulin dosing, as well as for exhaustion prediction studies based on objective data rather than the subject's perception.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JPhB...51d4004M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JPhB...51d4004M"><span><span class="hlt">Analytic</span> quantum-interference conditions in Coulomb corrected photoelectron holography</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Maxwell, A. S.; Al-Jawahiry, A.; Lai, X. Y.; Figueira de Morisson Faria, C.</p> <p>2018-02-01</p> <p>We provide <span class="hlt">approximate</span> <span class="hlt">analytic</span> expressions for above-threshold ionization (ATI) transition probabilities and photoelectron angular distributions. These <span class="hlt">analytic</span> expressions are more general than those existing in the literature and include the residual binding potential in the electron continuum propagation. They successfully reproduce the ATI side lobes and specific holographic structures such as the near-threshold fan-shaped pattern and the spider-like structure that extends up to relatively high photoelectron energies. We compare such expressions with the Coulomb quantum orbit strong-field <span class="hlt">approximation</span> (CQSFA) and the full solution of the time-dependent Schrödinger equation for different driving-field frequencies and intensities, and provide an in-depth analysis of the physical mechanisms behind specific holographic structures. Our results shed additional light on what aspects of the CQSFA must be prioritized in order to obtain the key holographic features, and highlight the importance of forward scattered trajectories. Furthermore, we find that the holographic patterns change considerably for different field parameters, even if the Keldysh parameter is kept roughly the same.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.A31D2202S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.A31D2202S"><span><span class="hlt">Accurate</span> single-scattering simulation of ice cloud using the invariant-imbedding T-matrix method and the physical-geometric optics method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sun, B.; Yang, P.; Kattawar, G. W.; Zhang, X.</p> <p>2017-12-01</p> <p>The ice cloud single-scattering properties can be <span class="hlt">accurately</span> simulated using the invariant-imbedding T-matrix method (IITM) and the physical-geometric optics method (PGOM). The IITM has been parallelized using the Message Passing Interface (MPI) method to remove the memory limitation so that the IITM can be used to obtain the single-scattering properties of ice clouds for sizes in the geometric optics regime. Furthermore, the results associated with random orientations can be <span class="hlt">analytically</span> achieved once the T-matrix is given. The PGOM is also parallelized in conjunction with random orientations. The single-scattering properties of a hexagonal prism with height 400 (in units of lambda/2*pi, where lambda is the incident wavelength) and an aspect ratio of 1 (defined as the height over two times of bottom side length) are given by using the parallelized IITM and compared to the counterparts using the parallelized PGOM. The two results are in close agreement. Furthermore, the integrated single-scattering properties, including the asymmetry factor, the extinction cross-section, and the scattering cross-section, are given in a completed size range. The present results show a smooth transition from the exact IITM solution to the <span class="hlt">approximate</span> PGOM result. Because the calculation of the IITM method has reached the geometric regime, the IITM and the PGOM can be efficiently employed to <span class="hlt">accurately</span> compute the single-scattering properties of ice cloud in a wide spectral range.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1981JMP....22.2704A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1981JMP....22.2704A"><span>Nonperturbative confinement in quantum chromodynamics. I. Study of an <span class="hlt">approximate</span> equation of Mandelstam</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Atkinson, D.; Drohm, J. K.; Johnson, P. W.; Stam, K.</p> <p>1981-11-01</p> <p>An <span class="hlt">approximated</span> form of the Dyson-Schwinger equation for the gluon propagator in quarkless QCD is subjected to nonlinear functional and numerical analysis. It is found that solutions exist, and that these have a double pole at the origin of the square of the propagator momentum, together with an accumulation of soft branch points. This <span class="hlt">analytic</span> structure is strongly suggestive of confinement by infrared slavery.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1123534-enhancing-adaptive-sparse-grid-approximations-improving-refinement-strategies-using-adjoint-based-posteriori-error-estimates','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1123534-enhancing-adaptive-sparse-grid-approximations-improving-refinement-strategies-using-adjoint-based-posteriori-error-estimates"><span>Enhancing adaptive sparse grid <span class="hlt">approximations</span> and improving refinement strategies using adjoint-based a posteriori error estimates</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Jakeman, J. D.; Wildey, T.</p> <p>2015-01-01</p> <p>In this paper we present an algorithm for adaptive sparse grid <span class="hlt">approximations</span> of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid <span class="hlt">approximation</span> and to drive adaptivity. We show that utilizing these error estimates provides significantly more <span class="hlt">accurate</span> functional values for random samples of the sparse grid <span class="hlt">approximation</span>. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the <span class="hlt">approximation</span> over traditional hierarchical surplus based strategies. Throughout this papermore » we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid <span class="hlt">approximation</span>.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhRvB..92h1108L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhRvB..92h1108L"><span>Finite-temperature Gutzwiller <span class="hlt">approximation</span> from the time-dependent variational principle</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lanatà, Nicola; Deng, Xiaoyu; Kotliar, Gabriel</p> <p>2015-08-01</p> <p>We develop an extension of the Gutzwiller <span class="hlt">approximation</span> to finite temperatures based on the Dirac-Frenkel variational principle. Our method does not rely on any entropy inequality, and is substantially more <span class="hlt">accurate</span> than the approaches proposed in previous works. We apply our theory to the single-band Hubbard model at different fillings, and show that our results compare quantitatively well with dynamical mean field theory in the metallic phase. We discuss potential applications of our technique within the framework of first-principle calculations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3969837','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3969837"><span><span class="hlt">Approximate</span> Algorithms for Computing Spatial Distance Histograms with Accuracy Guarantees</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Grupcev, Vladimir; Yuan, Yongke; Tu, Yi-Cheng; Huang, Jin; Chen, Shaoping; Pandit, Sagar; Weng, Michael</p> <p>2014-01-01</p> <p>Particle simulation has become an important research tool in many scientific and engineering fields. Data generated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial distance histogram (SDH) query, is the building block of many high-level <span class="hlt">analytics</span>, and requires quadratic time to compute using a straightforward algorithm. Previous work has developed efficient algorithms that compute exact SDHs. While beating the naive solution, such algorithms are still not practical in processing SDH queries against large-scale simulation data. In this paper, we take a different path to tackle this problem by focusing on <span class="hlt">approximate</span> algorithms with provable error bounds. We first present a solution derived from the aforementioned exact SDH algorithm, and this solution has running time that is unrelated to the system size N. We also develop a mathematical model to analyze the mechanism that leads to errors in the basic <span class="hlt">approximate</span> algorithm. Our model provides insights on how the algorithm can be improved to achieve higher accuracy and efficiency. Such insights give rise to a new <span class="hlt">approximate</span> algorithm with improved time/accuracy tradeoff. Experimental results confirm our analysis. PMID:24693210</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFMNG13A..08E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFMNG13A..08E"><span>An <span class="hlt">analytical</span> model of iceberg drift</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Eisenman, I.; Wagner, T. J. W.; Dell, R.</p> <p>2017-12-01</p> <p>Icebergs transport freshwater from glaciers and ice shelves, releasing the freshwater into the upper ocean thousands of kilometers from the source. This influences ocean circulation through its effect on seawater density. A standard empirical rule-of-thumb for estimating iceberg trajectories is that they drift at the ocean surface current velocity plus 2% of the atmospheric surface wind velocity. This relationship has been observed in empirical studies for decades, but it has never previously been physically derived or justified. In this presentation, we consider the momentum balance for an individual iceberg, which includes nonlinear drag terms. Applying a series of <span class="hlt">approximations</span>, we derive an <span class="hlt">analytical</span> solution for the iceberg velocity as a function of time. In order to validate the model, we force it with surface velocity and temperature data from an observational state estimate and compare the results with iceberg observations in both hemispheres. We show that the <span class="hlt">analytical</span> solution reduces to the empirical 2% relationship in the asymptotic limit of small icebergs (or strong winds), which <span class="hlt">approximately</span> applies for typical Arctic icebergs. We find that the 2% value arises due to a term involving the drag coefficients for water and air and the densities of the iceberg, ocean, and air. In the opposite limit of large icebergs (or weak winds), which <span class="hlt">approximately</span> applies for typical Antarctic icebergs with horizontal length scales greater than about 12 km, we find that the 2% relationship is not applicable and that icebergs instead move with the ocean current, unaffected by the wind. The two asymptotic regimes can be understood by considering how iceberg size influences the relative importance of the wind and ocean current drag terms compared with the Coriolis and pressure gradient force terms in the iceberg momentum balance.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930091995','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930091995"><span>An <span class="hlt">analytical</span> method of estimating turbine performance</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kochendorfer, Fred D; Nettles, J Cary</p> <p>1949-01-01</p> <p>A method is developed by which the performance of a turbine over a range of operating conditions can be <span class="hlt">analytically</span> estimated from the blade angles and flow areas. In order to use the method, certain coefficients that determine the weight flow and the friction losses must be <span class="hlt">approximated</span>. The method is used to calculate the performance of the single-stage turbine of a commercial aircraft gas-turbine engine and the calculated performance is compared with the performance indicated by experimental data. For the turbine of the typical example, the assumed pressure losses and the tuning angles give a calculated performance that represents the trends of the experimental performance with reasonable accuracy. The exact agreement between <span class="hlt">analytical</span> performance and experimental performance is contingent upon the proper selection of a blading-loss parameter.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20120017356','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20120017356"><span>Spectrally-Invariant <span class="hlt">Approximation</span> Within Atmospheric Radiative Transfer</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Marshak, A.; Knyazikhin, Y.; Chiu, J. C.; Wiscombe, W. J.</p> <p>2011-01-01</p> <p>Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These "spectrally invariant relationships" are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in clouddominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant <span class="hlt">approximation</span> can <span class="hlt">accurately</span> describe the extinction. and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the <span class="hlt">approximation</span> are tested with ID radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/11220826','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/11220826"><span>Precise and <span class="hlt">accurate</span> isotope ratio measurements by ICP-MS.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Becker, J S; Dietze, H J</p> <p>2000-09-01</p> <p>The precise and <span class="hlt">accurate</span> determination of isotope ratios by inductively coupled plasma mass spectrometry (ICP-MS) and laser ablation ICP-MS (LA-ICP-MS) is important for quite different application fields (e.g. for isotope ratio measurements of stable isotopes in nature, especially for the investigation of isotope variation in nature or age dating, for determining isotope ratios of radiogenic elements in the nuclear industry, quality assurance of fuel material, for reprocessing plants, nuclear material accounting and radioactive waste control, for tracer experiments using stable isotopes or long-lived radionuclides in biological or medical studies). Thermal ionization mass spectrometry (TIMS), which used to be the dominant <span class="hlt">analytical</span> technique for precise isotope ratio measurements, is being increasingly replaced for isotope ratio measurements by ICP-MS due to its excellent sensitivity, precision and good accuracy. Instrumental progress in ICP-MS was achieved by the introduction of the collision cell interface in order to dissociate many disturbing argon-based molecular ions, thermalize the ions and neutralize the disturbing argon ions of plasma gas (Ar+). The application of the collision cell in ICP-QMS results in a higher ion transmission, improved sensitivity and better precision of isotope ratio measurements compared to quadrupole ICP-MS without the collision cell [e.g., for 235U/238U <span class="hlt">approximately</span> 1 (10 microg x L(-1) uranium) 0.07% relative standard deviation (RSD) vs. 0.2% RSD in short-term measurements (n = 5)]. A significant instrumental improvement for ICP-MS is the multicollector device (MC-ICP-MS) in order to obtain a better precision of isotope ratio measurements (with a precision of up to 0.002%, RSD). CE- and HPLC-ICP-MS are used for the separation of isobaric interferences of long-lived radionuclides and stable isotopes by determination of spallation nuclide abundances in an irradiated tantalum target.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19860029700&hterms=2018&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3D2018','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19860029700&hterms=2018&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3D2018"><span>Error analysis of <span class="hlt">analytic</span> solutions for self-excited near-symmetric rigid bodies - A numerical study</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kia, T.; Longuski, J. M.</p> <p>1984-01-01</p> <p><span class="hlt">Analytic</span> error bounds are presented for the solutions of <span class="hlt">approximate</span> models for self-excited near-symmetric rigid bodies. The error bounds are developed for <span class="hlt">analytic</span> solutions to Euler's equations of motion. The results are applied to obtain a simplified <span class="hlt">analytic</span> solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/902887','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/902887"><span>Modeling Biodegradation and Reactive Transport: <span class="hlt">Analytical</span> and Numerical Models</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Sun, Y; Glascoe, L</p> <p></p> <p>The computational modeling of the biodegradation of contaminated groundwater systems accounting for biochemical reactions coupled to contaminant transport is a valuable tool for both the field engineer/planner with limited computational resources and the expert computational researcher less constrained by time and computer power. There exists several <span class="hlt">analytical</span> and numerical computer models that have been and are being developed to cover the practical needs put forth by users to fulfill this spectrum of computational demands. Generally, <span class="hlt">analytical</span> models provide rapid and convenient screening tools running on very limited computational power, while numerical models can provide more detailed information with consequent requirementsmore » of greater computational time and effort. While these <span class="hlt">analytical</span> and numerical computer models can provide <span class="hlt">accurate</span> and adequate information to produce defensible remediation strategies, decisions based on inadequate modeling output or on over-analysis can have costly and risky consequences. In this chapter we consider both <span class="hlt">analytical</span> and numerical modeling approaches to biodegradation and reactive transport. Both approaches are discussed and analyzed in terms of achieving bioremediation goals, recognizing that there is always a tradeoff between computational cost and the resolution of simulated systems.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvL.120t6801T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvL.120t6801T"><span>Molecular Model of a Quantum Dot Beyond the Constant Interaction <span class="hlt">Approximation</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Temirov, Ruslan; Green, Matthew F. B.; Friedrich, Niklas; Leinen, Philipp; Esat, Taner; Chmielniak, Pawel; Sarwar, Sidra; Rawson, Jeff; Kögerler, Paul; Wagner, Christian; Rohlfing, Michael; Tautz, F. Stefan</p> <p>2018-05-01</p> <p>We present a physically intuitive model of molecular quantum dots beyond the constant interaction <span class="hlt">approximation</span>. It <span class="hlt">accurately</span> describes their charging behavior and allows the extraction of important molecular properties that are otherwise experimentally inaccessible. The model is applied to data recorded with a noncontact atomic force microscope on three different molecules that act as a quantum dot when attached to the microscope tip. The results are in excellent agreement with first-principles simulations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3830866','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3830866"><span>Selecting Summary Statistics in <span class="hlt">Approximate</span> Bayesian Computation for Calibrating Stochastic Models</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Burr, Tom</p> <p>2013-01-01</p> <p><span class="hlt">Approximate</span> Bayesian computation (ABC) is an approach for using measurement data to calibrate stochastic computer models, which are common in biology applications. ABC is becoming the “go-to” option when the data and/or parameter dimension is large because it relies on user-chosen summary statistics rather than the full data and is therefore computationally feasible. One technical challenge with ABC is that the quality of the <span class="hlt">approximation</span> to the posterior distribution of model parameters depends on the user-chosen summary statistics. In this paper, the user requirement to choose effective summary statistics in order to <span class="hlt">accurately</span> estimate the posterior distribution of model parameters is investigated and illustrated by example, using a model and corresponding real data of mitochondrial DNA population dynamics. We show that for some choices of summary statistics, the posterior distribution of model parameters is closely <span class="hlt">approximated</span> and for other choices of summary statistics, the posterior distribution is not closely <span class="hlt">approximated</span>. A strategy to choose effective summary statistics is suggested in cases where the stochastic computer model can be run at many trial parameter settings, as in the example. PMID:24288668</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvA..97b2304W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvA..97b2304W"><span>Quantum <span class="hlt">approximate</span> optimization algorithm for MaxCut: A fermionic view</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang; Rieffel, Eleanor G.</p> <p>2018-02-01</p> <p>Farhi et al. recently proposed a class of quantum algorithms, the quantum <span class="hlt">approximate</span> optimization algorithm (QAOA), for <span class="hlt">approximately</span> solving combinatorial optimization problems (E. Farhi et al., arXiv:1411.4028</pub-id>; <pub-id pub-id-type="arxiv">arXiv:1412.6062</pub-id>; <pub-id pub-id-type="arxiv">arXiv:1602.07674). A level-p QAOA circuit consists of p steps; in each step a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2 p times for which these two Hamiltonians are applied are the parameters of the algorithm, which are to be optimized classically for the best performance. As p increases, parameter optimization becomes inefficient due to the curse of dimensionality. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here we <span class="hlt">analytically</span> and numerically study parameter setting for the QAOA applied to MaxCut. For the level-1 QAOA, we derive an <span class="hlt">analytical</span> expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MaxCut, the "ring of disagrees," or the one-dimensional antiferromagnetic ring, we provide an analysis for an arbitrarily high level. Using a fermionic representation, the evolution of the system under the QAOA translates into quantum control of an ensemble of independent spins. This treatment enables us to obtain <span class="hlt">analytical</span> expressions for the performance of the QAOA for any p . It also greatly simplifies the numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional submanifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24925766','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24925766"><span>L.U.St: a tool for <span class="hlt">approximated</span> maximum likelihood supertree reconstruction.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Akanni, Wasiu A; Creevey, Christopher J; Wilkinson, Mark; Pisani, Davide</p> <p>2014-06-12</p> <p>Supertrees combine disparate, partially overlapping trees to generate a synthesis that provides a high level perspective that cannot be attained from the inspection of individual phylogenies. Supertrees can be seen as meta-<span class="hlt">analytical</span> tools that can be used to make inferences based on results of previous scientific studies. Their meta-<span class="hlt">analytical</span> application has increased in popularity since it was realised that the power of statistical tests for the study of evolutionary trends critically depends on the use of taxon-dense phylogenies. Further to that, supertrees have found applications in phylogenomics where they are used to combine gene trees and recover species phylogenies based on genome-scale data sets. Here, we present the L.U.St package, a python tool for <span class="hlt">approximate</span> maximum likelihood supertree inference and illustrate its application using a genomic data set for the placental mammals. L.U.St allows the calculation of the <span class="hlt">approximate</span> likelihood of a supertree, given a set of input trees, performs heuristic searches to look for the supertree of highest likelihood, and performs statistical tests of two or more supertrees. To this end, L.U.St implements a winning sites test allowing ranking of a collection of a-priori selected hypotheses, given as a collection of input supertree topologies. It also outputs a file of input-tree-wise likelihood scores that can be used as input to CONSEL for calculation of standard tests of two trees (e.g. Kishino-Hasegawa, Shimidoara-Hasegawa and <span class="hlt">Approximately</span> Unbiased tests). This is the first fully parametric implementation of a supertree method, it has clearly understood properties, and provides several advantages over currently available supertree approaches. It is easy to implement and works on any platform that has python installed. bitBucket page - https://afro-juju@bitbucket.org/afro-juju/l.u.st.git. Davide.Pisani@bristol.ac.uk.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4129492','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4129492"><span>The Validity of Quasi-Steady-State <span class="hlt">Approximations</span> in Discrete Stochastic Simulations</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R.</p> <p>2014-01-01</p> <p>In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state <span class="hlt">approximation</span> (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an <span class="hlt">accurate</span> <span class="hlt">approximation</span> of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more <span class="hlt">accurate</span> when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more <span class="hlt">accurate</span> when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales. PMID:25099817</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PDU....19...36N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PDU....19...36N"><span>An <span class="hlt">analytical</span> approach to the CMB polarization in a spatially closed background</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Niazy, Pedram; Abbassi, Amir H.</p> <p>2018-03-01</p> <p>The scalar mode polarization of the cosmic microwave background is derived in a spatially closed universe from the Boltzmann equation using the line of sight integral method. The EE and TE multipole coefficients have been extracted <span class="hlt">analytically</span> by considering some tolerable <span class="hlt">approximations</span> such as considering the evolution of perturbation hydrodynamically and sudden transition from opacity to transparency at the time of last scattering. As the major advantage of <span class="hlt">analytic</span> expressions, CEE,ℓS and CTE,ℓ<S/SUP> explicitly show the dependencies on baryon density ΩB, matter density ΩM, curvature ΩK, primordial spectral index ns, primordial power spectrum amplitude As, Optical depth τreion, recombination width σt and recombination time tL. Using a realistic set of cosmological parameters taken from a fit to data from Planck, the closed universe EE and TE power spectrums in the scalar mode are compared with numerical results from the CAMB code and also latest observational data. The <span class="hlt">analytic</span> results agree with the numerical ones on the big and moderate scales. The peak positions are in good agreement with the numerical result on these scales while the peak heights agree with that to within 20% due to the <span class="hlt">approximations</span> have been considered for these derivations. Also, several interesting properties of CMB polarization are revealed by the <span class="hlt">analytic</span> spectra.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li class="active"><span>25</span></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_25 --> <div class="footer-extlink text-muted" style="margin-bottom:1rem; text-align:center;">Some links on this page may take you to non-federal websites. Their policies may differ from this site.</div> </div><!-- container --> <footer><a id="backToTop" href="#top"> </a><nav><a id="backToTop" href="#top"> </a><ul class="links"><a id="backToTop" href="#top"> </a><li><a id="backToTop" href="#top"></a><a href="/sitemap.html">Site Map</a></li> <li><a href="/members/index.html">Members Only</a></li> <li><a href="/website-policies.html">Website Policies</a></li> <li><a href="https://doe.responsibledisclosure.com/hc/en-us" target="_blank">Vulnerability Disclosure Program</a></li> <li><a href="/contact.html">Contact Us</a></li> </ul> <div class="small">Science.gov is maintained by the U.S. Department of Energy's <a href="https://www.osti.gov/" target="_blank">Office of Scientific and Technical Information</a>, in partnership with <a href="https://www.cendi.gov/" target="_blank">CENDI</a>.</div> </nav> </footer> <script type="text/javascript"><!-- // var lastDiv = ""; function showDiv(divName) { // hide last div if (lastDiv) { document.getElementById(lastDiv).className = "hiddenDiv"; } //if value of the box is not nothing and an object with that name exists, then change the class if (divName && document.getElementById(divName)) { document.getElementById(divName).className = "visibleDiv"; lastDiv = divName; } } //--> </script> <script> /** * Function that tracks a click on an outbound link in Google Analytics. * This function takes a valid URL string as an argument, and uses that URL string * as the event label. */ var trackOutboundLink = function(url,collectionCode) { try { h = window.open(url); setTimeout(function() { ga('send', 'event', 'topic-page-click-through', collectionCode, url); }, 1000); } catch(err){} }; </script> <!-- Google Analytics --> <script> (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'script','//www.google-analytics.com/analytics.js','ga'); ga('create', 'UA-1122789-34', 'auto'); ga('send', 'pageview'); </script> <!-- End Google Analytics --> <script> showDiv('page_1') </script> </body> </html>