NASA Astrophysics Data System (ADS)
Colalongo, Luigi; Ghittorelli, Matteo; Torricelli, Fabrizio; Kovács-Vajna, Zsolt Miklos
2015-12-01
Surface-potential-based mathematical models are among the most accurate and physically based compact models of Thin-Film Transistors (TFTs) and, in turn, of Organic Thin-Film Transistors (OTFTs), available today. However, the need for 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 enough accurate to model OTFTs and, in particular, transconductances and transcapacitances. In this paper we present an accurate and computationally efficient closed-form approximation of the surface potential, based on the Lagrange Reversion Theorem, that can be exploited in advanced surface-potential-based OTFTs and TFTs device models.
NASA Technical Reports Server (NTRS)
Schlosser, Herbert; Ferrante, John
1989-01-01
An accurate analytic expression for the nonlinear change of the volume of a solid as a function of applied pressure is of great interest in high-pressure experimentation. It is found that a two-parameter analytic expression, fits the experimental volume-change data to within a few percent over the entire experimentally attainable pressure range. Results are presented for 24 different materials including metals, ceramic semiconductors, polymers, and ionic and rare-gas solids.
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.
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.
Analytic Approximate Solution for Falkner-Skan Equation
Marinca, Bogdan
2014-01-01
This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration. PMID:24883417
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.
Analytic approximation to randomly oriented spheroid extinction
NASA Astrophysics Data System (ADS)
Evans, B. T. N.; Fournier, G. R.
1993-12-01
The estimation of electromagnetic extinction through dust or other nonspherical atmospheric aerosols and hydrosols is an essential first step in the evaluation of the performance of all electro-optic systems. Investigations were conducted to reduce the computational burden in calculating the extinction from nonspherical particles. An analytic semi-empirical approximation to the extinction efficiency Q(sub ext) for randomly oriented spheroids, based on an extension of the anomalous diffraction formula, is given and compared with the extended boundary condition or T-matrix method. This will allow for better and more general modeling of obscurants. Using this formula, Q(sub ext) can be evaluated over 10,000 times faster than with previous methods. This approximation has been verified for complex refractive indices m=n-ik, where n ranges from one to infinity and k from zero to infinity, and aspect ratios of 0.2 to 5. It is believed that the approximation is uniformly valid over all size parameters and aspect ratios. It has the correct Rayleigh, refractive index, and large particle asymptotic behaviors. The accuracy and limitations of this formula are extensively discussed.
Analytic approximate radiation effects due to Bremsstrahlung
Ben-Zvi I.
2012-02-01
The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R&D Energy Recovery Linac.
Robust Accurate Non-Invasive Analyte Monitor
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.
Approximate analytical calculations of photon geodesics in the Schwarzschild metric
NASA Astrophysics Data System (ADS)
De Falco, Vittorio; Falanga, Maurizio; Stella, Luigi
2016-10-01
We develop a method for deriving approximate analytical formulae to integrate photon geodesics in a Schwarzschild spacetime. Based on this, we derive the approximate equations for light bending and propagation delay that have been introduced empirically. We then derive for the first time an approximate analytical equation for the solid angle. We discuss the accuracy and range of applicability of the new equations and present a few simple applications of them to known astrophysical problems.
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.
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.
Approximate analytic solutions for singular non-linear oscillators
NASA Technical Reports Server (NTRS)
Bota, K. B.; Mickens, R. E.
1984-01-01
Mickens (1981, 1984) has considered analytic techniques for obtaining approximate solutions to one-dimensional nonlinear oscillatory systems x(double-dot) + x = lambda f(x, x/dot/, lambda) where lambda is a small positive parameter and f is a nonlinear polynomial function of its arguments. However, in certain cases there is interest in the analysis of physical systems for which the nonlinear function f(x, x/dot/, lambda) is singular for finite values of x or x(dot). The present investigation is concerned with the use of existing approximate analytic schemes to obtain solutions to singular nonlinear oscillatory differential equations.
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.
Analytic Approximations for the Extrapolation of Lattice Data
Masjuan, Pere
2010-12-22
We present analytic approximations of chiral SU(3) amplitudes for the extrapolation of lattice data to the physical masses and the determination of Next-to-Next-to-Leading-Order low-energy constants. Lattice data for the ratio F{sub K}/F{sub {pi}} is used to test the method.
A simple analytic approximation for dusty Stroemgren spheres
NASA Technical Reports Server (NTRS)
Petrosian, V.; Silk, J.; Field, G. B.
1972-01-01
An analytic approximation is illustrated to Stromgren's solution for H II regions which permits explicit exhibition of the effects of internal dust on the ionization structure. Far infrared observations of H II regions are accounted for in terms of true absorption by internal dust of a significant fraction of the Lyman continuum photons.
Convergence of multipoint Pade approximants of piecewise analytic functions
Buslaev, Viktor I
2013-02-28
The behaviour as n{yields}{infinity} of multipoint Pade approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Pade approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Pade approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points. Bibliography: 11 titles.
Nonlinear acoustic behavior at a caustic - An approximate analytical solution
NASA Technical Reports Server (NTRS)
Gill, P. M.; Seebass, A. R.
1975-01-01
The present paper discusses an approximate analytical solution to the nonlinear behavior of a discontinuous acoustic signal near a caustic. The Seebass transformation (1970) is refined to provide results which satisfy the governing equation to any prescribed accuracy, except across the shock wave produced by reflection of the simple wave at the caustic. The solution is approximate in the sense that the basic equation is satisfied wherever the solution is continuous but can satisfy only one of the two jump conditions at the reflected shock. The results give essential geometric features of the exact solution and provide a quantitative estimate of the strength of the so-called superboom.
Massive neutrinos in cosmology: Analytic solutions and fluid approximation
Shoji, Masatoshi; Komatsu, Eiichiro
2010-06-15
We study the evolution of linear density fluctuations of free-streaming massive neutrinos at redshift of z<1000, with an explicit justification on the use of a fluid approximation. We solve the collisionless Boltzmann equation in an Einstein de-Sitter (EdS) universe, truncating the Boltzmann hierarchy at l{sub max}=1 and 2, and compare the resulting density contrast of neutrinos {delta}{sub {nu}}{sup fluid} with that of the exact solutions of the Boltzmann equation that we derive in this paper. Roughly speaking, the fluid approximation is accurate if neutrinos were already nonrelativistic when the neutrino density fluctuation of a given wave number entered the horizon. We find that the fluid approximation is accurate at subpercent levels for massive neutrinos with m{sub {nu}>}0.05 eV at the scale of k < or approx. 1.0h Mpc{sup -1} and redshift of z<100. This result validates the use of the fluid approximation, at least for the most massive species of neutrinos suggested by the neutrino oscillation experiments. We also find that the density contrast calculated from fluid equations (i.e., continuity and Euler equations) becomes a better approximation at a lower redshift, and the accuracy can be further improved by including an anisotropic stress term in the Euler equation. The anisotropic stress term effectively increases the pressure term by a factor of 9/5.
Analytical approximations for x-ray cross sections III
Biggs, F; Lighthill, R
1988-08-01
This report updates our previous work that provided analytical approximations to cross sections for both photoelectric absorption of photons by atoms and incoherent scattering of photons by atoms. This representation is convenient for use in programmable calculators and in computer programs to evaluate these cross sections numerically. The results apply to atoms of atomic numbers between 1 and 100 and for photon energiesgreater than or equal to10 eV. The photoelectric cross sections are again approximated by four-term polynomials in reciprocal powers of the photon energy. There are now more fitting intervals, however, than were used previously. The incoherent-scattering cross sections are based on the Klein-Nishina relation, but use simpler approximate equations for efficient computer evaluation. We describe the averaging scheme for applying these atomic results to any composite material. The fitting coefficients are included in tables, and the cross sections are shown graphically. 100 graphs, 1 tab.
Approximate analytical description of the nonaffine response of amorphous solids
Zaccone, Alessio; Scossa-Romano, Enzo
2011-05-01
An approximation scheme for model disordered solids is proposed that leads to the fully analytical evaluation of the elastic constants under explicit account of the inhomogeneity (nonaffinity) of the atomic displacements. The theory is in quantitative agreement with simulations for central-force systems and predicts the vanishing of the shear modulus at the isostatic point with the linear law {mu}{approx}(z-2d), where z is the coordination number. The vanishing of rigidity at the isostatic point is shown to be a consequence of the canceling out of positive affine and negative nonaffine terms.
Lee, Ping I
2011-10-10
The purpose of this review is to provide an overview of approximate analytical solutions to the general moving boundary diffusion problems encountered during the release of a dispersed drug from matrix systems. Starting from the theoretical basis of the Higuchi equation and its subsequent improvement and refinement, available approximate analytical solutions for the more complicated cases involving heterogeneous matrix, boundary layer effect, finite release medium, surface erosion, and finite dissolution rate are also discussed. Among various modeling approaches, the pseudo-steady state assumption employed in deriving the Higuchi equation and related approximate analytical solutions appears to yield reasonably accurate results in describing the early stage release of a dispersed drug from matrices of different geometries whenever the initial drug loading (A) is much larger than the drug solubility (C(s)) in the matrix (or A≫C(s)). However, when the drug loading is not in great excess of the drug solubility (i.e. low A/C(s) values) or when the drug loading approaches the drug solubility (A→C(s)) which occurs often with drugs of high aqueous solubility, approximate analytical solutions based on the pseudo-steady state assumption tend to fail, with the Higuchi equation for planar geometry exhibiting a 11.38% error as compared with the exact solution. In contrast, approximate analytical solutions to this problem without making the pseudo-steady state assumption, based on either the double-integration refinement of the heat balance integral method or the direct simplification of available exact analytical solutions, show close agreement with the exact solutions in different geometries, particularly in the case of low A/C(s) values or drug loading approaching the drug solubility (A→C(s)). However, the double-integration heat balance integral approach is generally more useful in obtaining approximate analytical solutions especially when exact solutions are not
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.
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).
Approximate explicit analytic solution of the Elenbaas-Heller equation
NASA Astrophysics Data System (ADS)
Liao, Meng-Ran; Li, Hui; Xia, Wei-Dong
2016-08-01
The Elenbaas-Heller equation describing the temperature field of a cylindrically symmetrical non-radiative electric arc has been solved, and approximate explicit analytic solutions are obtained. The radial distributions of the heat-flux potential and the electrical conductivity have been figured out briefly by using some special simplification techniques. The relations between both the core heat-flux potential and the electric field with the total arc current have also been given in several easy explicit formulas. Besides, the special voltage-ampere characteristic of electric arcs is explained intuitionally by a simple expression involving the Lambert W-function. The analyses also provide a preliminary estimation of the Joule heating per unit length, which has been verified in previous investigations. Helium arc is used to examine the theories, and the results agree well with the numerical computations.
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
Bruce, S D; Higinbotham, J; Marshall, I; Beswick, P H
2000-01-01
The approximation of the Voigt line shape by the linear summation of Lorentzian and Gaussian line shapes of equal width is well documented and has proved to be a useful function for modeling in vivo (1)H NMR spectra. We show that the error in determining peak areas is less than 0.72% over a range of simulated Voigt line shapes. Previous work has concentrated on empirical analysis of the Voigt function, yielding accurate expressions for recovering the intrinsic Lorentzian component of simulated line shapes. In this work, an analytical approach to the approximation is presented which is valid for the range of Voigt line shapes in which either the Lorentzian or Gaussian component is dominant. With an empirical analysis of the approximation, the direct recovery of T(2) values from simulated line shapes is also discussed. PMID:10617435
NASA Astrophysics Data System (ADS)
Lima, F. M. S.
2009-11-01
In a previous work, O'Connell (Phys. Teach. 40, 24 (2002)) investigated the time dependence of the tension in the string of a simple pendulum oscillating within the small-angle regime. In spite of the approximation sin θ ≈ θ being accurate only for amplitudes below 7°, his experimental results are for a pendulum oscillating with an amplitude of about 18°, therefore beyond the small-angle regime. This lapse may also be found in some textbooks, laboratory manuals and internet. By noting that the exact analytical solution for this problem involves the so-called Jacobi elliptic functions, which are unknown to most students (even instructors), I take into account a sinusoidal approximate solution for the pendulum equation I introduced in a recent work (Eur. J. Phys. 29 1091 (2008)) for deriving a simple trigonometric approximation for the tension valid for all possible amplitudes. This approximation is compared to both the O'Connell and the exact results, revealing that it is accurate enough for analysing large-angle pendulum experiments.
An accurate two-phase approximate solution to the acute viral infection model
Perelson, Alan S
2009-01-01
During an acute viral infection, virus levels rise, reach a peak and then decline. Data and numerical solutions suggest the growth and decay phases are linear on a log scale. While viral dynamic models are typically nonlinear with analytical solutions difficult to obtain, the exponential nature of the solutions suggests approximations can be found. We derive a two-phase approximate solution to the target cell limited influenza model and illustrate the accuracy using data and previously established parameter values of six patients infected with influenza A. For one patient, the subsequent fall in virus concentration was not consistent with our predictions during the decay phase and an alternate approximation is derived. We find expressions for the rate and length of initial viral growth in terms of the parameters, the extent each parameter is involved in viral peaks, and the single parameter responsible for virus decay. We discuss applications of this analysis in antiviral treatments and investigating host and virus heterogeneities.
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- and 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.
Simple accurate approximations for the optical properties of metallic nanospheres and nanoshells.
Schebarchov, Dmitri; Auguié, Baptiste; Le Ru, Eric C
2013-03-28
This work aims to provide simple and accurate closed-form approximations to predict the scattering and absorption spectra of metallic nanospheres and nanoshells supporting localised surface plasmon resonances. Particular attention is given to the validity and accuracy of these expressions in the range of nanoparticle sizes relevant to plasmonics, typically limited to around 100 nm in diameter. Using recent results on the rigorous radiative correction of electrostatic solutions, we propose a new set of long-wavelength polarizability approximations for both nanospheres and nanoshells. The improvement offered by these expressions is demonstrated with direct comparisons to other approximations previously obtained in the literature, and their absolute accuracy is tested against the exact Mie theory. PMID:23358525
Fast and accurate read mapping with approximate seeds and multiple backtracking
Siragusa, Enrico; Weese, David; Reinert, Knut
2013-01-01
We present Masai, a read mapper representing the state-of-the-art in terms of speed and accuracy. Our tool is an order of magnitude faster than RazerS 3 and mrFAST, 2–4 times faster and more accurate than Bowtie 2 and BWA. The novelties of our read mapper are filtration with approximate seeds and a method for multiple backtracking. Approximate seeds, compared with exact seeds, increase filtration specificity while preserving sensitivity. Multiple backtracking amortizes the cost of searching a large set of seeds by taking advantage of the repetitiveness of next-generation sequencing data. Combined together, these two methods significantly speed up approximate search on genomic data sets. Masai is implemented in C++ using the SeqAn library. The source code is distributed under the BSD license and binaries for Linux, Mac OS X and Windows can be freely downloaded from http://www.seqan.de/projects/masai. PMID:23358824
NASA Astrophysics Data System (ADS)
Lin, Yezhi; Liu, Yinping; Li, Zhibin
2012-01-01
The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. Program summaryProgram title: NAPA Catalogue identifier: AEJZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJZ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4060 No. of bytes in distributed program, including test data, etc.: 113 498 Distribution format: tar.gz Programming language: MAPLE R13 Computer: PC Operating system: Windows XP/7 RAM: 2 Gbytes Classification: 4.3 Nature of problem: Solve nonlinear differential equations with initial conditions. Solution method: Adomian decomposition method and Padé technique. Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.
New analytical approximations for the liquid rise in a capillary tube
NASA Astrophysics Data System (ADS)
González-Santander, J. L.; Martín, G.
2015-04-01
We present the ordinary differential equation (ODE) that governs the motion of a liquid rising in a capillary tube in such a way that we can easily derive the principal analytical approximations given in the literature. From this presentation, the numerical solution of the liquid rise over time could be computed very quickly and easily. Furthermore, we derive other analytical approximations not given in the literature, providing a mathematical justification for the cases in which such approximations are good. Some of the approximations found fit the experimental data better than the analytical approximations given in the literature.
Zonal Flows Below the Sun's Convection: Analytic Approximation
NASA Technical Reports Server (NTRS)
Wolff, Charles L.; Mayr, Hans G.
2004-01-01
We have derived a simple analytic solution showing how the Sun's global oscillations (g-modes) can drive east-west flows at low latitude deep inside the Sun. This flow is analogous to the Quasi Biennial Oscillation in the Earth s upper atmosphere. It has an observed period of 1.3 years in the solar case but its cause was not known until we published an explanation in a Letter to the Editor a few months ago. Now we give full details of the model and show how it can be used to limit the range of g-modes that can be actively driving the reversing flows. A nonlinear feedback feature of the model is that the flow itself creates the turbulent dissipation that extracts momentum from the g-modes that, in turn, drives the flow.
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
Accurate response surface approximations for weight equations based on structural optimization
NASA Astrophysics Data System (ADS)
Papila, Melih
Accurate weight prediction methods are vitally important for aircraft design optimization. Therefore, designers seek weight prediction techniques with low computational cost and high accuracy, and usually require a compromise between the two. The compromise can be achieved by combining stress analysis and response surface (RS) methodology. While stress analysis provides accurate weight information, RS techniques help to transmit effectively this information to the optimization procedure. The focus of this dissertation is structural weight equations in the form of RS approximations and their accuracy when fitted to results of structural optimizations that are based on finite element analyses. Use of RS methodology filters out the numerical noise in structural optimization results and provides a smooth weight function that can easily be used in gradient-based configuration optimization. In engineering applications RS approximations of low order polynomials are widely used, but the weight may not be modeled well by low-order polynomials, leading to bias errors. In addition, some structural optimization results may have high-amplitude errors (outliers) that may severely affect the accuracy of the weight equation. Statistical techniques associated with RS methodology are sought in order to deal with these two difficulties: (1) high-amplitude numerical noise (outliers) and (2) approximation model inadequacy. The investigation starts with reducing approximation error by identifying and repairing outliers. A potential reason for outliers in optimization results is premature convergence, and outliers of such nature may be corrected by employing different convergence settings. It is demonstrated that outlier repair can lead to accuracy improvements over the more standard approach of removing outliers. The adequacy of approximation is then studied by a modified lack-of-fit approach, and RS errors due to the approximation model are reduced by using higher order polynomials. In
Approximate analytical solutions for excitation and propagation in cardiac tissue
NASA Astrophysics Data System (ADS)
Greene, D'Artagnan; Shiferaw, Yohannes
2015-04-01
It is well known that a variety of cardiac arrhythmias are initiated by a focal excitation in heart tissue. At the single cell level these currents are typically induced by intracellular processes such as spontaneous calcium release (SCR). However, it is not understood how the size and morphology of these focal excitations are related to the electrophysiological properties of cardiac cells. In this paper a detailed physiologically based ionic model is analyzed by projecting the excitation dynamics to a reduced one-dimensional parameter space. Based on this analysis we show that the inward current required for an excitation to occur is largely dictated by the voltage dependence of the inward rectifier potassium current (IK 1) , and is insensitive to the detailed properties of the sodium current. We derive an analytical expression relating the size of a stimulus and the critical current required to induce a propagating action potential (AP), and argue that this relationship determines the necessary number of cells that must undergo SCR in order to induce ectopic activity in cardiac tissue. Finally, we show that, once a focal excitation begins to propagate, its propagation characteristics, such as the conduction velocity and the critical radius for propagation, are largely determined by the sodium and gap junction currents with a substantially lesser effect due to repolarizing potassium currents. These results reveal the relationship between ion channel properties and important tissue scale processes such as excitation and propagation.
Accurate and approximate calculations of Raman scattering in the atmosphere of Neptune
NASA Astrophysics Data System (ADS)
Sromovsky, L. A.
2005-01-01
Raman scattering by H 2 in Neptune's atmosphere has significant effects on its reflectivity for λ<0.5 μm, producing baseline decreases of ˜20% in a clear atmosphere and ˜10% in a hazy atmosphere. However, few accurate Raman calculations are carried out because of their complexity and computational costs. Here we present the first radiation transfer algorithm that includes both polarization and Raman scattering and facilitates computation of spatially resolved spectra. New calculations show that Cochran and Trafton's (1978, Astrophys. J. 219, 756-762) suggestion that light reflected in the deep CH 4 bands is mainly Raman scattered is not valid for current estimates of the CH 4 vertical distribution, which implies only a 4% Raman contribution. Comparisons with IUE, HST, and groundbased observations confirm that high altitude haze absorption is reducing Neptune's geometric albedo by ˜6% in the 0.22-0.26 μm range and by ˜13% in the 0.35-0.45 μm range. A sample haze model with 0.2 optical depths of 0.2-μm radius particles between 0.1 and 0.8 bars fits reasonably well, but is not a unique solution. We used accurate calculations to evaluate several approximations of Raman scattering. The Karkoschka (1994, Icarus 111, 174-192) method of applying Raman corrections to calculated spectra and removing Raman effects from observed spectra is shown to have limited applicability and to undercorrect the depths of weak CH 4 absorption bands. The relatively large Q-branch contribution observed by Karkoschka is shown to be consistent with current estimates of Raman cross-sections. The Wallace (1972, Astrophys. J. 176, 249-257) approximation, produces geometric albedo ˜5% low as originally proposed, but can be made much more accurate by including a scattering contribution from the vibrational transition. The original Pollack et al. (1986, Icarus 65, 442-466) approximation is inaccurate and unstable, but can be greatly improved by several simple modifications. A new
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.
Shu, Yu-Chen; Chern, I-Liang; Chang, Chien C.
2014-10-15
Most elliptic interface solvers become complicated for complex interface problems at those “exceptional points” where there are not enough neighboring interior points for high order interpolation. Such complication increases especially in three dimensions. Usually, the solvers are thus reduced to low order accuracy. In this paper, we classify these exceptional points and propose two recipes to maintain order of accuracy there, aiming at improving the previous coupling interface method [26]. Yet the idea is also applicable to other interface solvers. The main idea is to have at least first order approximations for second order derivatives at those exceptional points. Recipe 1 is to use the finite difference approximation for the second order derivatives at a nearby interior grid point, whenever this is possible. Recipe 2 is to flip domain signatures and introduce a ghost state so that a second-order method can be applied. This ghost state is a smooth extension of the solution at the exceptional point from the other side of the interface. The original state is recovered by a post-processing using nearby states and jump conditions. The choice of recipes is determined by a classification scheme of the exceptional points. The method renders the solution and its gradient uniformly second-order accurate in the entire computed domain. Numerical examples are provided to illustrate the second order accuracy of the presently proposed method in approximating the gradients of the original states for some complex interfaces which we had tested previous in two and three dimensions, and a real molecule ( (1D63)) which is double-helix shape and composed of hundreds of atoms.
Approximate likelihood-ratio test for branches: A fast, accurate, and powerful alternative.
Anisimova, Maria; Gascuel, Olivier
2006-08-01
We revisit statistical tests for branches of evolutionary trees reconstructed upon molecular data. A new, fast, approximate likelihood-ratio test (aLRT) for branches is presented here as a competitive alternative to nonparametric bootstrap and Bayesian estimation of branch support. The aLRT is based on the idea of the conventional LRT, with the null hypothesis corresponding to the assumption that the inferred branch has length 0. We show that the LRT statistic is asymptotically distributed as a maximum of three random variables drawn from the chi(0)2 + chi(1)2 distribution. The new aLRT of interior branch uses this distribution for significance testing, but the test statistic is approximated in a slightly conservative but practical way as 2(l1- l2), i.e., double the difference between the maximum log-likelihood values corresponding to the best tree and the second best topological arrangement around the branch of interest. Such a test is fast because the log-likelihood value l2 is computed by optimizing only over the branch of interest and the four adjacent branches, whereas other parameters are fixed at their optimal values corresponding to the best ML tree. The performance of the new test was studied on simulated 4-, 12-, and 100-taxon data sets with sequences of different lengths. The aLRT is shown to be accurate, powerful, and robust to certain violations of model assumptions. The aLRT is implemented within the algorithm used by the recent fast maximum likelihood tree estimation program PHYML (Guindon and Gascuel, 2003).
Fast and accurate approximate inference of transcript expression from RNA-seq data
Hensman, James; Papastamoulis, Panagiotis; Glaus, Peter; Honkela, Antti; Rattray, Magnus
2015-01-01
Motivation: Assigning RNA-seq reads to their transcript of origin is a fundamental task in transcript expression estimation. Where ambiguities in assignments exist due to transcripts sharing sequence, e.g. alternative isoforms or alleles, the problem can be solved through probabilistic inference. Bayesian methods have been shown to provide accurate transcript abundance estimates compared with competing methods. However, exact Bayesian inference is intractable and approximate methods such as Markov chain Monte Carlo and Variational Bayes (VB) are typically used. While providing a high degree of accuracy and modelling flexibility, standard implementations can be prohibitively slow for large datasets and complex transcriptome annotations. Results: We propose a novel approximate inference scheme based on VB and apply it to an existing model of transcript expression inference from RNA-seq data. Recent advances in VB algorithmics are used to improve the convergence of the algorithm beyond the standard Variational Bayes Expectation Maximization algorithm. We apply our algorithm to simulated and biological datasets, demonstrating a significant increase in speed with only very small loss in accuracy of expression level estimation. We carry out a comparative study against seven popular alternative methods and demonstrate that our new algorithm provides excellent accuracy and inter-replicate consistency while remaining competitive in computation time. Availability and implementation: The methods were implemented in R and C++, and are available as part of the BitSeq project at github.com/BitSeq. The method is also available through the BitSeq Bioconductor package. The source code to reproduce all simulation results can be accessed via github.com/BitSeq/BitSeqVB_benchmarking. Contact: james.hensman@sheffield.ac.uk or panagiotis.papastamoulis@manchester.ac.uk or Magnus.Rattray@manchester.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online
Development of highly accurate approximate scheme for computing the charge transfer integral.
Pershin, Anton; Szalay, Péter G
2015-08-21
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, it 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. PMID:26298117
Development of highly accurate approximate scheme for computing the charge transfer integral
Pershin, Anton; Szalay, Péter G.
2015-08-21
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, it 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.
Efficient yet accurate approximations for ab initio calculations of alcohol cluster thermochemistry.
Umer, Muhammad; Kopp, Wassja A; Leonhard, Kai
2015-12-01
We have calculated the binding enthalpies and entropies of gas phase alcohol clusters from ethanol to 1-decanol. In addition to the monomers, we have investigated dimers, tetramers, and pentamers. Geometries have been obtained at the B3LYP/TZVP level and single point energy calculations have been performed with the Resolution of the Identity-MP2 (RIMP2) method and basis set limit extrapolation using aug-cc-pVTZ and aug-cc-pVQZ basis sets. Thermochemistry is calculated with decoupled hindered rotor treatment for large amplitude motions. The results show three points: First, it is more accurate to transfer the rigid-rotor harmonic oscillator entropies from propanol to longer alcohols than to compute them with an ultra-fine grid and tight geometry convergence criteria. Second, the computational effort can be reduced considerably by using dimerization energies of longer alcohols at density functional theory (B3LYP) level plus a RIMP2 correction obtained from 1-propanol. This approximation yields results almost with the same accuracy as RIMP2 - both methods differ for 1-decanol only 0.4 kJ/mol. Third, the entropy of dimerization including the hindered rotation contribution is converged at 1-propanol with respect to chain length. This allows for a transfer of hindered rotation contributions from smaller alcohols to longer ones which reduces the required computational and man power considerably. PMID:26646881
Efficient yet accurate approximations for ab initio calculations of alcohol cluster thermochemistry
NASA Astrophysics Data System (ADS)
Umer, Muhammad; Kopp, Wassja A.; Leonhard, Kai
2015-12-01
We have calculated the binding enthalpies and entropies of gas phase alcohol clusters from ethanol to 1-decanol. In addition to the monomers, we have investigated dimers, tetramers, and pentamers. Geometries have been obtained at the B3LYP/TZVP level and single point energy calculations have been performed with the Resolution of the Identity-MP2 (RIMP2) method and basis set limit extrapolation using aug-cc-pVTZ and aug-cc-pVQZ basis sets. Thermochemistry is calculated with decoupled hindered rotor treatment for large amplitude motions. The results show three points: First, it is more accurate to transfer the rigid-rotor harmonic oscillator entropies from propanol to longer alcohols than to compute them with an ultra-fine grid and tight geometry convergence criteria. Second, the computational effort can be reduced considerably by using dimerization energies of longer alcohols at density functional theory (B3LYP) level plus a RIMP2 correction obtained from 1-propanol. This approximation yields results almost with the same accuracy as RIMP2 — both methods differ for 1-decanol only 0.4 kJ/mol. Third, the entropy of dimerization including the hindered rotation contribution is converged at 1-propanol with respect to chain length. This allows for a transfer of hindered rotation contributions from smaller alcohols to longer ones which reduces the required computational and man power considerably.
Are Quasi-Steady-State Approximated Models Suitable for Quantifying Intrinsic Noise Accurately?
Sengupta, Dola; Kar, Sandip
2015-01-01
Large gene regulatory networks (GRN) are often modeled with quasi-steady-state approximation (QSSA) to reduce the huge computational time required for intrinsic noise quantification using Gillespie stochastic simulation algorithm (SSA). However, the question still remains whether the stochastic QSSA model measures the intrinsic noise as accurately as the SSA performed for a detailed mechanistic model or not? To address this issue, we have constructed mechanistic and QSSA models for few frequently observed GRNs exhibiting switching behavior and performed stochastic simulations with them. Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN. The extent of accuracy level achieved by the stochastic QSSA model calculations will depend on the level of bursting frequency generated due to the absolute value of the half-life of either mRNA or protein or for both the species. For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives. Further, we have clearly demonstrated that the abundance levels of mRNA and protein hardly matter for such comparison between QSSA and mechanistic models. Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature. PMID:26327626
Amore, Paolo; Fernández, Francisco M
2013-02-28
We analyze the Rayleigh equation for the collapse of an empty bubble and provide an explanation for some recent analytical approximations to the model. We derive the form of the singularity at the second boundary point and discuss the convergence of the approximants. We also give a rigorous proof of the asymptotic behavior of the coefficients of the power series that are the basis for the approximate expressions.
A transformed analytical model for thermal noise of FinFET based on fringing field approximation
NASA Astrophysics Data System (ADS)
Madhulika Sharma, Savitesh; Dasgupta, S.; Kartikeyant, M. V.
2016-09-01
This paper delineates the effect of nonplanar structure of FinFETs on noise performance. We demonstrate the thermal noise analytical model that has been inferred by taking into account the presence of an additional inverted region in the extended (underlap) S/D region due to finite gate electrode thickness. Noise investigation includes the effects of source drain resistances which become significant as channel length becomes shorter. In this paper, we evaluate the additional noise caused by three dimensional (3-D) structure of the single fin device and then extended analysis of the multi-fin and multi-fingers structure. The addition of fringe field increases its minimum noise figure and noise resistance of approximately 1 dB and 100 Ω respectively and optimum admittance increases to 5.45 mƱ at 20 GHz for a device operating under saturation region. Hence, our transformed model plays a significant function in evaluation of accurate noise performance at circuit level. Project supported in part by the All India Council for Technical Education (AICTE).
Barbati, Alexander C; Kirby, Brian J
2016-07-01
We derive an approximate analytical representation of the conductivity for a 1D system with porous and charged layers grafted onto parallel plates. Our theory improves on prior work by developing approximate analytical expressions applicable over an arbitrary range of potentials, both large and small as compared to the thermal voltage (RTF). Further, we describe these results in a framework of simplifying nondimensional parameters, indicating the relative dominance of various physicochemical processes. We demonstrate the efficacy of our approximate expression with comparisons to numerical representations of the exact analytical conductivity. Finally, we utilize this conductivity expression, in concert with other components of the electrokinetic coupling matrix, to describe the streaming potential and electroviscous effect in systems with porous and charged layers.
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.
Analytical approximate solution of the cooling problem by Adomian decomposition method
NASA Astrophysics Data System (ADS)
Alizadeh, Ebrahim; Sedighi, Kurosh; Farhadi, Mousa; Ebrahimi-Kebria, H. R.
2009-02-01
The Adomian decomposition method (ADM) can provide analytical approximation or approximated solution to a rather wide class of nonlinear (and stochastic) equations without linearization, perturbation, closure approximation, or discretization methods. In the present work, ADM is employed to solve the momentum and energy equations for laminar boundary layer flow over flat plate at zero incidences with neglecting the frictional heating. A trial and error strategy has been used to obtain the constant coefficient in the approximated solution. ADM provides an analytical solution in the form of an infinite power series. The effect of Adomian polynomial terms is considered and shows that the accuracy of results is increased with the increasing of Adomian polynomial terms. The velocity and thermal profiles on the boundary layer are calculated. Also the effect of the Prandtl number on the thermal boundary layer is obtained. Results show ADM can solve the nonlinear differential equations with negligible error compared to the exact solution.
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.
NASA Astrophysics Data System (ADS)
Gu, S.
2016-08-01
Despite its low accuracy and consistency, growing degree days (GDD) has been widely used to approximate growing heat summation (GHS) for regional classification and phenological prediction. GDD is usually calculated from the mean of daily minimum and maximum temperatures (GDDmm) above a growing base temperature ( T gb). To determine approximation errors and accuracy, daily and cumulative GDDmm was compared to GDD based on daily average temperature (GDDavg), growing degree hours (GDH) based on hourly temperatures, and growing degree minutes (GDM) based on minute-by-minute temperatures. Finite error, due to the difference between measured and true temperatures above T gb is large in GDDmm but is negligible in GDDavg, GDH, and GDM, depending only upon the number of measured temperatures used for daily approximation. Hidden negative error, due to the temperatures below T gb when being averaged for approximation intervals larger than measuring interval, is large in GDDmm and GDDavg but is negligible in GDH and GDM. Both GDH and GDM improve GHS approximation accuracy over GDDmm or GDDavg by summation of multiple integration rectangles to reduce both finite and hidden negative errors. GDH is proposed as the standardized GHS approximation protocol, providing adequate accuracy and high precision independent upon T gb while requiring simple data recording and processing.
Barlow, Nathaniel S.; Schultz, Andrew J. Kofke, David A.; Weinstein, Steven J.
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.
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.
NASA Astrophysics Data System (ADS)
Döntgen, M.
2016-09-01
Energy-level densities are key for obtaining various chemical properties. In chemical kinetics, energy-level densities are used to predict thermochemistry and microscopic reaction rates. Here, an analytic energy-level density formulation is derived using inverse Laplace transformation of harmonic oscillator partition functions. Anharmonic contributions to the energy-level density are considered approximately using a literature model for the transition from harmonic to free motions. The present analytic energy-level density formulation for rigid rotor-harmonic oscillator systems is validated against the well-studied CO+O˙ H system. The approximate hindered rotor energy-level density corrections are validated against the well-studied H2O2 system. The presented analytic energy-level density formulation gives a basis for developing novel numerical simulation schemes for chemical processes.
NASA Astrophysics Data System (ADS)
Brody, Jed; Rohatgi, Ajeet
2001-09-01
New analytical equations are derived to approximate the effective surface recombination velocity ( Seff) on p-type silicon for three different cases: low-level injection (LLI) with surface hole concentration ( ps) much greater than surface electron concentration ( ns) and with silicon charge ( QSi) due primarily to ionized acceptors, LLI with ns≫ ps and QSi due primarily to ionized acceptors, and high-level injection with ns≫ ps and QSi due primarily to mobile electrons. The three new equations predict the dependence of Seff on individual parameters such as injection level ( Δn), doping level ( NA), and fixed dielectric charge ( Qf). The new equations complement a previously derived result (for LLI with ns≫ ps and QSi due primarily to mobile electrons) and together allow reasonable explanations to be given for all sections of all Seff vs. Δn and Seff vs. NA curves generated by a quasi-exact numerical method. The analytical approximations are compared with the full numerical solutions. Under appropriate conditions, the analytical approximations agree with the numerical solutions within a factor of 3. Guided by the analytical approximations, numerical solutions are fitted to two sets of experimental data: the injection level dependence of Seff for an oxide-passivated wafer; and the doping dependence of Seff for wafers passivated by plasma-enhanced chemical vapor deposited nitride (SiN x), conventional furnace oxide (CFO), and the SiN x/CFO stack. The SiN x/CFO stack not only provides surface passivation that is superior to either dielectric alone; it is also less doping dependent. The analytical approximations indicate that this suppressed doping dependence could be due to a lower interface state density or a higher fixed dielectric charge ( Qf).
Lim, C. W.; Wu, B. S.; He, L. H.
2001-12-01
A novel approach is presented for obtaining approximate analytical expressions for the dispersion relation of periodic wavetrains in the nonlinear Klein-Gordon equation with even potential function. By coupling linearization of the governing equation with the method of harmonic balance, we establish two general analytical approximate formulas for the dispersion relation, which depends on the amplitude of the periodic wavetrain. These formulas are valid for small as well as large amplitude of the wavetrain. They are also applicable to the large amplitude regime, which the conventional perturbation method fails to provide any solution, of the nonlinear system under study. Three examples are demonstrated to illustrate the excellent approximate solutions of the proposed formulas with respect to the exact solutions of the dispersion relation. (c) 2001 American Institute of Physics.
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.
Li, Rui; Ye, Hongfei; Zhang, Weisheng; Ma, Guojun; Su, Yewang
2015-01-01
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. PMID:26510769
A method for the accurate and smooth approximation of standard thermodynamic functions
NASA Astrophysics Data System (ADS)
Coufal, O.
2013-01-01
A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program summaryProgram title:SmoothSTF Catalogue identifier: AENH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 131965 Distribution format: tar.gz Programming language: C++. Computer: Any computer with gcc version 4.3.2 compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed, see http://gcc.gnu.org/install/specific.html. RAM: 256 MB are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are
Jenkinson, Garrett; Goutsias, John
2013-05-28
The master equation is used extensively to model chemical reaction systems with stochastic dynamics. However, and despite its phenomenological simplicity, it is not in general possible to compute the solution of this equation. Drawing exact samples from the master equation is possible, but can be computationally demanding, especially when estimating high-order statistical summaries or joint probability distributions. As a consequence, one often relies on analytical approximations to the solution of the master equation or on computational techniques that draw approximative samples from this equation. Unfortunately, it is not in general possible to check whether a particular approximation scheme is valid. The main objective of this paper is to develop an effective methodology to address this problem based on statistical hypothesis testing. By drawing a moderate number of samples from the master equation, the proposed techniques use the well-known Kolmogorov-Smirnov statistic to reject the validity of a given approximation method or accept it with a certain level of confidence. Our approach is general enough to deal with any master equation and can be used to test the validity of any analytical approximation method or any approximative sampling technique of interest. A number of examples, based on the Schlögl model of chemistry and the SIR model of epidemiology, clearly illustrate the effectiveness and potential of the proposed statistical framework.
NASA Astrophysics Data System (ADS)
Hosen, Md. Alal; Chowdhury, M. S. H.; Ali, Mohammad Yeakub; Ismail, Ahmad Faris
In the present paper, a novel analytical approximation technique has been proposed based on the energy balance method (EBM) to obtain approximate periodic solutions for the focus generalized highly nonlinear oscillators. The expressions of the natural frequency-amplitude relationship are obtained using a novel analytical way. The accuracy of the proposed method is investigated on three benchmark oscillatory problems, namely, the simple relativistic oscillator, the stretched elastic wire oscillator (with a mass attached to its midpoint) and the Duffing-relativistic oscillator. For an initial oscillation amplitude A0 = 100, the maximal relative errors of natural frequency found in three oscillators are 2.1637%, 0.0001% and 1.201%, respectively, which are much lower than the errors found using the existing methods. It is highly remarkable that an excellent accuracy of the approximate natural frequency has been found which is valid for the whole range of large values of oscillation amplitude as compared with the exact ones. Very simple solution procedure and high accuracy that is found in three benchmark problems reveal the novelty, reliability and wider applicability of the proposed analytical approximation technique.
Prasher, Ravi; Tong, Tao; Majumdar, Arun
2008-01-01
We introduce simple approximate analytical models for phonon specific heat and ballistic thermal conductance of nanowires. The analytical model is in excellent agreement with the detailed numerical calculations based on the solution of the elastic wave equation and is also in good agreement with the ballistic thermal conductance data by Schwab et al. (Nature 2000, 404, 974). Finally, we propose a demarcating criterion in terms of temperature, dimension, and material properties to capture the dimensional crossover from a three-dimensional (3D) bulk system to a one-dimensional (1D) system.
Highly accurate analytical energy of a two-dimensional exciton in a constant magnetic field
NASA Astrophysics Data System (ADS)
Hoang, Ngoc-Tram D.; Nguyen, Duy-Anh P.; Hoang, Van-Hung; Le, Van-Hoang
2016-08-01
Explicit expressions are given for analytically describing the dependence of the energy of a two-dimensional exciton on magnetic field intensity. These expressions are highly accurate with the precision of up to three decimal places for the whole range of the magnetic field intensity. The results are shown for the ground state and some excited states; moreover, we have all formulae to obtain similar expressions of any excited state. Analysis of numerical results shows that the precision of three decimal places is maintained for the excited states with the principal quantum number of up to n=100.
Accurate Analytic Results for the Steady State Distribution of the Eigen Model
NASA Astrophysics Data System (ADS)
Huang, Guan-Rong; Saakian, David B.; Hu, Chin-Kun
2016-04-01
Eigen model of molecular evolution is popular in studying complex biological and biomedical systems. Using the Hamilton-Jacobi equation method, we have calculated analytic equations for the steady state distribution of the Eigen model with a relative accuracy of O(1/N), where N is the length of genome. Our results can be applied for the case of small genome length N, as well as the cases where the direct numerics can not give accurate result, e.g., the tail of distribution.
NASA Astrophysics Data System (ADS)
Lin, Yezhi; Liu, Yinping; Li, Zhibin
2013-01-01
The Adomian decomposition method (ADM) is one of the most effective methods to construct analytic approximate solutions for nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, Rach (2008) [22], the Adomian decomposition method and the Padé approximants technique, a new algorithm is proposed to construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore, a MAPLE software package is developed to implement this new algorithm, which is user-friendly and efficient. One only needs to input the system equation, initial or boundary conditions and several necessary parameters, then our package will automatically deliver the analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for non-smooth initial value problems. Our package provides a helpful and easy-to-use tool in science and engineering simulations. Program summaryProgram title: ADMP Catalogue identifier: AENE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12011 No. of bytes in distributed program, including test data, etc.: 575551 Distribution format: tar.gz Programming language: MAPLE R15. Computer: PCs. Operating system: Windows XP/7. RAM: 2 Gbytes Classification: 4.3. Nature of problem: Constructing analytic approximate solutions of nonlinear fractional differential equations with initial or boundary conditions. Non-smooth initial value problems can be solved by this program. Solution method: Based on the new definition of the Adomian polynomials [1], the Adomian decomposition method and the Pad
Marelli, Damián; Baumgartner, Robert; Majdak, Piotr
2015-01-01
Head-related transfer functions (HRTFs) describe the acoustic filtering of incoming sounds by the human morphology and are essential for listeners to localize sound sources in virtual auditory displays. Since rendering complex virtual scenes is computationally demanding, we propose four algorithms for efficiently representing HRTFs in subbands, i.e., as an analysis filterbank (FB) followed by a transfer matrix and a synthesis FB. All four algorithms use sparse approximation procedures to minimize the computational complexity while maintaining perceptually relevant HRTF properties. The first two algorithms separately optimize the complexity of the transfer matrix associated to each HRTF for fixed FBs. The other two algorithms jointly optimize the FBs and transfer matrices for complete HRTF sets by two variants. The first variant aims at minimizing the complexity of the transfer matrices, while the second one does it for the FBs. Numerical experiments investigate the latency-complexity trade-off and show that the proposed methods offer significant computational savings when compared with other available approaches. Psychoacoustic localization experiments were modeled and conducted to find a reasonable approximation tolerance so that no significant localization performance degradation was introduced by the subband representation. PMID:26681930
NASA Astrophysics Data System (ADS)
Lin, Xue-lei; Lu, Xin; Ng, Micheal K.; Sun, Hai-Wei
2016-10-01
A fast accurate approximation method with multigrid solver is proposed to solve a two-dimensional fractional sub-diffusion equation. Using the finite difference discretization of fractional time derivative, a block lower triangular Toeplitz matrix is obtained where each main diagonal block contains a two-dimensional matrix for the Laplacian operator. Our idea is to make use of the block ɛ-circulant approximation via fast Fourier transforms, so that the resulting task is to solve a block diagonal system, where each diagonal block matrix is the sum of a complex scalar times the identity matrix and a Laplacian matrix. We show that the accuracy of the approximation scheme is of O (ɛ). Because of the special diagonal block structure, we employ the multigrid method to solve the resulting linear systems. The convergence of the multigrid method is studied. Numerical examples are presented to illustrate the accuracy of the proposed approximation scheme and the efficiency of the proposed solver.
Analytic solutions for the approximated 1-D Monge-Kantorovich mass transfer problems
NASA Astrophysics Data System (ADS)
Lu, Xiaojun; Lv, Xiaofen
2016-10-01
This paper mainly investigates the approximation of a global maximizer of the 1-D Monge-Kantorovich mass transfer problem through the approach of nonlinear differential equations with Dirichlet boundary. Using an approximation mechanism, the primal maximization problem can be transformed into a sequence of minimization problems. By applying the canonical duality theory, one is able to derive a sequence of analytic solutions for the minimization problems. In the final analysis, the convergence of the sequence to a global maximizer of the primal Monge-Kantorovich problem will be demonstrated.
Construction of approximate analytical solutions to a new class of non-linear oscillator equation
NASA Technical Reports Server (NTRS)
Mickens, R. E.; Oyedeji, K.
1985-01-01
The principle of harmonic balance is invoked in the development of an approximate analytic model for a class of nonlinear oscillators typified by a mass attached to a stretched wire. By assuming that harmonic balance will hold, solutions are devised for a steady state limit cycle and/or limit point motion. A method of slowly varying amplitudes then allows derivation of approximate solutions by determining the form of the exact solutions and substituting into them the lowest order terms of their respective Fourier expansions. The latter technique is actually a generalization of the method proposed by Kryloff and Bogoliuboff (1943).
NASA Astrophysics Data System (ADS)
Zingerman, K. M.; Shavyrin, D. A.
2016-06-01
The approximate analytical solution of a quasi-static plane problem of the theory of viscoelasticity is obtained under finite strains. This is the problem of the stress-strain state in an infinite body with circular viscoelastic inclusion. The perturbation technique, Laplace transform, and complex Kolosov-Muskhelishvili's potentials are used for the solution. The numerical results are presented. The nonlinear effects and the effects of viscosity are estimated.
Căruntu, Bogdan
2014-01-01
The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results. PMID:25003150
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. PMID:26298108
NASA Astrophysics Data System (ADS)
Chung, H. Y.; Guo, G. Y.; Chiang, H.-P.; Tsai, D. P.; Leung, P. T.
2010-10-01
The optical response of a multilayered spherical system of unlimited number of layers (a “matryushka”) in the long wavelength limit can be accounted for from the knowledge of the static multipole polarizability of the system to first-order accuracy. However, for systems of ultrasmall dimensions or systems with sizes not-too-small compared to the wavelength, this ordinary quasistatic long wavelength approximation (LWA) becomes inaccurate. Here we introduce two significant modifications of the LWA for such a nanomatryushka in each of the two limits: the nonlocal optical response for ultrasmall systems (<10nm) , and the “finite-wavelength corrections” for systems ˜100nm . This is accomplished by employing the previous work for a single-layer shell, in combination with a certain effective-medium approach formulated recently in the literature. Numerical calculations for the extinction cross sections for such a system of different dimensions are provided as illustrations for these effects. This formulation thus provides significant improvements on the ordinary LWA, yielding enough accuracy for the description of the optical response of these nanoshell systems over an appreciable range of sizes, without resorting to more involved quantum mechanical or fully electrodynamic calculations.
Approximate analytical time-domain Green's functions for the Caputo fractional wave equation.
Kelly, James F; McGough, Robert J
2016-08-01
The Caputo fractional wave equation [Geophys. J. R. Astron. Soc. 13, 529-539 (1967)] models power-law attenuation and dispersion for both viscoelastic and ultrasound wave propagation. The Caputo model can be derived from an underlying fractional constitutive equation and is causal. In this study, an approximate analytical time-domain Green's function is derived for the Caputo equation in three dimensions (3D) for power law exponents greater than one. The Green's function consists of a shifted and scaled maximally skewed stable distribution multiplied by a spherical spreading factor 1/(4πR). The approximate one dimensional (1D) and two dimensional (2D) Green's functions are also computed in terms of stable distributions. Finally, this Green's function is decomposed into a loss component and a diffraction component, revealing that the Caputo wave equation may be approximated by a coupled lossless wave equation and a fractional diffusion equation. PMID:27586735
Haider, S A; Cetas, T C; Roemer, R B
1993-05-01
An approximate analytical model based upon the bioheat transfer equation is derived and used to calculate temperatures within a perfused region implanted regularly with dielectrically coated hot source implants; for example, hot water tubes, electrically heated rods, or inductively heated ferromagnetic implants. The effect of a regular array of mutually parallel heat sources of cylindrical shape is approximated by idealizing one of the boundary conditions. The solution, as could be expected, is in terms of modified Bessel functions. In calculating the temperature of each thermoregulating source in the array, the steady state power balance is enforced. The important feature of the model is that the finite size of implant diameter and its dielectric coating can be incorporated. The effect of thickness and thermal conductivity of the coating on the source and tissue temperatures along with various other interesting features are deduced from this model. The analytically calculated implant and tissue temperatures are compared with those of a numerical 3-D finite difference model. The analytical model also is used to define a range of parameters such that minimal therapeutic temperatures will be achieved in the implanted volume without exceeding prescribed maximum temperatures. This approach leads to a simple means of selecting implant spacing and regulation temperatures of hot source methods prospectively.
Analytical approximations for the amplitude and period of a relaxation oscillator
Kut, Carmen; Golkhou, Vahid; Bader, Joel S
2009-01-01
Background Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters. Results We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10× less sensitive to protein decay rates), efficiency (2× more efficient), and dynamic range (30 to 60 decibel increase). The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level. Conclusion Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits. PMID:19144174
Analytical approximation of the neutrino oscillation matter effects at large θ 13
NASA Astrophysics Data System (ADS)
Agarwalla, Sanjib Kumar; Kao, Yee; Takeuchi, Tatsu
2014-04-01
We argue that the neutrino oscillation probabilities in matter are best understood by allowing the mixing angles and mass-squared differences in the standard parametrization to `run' with the matter effect parameter a = , where N e is the electron density in matter and E is the neutrino energy. We present simple analytical approximations to these `running' parameters. We show that for the moderately large value of θ 13, as discovered by the reactor experiments, the running of the mixing angle θ 23 and the CP violating phase δ can be neglected. It simplifies the analysis of the resulting expressions for the oscillation probabilities considerably. Approaches which attempt to directly provide approximate analytical expressions for the oscillation probabilities in matter suffer in accuracy due to their reliance on expansion in θ 13, or in simplicity when higher order terms in θ 13 are included. We demonstrate the accuracy of our method by comparing it to the exact numerical result, as well as the direct approximations of Cervera et al., Akhmedov et al., Asano and Minakata, and Freund. We also discuss the utility of our approach in figuring out the required baseline lengths and neutrino energies for the oscillation probabilities to exhibit certain desirable features.
Analytic Sensitivity and Approximation of Skin Buckling Constraints in Wing-Shape Synthesis
NASA Technical Reports Server (NTRS)
Livne, Eli; Milosavljevic, Radomir
1995-01-01
Explicit expressions for terms of the stiffness and geometric stiffness matrices are derived for the buckling analysis of trapezoidal fiber composite wing skin panels. The formulation is based on Ritz analysis using simple polynomials, and leads to explicit expressions for the analytic sensitivities of the stiffness and geometric stiffness matrices with respect to layer thickness, fiber directions, and panel shape. Integration with wing box analysis using either the equivalent plate approach or the finite element method, makes it possible to obtain sensitivities of panel buckling constraints with respect to wing planform shape or locations of internal ribs and spars. The analytic sensitivities are used to construct approximations of panel buckling constraints for integrated wing/panel design synthesis.
Fast and accurate analytical model to solve inverse problem in SHM using Lamb wave propagation
NASA Astrophysics Data System (ADS)
Poddar, Banibrata; Giurgiutiu, Victor
2016-04-01
Lamb wave propagation is at the center of attention of researchers for structural health monitoring of thin walled structures. This is due to the fact that Lamb wave modes are natural modes of wave propagation in these structures with long travel distances and without much attenuation. This brings the prospect of monitoring large structure with few sensors/actuators. However the problem of damage detection and identification is an "inverse problem" where we do not have the luxury to know the exact mathematical model of the system. On top of that the problem is more challenging due to the confounding factors of statistical variation of the material and geometric properties. Typically this problem may also be ill posed. Due to all these complexities the direct solution of the problem of damage detection and identification in SHM is impossible. Therefore an indirect method using the solution of the "forward problem" is popular for solving the "inverse problem". This requires a fast forward problem solver. Due to the complexities involved with the forward problem of scattering of Lamb waves from damages researchers rely primarily on numerical techniques such as FEM, BEM, etc. But these methods are slow and practically impossible to be used in structural health monitoring. We have developed a fast and accurate analytical forward problem solver for this purpose. This solver, CMEP (complex modes expansion and vector projection), can simulate scattering of Lamb waves from all types of damages in thin walled structures fast and accurately to assist the inverse problem solver.
ANALYTIC APPROXIMATE SEISMOLOGY OF PROPAGATING MAGNETOHYDRODYNAMIC WAVES IN THE SOLAR CORONA
Goossens, M.; Soler, R.; Arregui, I.
2012-12-01
Observations show that propagating magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. The technique of MHD seismology uses the wave observations combined with MHD wave theory to indirectly infer physical parameters of the solar atmospheric plasma and magnetic field. Here, we present an analytical seismological inversion scheme for propagating MHD waves. This scheme uses the observational information on wavelengths and damping lengths in a consistent manner, along with observed values of periods or phase velocities, and is based on approximate asymptotic expressions for the theoretical values of wavelengths and damping lengths. The applicability of the inversion scheme is discussed and an example is given.
Derivation of an analytical approximation of the spectrum of spinning dust emission
Stevenson, Matthew A.
2014-02-01
An analytical function for the spectrum of spinning dust emission is presented. It is derived through the application of careful approximations, with each step tested against numerical calculations. This approach ensures accuracy while providing an intuitive picture of the physics. The final result may be useful for fitting of anomalous microwave emission observations, as is demonstrated by a comparison with the Planck observations of the Perseus Molecular Cloud. It is hoped that this will lead to a broader consideration of the spinning dust model when interpreting microwave continuum observations, and that it will provide a standard framework for interpreting and comparing the variety of anomalous microwave emission observations.
Dismer, Florian; Hansen, Sigrid; Oelmeier, Stefan Alexander; Hubbuch, Jürgen
2013-03-01
Chromatography is the method of choice for the separation of proteins, at both analytical and preparative scale. Orthogonal purification strategies for industrial use can easily be implemented by combining different modes of adsorption. Nevertheless, with flexibility comes the freedom of choice and optimal conditions for consecutive steps need to be identified in a robust and reproducible fashion. One way to address this issue is the use of mathematical models that allow for an in silico process optimization. Although this has been shown to work, model parameter estimation for complex feedstocks becomes the bottleneck in process development. An integral part of parameter assessment is the accurate measurement of retention times in a series of isocratic or gradient elution experiments. As high-resolution analytics that can differentiate between proteins are often not readily available, pure protein is mandatory for parameter determination. In this work, we present an approach that has the potential to solve this problem. Based on the uniqueness of UV absorption spectra of proteins, we were able to accurately measure retention times in systems of up to four co-eluting compounds. The presented approach is calibration-free, meaning that prior knowledge of pure component absorption spectra is not required. Actually, pure protein spectra can be determined from co-eluting proteins as part of the methodology. The approach was tested for size-exclusion chromatograms of 38 mixtures of co-eluting proteins. Retention times were determined with an average error of 0.6 s (1.6% of average peak width), approximated and measured pure component spectra showed an average coefficient of correlation of 0.992.
NASA Astrophysics Data System (ADS)
Kokhanovsky, Alexander; Hopkinson, Ian
2008-03-01
We derive an analytical approximation in the framework of the radiative transfer theory for use in the analysis of diffuse reflectance measurements. This model uses two parameters to describe a material, the transport free path length, l, and the similarity parameter, s. Using a simple algebraic expression, s and l can be applied for the determination of the absorption coefficient Kabs, which can be easily compared to absorption coefficients measured using transmission spectroscopy. l and Kabs can be seen as equivalent to the S and K parameters, respectively, in the Kubelka-Munk formulation. The advantage of our approximation is a clear basis in the complete radiative transfer theory. We demonstrate the application of our model to a range of different paper types and to fabrics treated with known levels of a dye.
Approximate analytical solution to the Boussinesq equation with a sloping water-land boundary
NASA Astrophysics Data System (ADS)
Tang, Yuehao; Jiang, Qinghui; Zhou, Chuangbing
2016-04-01
An approximate solution is presented to the 1-D Boussinesq equation (BEQ) characterizing transient groundwater flow in an unconfined aquifer subject to a constant water variation at the sloping water-land boundary. The flow equation is decomposed to a linearized BEQ and a head correction equation. The linearized BEQ is solved using a Laplace transform. By means of the frozen-coefficient technique and Gauss function method, the approximate solution for the head correction equation can be obtained, which is further simplified to a closed-form expression under the condition of local energy equilibrium. The solutions of the linearized and head correction equations are discussed from physical concepts. Especially for the head correction equation, the well posedness of the approximate solution obtained by the frozen-coefficient method is verified to demonstrate its boundedness, which can be further embodied as the upper and lower error bounds to the exact solution of the head correction by statistical analysis. The advantage of this approximate solution is in its simplicity while preserving the inherent nonlinearity of the physical phenomenon. Comparisons between the analytical and numerical solutions of the BEQ validate that the approximation method can achieve desirable precisions, even in the cases with strong nonlinearity. The proposed approximate solution is applied to various hydrological problems, in which the algebraic expressions that quantify the water flow processes are derived from its basic solutions. The results are useful for the quantification of stream-aquifer exchange flow rates, aquifer response due to the sudden reservoir release, bank storage and depletion, and front position and propagation speed.
An approximate analytic solution for the radiation from a line-driven fluid-loaded plate
NASA Astrophysics Data System (ADS)
Diperna, Daniel T.; Feit, David
2001-12-01
In the analysis of a fluid loaded line-driven plate, the fields in the structure and the fluid are often expressed in terms of a Fourier transform. Once the boundary conditions are matched, the structural displacement can be expressed as an inverse transform, which can be evaluated using contour integration. The result is then a sum of propagating or decaying waves, each arising from poles in the complex plane, plus a branch cut integral. The branch cut is due to a square root in the transform of the acoustic impedance. The complex layer analysis (CLA) used here eliminates the branch cut singularity by approximating the square root with a rational function, causing the characteristic equation to become a polynomial in the transform variable. An approximate analytic solution to the characteristic equation is then found using a perturbation method. The result is four poles corresponding to the roots of the in vacuo plate, modified by the presence of the fluid, plus an infinity of poles located along the branch cut of the acoustic impedance. The solution is then found analytically using contour integration, with the integrand containing only simple poles.
Xia, T. Y.; Zhang, Y.
2009-04-15
We present an approximate, analytical calculation of the reionized spectra C{sub l}{sup XX} of cosmic microwave background radiation anisotropies and polarizations generated by relic gravitational waves (RGWs). Three simple models of reionization are explored, whose visibility functions are fitted by Gaussian types of functions as approximations. We have derived the analytical polarization {beta}{sub l} and temperature anisotropies {alpha}{sub l}, which both consist of two terms proportional to RGWs at the decoupling and at the reionization as well. The explicit dependence of {beta}{sub l} and {alpha}{sub l} upon the reionization time {eta}{sub r}, the duration {delta}{eta}{sub r}, and the optical depth {kappa}{sub r} is demonstrated. Moreover, {beta}{sub l} and {alpha}{sub l} contain {kappa}{sub r} in different coefficients, and the polarization spectra C{sub l}{sup EE} and C{sub l}{sup BB} are more sensitive probes of reionization than C{sub l}{sup TT}. These results facilitate examination of the reionization effects, in particular, the degeneracies of {kappa}{sub r} with the normalization amplitude and with the initial spectral index of RGWs. It is also found that reionization causes a {kappa}{sub r}-dependent shift {delta}l{approx}20 of the zero multipole l{sub 0} of C{sub l}{sup TE}, an effect that should be included in order to detect the traces of RGWs. Compared with numerical results, the analytical C{sub l}{sup XX} are approximate and have the limitation. For the primary peaks in the range l{approx_equal}(30,600), the error is {<=}3% in three different models. In the range l<20 for the reionization bumps, the error is {<=}15% for C{sub l}{sup EE} and C{sub l}{sup BB} in the two extended reionization models, and C{sub l}{sup TT} and C{sub l}{sup TE} have much larger departures for l<10. The bumps in the sudden reionization model are too low.
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 ).
Approximate semi-analytical solutions for the steady-state expansion of a contactor plasma
NASA Astrophysics Data System (ADS)
Camporeale, E.; Hogan, E. A.; MacDonald, E. A.
2015-04-01
We study the steady-state expansion of a collisionless, electrostatic, quasi-neutral plasma plume into vacuum, with a fluid model. We analyze approximate semi-analytical solutions, that can be used in lieu of much more expensive numerical solutions. In particular, we focus on the earlier studies presented in Parks and Katz (1979 American Institute of Aeronautics, Astronautics Conf. vol 1), Korsun and Tverdokhlebova (1997 33rd Joint Prop. Conf. (Seattle, WA) AIAA-97-3065), and Ashkenazy and Fruchtman (2001 27th Int. Electric Propulsion Conf. (Pasadena, CA)). By calculating the error with respect to the numerical solution, we can judge the range of validity for each solution. Moreover, we introduce a generalization of earlier models that has a wider range of applicability, in terms of plasma injection profiles. We conclude by showing a straightforward way to extend the discussed solutions to the case of a plasma plume injected with non-null azimuthal velocity.
Tolias, P.; Ratynskaia, S.; Angelis, U. de
2015-08-15
The soft mean spherical approximation is employed for the study of the thermodynamics of dusty plasma liquids, the latter treated as Yukawa one-component plasmas. Within this integral theory method, the only input necessary for the calculation of the reduced excess energy stems from the solution of a single non-linear algebraic equation. Consequently, thermodynamic quantities can be routinely computed without the need to determine the pair correlation function or the structure factor. The level of accuracy of the approach is quantified after an extensive comparison with numerical simulation results. The approach is solved over a million times with input spanning the whole parameter space and reliable analytic expressions are obtained for the basic thermodynamic quantities.
Communication: An efficient analytic gradient theory for approximate spin projection methods
NASA Astrophysics Data System (ADS)
Hratchian, Hrant P.
2013-03-01
Spin polarized and broken symmetry density functional theory are popular approaches for treating the electronic structure of open shell systems. However, spin contamination can significantly affect the quality of predicted geometries and properties. One scheme for addressing this concern in studies involving broken-symmetry states is the approximate projection method developed by Yamaguchi and co-workers. Critical to the exploration of potential energy surfaces and the study of properties using this method will be an efficient analytic gradient theory. This communication introduces such a theory formulated, for the first time, within the framework of general post-self consistent field (SCF) derivative theory. Importantly, the approach taken here avoids the need to explicitly solve for molecular orbital derivatives of each nuclear displacement perturbation, as has been used in a recent implementation. Instead, the well-known z-vector scheme is employed and only one SCF response equation is required.
NASA Astrophysics Data System (ADS)
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-01
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
Analytical descriptions of cross-polarisation dynamics: relaxing the secular approximations
NASA Astrophysics Data System (ADS)
Hirschinger, J.; Raya, J.
2015-11-01
In this work, analytical expressions of the cross-polarisation (CP) dynamics under both static and magic-angle spinning (MAS) conditions are obtained by solving the generalised Liouville-von Neumann quantum mechanical equation beyond the standard approximations, i.e., reintroducing neglected non-secular terms in the system superoperator. Although the simple model of a two-spin system interacting with a spin bath gives a rather crude description of CP dynamics, it accounts well for the orientation dependence of CP in a static sample of ferrocene powder and permits to detect slight departures from the Hartmann-Hahn matching condition. This approach also has the advantage of yielding manageable analytical expressions that can be used even by less inclined or experienced workers to obtain results that are good enough in an operational sense. Moreover, the resulting spin diffusion rate constants containing different sources of anisotropy of the system-environment interaction as well as their dependence on the MAS frequency are related semi-quantitatively to the local network of dipolar interactions. Finally, it is shown that non-secular solutions improve significantly the analysis of CPMAS-based separated-local-field spectroscopy experimental data in the absence of homonuclear decoupling.
Semi-analytical model of arrayed waveguide grating in SOI using Gaussian beam approximation.
Sidharth, R; Das, B K
2015-03-10
The arrayed waveguide grating structure can be used as an important component in high-speed CMOS optical interconnects in silicon-on-insulator (SOI) platform. However, the performance of such device is found to be extremely sensitive to the fabrication-related errors in defining the critical features. In the absence of an appropriate analytical model, one needs to rely on numerical computation to analyze the device characteristics and fabrication tolerances. Because compact design of such a device structure has foot-print ∼mm^{2} and the smallest features can be as small as ∼500 nm×220 nm (waveguide cross section), it demands a huge computational budget to optimize the design parameters. A semi-analytical model using Gaussian beam approximation of guided mode profiles has been developed to analyze the output spectrum of arrayed waveguide grating and to estimate the phase errors due to waveguide inhomogeneities. This model has been validated with existing numerical methods and published experimental results. It has been observed that a probabilistic waveguide width variations of ΔW∼5 nm can cause a cross-talk degradation of about 40 dB (25 dB) for a device (operating at λ∼1550 nm) fabricated on SOI substrate with 220 nm (2 μm) device layer thickness.
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.
Tian, Lian; Henningsen, Joseph; Salick, Max R; Crone, Wendy C; Gunderson, McLean; Dailey, Seth H; Chesler, Naomi C
2015-07-01
The mechanical properties of vascular tissues affect hemodynamics and can alter disease progression. The uniaxial tensile test is a simple and effective method for determining the stress-strain relationship in arterial tissue ex vivo. To enable calculation of strain, stretch can be measured directly with image tracking of markers on the tissue or indirectly from the distance between the grips used to hold the specimen. While the imaging technique is generally considered more accurate, it also requires more analysis, and the grip distance method is more widely used. The purpose of this study is to compare the stretch of the testing specimen calculated from the grip distance method to that obtained from the imaging method for canine descending aortas and large proximal pulmonary arteries. Our results showed a significant difference in stretch between the two methods; however, this difference was consistently less than 2%. Therefore, the grip distance method is an accurate approximation of the stretch in large elastic arteries in the uniaxial tensile test. PMID:25881308
NASA Astrophysics Data System (ADS)
Tao, Jianmin; Mo, Yuxiang; Tian, Guocai; Ruzsinszky, Adrienn
2016-08-01
Long-range van der Waals (vdW) interaction is critically important for intermolecular interactions in molecular complexes and solids. However, accurate modeling of vdW coefficients presents a great challenge for nanostructures, in particular for fullerene clusters, which have huge vdW coefficients but also display very strong nonadditivity. In this work, we calculate the coefficients between fullerenes, fullerene and sodium clusters, and fullerene and alkali atoms with the hollow-sphere model within the modified single-frequency approximation (MSFA). In the MSFA, we assume that the electron density is uniform in a molecule and that only valence electrons in the outmost subshell of atoms contribute. The input to the model is the static multipole polarizability, which provides a sharp cutoff for the plasmon contribution outside the effective vdW radius. We find that the model can generate C6 in excellent agreement with expensive wave-function-based ab initio calculations, with a mean absolute relative error of only 3 % , without suffering size-dependent error. We show that the nonadditivities of the coefficients C6 between fullerenes and C60 and sodium clusters Nan revealed by the model agree remarkably well with those based on the accurate reference values. The great flexibility, simplicity, and high accuracy make the model particularly suitable for the study of the nonadditivity of vdW coefficients between nanostructures, advancing the development of better vdW corrections to conventional density functional theory.
Wave-function frozen-density embedding: Approximate analytical nuclear ground-state gradients.
Heuser, Johannes; Höfener, Sebastian
2016-05-01
We report the derivation of approximate analytical nuclear ground-state uncoupled frozen density embedding (FDEu) gradients for the resolution of identity (RI) variant of the second-order approximate coupled cluster singles and doubles (RICC2) as well as density functional theory (DFT), and an efficient implementation thereof in the KOALA program. In order to guarantee a computationally efficient treatment, those gradient terms are neglected which would require the exchange of orbital information. This approach allows for geometry optimizations of single molecules surrounded by numerous molecules with fixed nuclei at RICC2-in-RICC2, RICC2-in-DFT, and DFT-in-DFT FDE level of theory using a dispersion correction, required due to the DFT-based treatment of the interaction in FDE theory. Accuracy and applicability are assessed by the example of two case studies: (a) the Watson-Crick pair adenine-thymine, for which the optimized structures exhibit a maximum error of about 0.08 Å for our best scheme compared to supermolecular reference calculations, (b) carbon monoxide on a magnesium oxide surface model, for which the error amount up to 0.1 Å for our best scheme. Efficiency is demonstrated by successively including environment molecules and comparing to an optimized conventional supermolecular implementation, showing that the method is able to outperform conventional RICC2 schemes already with a rather small number of environment molecules, gaining significant speed up in computation time. PMID:26804310
All-coupling polaron optical response: Analytic approaches beyond the adiabatic approximation
NASA Astrophysics Data System (ADS)
Klimin, S. N.; Tempere, J.; Devreese, J. T.
2016-09-01
In the present work, the problem of an all-coupling analytic description for the optical conductivity of the Fröhlich polaron is treated, with the goal being to bridge the gap in the validity range that exists between two complementary methods: on the one hand, the memory-function formalism and, on the other hand, the strong-coupling expansion based on the Franck-Condon picture for the polaron response. At intermediate coupling, both methods were found to fail as they do not reproduce diagrammatic quantum Monte Carlo results. To resolve this, we modify the memory-function formalism with respect to the Feynman-Hellwarth-Iddings-Platzman approach in order to take into account a nonquadratic interaction in a model system for the polaron. The strong-coupling expansion is extended beyond the adiabatic approximation by including in the treatment nonadiabatic transitions between excited polaron states. The polaron optical conductivity that we obtain at T =0 by combining the two extended methods agrees well, both qualitatively and quantitatively, with the diagrammatic quantum Monte Carlo results in the whole available range of the electron-phonon coupling strength.
NASA Astrophysics Data System (ADS)
Teo, L. P.
2011-09-01
We consider the small separation asymptotic expansions of the Casimir interaction energy and the Casimir interaction force between two parallel cylinders. The leading order terms and the next-to-leading order terms are computed analytically. Four combinations of boundary conditions are considered, which are Dirichlet-Dirichlet, Neumann-Neumann, Dirichlet-Neumann, and Neumann-Dirichlet. For the case where one cylinder is inside another cylinder, the computations are shown in detail. In this case, we restrict our attention to the situation where the cylinders are strictly eccentric and the distance between the cylinders d is much smaller than the distance between the centers of the cylinders. The computations for the case where the two cylinders are exterior to each other can be done in the same way and we only present the results, which turn up to be similar to the results for the case where one cylinder is inside another except for some changes of signs. In all the scenarios we consider, the leading order terms are of order d-7/2 and they agree completely with the proximity force approximations. The results for the next-to-leading order terms are new. In the limiting case where the radius of the larger cylinder approaches infinity, the well-known results for the cylinder-plate configuration with Dirichlet-Dirichlet or Neumann-Neumann boundary conditions are recovered.
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
NASA Astrophysics Data System (ADS)
Hofman, Radek; Seibert, Petra; Kovalets, Ivan; Andronopoulos, Spyros
2015-04-01
We are concerned with source term retrieval in the case of an accident in a nuclear power with off-site consequences. The goal is to optimize atmospheric dispersion model inputs using inverse modeling of gamma dose rate measurements (instantaneous or time-integrated). These are the most abundant type of measurements provided by various radiation monitoring networks across Europe and available continuously in near-real time. Usually, a source term of an accidental release comprises of a mixture of nuclides. Unfortunately, gamma dose rate measurements do not provide a direct information on the source term composition; however, physical properties of respective nuclides (deposition properties, decay half-life) can yield some insight. In the method presented, we assume that nuclide ratios are known at least approximately, e.g. from nuclide specific observations or reactor inventory and assumptions on the accident type. The source term can be in multiple phases, each being characterized by constant nuclide ratios. The method is an extension of a well-established source term inversion approach based on the optimization of an objective function (minimization of a cost function). This function has two quadratic terms: mismatch between model and measurements weighted by an observation error covariance matrix and the deviation of the solution from a first guess weighted by the first-guess error covariance matrix. For simplicity, both error covariance matrices are approximated as diagonal. Analytical minimization of the cost function leads to a liner system of equations. Possible negative parts of the solution are iteratively removed by the means of first guess error variance reduction. Nuclide ratios enter the problem in the form of additional linear equations, where the deviations from prescribed ratios are weighted by factors; the corresponding error variance allows us to control how strongly we want to impose the prescribed ratios. This introduces some freedom into the
Assessing the clinical impact of approximations in analytical dose calculations for proton therapy
Schuemann, J.; Giantsoudi, D.; Grassberger, C.; Moteabbed, M.; Min, C.H.; Paganetti, H.
2015-01-01
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 to 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 find that ADC overestimates the target doses on average by 1–2% for all patients considered. The mean dose, D95, D50 and D02 (the dose value covering 95%, 50% and 2% of the target volume, respectively) are predicted within 5% of the delivered dose. The γ-index passing rate for target volumes was above 96% for a 3%/3mm criteria. 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%. In order 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 in order to avoid biases due to systematic discrepancies in calculated dose distributions for clinical trials comparing proton therapy to conventional radiotherapy. PMID:26025779
Heng, Kevin; Mendonça, João M.; Lee, Jae-Min E-mail: joao.mendonca@csh.unibe.ch
2014-11-01
We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior), and solutions for the temperature-pressure profiles. Generally, the problem is mathematically underdetermined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat, and the properties of scattering in both the optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing, and incoming fluxes in the convective regime.
Assessing the Clinical Impact of Approximations in Analytical Dose Calculations for Proton Therapy
Schuemann, Jan Giantsoudi, Drosoula; Grassberger, Clemens; Moteabbed, Maryam; Min, Chul Hee; Paganetti, Harald
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% 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.
NASA Astrophysics Data System (ADS)
Zhang, Du; Yang, Weitao
2016-10-01
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 double 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(K4), 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.
NASA Astrophysics Data System (ADS)
Schütz, Martin; Masur, Oliver; Usvyat, Denis
2014-06-01
In order to arrive at linear scaling of the computational cost with molecular size, local coupled cluster methods discriminate pairs of local molecular orbitals according to the spatial separation R of the latter. Only strong pairs are treated at the full coupled cluster level, whereas for weak pairs a lower level of theory (usually Møller-Plesset perturbation theory of second order, MP2) is used. Yet an MP2 treatment of weak pairs is inadequate in certain situations (for example, for describing π-stacking), which calls for an improved but still inexpensive method for dealing with the weak pairs. In a previous contribution, we proposed as a substituent for MP2 the LrCCD3 method, which is based on ring coupled cluster doubles (ring-CCD) and includes all third-order diagrams with energy contributions decaying not quicker than R-6. In the present work, we explore a still more accurate method, which is based on the same principles. It turned out to be essential to abandon the restriction to ring-CCD, i.e., to include further CCD diagrams beyond the ring approximation. The occurring intermediates turn out to be formally very similar to LMP2 density matrices, such that an efficient evaluation of these non-ring CCD diagrams is possible. Furthermore, a computationally cheap a posteriori estimate for the fourth-order singles contribution to the weak pair energy, which also exhibits a decay behavior of R-6, is introduced. The resulting method, denoted as LCCD[S]-R-6, indeed provides a substantial improvement in accuracy over the previous LrCCD3 method at a relatively modest additional computational cost.
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
NASA Astrophysics Data System (ADS)
Kupriyanov, N. A.; Simankin, F. A.; Manabaev, K. K.
2016-04-01
A new approximate algorithm for calculating a stress-strain state of viscoelastic bodies is used. The algorithm is based on the derivation of the expressions of time-effective modules. These modules are obtained by iterative changes, compressing the fork of Voigt-Reuss. As an example the analytic solution about the action of a concentrated force on the viscoelastic half-space is compared with the approximate solution. Numerical calculations are performed for a wide range of relaxation characteristics of a viscoelastic half-space. Results of the comparison of stresses and displacements with the analytic solution give coincidence within 3... 15%.
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.
NASA Astrophysics Data System (ADS)
Jourdier, Bénédicte; Plougonven, Riwal; Drobinski, Philippe; Dupont, Jean-Charles
2014-05-01
Wind measurements are key for the wind resource assessment. But as wind turbines get higher, wind measurement masts are often lower than the future wind turbine hub height. Therefore one of the first steps in the energy yield assessment is the vertical extrapolation of wind measurements. Such extrapolation is often done by approximating the vertical profile of wind speed with an analytical expression: either a logarithmic law which has a theoretical basis in Monin-Obukhov similarity theory; or a power law which is empirical. The present study analyzes the variability of the wind profile and how this variability affects the results of the vertical extrapolation methods. The study is conducted with data from the SIRTA observatory, 20km south of Paris (France). A large set of instrumentation is available, including sonic anemometers at 10 and 30 meters, a LIDAR measuring wind speeds from 40 to 200 meters and a SODAR measuring wind speeds starting from 100m up to 1km. The comparison between the instruments enables to characterize the measurements uncertainties. The observations show that close to the ground the wind is stronger during daytime and weaker at night while higher, around 150 m, the wind is weaker during daytime and stronger at night. Indeed the wind shear has a pronounced diurnal cycle. The vertical extrapolation methods currently used in the industry do not usually take into account the strong variability of the wind profile. The often fit the parameters of the extrapolation law, not on each time step, but on time-averaged profiles. The averaging period may be the whole measurement period or some part of it: there may be one constant parameter computed on the wind profile that was averaged on the whole year of measures, or the year of measures may be divided into a small number of cases (for example into night or daytime data, or into 4 seasons) and the parameter is adjusted for each case. The study analyzes thoroughly the errors generated by both
Tan, C.Y.; Ranjbar, V.H.; /Tech-X, Boulder
2007-11-01
We will explore a method for measuring chromaticity by continuously kicking the beam transversely. This is called the continuous head-tail method for measuring chromaticity. The complete analytic approximation in terms of trigonometric functions is derived for zero transverse emittance beam. A simple formula for calculating chromaticity from experimental data is also shown. Finally the theory is compared with experimental data.
Hill, M.C.
1989-01-01
Inaccuracies in parameter values, parameterization, stresses, and boundary conditions of analytical solutions and numerical models of groundwater flow produce errors in simulated hydraulic heads. These errors can be quantified in terms of approximate, simultaneous, nonlinear confidence intervals presented in the literature. Approximate confidence intervals can be applied in both error and sensitivity analysis and can be used prior to calibration or when calibration was accomplished by trial and error. The method is expanded for use in numerical problems, and the accuracy of the approximate intervals is evaluated using Monte Carlo runs. Four test cases are reported. -from Author
A comment on the importance of numerical evaluation of analytic solutions involving approximations.
Overall, J E; Starbuck, R R; Doyle, S R
1994-07-01
An analytic solution proposed by Senn (1) for removing the effects of covariate imbalance in controlled clinical trials was subjected to Monte Carlo evaluation. For practical applications of his derivation, Senn proposed substitution of sample statistics for parameters of the bivariate normal model. Unfortunately, that substitution produces severe distortion in the size of tests of significance for treatment effects when covariate imbalance is present. Numerical verification of proposed substitutions into analytic models is recommended as a prudent approach. PMID:7951276
NASA Astrophysics Data System (ADS)
Tinoco Arenas, A.; González Bolívar, M.; Medina Covarrubias, R.; Raga, A. C.
2015-10-01
We present analytic models for a photoionized region in pressure equilibrium with the surrounding, neutral material. The models are based on the assumption of a linear relation between the H ionization fraction and the square of the sound speed of the gas. We show that under these assumptions the "grey" radiative transfer equation has analytic solutions that provide the ionization structure and the density of the nebula as a function of radius.
Interpolation method for accurate affinity ranking of arrayed ligand-analyte interactions.
Schasfoort, Richard B M; Andree, Kiki C; van der Velde, Niels; van der Kooi, Alex; Stojanović, Ivan; Terstappen, Leon W M M
2016-05-01
The values of the affinity constants (kd, ka, and KD) that are determined by label-free interaction analysis methods are affected by the ligand density. This article outlines a surface plasmon resonance (SPR) imaging method that yields high-throughput globally fitted affinity ranking values using a 96-plex array. A kinetic titration experiment without a regeneration step has been applied for various coupled antibodies binding to a single antigen. Globally fitted rate (kd and ka) and dissociation equilibrium (KD) constants for various ligand densities and analyte concentrations are exponentially interpolated to the KD at Rmax = 100 RU response level (KD(R100)).
Brunet, Edouard; Ajdari, Armand
2006-05-01
We set up an analytical framework that allows one to describe and compute streaming effects and electro-osmosis on an equal footing. This framework relies on the thin double layer approximation commonly used for description of electroosmotic flows, but rarely used for streaming problems. Using this framework we quantitatively assess the induction of bulk streaming current patterns by topographic or charge heterogeneities on surfaces. This too also permits analytical computation of all linear electrokinetic effects in complex microfluidic geometries, and we discuss a few immediate applications. PMID:16803036
NASA Astrophysics Data System (ADS)
Haven, Emmanuel
2005-11-01
Analytical solutions to the backward Kolmogorov PDE are very dependent on the functional form of b(y,t) and a(y,t). We suggest one solution technique for obtaining analytical solutions via the use of an adiabatic approximation to the Schrödinger PDE. This approximation takes the specific form of a so-called WKB (W D Wentzel [G. Wentzel, Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik, Z. Phys. 38 (1926) 518-529], K D Kramers [H. Kramers, Wellenmechanik und halbzahlige Quantisierung, Z. Phys. 39 (1926) 828-840], B D Brillouin [L. Brillouin, La mécanique ondulatoire de Schrödinger: une méthode générale de résolution par approximations successives, C. R. Acad. Sci. 183 (1926) 24-26]) approximation. We provide for two examples, in financial option pricing, where we show how the proposed approximation could be of use.
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.
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
Analytical approach to dynamics of transformed rotating-wave approximation with dephasing
NASA Astrophysics Data System (ADS)
Mirzaee, M.; Kamani, N.
2013-09-01
We study the dynamics of the Jaynes—Cummings model within transformed rotating-wave approximation (TRWA). We analyze this model coupled to a dephasing reservoir, through the Lindblad formalism in the master equation. Then, we examine the expectation value of the number operator. Finally, we investigate the validity of this model under dephasing using the Mandel parameter and the total number of quanta.
Analytical Approximation Method for the Center Manifold in the Nonlinear Output Regulation Problem
NASA Astrophysics Data System (ADS)
Suzuki, Hidetoshi; Sakamoto, Noboru; Celikovský, Sergej
In nonlinear output regulation problems, it is necessary to solve the so-called regulator equations consisting of a partial differential equation and an algebraic equation. It is known that, for the hyperbolic zero dynamics case, solving the regulator equations is equivalent to calculating a center manifold for zero dynamics of the system. The present paper proposes a successive approximation method for obtaining center manifolds and shows its effectiveness by applying it for an inverted pendulum example.
An Approximate Analytic Expression for the Flux Density of Scintillation Light at the Photocathode
Braverman, Joshua B; Harrison, Mark J; Ziock, Klaus-Peter
2012-01-01
The flux density of light exiting scintillator crystals is an important factor affecting the performance of radiation detectors, and is of particular importance for position sensitive instruments. Recent work by T. Woldemichael developed an analytic expression for the shape of the light spot at the bottom of a single crystal [1]. However, the results are of limited utility because there is generally a light pipe and photomultiplier entrance window between the bottom of the crystal and the photocathode. In this study, we expand Woldemichael s theory to include materials each with different indices of refraction and compare the adjusted light spot shape theory to GEANT 4 simulations [2]. Additionally, light reflection losses from index of refraction changes were also taken into account. We found that the simulations closely agree with the adjusted theory.
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.
Analytic approximation to 5 dimensional black holes with one compact dimension
NASA Astrophysics Data System (ADS)
Karasik, D.; Sahabandu, C.; Suranyi, P.; Wijewardhana, L. C.
2005-01-01
We study black hole solutions in R4×S1 space, using an expansion to second order in the square of the ratio of the radius of the horizon, μ, and the circumference of the compact dimension, L. A study of geometric and thermodynamic properties indicates that the black hole fills the space in the compact dimension at ɛ=(μ/L)2≃0.1. At the same value of ɛ the entropies of the uniform black string and of the black hole are approximately equal.
NASA Astrophysics Data System (ADS)
Xing, Zhi-zhong; Zhu, Jing-yu
2016-07-01
Given an accelerator-based neutrino experiment with the beam energy E ≲ 1 GeV, we expand the probabilities of ν μ → ν e and {overline{ν}}_{μ}to {overline{ν}}_e oscillations in matter in terms of two small quantities Δ21 /Δ31 and A/Δ31, where Δ 21≡ m 2 2 - m 1 2 and Δ 31≡ m 3 2 - m 1 2 are the neutrino mass-squared differences, and A measures the strength of terrestrial matter effects. Our analytical approximations are numerically more accurate than those made by Freund in this energy region, and thus they are particularly applicable for the study of leptonic CP violation in the low-energy MOMENT, ESS νSM and T2K oscillation experiments. As a by-product, the new analytical approximations help us to easily understand why the matter-corrected Jarlskog parameter tilde{J} peaks at the resonance energy E ∗ ≃ 0 .14GeV (or 0 .12 GeV) for the normal (or inverted) neutrino mass hierarchy, and how the three Dirac unitarity triangles are deformed due to the terrestrial matter contamination. We also affirm that a medium-baseline neutrino oscillation experiment with the beam energy E lying in the E ∗ ≲ E ≲ 2 E ∗ range is capable of exploring leptonic CP violation with little matter-induced suppression.
Analytical Approximation of the Deconvolution of Strongly Overlapping Broad Fluorescence Bands
NASA Astrophysics Data System (ADS)
Dubrovkin, J. M.; Tomin, V. I.; Ushakou, D. V.
2016-09-01
A method for deconvoluting strongly overlapping spectral bands into separate components that enables the uniqueness of the deconvolution procedure to be monitored was proposed. An asymmetric polynomial-modified function subjected to Fourier filtering (PMGFS) that allowed more accurate and physically reasonable band shapes to be obtained and also improved significantly the deconvolution convergence was used as the band model. The method was applied to the analysis of complexation in solutions of the molecular probe 4'-(diethylamino)-3-hydroxyflavone with added LiCl. Two-band fluorescence of the probe in such solutions was the result of proton transfer in an excited singlet state and overlapped strongly with stronger spontaneous emission of complexes with the ions. Physically correct deconvolutions of overlapping bands could not always be obtained using available software.
Analytical approximations for spatial stochastic gene expression in single cells and tissues
Smith, Stephen; Cianci, Claudia; Grima, Ramon
2016-01-01
Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686
Franck, Christopher T; Koffarnus, Mikhail N; House, Leanna L; Bickel, Warren K
2015-01-01
The study of delay discounting, or valuation of future rewards as a function of delay, has contributed to understanding the behavioral economics of addiction. Accurate characterization of discounting can be furthered by statistical model selection given that many functions have been proposed to measure future valuation of rewards. The present study provides a convenient Bayesian model selection algorithm that selects the most probable discounting model among a set of candidate models chosen by the researcher. The approach assigns the most probable model for each individual subject. Importantly, effective delay 50 (ED50) functions as a suitable unifying measure that is computable for and comparable between a number of popular functions, including both one- and two-parameter models. The combined model selection/ED50 approach is illustrated using empirical discounting data collected from a sample of 111 undergraduate students with models proposed by Laibson (1997); Mazur (1987); Myerson & Green (1995); Rachlin (2006); and Samuelson (1937). Computer simulation suggests that the proposed Bayesian model selection approach outperforms the single model approach when data truly arise from multiple models. When a single model underlies all participant data, the simulation suggests that the proposed approach fares no worse than the single model approach.
On the evolution of the snow line in protoplanetary discs - II. Analytic approximations
NASA Astrophysics Data System (ADS)
Martin, Rebecca G.; Livio, Mario
2013-09-01
We examine the evolution of the snow line in a protoplanetary disc that contains a dead zone (a region of zero or low turbulence). The snow line is within a self-gravitating part of the dead zone, and we obtain a fully analytic solution for its radius. Our formula could prove useful for future observational attempts to characterize the demographics of planets outside the snow line. External sources such as cosmic rays or X-rays from the central star can ionize the disc surface layers and allow the magnetorotational instability to drive turbulence there. We show that provided that the surface density in this layer is less than about 50 g cm-2, the dead zone solution exists, after an initial outbursting phase, until the disc is dispersed by photoevaporation. We demonstrate that the snow line radius is significantly larger than that predicted by a fully turbulent disc model, and that in our own Solar system it remains outside of the orbital radius of the Earth. Thus, the inclusion of a dead zone into a protoplanetary disc model explains how our Earth formed with very little water.
Khangulyan, D.; Kelner, S. R. E-mail: Felix.Aharonian@mpi-hd.mpg.de
2014-03-10
The inverse Compton (IC) scattering of relativistic electrons is one of the major gamma-ray production mechanisms in different environments. Often, the target photons for IC scattering are dominated by blackbody (or graybody) radiation. In this case, the precise treatment of the characteristics of IC radiation requires numerical integrations over the Planckian distribution. Formally, analytical integrations are also possible but they result in series of several special functions; this limits the efficiency of usage of these expressions. The aim of this work is the derivation of approximate analytical presentations that would provide adequate accuracy for the calculations of the energy spectra of upscattered radiation, the rate of electron energy losses, and the mean energy of emitted photons. Such formulae have been obtained by merging the analytical asymptotic limits. The coefficients in these expressions are calculated via the least-squares fitting of the results of numerical integrations. The simple analytical presentations, obtained for both the isotropic and anisotropic target radiation fields, provide adequate (as good as 1%) accuracy for broad astrophysical applications.
Wu, Gang
2016-08-01
The nuclear quadrupole transverse relaxation process of half-integer spins in liquid samples is known to exhibit multi-exponential behaviors. Within the framework of Redfield's relaxation theory, exact analytical expressions for describing such a process exist only for spin-3/2 nuclei. As a result, analyses of nuclear quadrupole transverse relaxation data for half-integer quadrupolar nuclei with spin >3/2 must rely on numerical diagonalization of the Redfield relaxation matrix over the entire motional range. In this work we propose an approximate analytical expression that can be used to analyze nuclear quadrupole transverse relaxation data of any half-integer spin in liquids over the entire motional range. The proposed equation yields results that are in excellent agreement with the exact numerical calculations. PMID:27343483
NASA Astrophysics Data System (ADS)
Liu, Jie; Herbert, John M.
2015-07-01
A novel formulation of time-dependent density functional theory (TDDFT) is derived, based on non-orthogonal, absolutely-localized molecular orbitals (ALMOs). We call this approach TDDFT(MI), in reference to ALMO-based methods for describing molecular interactions (MI) that have been developed for ground-state applications. TDDFT(MI) is intended for efficient excited-state calculations in systems composed of multiple, weakly interacting chromophores. The efficiency is based upon (1) a local excitation approximation; (2) monomer-based, singly-excited basis states; (3) an efficient localization procedure; and (4) a one-step Davidson method to solve the TDDFT(MI) working equation. We apply this methodology to study molecular dimers, water clusters, solvated chromophores, and aggregates of naphthalene diimide that form the building blocks of self-assembling organic nanotubes. Absolute errors of 0.1-0.3 eV with respect to supersystem methods are achievable for these systems, especially for cases involving an excited chromophore that is weakly coupled to several explicit solvent molecules. Excited-state calculations in an aggregate of nine naphthalene diimide monomers are ˜40 times faster than traditional TDDFT calculations.
Analytical approximations of K-corrections in optical and near-infrared bands
NASA Astrophysics Data System (ADS)
Chilingarian, Igor V.; Melchior, Anne-Laure; Zolotukhin, Ivan Yu.
2010-07-01
To compare photometric properties of galaxies at different redshifts, the fluxes need to be corrected for the changes of effective rest-frame wavelengths of filter bandpasses, called K-corrections. Usual approaches to compute them are based on the template fitting of observed spectral energy distributions (SED) and, thus, require multicolour photometry. Here, we demonstrate that, in cases of widely used optical and near-infrared (NIR) filters, K-corrections can be precisely approximated as two-dimensional low-order polynomials of only two parameters: redshift and one observed colour. With this minimalist approach, we present the polynomial fitting functions for K-corrections in Sloan Digital Sky Survey (SDSS) ugriz, United Kingdom Infrared Telescope (UKIRT) Wide Field Camera YJHK, Johnson-Cousins UBVRcIc and Two Micron All Sky Survey JHKs bands for galaxies at redshifts Z < 0.5 based on empirically computed values obtained by fitting combined optical-NIR SEDs of a set of 105 galaxies constructed from SDSS Data Release 7 (DR7) and UKIRT Infrared Deep Sky Survey DR5 photometry using the Virtual Observatory. For luminous red galaxies we provide K-corrections as functions of their redshifts only. In two filters, g and r, we validate our solutions by computing K-corrections directly from SDSS DR7 spectra. We also present a K-corrections calculator, a web-based service for computing K-corrections online.
Kristóf, T; Boda, D; Szalai, I
2012-08-22
An analytic formula is derived for the magnetization of a two-dimensional dipolar hard disk fluid using a variational functional series expansion of the free energy as a function of the orientational distribution function. The excess term expressing the effect of the intermolecular forces is calculated on the basis of the mean spherical approximation. Comparison with our own Monte Carlo simulation data shows excellent agreement for large external fields and for the zero-field susceptibility. At intermediate field strengths, the agreement is satisfactory for moderate dipole moments and densities. PMID:22810162
Dodin, Amro; Tscherbul, Timur V; Brumer, Paul
2016-06-28
Closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath, relevant to light harvesting processes, are obtained and discussed. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter ζ=12(γ1+γ2)/Δp, where γi are the radiative decay rates of the excited levels i = 1, 2, and Δp=Δ(2)+(1-p(2))γ1γ2 depends on the excited-state level splitting Δ > 0 and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit (ζ ≫ 1), approach a long-lived quasi-steady state in the overdamped limit (ζ ≪ 1), and display an intermediate behavior at critical damping (ζ = 1). The sudden incoherent turn-on is shown to generate a mixture of excited eigenstates |e1〉 and |e2〉 and their in-phase coherent superposition |ϕ+〉=1r1+r2(r1|e1〉+r2|e2〉), which is remarkably long-lived in the overdamped limit (where r1 and r2 are the incoherent pumping rates). Formation of this coherent superposition enhances the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, additional asymptotic quasistationary coherences are identified, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when r1 = r2 and the transition dipole moments are fully aligned. PMID:27369498
Delfino, A.; Silva, J.B.; Malheiro, M.
2006-03-15
We study nuclear matter, at the mean-field approximation, by considering as equal the values of the scalar and the vector density in the Walecka model, which is a very reasonable approximation up to the nuclear matter saturation density. It turns out that the model has an analytical solution for the scalar and vector couplings as functions only of the nuclear matter density and binding energy. The nuclear matter properties are very close to the original version of the model. This solution allows us to show that the correlation between the binding energy and the saturation density is Coester line like. The liquid-gas phase transition is also studied and the critical and flash temperatures are again very similar to the original ones.
NASA Astrophysics Data System (ADS)
Boisseau, Bruno; Forgács, Péter; Giacomini, Hector
2007-03-01
A new (algebraic) approximation scheme to find global solutions of two-point boundary value problems of ordinary differential equations (ODEs) is presented. The method is applicable for both linear and nonlinear (coupled) ODEs whose solutions are analytic near one of the boundary points. It is based on replacing the original ODEs by a sequence of auxiliary first-order polynomial ODEs with constant coefficients. The coefficients in the auxiliary ODEs are uniquely determined from the local behaviour of the solution in the neighbourhood of one of the boundary points. The problem of obtaining the parameters of the global (connecting) solutions, analytic at one of the boundary points, reduces to find the appropriate zeros of algebraic equations. The power of the method is illustrated by computing the approximate values of the 'connecting parameters' for a number of nonlinear ODEs arising in various problems in field theory. We treat in particular the static and rotationally symmetric global vortex, the skyrmion, the Abrikosov-Nielsen-Olesen vortex, as well as the 't Hooft-Polyakov magnetic monopole. The total energy of the skyrmion and of the monopole is also computed by the new method. We also consider some ODEs coming from the exact renormalization group. The ground-state energy level of the anharmonic oscillator is also computed for arbitrary coupling strengths with good precision.
NASA Astrophysics Data System (ADS)
Khan, Sheema; Morton, Thomas L.; Ronis, David
1987-05-01
The static correlations in highly charged colloidal and micellar suspensions, with and without added electrolyte, are examined using the hypernetted-chain approximation (HNC) for the macro-ion-macro-ion correlations and the mean-spherical approximation for the other correlations. By taking the point-ion limit for the counter-ions, an analytic solution for the counter-ion part of the problem can be obtained; this maps the macro-ion part of the problem onto a one-component problem where the macro-ions interact via a screened Coulomb potential with the Gouy-Chapman form for the screening length and an effective charge that depends on the macro-ion-macro-ion pair correlations. Numerical solutions of the effective one-component equation in the HNC approximation are presented, and in particular, the effects of macro-ion charge, nonadditive core diameters, and added electrolyte are examined. As we show, there can be a strong renormalization of the effective macro-ion charge and reentrant melting in colloidal crystals.
NASA Astrophysics Data System (ADS)
Liu, Fenglai; Gan, Zhengting; Shao, Yihan; Hsu, Chao-Ping; Dreuw, Andreas; Head-Gordon, Martin; Miller, Benjamin T.; Brooks, Bernard R.; Yu, Jian-Guo; Furlani, Thomas R.; Kong, Jing
2010-10-01
We derived the analytic gradient for the excitation energies from a time-dependent density functional theory calculation within the Tamm-Dancoff approximation (TDDFT/TDA) using Gaussian atomic orbital basis sets, and introduced an efficient serial and parallel implementation. Some timing results are shown from a B3LYP/6-31G**/SG-1-grid calculation on zincporphyrin. We also performed TDDFT/TDA geometry optimizations for low-lying excited states of 20 small molecules, and compared adiabatic excitation energies and optimized geometry parameters to experimental values using the B3LYP and ωB97 functionals. There are only minor differences between TDDFT and TDA optimized excited state geometries and adiabatic excitation energies. Optimized bond lengths are in better agreement with experiment for both functionals than either CC2 or SOS-CIS(D0), while adiabatic excitation energies are in similar or slightly poorer agreement. Optimized bond angles with both functionals are more accurate than CIS values, but less accurate than either CC2 or SOS-CIS(D0) ones.
Serdyuk, Vladimir; Rudnitsky, Anton
2015-05-01
We present an approximate 2D asymptotic analytic theory of light field excitation in a plane thin dielectric layer under conditions of frustrated total internal reflection, when an inclined Gaussian beam, falling from a triangular prism, excites a decaying field in air spacing between a prism and a plane dielectric. Ignoring the radiation scattering on the sharp edges of a prism, we have obtained the formulas that allow us to compute spatial structures of an electromagnetic field in every point of space and to estimate the integral efficiency of waveguide mode excitation in a plane dielectric layer and the total energy of a reflected beam. It is shown that the width of an initial Gaussian beam has an effect on waveguide mode intensity. PMID:26366908
Serdyuk, Vladimir; Rudnitsky, Anton
2015-05-01
We present an approximate 2D asymptotic analytic theory of light field excitation in a plane thin dielectric layer under conditions of frustrated total internal reflection, when an inclined Gaussian beam, falling from a triangular prism, excites a decaying field in air spacing between a prism and a plane dielectric. Ignoring the radiation scattering on the sharp edges of a prism, we have obtained the formulas that allow us to compute spatial structures of an electromagnetic field in every point of space and to estimate the integral efficiency of waveguide mode excitation in a plane dielectric layer and the total energy of a reflected beam. It is shown that the width of an initial Gaussian beam has an effect on waveguide mode intensity.
NASA Astrophysics Data System (ADS)
Bozkaya, Uǧur; Sherrill, C. David
2016-05-01
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 orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C10H22), 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.
NASA Astrophysics Data System (ADS)
Mourenas, D.; Artemyev, A. V.; Agapitov, O. V.; Krasnoselskikh, V.; Li, W.
2014-12-01
The distribution of trapped energetic electrons inside the Earth's radiation belts is the focus of intense studies aiming at better describing the evolution of the space environment in the presence of various disturbances induced by the solar wind or by an enhanced lightning activity. Such studies are usually performed by means of comparisons with full numerical simulations solving the Fokker-Planck quasi-linear diffusion equation for the particle distribution function. Here we present for the first time approximate but realistic analytical solutions for the electron distribution, which are shown to be in good agreement with exact numerical solutions in situations where resonant scattering of energetic electrons by whistler mode hiss, lightning-generated or chorus waves, is the dominant process. Quiet time distributions are well recovered, as well as the evolution of energized relativistic electron distributions during disturbed geomagnetic conditions. It is further shown that careful comparisons between the analytical solutions and measured distributions may allow to infer important bounce- and drift-averaged wave characteristics (such as wave amplitude). It could also help to improve the global understanding of underlying physical phenomena.
Shkel, Irina A
2010-08-26
An accurate analytical expression for the Coulombic free energy of DNA as a function of salt concentration ([salt]) is essential in applications to nucleic acid (NA) processes. The cylindrical model of DNA and the nonlinear Poisson-Boltzmann (NLPB) equation for ions in solution are among the simplest approaches capable of describing Coulombic interactions of NA and salt ions and of providing analytical expressions for thermodynamic quantities. Three approximations for Coulombic free energy G(u,infinity)(coul) of a polymeric nucleic acid are derived and compared with the numerical solution in a wide experimental range of 1:1 [salt] from 0.01 to 2 M. Two are obtained from the two asymptotic solutions of the cylindrical NLPB equation in the high-[salt] and low-[salt] limits: these are sufficient to determine G(u,infinity)(coul) of double-stranded (ds) DNA with 1% and of single-stranded (ss) DNA with 3% accuracy at any [salt]. The third approximation is experimentally motivated Taylor series up to the quadratic term in ln[salt] in the vicinity of the reference [salt] 0.15 M. This expression with three numerical coefficients (Coulombic free energy and its first and second derivatives at 0.15 M) predicts dependence of G(u,infinity)(coul) on [salt] within 2% of the numerical solution from 0.01 to 1 M for ss (a = 7 A, b = 3.4 A) and ds (a = 10 A, b = 1.7 A) DNA. Comparison of cylindrical free energy with that calculated for the all-atom structural model of linear B-DNA shows that the cylindrical model is completely sufficient above 0.01 M of 1:1 [salt]. The choice of two cylindrical parameters, the distance of closest approach of ion to cylinder axis (radius) a and the average axial charge separation b, is discussed in application to all-atom numerical calculations and analysis of experiment. Further development of analytical expression for Coulombic free energy with thermodynamic approaches accounting for ionic correlations and specific effects is suggested.
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.
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 volume 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.
NASA Astrophysics Data System (ADS)
van Westen, Thijs; Vlugt, Thijs J. H.; Gross, Joachim
2012-07-01
Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin (γ), where γ is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)], 10.1080/00268979500102391.
Terçariol, César Augusto Sangaletti; Martinez, Alexandre Souto
2008-09-01
Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2 , as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N1) is just n=e=2.72... while in the mu=2 case, the mean number n of visited points grows proportionally to N;{12} . Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones. PMID:18850997
NASA Astrophysics Data System (ADS)
Teo, L. P.
2013-08-01
We derive analytically the asymptotic behavior of the Casimir interaction between a sphere and a plate when the distance between them, d, is much smaller than the radius of the sphere, R. The leading-order and next-to-leading-order terms are derived from the exact formula for the Casimir interaction energy. They are found to depend nontrivially on the dielectric functions of the objects. As expected, the leading-order term coincides with that derived using the proximity force approximation. Numerical results are presented when the dielectric functions are given by the plasma model or the Drude model, with the plasma frequency (for plasma and Drude models) and relaxation frequency (for Drude model) given by the conventional values used for gold metal. It is found that if plasma model is used instead of the Drude model, the error in the sum of the first two leading terms is at most 2%, while the error in θ1, the ratio of the next-to-leading-order term divided by d/R to the leading-order term, can go up to 4.5%.
NASA Astrophysics Data System (ADS)
Lajohn, L. A.; Pratt, R. H.
2015-05-01
There is no simple parameter that can be used to predict when impulse approximation (IA) can yield accurate Compton scattering doubly differential cross sections (DDCS) in relativistic regimes. When Z is low, a small value of the parameter /q (where is the average initial electron momentum and q is the momentum transfer) suffices. For small Z the photon electron kinematic contribution described in relativistic S-matrix (SM) theory reduces to an expression, Xrel, which is present in the relativistic impulse approximation (RIA) formula for Compton DDCS. When Z is high, the S-Matrix photon electron kinematics no longer reduces to Xrel, and this along with the error characterized by the magnitude of /q contribute to the RIA error Δ. We demonstrate and illustrate in the form of contour plots that there are regimes of incident photon energy ωi and scattering angle θ in which the two types of errors at least partially cancel. Our calculations show that when θ is about 65° for Uranium K-shell scattering, Δ is less than 1% over an ωi range of 300 to 900 keV.
NASA Astrophysics Data System (ADS)
Whipple, K.; Meade, B.
2002-12-01
The recognition of a dynamic coupling among climate, erosion and tectonics is arguably one of the most exciting discoveries in the last 20 years. Numerical simulations using coupled thermo-mechanical and surface process models have been most influential. However, analyses to date leave the strength of the coupling between climate and tectonics uncertain. Can an intensification of erosion induce a sufficiently strong increase in rock uplift rate that steady-state relief is increased rather than reduced? In addition, it has remained unclear whether the details of the erosion processes are important to the geodynamic evolution of the orogen, and if so, how they come into play. We present an approximate analytical solution for two-sided orogenic wedges obeying a frictional rheology, and in a condition of flux steady state, that makes explicit the nature and sensitivity of the coupling between climate and rock uplift rate. A closed-form solution for the inter-relations among steady-state orogen width, rock uplift rate, patterns of internal deformation, and climate is found by combining (1) a statement of mass balance, (2) the geometry dictated by critical taper theory for a frictional wedge, (3) relations for equilibrium topography consistent with both the tapered wedge geometry and with erosion rates necessary to satisfy the mass balance condition, and (4) a kinematic solution for internal deformation. An approximate relation for the timescale of adjustment to a new steady state following a step-function change in climatic or tectonic conditions is also found. We make the simplifying assumption that the topographic taper is invariant with orogen width, tectonic influx rate, climate, and time. Erosion rates are assumed to be dictated by the bedrock channel network and are described by the stream-power model of bedrock channel incision. Erosional efficiency (and its spatial distribution) is shown to control steady-state orogen width, crest elevation, crustal thickness
Zeinali-Rafsanjani, B.; Mosleh-Shirazi, M. A.; Faghihi, R.; Karbasi, S.; Mosalaei, A.
2015-01-01
To accurately 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 approximately 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. PMID:26170553
Martinez, V P; Adelantado, J V; Garcia, A P; Reig, F B
1989-09-01
A selectivity index is proposed for defining the selectivity of a spectrophotometric procedure that is subject to interference by species which do not obey Beer's law in the system. The interactions between analyte and interferents which affect the absorbance of an analytical system are studied by means of a simple mathematical model. Theoretical expressions are derived which represent the selectivity as a function of the analyte or interfering species concentration. The treatment is illustrated by a study of the Zr(IV)-chloranilic acid system in presence of thorium as interferent.
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
NASA Astrophysics Data System (ADS)
Atteia, O.; Höhener, P.
2012-09-01
The aim of this work was to extend and to validate the flux tube-mixed instantaneous and kinetics superposition sequence approach (FT-MIKSS) to reaction chains of degrading species. Existing analytical solutions for the reactive transport of chains of decaying solutes were embedded in the flux-tube approach in order to conceive a semi-analytical model that allows fast parameter fitting. The model was applied for chloroethenes undergoing reductive dechlorination and oxidation in homogeneous and heterogeneous aquifers with sorption. The results from the semi-analytical model were compared to results from three numerical models (RT3D, PH3TD, PHAST). All models were validated in a homogeneous domain with an existing analytical solution. In heterogeneous domains, we found significant differences between the four models. FT-MIKSS gave intermediate results for all modelled cases. Results were obtained almost instantaneously, whereas other models had calculation times of up to several hours. Chloroethene plumes and redox conditions at the Plattsburgh field site were realistically modelled by FT-MIKSS, although results differed somewhat from those of PHT3D and PHAST. It is concluded that it may be tedious to obtain correct modelling results in heterogeneous media with degradation chain reactions and that the comparison of two different models may be useful. FT-MIKSS is a valuable tool for fast parameter fitting at field sites and should be used in the preparation of longer model runs with other numerical models.
NASA Technical Reports Server (NTRS)
Jordon, D. E.; Patterson, W.; Sandlin, D. R.
1985-01-01
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 analytical 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 analytical results by modeling a model rotor system for which direct download values were determinrd..
Thin film flow of an Oldroyd 6-constant fluid over a moving belt: an analytic approximate solution
NASA Astrophysics Data System (ADS)
Ene, Remus-Daniel; Marinca, Vasile; Marinca, Valentin Bogdan
2016-01-01
In this paper the thin film flow of an Oldroyd 6-constant fluid on a vertically moving belt is investigated. The basic equation of a non-Newtonian fluid in a container with a wide moving belt which passes through the container moving vertically upward with constant velocity, is reduced to an ordinary nonlinear differential equation. This equation is solved approximately by means of the Optimal Homotopy Asymptotic Method (OHAM). The solutions take into account the behavior of Newtonian and non-Newtonian fluids. Our procedure intended for solving nonlinear problems does not need small parameters in the equation and provides a convenient way to control the convergence of the approximate solutions.
Anderson, Oscar A.
2006-08-06
The well-known Kapchinskij-Vladimirskij (KV) equations are difficult to solve in general, but the problem is simplified for the matched-beam case with sufficient symmetry. They show that the interdependence of the two KV equations is eliminated, so that only one needs to be solved--a great simplification. They present an iterative method of solution which can potentially yield any desired level of accuracy. The lowest level, the well-known smooth approximation, yields simple, explicit results with good accuracy for weak or moderate focusing fields. The next level improves the accuracy for high fields; they previously showed how to maintain a simple explicit format for the results. That paper used expansion in a small parameter to obtain the second level. The present paper, using straightforward iteration, obtains equations of first, second, and third levels of accuracy. For a periodic lattice with beam matched to lattice, they use the lattice and beam parameters as input and solve for phase advances and envelope waveforms. They find excellent agreement with numerical solutions over a wide range of beam emittances and intensities.
Accurate Analytic Potential Functions for the a ^3Π_1 and X ^1Σ^+ States of {IBr}
NASA Astrophysics Data System (ADS)
Yukiya, Tokio; Nishimiya, Nobuo; Suzuki, Masao; Le Roy, Robert
2014-06-01
Spectra of IBr in various wavelength regions have been measured by a number of researchers using traditional diffraction grating and microwave methods, as well as using high-resolution laser techniques combined with a Fourier transform spectrometer. In a previous paper at this meeting, we reported a preliminary determination of analytic potential energy functions for the A ^3Π_1 and X ^1Σ^+ states of IBr from a direct-potential-fit (DPF) analysis of all of the data available at that time. That study also confirmed the presence of anomalous fluctuations in the v--dependence of the first differences of the inertial rotational constant, Δ Bv=Bv+1-Bv in the A ^3Π_1 state for vibrational levels with v'(A) in the mid 20's. However, our previous experience in a recent study of the analogous A ^3Π_1-X ^1Σ_g^+ system of Br_2 suggested that the effect of such fluctuations may be overcome if sufficient data are available. The present work therefore reports new measurements of transitions to levels in the v'(A)=23-26 region, together with a new global DPF analysis that uses ``robust" least-squares fits to average properly over the effect of such fluctuations in order to provide an optimum delineation of the underlying potential energy curve(s). L.E.Selin,Ark. Fys. 21,479(1962) E. Tiemann and Th. Moeller, Z. Naturforsch. A 30,986 (1975) E.M. Weinstock and A. Preston, J. Mol. Spectrosc. 70, 188 (1978) D.R.T. Appadoo, P.F. Bernath, and R.J. Le Roy, Can. J. Phys. 72, 1265 (1994) N. Nishimiya, T. Yukiya and M. Suzuki, J. Mol. Spectrosc. 173, 8 (1995). T. Yukiya, N. Nishimiya, and R.J. Le Roy, Paper MF12 at the 65th Ohio State University International Symposium on Molecular Spectroscopy, Columbus, Ohio, June 20-24, 2011. T. Yukiya, N. Nishimiya, Y. Samajima, K. Yamaguchi, M. Suzuki, C.D. Boone, I. Ozier and R.J. Le Roy, J. Mol. Spectrosc. 283, 32 (2013) J.K.G. Watson, J. Mol. Spectrosc. 219, 326 (2003).
NASA Astrophysics Data System (ADS)
Zhou, Kai
2011-12-01
of parameters over which the approximation is accurate. In the present contribution, we provide an exact solution to the charge and field-induced force for semi-spheroid standing on a ground plane, derive the commonly used approximation from the exact solution, and find that the commonly used approximate solution for the force on a rodlike particle agrees poorly with finite element computations of the force. We provide both "exact" and approximated formulas which agree well with finite element computations of the force on a rod-like particle for asperities from 2 to 100. An analytical expression is derived for the chemical potential of a water-filled spheroid in a dielectric medium based on Zeller's hypothesis for the chemical potential, against which Zeller's approximations for chemical potential could be compared for the same system. In doing so, we found that Zeller's approximation for DC component of the chemical potential is very good, although his expression for the conductivity at which the peak DC component occurs is not accurate at low spheroid asperities. However Zeller's approximation does not provide a very good approximation for the AC component of the chemical potential. Following Zeller's approach but with corrections, we have developed a much more accurate approximation for the AC component of the chemical potential which was compared with both the exact analytical solution and FEA computations.
Rigorous analytical approximation of tritronquée solution to Painlevé-I and the first singularity
NASA Astrophysics Data System (ADS)
Adali, A.; Tanveer, S.
2016-10-01
We use a recently developed method [1,2] to determine approximate expression for tritronquée solution for P-1: y″ + 6y2 - x = 0 in a domain D with rigorous bounds. In particular we rigorously confirm the location of the closest singularity from the origin to be at x = -770766/323285 = - 2.3841687675 ⋯ to within 5 ×10-6 accuracy, in agreement with previous numerical calculations [6].
NASA Astrophysics Data System (ADS)
Dondapati, Raja Sekhar; Ravula, Jeswanth; Thadela, S.; Usurumarti, Preeti Rao
2015-12-01
Future power transmission applications demand higher efficiency due to the limited resources of energy. In order to meet such demand, a novel method of transmission is being developed using High Temperature Superconducting (HTS) cables. However, these HTS cables need to be cooled below the critical temperature of superconductors used in constructing the cable to retain the superconductivity. With the advent of new superconductors whose critical temperatures having reached up to 134 K (Hg based), a need arises to find a suitable coolant which can accommodate the heating loads on the superconductors. The present work proposes, Supercritical Nitrogen (SCN) to be a feasible coolant to achieve the required cooling. Further, the feasibility of proposed coolant to be used in futuristic HTS cables is investigated by studying the thermophysical properties such as density, viscosity, specific heat and thermal conductivity with respect to temperature (TC + 10 K) and pressure (PC + 10 bar). In addition, few temperature dependent analytical functions are developed for thermophysical properties of SCN which are useful in predicting thermohydraulic performance (pressure drop, pumping power and cooling capacity) using numerical or computational techniques. Also, the developed analytical functions are used to calculate the pumping power and the temperature difference between inlet and outlet of HTS cable. These results are compared with those of liquid nitrogen (LN2) and found that the circulating pumping power required to pump SCN is significantly smaller than that to pump LN2. Further, it is found that the temperature difference between the inlet and outlet is smaller as compared to that when LN2 is used, SCN can be preferred to cool long length Hg based HTS cables.
DiFrancesco, D; Noble, D
1980-01-01
1. Regular perturbation theory was used to obtain analytical solutions for the time course of membrane current decay following voltage-clamp depolarizing pulses when both time-dependent K conductance mechanisms and the process of K accumulation in extracellular spaces are present. These solutions apply when the current and K concentration changes are small enough for linear relations to be assumed between current and K concentration. 2. In the case of a single Hodgkin-Huxley type conductance variable with time constant tau chi the presence of an accumulation process which, by itself, would produce a current decay with time constant tau alpha, induces the appearance of two infinite sets of components with decreasing time constants (1/(n+1/tau chi) and 1/(1/tau alpha + n/tau chi), where n is integer), and decreasing magnitudes. 3. The analytical solutions are used to investigate the range of conditions over which semi-exponential (curve-stripping) analysis of current decay tails may give useful information on the kinetics of current change. It is shown that, except at very large decay tail amplitudes, the method may give a good estimate of the true time constants of conductance decay even when the currents are assumed to be strongly dependent on external K concentration. 4. The method introduces error in current amplitude, but over the range in which curve-stripping gives useful results, the direct distortion of activation curves by variations in external K concentration is fairly small. However, as the current decay becomes grossly distorted in its time course by accumulation, so does the activation curve. The effects are very similar both to those obtained using numerical computation without linearization, and to those obtained experimentally. 5. Even with a large dependence of current on external K concentration the linear model does not reproduce i chi, fast as a perturbation of i chi, slow by K accumulation. PMID:7463358
Srinivasan, B.; Shumlak, U.
2011-09-15
The 5-moment two-fluid plasma model uses Euler equations to describe the ion and electron fluids and Maxwell's equations to describe the electric and magnetic fields. Two-fluid physics becomes significant when the characteristic spatial scales are on the order of the ion skin depth and characteristic time scales are on the order of the ion cyclotron period. The full two-fluid plasma model has disparate characteristic speeds ranging from the ion and electron speeds of sound to the speed of light. Two asymptotic approximations are applied to the full two-fluid plasma to arrive at the Hall-MHD model, namely negligible electron inertia and infinite speed of light. The full two-fluid plasma model and the Hall-MHD model are studied for applications to an electromagnetic plasma shock, geospace environmental modeling (GEM challenge) magnetic reconnection, an axisymmetric Z-pinch, and an axisymmetric field reversed configuration (FRC).
NASA Astrophysics Data System (ADS)
Le Roy, Robert J.; Walji, Sadru; Sentjens, Katherine
2013-06-01
Alkali hydride diatomic molecules have long been the object of spectroscopic studies. However, their small reduced mass makes them species for which the conventional semiclassical-based methods of analysis tend to have the largest errors. To date, the only quantum-mechanically accurate direct-potential-fit (DPF) analysis for one of these molecules was the one for LiH reported by Coxon and Dickinson. The present paper extends this level of analysis to NaH, and reports a DPF analysis of all available spectroscopic data for the A ^1Σ^+-X ^1Σ^+ system of NaH which yields analytic potential energy functions for these two states that account for those data (on average) to within the experimental uncertainties. W.C. Stwalley, W.T. Zemke and S.C. Yang, J. Phys. Chem. Ref. Data {20}, 153-187 (1991). J.A. Coxon and C.S. Dickinson, J. Chem. Phys. {121}, 8378 (2004).
NASA Astrophysics Data System (ADS)
Amador, Davi H. T.; de Oliveira, Heibbe C. B.; Sambrano, Julio R.; Gargano, Ricardo; de Macedo, Luiz Guilherme M.
2016-10-01
A prolapse-free basis set for Eka-Actinium (E121, Z = 121), numerical atomic calculations on E121, spectroscopic constants and accurate analytical form for the potential energy curve of diatomic E121F obtained at 4-component all-electron CCSD(T) level including Gaunt interaction are presented. The results show a strong and polarized bond (≈181 kcal/mol in strength) between E121 and F, the outermost frontier molecular orbitals from E121F should be fairly similar to the ones from AcF and there is no evidence of break of periodic trends. Moreover, the Gaunt interaction, although small, is expected to influence considerably the overall rovibrational spectra.
NASA Astrophysics Data System (ADS)
Boyd, John P.
2011-02-01
Radial basis function (RBF) interpolants have become popular in computer graphics, neural networks and for solving partial differential equations in many fields of science and engineering. In this article, we compare five different species of RBFs: Gaussians, hyperbolic secant (sech's), inverse quadratics, multiquadrics and inverse multiquadrics. We show that the corresponding cardinal functions for a uniform, unbounded grid are all approximated by the same function: C(X) ∼ (1/(ρ)) sin (πX)/sinh (πX/ρ) for some constant ρ(α) which depends on the inverse width parameter (“shape parameter”) α of the RBF and also on the RBF species. The error in this approximation is exponentially small in 1/α for sech's and inverse quadratics and exponentially small in 1/α2 for Gaussians; the error is proportional to α4 for multiquadrics and inverse multiquadrics. The error in all cases is small even for α ∼ O(1). These results generalize to higher dimensions. The Gaussian RBF cardinal functions in any number of dimensions d are, without approximation, the tensor product of one dimensional Gaussian cardinal functions: Cd(x1,x2…,xd)=∏j=1dC(xj). For other RBF species, we show that the two-dimensional cardinal functions are well approximated by the products of one-dimensional cardinal functions; again the error goes to zero as α → 0. The near-identity of the cardinal functions implies that all five species of RBF interpolants are (almost) the same, despite the great differences in the RBF ϕ's themselves.
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.
NASA Technical Reports Server (NTRS)
Chaudhuri, Reaz A.; Seide, Paul
1987-01-01
An approximate semianalytical method for determination of interlaminar shear stress distribution through the thickness of an arbitrarily laminated thick plate has been presented. The method is based on the assumptions of transverse inextensibility and layerwise constant shear angle theory (LCST) and utilizes an assumed quadratic displacement potential energy based finite element method (FEM). Centroid of the triangular surface has been proved from a rigorous mathematical point of view (Aubin-Nitsche theory), to be the point of exceptional accuracy for the interlaminar shear stresses. Numerical results indicate close agreement with the available three-dimensional elasticity theory solutions. A comparison between the present theory and that due to an assumed stress hybrid FEM suggest that the (normal) traction-free-edge condition is not satisfied in the latter approach. Furthermore, the present paper is the first to present the results for interlaminar shear stresses in a two-layer thick square plate of balanced unsymmetric angle-ply construction. A comparison with the recently proposed Equilibrium Method (EM) indicates the superiority of the present method, because the latter assures faster convergence as well as simultaneous vanishing of the transverse shear stresses on both of the exposed surfaces of the laminate. Superiority of the present method over the EM, in the case of a symmetric laminate, is limited to faster convergence alone. It has also been demonstrated that the combination of the present method and the reduced (quadratic order) numerical integration scheme yields convergence of the interlaminar shear stresses almost as rapidly as that of the nodal displacements, in the case of a thin plate.
NASA Astrophysics Data System (ADS)
Bykov, Dmytro; Petrenko, Taras; Izsák, Róbert; Kossmann, Simone; Becker, Ute; Valeev, Edward; Neese, Frank
2015-07-01
In this paper, various implementations of the analytic Hartree-Fock and hybrid density functional energy second derivatives are studied. An approximation-free four-centre implementation is presented, and its accuracy is rigorously analysed in terms of self-consistent field (SCF), coupled-perturbed SCF (CP-SCF) convergence and prescreening criteria. The CP-SCF residual norm convergence threshold turns out to be the most important of these. Final choices of convergence thresholds are made such that an accuracy of the vibrational frequencies of better than 5 cm-1 compared to the numerical noise-free results is obtained, even for the highly sensitive low frequencies (<100-200 cm-1). The effects of the choice of numerical grid for density functional exchange-correlation integrations are studied and various weight derivative schemes are analysed in detail. In the second step of the work, approximations are introduced in order to speed up the computation without compromising its accuracy. To this end, the accuracy and efficiency of the resolution of identity approximation for the Coulomb terms and the semi-numerical chain of spheres approximation to the exchange terms are carefully analysed. It is shown that the largest performance improvements are realised if either Hartree-Fock exchange is absent (pure density functionals) and otherwise, if the exchange terms in the CP-SCF step of the calculation are approximated by the COSX method in conjunction with a small integration grid. Default values for all the involved truncation parameters are suggested. For vancomycine (176 atoms and 3593 basis functions), the RIJCOSX Hessian calculation with the B3LYP functional and the def2-TZVP basis set takes ∼3 days using 16 Intel® Xeon® 2.60GHz processors with the COSX algorithm having a net parallelisation scaling of 11.9 which is at least ∼20 times faster than the calculation without the RIJCOSX approximation.
Lee, Ming-Wei; Hung, Cheng-Hung; Liao, Jung-Li; Cheng, Nan-Yu; Hou, Ming-Feng; Tseng, Sheng-Hao
2014-10-01
In this paper, we demonstrate that a scanning MEMS mirror can be employed to create a linear gradient line source that is equivalent to a planar source. This light source setup facilitates the use of diffusion models of increased orders of approximation having closed form solution, and thus enhance the efficiency and accuracy in sample optical properties recovery. In addition, compared with a regular planar light source, the linear gradient line source occupies much less source area and has an elevated measurement efficiency. We employed a δ-P1 diffusion equation with a closed form solution and carried out a phantom study to understand the performance of this new method in determining the absorption and scattering properties of turbid samples. Moreover, our Monte Carlo simulation results indicated that this geometry had probing depths comparable to those of the conventional diffuse reflectance measurement geometry with a source-detector separation of 3 mm. We expect that this new source setup would facilitate the investigating of superficial volumes of turbid samples in the wavelength regions where tissue absorption coefficients are comparable to scattering coefficients.
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.
Pyell, Ute; Jalil, Alaa H; Pfeiffer, Christian; Pelaz, Beatriz; Parak, Wolfgang J
2015-07-15
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 analytic approximation 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 approximated 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. PMID:25828436
A classical path approximation for diffractive surface scattering
NASA Astrophysics Data System (ADS)
Meyer, Hans-Dieter; Toennies, J. Peter
1984-12-01
The well-known classical path approximation is applied to a calculation of diffraction intensities in the scattering of atoms from a rigid crystal with a soft interaction potential. A general expression is derived for the diffraction intensities which can be applied to potentials with several higher-order terms in the Fourier series. For an uncorrugated Morse potential with a first-order exponential corrugation term an analytic solution is obtained which is compared with the infinite order suddent (IOS) approximation calculations for Ne/W(110) and He/LiF(100). Both approximations are very accurate for the weakly corrugated Ne/W system. For He/LiF the present approximation is more accurate than the sudden (IOS) approximation and has the added advantage of providing an analytic solution. Several improvements are suggested.
Lanman, Richard B; Mortimer, Stefanie A; Zill, Oliver A; Sebisanovic, Dragan; Lopez, Rene; Blau, Sibel; Collisson, Eric A; Divers, Stephen G; Hoon, Dave S B; Kopetz, E Scott; Lee, Jeeyun; Nikolinakos, Petros G; Baca, Arthur M; Kermani, Bahram G; Eltoukhy, Helmy; Talasaz, AmirAli
2015-01-01
Next-generation sequencing of cell-free circulating solid tumor DNA addresses two challenges in contemporary cancer care. First this method of massively parallel and deep sequencing enables assessment of a comprehensive panel of genomic targets from a single sample, and second, it obviates the need for repeat invasive tissue biopsies. Digital Sequencing™ is a novel method for high-quality sequencing of circulating tumor DNA simultaneously across a comprehensive panel of over 50 cancer-related genes with a simple blood test. Here we report the analytic and clinical validation of the gene panel. Analytic sensitivity down to 0.1% mutant allele fraction is demonstrated via serial dilution studies of known samples. Near-perfect analytic specificity (> 99.9999%) enables complete coverage of many genes without the false positives typically seen with traditional sequencing assays at mutant allele frequencies or fractions below 5%. We compared digital sequencing of plasma-derived cell-free DNA to tissue-based sequencing on 165 consecutive matched samples from five outside centers in patients with stage III-IV solid tumor cancers. Clinical sensitivity of plasma-derived NGS was 85.0%, comparable to 80.7% sensitivity for tissue. The assay success rate on 1,000 consecutive samples in clinical practice was 99.8%. Digital sequencing of plasma-derived DNA is indicated in advanced cancer patients to prevent repeated invasive biopsies when the initial biopsy is inadequate, unobtainable for genomic testing, or uninformative, or when the patient's cancer has progressed despite treatment. Its clinical utility is derived from reduction in the costs, complications and delays associated with invasive tissue biopsies for genomic testing.
Zill, Oliver A.; Sebisanovic, Dragan; Lopez, Rene; Blau, Sibel; Collisson, Eric A.; Divers, Stephen G.; Hoon, Dave S. B.; Kopetz, E. Scott; Lee, Jeeyun; Nikolinakos, Petros G.; Baca, Arthur M.; Kermani, Bahram G.; Eltoukhy, Helmy; Talasaz, AmirAli
2015-01-01
Next-generation sequencing of cell-free circulating solid tumor DNA addresses two challenges in contemporary cancer care. First this method of massively parallel and deep sequencing enables assessment of a comprehensive panel of genomic targets from a single sample, and second, it obviates the need for repeat invasive tissue biopsies. Digital SequencingTM is a novel method for high-quality sequencing of circulating tumor DNA simultaneously across a comprehensive panel of over 50 cancer-related genes with a simple blood test. Here we report the analytic and clinical validation of the gene panel. Analytic sensitivity down to 0.1% mutant allele fraction is demonstrated via serial dilution studies of known samples. Near-perfect analytic specificity (> 99.9999%) enables complete coverage of many genes without the false positives typically seen with traditional sequencing assays at mutant allele frequencies or fractions below 5%. We compared digital sequencing of plasma-derived cell-free DNA to tissue-based sequencing on 165 consecutive matched samples from five outside centers in patients with stage III-IV solid tumor cancers. Clinical sensitivity of plasma-derived NGS was 85.0%, comparable to 80.7% sensitivity for tissue. The assay success rate on 1,000 consecutive samples in clinical practice was 99.8%. Digital sequencing of plasma-derived DNA is indicated in advanced cancer patients to prevent repeated invasive biopsies when the initial biopsy is inadequate, unobtainable for genomic testing, or uninformative, or when the patient’s cancer has progressed despite treatment. Its clinical utility is derived from reduction in the costs, complications and delays associated with invasive tissue biopsies for genomic testing. PMID:26474073
NASA Astrophysics Data System (ADS)
Vjačeslavov, N. S.
1980-02-01
In this paper estimates are found for L_pR_n(f) - the least deviation in the L_p-metric, 0 < p\\leq\\infty, of a piecewise analytic function f from the rational functions of degree at most n. It is shown that these estimates are sharp in a well-defined sense.Bibliography: 12 titles.
Bicanic, Dane; Swarts, Jan; Luterotti, Svjetlana; Pietraperzia, Giangaetano; Dóka, Otto; de Rooij, Hans
2004-09-01
The concept of the optothermal window (OW) is proposed as a reliable analytical tool to rapidly determine the concentration of lycopene in a large variety of commercial tomato products in an extremely simple way (the determination is achieved without the need for pretreatment of the sample). The OW is a relative technique as the information is deduced from the calibration curve that relates the OW data (i.e., the product of the absorption coefficient beta and the thermal diffusion length micro) with the lycopene concentration obtained from spectrophotometric measurements. The accuracy of the method has been ascertained with a high correlation coefficient (R = 0.98) between the OW data and results acquired from the same samples by means of the conventional extraction spectrophotometric method. The intrinsic precision of the OW method is quite high (better than 1%), whereas the repeatability of the determination (RSD = 0.4-9.5%, n= 3-10) is comparable to that of spectrophotometry.
NASA Astrophysics Data System (ADS)
Bozkaya, Uǧur; Sherrill, C. David
2013-08-01
Orbital-optimized coupled-electron pair theory [or simply "optimized CEPA(0)," OCEPA(0), for short] and its analytic energy gradients are presented. For variational optimization of the molecular orbitals for the OCEPA(0) method, a Lagrangian-based approach is used along with an orbital direct inversion of the iterative subspace algorithm. The cost of the method is comparable to that of CCSD [O(N6) scaling] for energy computations. However, for analytic gradient computations the OCEPA(0) method is only half as expensive as CCSD since there is no need to solve the λ2-amplitude equation for OCEPA(0). The performance of the OCEPA(0) method is compared with that of the canonical MP2, CEPA(0), CCSD, and CCSD(T) methods, for equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions between radicals. For bond lengths of both closed and open-shell molecules, the OCEPA(0) method improves upon CEPA(0) and CCSD by 25%-43% and 38%-53%, respectively, with Dunning's cc-pCVQZ basis set. Especially for the open-shell test set, the performance of OCEPA(0) is comparable with that of CCSD(T) (ΔR is 0.0003 Å on average). For harmonic vibrational frequencies of closed-shell molecules, the OCEPA(0) method again outperforms CEPA(0) and CCSD by 33%-79% and 53%-79%, respectively. For harmonic vibrational frequencies of open-shell molecules, the mean absolute error (MAE) of the OCEPA(0) method (39 cm-1) is fortuitously even better than that of CCSD(T) (50 cm-1), while the MAEs of CEPA(0) (184 cm-1) and CCSD (84 cm-1) are considerably higher. For complete basis set estimates of hydrogen transfer reaction energies, the OCEPA(0) method again exhibits a substantially better performance than CEPA(0), providing a mean absolute error of 0.7 kcal mol-1, which is more than 6 times lower than that of CEPA(0) (4.6 kcal mol-1), and comparing to MP2 (7.7 kcal mol-1) there is a more than 10-fold reduction in errors. Whereas the MAE for the CCSD method is only 0.1 kcal
Bozkaya, Uğur; Sherrill, C David
2013-08-01
Orbital-optimized coupled-electron pair theory [or simply "optimized CEPA(0)," OCEPA(0), for short] and its analytic energy gradients are presented. For variational optimization of the molecular orbitals for the OCEPA(0) method, a Lagrangian-based approach is used along with an orbital direct inversion of the iterative subspace algorithm. The cost of the method is comparable to that of CCSD [O(N(6)) scaling] for energy computations. However, for analytic gradient computations the OCEPA(0) method is only half as expensive as CCSD since there is no need to solve the λ2-amplitude equation for OCEPA(0). The performance of the OCEPA(0) method is compared with that of the canonical MP2, CEPA(0), CCSD, and CCSD(T) methods, for equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions between radicals. For bond lengths of both closed and open-shell molecules, the OCEPA(0) method improves upon CEPA(0) and CCSD by 25%-43% and 38%-53%, respectively, with Dunning's cc-pCVQZ basis set. Especially for the open-shell test set, the performance of OCEPA(0) is comparable with that of CCSD(T) (ΔR is 0.0003 Å on average). For harmonic vibrational frequencies of closed-shell molecules, the OCEPA(0) method again outperforms CEPA(0) and CCSD by 33%-79% and 53%-79%, respectively. For harmonic vibrational frequencies of open-shell molecules, the mean absolute error (MAE) of the OCEPA(0) method (39 cm(-1)) is fortuitously even better than that of CCSD(T) (50 cm(-1)), while the MAEs of CEPA(0) (184 cm(-1)) and CCSD (84 cm(-1)) are considerably higher. For complete basis set estimates of hydrogen transfer reaction energies, the OCEPA(0) method again exhibits a substantially better performance than CEPA(0), providing a mean absolute error of 0.7 kcal mol(-1), which is more than 6 times lower than that of CEPA(0) (4.6 kcal mol(-1)), and comparing to MP2 (7.7 kcal mol(-1)) there is a more than 10-fold reduction in errors. Whereas the MAE for the CCSD method is
Hertäg, Loreen; Durstewitz, Daniel; Brunel, Nicolas
2014-01-01
Computational models offer a unique tool for understanding the network-dynamical mechanisms which mediate between physiological and biophysical properties, and behavioral function. A traditional challenge in computational neuroscience is, however, that simple neuronal models which can be studied analytically fail to reproduce the diversity of electrophysiological behaviors seen in real neurons, while detailed neuronal models which do reproduce such diversity are intractable analytically and computationally expensive. A number of intermediate models have been proposed whose aim is to capture the diversity of firing behaviors and spike times of real neurons while entailing the simplest possible mathematical description. One such model is the exponential integrate-and-fire neuron with spike rate adaptation (aEIF) which consists of two differential equations for the membrane potential (V) and an adaptation current (w). Despite its simplicity, it can reproduce a wide variety of physiologically observed spiking patterns, can be fit to physiological recordings quantitatively, and, once done so, is able to predict spike times on traces not used for model fitting. Here we compute the steady-state firing rate of aEIF in the presence of Gaussian synaptic noise, using two approaches. The first approach is based on the 2-dimensional Fokker-Planck equation that describes the (V,w)-probability distribution, which is solved using an expansion in the ratio between the time constants of the two variables. The second is based on the firing rate of the EIF model, which is averaged over the distribution of the w variable. These analytically derived closed-form expressions were tested on simulations from a large variety of model cells quantitatively fitted to in vitro electrophysiological recordings from pyramidal cells and interneurons. Theoretical predictions closely agreed with the firing rate of the simulated cells fed with in-vivo-like synaptic noise. PMID:25278872
Approximations for photoelectron scattering
NASA Astrophysics Data System (ADS)
Fritzsche, V.
1989-04-01
The errors of several approximations in the theoretical approach of photoelectron scattering are systematically studied, in tungsten, for electron energies ranging from 10 to 1000 eV. The large inaccuracies of the plane-wave approximation (PWA) are substantially reduced by means of effective scattering amplitudes in the modified small-scattering-centre approximation (MSSCA). The reduced angular momentum expansion (RAME) is so accurate that it allows reliable calculations of multiple-scattering contributions for all the energies considered.
Sparse pseudospectral approximation method
NASA Astrophysics Data System (ADS)
Constantine, Paul G.; Eldred, Michael S.; Phipps, Eric T.
2012-07-01
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses a numerical integration rule to approximate the Fourier-type coefficients of a truncated expansion in orthogonal polynomials. For problems in more than two or three dimensions, a sparse grid numerical integration rule offers accuracy with a smaller node set compared to tensor product approximation. However, when using a sparse rule to approximately integrate these coefficients, one often finds unacceptable errors in the coefficients associated with higher degree polynomials. By reexamining Smolyak's algorithm and exploiting the connections between interpolation and projection in tensor product spaces, we construct a sparse pseudospectral approximation method that accurately reproduces the coefficients of basis functions that naturally correspond to the sparse grid integration rule. The compelling numerical results show that this is the proper way to use sparse grid integration rules for pseudospectral approximation.
NASA Technical Reports Server (NTRS)
Schwenke, David W.
1993-01-01
We report the results of a series of calculations of state-to-state integral cross sections for collisions between O and nonvibrating H2O in the gas phase on a model nonreactive potential energy surface. The dynamical methods used include converged quantum mechanical scattering calculations, the j(z) conserving centrifugal sudden (j(z)-CCS) approximation, and quasi-classical trajectory (QCT) calculations. We consider three total energies 0.001, 0.002, and 0.005 E(h) and the nine initial states with rotational angular momentum less than or equal to 2 (h/2 pi). The j(z)-CCS approximation gives good results, while the QCT method can be quite unreliable for transitions to specific rotational sublevels. However, the QCT cross sections summed over final sublevels and averaged over initial sublevels are in better agreement with the quantum results.
Goheen, Steven C.
2001-07-01
Characterizing environmental samples has been exhaustively addressed in the literature for most analytes of environmental concern. One of the weak areas of environmental analytical chemistry is that of radionuclides and samples contaminated with radionuclides. The analysis of samples containing high levels of radionuclides can be far more complex than that of non-radioactive samples. This chapter addresses the analysis of samples with a wide range of radioactivity. The other areas of characterization examined in this chapter are the hazardous components of mixed waste, and special analytes often associated with radioactive materials. Characterizing mixed waste is often similar to characterizing waste components in non-radioactive materials. The largest differences are in associated safety precautions to minimize exposure to dangerous levels of radioactivity. One must attempt to keep radiological dose as low as reasonably achievable (ALARA). This chapter outlines recommended procedures to safely and accurately characterize regulated components of radioactive samples.
Kokhanovsky, Alexander A
2002-05-01
A simple, approximate analytical formula is proposed for the reflection function of a semi-infinite, homogeneous particulate layer. It is assumed that the zenith angle of the viewing direction is equal to zero (thus corresponding to the case of nadir observations), whereas the light incidence direction is arbitrary. The formula yields accurate results for incidence-zenith angles less than approximately 85 degrees and can be useful in analyzing satellite nadir observations of optically thick clouds.
Variational extensions of the mean spherical approximation
NASA Astrophysics Data System (ADS)
Blum, L.; Ubriaco, M.
2000-04-01
In a previous work we have proposed a method to study complex systems with objects of arbitrary size. For certain specific forms of the atomic and molecular interactions, surprisingly simple and accurate theories (The Variational Mean Spherical Scaling Approximation, VMSSA) [(Velazquez, Blum J. Chem. Phys. 110 (1990) 10 931; Blum, Velazquez, J. Quantum Chem. (Theochem), in press)] can be obtained. The basic idea is that if the interactions can be expressed in a rapidly converging sum of (complex) exponentials, then the Ornstein-Zernike equation (OZ) has an analytical solution. This analytical solution is used to construct a robust interpolation scheme, the variation mean spherical scaling approximation (VMSSA). The Helmholtz excess free energy Δ A=Δ E- TΔ S is then written as a function of a scaling matrix Γ. Both the excess energy Δ E( Γ) and the excess entropy Δ S( Γ) will be functionals of Γ. In previous work of this series the form of this functional was found for the two- (Blum, Herrera, Mol. Phys. 96 (1999) 821) and three-exponential closures of the OZ equation (Blum, J. Stat. Phys., submitted for publication). In this paper we extend this to M Yukawas, a complete basis set: We obtain a solution for the one-component case and give a closed-form expression for the MSA excess entropy, which is also the VMSSA entropy.
A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches
NASA Astrophysics Data System (ADS)
Sedighi, Hamid M.; Shirazi, Kourosh H.; Attarzadeh, Mohammad A.
2013-10-01
This paper intends to promote the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams. Four new studied methods are Stiffness analytical approximation method, Homotopy Perturbation Method with an Auxiliary Term, Max-Min Approach (MMA) and Iteration Perturbation Method (IPM). The powerful analytical approaches are used to obtain the nonlinear frequency-amplitude relationship for dynamic behavior of vibrating beams with quintic nonlinearity. It is demonstrated that the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the integrity of the asymptotic methods.
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.
Accurate quantum chemical calculations
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.; Taylor, Peter R.
1989-01-01
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 accurate 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 approximate 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 accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.
Optimizing the Zeldovich approximation
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Pellman, Todd F.; Shandarin, Sergei F.
1994-01-01
We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment
Quo vadis, analytical chemistry?
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. PMID:26631024
Quo vadis, analytical chemistry?
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.
Effenberger, Frederic; Litvinenko, Yuri E.
2014-03-01
The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wave-like aspects of the cosmic-ray transport.
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.
An approximation technique for jet impingement flow
Najafi, Mahmoud; Fincher, Donald; Rahni, Taeibi; Javadi, KH.; Massah, H.
2015-03-10
The analytical approximate solution of a non-linear jet impingement flow model will be demonstrated. We will show that this is an improvement over the series approximation obtained via the Adomian decomposition method, which is itself, a powerful method for analysing non-linear differential equations. The results of these approximations will be compared to the Runge-Kutta approximation in order to demonstrate their validity.
Guggenheim, James A.; Bargigia, Ilaria; Farina, Andrea; Pifferi, Antonio; Dehghani, Hamid
2016-01-01
A novel straightforward, accessible and efficient approach is presented for performing hyperspectral time-domain diffuse optical spectroscopy to determine the optical properties of samples accurately using geometry specific models. To allow bulk parameter recovery from measured spectra, a set of libraries based on a numerical model of the domain being investigated is developed as opposed to the conventional approach of using an analytical semi-infinite slab approximation, which is known and shown to introduce boundary effects. Results demonstrate that the method improves the accuracy of derived spectrally varying optical properties over the use of the semi-infinite approximation. PMID:27699137
Guggenheim, James A.; Bargigia, Ilaria; Farina, Andrea; Pifferi, Antonio; Dehghani, Hamid
2016-01-01
A novel straightforward, accessible and efficient approach is presented for performing hyperspectral time-domain diffuse optical spectroscopy to determine the optical properties of samples accurately using geometry specific models. To allow bulk parameter recovery from measured spectra, a set of libraries based on a numerical model of the domain being investigated is developed as opposed to the conventional approach of using an analytical semi-infinite slab approximation, which is known and shown to introduce boundary effects. Results demonstrate that the method improves the accuracy of derived spectrally varying optical properties over the use of the semi-infinite approximation.
NASA Astrophysics Data System (ADS)
Dattani, Nikesh S.; Welsh, Staszek
2014-06-01
Being the simplest neutral open shell molecule, BeH is a very important benchmark system for ab initio calculations. However, the most accurate empirical potentials and Born-Oppenheimer breakdown (BOB) functions for this system are nearly a decade old and are not reliable in the long-range region. Particularly, the uncertainties in their dissociation energies were about ±200 cm-1, and even the number of vibrational levels predicted was at the time very questionable, meaning that no good benchmark exists for ab initio calculations on neutral open shell molecules. We build new empirical potentials for BeH, BeD, and BeT that are much more reliable in the long-range. Being the second lightest heteronuclear molecule with a stable ground electronic state, BeH is also very important for the study of isotope effects, such as BOB. We extensively study isotope effects in this system, and we show that the empirical BOB functions fitted from the data of any two isotopologues, is sufficient to predict crucial properties of the third isotopologue.
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.
NASA Astrophysics Data System (ADS)
Pratiwi, B. N.; Suparmi, A.; Cari, C.; Husein, A. S.; Yunianto, M.
2016-08-01
We apllied asymptotic iteration method (AIM) to obtain the analytical solution of the Dirac equation in case exact pseudospin symmetry in the presence of modified Pcischl- Teller potential and trigonometric Scarf II non-central potential. The Dirac equation was solved by variables separation into one dimensional Dirac equation, the radial part and angular part equation. The radial and angular part equation can be reduced into hypergeometric type equation by variable substitution and wavefunction substitution and then transform it into AIM type equation to obtain relativistic energy eigenvalue and wavefunctions. Relativistic energy was calculated numerically by Matlab software. And then relativistic energy spectrum and wavefunctions were visualized by Matlab software. The results show that the increase in the radial quantum number nr causes decrease in the relativistic energy spectrum. The negative value of energy is taken due to the pseudospin symmetry limit. Several quantum wavefunctions were presented in terms of the hypergeometric functions.
Approximate Bayesian multibody tracking.
Lanz, Oswald
2006-09-01
Visual tracking of multiple targets is a challenging problem, especially when efficiency is an issue. Occlusions, if not properly handled, are a major source of failure. Solutions supporting principled occlusion reasoning have been proposed but are yet unpractical for online applications. This paper presents a new solution which effectively manages the trade-off between reliable modeling and computational efficiency. The Hybrid Joint-Separable (HJS) filter is derived from a joint Bayesian formulation of the problem, and shown to be efficient while optimal in terms of compact belief representation. Computational efficiency is achieved by employing a Markov random field approximation to joint dynamics and an incremental algorithm for posterior update with an appearance likelihood that implements a physically-based model of the occlusion process. A particle filter implementation is proposed which achieves accurate tracking during partial occlusions, while in cases of complete occlusion, tracking hypotheses are bound to estimated occlusion volumes. Experiments show that the proposed algorithm is efficient, robust, and able to resolve long-term occlusions between targets with identical appearance. PMID:16929730
Abrupt PN junctions: Analytical solutions under equilibrium and non-equilibrium
NASA Astrophysics Data System (ADS)
Khorasani, Sina
2016-08-01
We present an explicit solution of carrier and field distributions in abrupt PN junctions under equilibrium. An accurate logarithmic numerical method is implemented and results are compared to the analytical solutions. Analysis of results shows reasonable agreement with numerical solution as well as the depletion layer approximation. We discuss extensions to the asymmetric junctions. Approximate relations for differential capacitance C-V and current-voltage I-V characteristics are also found under non-zero external bias.
NASA Astrophysics Data System (ADS)
Liu, Fang; Lin, Lin; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F.; Sharifzadeh, Sahar; da Jornada, Felipe H.; Deslippe, Jack; Yang, Chao; Neaton, Jeffrey B.; Louie, Steven G.
2015-04-01
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 of using different self energy expressions to perform the numerical convolution at different frequencies.
Approximate probability distributions of the master equation
NASA Astrophysics Data System (ADS)
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
Approximation by hinge functions
Faber, V.
1997-05-01
Breiman has defined {open_quotes}hinge functions{close_quotes} for use as basis functions in least squares approximations to data. A hinge function is the max (or min) function of two linear functions. In this paper, the author assumes the existence of smooth function f(x) and a set of samples of the form (x, f(x)) drawn from a probability distribution {rho}(x). The author hopes to find the best fitting hinge function h(x) in the least squares sense. There are two problems with this plan. First, Breiman has suggested an algorithm to perform this fit. The author shows that this algorithm is not robust and also shows how to create examples on which the algorithm diverges. Second, if the author tries to use the data to minimize the fit in the usual discrete least squares sense, the functional that must be minimized is continuous in the variables, but has a derivative which jumps at the data. This paper takes a different approach. This approach is an example of a method that the author has developed called {open_quotes}Monte Carlo Regression{close_quotes}. (A paper on the general theory is in preparation.) The author shall show that since the function f is continuous, the analytic form of the least squares equation is continuously differentiable. A local minimum is solved for by using Newton`s method, where the entries of the Hessian are estimated directly from the data by Monte Carlo. The algorithm has the desirable properties that it is quadratically convergent from any starting guess sufficiently close to a solution and that each iteration requires only a linear system solve.
Mathematical algorithms for approximate reasoning
NASA Technical Reports Server (NTRS)
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
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.
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.
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.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
NASA Astrophysics Data System (ADS)
Niiniluoto, Ilkka
2014-03-01
Approximation of laws is an important theme in the philosophy of science. If we can make sense of the idea that two scientific laws are "close" to each other, then we can also analyze such methodological notions as approximate explanation of laws, approximate reduction of theories, approximate empirical success of theories, and approximate truth of laws. Proposals for measuring the distance between quantitative scientific laws were given in Niiniluoto (1982, 1987). In this paper, these definitions are reconsidered as a response to the interesting critical remarks by Liu (1999).
Bent approximations to synchrotron radiation optics
Heald, S.
1981-01-01
Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors.
Generalized Gradient Approximation Made Simple
Perdew, J.P.; Burke, K.; Ernzerhof, M.
1996-10-01
Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
An approximate model for pulsar navigation simulation
NASA Astrophysics Data System (ADS)
Jovanovic, Ilija; Enright, John
2016-02-01
This paper presents an approximate model for the simulation of pulsar aided navigation systems. High fidelity simulations of these systems are computationally intensive and impractical for simulating periods of a day or more. Simulation of yearlong missions is done by abstracting navigation errors as periodic Gaussian noise injections. This paper presents an intermediary approximate model to simulate position errors for periods of several weeks, useful for building more accurate Gaussian error models. This is done by abstracting photon detection and binning, replacing it with a simple deterministic process. The approximate model enables faster computation of error injection models, allowing the error model to be inexpensively updated throughout a simulation. Testing of the approximate model revealed an optimistic performance prediction for non-millisecond pulsars with more accurate predictions for pulsars in the millisecond spectrum. This performance gap was attributed to noise which is not present in the approximate model but can be predicted and added to improve accuracy.
High-order parabolic beam approximation for aero-optics
White, Michael D.
2010-08-01
The parabolic beam equations are solved using high-order compact differences for the Laplacians and Runge-Kutta integration along the beam path. The solution method is verified by comparison to analytical solutions for apertured beams and both constant and complex index of refraction. An adaptive 4th-order Runge-Kutta using an embedded 2nd-order method is presented that has demonstrated itself to be very robust. For apertured beams, the results show that the method fails to capture near aperture effects due to a violation of the paraxial approximation in that region. Initial results indicate that the problem appears to be correctable by successive approximations. A preliminary assessment of the effect of turbulent scales is undertaken using high-order Lagrangian interpolation. The results show that while high fidelity methods are necessary to accurately capture the large scale flow structure, the method may not require the same level of fidelity in sampling the density for the index of refraction. The solution is used to calculate a phase difference that is directly compared with that commonly calculated via the optical path difference. Propagation through a supersonic boundary layer shows that for longer wavelengths, the traditional method to calculate the optical path is less accurate than for shorter wavelengths. While unlikely to supplant more traditional methods for most aero-optics applications, the current method can be used to give a quantitative assessment of the other methods as well as being amenable to the addition of more physics.
Accurate monotone cubic interpolation
NASA Technical Reports Server (NTRS)
Huynh, Hung T.
1991-01-01
Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.
Accurate Finite Difference Algorithms
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1996-01-01
Two families of finite difference algorithms for computational aeroacoustics are presented and compared. All of the algorithms are single step explicit methods, they have the same order of accuracy in both space and time, with examples up to eleventh order, and they have multidimensional extensions. One of the algorithm families has spectral like high resolution. Propagation with high order and high resolution algorithms can produce accurate results after O(10(exp 6)) periods of propagation with eight grid points per wavelength.
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.
Analytic barrage attack model. Final report, January 1986-January 1989
St Ledger, J.W.; Naegeli, R.E.; Dowden, N.A.
1989-01-01
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 the analytic model and for a numerical model used to check the analytic results.
Accurate verification of the conserved-vector-current and standard-model predictions
Sirlin, A.; Zucchini, R.
1986-10-20
An approximate analytic calculation of O(Z..cap alpha../sup 2/) corrections to Fermi decays is presented. When the analysis of Koslowsky et al. is modified to take into account the new results, it is found that each of the eight accurately studied scrFt values differs from the average by approx. <1sigma, thus significantly improving the comparison of experiments with conserved-vector-current predictions. The new scrFt values are lower than before, which also brings experiments into very good agreement with the three-generation standard model, at the level of its quantum corrections.
Approximate Solutions Of Equations Of Steady Diffusion
NASA Technical Reports Server (NTRS)
Edmonds, Larry D.
1992-01-01
Rigorous analysis yields reliable criteria for "best-fit" functions. Improved "curve-fitting" method yields approximate solutions to differential equations of steady-state diffusion. Method applies to problems in which rates of diffusion depend linearly or nonlinearly on concentrations of diffusants, approximate solutions analytic or numerical, and boundary conditions of Dirichlet type, of Neumann type, or mixture of both types. Applied to equations for diffusion of charge carriers in semiconductors in which mobilities and lifetimes of charge carriers depend on concentrations.
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.
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.
Computer Experiments for Function Approximations
Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C
2007-10-15
This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.
NASA Technical Reports Server (NTRS)
Flannelly, W. G.; Fabunmi, J. A.; Nagy, E. J.
1981-01-01
Analytical methods for combining flight acceleration and strain data with shake test mobility data to predict the effects of structural changes on flight vibrations and strains are presented. This integration of structural dynamic analysis with flight performance is referred to as analytical testing. The objective of this methodology is to analytically estimate the results of flight testing contemplated structural changes with minimum flying and change trials. The category of changes to the aircraft includes mass, stiffness, absorbers, isolators, and active suppressors. Examples of applying the analytical testing methodology using flight test and shake test data measured on an AH-1G helicopter are included. The techniques and procedures for vibration testing and modal analysis are also described.
Generalized string models and their semiclassical approximation
NASA Astrophysics Data System (ADS)
Elizalde, E.
1984-04-01
We construct an extensive family of Bose string models, all of them classically equivalent to the Nambu and Eguchi models. The new models involve an arbitrary analytical function f(u), with f(0)=0, and are based on the Brink-Di Vecchia-Howe and Polyakov string action. The semiclassical approximation of the models is worked out in detail.
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches.
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. PMID:25528318
Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling.
Yudovsky, Dmitry; Durkin, Anthony J
2011-07-20
Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.
Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling
NASA Astrophysics Data System (ADS)
Yudovsky, Dmitry; Durkin, Anthony J.
2011-07-01
Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.
NASA Astrophysics Data System (ADS)
Zaghloul, Mofreh R.; Bourham, Mohamed A.; Doster, J. Michael
2000-02-01
An exact analytical expression for the energy-averaged electron-ion momentum transport cross section in the Born approximation and Debye-Hückel exponentially screened potential has been derived and compared with the formulae given by other authors. A quantitative comparison between cut-off theory and quantum mechanical perturbation theory has been presented. Based on results from the Born approximation and Spitzer's formula, a new approximate formula for the quantum Coulomb logarithm has been derived and shown to be more accurate than previous expressions.
NASA Astrophysics Data System (ADS)
Zaghloul, Mofreh R.; Bourham, Mohamed A.; Doster, J. Michael
2000-04-01
An exact analytical expression for the energy-averaged electron-ion momentum transport cross section in the Born approximation and Debye-Hückel exponentially screened potential has been derived and compared with the formulae given by other authors. A quantitative comparison between cut-off theory and quantum mechanical perturbation theory has been presented. Based on results from the Born approximation and Spitzer's formula, a new approximate formula for the quantum Coulomb logarithm has been derived and shown to be more accurate than previous expressions.
Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations
Weinstein, Marvin; /SLAC
2009-02-12
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for the behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will
Frankenstein's glue: transition functions for approximate solutions
NASA Astrophysics Data System (ADS)
Yunes, Nicolás
2007-09-01
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate analytic solutions together. In particular, we propose certain sufficient conditions on these functions and prove that these conditions guarantee that the joined solution still satisfies the Einstein equations analytically to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the proposed conditions, then the joined solution does not contain any violations to the Einstein equations larger than those already inherent in the approximations. We further show that if these functions violate the proposed conditions, then the matter content of the spacetime is modified by the introduction of a matter shell, whose stress energy tensor depends on derivatives of these functions.
NASA Astrophysics Data System (ADS)
Papp, P.; Matejčík, Š.; Mach, P.; Urban, J.; Paidarová, I.; Horáček, J.
2013-06-01
The method of analytic continuation in the coupling constant (ACCC) in combination with use of the statistical Padé approximation is applied to the determination of resonance energy and width of some amino acids and formic acid dimer. Standard quantum chemistry codes provide accurate data which can be used for analytic continuation in the coupling constant to obtain the resonance energy and width of organic molecules with a good accuracy. The obtained results are compared with the existing experimental ones.
Analytical scatter kernels for portal imaging at 6 MV.
Spies, L; Bortfeld, T
2001-04-01
X-ray photon scatter kernels for 6 MV electronic portal imaging are investigated using an analytical and a semi-analytical model. The models are tested on homogeneous phantoms for a range of uniform circular fields and scatterer-to-detector air gaps relevant for clinical use. It is found that a fully analytical model based on an exact treatment of photons undergoing a single Compton scatter event and an approximate treatment of second and higher order scatter events, assuming a multiple-scatter source at the center of the scatter volume, is accurate within 1% (i.e., the residual scatter signal is less than 1% of the primary signal) for field sizes up to 100 cm2 and air gaps over 30 cm, but shows significant discrepancies for larger field sizes. Monte Carlo results are presented showing that the effective multiple-scatter source is located toward the exit surface of the scatterer, rather than at its center. A second model is therefore investigated where second and higher-order scattering is instead modeled by fitting an analytical function describing a nonstationary isotropic point-scatter source to Monte Carlo generated data. This second model is shown to be accurate to within 1% for air gaps down to 20 cm, for field sizes up to 900 cm2 and phantom thicknesses up to 50 cm. PMID:11339752
Towards numerically accurate many-body perturbation theory: Short-range correlation effects
Gulans, Andris
2014-10-28
The example of the uniform electron gas is used for showing that the short-range electron correlation is difficult to handle numerically, while it noticeably contributes to the self-energy. Nonetheless, in condensed-matter applications studied with advanced methods, such as the GW and random-phase approximations, it is common to neglect contributions due to high-momentum (large q) transfers. Then, the short-range correlation is poorly described, which leads to inaccurate correlation energies and quasiparticle spectra. To circumvent this problem, an accurate extrapolation scheme is proposed. It is based on an analytical derivation for the uniform electron gas presented in this paper, and it provides an explanation why accurate GW quasiparticle spectra are easy to obtain for some compounds and very difficult for others.
Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen; Ringler, Todd
2012-01-01
The numerical modeling of glacier and ice sheet evolution is a subject of growing interest, in part because of the potential for models to inform estimates of global sea level change. This paper focuses on the development of a numerical model that determines the velocity and pressure fields within an ice sheet. Our numerical model features a high-fidelity mathematical model involving the nonlinear Stokes system and combinations of no-sliding and sliding basal boundary conditions, high-order accurate finite element discretizations based on variable resolution grids, and highly scalable parallel solution strategies, all of which contribute to a numerical model that can achieve accurate velocity and pressure approximations in a highly efficient manner. We demonstrate the accuracy and efficiency of our model by analytical solution tests, established ice sheet benchmark experiments, and comparisons with other well-established ice sheet models.
Not Available
2006-06-01
In the Analytical Microscopy group, within the National Center for Photovoltaic's Measurements and Characterization Division, we combine two complementary areas of analytical microscopy--electron microscopy and proximal-probe techniques--and use a variety of state-of-the-art imaging and analytical tools. We also design and build custom instrumentation and develop novel techniques that provide unique capabilities for studying materials and devices. In our work, we collaborate with you to solve materials- and device-related R&D problems. This sheet summarizes the uses and features of four major tools: transmission electron microscopy, scanning electron microscopy, the dual-beam focused-ion-beam workstation, and scanning probe microscopy.
Plasma Physics Approximations in Ares
Managan, R. A.
2015-01-08
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} (ζ ),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.
Accurate Optical Reference Catalogs
NASA Astrophysics Data System (ADS)
Zacharias, N.
2006-08-01
Current and near future all-sky astrometric catalogs on the ICRF are reviewed with the emphasis on reference star data at optical wavelengths for user applications. The standard error of a Hipparcos Catalogue star position is now about 15 mas per coordinate. For the Tycho-2 data it is typically 20 to 100 mas, depending on magnitude. The USNO CCD Astrograph Catalog (UCAC) observing program was completed in 2004 and reductions toward the final UCAC3 release are in progress. This all-sky reference catalogue will have positional errors of 15 to 70 mas for stars in the 10 to 16 mag range, with a high degree of completeness. Proper motions for the about 60 million UCAC stars will be derived by combining UCAC astrometry with available early epoch data, including yet unpublished scans of the complete set of AGK2, Hamburg Zone astrograph and USNO Black Birch programs. Accurate positional and proper motion data are combined in the Naval Observatory Merged Astrometric Dataset (NOMAD) which includes Hipparcos, Tycho-2, UCAC2, USNO-B1, NPM+SPM plate scan data for astrometry, and is supplemented by multi-band optical photometry as well as 2MASS near infrared photometry. The Milli-Arcsecond Pathfinder Survey (MAPS) mission is currently being planned at USNO. This is a micro-satellite to obtain 1 mas positions, parallaxes, and 1 mas/yr proper motions for all bright stars down to about 15th magnitude. This program will be supplemented by a ground-based program to reach 18th magnitude on the 5 mas level.
ERIC Educational Resources Information Center
Wolff, Hans
This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…
NASA Astrophysics Data System (ADS)
Huang, Siendong
2009-11-01
The nonlocality of quantum states on a bipartite system \\mathcal {A+B} is tested by comparing probabilistic outcomes of two local observables of different subsystems. For a fixed observable A of the subsystem \\mathcal {A,} its optimal approximate double A' of the other system \\mathcal {B} is defined such that the probabilistic outcomes of A' are almost similar to those of the fixed observable A. The case of σ-finite standard von Neumann algebras is considered and the optimal approximate double A' of an observable A is explicitly determined. The connection between optimal approximate doubles and quantum correlations is explained. Inspired by quantum states with perfect correlation, like Einstein-Podolsky-Rosen states and Bohm states, the nonlocality power of an observable A for general quantum states is defined as the similarity that the outcomes of A look like the properties of the subsystem \\mathcal {B} corresponding to A'. As an application of optimal approximate doubles, maximal Bell correlation of a pure entangled state on \\mathcal {B}(\\mathbb {C}^{2})\\otimes \\mathcal {B}(\\mathbb {C}^{2}) is found explicitly.
Approximating Integrals Using Probability
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.; Caudle, Kyle A.
2005-01-01
As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…
NASA Astrophysics Data System (ADS)
Zlochower, Yosef; Nakano, Hiroyuki; Mundim, Bruno C.; Campanelli, Manuela; Noble, Scott; Zilhão, Miguel
2016-06-01
We explore how a recently developed analytical black-hole binary spacetime can be extended using numerical simulations to go beyond the slow-inspiral phase. The analytic spacetime solves the Einstein field equations approximately, with the approximation error becoming progressively smaller the more separated the binary. To continue the spacetime beyond the slow-inspiral phase, we need to transition. Such a transition was previously explored at smaller separations. Here, we perform this transition at a separation of D =20 M (large enough that the analytical metric is expected to be accurate), and evolve for six orbits. We find that small constraint violations can have large dynamical effects, but these can be removed by using a constraint-damping system like the conformal covariant formulation of the Z4 system. We find agreement between the subsequent numerical spacetime and the predictions of post-Newtonian theory for the waveform and inspiral rate that is within the post-Newtonian truncation error.
Mappings and accuracy for Chebyshev pseudo-spectral approximations
NASA Technical Reports Server (NTRS)
Bayliss, Alvin; Turkel, Eli
1992-01-01
The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed.
Mappings and accuracy for Chebyshev pseudo-spectral approximations
NASA Technical Reports Server (NTRS)
Bayliss, Alvin; Turkel, Eli
1990-01-01
The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed.
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.
Exact PDF equations and closure approximations for advective-reactive transport
Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.; Karniadakis, George E.
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 recently 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.
Novel bivariate moment-closure approximations.
Krishnarajah, Isthrinayagy; Marion, Glenn; Gibson, Gavin
2007-08-01
Nonlinear stochastic models are typically intractable to analytic solutions and hence, moment-closure schemes are used to provide approximations to these models. Existing closure approximations are often unable to describe transient aspects caused by extinction behaviour in a stochastic process. Recent work has tackled this problem in the univariate case. In this study, we address this problem by introducing novel bivariate moment-closure methods based on mixture distributions. Novel closure approximations are developed, based on the beta-binomial, zero-modified distributions and the log-Normal, designed to capture the behaviour of the stochastic SIS model with varying population size, around the threshold between persistence and extinction of disease. The idea of conditional dependence between variables of interest underlies these mixture approximations. In the first approximation, we assume that the distribution of infectives (I) conditional on population size (N) is governed by the beta-binomial and for the second form, we assume that I is governed by zero-modified beta-binomial distribution where in either case N follows a log-Normal distribution. We analyse the impact of coupling and inter-dependency between population variables on the behaviour of the approximations developed. Thus, the approximations are applied in two situations in the case of the SIS model where: (1) the death rate is independent of disease status; and (2) the death rate is disease-dependent. Comparison with simulation shows that these mixture approximations are able to predict disease extinction behaviour and describe transient aspects of the process.
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.
Lewis, D.W. . Dept. of Geology); McConchie, D.M. . Centre for Coastal Management)
1994-01-01
Both a self instruction manual and a cookbook'' guide to field and laboratory analytical procedures, this book provides an essential reference for non-specialists. With a minimum of mathematics and virtually no theory, it introduces practitioners to easy, inexpensive options for sample collection and preparation, data acquisition, analytic protocols, result interpretation and verification techniques. This step-by-step guide considers the advantages and limitations of different procedures, discusses safety and troubleshooting, and explains support skills like mapping, photography and report writing. It also offers managers, off-site engineers and others using sediments data a quick course in commissioning studies and making the most of the reports. This manual will answer the growing needs of practitioners in the field, either alone or accompanied by Practical Sedimentology, which surveys the science of sedimentology and provides a basic overview of the principles behind the applications.
Second-order analytic solutions for re-entry trajectories
NASA Astrophysics Data System (ADS)
Kim, Eun-Kyou
1993-01-01
With the development of aeroassist technology, either for near-earth orbital transfer with or without a plane change or for planetary aerocapture, it is of interest to have accurate analytic solutions for reentry trajectories in an explicit form. Starting with the equations of motion of a non-thrusting aerodynamic vehicle entering a non-rotating spherical planetary atmosphere, a normalization technique is used to transform the equations into a form suitable for an analytic integration. Then, depending on the type of planar entry modes with a constant angle-of-attack, namely, ballistic fly-through, lifting skip, and equilibrium glide trajectories, the first-order solutions are obtained with the appropriate simplification. By analytic continuation, the second-order solutions for the altitude, speed, and flight path angle are derived. The closed form solutions lead to explicit forms for the physical quantities of interest, such as the deceleration and aerodynamic heating rates. The analytic solutions for the planar case are extended to three-dimensional skip trajectories with a constant bank angle. The approximate solutions for the heading and latitude are developed to the second order. In each type of trajectory examined, explicit relations among the principal variables are in a form suitable for guidance and navigation purposes. The analytic solutions have excellent agreement with the numerical integrations. They also provide some new results which were not reported in the existing classical theory.
Approximating the physical inner product of loop quantum cosmology
NASA Astrophysics Data System (ADS)
Bahr, Benjamin; Thiemann, Thomas
2007-04-01
In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity.
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.
Chalasani, P.; Saias, I.; Jha, S.
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Second derivatives for approximate spin projection methods
Thompson, Lee M.; Hratchian, Hrant P.
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 second derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.
An effective analytic approach for solving nonlinear fractional partial differential equations
NASA Astrophysics Data System (ADS)
Ma, Junchi; Zhang, Xiaolong; Liang, Songxin
2016-08-01
Nonlinear fractional differential equations are widely used for modelling problems in applied mathematics. A new analytic approach with two parameters c1 and c2 is first proposed for solving nonlinear fractional partial differential equations. These parameters are used to improve the accuracy of the resulting series approximations. It turns out that much more accurate series approximations are obtained by choosing proper values of c1 and c2. To demonstrate the applicability and effectiveness of the new method, two typical fractional partial differential equations, the nonlinear gas dynamics equation and the nonlinear KdV-Burgers equation, are solved.
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.
IONIS: Approximate atomic photoionization intensities
NASA Astrophysics Data System (ADS)
Heinäsmäki, Sami
2012-02-01
A program to compute relative atomic photoionization cross sections is presented. The code applies the output of the multiconfiguration Dirac-Fock method for atoms in the single active electron scheme, by computing the overlap of the bound electron states in the initial and final states. The contribution from the single-particle ionization matrix elements is assumed to be the same for each final state. This method gives rather accurate relative ionization probabilities provided the single-electron ionization matrix elements do not depend strongly on energy in the region considered. The method is especially suited for open shell atoms where electronic correlation in the ionic states is large. Program summaryProgram title: IONIS Catalogue identifier: AEKK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1149 No. of bytes in distributed program, including test data, etc.: 12 877 Distribution format: tar.gz Programming language: Fortran 95 Computer: Workstations Operating system: GNU/Linux, Unix Classification: 2.2, 2.5 Nature of problem: Photoionization intensities for atoms. Solution method: The code applies the output of the multiconfiguration Dirac-Fock codes Grasp92 [1] or Grasp2K [2], to compute approximate photoionization intensities. The intensity is computed within the one-electron transition approximation and by assuming that the sum of the single-particle ionization probabilities is the same for all final ionic states. Restrictions: The program gives nonzero intensities for those transitions where only one electron is removed from the initial configuration(s). Shake-type many-electron transitions are not computed. The ionized shell must be closed in the initial state. Running time: Few seconds for a
Roy, Swapnoneel; Thakur, Ashok Kumar
2008-01-01
Genome rearrangements have been modelled by a variety of primitives such as reversals, transpositions, block moves and block interchanges. We consider such a genome rearrangement primitive Strip Exchanges. Given a permutation, the challenge is to sort it by using minimum number of strip exchanges. A strip exchanging move interchanges the positions of two chosen strips so that they merge with other strips. The strip exchange problem is to sort a permutation using minimum number of strip exchanges. We present here the first non-trivial 2-approximation algorithm to this problem. We also observe that sorting by strip-exchanges is fixed-parameter-tractable. Lastly we discuss the application of strip exchanges in a different area Optical Character Recognition (OCR) with an example.
Hierarchical Approximate Bayesian Computation
Turner, Brandon M.; Van Zandt, Trisha
2013-01-01
Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model’s parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function. PMID:24297436
Flanagan, R J; Widdop, B; Ramsey, J D; Loveland, M
1988-09-01
1. Major advances in analytical toxicology followed the introduction of spectroscopic and chromatographic techniques in the 1940s and early 1950s and thin layer chromatography remains important together with some spectrophotometric and other tests. However, gas- and high performance-liquid chromatography together with a variety of immunoassay techniques are now widely used. 2. The scope and complexity of forensic and clinical toxicology continues to increase, although the compounds for which emergency analyses are needed to guide therapy are few. Exclusion of the presence of hypnotic drugs can be important in suspected 'brain death' cases. 3. Screening for drugs of abuse has assumed greater importance not only for the management of the habituated patient, but also in 'pre-employment' and 'employment' screening. The detection of illicit drug administration in sport is also an area of increasing importance. 4. In industrial toxicology, the range of compounds for which blood or urine measurements (so called 'biological monitoring') can indicate the degree of exposure is increasing. The monitoring of environmental contaminants (lead, chlorinated pesticides) in biological samples has also proved valuable. 5. In the near future a consensus as to the units of measurement to be used is urgently required and more emphasis will be placed on interpretation, especially as regards possible behavioural effects of drugs or other poisons. Despite many advances in analytical techniques there remains a need for reliable, simple tests to detect poisons for use in smaller hospital and other laboratories.
Chiral logs and the quenched approximation on the lattice
NASA Astrophysics Data System (ADS)
Perrucci, Stefania
1997-12-01
The phenomenological success of the quenched approximation has been impressive in obtaining accurate results for the mass spectrum and other aspects of hadron structure. However, an independent theoretical estimate of the systematic error introduced by quenching is still missing. To this end, it can be useful to consider chiral theories which, at the one-loop level, introduced peculiar non analytical terms (the so-called chiral logs). Sharpe showed that when this framework is adapted to the quenched approximation, the dependence of the pion mass squared on the quark mass can be described by an anomalous power δ (the 'hairpin' diagram on the pion mass shell) associated with flavor singlet loops and enhanced chiral logs. Treating the hairpin as a momentum independent mass insertion, he estimated δ≃0.2. However, numerical calculations in quenched lattice quantum chromodynamics show little or no evidence for chiral logs at such a level. The following work determines the anomalous power numerically by studying the pion mass as a function of the bare quark mass, as well as its volume dependence. Sources of systematic error are carefully examined. Last, the coefficient of the chiral log is calculated from the two quark-loops pion propagator. The results consistently indicate a value for the anomalous power that is approximately one order of magnitude smaller than the earlier theoretical estimate, in particular/delta = 0.013(2)From this one can see that for all pion masses considered, the systematic error introduced by quenching is small and always within the statistical error. Finally, by a direct calculation of the topological susceptibility of the lattice configurations, I conclude that the reason why the anomalous power is so small is a strong momentum dependence giving rise to a suppression of the hairpin at momenta comparable with the pion mass.
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.
Testing validity of the Kirkwood approximation using an extended Sznajd model.
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)]. This approximation is peculiar in that, in spite of the agreement with simulation results [F. Slanina et al., Europhys. Lett. 82, 18006 (2008); R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008); A. M. Timpanaro and C. P. C. Prado, Phys. Rev. E 89, 052808 (2014)], 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); K. Sznajd-Weron and J. Sznajd, Int. J. Mod. Phys. C 11, 1157 (2000)] 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 10(3) 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.
An Analytic Function of Lunar Surface Temperature for Exospheric Modeling
NASA Technical Reports Server (NTRS)
Hurley, Dana M.; Sarantos, Menelaos; Grava, Cesare; Williams, Jean-Pierre; Retherford, Kurt D.; Siegler, Matthew; Greenhagen, Benjamin; Paige, David
2014-01-01
We present an analytic expression to represent the lunar surface temperature as a function of Sun-state latitude and local time. The approximation represents neither topographical features nor compositional effects and therefore does not change as a function of selenographic latitude and longitude. The function reproduces the surface temperature measured by Diviner to within +/-10 K at 72% of grid points for dayside solar zenith angles of less than 80, and at 98% of grid points for nightside solar zenith angles greater than 100. The analytic function is least accurate at the terminator, where there is a strong gradient in the temperature, and the polar regions. Topographic features have a larger effect on the actual temperature near the terminator than at other solar zenith angles. For exospheric modeling the effects of topography on the thermal model can be approximated by using an effective longitude for determining the temperature. This effective longitude is randomly redistributed with 1 sigma of 4.5deg. The resulting ''roughened'' analytical model well represents the statistical dispersion in the Diviner data and is expected to be generally useful for future models of lunar surface temperature, especially those implemented within exospheric simulations that address questions of volatile transport.
Perturbation approximation for orbits in axially symmetric funnels
NASA Astrophysics Data System (ADS)
Nauenberg, Michael
2014-11-01
A perturbation method that can be traced back to Isaac Newton is applied to obtain approximate analytic solutions for objects sliding in axially symmetric funnels in near circular orbits. Some experimental observations are presented for balls rolling in inverted cones with different opening angles, and in a funnel with a hyperbolic surface that approximately simulates the gravitational force.
An improved proximity force approximation for electrostatics
Fosco, Cesar D.; Lombardo, Fernando C.; Mazzitelli, Francisco D.
2012-08-15
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called 'proximity force approximation' the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction in atomic force microscopes. - Highlights: Black-Right-Pointing-Pointer The proximity force approximation (PFA) has been widely used in different areas. Black-Right-Pointing-Pointer The PFA can be improved using a derivative expansion in the shape of the surfaces. Black-Right-Pointing-Pointer We use the improved PFA to compute electrostatic forces between conductors. Black-Right-Pointing-Pointer The results can be used as an analytic benchmark for numerical calculations in AFM. Black-Right-Pointing-Pointer Insight is provided for people who use the PFA to compute nuclear and Casimir forces.
White, J A; Dutton, A W; Schmidt, J A; Roemer, R B
2000-01-01
An automated three-element meshing method for generating finite element based models for the accurate thermal analysis of blood vessels imbedded in tissue has been developed and evaluated. The meshing method places eight noded hexahedral elements inside the vessels where advective flows exist, and four noded tetrahedral elements in the surrounding tissue. The higher order hexahedrals are used where advective flow fields occur, since high accuracy is required and effective upwinding algorithms exist. Tetrahedral elements are placed in the remaining tissue region, since they are computationally more efficient and existing automatic tetrahedral mesh generators can be used. Five noded pyramid elements connect the hexahedrals and tetrahedrals. A convective energy equation (CEE) based finite element algorithm solves for the temperature distributions in the flowing blood, while a finite element formulation of a generalized conduction equation is used in the surrounding tissue. Use of the CEE allows accurate solutions to be obtained without the necessity of assuming ad hoc values for heat transfer coefficients. Comparisons of the predictions of the three-element model to analytical solutions show that the three-element model accurately simulates temperature fields. Energy balance checks show that the three-element model has small, acceptable errors. In summary, this method provides an accurate, automatic finite element gridding procedure for thermal analysis of irregularly shaped tissue regions that contain important blood vessels. At present, the models so generated are relatively large (in order to obtain accurate results) and are, thus, best used for providing accurate reference values for checking other approximate formulations to complicated, conjugated blood heat transfer problems.
NASA Astrophysics Data System (ADS)
Lubkin, Elihu
2002-04-01
In 1993,(E. & T. Lubkin, Int.J.Theor.Phys. 32), 993 (1993) we gave exact mean trace
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.
NASA Astrophysics Data System (ADS)
Ngo-Cong, D.; Mohammed, F. J.; Strunin, D. V.; Skvortsov, A. T.; Mai-Duy, N.; Tran-Cong, T.
2015-06-01
The contaminant transport process governed by the advection-diffusion equation plays an important role in modelling industrial and environmental flows. In this article, our aim is to accurately reduce the 2-D advection-diffusion equation governing the dispersion of a contaminant in a turbulent open channel flow to its 1-D approximation. The 1-D model helps to quickly estimate the horizontal size of contaminant clouds based on the values of the model coefficients. We derive these coefficients analytically and investigate numerically the model convergence. The derivation is based on the centre manifold theory to obtain successively more accurate approximations in a consistent manner. Two types of the average velocity profile are considered: the classical logarithmic profile and the power profile. We further develop the one-dimensional integrated radial basis function network method as a numerical approach to obtain the numerical solutions to both the original 2-D equation and the approximate 1-D equations. We compare the solutions of the original models with their centre-manifold approximations at very large Reynolds numbers. The numerical results obtained from the approximate 1-D models are in good agreement with those of the original 2-D model for both the logarithmic and power velocity profiles.
Universality: Accurate Checks in Dyson's Hierarchical Model
NASA Astrophysics Data System (ADS)
Godina, J. J.; Meurice, Y.; Oktay, M. B.
2003-06-01
In this talk we present high-accuracy calculations of the susceptibility near βc for Dyson's hierarchical model in D = 3. Using linear fitting, we estimate the leading (γ) and subleading (Δ) exponents. Independent estimates are obtained by calculating the first two eigenvalues of the linearized renormalization group transformation. We found γ = 1.29914073 ± 10 -8 and, Δ = 0.4259469 ± 10-7 independently of the choice of local integration measure (Ising or Landau-Ginzburg). After a suitable rescaling, the approximate fixed points for a large class of local measure coincide accurately with a fixed point constructed by Koch and Wittwer.
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.
Chen, Carl G; Konkola, Paul T; Ferrera, Juan; Heilmann, Ralf K; Schattenburg, Mark L
2002-02-01
The analysis of many systems in optical communications and metrology utilizing Gaussian beams, such as free-space propagation from single-mode fibers, point diffraction interferometers, and interference lithography, would benefit from an accurate analytical model of Gaussian beam propagation. We present a full vector analysis of Gaussian beam propagation by using the well-known method of the angular spectrum of plane waves. A Gaussian beam is assumed to traverse a charge-free, homogeneous, isotropic, linear, and nonmagnetic dielectric medium. The angular spectrum representation, in its vector form, is applied to a problem with a Gaussian intensity boundary condition. After some mathematical manipulation, each nonzero propagating electric field component is expressed in terms of a power-series expansion. Previous analytical work derived a power series for the transverse field, where the first term (zero order) in the expansion corresponds to the usual scalar paraxial approximation. We confirm this result and derive a corresponding longitudinal power series. We show that the leading longitudinal term is comparable in magnitude with the first transverse term above the scalar paraxial term, thus indicating that a full vector theory is required when going beyond the scalar paraxial approximation. In spite of the advantages of a compact analytical formalism, enabling rapid and accurate modeling of Gaussian beam systems, this approach has a notable drawback. The higher-order terms diverge at locations that are sufficiently far from the initial boundary, yielding unphysical results. Hence any meaningful use of the expansion approach calls for a careful study of its range of applicability. By considering the transition of a Gaussian wave from the paraxial to the spherical regime, we are able to derive a simple expression for the range within which the series produce numerically satisfying answers.
A New Analytic Alignment Method for a SINS.
Tan, Caiming; Zhu, Xinhua; Su, Yan; Wang, Yu; Wu, Zhiqiang; Gu, Dongbing
2015-01-01
Analytic alignment is a type of self-alignment for a Strapdown inertial navigation system (SINS) that is based solely on two non-collinear vectors, which are the gravity and rotational velocity vectors of the Earth at a stationary base on the ground. The attitude of the SINS with respect to the Earth can be obtained directly using the TRIAD algorithm given two vector measurements. For a traditional analytic coarse alignment, all six outputs from the inertial measurement unit (IMU) are used to compute the attitude. In this study, a novel analytic alignment method called selective alignment is presented. This method uses only three outputs of the IMU and a few properties from the remaining outputs such as the sign and the approximate value to calculate the attitude. Simulations and experimental results demonstrate the validity of this method, and the precision of yaw is improved using the selective alignment method compared to the traditional analytic coarse alignment method in the vehicle experiment. The selective alignment principle provides an accurate relationship between the outputs and the attitude of the SINS relative to the Earth for a stationary base, and it is an extension of the TRIAD algorithm. The selective alignment approach has potential uses in applications such as self-alignment, fault detection, and self-calibration.
A New Analytic Alignment Method for a SINS.
Tan, Caiming; Zhu, Xinhua; Su, Yan; Wang, Yu; Wu, Zhiqiang; Gu, Dongbing
2015-01-01
Analytic alignment is a type of self-alignment for a Strapdown inertial navigation system (SINS) that is based solely on two non-collinear vectors, which are the gravity and rotational velocity vectors of the Earth at a stationary base on the ground. The attitude of the SINS with respect to the Earth can be obtained directly using the TRIAD algorithm given two vector measurements. For a traditional analytic coarse alignment, all six outputs from the inertial measurement unit (IMU) are used to compute the attitude. In this study, a novel analytic alignment method called selective alignment is presented. This method uses only three outputs of the IMU and a few properties from the remaining outputs such as the sign and the approximate value to calculate the attitude. Simulations and experimental results demonstrate the validity of this method, and the precision of yaw is improved using the selective alignment method compared to the traditional analytic coarse alignment method in the vehicle experiment. The selective alignment principle provides an accurate relationship between the outputs and the attitude of the SINS relative to the Earth for a stationary base, and it is an extension of the TRIAD algorithm. The selective alignment approach has potential uses in applications such as self-alignment, fault detection, and self-calibration. PMID:26556353
A New Analytic Alignment Method for a SINS
Tan, Caiming; Zhu, Xinhua; Su, Yan; Wang, Yu; Wu, Zhiqiang; Gu, Dongbing
2015-01-01
Analytic alignment is a type of self-alignment for a Strapdown inertial navigation system (SINS) that is based solely on two non-collinear vectors, which are the gravity and rotational velocity vectors of the Earth at a stationary base on the ground. The attitude of the SINS with respect to the Earth can be obtained directly using the TRIAD algorithm given two vector measurements. For a traditional analytic coarse alignment, all six outputs from the inertial measurement unit (IMU) are used to compute the attitude. In this study, a novel analytic alignment method called selective alignment is presented. This method uses only three outputs of the IMU and a few properties from the remaining outputs such as the sign and the approximate value to calculate the attitude. Simulations and experimental results demonstrate the validity of this method, and the precision of yaw is improved using the selective alignment method compared to the traditional analytic coarse alignment method in the vehicle experiment. The selective alignment principle provides an accurate relationship between the outputs and the attitude of the SINS relative to the Earth for a stationary base, and it is an extension of the TRIAD algorithm. The selective alignment approach has potential uses in applications such as self-alignment, fault detection, and self-calibration. PMID:26556353
NNLOPS accurate associated HW production
NASA Astrophysics Data System (ADS)
Astill, William; Bizon, Wojciech; Re, Emanuele; Zanderighi, Giulia
2016-06-01
We present a next-to-next-to-leading order accurate description of associated HW production consistently matched to a parton shower. The method is based on reweighting events obtained with the HW plus one jet NLO accurate calculation implemented in POWHEG, extended with the MiNLO procedure, to reproduce NNLO accurate Born distributions. Since the Born kinematics is more complex than the cases treated before, we use a parametrization of the Collins-Soper angles to reduce the number of variables required for the reweighting. We present phenomenological results at 13 TeV, with cuts suggested by the Higgs Cross section Working Group.
Precise and Accurate Density Determination of Explosives Using Hydrostatic Weighing
B. Olinger
2005-07-01
Precise and accurate density determination requires weight measurements in air and water using sufficiently precise analytical balances, knowledge of the densities of air and water, knowledge of thermal expansions, availability of a density standard, and a method to estimate the time to achieve thermal equilibrium with water. Density distributions in pressed explosives are inferred from the densities of elements from a central slice.
Accurate momentum transfer cross section for the attractive Yukawa potential
Khrapak, S. A.
2014-04-15
Accurate expression for the momentum transfer cross section for the attractive Yukawa potential is proposed. This simple analytic expression agrees with the numerical results better than to within ±2% in the regime relevant for ion-particle collisions in complex (dusty) plasmas.
ERIC Educational Resources Information Center
Bellera, Carine A.; Julien, Marilyse; Hanley, James A.
2010-01-01
The Wilcoxon statistics are usually taught as nonparametric alternatives for the 1- and 2-sample Student-"t" statistics in situations where the data appear to arise from non-normal distributions, or where sample sizes are so small that we cannot check whether they do. In the past, critical values, based on exact tail areas, were presented in…
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics.
Montoya-Castillo, Andrés; Reichman, David R
2016-05-14
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics. PMID:27179468
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics
NASA Astrophysics Data System (ADS)
Montoya-Castillo, Andrés; Reichman, David R.
2016-05-01
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.
Analytical determination of orbital elements using Fourier analysis. I. The radial velocity case
NASA Astrophysics Data System (ADS)
Delisle, J.-B.; Ségransan, D.; Buchschacher, N.; Alesina, F.
2016-05-01
We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is mainly limited by the accuracy of the computation of the Fourier decomposition of the signal which is sensitive to sampling and noise. Our method is complementary with more accurate (and more expensive in computer time) numerical algorithms (e.g. Levenberg-Marquardt, Markov chain Monte Carlo, genetic algorithms). Indeed, the analytical approximation can be used as an initial condition to accelerate the convergence of these numerical methods. Our method can be applied iteratively to search for multiple planets in the same system.
Accurate basis set truncation for wavefunction embedding
NASA Astrophysics Data System (ADS)
Barnes, Taylor A.; Goodpaster, Jason D.; Manby, Frederick R.; Miller, Thomas F.
2013-07-01
Density functional theory (DFT) provides a formally exact framework for performing embedded subsystem electronic structure calculations, including DFT-in-DFT and wavefunction theory-in-DFT descriptions. In the interest of efficiency, it is desirable to truncate the atomic orbital basis set in which the subsystem calculation is performed, thus avoiding high-order scaling with respect to the size of the MO virtual space. In this study, we extend a recently introduced projection-based embedding method [F. R. Manby, M. Stella, J. D. Goodpaster, and T. F. Miller III, J. Chem. Theory Comput. 8, 2564 (2012)], 10.1021/ct300544e to allow for the systematic and accurate truncation of the embedded subsystem basis set. The approach is applied to both covalently and non-covalently bound test cases, including water clusters and polypeptide chains, and it is demonstrated that errors associated with basis set truncation are controllable to well within chemical accuracy. Furthermore, we show that this approach allows for switching between accurate projection-based embedding and DFT embedding with approximate kinetic energy (KE) functionals; in this sense, the approach provides a means of systematically improving upon the use of approximate KE functionals in DFT embedding.
Assessment of the analytical capabilities of inductively coupled plasma-mass spectrometry
Taylor, H.E.; Garbarino, J.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.
Hadjitheodorou, Amalia; Kalosakas, George
2014-09-01
We investigate, both analytically and numerically, diffusion-controlled drug release from composite spherical formulations consisting of an inner core and an outer shell of different drug diffusion coefficients. Theoretically derived analytical results are based on the exact solution of Fick's second law of diffusion for a composite sphere, while numerical data are obtained using Monte Carlo simulations. In both cases, and for the range of matrix parameter values considered in this work, fractional drug release profiles are described accurately by a stretched exponential function. The release kinetics obtained is quantified through a detailed investigation of the dependence of the two stretched exponential release parameters on the device characteristics, namely the geometrical radii of the inner core and outer shell and the corresponding drug diffusion coefficients. Similar behaviors are revealed by both the theoretical results and the numerical simulations, and approximate analytical expressions are presented for the dependencies. PMID:25063169
Gravitational lensing from compact bodies: Analytical results for strong and weak deflection limits
Amore, Paolo; Cervantes, Mayra; De Pace, Arturo; Fernandez, Francisco M.
2007-04-15
We develop a nonperturbative method that yields analytical expressions for the deflection angle of light in a general static and spherically symmetric metric. The method works by introducing into the problem an artificial parameter, called {delta}, and by performing an expansion in this parameter to a given order. The results obtained are analytical and nonperturbative because they do not correspond to a polynomial expression in the physical parameters. Already to first order in {delta} the analytical formulas obtained using our method provide at the same time accurate approximations both at large distances (weak deflection limit) and at distances close to the photon sphere (strong deflection limit). We have applied our technique to different metrics and verified that the error is at most 0.5% for all regimes. We have also proposed an alternative approach which provides simpler formulas, although with larger errors.
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.
An accurate and practical method for inference of weak gravitational lensing from galaxy images
NASA Astrophysics Data System (ADS)
Bernstein, Gary M.; Armstrong, Robert; Krawiec, Christina; March, Marisa C.
2016-07-01
We demonstrate highly accurate recovery of weak gravitational lensing shear using an implementation of the Bayesian Fourier Domain (BFD) method proposed by Bernstein & Armstrong, extended to correct for selection biases. The BFD formalism is rigorously correct for Nyquist-sampled, background-limited, uncrowded images of background galaxies. BFD does not assign shapes to galaxies, instead compressing the pixel data D into a vector of moments M, such that we have an analytic expression for the probability P(M|g) of obtaining the observations with gravitational lensing distortion g along the line of sight. We implement an algorithm for conducting BFD's integrations over the population of unlensed source galaxies which measures ≈10 galaxies s-1 core-1 with good scaling properties. Initial tests of this code on ≈109 simulated lensed galaxy images recover the simulated shear to a fractional accuracy of m = (2.1 ± 0.4) × 10-3, substantially more accurate than has been demonstrated previously for any generally applicable method. Deep sky exposures generate a sufficiently accurate approximation to the noiseless, unlensed galaxy population distribution assumed as input to BFD. Potential extensions of the method include simultaneous measurement of magnification and shear; multiple-exposure, multiband observations; and joint inference of photometric redshifts and lensing tomography.
NASA Astrophysics Data System (ADS)
Sultan, Cornel
2010-10-01
The design of vector second-order linear systems for accurate proportional damping approximation is addressed. For this purpose an error system is defined using the difference between the generalized coordinates of the non-proportionally damped system and its proportionally damped approximation in modal space. The accuracy of the approximation is characterized using the energy gain of the error system and the design problem is formulated as selecting parameters of the non-proportionally damped system to ensure that this gain is sufficiently small. An efficient algorithm that combines linear matrix inequalities and simultaneous perturbation stochastic approximation is developed to solve the problem and examples of its application to tensegrity structures design are presented.
Structural design utilizing updated, approximate sensitivity derivatives
NASA Technical Reports Server (NTRS)
Scotti, Stephen J.
1993-01-01
A method to improve the computational efficiency of structural optimization algorithms is investigated. In this method, the calculations of 'exact' sensitivity derivatives of constraint functions are performed only at selected iterations during the optimization process. The sensitivity derivatives utilized within other iterations are approximate derivatives which are calculated using an inexpensive derivative update formula. Optimization results are presented for an analytic optimization problem (i.e., one having simple polynomial expressions for the objective and constraint functions) and for two structural optimization problems. The structural optimization results indicate that up to a factor of three improvement in computation time is possible when using the updated sensitivity derivatives.
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.
Approximate Solutions in Planted 3-SAT
NASA Astrophysics Data System (ADS)
Hsu, Benjamin; Laumann, Christopher; Moessner, Roderich; Sondhi, Shivaji
2013-03-01
In many computational settings, there exists many instances where finding a solution requires a computing time that grows exponentially in the number of variables. Concrete examples occur in combinatorial optimization problems and cryptography in computer science or glassy systems in physics. However, while exact solutions are often known to require exponential time, a related and important question is the running time required to find approximate solutions. Treating this problem as a problem in statistical physics at finite temperature, we examine the computational running time in finding approximate solutions in 3-satisfiability for randomly generated 3-SAT instances which are guaranteed to have a solution. Analytic predictions are corroborated by numerical evidence using stochastic local search algorithms. A first order transition is found in the running time of these algorithms.
Numerical and approximate solutions for plume rise
NASA Astrophysics Data System (ADS)
Krishnamurthy, Ramesh; Gordon Hall, J.
Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585-590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).
Analytical Chemistry of Nitric Oxide
Hetrick, Evan M.
2013-01-01
Nitric oxide (NO) is the focus of intense research, owing primarily to its wide-ranging biological and physiological actions. A requirement for understanding its origin, activity, and regulation is the need for accurate and precise measurement techniques. Unfortunately, analytical assays for monitoring NO are challenged by NO’s unique chemical and physical properties, including its reactivity, rapid diffusion, and short half-life. Moreover, NO concentrations may span pM to µM in physiological milieu, requiring techniques with wide dynamic response ranges. Despite such challenges, many analytical techniques have emerged for the detection of NO. Herein, we review the most common spectroscopic and electrochemical methods, with special focus on the fundamentals behind each technique and approaches that have been coupled with modern analytical measurement tools or exploited to create novel NO sensors. PMID:20636069
Fast and Provably Accurate Bilateral Filtering.
Chaudhury, Kunal N; Dabhade, Swapnil D
2016-06-01
The bilateral filter is a non-linear filter that uses a range filter along with a spatial filter to perform edge-preserving smoothing of images. A direct computation of the bilateral filter requires O(S) operations per pixel, where S is the size of the support of the spatial filter. In this paper, we present a fast and provably accurate algorithm for approximating the bilateral filter when the range kernel is Gaussian. In particular, for box and Gaussian spatial filters, the proposed algorithm can cut down the complexity to O(1) per pixel for any arbitrary S . The algorithm has a simple implementation involving N+1 spatial filterings, where N is the approximation order. We give a detailed analysis of the filtering accuracy that can be achieved by the proposed approximation in relation to the target bilateral filter. This allows us to estimate the order N required to obtain a given accuracy. We also present comprehensive numerical results to demonstrate that the proposed algorithm is competitive with the state-of-the-art methods in terms of speed and accuracy. PMID:27093722
NASA Technical Reports Server (NTRS)
Meador, W. E.; Weaver, W. R.
1980-01-01
Existing two-stream approximations to radiative transfer theory for particulate media are shown to be represented by identical forms of coupled differential equations if the intensity is replaced by integrals of the intensity over hemispheres. One set of solutions thus suffices for all methods and provides convenient analytical comparisons. The equations also suggest modifications of the standard techniques so as to duplicate exact solutions for thin atmospheres and thus permit accurate determinations of the effects of typical aerosol layers. Numerical results for the plane albedos of plane-parallel atmospheres are given for conventional and modified Eddington approximations, conventional and modified two-point quadrature schemes, the hemispheric-constant method and the delta-function method, all for comparison with accurate discrete-ordinate solutions. A new two-stream approximation is introduced that reduces to the modified Eddington approximation in the limit of isotropic phase functions and to the exact solution in the limit of extreme anisotropic scattering. Comparisons of plane albedos and transmittances show the new method to be generally superior over a wide range of atmospheric conditions (including cloud and aerosol layers), especially in the case of nonconservative scattering.
Visual analytics of brain networks.
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.
Visual Analytics of Brain Networks
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
2014-01-01
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. PMID:22414991
Structural interfaces in linear elasticity. Part I: Nonlocality and gradient approximations
NASA Astrophysics Data System (ADS)
Bertoldi, K.; Bigoni, D.; Drugan, W. J.
2007-01-01
Many biological and optimal materials, at multiple scales, consist of what can be idealized as continuous bodies joined by structural interfaces. Mechanical characterization of the microstructure defining the interface can nowadays be accurately done; however, such interfaces are usually analyzed employing models where those properties are overly simplified. To introduce into the analysis the microstructure properties, a new model of structural interfaces is proposed and developed: a true structure is introduced in the transition zone, joining continuous bodies, with geometrical and material properties directly obtained from those of the interfacial microstructure. First, the case of an elliptical inclusion connected by a structural interface to an infinite matrix is solved analytically, showing that nonlocal effects follow directly from the introduction of the structure, related to the inclination of the connecting elements. Second, starting from a discrete structure, a continuous model of a structural interface is derived. The usual zero-thickness linear interface model is shown to be a special case of this more general continuous structural interface model. Then, a gradient approximation of the interface constitutive law is rigorously derived: it is the first example of the analytical derivation of a nonlocal interface model from the microstructure properties. The effects introduced in the mechanical behavior by both the continuous model and its gradient approximation are illustrated by solving, for the first time, the problem of a circular inclusion connected to an infinite matrix by a structural interface and subject to remote uniform stress.
How to Solve Schroedinger Problems by Approximating the Potential Function
Ledoux, Veerle; Van Daele, Marnix
2010-09-30
We give a survey over the efforts in the direction of solving the Schroedinger equation by using piecewise approximations of the potential function. Two types of approximating potentials have been considered in the literature, that is piecewise constant and piecewise linear functions. For polynomials of higher degree the approximating problem is not so easy to integrate analytically. This obstacle can be circumvented by using a perturbative approach to construct the solution of the approximating problem, leading to the so-called piecewise perturbation methods (PPM). We discuss the construction of a PPM in its most convenient form for applications and show that different PPM versions (CPM,LPM) are in fact equivalent.
Scattering from rough thin films: discrete-dipole-approximation simulations.
Parviainen, Hannu; Lumme, Kari
2008-01-01
We investigate the wave-optical light scattering properties of deformed thin circular films of constant thickness using the discrete-dipole approximation. Effects on the intensity distribution of the scattered light due to different statistical roughness models, model dependent roughness parameters, and uncorrelated, random, small-scale porosity of the inhomogeneous medium are studied. The suitability of the discrete-dipole approximation for rough-surface scattering problems is evaluated by considering thin films as computationally feasible rough-surface analogs. The effects due to small-scale inhomogeneity of the scattering medium are compared with the analytic approximation by Maxwell Garnett, and the results are found to agree with the approximation.
Accurate theoretical chemistry with coupled pair models.
Neese, Frank; Hansen, Andreas; Wennmohs, Frank; Grimme, Stefan
2009-05-19
Quantum chemistry has found its way into the everyday work of many experimental chemists. Calculations can predict the outcome of chemical reactions, afford insight into reaction mechanisms, and be used to interpret structure and bonding in molecules. Thus, contemporary theory offers tremendous opportunities in experimental chemical research. However, even with present-day computers and algorithms, we cannot solve the many particle Schrodinger equation exactly; inevitably some error is introduced in approximating the solutions of this equation. Thus, the accuracy of quantum chemical calculations is of critical importance. The affordable accuracy depends on molecular size and particularly on the total number of atoms: for orientation, ethanol has 9 atoms, aspirin 21 atoms, morphine 40 atoms, sildenafil 63 atoms, paclitaxel 113 atoms, insulin nearly 800 atoms, and quaternary hemoglobin almost 12,000 atoms. Currently, molecules with up to approximately 10 atoms can be very accurately studied by coupled cluster (CC) theory, approximately 100 atoms with second-order Møller-Plesset perturbation theory (MP2), approximately 1000 atoms with density functional theory (DFT), and beyond that number with semiempirical quantum chemistry and force-field methods. The overwhelming majority of present-day calculations in the 100-atom range use DFT. Although these methods have been very successful in quantum chemistry, they do not offer a well-defined hierarchy of calculations that allows one to systematically converge to the correct answer. Recently a number of rather spectacular failures of DFT methods have been found-even for seemingly simple systems such as hydrocarbons, fueling renewed interest in wave function-based methods that incorporate the relevant physics of electron correlation in a more systematic way. Thus, it would be highly desirable to fill the gap between 10 and 100 atoms with highly correlated ab initio methods. We have found that one of the earliest (and now
The analytic renormalization group
NASA Astrophysics Data System (ADS)
Ferrari, Frank
2016-08-01
Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k ∈ Z, associated with the Matsubara frequencies νk = 2 πk / β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct "Analytic Renormalization Group" linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk | < μ (with the possible exception of the zero mode G0), together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk | ≥ μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately 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 approximate 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 approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated 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 approximations to f. Each of these new approximations 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 approximations, 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.
McCullagh, Nuala; Szalay, Alexander S.
2015-01-10
Baryon acoustic oscillations (BAO) are a powerful probe of the expansion history of the universe, which can tell us about the nature of dark energy. In order to accurately characterize the dark energy equation of state using BAO, we must understand the effects of both nonlinearities and redshift space distortions on the location and shape of the acoustic peak. In a previous paper, we introduced a novel approach to second order perturbation theory in configuration space using the Zel'dovich approximation, and presented a simple result for the first nonlinear term of the correlation function. In this paper, we extend this approach to redshift space. We show how to perform the computation and present the analytic result for the first nonlinear term in the correlation function. Finally, we validate our result through comparison with numerical simulations.
Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport
NASA Astrophysics Data System (ADS)
Litvinenko, Yuri E.; Noble, P. L.
2016-06-01
The telegraph equation and its generalizations have been repeatedly considered in the models of diffusive cosmic-ray transport. Yet the telegraph model has well-known limitations, and analytical arguments suggest that a hyperdiffusion model should serve as a more accurate alternative to the telegraph model, especially on the timescale of a few scattering times. We present a detailed side-by-side comparison of an evolving particle density profile, predicted by the telegraph and hyperdiffusion models in the context of a simple but physically meaningful initial-value problem, compare the predictions with the solution based on the Fokker-Planck equation, and discuss the applicability of the telegraph and hyperdiffusion approximations to the description of strongly anisotropic particle distributions.
An approximation based global optimization strategy for structural synthesis
NASA Technical Reports Server (NTRS)
Sepulveda, A. E.; Schmit, L. A.
1991-01-01
A global optimization strategy for structural synthesis based on approximation concepts is presented. The methodology involves the solution of a sequence of highly accurate approximate problems using a global optimization algorithm. The global optimization algorithm implemented consists of a branch and bound strategy based on the interval evaluation of the objective function and constraint functions, combined with a local feasible directions algorithm. The approximate design optimization problems are constructed using first order approximations of selected intermediate response quantities in terms of intermediate design variables. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure setforth.
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.
Phenomenological applications of rational approximants
NASA Astrophysics Data System (ADS)
Gonzàlez-Solís, Sergi; Masjuan, Pere
2016-08-01
We illustrate the powerfulness of Padé approximants (PAs) as a summation method and explore one of their extensions, the so-called quadratic approximant (QAs), to access both space- and (low-energy) time-like (TL) regions. As an introductory and pedagogical exercise, the function 1 zln(1 + z) is approximated by both kind of approximants. Then, PAs are applied to predict pseudoscalar meson Dalitz decays and to extract Vub from the semileptonic B → πℓνℓ decays. Finally, the π vector form factor in the TL region is explored using QAs.
Profitable capitation requires accurate costing.
West, D A; Hicks, L L; Balas, E A; West, T D
1996-01-01
In the name of costing accuracy, nurses are asked to track inventory use on per treatment basis when more significant costs, such as general overhead and nursing salaries, are usually allocated to patients or treatments on an average cost basis. Accurate treatment costing and financial viability require analysis of all resources actually consumed in treatment delivery, including nursing services and inventory. More precise costing information enables more profitable decisions as is demonstrated by comparing the ratio-of-cost-to-treatment method (aggregate costing) with alternative activity-based costing methods (ABC). Nurses must participate in this costing process to assure that capitation bids are based upon accurate costs rather than simple averages. PMID:8788799
Problems with the quenched approximation in the chiral limit
Sharpe, S.R.
1992-01-01
In the quenched approximation, loops of the light singlet meson (the [eta][prime]) give rise to a type of chiral logarithm absent in full QCD. These logarithms are singular in the chiral limit, throwing doubt upon the utility of the quenched approximation. In previous work, I summed a class of diagrams, leading to non-analytic power dependencies such as [l angle][anti [psi
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.
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.
Approximating Functions with Exponential Functions
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2005-01-01
The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…
Toward more accurate loss tangent measurements in reentrant cavities
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.
Impact of inflow transport approximation on light water reactor analysis
NASA Astrophysics Data System (ADS)
Choi, Sooyoung; Smith, Kord; Lee, Hyun Chul; Lee, Deokjung
2015-10-01
The impact of the inflow transport approximation on light water reactor analysis is investigated, and it is verified that the inflow transport approximation significantly improves the accuracy of the transport and transport/diffusion solutions. A methodology for an inflow transport approximation is implemented in order to generate an accurate transport cross section. The inflow transport approximation is compared to the conventional methods, which are the consistent-PN and the outflow transport approximations. The three transport approximations are implemented in the lattice physics code STREAM, and verification is performed for various verification problems in order to investigate their effects and accuracy. From the verification, it is noted that the consistent-PN and the outflow transport approximations cause significant error in calculating the eigenvalue and the power distribution. The inflow transport approximation shows very accurate and precise results for the verification problems. The inflow transport approximation shows significant improvements not only for the high leakage problem but also for practical large core problem analyses.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
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.
Two-level laser: Analytical results and the laser transition
Gartner, Paul
2011-11-15
The problem of the two-level laser is studied analytically. The steady-state solution is expressed as a continued fraction and allows for accurate approximation by rational functions. Moreover, we show that the abrupt change observed in the pump dependence of the steady-state population is directly connected to the transition to the lasing regime. The condition for a sharp transition to Poissonian statistics is expressed as a scaling limit of vanishing cavity loss and light-matter coupling, {kappa}{yields}0, g{yields}0, such that g{sup 2}/{kappa} stays finite and g{sup 2}/{kappa}>2{gamma}, where {gamma} is the rate of nonradiative losses. The same scaling procedure is also shown to describe a similar change to the Poisson distribution in the Scully-Lamb laser model, suggesting that the low-{kappa}, low-g asymptotics is of more general significance for the laser transition.
A high order accurate difference scheme for complex flow fields
Dexun Fu; Yanwen Ma
1997-06-01
A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed. It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible N-S equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage R-K method is used to advance in time. In order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets. 18 refs., 12 figs., 1 tab.
NASA Astrophysics Data System (ADS)
Zhou, Yong; Ni, Sidao; Chu, Risheng; Yao, Huajian
2016-06-01
Numerical solvers of wave equations have been widely used to simulate global seismic waves including PP waves for modeling 410/660 km discontinuity and Rayleigh waves for imaging crustal structure. In order to avoid extra computation cost due to ocean water effects, these numerical solvers usually adopt water column approximation, whose accuracy depends on frequency and needs to be investigated quantitatively. In this paper, we describe a unified representation of accurate and approximate forms of the equivalent water column boundary condition as well as the free boundary condition. Then we derive an analytical form of the PP-wave reflection coefficient with the unified boundary condition, and quantify the effects of water column approximation on amplitude and phase shift of the PP waves. We also study the effects of water column approximation on phase velocity dispersion of the fundamental mode Rayleigh wave with a propagation matrix method. We find that with the water column approximation: (1) The error of PP amplitude and phase shift is less than 5% and 9 ° at periods greater than 25 s for most oceanic regions. But at periods of 15 s or less, PP is inaccurate up to 10% in amplitude and a few seconds in time shift for deep oceans. (2) The error in Rayleigh wave phase velocity is less than 1% at periods greater than 30 s in most oceanic regions, but the error is up to 2% for deep oceans at periods of 20 s or less. This study confirms that the water column approximation is only accurate at long periods and it needs to be improved at shorter periods.
NASA Astrophysics Data System (ADS)
Zhou, Yong; Ni, Sidao; Chu, Risheng; Yao, Huajian
2016-08-01
Numerical solvers of wave equations have been widely used to simulate global seismic waves including PP waves for modelling 410/660 km discontinuity and Rayleigh waves for imaging crustal structure. In order to avoid extra computation cost due to ocean water effects, these numerical solvers usually adopt water column approximation, whose accuracy depends on frequency and needs to be investigated quantitatively. In this paper, we describe a unified representation of accurate and approximate forms of the equivalent water column boundary condition as well as the free boundary condition. Then we derive an analytical form of the PP-wave reflection coefficient with the unified boundary condition, and quantify the effects of water column approximation on amplitude and phase shift of the PP waves. We also study the effects of water column approximation on phase velocity dispersion of the fundamental mode Rayleigh wave with a propagation matrix method. We find that with the water column approximation: (1) The error of PP amplitude and phase shift is less than 5 per cent and 9° at periods greater than 25 s for most oceanic regions. But at periods of 15 s or less, PP is inaccurate up to 10 per cent in amplitude and a few seconds in time shift for deep oceans. (2) The error in Rayleigh wave phase velocity is less than 1 per cent at periods greater than 30 s in most oceanic regions, but the error is up to 2 per cent for deep oceans at periods of 20 s or less. This study confirms that the water column approximation is only accurate at long periods and it needs to be improved at shorter periods.
Accurate documentation and wound measurement.
Hampton, Sylvie
This article, part 4 in a series on wound management, addresses the sometimes routine yet crucial task of documentation. Clear and accurate records of a wound enable its progress to be determined so the appropriate treatment can be applied. Thorough records mean any practitioner picking up a patient's notes will know when the wound was last checked, how it looked and what dressing and/or treatment was applied, ensuring continuity of care. Documenting every assessment also has legal implications, demonstrating due consideration and care of the patient and the rationale for any treatment carried out. Part 5 in the series discusses wound dressing characteristics and selection.
Quantum instanton approximation for thermal rate constants of chemical reactions
NASA Astrophysics Data System (ADS)
Miller, William H.; Zhao, Yi; Ceotto, Michele; Yang, Sandy
2003-07-01
A quantum mechanical theory for chemical reaction rates is presented which is modeled after the [semiclassical (SC)] instanton approximation. It incorporates the desirable aspects of the instanton picture, which involves only properties of the (SC approximation to the) Boltzmann operator, but corrects its quantitative deficiencies by replacing the SC approximation for the Boltzmann operator by the quantum Boltzmann operator, exp(-βĤ). Since a calculation of the quantum Boltzmann operator is feasible for quite complex molecular systems (by Monte Carlo path integral methods), having an accurate rate theory that involves only the Boltzmann operator could be quite useful. The application of this quantum instanton approximation to several one- and two-dimensional model problems illustrates its potential; e.g., it is able to describe thermal rate constants accurately (˜10-20% error) from high to low temperatures deep in the tunneling regime, and applies equally well to asymmetric and symmetric potentials.
Uniformly high order accurate essentially non-oscillatory schemes 3
NASA Technical Reports Server (NTRS)
Harten, A.; Engquist, B.; Osher, S.; Chakravarthy, S. R.
1986-01-01
In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.
A more accurate method for measurement of tuberculocidal activity of disinfectants.
Ascenzi, J M; Ezzell, R J; Wendt, T M
1987-01-01
The current Association of Official Analytical Chemists method for testing tuberculocidal activity of disinfectants has been shown to be inaccurate and to have a high degree of variability. An alternate test method is proposed which is more accurate, more precise, and quantitative. A suspension of Mycobacterium bovis BCG was exposed to a variety of disinfectant chemicals and a kill curve was constructed from quantitative data. Data are presented that show the discrepancy between current claims, determined by the Association of Official Analytical Chemists method, of selected commercially available products and claims generated by the proposed method. The effects of different recovery media were examined. The data indicated that Mycobacteria 7H11 and Middlebrook 7H10 agars were equal in recovery of the different chemically treated cells, with Lowenstein-Jensen agar having approximately the same recovery rate but requiring incubation for up to 3 weeks longer for countability. The kill curves generated for several different chemicals were reproducible, as indicated by the standard deviations of the slopes and intercepts of the linear regression curves. PMID:3314707
ERIC Educational Resources Information Center
MacNeill, Sheila; Campbell, Lorna M.; Hawksey, Martin
2014-01-01
This article presents an overview of the development and use of analytics in the context of education. Using Buckingham Shum's three levels of analytics, the authors present a critical analysis of current developments in the domain of learning analytics, and contrast the potential value of analytics research and development with real world…
ERIC Educational Resources Information Center
Oblinger, Diana G.
2012-01-01
Talk about analytics seems to be everywhere. Everyone is talking about analytics. Yet even with all the talk, many in higher education have questions about--and objections to--using analytics in colleges and universities. In this article, the author explores the use of analytics in, and all around, higher education. (Contains 1 note.)
Approximate solutions for certain bidomain problems in electrocardiography
NASA Astrophysics Data System (ADS)
Johnston, Peter R.
2008-10-01
The simulation of problems in electrocardiography using the bidomain model for cardiac tissue often creates issues with satisfaction of the boundary conditions required to obtain a solution. Recent studies have proposed approximate methods for solving such problems by satisfying the boundary conditions only approximately. This paper presents an analysis of their approximations using a similar method, but one which ensures that the boundary conditions are satisfied during the whole solution process. Also considered are additional functional forms, used in the approximate solutions, which are more appropriate to specific boundary conditions. The analysis shows that the approximations introduced by Patel and Roth [Phys. Rev. E 72, 051931 (2005)] generally give accurate results. However, there are certain situations where functional forms based on the geometry of the problem under consideration can give improved approximations. It is also demonstrated that the recent methods are equivalent to different approaches to solving the same problems introduced 20years earlier.
Generalized Quasilinear Approximation: Application to Zonal Jets.
Marston, J B; Chini, G P; Tobias, S M
2016-05-27
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems. PMID:27284660
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…
Technology Transfer Automated Retrieval System (TEKTRAN)
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 ...
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.
Baby Skyrme model, near-BPS approximations, and supersymmetric extensions
NASA Astrophysics Data System (ADS)
Bolognesi, S.; Zakrzewski, W.
2015-02-01
We study the baby Skyrme model as a theory that interpolates between two distinct BPS systems. For this, a near-BPS approximation can be used when there is a small deviation from each of the two BPS limits. We provide analytical explanation and numerical support for the validity of this approximation. We then study the set of all possible supersymmetric extensions of the baby Skyrme model with N =1 and the particular ones with extended N =2 supersymmetries and relate this to the above mentioned almost-BPS approximation.
Approximating random quantum optimization problems
NASA Astrophysics Data System (ADS)
Hsu, B.; Laumann, C. R.; Läuchli, A. M.; Moessner, R.; Sondhi, S. L.
2013-06-01
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem k-body quantum satisfiability (k-QSAT) on large random graphs. As an approximation strategy, we optimize the solution space over “classical” product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are (i) the derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment; (ii) a demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects the structure of the solution space of random k-QSAT. Simulated annealing exhibits metastability in similar “hard” regions of parameter space; and (iii) a generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy “landscape” of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random k-QSAT in a two-dimensional energy-density-clause-density space.
Approximation methods in relativistic eigenvalue perturbation theory
NASA Astrophysics Data System (ADS)
Noble, Jonathan Howard
In this dissertation, three questions, concerning approximation methods for the eigenvalues of quantum mechanical systems, are investigated: (i) What is a pseudo--Hermitian Hamiltonian, and how can its eigenvalues be approximated 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 approximated eigenvalues. (ii) Within an analytic 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 approximated 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.
Approximation methods for stochastic petri nets
NASA Technical Reports Server (NTRS)
Jungnitz, Hauke Joerg
1992-01-01
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 analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation 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 approximation 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 approximation 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 approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay
SPLASH: Accurate OH maser positions
NASA Astrophysics Data System (ADS)
Walsh, Andrew; Gomez, Jose F.; Jones, Paul; Cunningham, Maria; Green, James; Dawson, Joanne; Ellingsen, Simon; Breen, Shari; Imai, Hiroshi; Lowe, Vicki; Jones, Courtney
2013-10-01
The hydroxyl (OH) 18 cm lines are powerful and versatile probes of diffuse molecular gas, that may trace a largely unstudied component of the Galactic ISM. SPLASH (the Southern Parkes Large Area Survey in Hydroxyl) is a large, unbiased and fully-sampled survey of OH emission, absorption and masers in the Galactic Plane that will achieve sensitivities an order of magnitude better than previous work. In this proposal, we request ATCA time to follow up OH maser candidates. This will give us accurate (~10") positions of the masers, which can be compared to other maser positions from HOPS, MMB and MALT-45 and will provide full polarisation measurements towards a sample of OH masers that have not been observed in MAGMO.
Accurate thickness measurement of graphene
NASA Astrophysics Data System (ADS)
Shearer, Cameron J.; Slattery, Ashley D.; Stapleton, Andrew J.; Shapter, Joseph G.; Gibson, Christopher T.
2016-03-01
Graphene has emerged as a material with a vast variety of applications. The electronic, optical and mechanical properties of graphene are strongly influenced by the number of layers present in a sample. As a result, the dimensional characterization of graphene films is crucial, especially with the continued development of new synthesis methods and applications. A number of techniques exist to determine the thickness of graphene films including optical contrast, Raman scattering and scanning probe microscopy techniques. Atomic force microscopy (AFM), in particular, is used extensively since it provides three-dimensional images that enable the measurement of the lateral dimensions of graphene films as well as the thickness, and by extension the number of layers present. However, in the literature AFM has proven to be inaccurate with a wide range of measured values for single layer graphene thickness reported (between 0.4 and 1.7 nm). This discrepancy has been attributed to tip-surface interactions, image feedback settings and surface chemistry. In this work, we use standard and carbon nanotube modified AFM probes and a relatively new AFM imaging mode known as PeakForce tapping mode to establish a protocol that will allow users to accurately determine the thickness of graphene films. In particular, the error in measuring the first layer is reduced from 0.1-1.3 nm to 0.1-0.3 nm. Furthermore, in the process we establish that the graphene-substrate adsorbate layer and imaging force, in particular the pressure the tip exerts on the surface, are crucial components in the accurate measurement of graphene using AFM. These findings can be applied to other 2D materials.
Accurate thickness measurement of graphene.
Shearer, Cameron J; Slattery, Ashley D; Stapleton, Andrew J; Shapter, Joseph G; Gibson, Christopher T
2016-03-29
Graphene has emerged as a material with a vast variety of applications. The electronic, optical and mechanical properties of graphene are strongly influenced by the number of layers present in a sample. As a result, the dimensional characterization of graphene films is crucial, especially with the continued development of new synthesis methods and applications. A number of techniques exist to determine the thickness of graphene films including optical contrast, Raman scattering and scanning probe microscopy techniques. Atomic force microscopy (AFM), in particular, is used extensively since it provides three-dimensional images that enable the measurement of the lateral dimensions of graphene films as well as the thickness, and by extension the number of layers present. However, in the literature AFM has proven to be inaccurate with a wide range of measured values for single layer graphene thickness reported (between 0.4 and 1.7 nm). This discrepancy has been attributed to tip-surface interactions, image feedback settings and surface chemistry. In this work, we use standard and carbon nanotube modified AFM probes and a relatively new AFM imaging mode known as PeakForce tapping mode to establish a protocol that will allow users to accurately determine the thickness of graphene films. In particular, the error in measuring the first layer is reduced from 0.1-1.3 nm to 0.1-0.3 nm. Furthermore, in the process we establish that the graphene-substrate adsorbate layer and imaging force, in particular the pressure the tip exerts on the surface, are crucial components in the accurate measurement of graphene using AFM. These findings can be applied to other 2D materials.
IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory.
Romero, M; de Madrid, A P; Mañoso, C; Vinagre, B M
2013-07-01
This paper deals with the use of Chebyshev polynomials theory to achieve accurate discrete-time approximations to the fractional-order differentiator/integrator in terms of IIR filters. These filters are obtained using the Chebyshev-Padé and the Rational Chebyshev approximations, two highly accurate numerical methods that can be computed with ease using available software. They are compared against other highly accurate approximations proposed in the literature. It is also shown how the frequency response of the fractional-order integrator approximations can be easily improved at low frequencies. PMID:23507506
Solving Math Problems Approximately: A Developmental Perspective
Ganor-Stern, Dana
2016-01-01
Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults’ ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner. PMID:27171224
Integral approximants for functions of higher monodromic dimension
Baker, G.A. Jr.
1987-01-01
In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.
Wavelet Sparse Approximate Inverse Preconditioners
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Tang, W.-P.; Wan, W. L.
1996-01-01
There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.
Accurate Cross Sections for Microanalysis
Rez, Peter
2002-01-01
To calculate the intensity of x-ray emission in electron beam microanalysis requires a knowledge of the energy distribution of the electrons in the solid, the energy variation of the ionization cross section of the relevant subshell, the fraction of ionizations events producing x rays of interest and the absorption coefficient of the x rays on the path to the detector. The theoretical predictions and experimental data available for ionization cross sections are limited mainly to K shells of a few elements. Results of systematic plane wave Born approximation calculations with exchange for K, L, and M shell ionization cross sections over the range of electron energies used in microanalysis are presented. Comparisons are made with experimental measurement for selected K shells and it is shown that the plane wave theory is not appropriate for overvoltages less than 2.5 V. PMID:27446747
Analytical and numerical modeling of non-collinear shear wave mixing at an imperfect interface.
Zhang, Ziyin; Nagy, Peter B; Hassan, Waled
2016-02-01
Non-collinear shear wave mixing at an imperfect interface between two solids can be exploited for nonlinear ultrasonic assessment of bond quality. In this study we developed two analytical models for nonlinear imperfect interfaces. The first model uses a finite nonlinear interfacial stiffness representation of an imperfect interface of vanishing thickness, while the second model relies on a thin nonlinear interphase layer to represent an imperfect interface region. The second model is actually a derivative of the first model obtained by calculating the equivalent interfacial stiffness of a thin isotropic nonlinear interphase layer in the quasi-static approximation. The predictions of both analytical models were numerically verified by comparison to COMSOL finite element simulations. These models can accurately predict the additional nonlinearity caused by interface imperfections based on the strength of the reflected and transmitted mixed longitudinal waves produced by them under non-collinear shear wave interrogation. PMID:26482394
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.
Fast Approximate Quadratic Programming for Graph Matching
Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624
NASA Astrophysics Data System (ADS)
Sedighi, H. M.; Shirazi, K. H.
2014-11-01
This article attains a new formulation of beam vibrations on an elastic foundation with quintic nonlinearity, including exact expressions for the beam curvature. To achieve a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode, which, in turn, yields the natural frequency of the system. In this direction, a powerful analytical method called the parameter expansion method is employed to obtain the exact solution of the frequency-amplitude relationship. It is clearly shown that the first term in series expansions is sufficient to produce a highly accurate approximation of the above-mentioned system. Finally, the accuracy of the present analytic procedure is evaluated through comparisons with numerical calculations.
Analytical transmission electron microscopy in materials science
Fraser, H.L.
1980-01-01
Microcharacterization of materials on a scale of less than 10 nm has been afforded by recent advances in analytical transmission electron microscopy. The factors limiting accurate analysis at the limit of spatial resolution for the case of a combination of scanning transmission electron microscopy and energy dispersive x-ray spectroscopy are examined in this paper.
Adaptive approximation models in optimization
Voronin, A.N.
1995-05-01
The paper proposes a method for optimization of functions of several variables that substantially reduces the number of objective function evaluations compared to traditional methods. The method is based on the property of iterative refinement of approximation models of the optimand function in approximation domains that contract to the extremum point. It does not require subjective specification of the starting point, step length, or other parameters of the search procedure. The method is designed for efficient optimization of unimodal functions of several (not more than 10-15) variables and can be applied to find the global extremum of polymodal functions and also for optimization of scalarized forms of vector objective functions.
Digitalized accurate modeling of SPCB with multi-spiral surface based on CPC algorithm
NASA Astrophysics Data System (ADS)
Huang, Yanhua; Gu, Lizhi
2015-09-01
The main methods of the existing multi-spiral surface geometry modeling include spatial analytic geometry algorithms, graphical method, interpolation and approximation algorithms. However, there are some shortcomings in these modeling methods, such as large amount of calculation, complex process, visible errors, and so on. The above methods have, to some extent, restricted the design and manufacture of the premium and high-precision products with spiral surface considerably. This paper introduces the concepts of the spatially parallel coupling with multi-spiral surface and spatially parallel coupling body. The typical geometry and topological features of each spiral surface forming the multi-spiral surface body are determined, by using the extraction principle of datum point cluster, the algorithm of coupling point cluster by removing singular point, and the "spatially parallel coupling" principle based on the non-uniform B-spline for each spiral surface. The orientation and quantitative relationships of datum point cluster and coupling point cluster in Euclidean space are determined accurately and in digital description and expression, coupling coalescence of the surfaces with multi-coupling point clusters under the Pro/E environment. The digitally accurate modeling of spatially parallel coupling body with multi-spiral surface is realized. The smooth and fairing processing is done to the three-blade end-milling cutter's end section area by applying the principle of spatially parallel coupling with multi-spiral surface, and the alternative entity model is processed in the four axis machining center after the end mill is disposed. And the algorithm is verified and then applied effectively to the transition area among the multi-spiral surface. The proposed model and algorithms may be used in design and manufacture of the multi-spiral surface body products, as well as in solving essentially the problems of considerable modeling errors in computer graphics and
Accurate upwind-monotone (nonoscillatory) methods for conservation laws
NASA Technical Reports Server (NTRS)
Huynh, Hung T.
1992-01-01
The well known MUSCL scheme of Van Leer is constructed using a piecewise linear approximation. The MUSCL scheme is second order accurate at the smooth part of the solution except at extrema where the accuracy degenerates to first order due to the monotonicity constraint. To construct accurate schemes which are free from oscillations, the author introduces the concept of upwind monotonicity. Several classes of schemes, which are upwind monotone and of uniform second or third order accuracy are then presented. Results for advection with constant speed are shown. It is also shown that the new scheme compares favorably with state of the art methods.
Hanford transuranic analytical capability
McVey, C.B.
1995-02-24
With the current DOE focus on ER/WM programs, an increase in the quantity of waste samples that requires detailed analysis is forecasted. One of the prime areas of growth is the demand for DOE environmental protocol analyses of TRU waste samples. Currently there is no laboratory capacity to support analysis of TRU waste samples in excess of 200 nCi/gm. This study recommends that an interim solution be undertaken to provide these services. By adding two glove boxes in room 11A of 222S the interim waste analytical needs can be met for a period of four to five years or until a front end facility is erected at or near the 222-S facility. The yearly average of samples is projected to be approximately 600 samples. The figure has changed significantly due to budget changes and has been downgraded from 10,000 samples to the 600 level. Until these budget and sample projection changes become firmer, a long term option is not recommended at this time. A revision to this document is recommended by March 1996 to review the long term option and sample projections.
Multimedia Analysis plus Visual Analytics = Multimedia Analytics
Chinchor, Nancy; Thomas, James J.; Wong, Pak C.; Christel, Michael; Ribarsky, Martin W.
2010-10-01
Multimedia analysis has focused on images, video, and to some extent audio and has made progress in single channels excluding text. Visual analytics has focused on the user interaction with data during the analytic process plus the fundamental mathematics and has continued to treat text as did its precursor, information visualization. The general problem we address in this tutorial is the combining of multimedia analysis and visual analytics to deal with multimedia information gathered from different sources, with different goals or objectives, and containing all media types and combinations in common usage.
Promislow, K.S.
1991-01-01
In this work the author considers the long-time behavior of dissipative evolution equations; in particular, the construction of Approximate Inertial Manifolds (AIMs) for the Ginzburg-Landau equation (GLE) and their subsequent application to the creation of more efficient and more accurate numerical schemes. In the first part, the time analyticity for the solutions of a class of dissipative evolution equations is shown. This class includes Reaction-Diffusion, GLE, Navier-Stokes, and Cahn-Hilliard equations. Existing methods are generalized and extended, and it is shown that the solutions of these equations have a unique analytic extension to an infinite pencil-shaped domain about the positive real axis in the complex plane. In the second part, the preceding result is applied to develop a new method of construction of AIMs which produces an infinite series of increasingly higher order AIMs for the GLE and associates with each a thin neighborhood into which the orbits enter in finite time and with exponential speed. These manifolds are a substitute for Inertial Manifolds when the existence of the Inertial Manifold is not known and are shown to localize the universal attractor in the phase space. Finally, in the third part, using the explicit non-linear equations of the first two nontrivial AIMs, two numerical schemes are implemented for the GLE, as well as a traditional, linear Galerkin scheme. Comparisons of the accuracy of these three schemes are made, showing gains in stability and accuracy.
NASA Astrophysics Data System (ADS)
Xu, Xun-Jie
2015-10-01
The conventional approximate formula for neutrino oscillation in matter which is obtained from the expansion in terms of the ratio of mass square differences α = Δ m 21 2 /Δ m 31 2 ≈ 0.03, first proposed by Cervera, et al. and Freund, turns out to be an accurate formula for accelerator neutrino experiments. Originally it required the neutrino energy to be well above the solar resonance to validate the expansion but it is found to be still very accurate when the formula is extrapolated to the resonance, which is practically important for the T2K experiment. This paper shows that the accuracy is guaranteed by cancellations of branch cut singularities and also, for the first time, analytically computes the actual error of the formula. The actual error implies that the original requirement can be safely removed in current experiments.
Pythagorean Approximations and Continued Fractions
ERIC Educational Resources Information Center
Peralta, Javier
2008-01-01
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
Error Bounds for Interpolative Approximations.
ERIC Educational Resources Information Center
Gal-Ezer, J.; Zwas, G.
1990-01-01
Elementary error estimation in the approximation of functions by polynomials as a computational assignment, error-bounding functions and error bounds, and the choice of interpolation points are discussed. Precalculus and computer instruction are used on some of the calculations. (KR)
Analytical Challenges in Biotechnology.
ERIC Educational Resources Information Center
Glajch, Joseph L.
1986-01-01
Highlights five major analytical areas (electrophoresis, immunoassay, chromatographic separations, protein and DNA sequencing, and molecular structures determination) and discusses how analytical chemistry could further improve these techniques and thereby have a major impact on biotechnology. (JN)
Strong washout approximation to resonant leptogenesis
Garbrecht, Björn; Gautier, Florian; Klaric, Juraj E-mail: florian.gautier@tum.de
2014-09-01
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 approximated 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 approximation 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 the 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 analytic criteria for the validity of the late-time approximation 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.
Chemical Laws, Idealization and Approximation
NASA Astrophysics Data System (ADS)
Tobin, Emma
2013-07-01
This paper examines the notion of laws in chemistry. Vihalemm ( Found Chem 5(1):7-22, 2003) argues that the laws of chemistry are fundamentally the same as the laws of physics they are all ceteris paribus laws which are true "in ideal conditions". In contrast, Scerri (2000) contends that the laws of chemistry are fundamentally different to the laws of physics, because they involve approximations. Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34-50, 2000) agree that the laws of chemistry are operationally different to the laws of physics, but claim that the distinction between exact and approximate laws is too simplistic to taxonomise them. Approximations in chemistry involve diverse kinds of activity and often what counts as a scientific law in chemistry is dictated by the context of its use in scientific practice. This paper addresses the question of what makes chemical laws distinctive independently of the separate question as to how they are related to the laws of physics. From an analysis of some candidate ceteris paribus laws in chemistry, this paper argues that there are two distinct kinds of ceteris paribus laws in chemistry; idealized and approximate chemical laws. Thus, while Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34--50, 2000) are correct to point out that the candidate generalisations in chemistry are diverse and heterogeneous, a distinction between idealizations and approximations can nevertheless be used to successfully taxonomise them.
Spectrally Invariant Approximation within Atmospheric Radiative Transfer
NASA Technical Reports Server (NTRS)
Marshak, A.; Knyazikhin, Y.; Chiu, J. C.; Wiscombe, W. J.
2011-01-01
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 cloud-dominated 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 approximation can accurately describe the extinction and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with 1D 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.
Analyticity without Differentiability
ERIC Educational Resources Information Center
Kirillova, Evgenia; Spindler, Karlheinz
2008-01-01
In this article we derive all salient properties of analytic functions, including the analytic version of the inverse function theorem, using only the most elementary convergence properties of series. Not even the notion of differentiability is required to do so. Instead, analytical arguments are replaced by combinatorial arguments exhibiting…
Accurate Potential Energy Curves for the Ground Electronic States of NeH^{+} and ArH^{+}
NASA Astrophysics Data System (ADS)
Coxon, John A.; Hajigeorgiou, Photos G.
2013-06-01
All available microwave and infrared spectroscopic line positions for the ground electronic states of the molecular cations NeH^{+} and ArH^{+} were employed in a direct potential fitting procedure to determine compact analytical potential curves and radial functions describing breakdown of the Born-Oppenheimer approximation. For NeH^{+}, 17 adjustable parameters were required to represent a total of 183 line positions for 4 isotopologues, whereas for ArH^{+}, 23 adjustable parameters were required to represent 440 line positions for 6 isotopologues. The MLR3 potential energy functional form was employed, taking full account of the proper 1/r{^4} limiting long-range dependence of the ion-atom dispersion energy interactions. Accurate vibrational energies, rotational constants and centrifugal distortion constants have been calculated for both diatomic cations.
Tung, Wei-Cheng; Adamowicz, Ludwik
2014-03-28
Very accurate calculations of the ground-state potential energy curve (PEC) of the LiH{sup +} ion performed with all-electron explicitly correlated Gaussian functions with shifted centers are presented. The variational method is employed. The calculations involve optimization of nonlinear exponential parameters of the Gaussians performed with the aid of the analytical first derivatives of the energy determined with respect to the parameters. The diagonal adiabatic correction is also calculated for each PEC point. The PEC is then used to calculate the vibrational energies of the system. In that calculation, the non-adiabatic effects are accounted for by using an effective vibrational mass obtained by the minimization of the difference between the vibrational energies obtained from the calculations where the Born-Oppenheimer approximation was not assumed and the results of the present calculations.
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
Modern analytical chemistry in the contemporary world
NASA Astrophysics Data System (ADS)
Šíma, Jan
2016-02-01
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.
Fast and accurate predictions of covalent bonds in chemical space.
Chang, K Y Samuel; Fias, Stijn; Ramakrishnan, Raghunathan; von Lilienfeld, O Anatole
2016-05-01
We assess the predictive accuracy of perturbation theory based estimates of changes in covalent bonding due to linear alchemical interpolations among molecules. We have investigated σ bonding to hydrogen, as well as σ and π bonding between main-group elements, occurring in small sets of iso-valence-electronic molecules with elements drawn from second to fourth rows in the p-block of the periodic table. Numerical evidence suggests that first order Taylor expansions of covalent bonding potentials can achieve high accuracy if (i) the alchemical interpolation is vertical (fixed geometry), (ii) it involves elements from the third and fourth rows of the periodic table, and (iii) an optimal reference geometry is used. This leads to near linear changes in the bonding potential, resulting in analytical predictions with chemical accuracy (∼1 kcal/mol). Second order estimates deteriorate the prediction. If initial and final molecules differ not only in composition but also in geometry, all estimates become substantially worse, with second order being slightly more accurate than first order. The independent particle approximation based second order perturbation theory performs poorly when compared to the coupled perturbed or finite difference approach. Taylor series expansions up to fourth order of the potential energy curve of highly symmetric systems indicate a finite radius of convergence, as illustrated for the alchemical stretching of H2 (+). Results are presented for (i) covalent bonds to hydrogen in 12 molecules with 8 valence electrons (CH4, NH3, H2O, HF, SiH4, PH3, H2S, HCl, GeH4, AsH3, H2Se, HBr); (ii) main-group single bonds in 9 molecules with 14 valence electrons (CH3F, CH3Cl, CH3Br, SiH3F, SiH3Cl, SiH3Br, GeH3F, GeH3Cl, GeH3Br); (iii) main-group double bonds in 9 molecules with 12 valence electrons (CH2O, CH2S, CH2Se, SiH2O, SiH2S, SiH2Se, GeH2O, GeH2S, GeH2Se); (iv) main-group triple bonds in 9 molecules with 10 valence electrons (HCN, HCP, HCAs, HSiN, HSi
Fast and accurate predictions of covalent bonds in chemical space
NASA Astrophysics Data System (ADS)
Chang, K. Y. Samuel; Fias, Stijn; Ramakrishnan, Raghunathan; von Lilienfeld, O. Anatole
2016-05-01
We assess the predictive accuracy of perturbation theory based estimates of changes in covalent bonding due to linear alchemical interpolations among molecules. We have investigated σ bonding to hydrogen, as well as σ and π bonding between main-group elements, occurring in small sets of iso-valence-electronic molecules with elements drawn from second to fourth rows in the p-block of the periodic table. Numerical evidence suggests that first order Taylor expansions of covalent bonding potentials can achieve high accuracy if (i) the alchemical interpolation is vertical (fixed geometry), (ii) it involves elements from the third and fourth rows of the periodic table, and (iii) an optimal reference geometry is used. This leads to near linear changes in the bonding potential, resulting in analytical predictions with chemical accuracy (˜1 kcal/mol). Second order estimates deteriorate the prediction. If initial and final molecules differ not only in composition but also in geometry, all estimates become substantially worse, with second order being slightly more accurate than first order. The independent particle approximation based second order perturbation theory performs poorly when compared to the coupled perturbed or finite difference approach. Taylor series expansions up to fourth order of the potential energy curve of highly symmetric systems indicate a finite radius of convergence, as illustrated for the alchemical stretching of H 2+ . Results are presented for (i) covalent bonds to hydrogen in 12 molecules with 8 valence electrons (CH4, NH3, H2O, HF, SiH4, PH3, H2S, HCl, GeH4, AsH3, H2Se, HBr); (ii) main-group single bonds in 9 molecules with 14 valence electrons (CH3F, CH3Cl, CH3Br, SiH3F, SiH3Cl, SiH3Br, GeH3F, GeH3Cl, GeH3Br); (iii) main-group double bonds in 9 molecules with 12 valence electrons (CH2O, CH2S, CH2Se, SiH2O, SiH2S, SiH2Se, GeH2O, GeH2S, GeH2Se); (iv) main-group triple bonds in 9 molecules with 10 valence electrons (HCN, HCP, HCAs, HSiN, HSi
Fast and accurate predictions of covalent bonds in chemical space.
Chang, K Y Samuel; Fias, Stijn; Ramakrishnan, Raghunathan; von Lilienfeld, O Anatole
2016-05-01
We assess the predictive accuracy of perturbation theory based estimates of changes in covalent bonding due to linear alchemical interpolations among molecules. We have investigated σ bonding to hydrogen, as well as σ and π bonding between main-group elements, occurring in small sets of iso-valence-electronic molecules with elements drawn from second to fourth rows in the p-block of the periodic table. Numerical evidence suggests that first order Taylor expansions of covalent bonding potentials can achieve high accuracy if (i) the alchemical interpolation is vertical (fixed geometry), (ii) it involves elements from the third and fourth rows of the periodic table, and (iii) an optimal reference geometry is used. This leads to near linear changes in the bonding potential, resulting in analytical predictions with chemical accuracy (∼1 kcal/mol). Second order estimates deteriorate the prediction. If initial and final molecules differ not only in composition but also in geometry, all estimates become substantially worse, with second order being slightly more accurate than first order. The independent particle approximation based second order perturbation theory performs poorly when compared to the coupled perturbed or finite difference approach. Taylor series expansions up to fourth order of the potential energy curve of highly symmetric systems indicate a finite radius of convergence, as illustrated for the alchemical stretching of H2 (+). Results are presented for (i) covalent bonds to hydrogen in 12 molecules with 8 valence electrons (CH4, NH3, H2O, HF, SiH4, PH3, H2S, HCl, GeH4, AsH3, H2Se, HBr); (ii) main-group single bonds in 9 molecules with 14 valence electrons (CH3F, CH3Cl, CH3Br, SiH3F, SiH3Cl, SiH3Br, GeH3F, GeH3Cl, GeH3Br); (iii) main-group double bonds in 9 molecules with 12 valence electrons (CH2O, CH2S, CH2Se, SiH2O, SiH2S, SiH2Se, GeH2O, GeH2S, GeH2Se); (iv) main-group triple bonds in 9 molecules with 10 valence electrons (HCN, HCP, HCAs, HSiN, HSi
NASA Astrophysics Data System (ADS)
Guo, Kongming; Jiang, Jun; Xu, Yalan
2016-09-01
In this paper, a simple but accurate semi-analytical method to approximate probability density function of stochastic closed curve attractors is proposed. The expression of distribution applies to systems with strong nonlinearities, while only weak noise condition is needed. With the understanding that additive noise does not change the longitudinal distribution of the attractors, the high-dimensional probability density distribution is decomposed into two low-dimensional distributions: the longitudinal and the transverse probability density distributions. The longitudinal distribution can be calculated from the deterministic systems, while the probability density in the transverse direction of the curve can be approximated by the stochastic sensitivity function method. The effectiveness of this approach is verified by comparing the expression of distribution with the results of Monte Carlo numerical simulations in several planar systems.
Testing the frozen flow approximation
NASA Technical Reports Server (NTRS)
Lucchin, Francesco; Matarrese, Sabino; Melott, Adrian L.; Moscardini, Lauro
1993-01-01
We investigate the accuracy of the frozen-flow approximation (FFA), recently proposed by Matarrese, et al. (1992), for following the nonlinear evolution of cosmological density fluctuations under gravitational instability. We compare a number of statistics between results of the FFA and n-body simulations, including those used by Melott, Pellman & Shandarin (1993) to test the Zel'dovich approximation. The FFA performs reasonably well in a statistical sense, e.g. in reproducing the counts-in-cell distribution, at small scales, but it does poorly in the crosscorrelation with n-body which means it is generally not moving mass to the right place, especially in models with high small-scale power.
Analytical technique for satellite projected cross-sectional area calculation
NASA Astrophysics Data System (ADS)
Ben-Yaacov, Ohad; Edlerman, Eviatar; Gurfil, Pini
2015-07-01
Calculating the projected cross-sectional area (PCSA) of a satellite along a given direction is essential for implementing attitude control modes such as Sun pointing or minimum-drag. The PCSA may also be required for estimating the forces and torques induced by atmospheric drag and solar radiation pressure. This paper develops a new analytical method for calculating the PCSA, the concomitant torques and the satellite exposed surface area, based on the theory of convex polygons. A scheme for approximating the outer surface of any satellite by polygons is developed. Then, a methodology for calculating the projections of the polygons along a given vector is employed. The methodology also accounts for overlaps among projections, and is capable of providing the true PCSA in a computationally-efficient manner. Using the Space Autonomous Mission for Swarming and Geo-locating Nanosatellites mechanical model, it is shown that the new analytical method yields accurate results, which are similar to results obtained from alternative numerical tools.
Analytical model of diffuse reflectance spectrum of skin tissue
Lisenko, S A; Kugeiko, M M; Firago, V A; Sobchuk, A N
2014-01-31
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. (biophotonics)
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.
Approximate line shapes for hydrogen
NASA Technical Reports Server (NTRS)
Sutton, K.
1978-01-01
Two independent methods are presented for calculating radiative transport within hydrogen lines. In Method 1, a simple equation is proposed for calculating the line shape. In Method 2, the line shape is assumed to be a dispersion profile and an equation is presented for calculating the half half-width. The results obtained for the line shapes and curves of growth by the two approximate methods are compared with similar results using the detailed line shapes by Vidal et al.
Approximate reasoning using terminological models
NASA Technical Reports Server (NTRS)
Yen, John; Vaidya, Nitin
1992-01-01
Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.
Ultrafast approximation for phylogenetic bootstrap.
Minh, Bui Quang; Nguyen, Minh Anh Thi; von Haeseler, Arndt
2013-05-01
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and the Shimodaira-Hasegawa-like approximate likelihood ratio test have been introduced to speed up the bootstrap. Here, we suggest an ultrafast bootstrap approximation approach (UFBoot) to compute the support of phylogenetic groups in maximum likelihood (ML) based trees. To achieve this, we combine the resampling estimated log-likelihood method with a simple but effective collection scheme of candidate trees. We also propose a stopping rule that assesses the convergence of branch support values to automatically determine when to stop collecting candidate trees. UFBoot achieves a median speed up of 3.1 (range: 0.66-33.3) to 10.2 (range: 1.32-41.4) compared with RAxML RBS for real DNA and amino acid alignments, respectively. Moreover, our extensive simulations show that UFBoot is robust against moderate model violations and the support values obtained appear to be relatively unbiased compared with the conservative standard bootstrap. This provides a more direct interpretation of the bootstrap support. We offer an efficient and easy-to-use software (available at http://www.cibiv.at/software/iqtree) to perform the UFBoot analysis with ML tree inference.
Approximate Counting of Graphical Realizations
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994
Accurate Mass Measurements in Proteomics
Liu, Tao; Belov, Mikhail E.; Jaitly, Navdeep; Qian, Weijun; Smith, Richard D.
2007-08-01
proteins can also be extensively modified by PTMs26-31 or by their interactions with other biomolecules or small molecules.32,33 Thus, it is highly desirable that proteins, the primary functional macromolecules involved in almost all biological activities, can be studied directly and systematically to determine their diverse properties and interplay. Such proteome-wide analysis is expected to provide a wealth of biological information, such as sequence, quantity, PTMs, interactions, activities, subcellular distribution and structure of proteins, which is critical to the comprehensive understanding of the biological systems. However, the de novo analysis of proteins isolated from cells, tissues or bodily fluids poses significant challenges due to the tremendous complexity and depth of the proteome, which necessitates high-throughput and highly sensitive analytical techniques. It is therefore not surprising that mass spectrometry (MS) has become an indispensable technology for proteome analysis.
Accurate thermoelastic tensor and acoustic velocities of NaCl
NASA Astrophysics Data System (ADS)
Marcondes, Michel L.; Shukla, Gaurav; da Silveira, Pedro; Wentzcovitch, Renata M.
2015-12-01
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 by 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.
Accurate thermoelastic tensor and acoustic velocities of NaCl
Marcondes, Michel L.; Shukla, Gaurav; Silveira, Pedro da; Wentzcovitch, Renata M.
2015-12-15
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 by 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.
A coefficient average approximation towards Gutzwiller wavefunction formalism
NASA Astrophysics Data System (ADS)
Liu, Jun; Yao, Yongxin; Wang, Cai-Zhuang; Ho, Kai-Ming
2015-06-01
Gutzwiller wavefunction is a physically well-motivated trial wavefunction for describing correlated electron systems. In this work, a new approximation is introduced to facilitate the evaluation of the expectation value of any operator within the Gutzwiller wavefunction formalism. The basic idea is to make use of a specially designed average over Gutzwiller wavefunction coefficients expanded in the many-body Fock space to approximate the ratio of expectation values between a Gutzwiller wavefunction and its underlying noninteracting wavefunction. To check with the standard Gutzwiller approximation (GA), we test its performance on single band systems and find quite interesting properties. On finite systems, we noticed that it gives superior performance over GA, while on infinite systems it asymptotically approaches GA. Analytic analysis together with numerical tests are provided to support this claimed asymptotical behavior. Finally, possible improvements on the approximation and its generalization towards multiband systems are illustrated and discussed.
A coefficient average approximation towards Gutzwiller wavefunction formalism.
Liu, Jun; Yao, Yongxin; Wang, Cai-Zhuang; Ho, Kai-Ming
2015-06-24
Gutzwiller wavefunction is a physically well-motivated trial wavefunction for describing correlated electron systems. In this work, a new approximation is introduced to facilitate the evaluation of the expectation value of any operator within the Gutzwiller wavefunction formalism. The basic idea is to make use of a specially designed average over Gutzwiller wavefunction coefficients expanded in the many-body Fock space to approximate the ratio of expectation values between a Gutzwiller wavefunction and its underlying noninteracting wavefunction. To check with the standard Gutzwiller approximation (GA), we test its performance on single band systems and find quite interesting properties. On finite systems, we noticed that it gives superior performance over GA, while on infinite systems it asymptotically approaches GA. Analytic analysis together with numerical tests are provided to support this claimed asymptotical behavior. Finally, possible improvements on the approximation and its generalization towards multiband systems are illustrated and discussed.
Approximate penetration factors for nuclear reactions of astrophysical interest
NASA Technical Reports Server (NTRS)
Humblet, J.; Fowler, W. A.; Zimmerman, B. A.
1987-01-01
The ranges of validity of approximations of P(l), the penetration factor which appears in the parameterization of nuclear-reaction cross sections at low energies and is employed in the extrapolation of laboratory data to even lower energies of astrophysical interest, are investigated analytically. Consideration is given to the WKB approximation, P(l) at the energy of the total barrier, approximations derived from the asymptotic expansion of G(l) for large eta, approximations for small values of the parameter x, applications of P(l) to nuclear reactions, and the dependence of P(l) on channel radius. Numerical results are presented in tables and graphs, and parameter ranges where the danger of serious errors is high are identified.
Improved Measurement of the Rotor Temperature in Analytical Ultracentrifugation
Zhao, Huaying; Balbo, Andrea; Metger, Howard; Clary, Robert; Ghirlando, Rodolfo; Schuck, Peter
2014-01-01
Sedimentation velocity is a classical method for measuring the hydrodynamic, translational friction coefficient of biological macromolecules. In a recent study, comparing various analytical ultracentrifuges, we have shown that external calibration of the scan time, radial magnification, and temperature are critically important for accurate measurements (Anal. Biochem., 2013, doi: 10.1016/j.ab.2013.05.011). To achieve accurate temperature calibration, we have introduced the use of an autonomous miniature temperature logging integrated circuit (Maxim Thermochron iButton ™) that can be inserted in an ultracentrifugation cell assembly and spun at low rotor speeds. In the present work, we developed an improved holder for the temperature sensor located in the rotor handle. This has the advantage of not reducing the rotor capacity and allows for a direct temperature measurement of the spinning rotor during high-speed sedimentation velocity experiments up to 60,000 rpm. We demonstrate the sensitivity of this approach by monitoring the adiabatic cooling due to rotor stretching during rotor acceleration, and the reverse process upon rotor deceleration. Based on this, we developed a procedure to approximate isothermal rotor acceleration for better temperature control. PMID:24530285
Extracting Time-Accurate Acceleration Vectors From Nontrivial Accelerometer Arrangements.
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 to
Hydration thermodynamics beyond the linear response approximation.
Raineri, Fernando O
2016-10-19
The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute
Hydration thermodynamics beyond the linear response approximation.
Raineri, Fernando O
2016-10-19
The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2013-07-01 2013-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2011-07-01 2011-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2014-07-01 2014-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2012-07-01 2012-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
Lunar ash flows - Isothermal approximation.
NASA Technical Reports Server (NTRS)
Pai, S. I.; Hsieh, T.; O'Keefe, J. A.
1972-01-01
Suggestion of the ash flow mechanism as one of the major processes required to account for some features of lunar soil. First the observational background and the gardening hypothesis are reviewed, and the shortcomings of the gardening hypothesis are shown. Then a general description of the lunar ash flow is given, and a simple mathematical model of the isothermal lunar ash flow is worked out with numerical examples to show the differences between the lunar and the terrestrial ash flow. The important parameters of the ash flow process are isolated and analyzed. It appears that the lunar surface layer in the maria is not a residual mantle rock (regolith) but a series of ash flows due, at least in part, to great meteorite impacts. The possibility of a volcanic contribution is not excluded. Some further analytic research on lunar ash flows is recommended.
Validity criterion for the Born approximation convergence in microscopy imaging.
Trattner, Sigal; Feigin, Micha; Greenspan, Hayit; Sochen, Nir
2009-05-01
The need for the reconstruction and quantification of visualized objects from light microscopy images requires an image formation model that adequately describes the interaction of light waves with biological matter. Differential interference contrast (DIC) microscopy, as well as light microscopy, uses the common model of the scalar Helmholtz equation. Its solution is frequently expressed via the Born approximation. A theoretical bound is known that limits the validity of such an approximation to very small objects. We present an analytic criterion for the validity region of the Born approximation. In contrast to the theoretical known bound, the suggested criterion considers the field at the lens, external to the object, that corresponds to microscopic imaging and extends the validity region of the approximation. An analytical proof of convergence is presented to support the derived criterion. The suggested criterion for the Born approximation validity region is described in the context of a DIC microscope, yet it is relevant for any light microscope with similar fundamental apparatus. PMID:19412231
Some analytical models of radiating collapsing spheres
Herrera, L.; Di Prisco, A; Ospino, J.
2006-08-15
We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each solution, using a hyperbolic transport equation, which permits to exhibit the influence of relaxational effects on the dynamics of the system.
An approximate method for calculating aircraft downwash on parachute trajectories
Strickland, J.H.
1989-01-01
An approximate method for calculating velocities induced by aircraft on parachute trajectories is presented herein. A simple system of quadrilateral vortex panels is used to model the aircraft wing and its wake. The purpose of this work is to provide a simple analytical tool which can be used to approximate the effect of aircraft-induced velocities on parachute performance. Performance issues such as turnover and wake recontact may be strongly influenced by velocities induced by the wake of the delivering aircraft, especially if the aircraft is maneuvering at the time of parachute deployment. 7 refs., 9 figs.
Accurate masses for dispersion-supported galaxies
NASA Astrophysics Data System (ADS)
Wolf, Joe; Martinez, Gregory D.; Bullock, James S.; Kaplinghat, Manoj; Geha, Marla; Muñoz, Ricardo R.; Simon, Joshua D.; Avedo, Frank F.
2010-08-01
We derive an accurate mass estimator for dispersion-supported stellar systems and demonstrate its validity by analysing resolved line-of-sight velocity data for globular clusters, dwarf galaxies and elliptical galaxies. Specifically, by manipulating the spherical Jeans equation we show that the mass enclosed within the 3D deprojected half-light radius r1/2 can be determined with only mild assumptions about the spatial variation of the stellar velocity dispersion anisotropy as long as the projected velocity dispersion profile is fairly flat near the half-light radius, as is typically observed. We find M1/2 = 3 G-1< σ2los > r1/2 ~= 4 G-1< σ2los > Re, where < σ2los > is the luminosity-weighted square of the line-of-sight velocity dispersion and Re is the 2D projected half-light radius. While deceptively familiar in form, this formula is not the virial theorem, which cannot be used to determine accurate masses unless the radial profile of the total mass is known a priori. We utilize this finding to show that all of the Milky Way dwarf spheroidal galaxies (MW dSphs) are consistent with having formed within a halo of a mass of approximately 3 × 109 Msolar, assuming a Λ cold dark matter cosmology. The faintest MW dSphs seem to have formed in dark matter haloes that are at least as massive as those of the brightest MW dSphs, despite the almost five orders of magnitude spread in luminosity between them. We expand our analysis to the full range of observed dispersion-supported stellar systems and examine their dynamical I-band mass-to-light ratios ΥI1/2. The ΥI1/2 versus M1/2 relation for dispersion-supported galaxies follows a U shape, with a broad minimum near ΥI1/2 ~= 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to ΥI1/2 ~= 3200 for ultra-faint dSphs and a more shallow rise to ΥI1/2 ~= 800 for galaxy cluster spheroids.
Approximately Independent Features of Languages
NASA Astrophysics Data System (ADS)
Holman, Eric W.
To facilitate the testing of models for the evolution of languages, the present paper offers a set of linguistic features that are approximately independent of each other. To find these features, the adjusted Rand index (R‧) is used to estimate the degree of pairwise relationship among 130 linguistic features in a large published database. Many of the R‧ values prove to be near zero, as predicted for independent features, and a subset of 47 features is found with an average R‧ of -0.0001. These 47 features are recommended for use in statistical tests that require independent units of analysis.
The structural physical approximation conjecture
NASA Astrophysics Data System (ADS)
Shultz, Fred
2016-01-01
It was conjectured that the structural physical approximation (SPA) of an optimal entanglement witness is separable (or equivalently, that the SPA of an optimal positive map is entanglement breaking). This conjecture was disproved, first for indecomposable maps and more recently for decomposable maps. The arguments in both cases are sketched along with important related results. This review includes background material on topics including entanglement witnesses, optimality, duality of cones, decomposability, and the statement and motivation for the SPA conjecture so that it should be accessible for a broad audience.
Quantum tunneling beyond semiclassical approximation
NASA Astrophysics Data System (ADS)
Banerjee, Rabin; Ranjan Majhi, Bibhas
2008-06-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.
Fermion tunneling beyond semiclassical approximation
NASA Astrophysics Data System (ADS)
Majhi, Bibhas Ranjan
2009-02-01
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in R. Banerjee and B. R. Majhi, J. High Energy Phys.JHEPFG1029-8479 06 (2008) 09510.1088/1126-6708/2008/06/095 for the scalar particle, Hawking radiation as tunneling of the Dirac particle through an event horizon is analyzed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.
Analytical phase diagrams for colloids and non-adsorbing polymer.
Fleer, Gerard J; Tuinier, Remco
2008-11-01
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
Understanding multi-quantum NMR through secular approximation.
Srivastava, Deepansh; SubbaRao, R Venkata; Ramachandran, Ramesh
2013-05-14
With the development of technology and improved understanding of nuclear spin-spin interactions and their behavior in static/oscillating magnetic fields, NMR spectroscopy has emerged as a powerful tool for characterizing molecular structure in a wide range of systems of chemical, physical and biological relevance. Here in this article, we revisit the important connection between "Secular-Approximation" (a well-known fundamental concept) and NMR spectroscopy. Employing recent experimental results as the background, an alternate interpretation of the secular approximation is presented for describing and understanding the nuances of Multi-Quantum (MQ) NMR spectroscopy of quadrupolar nuclei. Since MQ NMR spectroscopy of quadrupolar nuclei forms the basis of the structural characterization of inorganic solids and clusters, we believe that the analytic theory presented herein would be beneficial both in the understanding and design of MQ NMR experiments. Additionally, the analytic results are corroborated with rigorous numerical simulations and could be employed in the quantitative interpretation of experimental results.
Analytical investigation of squeeze film dampers
NASA Astrophysics Data System (ADS)
Bicak, Mehmet Murat Altug
Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Starting from linear Reynolds equation which governs the fluid behavior coupled with structure domain which is modeled by Kirchhoff plate equation, the effects of nondimensional parameters on the damped natural frequencies are presented using boundary characteristic orthogonal functions. For this purpose, the nondimensional coupled partial differential equations are obtained using Rayleigh-Ritz method and the weak formulation, are solved using polynomial and sinusoidal boundary characteristic orthogonal functions for structure and fluid domain respectively. In order to implement present approach to the complex geometries, a two dimensional isoparametric coupled finite element is developed based on Reissner-Mindlin plate theory and linearized Reynolds equation. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. As the next logical step, an analytical method for solution of squeeze film damping based upon Green's function to the nonlinear Reynolds equation considering elastic plate is studied. This allows calculating modal damping and stiffness force rapidly for various boundary conditions. The nonlinear Reynolds equation is divided into multiple linear non-homogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling calculation of damping ratio and frequency shift as well as complex resistant pressure. Moreover, the theoretical results are correlated and compared with experimental results both in the
Integral approximations to classical diffusion and smoothed particle hydrodynamics
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. 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.
Integral approximations to classical diffusion and smoothed particle hydrodynamics
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
Integral approximations to classical diffusion and smoothed particle hydrodynamics
Du, Q.; Lehoucq, Richard B.; Tartakovsky, Alexandre M.
2015-04-01
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. The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. An immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.
Vacancy-rearrangement theory in the first Magnus approximation
Becker, R.L.
1984-01-01
In the present paper we employ the first Magnus approximation (M1A), a unitarized Born approximation, in semiclassical collision theory. We have found previously that the M1A gives a substantial improvement over the first Born approximation (B1A) and can give a good approximation to a full coupled channels calculation of the mean L-shell vacancy probability per electron, p/sub L/, when the L-vacancies are accompanied by a K-shell vacancy (p/sub L/ is obtained experimentally from measurements of K/sub ..cap alpha../-satellite intensities). For sufficiently strong projectile-electron interactions (sufficiently large Z/sub p/ or small v) the M1A ceases to reproduce the coupled channels results, but it is accurate over a much wider range of Z/sub p/ and v than the B1A. 27 references.
Importance Sampling Approach for the Nonstationary Approximation Error Method
NASA Astrophysics Data System (ADS)
Huttunen, J. M. J.; Lehikoinen, A.; Hämäläinen, J.; Kaipio, J. P.
2010-09-01
The approximation error approach has been earlier proposed to handle modelling, numerical and computational errors in inverse problems. The idea of the approach is to include the errors to the forward model and compute the approximate statistics of the errors using Monte Carlo sampling. This can be a computationally tedious task but the key property of the approach is that the approximate statistics can be calculated off-line before measurement process takes place. In nonstationary problems, however, information is accumulated over time, and the initial uncertainties may turn out to have been exaggerated. In this paper, we propose an importance weighing algorithm with which the approximation error statistics can be updated during the accumulation of measurement information. As a computational example, we study an estimation problem that is related to a convection-diffusion problem in which the velocity field is not accurately specified.
Gray, John G; Graham, Catherine; Dudas, Sandor; Paxman, Eric; Vuong, Ben; Czub, Stefanie
2016-05-01
Transmissible spongiform encephalopathies (TSEs) are infectious, fatal neurodegenerative diseases that affect production animal health, and thus human food safety. Enhanced TSE detection methods mimic the conjectured basis for prion replication, in vitro; biological matrices can be tested for prion activity via their ability to convert recombinant cellular prion protein (PrP) into amyloid fibrils; fluorescent spectra changes of amyloid-binding fluorophores in the reaction vessel detect fibril formation. In vitro PrP conversion techniques have high analytical sensitivity for prions, comparable with that of bioassays, yet no such protocol has gained regulatory approval for use in animal TSE surveillance programs. This study describes a timed in vitro PrP conversion protocol with accurate, well-defined analytical criteria based on probability density and mass functions of TSE(+) and TSE(-) associated thioflavin T signal times, a new approach within this field. The prion detection model used is elk chronic wasting disease (CWD) in brain tissues. The protocol and analytical criteria proved as sensitive for elk CWD as two bioassay models, and upward of approximately 1.2 log10 more sensitive than the most sensitive TSE rapid test we assessed. Furthermore, we substantiate that timing in vitro PrP conversion may be used to titrate TSE infectivity, and, as a result, provide a comprehensive extrapolation of analytical sensitivity differences between bioassay, TSE rapid tests, and in vitro PrP conversion for elk CWD.
Gray, John G; Graham, Catherine; Dudas, Sandor; Paxman, Eric; Vuong, Ben; Czub, Stefanie
2016-05-01
Transmissible spongiform encephalopathies (TSEs) are infectious, fatal neurodegenerative diseases that affect production animal health, and thus human food safety. Enhanced TSE detection methods mimic the conjectured basis for prion replication, in vitro; biological matrices can be tested for prion activity via their ability to convert recombinant cellular prion protein (PrP) into amyloid fibrils; fluorescent spectra changes of amyloid-binding fluorophores in the reaction vessel detect fibril formation. In vitro PrP conversion techniques have high analytical sensitivity for prions, comparable with that of bioassays, yet no such protocol has gained regulatory approval for use in animal TSE surveillance programs. This study describes a timed in vitro PrP conversion protocol with accurate, well-defined analytical criteria based on probability density and mass functions of TSE(+) and TSE(-) associated thioflavin T signal times, a new approach within this field. The prion detection model used is elk chronic wasting disease (CWD) in brain tissues. The protocol and analytical criteria proved as sensitive for elk CWD as two bioassay models, and upward of approximately 1.2 log10 more sensitive than the most sensitive TSE rapid test we assessed. Furthermore, we substantiate that timing in vitro PrP conversion may be used to titrate TSE infectivity, and, as a result, provide a comprehensive extrapolation of analytical sensitivity differences between bioassay, TSE rapid tests, and in vitro PrP conversion for elk CWD. PMID:27068712
Wavelet Approximation in Data Assimilation
NASA Technical Reports Server (NTRS)
Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
Approximate Green's function methods for HZE transport in multilayered materials
NASA Technical Reports Server (NTRS)
Wilson, John W.; Badavi, Francis F.; Shinn, Judy L.; Costen, Robert C.
1993-01-01
A nonperturbative analytic 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 approximation.
Constant Entropy Properties for an Approximate Model of Equilibrium Air
NASA Technical Reports Server (NTRS)
Hansen, C. Frederick; Hodge, Marion E.
1961-01-01
Approximate analytic solutions for properties of equilibrium air up to 15,000 K have been programmed for machine computation. Temperature, compressibility, enthalpy, specific heats, and speed of sound are tabulated as constant entropy functions of temperature. The reciprocal of acoustic impedance and its integral with respect to pressure are also given for the purpose of evaluating the Riemann constants for one-dimensional, isentropic flow.
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…
Networked analytical sample management system
Kerrigan, W.J.; Spencer, W.A.
1986-01-01
Since 1982, the Savannah River Laboratory (SRL) has operated a computer-controlled analytical sample management system. The system, pogrammed in COBOL, runs on the site IBM 3081 mainframe computer. The system provides for the following subtasks: sample logging, analytical method assignment, worklist generation, cost accounting, and results reporting. Within these subtasks the system functions in a time-sharing mode. Communications between subtasks are done overnight in a batch mode. The system currently supports management of up to 3000 samples a month. Each sample requires, on average, three independent methods. Approximately 100 different analytical techniques are available for customized input of data. The laboratory has implemented extensive computer networking using Ethernet. Electronic mail, RS/1, and online literature searches are in place. Based on our experience with the existing sample management system, we have begun a project to develop a second generation system. The new system will utilize the panel designs developed for the present LIMS, incorporate more realtime features, and take advantage of the many commercial LIMS systems.
Analytical Chemistry in Russia.
Zolotov, Yuri
2016-09-01
Research in Russian analytical chemistry (AC) is carried out on a significant scale, and the analytical service solves practical tasks of geological survey, environmental protection, medicine, industry, agriculture, etc. The education system trains highly skilled professionals in AC. The development and especially manufacturing of analytical instruments should be improved; in spite of this, there are several good domestic instruments and other satisfy some requirements. Russian AC has rather good historical roots.
Science Update: Analytical Chemistry.
ERIC Educational Resources Information Center
Worthy, Ward
1980-01-01
Briefly discusses new instrumentation in the field of analytical chemistry. Advances in liquid chromatography, photoacoustic spectroscopy, the use of lasers, and mass spectrometry are also discussed. (CS)
Road Transportable Analytical Laboratory (RTAL) system
Finger, S.M.
1995-10-01
The goal of the Road Transportable Analytical Laboratory (RTAL) Project is the development and demonstration of a system to meet the unique needs of the DOE for rapid, accurate analysis of a wide variety of hazardous and radioactive contaminants in soil, groundwater, and surface waters. This laboratory system has been designed to provide the field and laboratory analytical equipment necessary to detect and quantify radionuclides, organics, heavy metals and other inorganic compounds. The laboratory system consists of a set of individual laboratory modules deployable independently or as an interconnected group to meet each DOE site`s specific needs.
service line analytics in the new era.
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.
service line analytics in the new era.
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. PMID:26548137
Approximating metal-insulator transitions
NASA Astrophysics Data System (ADS)
Danieli, Carlo; Rayanov, Kristian; Pavlov, Boris; Martin, Gaven; Flach, Sergej
2015-12-01
We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step, the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate Metal-Insulator Transitions (MIT) at the finite iteration steps. We also report evidence on mobility edges, which are at variance to the celebrated Aubry-André model. The dynamics near the MIT shows a critical slowing down of the ballistic group velocity in the metallic phase, similar to the divergence of the localization length in the insulating phase.
New generalized gradient approximation functionals
NASA Astrophysics Data System (ADS)
Boese, A. Daniel; Doltsinis, Nikos L.; Handy, Nicholas C.; Sprik, Michiel
2000-01-01
New generalized gradient approximation (GGA) functionals are reported, using the expansion form of A. D. Becke, J. Chem. Phys. 107, 8554 (1997), with 15 linear parameters. Our original such GGA functional, called HCTH, was determined through a least squares refinement to data of 93 systems. Here, the data are extended to 120 systems and 147 systems, introducing electron and proton affinities, and weakly bound dimers to give the new functionals HCTH/120 and HCTH/147. HCTH/120 has already been shown to give high quality predictions for weakly bound systems. The functionals are applied in a comparative study of the addition reaction of water to formaldehyde and sulfur trioxide, respectively. Furthermore, the performance of the HCTH/120 functional in Car-Parrinello molecular dynamics simulations of liquid water is encouraging.
Interplay of approximate planning strategies.
Huys, Quentin J M; Lally, Níall; Faulkner, Paul; Eshel, Neir; Seifritz, Erich; Gershman, Samuel J; Dayan, Peter; Roiser, Jonathan P
2015-03-10
Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and hierarchically decompose hard tasks into simpler subtasks. Theoretical and cognitive research has revealed several such strategies; however, little is known about their establishment, interaction, and efficiency. Here, we use model-based behavioral analysis to provide a detailed examination of the performance of human subjects in a moderately deep planning task. We find that subjects exploit the structure of the domain to establish subgoals in a way that achieves a nearly maximal reduction in the cost of computing values of choices, but then combine partial searches with greedy local steps to solve subtasks, and maladaptively prune the decision trees of subtasks in a reflexive manner upon encountering salient losses. Subjects come idiosyncratically to favor particular sequences of actions to achieve subgoals, creating novel complex actions or "options." PMID:25675480
Indexing the approximate number system.
Inglis, Matthew; Gilmore, Camilla
2014-01-01
Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects. PMID:24361686
Optimal approximation of harmonic growth clusters by orthogonal polynomials
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.
Decoupling approximation design using the peak to peak gain
NASA Astrophysics Data System (ADS)
Sultan, Cornel
2013-04-01
Linear system design for accurate decoupling approximation is examined using the peak to peak gain of the error system. The design problem consists in finding values of system parameters to ensure that this gain is small. For this purpose a computationally inexpensive upper bound on the peak to peak gain, namely the star norm, is minimized using a stochastic method. Examples of the methodology's application to tensegrity structures design are presented. Connections between the accuracy of the approximation, the damping matrix, and the natural frequencies of the system are examined, as well as decoupling in the context of open and closed loop control.
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.
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{sub 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{sub i}. A summarizing discussion highlights the achievements of the new theory and of its approximate solution
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
Photovoltaic Degradation Rates -- An Analytical Review
Jordan, D. C.; Kurtz, S. R.
2012-06-01
As photovoltaic penetration of the power grid increases, accurate predictions of return on investment require accurate prediction of decreased power output over time. Degradation rates must be known in order to predict power delivery. This article reviews degradation rates of flat-plate terrestrial modules and systems reported in published literature from field testing throughout the last 40 years. Nearly 2000 degradation rates, measured on individual modules or entire systems, have been assembled from the literature, showing a median value of 0.5%/year. The review consists of three parts: a brief historical outline, an analytical summary of degradation rates, and a detailed bibliography partitioned by technology.
DeHart, M.D.
1992-12-01
A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. The present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of non-reentrant polygons can therefore be used to represent any given two dimensional space. Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple one-dimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods.
Learning Analytics Considered Harmful
ERIC Educational Resources Information Center
Dringus, Laurie P.
2012-01-01
This essay is written to present a prospective stance on how learning analytics, as a core evaluative approach, must help instructors uncover the important trends and evidence of quality learner data in the online course. A critique is presented of strategic and tactical issues of learning analytics. The approach to the critique is taken through…
ERIC Educational Resources Information Center
Ember, Lois R.
1977-01-01
The procedures utilized by the Association of Official Analytical Chemists (AOAC) to develop, evaluate, and validate analytical methods for the analysis of chemical pollutants are detailed. Methods validated by AOAC are used by the EPA and FDA in their enforcement programs and are granted preferential treatment by the courts. (BT)
Not Available
1990-01-01
This 43rd Annual Summer Symposium on Analytical Chemistry was held July 24--27, 1990 at Oak Ridge, TN and contained sessions on the following topics: Fundamentals of Analytical Mass Spectrometry (MS), MS in the National Laboratories, Lasers and Fourier Transform Methods, Future of MS, New Ionization and LC/MS Methods, and an extra session. (WET)
Analytical mass spectrometry. Abstracts
Not Available
1990-12-31
This 43rd Annual Summer Symposium on Analytical Chemistry was held July 24--27, 1990 at Oak Ridge, TN and contained sessions on the following topics: Fundamentals of Analytical Mass Spectrometry (MS), MS in the National Laboratories, Lasers and Fourier Transform Methods, Future of MS, New Ionization and LC/MS Methods, and an extra session. (WET)
Extreme Scale Visual Analytics
Wong, Pak C.; Shen, Han-Wei; Pascucci, Valerio
2012-05-08
Extreme-scale visual analytics (VA) is about applying VA to extreme-scale data. The articles in this special issue examine advances related to extreme-scale VA problems, their analytical and computational challenges, and their real-world applications.
Signals: Applying Academic Analytics
ERIC Educational Resources Information Center
Arnold, Kimberly E.
2010-01-01
Academic analytics helps address the public's desire for institutional accountability with regard to student success, given the widespread concern over the cost of higher education and the difficult economic and budgetary conditions prevailing worldwide. Purdue University's Signals project applies the principles of analytics widely used in…
ERIC Educational Resources Information Center
Jackson, Brian
2010-01-01
Using a survey of 138 writing programs, I argue that we must be more explicit about what we think students should get out of analysis to make it more likely that students will transfer their analytical skills to different settings. To ensure our students take analytical skills with them at the end of the semester, we must simplify the task we…
Adaptive approximation of higher order posterior statistics
Lee, Wonjung
2014-02-01
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively.
Rainbows: Mie computations and the Airy approximation.
Wang, R T; van de Hulst, H C
1991-01-01
Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution f rom the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work. PMID:20581954
Evaluating the Accuracy of Hessian Approximations for Direct Dynamics Simulations.
Zhuang, Yu; Siebert, Matthew R; Hase, William L; Kay, Kenneth G; Ceotto, Michele
2013-01-01
Direct dynamics simulations are a very useful and general approach for studying the atomistic properties of complex chemical systems, since an electronic structure theory representation of a system's potential energy surface is possible without the need for fitting an analytic potential energy function. In this paper, recently introduced compact finite difference (CFD) schemes for approximating the Hessian [J. Chem. Phys.2010, 133, 074101] are tested by employing the monodromy matrix equations of motion. Several systems, including carbon dioxide and benzene, are simulated, using both analytic potential energy surfaces and on-the-fly direct dynamics. The results show, depending on the molecular system, that electronic structure theory Hessian direct dynamics can be accelerated up to 2 orders of magnitude. The CFD approximation is found to be robust enough to deal with chaotic motion, concomitant with floppy and stiff mode dynamics, Fermi resonances, and other kinds of molecular couplings. Finally, the CFD approximations allow parametrical tuning of different CFD parameters to attain the best possible accuracy for different molecular systems. Thus, a direct dynamics simulation requiring the Hessian at every integration step may be replaced with an approximate Hessian updating by tuning the appropriate accuracy. PMID:26589009
Efficient and accurate numerical methods for the Klein-Gordon-Schroedinger equations
Bao, Weizhu . E-mail: bao@math.nus.edu.sg; Yang, Li . E-mail: yangli@nus.edu.sg
2007-08-10
In this paper, we present efficient, unconditionally stable and accurate numerical methods for approximations of the Klein-Gordon-Schroedinger (KGS) equations with/without damping terms. The key features of our methods are based on: (i) the application of a time-splitting spectral discretization for a Schroedinger-type equation in KGS (ii) the utilization of Fourier pseudospectral discretization for spatial derivatives in the Klein-Gordon equation in KGS (iii) the adoption of solving the ordinary differential equations (ODEs) in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying Crank-Nicolson/leap-frog for linear/nonlinear terms for time derivatives. The numerical methods are either explicit or implicit but can be solved explicitly, unconditionally stable, and of spectral accuracy in space and second-order accuracy in time. Moreover, they are time reversible and time transverse invariant when there is no damping terms in KGS, conserve (or keep the same decay rate of) the wave energy as that in KGS without (or with a linear) damping term, keep the same dynamics of the mean value of the meson field, and give exact results for the plane-wave solution. Extensive numerical tests are presented to confirm the above properties of our numerical methods for KGS. Finally, the methods are applied to study solitary-wave collisions in one dimension (1D), as well as dynamics of a 2D problem in KGS.
High accurate interpolation of NURBS tool path for CNC machine tools
NASA Astrophysics Data System (ADS)
Liu, Qiang; Liu, Huan; Yuan, Songmei
2016-06-01
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.
An efficient and accurate molecular alignment and docking technique using ab initio quality scoring
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
NASA Astrophysics Data System (ADS)
Diwakar, S. V.; Das, Sarit K.; Sundararajan, T.
2009-12-01
A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function ( C0) and derivative ( C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.
Accurate FDTD modelling for dispersive media using rational function and particle swarm optimisation
NASA Astrophysics Data System (ADS)
Chung, Haejun; Ha, Sang-Gyu; Choi, Jaehoon; Jung, Kyung-Young
2015-07-01
This article presents an accurate finite-difference time domain (FDTD) dispersive modelling suitable for complex dispersive media. A quadratic complex rational function (QCRF) is used to characterise their dispersive relations. To obtain accurate coefficients of QCRF, in this work, we use an analytical approach and a particle swarm optimisation (PSO) simultaneously. In specific, an analytical approach is used to obtain the QCRF matrix-solving equation and PSO is applied to adjust a weighting function of this equation. Numerical examples are used to illustrate the validity of the proposed FDTD dispersion model.
Multidimensional stochastic approximation Monte Carlo.
Zablotskiy, Sergey V; Ivanov, Victor A; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g(E), of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g(E_{1},E_{2}). We show when and why care has to be exercised when obtaining the microcanonical density of states g(E_{1}+E_{2}) from g(E_{1},E_{2}). PMID:27415383
Interplay of approximate planning strategies
Huys, Quentin J. M.; Lally, Níall; Faulkner, Paul; Eshel, Neir; Seifritz, Erich; Gershman, Samuel J.; Dayan, Peter; Roiser, Jonathan P.
2015-01-01
Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and hierarchically decompose hard tasks into simpler subtasks. Theoretical and cognitive research has revealed several such strategies; however, little is known about their establishment, interaction, and efficiency. Here, we use model-based behavioral analysis to provide a detailed examination of the performance of human subjects in a moderately deep planning task. We find that subjects exploit the structure of the domain to establish subgoals in a way that achieves a nearly maximal reduction in the cost of computing values of choices, but then combine partial searches with greedy local steps to solve subtasks, and maladaptively prune the decision trees of subtasks in a reflexive manner upon encountering salient losses. Subjects come idiosyncratically to favor particular sequences of actions to achieve subgoals, creating novel complex actions or “options.” PMID:25675480
Multidimensional stochastic approximation Monte Carlo
NASA Astrophysics Data System (ADS)
Zablotskiy, Sergey V.; Ivanov, Victor A.; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g (E ) , of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g (E1,E2) . We show when and why care has to be exercised when obtaining the microcanonical density of states g (E1+E2) from g (E1,E2) .
Semiclassics beyond the diagonal approximation
NASA Astrophysics Data System (ADS)
Turek, Marko
2004-05-01
The statistical properties of the energy spectrum of classically chaotic closed quantum systems are the central subject of this thesis. It has been conjectured by O.Bohigas, M.-J.Giannoni and C.Schmit that the spectral statistics of chaotic systems is universal and can be described by random-matrix theory. This conjecture has been confirmed in many experiments and numerical studies but a formal proof is still lacking. In this thesis we present a semiclassical evaluation of the spectral form factor which goes beyond M.V.Berry's diagonal approximation. To this end we extend a method developed by M.Sieber and K.Richter for a specific system: the motion of a particle on a two-dimensional surface of constant negative curvature. In particular we prove that these semiclassical methods reproduce the random-matrix theory predictions for the next to leading order correction also for a much wider class of systems, namely non-uniformly hyperbolic systems with f>2 degrees of freedom. We achieve this result by extending the configuration-space approach of M.Sieber and K.Richter to a canonically invariant phase-space approach.
Randomized approximate nearest neighbors algorithm.
Jones, Peter Wilcox; Osipov, Andrei; Rokhlin, Vladimir
2011-09-20
We present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {x(j)} in R(d), the algorithm attempts to find k nearest neighbors for each of x(j), where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T·N·(d·(log d) + k·(d + log k)·(log N)) + N·k(2)·(d + log k), with T the number of iterations performed. The memory requirements of the procedure are of the order N·(d + k). A by-product of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among {x(j)} for an arbitrary point x ∈ R(d). The cost of each such query is proportional to T·(d·(log d) + log(N/k)·k·(d + log k)), and the memory requirements for the requisite data structure are of the order N·(d + k) + T·(d + N). The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme's behavior for certain types of distributions of {x(j)} and illustrate its performance via several numerical examples.
Optimal Slater-determinant approximation of fermionic wave functions
NASA Astrophysics Data System (ADS)
Zhang, J. M.; Mauser, Norbert J.
2016-09-01
We study the optimal Slater-determinant approximation of an N -fermion wave function analytically. That is, we seek the Slater-determinant (constructed out of N orthonormal single-particle orbitals) wave function having largest overlap with a given N -fermion wave function. Some simple lemmas have been established and their usefulness is demonstrated on some structured states, such as the Greenberger-Horne-Zeilinger state. In the simplest nontrivial case of three fermions in six orbitals, which the celebrated Borland-Dennis discovery is about, the optimal Slater approximation wave function is proven to be built out of the natural orbitals in an interesting way. We also show that the Hadamard inequality is useful for finding the optimal Slater approximation of some special target wave functions.
Algebraic approximations for transcendental equations with applications in nanophysics
NASA Astrophysics Data System (ADS)
Barsan, Victor
2015-09-01
Using algebraic approximations of trigonometric or hyperbolic functions, a class of transcendental equations can be transformed in tractable, algebraic equations. Studying transcendental equations this way gives the eigenvalues of Sturm-Liouville problems associated to wave equation, mainly to Schroedinger equation; these algebraic approximations provide approximate analytical expressions for the energy of electrons and phonons in quantum wells, quantum dots (QDs) and quantum wires, in the frame of one-particle models of such systems. The advantage of this approach, compared to the numerical calculations, is that the final result preserves the functional dependence on the physical parameters of the problem. The errors of this method, situated between some few percentages and ?, are carefully analysed. Several applications, for quantum wells, QDs and quantum wires, are presented.
Resonant-state-expansion Born approximation for waveguides with dispersion
NASA Astrophysics Data System (ADS)
Doost, M. B.
2016-02-01
The resonant-state-expansion (RSE) Born approximation, a rigorous perturbative method developed for electrodynamic and quantum mechanical open systems, is further developed to treat waveguides with a Sellmeier dispersion. For media that can be described by these types of dispersion over the relevant frequency range, such as optical glass, I show that the the perturbed RSE problem can be solved by diagonalizing a second-order eigenvalue problem. In the case of a single resonance at zero frequency, this is simplified to a generalized eigenvalue problem. Results are presented using analytically solvable planar waveguides and parameters of borosilicate BK7 glass, for a perturbation in the waveguide width. The efficiency of using either an exact dispersion over all frequencies or an approximate dispersion over a narrow frequency range is compared. I included a derivation of the RSE Born approximation for waveguides to make use of the resonances calculated by the RSE.
An approximate method for residual stress calculation infunctionally graded materials
Becker, T.L.
1999-06-02
Thermal residual stresses in functionally graded materials(FGMs) arise primarily from nonlinear spatial variations in the thermalexpansion coefficient, but can be significantly adjusted by variations inmodulus. Thermoelastic analysis of FGMs is complicated by such modulusgradients. A class of problems for which thermal stress solutions formaterials with constant modulus can be used as a basis for approximationsfor FGMs is discussed. The size of the error in this approximation due togradients in elastic modulus is investigated. Analytical and finiteelement solutions for the thermal stresses in various FGM geometries arecompared to results from this approximate method. In a geometry ofpractical interest, a right cylinder graded along the z-axis, the errorfor a Ni-Al2O3 FGM was found to be within 15 percent for all gradientsconsidered. The form of the approximation makes it easier to identifydesirable types of spatial nonlinearity in expansion coefficient andvariations in modulus: this would allow the manipulation of the locationof compressive stresses.
An approximate method for sonic fatigue analysis of plates and shells
NASA Astrophysics Data System (ADS)
Blevins, R. D.
1989-02-01
Approximate analytical methods are developed for determining the response of plate and shell structures to coherent sound fields. The methods are based on separating the spatial and temporal aspects of the problem and then developing approximations for both. Direct comparison is made with experimental data.
Accurate analytical modelling of cosmic ray induced failure rates of power semiconductor devices
NASA Astrophysics Data System (ADS)
Bauer, Friedhelm D.
2009-06-01
A new, simple and efficient approach is presented to conduct estimations of the cosmic ray induced failure rate for high voltage silicon power devices early in the design phase. This allows combining common design issues such as device losses and safe operating area with the constraints imposed by the reliability to result in a better and overall more efficient design methodology. Starting from an experimental and theoretical background brought forth a few yeas ago [Kabza H et al. Cosmic radiation as a cause for power device failure and possible countermeasures. In: Proceedings of the sixth international symposium on power semiconductor devices and IC's, Davos, Switzerland; 1994. p. 9-12, Zeller HR. Cosmic ray induced breakdown in high voltage semiconductor devices, microscopic model and possible countermeasures. In: Proceedings of the sixth international symposium on power semiconductor devices and IC's, Davos, Switzerland; 1994. p. 339-40, and Matsuda H et al. Analysis of GTO failure mode during d.c. blocking. In: Proceedings of the sixth international symposium on power semiconductor devices and IC's, Davos, Switzerland; 1994. p. 221-5], an exact solution of the failure rate integral is derived and presented in a form which lends itself to be combined with the results available from commercial semiconductor simulation tools. Hence, failure rate integrals can be obtained with relative ease for realistic two- and even three-dimensional semiconductor geometries. Two case studies relating to IGBT cell design and planar junction termination layout demonstrate the purpose of the method.
NASA Astrophysics Data System (ADS)
Martínez, M. J.; Marco, F. J.; López, J. A.
2009-02-01
The Hipparcos catalog provides a reference frame at optical wavelengths for the new International Celestial Reference System (ICRS). This new reference system was adopted following the resolution agreed at the 23rd IAU General Assembly held in Kyoto in 1997. Differences in the Hipparcos system of proper motions and the previous materialization of the reference frame, the FK5, are expected to be caused only by the combined effects of the motion of the equinox of the FK5 and the precession of the equator and the ecliptic. Several authors have pointed out an inconsistency between the differences in proper motion of the Hipparcos-FK5 and the correction of the precessional values derived from VLBI and lunar laser ranging (LLR) observations. Most of them have claimed that these discrepancies are due to slightly biased proper motions in the FK5 catalog. The different mathematical models that have been employed to explain these errors have not fully accounted for the discrepancies in the correction of the precessional parameters. Our goal here is to offer an explanation for this fact. We propose the use of independent parametric and nonparametric models. The introduction of a nonparametric model, combined with the inner product in the square integrable functions over the unitary sphere, would give us values which do not depend on the possible interdependencies existing in the data set. The evidence shows that zonal studies are needed. This would lead us to introduce a local nonparametric model. All these models will provide independent corrections to the precessional values, which could then be compared in order to study the reliability in each case. Finally, we obtain values for the precession corrections that are very consistent with those that are currently adopted.
Numerical evolution of multiple black holes with accurate initial data
Galaviz, Pablo; Bruegmann, Bernd; Cao Zhoujian
2010-07-15
We present numerical evolutions of three equal-mass black holes using the moving puncture approach. We calculate puncture initial data for three black holes solving the constraint equations by means of a high-order multigrid elliptic solver. Using these initial data, we show the results for three black hole evolutions with sixth-order waveform convergence. We compare results obtained with the BAM and AMSS-NCKU codes with previous results. The approximate analytic solution to the Hamiltonian constraint used in previous simulations of three black holes leads to different dynamics and waveforms. We present some numerical experiments showing the evolution of four black holes and the resulting gravitational waveform.
Hydration thermodynamics beyond the linear response approximation
NASA Astrophysics Data System (ADS)
Raineri, Fernando O.
2016-10-01
The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, {{\\Psi}\\text{A}} and {{\\Psi}\\text{B}} , with the solvent environment. Throughout the A \\to B transformation of the solute, the solvation system is described by a Hamiltonian H≤ft(ξ \\right) that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density {{\\wp}ξ}≤ft( y\\right) that the dimensionless perturbational solute-solvent interaction energy Y=β ≤ft({{\\Psi}\\text{B}}-{{\\Psi}\\text{A}}\\right) has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both {{\\wp}ξ} ≤ft( y\\right) and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density {{\\wp}ξ} ≤ft( y\\right) . The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in
Inflation model building with an accurate measure of e -folding
NASA Astrophysics Data System (ADS)
Chongchitnan, Sirichai
2016-08-01
It has become standard practice to take the logarithmic growth of the scale factor as a measure of the amount of inflation, despite the well-known fact that this is only an approximation for the true amount of inflation required to solve the horizon and flatness problems. The aim of this work is to show how this approximation can be completely avoided using an alternative framework for inflation model building. We show that using the inverse Hubble radius, H =a H , as the key dynamical parameter, the correct number of e -folding arises naturally as a measure of inflation. As an application, we present an interesting model in which the entire inflationary dynamics can be solved analytically and exactly, and, in special cases, reduces to the familiar class of power-law models.
Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas
Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.
2010-03-15
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.
Efficient evaluation of analytic Fukui functions.
Flores-Moreno, Roberto; Melin, Junia; Ortiz, J V; Merino, Gabriel
2008-12-14
An efficient method for the analytic evaluation of Fukui functions is proposed. Working equations are derived and numerical results are used to validate the method on medium size set of molecules. In addition to the obvious advantages of analytic differentiation, the proposed method is efficient enough to be considered a practical alternative to the finite difference formulation used routinely. The reliability of the approximations used here is demonstrated and discussed. Problems found in other methods for prediction of electrophilic centers are corrected automatically when using the new method.
Analytical studies of coherent electron cooling
Wang,G.; Blaskiewicz, M.; Litvinenko, V.N.
2009-05-04
Under certain assumptions and simplifications, we studied a few physics processes of Coherent Electron Cooling using analytical approach. In the modulation process, the effect due to merging the ion beam with the electron beam is studied under single kick approximation. In the free electron laser (FEL) amplifier, we studied the amplification of the electron density modulation using 1D analytical approach. Both the electron charge density and the phase space density are derived in the frequency domain. The solutions are then transformed into the space domain through Fast Fourier Transformation (FFT).
Analytic solution for vertical launch into orbit
NASA Technical Reports Server (NTRS)
Boltz, Frederick W.
1989-01-01
An approximate analytic solution is presented for the motion and heating of nonlifting spacecraft launched vertically for ascending flight through the atmosphere into earth orbit. The solution is based on Chapman's Z-function transformation of the equations of motion with the assumption of an exponential atmosphere. The transformed equations have been modified to include the effects of thrusting with mass loss. It is assumed that the vehicle negotiates a gravity turn during ascent so that the thrust vector is aligned in the flight-path direction. Numerical results are presented to document the analytic solution and provide evidence of the useful information generated by it.
Analytic solutions of the relativistic Boltzmann equation
NASA Astrophysics Data System (ADS)
Hatta, Yoshitaka; Martinez, Mauricio; Xiao, Bo-Wen
2015-04-01
We present new analytic solutions to the relativistic Boltzmann equation within the relaxation time approximation. We first obtain spherically expanding solutions which are the kinetic counterparts of the exact solutions of the Israel-Stewart equation in the literature. This allows us to compare the solutions of the kinetic and hydrodynamic equations at an analytical level. We then derive a novel boost-invariant solution of the Boltzmann equation which has an unconventional dependence on the proper time. The existence of such a solution is also suggested in second-order hydrodynamics and fluid-gravity correspondence.
Benchmarking accurate spectral phase retrieval of single attosecond pulses
NASA Astrophysics Data System (ADS)
Wei, Hui; Le, Anh-Thu; Morishita, Toru; Yu, Chao; Lin, C. D.
2015-02-01
A single extreme-ultraviolet (XUV) attosecond pulse or pulse train in the time domain is fully characterized if its spectral amplitude and phase are both determined. The spectral amplitude can be easily obtained from photoionization of simple atoms where accurate photoionization cross sections have been measured from, e.g., synchrotron radiations. To determine the spectral phase, at present the standard method is to carry out XUV photoionization in the presence of a dressing infrared (IR) laser. In this work, we examine the accuracy of current phase retrieval methods (PROOF and iPROOF) where the dressing IR is relatively weak such that photoelectron spectra can be accurately calculated by second-order perturbation theory. We suggest a modified method named swPROOF (scattering wave phase retrieval by omega oscillation filtering) which utilizes accurate one-photon and two-photon dipole transition matrix elements and removes the approximations made in PROOF and iPROOF. We show that the swPROOF method can in general retrieve accurate spectral phase compared to other simpler models that have been suggested. We benchmark the accuracy of these phase retrieval methods through simulating the spectrogram by solving the time-dependent Schrödinger equation numerically using several known single attosecond pulses with a fixed spectral amplitude but different spectral phases.
Laser Guided Automated Calibrating System for Accurate Bracket Placement
Anitha, A; Kumar, AJ; Mascarenhas, R; Husain, A
2015-01-01
Background: The basic premise of preadjusted bracket system is accurate bracket positioning. It is widely recognized that accurate bracket placement is of critical importance in the efficient application of biomechanics and in realizing the full potential of a preadjusted edgewise appliance. Aim: The purpose of this study was to design a calibrating system to accurately detect a point on a plane as well as to determine the accuracy of the Laser Guided Automated Calibrating (LGAC) System. Materials and Methods: To the lowest order of approximation a plane having two parallel lines is used to verify the accuracy of the system. On prescribing the distance of a point from the line, images of the plane are analyzed from controlled angles, calibrated and the point is identified with a laser marker. Results: The image was captured and analyzed using MATLAB ver. 7 software (The MathWorks Inc.). Each pixel in the image corresponded to a distance of 1cm/413 (10 mm/413) = 0.0242 mm (L/P). This implies any variations in distance above 0.024 mm can be measured and acted upon, and sets the highest possible accuracy for this system. Conclusion: A new automated system is introduced having an accuracy of 0.024 mm for accurate bracket placement. PMID:25745575
Generalised quasilinear approximation of the helical magnetorotational instability
NASA Astrophysics Data System (ADS)
Child, Adam; Hollerbach, Rainer; Marston, Brad; Tobias, Steven
2016-06-01
> Motivated by recent advances in direct statistical simulation (DSS) of astrophysical phenomena such as out-of-equilibrium jets, we perform a direct numerical simulation (DNS) of the helical magnetorotational instability (HMRI) under the generalised quasilinear approximation (GQL). This approximation generalises the quasilinear approximation (QL) to include the self-consistent interaction of large-scale modes, interpolating between fully nonlinear DNS and QL DNS whilst still remaining formally linear in the small scales. In this paper we address whether GQL can more accurately describe low-order statistics of axisymmetric HMRI when compared with QL by performing DNS under various degrees of GQL approximation. We utilise various diagnostics, such as energy spectra in addition to first and second cumulants, for calculations performed for a range of Reynolds and Hartmann numbers (describing rotation and imposed magnetic field strength respectively). We find that GQL performs significantly better than QL in describing the statistics of the HMRI even when relatively few large-scale modes are kept in the formalism. We conclude that DSS based on GQL (GCE2) will be significantly more accurate than that based on QL (CE2).
Accurate determination of the amino acid content of selected feedstuffs.
Rutherfurd, Shane M
2009-01-01
The accurate determination of the amino acid content is important. In the present study, a least-squares non-linear regression model of the amino acid content determined over multiple hydrolysis times was used to accurately determine the content of amino acids in five different feedstuffs. These values were compared with 24-h hydrolysis values determined for the same feedstuffs. Overall, approximately two-thirds of the amino acids determined in this study (aspartic acid, threonine, glutamic acid, proline, glycine, alanine, leucine, tyrosine, phenylalanine and arginine) using 24-h hydrolysis were in good agreement (<3% difference). When examined across feedstuffs, the concentration of serine was underestimated by the 24-h hydrolysis method by 4.8%, while the concentrations of histidine and lysine were overestimated by 3.9% and 3.1%, respectively.
Two Timescale Approximation Applied to Gravitational Waves from Eccentric EMRIs
NASA Astrophysics Data System (ADS)
Moxon, Jordan; Flanagan, Eanna; Hinderer, Tanja; Pound, Adam
2016-03-01
Gravitational-wave driven inspirals of compact objects into massive black holes (Extreme Mass Ratio Inspirals - EMRIs) form an interesting, long-lived signal for future space-based gravitational wave detectors. Accurate signal predictions will be necessary to take full advantage of matched filtering techniques, motivating the development of a calculational technique for deriving the gravitational wave signal to good approximation throughout the inspiral. We report on recent work on developing the two-timescale technique with the goal of predicting waveforms from eccentric equatorial systems to subleading (post-adiabatic) order in the phase, building on recent work by Pound in the scalar case. The computation requires us to understand the dissipative component of the second-order self force. It also demands careful consideration of how the two timescale (near-zone) approximation should match with the post-Minkowski approximation of the gravitational waves at great distances.
Low rank approximation in G 0 W 0 calculations
NASA Astrophysics Data System (ADS)
Shao, MeiYue; Lin, Lin; Yang, Chao; Liu, Fang; Da Jornada, Felipe H.; Deslippe, Jack; Louie, Steven G.
2016-08-01
The single particle energies obtained in a Kohn--Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, 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 approximated. The $G_0W_0$ approximation is a widely used technique in which the self energy is expressed as the convolution of a non-interacting 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 approximation to the frequency dependent part of $W_0$. In particular, we examine the effect of such a low rank approximation on the accuracy of the $G_0W_0$ approximation. We also discuss how the numerical convolution of $G_0$ and $W_0$ can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.
Enzymes in Analytical Chemistry.
ERIC Educational Resources Information Center
Fishman, Myer M.
1980-01-01
Presents tabular information concerning recent research in the field of enzymes in analytic chemistry, with methods, substrate or reaction catalyzed, assay, comments and references listed. The table refers to 128 references. Also listed are 13 general citations. (CS)
UNAERO: A package of FORTRAN subroutines for approximating unsteady aerodynamics in the time domain
NASA Technical Reports Server (NTRS)
Dunn, H. J.
1985-01-01
This report serves as an instruction and maintenance manual for a collection of CDC CYBER FORTRAN IV subroutines for approximating the unsteady aerodynamic forces in the time domain. The result is a set of constant-coefficient first-order differential equations that approximate the dynamics of the vehicle. Provisions are included for adjusting the number of modes used for calculating the approximations so that an accurate approximation is generated. The number of data points at different values of reduced frequency can also be varied to adjust the accuracy of the approximation over the reduced-frequency range. The denominator coefficients of the approximation may be calculated by means of a gradient method or a least-squares approximation technique. Both the approximation methods use weights on the residual error. A new set of system equations, at a different dynamic pressure, can be generated without the approximations being recalculated.
Extreme Scale Visual Analytics
Steed, Chad A; Potok, Thomas E; Pullum, Laura L; Ramanathan, Arvind; Shipman, Galen M; Thornton, Peter E; Potok, Thomas E
2013-01-01
Given the scale and complexity of today s data, visual analytics is rapidly becoming a necessity rather than an option for comprehensive exploratory analysis. In this paper, we provide an overview of three applications of visual analytics for addressing the challenges of analyzing climate, text streams, and biosurveilance data. These systems feature varying levels of interaction and high performance computing technology integration to permit exploratory analysis of large and complex data of global significance.
Analytical Improvements in PV Degradation Rate Determination
Jordan, D. C.; Kurtz, S. R.
2011-02-01
As photovoltaic (PV) penetration of the power grid increases, it becomes vital to know how decreased power output may affect cost over time. In order to predict power delivery, the decline or degradation rates must be determined accurately. For non-spectrally corrected data several complete seasonal cycles (typically 3-5 years) are required to obtain reasonably accurate degradation rates. In a rapidly evolving industry such a time span is often unacceptable and the need exists to determine degradation rates accurately in a shorter period of time. Occurrence of outliers and data shifts are two examples of analytical problems leading to greater uncertainty and therefore to longer observation times. In this paper we compare three methodologies of data analysis for robustness in the presence of outliers, data shifts and shorter measurement time periods.
Exploring the Random Phase Approximately for materials chemistry and physics
Ruzsinsky, Adrienn
2015-03-23
This proposal focuses on improved accuracy for the delicate energy differences of interest in materials chemistry with the fully nonlocal random phase approximation (RPA) in a density functional context. Could RPA or RPA-like approaches become standard methods of first-principles electronic-structure calculation for atoms, molecules, solids, surfaces, and nano-structures? Direct RPA includes the full exact exchange energy and a nonlocal correlation energy from the occupied and unoccupied Kohn-Sham orbitals and orbital energies, with an approximate but universal description of long-range van der Waals attraction. RPA also improves upon simple pair-wise interaction potentials or vdW density functional theory. This improvement is essential to capture accurate energy differences in metals and different phases of semiconductors. The applications in this proposal are challenges for the simpler approximations of Kohn-Sham density functional theory, which are part of the current “standard model” for quantum chemistry and condensed matter physics. Within this project we already applied RPA on different structural phase transitions on semiconductors, metals and molecules. Although RPA predicts accurate structural parameters, RPA has proven not equally accurate in all kinds of structural phase transitions. Therefore a correction to RPA can be necessary in many cases. We are currently implementing and testing a nonempirical, spatially nonlocal, frequency-dependent model for the exchange-correlation kernel in the adiabatic-connection fluctuation-dissipation context. This kernel predicts a nearly-exact correlation energy for the electron gas of uniform density. If RPA or RPA-like approaches prove to be reliably accurate, then expected increases in computer power may make them standard in the electronic-structure calculations of the future.
The Second Order Approximation to Sample Influence Curve in Canonical Correlation Analysis.
ERIC Educational Resources Information Center
Fung, Wing K.; Gu, Hong
1998-01-01
A second order approximation to the sample influence curve (SIC) has been derived in the literature. This paper presents a more accurate second order approximation, which is exact for the SIC of the squared multiple correction coefficient. An example is presented. (SLD)
Accurate numerical forward model for optimal retracking of SIRAL2 SAR echoes over open ocean
NASA Astrophysics Data System (ADS)
Phalippou, L.; Demeestere, F.
2011-12-01
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 accurate modelling. The step forward to optimal retracking using numerical forward model (NFM) was also pointed out. NFM of the power waveform avoids analytical approximation, 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 analytical 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 approximated by a simple analytical 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
NASA Astrophysics Data System (ADS)
Klein, Stefan; Staring, Marius; Pluim, Josien P. W.
2005-04-01
Nonrigid registration of medical images by maximisation of their mutual information, in combination with a deformation field parameterised by cubic B-splines, has been shown to be robust and accurate in many applications. However, the high computation time is a big disadvantage. This work focusses on the optimisation procedure. Many implementations follow a gradient-descent like approach. The time needed for computing the derivative of the mutual information with respect to the B-spline parameters is the bottleneck in this process. We investigate the influence of several gradient approximation techniques on the number of iterations needed and the computation time per iteration. Three methods are studied: a simple finite difference strategy, the so-called simultaneous perturbation method, and a more analytic computation of the gradient based on a continuous, and differentiable representation of the joint histogram. In addition, the effect of decreasing the number of image samples, used for computing the gradient in each iteration, is investigated. Two types of experiments are performed. Firstly, the registration of an image to itself, after application of a known, randomly generated deformation, is considered. Secondly, experiments are performed with 3D ultrasound brain scans, and 3D CT follow-up scans of the chest. The experiments show that the method using an analytic gradient computation outperforms the other two. Furthermore, the computation time per iteration can be extremely decreased, without affecting the rate of convergence and final accuracy, by using very few samples of the image (randomly chosen every iteration) to compute the derivative. With this approach, large data sets (2563) can be registered within 5 minutes on a moderate PC.
NASA Technical Reports Server (NTRS)
Desmarais, R. N.
1982-01-01
The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.
Practical Schemes for Accurate Forces in Quantum Monte Carlo.
Moroni, S; Saccani, S; Filippi, C
2014-11-11
While the computation of interatomic forces has become a well-established practice within variational Monte Carlo (VMC), the use of the more accurate Fixed-Node Diffusion Monte Carlo (DMC) method is still largely limited to the computation of total energies on structures obtained at a lower level of theory. Algorithms to compute exact DMC forces have been proposed in the past, and one such scheme is also put forward in this work, but remain rather impractical due to their high computational cost. As a practical route to DMC forces, we therefore revisit here an approximate method, originally developed in the context of correlated sampling and named here the Variational Drift-Diffusion (VD) approach. We thoroughly investigate its accuracy by checking the consistency between the approximate VD force and the derivative of the DMC potential energy surface for the SiH and C2 molecules and employ a wide range of wave functions optimized in VMC to assess its robustness against the choice of trial function. We find that, for all but the poorest wave function, the discrepancy between force and energy is very small over all interatomic distances, affecting the equilibrium bond length obtained with the VD forces by less than 0.004 au. Furthermore, when the VMC forces are approximate due to the use of a partially optimized wave function, the DMC forces have smaller errors and always lead to an equilibrium distance in better agreement with the experimental value. We also show that the cost of computing the VD forces is only slightly larger than the cost of calculating the DMC energy. Therefore, the VD approximation represents a robust and efficient approach to compute accurate DMC forces, superior to the VMC counterparts.
Approximation for Horizontal Photon Transport in Cloud Remote Sensing Problems
NASA Technical Reports Server (NTRS)
Plantnick, Steven
1999-01-01
The effect of horizontal photon transport within real-world clouds can be of consequence to remote sensing problems based on plane-parallel cloud models. An analytic approximation for the root-mean-square horizontal displacement of reflected and transmitted photons relative to the incident cloud-top location is derived from random walk theory. The resulting formula is a function of the average number of photon scatterings, and particle asymmetry parameter and single scattering albedo. In turn, the average number of scatterings can be determined from efficient adding/doubling radiative transfer procedures. The approximation is applied to liquid water clouds for typical remote sensing solar spectral bands, involving both conservative and non-conservative scattering. Results compare well with Monte Carlo calculations. Though the emphasis is on horizontal photon transport in terrestrial clouds, the derived approximation is applicable to any multiple scattering plane-parallel radiative transfer problem. The complete horizontal transport probability distribution can be described with an analytic distribution specified by the root-mean-square and average displacement values. However, it is shown empirically that the average displacement can be reasonably inferred from the root-mean-square value. An estimate for the horizontal transport distribution can then be made from the root-mean-square photon displacement alone.
Extension of the weak-line approximation and application to correlated-k methods
Conley, A.J.; Collins, W.D.
2011-03-15
Global climate models require accurate and rapid computation of the radiative transfer through the atmosphere. Correlated-k methods are often used. One of the approximations used in correlated-k models is the weakline approximation. We introduce an approximation T/sub g/ which reduces to the weak-line limit when optical depths are small, and captures the deviation from the weak-line limit as the extinction deviates from the weak-line limit. This approximation is constructed to match the first two moments of the gamma distribution to the k-distribution of the transmission. We compare the errors of the weak-line approximation with T/sub g/ in the context of a water vapor spectrum. The extension T/sub g/ is more accurate and converges more rapidly than the weak-line approximation.
Accurate ionization potential of semiconductors from efficient density functional calculations
NASA Astrophysics Data System (ADS)
Ye, Lin-Hui
2016-07-01
Despite its huge successes in total-energy-related applications, the Kohn-Sham scheme of density functional theory cannot get reliable single-particle excitation energies for solids. In particular, it has not been able to calculate the ionization potential (IP), one of the most important material parameters, for semiconductors. We illustrate that an approximate exact-exchange optimized effective potential (EXX-OEP), the Becke-Johnson exchange, can be used to largely solve this long-standing problem. For a group of 17 semiconductors, we have obtained the IPs to an accuracy similar to that of the much more sophisticated G W approximation (GWA), with the computational cost of only local-density approximation/generalized gradient approximation. The EXX-OEP, therefore, is likely as useful for solids as for finite systems. For solid surfaces, the asymptotic behavior of the vx c has effects similar to those of finite systems which, when neglected, typically cause the semiconductor IPs to be underestimated. This may partially explain why standard GWA systematically underestimates the IPs and why using the same GWA procedures has not been able to get an accurate IP and band gap at the same time.
Symmetry-broken local-density approximation for one-dimensional systems
NASA Astrophysics Data System (ADS)
Rogers, Fergus J. M.; Ball, Caleb J.; Loos, Pierre-François
2016-06-01
Within density-functional theory, the local-density approximation (LDA) correlation functional is typically built by fitting the difference between the near-exact and Hartree-Fock (HF) energies of the uniform electron gas (UEG), together with analytic perturbative results from the high- and low-density regimes. Near-exact energies are obtained by performing accurate diffusion Monte Carlo calculations, while HF energies are usually assumed to be the Fermi fluid HF energy. However, it has been known since the seminal work of A. W. Overhauser [Phys. Rev. Lett. 3, 414 (1959), 10.1103/PhysRevLett.3.414; Phys. Rev. 128, 1437 (1962), 10.1103/PhysRev.128.1437] that one can obtain lower, symmetry-broken (SB) HF energies at any density. Here, we have computed the SBHF energies of the one-dimensional UEG and constructed a SB version of the LDA (SBLDA) from the results. We compare the performance of the LDA and SBLDA functionals when applied to one-dimensional systems, including atoms and molecules. Generalization to higher dimensions is also discussed.