Accurate analytical approximation of asteroid deflection with constant tangential thrust
NASA Astrophysics Data System (ADS)
Bombardelli, Claudio; Baù, Giulio
2012-11-01
We present analytical formulas to estimate the variation of achieved deflection for an Earth-impacting asteroid following a continuous tangential low-thrust deflection strategy. Relatively simple analytical expressions are obtained with the aid of asymptotic theory and the use of Peláez orbital elements set, an approach that is particularly suitable to the asteroid deflection problem and is not limited to small eccentricities. The accuracy of the proposed formulas is evaluated numerically showing negligible error for both early and late deflection campaigns. The results will be of aid in planning future low-thrust asteroid deflection missions.
Analytical approximations for spiral waves
Löber, Jakob Engel, Harald
2013-12-15
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
Analytical approximations for spiral waves.
Löber, Jakob; Engel, Harald
2013-12-01
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R(0). For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R(+)) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R(+) with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
Approximate analytic solutions to the NPDD: Short exposure approximations
NASA Astrophysics Data System (ADS)
Close, Ciara E.; Sheridan, John T.
2014-04-01
There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more 'opaque'. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects resulting from the photo-polymerisation process, and have accurately described these processes in a number of different materials. It is our aim to develop accessible mathematical expressions which provide physical insights and simple quantitative predictions of practical value to material designers and users. In this paper, starting with the Non-Local Photo-Polymerisation Driven Diffusion (NPDD) model coupled integro-differential equations, we first simplify these equations and validate the accuracy of the resulting approximate model. This new set of governing equations are then used to produce accurate analytic solutions (polynomials) describing the evolution of the monomer and polymer concentrations, and the grating refractive index modulation, in the case of short low intensity sinusoidal exposures. The physical significance of the results and their consequences for holographic data storage (HDS) are then discussed.
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.
Analytical approximations to the spectra of quark antiquark potentials
NASA Astrophysics Data System (ADS)
Amore, Paolo; DePace, Arturo; Lopez, Jorge
2006-07-01
A method recently devised to obtain analytical approximations to certain classes of integrals is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of our results is verified by comparing them both with the literature on the subject and with the numerical results obtained with a Fortran code. As an application of the method that we propose, we consider meson spectroscopy with various phenomenological potentials.
Analytic Approximation to Randomly Oriented Spheroid Extinction
1993-12-01
104 times faster than by the T - matrix code . Since the T-matrix scales as at least the cube of the optical size whereas the analytic approximation is...coefficient estimate, and with the Rayleigh formula. Since it is difficult estimate the accuracy near the limit of stability of the T - matrix code some...additional error due to the T - matrix code could be present. UNCLASSIFIED 30 Max Ret Error, Analytic vs T-Mat, r= 1/5 0.0 20 25 10 ~ 0.5 100 . 7.5 S-1.0
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 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.
Approximated analytical solution to an Ebola optimal control problem
NASA Astrophysics Data System (ADS)
Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.
2016-11-01
An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.
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.
Accurate thermochemistry from explicitly correlated distinguishable cluster approximation.
Kats, Daniel; Kreplin, David; Werner, Hans-Joachim; Manby, Frederick R
2015-02-14
An explicitly correlated version of the distinguishable-cluster approximation is presented and extensively benchmarked. It is shown that the usual F12-type explicitly correlated approaches are applicable to distinguishable-cluster theory with single and double excitations, and the results show a significant improvement compared to coupled-cluster theory with singles and doubles for closed and open-shell systems. The resulting method can be applied in a black-box manner to systems with single- and multireference character. Most noticeably, optimized geometries are of coupled-cluster singles and doubles with perturbative triples quality or even better.
NASA Astrophysics Data System (ADS)
Gillespie, Dirk
2011-01-01
The mean spherical approximation (MSA) for the primitive model of electrolytes provides reasonable estimates of thermodynamic quantities such as the excess chemical potential and screening length. It is especially widely used because of its explicit formulas so that numerically solving equations is minimized. As originally formulated, the MSA screening parameter Γ (akin to the reciprocal of the Debye screening length) does not have an explicit analytic formula; an equation for Γ must be solved numerically. Here, an analytic approximation for Γ is presented whose relative error is generally ≲ 10^{-5}. If more accuracy is desired, one step of an iterative procedure (which also produces an explicit formula for Γ) is shown to give relative errors within machine precision in many cases. Even when ion diameter ratios are ˜10 and ion valences are ˜10, the relative error for the analytic approximation is still ≲ 10^{-3} and for the single iterative substitution it is ≲ 10^{-9}.
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.
Applying generalized Padé approximants in analytic QCD models
NASA Astrophysics Data System (ADS)
Cvetič, Gorazd; Kögerler, Reinhart
2011-09-01
A method of resummation of truncated perturbation series, related to diagonal Padé approximants but giving results independent of the renormalization scale, was developed more than ten years ago by us with a view of applying it in perturbative QCD. We now apply this method in analytic QCD models, i.e., models where the running coupling has no unphysical singularities, and we show that the method has attractive features, such as a rapid convergence. The method can be regarded as a generalization of the scale-setting methods of Stevenson, Grunberg, and Brodsky-Lepage-Mackenzie. The method involves the fixing of various scales and weight coefficients via an auxiliary construction of diagonal Padé approximant. In low-energy QCD observables, some of these scales become sometimes low at high order, which prevents the method from being effective in perturbative QCD, where the coupling has unphysical singularities at low spacelike momenta. There are no such problems in analytic QCD.
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.
How accurate is the Pearson r-from-Z approximation? A Monte Carlo simulation study.
Hittner, James B; May, Kim
2012-01-01
The Pearson r-from-Z approximation estimates the sample correlation (as an effect size measure) from the ratio of two quantities: the standard normal deviate equivalent (Z-score) corresponding to a one-tailed p-value divided by the square root of the total (pooled) sample size. The formula has utility in meta-analytic work when reports of research contain minimal statistical information. Although simple to implement, the accuracy of the Pearson r-from-Z approximation has not been empirically evaluated. To address this omission, we performed a series of Monte Carlo simulations. Results indicated that in some cases the formula did accurately estimate the sample correlation. However, when sample size was very small (N = 10) and effect sizes were small to small-moderate (ds of 0.1 and 0.3), the Pearson r-from-Z approximation was very inaccurate. Detailed figures that provide guidance as to when the Pearson r-from-Z formula will likely yield valid inferences are presented.
Analytical approximations for X-ray cross sections 3
NASA Astrophysics Data System (ADS)
Biggs, Frank; Lighthill, Ruth
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 energies greater than or equal to 10 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.
Approximate reanalysis based on the exact analytic expressions
NASA Astrophysics Data System (ADS)
Fuchs, Moshe B.; Maslovitz, Gilad
1992-06-01
Fuchs has recently given the exact analytic expressions of the inverse of the stiffness matrix, the nodal displacements, and the stress resultants in linear elastic structures composed of prismatic elements. For structures of constant geometry, the expressions are explicit in terms of the unimodal stiffnesses of the components of the structures. However, the expressions are intractable in their exact form due to their inordinate length. It all has to do with the number of statically determinate substructures embedded in common engineering structures. This paper describes some preliminary results obtained from approximate analysis models for the internal forces using truncated expressions that are similar in form to the exact analytic ones. The approach is illustrated with numerical examples.
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
Linaro, Daniele; Storace, Marco; Giugliano, Michele
2011-03-01
Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here.
Nonperturbative analytical approximate solutions in intrinsically nonlinear systems
NASA Astrophysics Data System (ADS)
Kindall, Kevin Gaylynn
The basis for obtaining analytical approximations in this dissertation is a new nonperturbative iterative approach that preserves the intrinsic nonlinearity of the system. The traditional method for approaching nonlinear equations has been the small amplitude approximation of classical perturbation theory. However, it is becoming increasingly evident that intrinsic nonlinearity or persistence of the interaction is a primary feature of the solutions for the nonlinear equations that have been solved. Although perturbation theory may be useful in certain physical domains, it is a domain which excludes the effects of the persistent interaction, since perturbation theory nullifies any intrinsically nonlinear property. The method of solution used here proceeds by analogy to the well-known result that second order, linear ordinary differential equations can be transformed to a Riccati equation by a change in dependent variable. An analogous transformation for nonlinear partial differential equations leads to a set of integro- differential equations for which the basic structure is Riccati. Approximations are introduced in the integral part of the integro-differential equation which allow for systematic iteration while making no expansion in powers of the coupling constant. Two sets of differential equations are examined: the Maxwell-Bloch set and the Rossler set. The importance of the former lies in its importance to the phenomenon of optical bistability. The latter represents the minimal set necessary to display chaos. In each case, their intrinsic nonlinearity is demonstrated, and nonperturbative approximate solutions are constructed.
Construction and use of numerical-analytical approximating functions
NASA Astrophysics Data System (ADS)
Serazutdinov, M. N.
2016-11-01
The article goes over the methodology of constructing numerical-analytical approximating functions, satisfying the given boundary conditions for the function of its derivatives in the circuit areas of various shapes. The methodology is based on presenting the unknown function as a series in a complete set of functions that do not satisfy the given boundary conditions on the contour of the area, but additionally numerically defined near the contour to satisfy the boundary conditions. The additional definition of the functions near the area contour is performed numerically based on finite-difference relations. The main advantage of the stated method is the ability to build a relatively simple approximating functions satisfying the given boundary conditions on the boundary of complex shaped areas. The examples of applying the described method for solving the boundary value problem of a plate of different shapes. The possibility of using numerical-analytical functions for solving boundary value problems that contain higher derivatives up to fourth order is shown.
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.
Analytical approximations for effective relative permeability in the capillary limit
NASA Astrophysics Data System (ADS)
Rabinovich, Avinoam; Li, Boxiao; Durlofsky, Louis J.
2016-10-01
We present an analytical method for calculating two-phase effective relative permeability, krjeff, where j designates phase (here CO2 and water), under steady state and capillary-limit assumptions. These effective relative permeabilities may be applied in experimental settings and for upscaling in the context of numerical flow simulations, e.g., for CO2 storage. An exact solution for effective absolute permeability, keff, in two-dimensional log-normally distributed isotropic permeability (k) fields is the geometric mean. We show that this does not hold for krjeff since log normality is not maintained in the capillary-limit phase permeability field (Kj=k·krj) when capillary pressure, and thus the saturation field, is varied. Nevertheless, the geometric mean is still shown to be suitable for approximating krjeff when the variance of lnk is low. For high-variance cases, we apply a correction to the geometric average gas effective relative permeability using a Winsorized mean, which neglects large and small Kj values symmetrically. The analytical method is extended to anisotropically correlated log-normal permeability fields using power law averaging. In these cases, the Winsorized mean treatment is applied to the gas curves for cases described by negative power law exponents (flow across incomplete layers). The accuracy of our analytical expressions for krjeff is demonstrated through extensive numerical tests, using low-variance and high-variance permeability realizations with a range of correlation structures. We also present integral expressions for geometric-mean and power law average krjeff for the systems considered, which enable derivation of closed-form series solutions for krjeff without generating permeability realizations.
Approximate analytic solutions to coupled nonlinear Dirac equations
NASA Astrophysics Data System (ADS)
Khare, Avinash; Cooper, Fred; Saxena, Avadh
2017-03-01
We consider the coupled nonlinear Dirac equations (NLDEs) in 1 + 1 dimensions with scalar-scalar self-interactions g12 / 2 (ψ bar ψ) 2 + g22/2 (ϕ bar ϕ) 2 + g32 (ψ bar ψ) (ϕ bar ϕ) as well as vector-vector interactions of the form g1/22 (ψ bar γμ ψ) (ψ bar γμ ψ) + g22/2 (ϕ bar γμ ϕ) (ϕ bar γμ ϕ) + g32 (ψ bar γμ ψ) (ϕ bar γμ ϕ). Writing the two components of the assumed rest frame solution of the coupled NLDE equations in the form ψ =e - iω1 t {R1 cos θ ,R1 sin θ }, ϕ =e - iω2 t {R2 cos η ,R2 sin η }, and assuming that θ (x) , η (x) have the same functional form they had when g3 = 0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri (x) which are valid for small values of g32 / g22 and g32 / g12. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ± ∞.
Approximate analytic solutions to coupled nonlinear Dirac equations
Khare, Avinash; Cooper, Fred; Saxena, Avadh
2017-01-30
Here, we consider the coupled nonlinear Dirac equations (NLDEs) in 1+11+1 dimensions with scalar–scalar self-interactions g12/2(more » $$\\bar{ψ}$$ψ)2 + g22/2($$\\bar{Φ}$$Φ)2 + g23($$\\bar{ψ}$$ψ)($$\\bar{Φ}$$Φ) as well as vector–vector interactions g12/2($$\\bar{ψ}$$γμψ)($$\\bar{ψ}$$γμψ) + g22/2($$\\bar{Φ}$$γμΦ)($$\\bar{Φ}$$γμΦ) + g23($$\\bar{ψ}$$γμψ)($$\\bar{Φ}$$γμΦ). Writing the two components of the assumed rest frame solution of the coupled NLDE equations in the form ψ=e–iω1tR1cosθ,R1sinθΦ=e–iω2tR2cosη,R2sinη, and assuming that θ(x),η(x) have the same functional form they had when g3 = 0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri(x) which are valid for small values of g32/g22 and g32/g12. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ±∞.« less
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
Analytic Approximation of Carbon Condensation Issues in Type ii Supernovae
NASA Astrophysics Data System (ADS)
Clayton, Donald D.
2013-01-01
I present analytic approximations for some issues related to condensation of graphite, TiC, and silicon carbide in oxygen-rich cores of supernovae of Type II. Increased understanding, which mathematical analysis can support, renders researchers more receptive to condensation in O-rich supernova gases. Taking SN 1987A as typical, my first analysis shows why the abundance of CO molecules reaches an early maximum in which free carbon remains more abundant than CO. This analysis clarifies why O-rich gas cannot oxidize C if 56Co radioactivity is as strong as in SN 1987A. My next analysis shows that the CO abundance could be regarded as being in chemical equilibrium if the CO molecule is given an effective binding energy rather than its laboratory dissociation energy. The effective binding energy makes the thermal dissociation rate of CO equal to its radioactive dissociation rate. This preserves possible relevance for the concept of chemical equilibrium. My next analysis shows that the observed abundances of CO and SiO molecules in SN 1987A rule out frequent suggestions that equilibrium condensation of SUNOCONs has occurred following atomic mixing of the He-burning shell with more central zones in such a way as to reproduce roughly the observed spectrum of isotopes in SUNOCONs while preserving C/O > 1. He atoms admixed along with the excess carbon would destroy CO and SiO molecules, leaving their observed abundances unexplained. The final analysis argues that a chemical quasiequilibrium among grains (but not gas) may exist approximately during condensation, so that its computational use is partially justified as a guide to which mineral phases would be stable against reactions with gas. I illustrate this point with quasiequilibrium calculations by Ebel & Grossman that have shown that graphite is stable even when O/C >1 if prominent molecules are justifiably excluded from the calculation of chemical equilibrium.
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.
Highly accurate analytic formulae for projectile motion subjected to quadratic drag
NASA Astrophysics Data System (ADS)
Turkyilmazoglu, Mustafa
2016-05-01
The classical phenomenon of motion of a projectile fired (thrown) into the horizon through resistive air charging a quadratic drag onto the object is revisited in this paper. No exact solution is known that describes the full physical event under such an exerted resistance force. Finding elegant analytical approximations for the most interesting engineering features of dynamical behavior of the projectile is the principal target. Within this purpose, some analytical explicit expressions are derived that accurately predict the maximum height, its arrival time as well as the flight range of the projectile at the highest ascent. The most significant property of the proposed formulas is that they are not restricted to the initial speed and firing angle of the object, nor to the drag coefficient of the medium. In combination with the available approximations in the literature, it is possible to gain information about the flight and complete the picture of a trajectory with high precision, without having to numerically simulate the full governing equations of motion.
Analytic Interatomic Forces in the Random Phase Approximation
NASA Astrophysics Data System (ADS)
Ramberger, Benjamin; Schäfer, Tobias; Kresse, Georg
2017-03-01
We discuss that in the random phase approximation (RPA) the first derivative of the energy with respect to the Green's function is the self-energy in the G W approximation. This relationship allows us to derive compact equations for the RPA interatomic forces. We also show that position dependent overlap operators are elegantly incorporated in the present framework. The RPA force equations have been implemented in the projector augmented wave formalism, and we present illustrative applications, including ab initio molecular dynamics simulations, the calculation of phonon dispersion relations for diamond and graphite, as well as structural relaxations for water on boron nitride. The present derivation establishes a concise framework for forces within perturbative approaches and is also applicable to more involved approximations for the correlation energy.
Approximate analytic solutions for the optical pumping of fluorescent dyes
NASA Technical Reports Server (NTRS)
Lawandy, N. M.
1978-01-01
A general technique for solving a system of rate equations describing the interaction of an electromagnetic field and a molecular system is presented. The method is used to obtain approximate time-dependent solutions for the upper-level population of fluorescent dyes in the presence of a pump field.
NASA Astrophysics Data System (ADS)
Lau, Chun Sing
This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in
Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation
NASA Astrophysics Data System (ADS)
Exl, Lukas; Mauser, Norbert J.; Zhang, Yong
2016-12-01
We introduce an accurate and efficient method for the numerical evaluation of nonlocal potentials, including the 3D/2D Coulomb, 2D Poisson and 3D dipole-dipole potentials. Our method is based on a Gaussian-sum approximation of the singular convolution kernel combined with a Taylor expansion of the density. Starting from the convolution formulation of the nonlocal potential, for smooth and fast decaying densities, we make a full use of the Fourier pseudospectral (plane wave) approximation of the density and a separable Gaussian-sum approximation of the kernel in an interval where the singularity (the origin) is excluded. The potential is separated into a regular integral and a near-field singular correction integral. The first is computed with the Fourier pseudospectral method, while the latter is well resolved utilizing a low-order Taylor expansion of the density. Both parts are accelerated by fast Fourier transforms (FFT). The method is accurate (14-16 digits), efficient (O (Nlog N) complexity), low in storage, easily adaptable to other different kernels, applicable for anisotropic densities and highly parallelizable.
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.
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
NASA Astrophysics Data System (ADS)
Du, Qiang; Yang, Jiang
2017-03-01
This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge-Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge-Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen-Cahn equations, nonlocal Cahn-Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.
Analytical approximation of transit time scattering due to magnetosonic waves
NASA Astrophysics Data System (ADS)
Bortnik, J.; Thorne, R. M.; Ni, B.; Li, J.
2015-03-01
Recent test particle simulations have shown that energetic electrons traveling through fast magnetosonic (MS) wave packets can experience an effect which is specifically associated with the tight equatorial confinement of these waves, known as transit time scattering. However, such test particle simulations can be computationally cumbersome and offer limited insight into the dominant physical processes controlling the wave-particle interactions, that is, in determining the effects of the various wave parameters and equatorial confinement on the particle scattering. In this paper, we show that such nonresonant effects can be effectively captured with a straightforward analytical treatment that is made possible with a set of reasonable, simplifying assumptions. It is shown that the effect of the wave confinement, which is not captured by the standard quasi-linear theory approach, acts in such a way as to broaden the range of particle energies and pitch angles that can effectively resonate with the wave. The resulting diffusion coefficients can be readily incorporated into global diffusion models in order to test the effects of transit time scattering on the dynamical evolution of radiation belt fluxes.
Large deflection of clamped circular plate and accuracy of its approximate analytical solutions
NASA Astrophysics Data System (ADS)
Zhang, Yin
2016-02-01
A different set of governing equations on the large deflection of plates are derived by the principle of virtual work (PVW), which also leads to a different set of boundary conditions. Boundary conditions play an important role in determining the computation accuracy of the large deflection of plates. Our boundary conditions are shown to be more appropriate by analyzing their difference with the previous ones. The accuracy of approximate analytical solutions is important to the bulge/blister tests and the application of various sensors with the plate structure. Different approximate analytical solutions are presented and their accuracies are evaluated by comparing them with the numerical results. The error sources are also analyzed. A new approximate analytical solution is proposed and shown to have a better approximation. The approximate analytical solution offers a much simpler and more direct framework to study the plate-membrane transition behavior of deflection as compared with the previous approaches of complex numerical integration.
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.
NASA Astrophysics Data System (ADS)
Liu, Qiang; Van Mieghem, Piet
2017-04-01
One of the most important quantities of the exact Markovian SIS epidemic process is the time-dependent prevalence, which is the average fraction of infected nodes. Unfortunately, the Markovian SIS epidemic model features an exponentially increasing computational complexity with growing network size N. In this paper, we evaluate a recently proposed analytic approximate prevalence function introduced in Van Mieghem (2016). We compare the approximate function with the N-Intertwined Mean-Field Approximation (NIMFA) and with simulation of the Markovian SIS epidemic process. The results show that the new analytic prevalence function is comparable with other approximate methods.
NASA Astrophysics Data System (ADS)
Shizgal, Bernie D.
2016-12-01
There has been intense interest for several decades by different research groups to accurately model the temperature dependence of a large number of nuclear reaction rate coefficients for both light and heavy nuclides. The rate coefficient, k(T) , is given by the Maxwellian average of the reactive cross section expressed in terms of the astrophysical factor, S(E) , which for nonresonant reactions is generally written as a power series in the relative energy E. A computationally efficient algorithm for the temperature dependence of nuclear reaction rate coefficients is required for fusion reactor research and for models of nucleosynthesis and stellar evolution. In this paper, an accurate analytical expression for the temperature dependence of nuclear reaction rate coefficients is provided in terms of τ = 3(b / 2) 2/3 or equivalently, T - 1/3 , where b = B /√{kB T }, B is the Gamow factor and kB is the Boltzmann constant. The methodology is appropriate for all nonresonant nuclear reactions for which S(E) can be represented as a power series in E. The explicit expression for the rate coefficient versus temperature is derived with the asymptotic expansions of the moments of w(E) = exp(- E /kB T - B /√{ E }) in terms of τ. The zeroth order moment is the familiar Gaussian approximation to the rate coefficient. Results are reported for the representative reactions D(d, p)T, D(d, n)3He and 7Li(p, α) α and compared with several different fitting procedures reported in the literature.
Approximate analytic solutions of stagnation point flow in a porous medium
NASA Astrophysics Data System (ADS)
Kumaran, V.; Tamizharasi, R.; Vajravelu, K.
2009-06-01
An efficient and new implicit perturbation technique is used to obtain approximate analytical series solution of Brinkmann equation governing the two-dimensional stagnation point flow in a porous medium. Analytical approximate solution of the classical two-dimensional stagnation point flow is obtained as a limiting case. Also, it is shown that the obtained higher order series solutions agree well with the computed numerical solutions.
Efficient yet accurate approximations for ab initio calculations of alcohol cluster thermochemistry.
Umer, Muhammad; Kopp, Wassja A; Leonhard, Kai
2015-12-07
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.
Development of highly accurate approximate scheme for computing the charge transfer integral
NASA Astrophysics Data System (ADS)
Pershin, Anton; Szalay, Péter G.
2015-08-01
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.
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
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.
Montoya-Castillo, Andrés; Reichman, David R
2017-02-28
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩, we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
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.
NASA Technical Reports Server (NTRS)
Livne, Eli; Mineau, David
1997-01-01
Analytical sensitivities of panel flutter constraints with respect to panel shape as well as thickness and material properties are derived and numerically tested. Cases of fixed in-plane loads and cases in which in-plane loads are variable (depending on panel and overall wing shape as well as material and sizing design variables) are considered. Accuracy of approximations and range of move limits required are studied in preparation for integration with nonlinear programming/approximation concept aeroelastic design synthesis methodology.
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; 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.
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.
Bonetto, Paola; Qi, Jinyi; Leahy, Richard M.
1999-10-01
We describe a method for computing linear observer statistics for maximum a posteriori (MAP) reconstructions of PET images. The method is based on a theoretical approximation for the mean and covariance of MAP reconstructions. In particular, we derive here a closed form for the channelized Hotelling observer (CHO) statistic applied to 2D MAP images. We show reasonably good correspondence between these theoretical results and Monte Carlo studies. The accuracy and low computational cost of the approximation allow us to analyze the observer performance over a wide range of operating conditions and parameter settings for the MAP reconstruction algorithm.
NASA Astrophysics Data System (ADS)
Dutta, Ivy; Chowdhury, Anirban Roy; Kumbhakar, Dharmadas
2013-03-01
Using Chebyshev power series approach, accurate description for the first higher order (LP11) mode of graded index fibers having three different profile shape functions are presented in this paper and applied to predict their propagation characteristics. These characteristics include fractional power guided through the core, excitation efficiency and Petermann I and II spot sizes with their approximate analytic formulations. We have shown that where two and three Chebyshev points in LP11 mode approximation present fairly accurate results, the values based on our calculations involving four Chebyshev points match excellently with available exact numerical results.
Burow, Asbjörn M; Bates, Jefferson E; Furche, Filipp; Eshuis, Henk
2014-01-14
The random phase approximation (RPA) is an increasingly popular method for computing molecular ground-state correlation energies within the adiabatic connection fluctuation-dissipation theorem framework of density functional theory. We present an efficient analytical implementation of first-order RPA molecular properties and nuclear forces using the resolution-of-the-identity (RI) approximation and imaginary frequency integration. The centerpiece of our approach is a variational RPA energy Lagrangian invariant under unitary transformations of occupied and virtual reference orbitals, respectively. Its construction requires the solution of a single coupled-perturbed Kohn-Sham equation independent of the number of perturbations. Energy gradients with respect to nuclear displacements and other first-order properties such as one-particle densities or dipole moments are obtained from partial derivatives of the Lagrangian. Our RPA energy gradient implementation exhibits the same [Formula: see text] scaling with system size N as a single-point RPA energy calculation. In typical applications, the cost for computing the entire gradient vector with respect to nuclear displacements is ∼5 times that of a single-point RPA energy calculation. Derivatives of the quadrature nodes and weights used for frequency integration are essential for RPA gradients with an accuracy consistent with RPA energies and can be included in our approach. The quality of RPA equilibrium structures is assessed by comparison to accurate theoretical and experimental data for covalent main group compounds, weakly bonded dimers, and transition metal complexes. RPA outperforms semilocal functionals as well as second-order Møller-Plesset (MP2) theory, which fails badly for the transition metal compounds. Dipole moments of polarizable molecules and weakly bound dimers show a similar trend. RPA harmonic vibrational frequencies are nearly of coupled cluster singles, doubles, and perturbative triples quality
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.
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
Analytical approximation for photonic array modes in 1D photonic crystal superlattices.
Smith, Elena; Shteeman, Vladislav; Hardy, Amos A
2016-04-01
We present a comprehensive analytical approximation for array modes (both the modal fields and their associated propagation constants) for 1D photonic crystal superlattices (i.e., large periodic arrays of repeated sequences of different coupled waveguides/lasers). In this class, a regular periodicity of a photonic lattice is supplemented with the additional periodicity of a larger scale. Our approximation is a vectorial approach, accounting for the TE and TM polarizations. It can be applied to both the low- and high-contrast photonic devices. We used the model of standing waves for analytical evaluation of envelopes of array modes in a photonic superlattice. Combination of the model of standing waves with the coupled-mode formalism for infinite photonic superlattices allows evaluation of propagation constants of the array modes. Both the evaluations require only a fraction of a second for computation. Still, the results, acquired with the analytical approximation, are very close to those of well-established approaches. Furthermore, for the first time, analytical expressions for the modal fields and propagation constants become available.
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.
An analytical technique for approximating unsteady aerodynamics in the time domain
NASA Technical Reports Server (NTRS)
Dunn, H. J.
1980-01-01
An analytical technique is presented for approximating unsteady aerodynamic forces in the time domain. The order of elements of a matrix Pade approximation was postulated, and the resulting polynomial coefficients were determined through a combination of least squares estimates for the numerator coefficients and a constrained gradient search for the denominator coefficients which insures stable approximating functions. The number of differential equations required to represent the aerodynamic forces to a given accuracy tends to be smaller than that employed in certain existing techniques where the denominator coefficients are chosen a priori. Results are shown for an aeroelastic, cantilevered, semispan wing which indicate a good fit to the aerodynamic forces for oscillatory motion can be achieved with a matrix Pade approximation having fourth order numerator and second order denominator polynomials.
Analytical approximations to the Hotelling trace for digital x-ray detectors
NASA Astrophysics Data System (ADS)
Clarkson, Eric; Pineda, Angel R.; Barrett, Harrison H.
2001-06-01
The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.
Bales, Barney L
2016-09-19
A simple analytical approximation to an inhomogeneously-broadened dispersion signal is proposed and tested with resonance lines broadened by unresolved hyperfine structure. Spectral parameters may be rapidly and accurately extracted using a nonlinear least-squares fitting algorithm. Combining the new approximation to a dispersion signal with a well-known approximation to the absorption signal allows dispersion-absorption admixtures, a problem of growing importance, to be analyzed quickly and accurately. For pure dispersion signals, the maximum difference between the fit and the signal for unresolved lines is 1.1 % of the maximum intensity. For pure absorption, the difference is 0.33 % of the peak-to-peak intensity, and for admixtures up to 40 % dispersion (maximum intensity/peak-to-peak intensity), the difference is 0.7 %. The accuracy of the recovered spectral parameters depends on the degree of inhomogeneously-broadened and the percentage admixture, but they are generally about 1 % at most. A significant finding of the work is that the parameters pertinent to the dispersion or the absorption are insignificantly different when fitting isolated lines vs. fitting admixtures. Admixtures with added noise or an unsuspected extraneous line are investigated.
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.
NASA Astrophysics Data System (ADS)
Aymard, François; Gulminelli, Francesca; Margueron, Jérôme
2016-08-01
We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas-Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.
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.
Approximate Analytic Solutions for the Primary Auroral Electron Flux and Related Quantities.
1981-03-03
Preliminary Remarks 18 8.2 Unidirectional- Monoenergetic Incident Flux 19 8.3 Isotropic-Maxwellian Incident Flux 20 8.4 Isotropic- Monoenergetic Incident...PSEUDOPARTICLES To APPROXIMATE THE SUMS 25 51 Contents 11. COMPARISONS 28 11. 1 Preliminary Remarks 28 11. 2 Comparisons for Isotropic - Monoenerget ie...the Analytic, Range, and Rees Models for 10, 5, and 2 KeV Isotrqpic- Monoenergetic Sources Each Containing 1 erg/cm s 30 6. Incident Maxwellian Energy
Approximated and User Steerable tSNE for Progressive Visual Analytics.
Pezzotti, Nicola; Lelieveldt, Boudewijn; van der Maaten, Laurens; Hollt, Thomas; Eisemann, Elmar; Vilanova, Anna
2016-05-19
Progressive Visual Analytics aims at improving the interactivity in existing analytics techniques by means of visualization as well as interaction with intermediate results. One key method for data analysis is dimensionality reduction, for example, to produce 2D embeddings that can be visualized and analyzed efficiently. t-Distributed Stochastic Neighbor Embedding (tSNE) is a well-suited technique for the visualization of high-dimensional data. tSNE can create meaningful intermediate results but suffers from a slow initialization that constrains its application in Progressive Visual Analytics. We introduce a controllable tSNE approximation (A-tSNE), which trades off speed and accuracy, to enable interactive data exploration. We offer real-time visualization techniques, including a density-based solution and a Magic Lens to inspect the degree of approximation. With this feedback, the user can decide on local refinements and steer the approximation level during the analysis. We demonstrate our technique with several datasets, in a real-world research scenario and for the real-time analysis of high-dimensional streams to illustrate its effectiveness for interactive data analysis.
Analytical approximations for flow in compressible, saturated, one-dimensional porous media
NASA Astrophysics Data System (ADS)
Barry, D. A.; Lockington, D. A.; Jeng, D.-S.; Parlange, J.-Y.; Li, L.; Stagnitti, F.
2007-04-01
A nonlinear model for single-phase fluid flow in slightly compressible porous media is presented and solved approximately. The model assumes state equations for density, porosity, viscosity and permeability that are exponential functions of the fluid (either gas or liquid) pressure. The governing equation is transformed into a nonlinear diffusion equation. It is solved for a semi-infinite domain for either constant pressure or constant flux boundary conditions at the surface. The solutions obtained, although approximate, are extremely accurate as demonstrated by comparisons with numerical results. Predictions for the surface pressure resulting from a constant flux into a porous medium are compared with published experimental data.
NASA Technical Reports Server (NTRS)
Fymat, A. L.
1978-01-01
Consideration is given to analytical inversions in the remote sensing of particle size distributions, noting multispectral extinctions in anomalous diffraction approximation and angular and spectral scattering in diffraction approximation. A closed-form analytical inverse solution is derived in order to reconstruct the size distribution of atmospheric aerosols. The anomalous diffraction approximation to Mie's solution is used to describe the particles. Experimental data yield the geometrical area of aerosol polydispersion. Size distribution is thus found from a set of multispectral extinction measurements. In terms of the angular and spectral scattering of light in a narrow forward cone, it is shown that an analytical inverse solution may also be found for the Fraunhofer approximation to the Kirchhoff diffraction, and for an improved expression of this approximation due to Penndorf (1962) and Shifrin-Punina (1968).
NASA Astrophysics Data System (ADS)
Zou, Li; Liang, Songxin; Li, Yawei; Jeffrey, David J.
2017-03-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning
2016-11-21
We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.
NASA Astrophysics Data System (ADS)
Rigby, J. R.; Yin, Jun; Albertson, John D.; Porporato, Amilcare
2015-07-01
Simplified numerical models of the atmospheric boundary layer (ABL) are useful both for understanding the underlying dynamics and potentially providing parsimonious modelling approaches for inclusion in larger models. Herein the governing equations of a simplified slab model of the uniformly mixed, purely convective, diurnal ABL are shown to allow immediate solutions for the potential temperature and specific humidity as functions of the ABL height and net radiation when expressed in integral form. By employing a linearized saturation vapour relation, the height of the mixed layer is shown to obey a non-linear ordinary differential equation with quadratic dependence on ABL height. A perturbation solution provides general analytical approximations, of which the leading term is shown to represent the contribution under equilibrium evaporation. These solutions allow the diurnal evolution of the height, potential temperature, and specific humidity (i.e., also vapour pressure deficit) of the mixed layer to be expressed analytically for arbitrary radiative forcing functions.
Approximate analytical solution for MHD stagnation-point flow in porous media
NASA Astrophysics Data System (ADS)
Awang Kechil, S.; Hashim, I.
2009-04-01
In this paper, the steady two-dimensional laminar forced MHD Hiemenz flow against a flat plate with variable wall temperature in a porous medium which was solved numerically using the implicit finite-difference of Keller-box method [Yih KA. The effect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous media. Acta Mech 1998;130:147-58] is revisited. A simple analytic approach of the Adomian decomposition method (ADM) is employed to obtain an approximate analytical solution of the problem. The skin friction coefficient and the rate of heat transfer given by the ADM are in good agreement with the numerical solutions of the Keller-box method.
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.
Walter, Johannes; Thajudeen, Thaseem; Süss, Sebastian; Segets, Doris; Peukert, Wolfgang
2015-04-21
Analytical centrifugation (AC) is a powerful technique for the characterisation of nanoparticles in colloidal systems. As a direct and absolute technique it requires no calibration or measurements of standards. Moreover, it offers simple experimental design and handling, high sample throughput as well as moderate investment costs. However, the full potential of AC for nanoparticle size analysis requires the development of powerful data analysis techniques. In this study we show how the application of direct boundary models to AC data opens up new possibilities in particle characterisation. An accurate analysis method, successfully applied to sedimentation data obtained by analytical ultracentrifugation (AUC) in the past, was used for the first time in analysing AC data. Unlike traditional data evaluation routines for AC using a designated number of radial positions or scans, direct boundary models consider the complete sedimentation boundary, which results in significantly better statistics. We demonstrate that meniscus fitting, as well as the correction of radius and time invariant noise significantly improves the signal-to-noise ratio and prevents the occurrence of false positives due to optical artefacts. Moreover, hydrodynamic non-ideality can be assessed by the residuals obtained from the analysis. The sedimentation coefficient distributions obtained by AC are in excellent agreement with the results from AUC. Brownian dynamics simulations were used to generate numerical sedimentation data to study the influence of diffusion on the obtained distributions. Our approach is further validated using polystyrene and silica nanoparticles. In particular, we demonstrate the strength of AC for analysing multimodal distributions by means of gold nanoparticles.
Houairi, Kamel; Cassaing, Frédéric
2009-12-01
Two-wavelength interferometry combines measurement at two wavelengths lambda(1) and lambda(2) in order to increase the unambiguous range (UR) for the measurement of an optical path difference. With the usual algorithm, the UR is equal to the synthetic wavelength Lambda=lambda(1)lambda(2)/|lambda(1)-lambda(2)|, and the accuracy is a fraction of Lambda. We propose here a new analytical algorithm based on arithmetic properties, allowing estimation of the absolute fringe order of interference in a noniterative way. This algorithm has nice properties compared with the usual algorithm: it is at least as accurate as the most accurate measurement at one wavelength, whereas the UR is extended to several times the synthetic wavelength. The analysis presented shows how the actual UR depends on the wavelengths and different sources of error. The simulations presented are confirmed by experimental results, showing that the new algorithm has enabled us to reach an UR of 17.3 microm, much larger than the synthetic wavelength, which is only Lambda=2.2 microm. Applications to metrology and fringe tracking are discussed.
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.
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.
Medendorp, Joseph; Lodder, Robert A
2006-03-01
This research was performed to test the hypothesis that acoustic-resonance spectrometry (ARS) is able to rapidly and accurately differentiate tablets of similar size and shape. The US Food and Drug Administration frequently orders recalls of tablets because of labeling problems (eg, the wrong tablet appears in a bottle). A high-throughput, nondestructive method of online analysis and label comparison before shipping could obviate the need for recall or disposal of a batch of mislabeled drugs, thus saving a company considerable expense and preventing a major safety risk. ARS is accurate and precise as well as inexpensive and nondestructive, and the sensor, is constructed from readily available parts, suggesting utility as a process analytical technology (PAT). To test the classification ability of ARS, 5 common household tablets of similar size and shape were chosen for analysis (aspirin, ibuprofen, acetaminophen, vitamin C, and vitamin B12). The measures of successful tablet identification were intertablet distances in nonparametric multidimensional standard deviations (MSDs) greater than, 3 and intratablet MSDs less than 3, as calculated from an extended bootstrap erroradjusted single sample technique. The average intertablet MSD was 65.64, while the average intratablet MSD from cross-validation was 1.91. Tablet mass (r(2)=0.977), thickness (r(2)=0.977), and density (r(2)=0.900) were measured very accurately from the AR spectra, each with less than 10% error. Tablets were identified correctly with only 250 ms data collection time. These results demonstrate that ARS effectively identified and characterized the 5 types of tablets and could potentially serve as a rapid high-throughput online pharmaceutical sensor.
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.
Kocifaj, Miroslav
2011-06-10
The approximate bulk-scattering phase function of a polydisperse system of dust particles is derived in an analytical form. In the theoretical solution, the particle size distribution is modeled by a modified gamma function that can satisfy various media differing in modal radii. Unlike the frequently applied power law, the modified gamma distribution shows no singularity when the particle radius approaches zero. The approximate scattering phase function is related to the parameters of the size distribution function. This is an important advantage compared to the empirical Henyey-Greenstein (HG) approximation, which is a simple function of the average cosine. However, any optimized value of average cosine of the HG function cannot provide the information on particle microphysical characteristics, such as the size distribution function. In this paper, the mapping between average cosine and the parameters of size distribution function is given by a semianalytical expression that is applicable in rapid numerical simulations on various dust populations. In particular, the modal radius and half-width can be quickly estimated using the presented formulas.
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 ).
NASA Technical Reports Server (NTRS)
Williams, Craig Hamilton
1995-01-01
A simple, analytic approximation is derived to calculate trip time and performance for propulsion systems of very high specific impulse (50,000 to 200,000 seconds) and very high specific power (10 to 1000 kW/kg) for human interplanetary space missions. The approach assumed field-free space, constant thrust/constant specific power, and near straight line (radial) trajectories between the planets. Closed form, one dimensional equations of motion for two-burn rendezvous and four-burn round trip missions are derived as a function of specific impulse, specific power, and propellant mass ratio. The equations are coupled to an optimizing parameter that maximizes performance and minimizes trip time. Data generated for hypothetical one-way and round trip human missions to Jupiter were found to be within 1% and 6% accuracy of integrated solutions respectively, verifying that for these systems, credible analysis does not require computationally intensive numerical techniques.
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.
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.
NASA Astrophysics Data System (ADS)
El-Ajou, Ahmad; Arqub, Omar Abu; Momani, Shaher
2015-07-01
In this paper, explicit and approximate solutions of the nonlinear fractional KdV-Burgers equation with time-space-fractional derivatives are presented and discussed. The solutions of our equation are calculated in the form of rabidly convergent series with easily computable components. The utilized method is a numerical technique based on the generalized Taylor series formula which constructs an analytical solution in the form of a convergent series. Five illustrative applications are given to demonstrate the effectiveness and the leverage of the present method. Graphical results and series formulas are utilized and discussed quantitatively to illustrate the solution. The results reveal that the method is very effective and simple in determination of solution of the fractional KdV-Burgers equation.
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
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-07
In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The
Approximate analytical solutions to the bidomain equations with unequal anisotropy ratios
NASA Astrophysics Data System (ADS)
Roth, Bradley J.
1997-02-01
The anisotropic electrical properties of cardiac tissue are described by the bidomain model. In this model, the ratio of the electrical conductivities parallel to and perpendicular to the myocardial fibers is greater in the intracellular space than in the extracellular space, resulting in a condition called unequal anisotropy ratios. No analytical solutions exist in this case. In this paper, we present approximate analytical solutions to the bidomain equations. The gist of our method is a perturbation expansion in a parameter that is defined as one minus the ratio of the anisotropy ratios in the extracellular and intracellular spaces. Three applications are considered: stimulation of the tissue by an electrode, an expanding action potential wave front, and injury currents. In the first application, the first-order perturbation term of the transmembrane potential depends on orientation by a second-order Legendre polynomial and induces adjacent regions of depolarization and hyperpolarization. In the second and third applications, the extracellular potential outside a wave front or an injured region depends on orientation by a second-order Legendre polynomial and creates regions of positive extracellular potential in the direction parallel to the fibers.
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.
2015-01-01
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
Electrolyte diodes with weak acids and bases. I. Theory and an approximate analytical solution.
Iván, Kristóf; Simon, Péter L; Wittmann, Mária; Noszticzius, Zoltán
2005-10-22
Until now acid-base diodes and transistors applied strong mineral acids and bases exclusively. In this work properties of electrolyte diodes with weak electrolytes are studied and compared with those of diodes with strong ones to show the advantages of weak acids and bases in these applications. The theoretical model is a one dimensional piece of gel containing fixed ionizable groups and connecting reservoirs of an acid and a base. The electric current flowing through the gel is measured as a function of the applied voltage. The steady-state current-voltage characteristic (CVC) of such a gel looks like that of a diode under these conditions. Results of our theoretical, numerical, and experimental investigations are reported in two parts. In this first, theoretical part governing equations necessary to calculate the steady-state CVC of a reverse-biased electrolyte diode are presented together with an approximate analytical solution of this reaction-diffusion-ionic migration problem. The applied approximations are quasielectroneutrality and quasiequilibrium. It is shown that the gel can be divided into an alkaline and an acidic zone separated by a middle weakly acidic region. As a further approximation it is assumed that the ionization of the fixed acidic groups is complete in the alkaline zone and that it is completely suppressed in the acidic one. The general solution given here describes the CVC and the potential and ionic concentration profiles of diodes applying either strong or weak electrolytes. It is proven that previous formulas valid for a strong acid-strong base diode can be regarded as a special case of the more general formulas presented here.
Rankin, Blake M; Ben-Amotz, Dor; Widom, B
2015-09-14
Molecular processes, ranging from hydrophobic aggregation and protein binding to mesoscopic self-assembly, are typically driven by a delicate balance of energetic and entropic non-covalent interactions. Here, we focus on a broad class of such processes in which multiple ligands bind to a central solute molecule as a result of solute-ligand (direct) and/or ligand-ligand (cooperative) interaction energies. Previously, we described a weighted random mixing (WRM) mean-field model for such processes and compared the resulting adsorption isotherms and aggregate size distributions with exact finite lattice (FL) predictions, for lattices with up to n = 20 binding sites. Here, we compare FL predictions obtained using both Bethe-Guggenheim (BG) and WRM approximations, and find that the latter two approximations are complementary, as they are each most accurate in different aggregation regimes. Moreover, we describe a computationally efficient method for exhaustively counting nearest neighbors in FL configurations, thus making it feasible to obtain FL predictions for systems with up n = 48 binding sites, whose properties approach the thermodynamic (infinite lattice) limit. We further illustrate the applicability of our results by comparing lattice model and molecular dynamics simulation predictions pertaining to the aggregation of methane around neopentane.
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.
Looking into analytical approximations for three-flavor neutrino oscillation probabilities in matter
NASA Astrophysics Data System (ADS)
Li, Yu-Feng; Zhang, Jue; Zhou, Shun; Zhu, Jing-yu
2016-12-01
Motivated by tremendous progress in neutrino oscillation experiments, we derive a new set of simple and compact formulas for three-flavor neutrino oscillation probabilities in matter of a constant density. A useful definition of the η-gauge neutrino mass-squared difference Δ∗ ≡ ηΔ31 + (1 - η)Δ32 is introduced, where Δ ji ≡ m j 2 - m i 2 for ji = 21 , 31 , 32 are the ordinary neutrino mass-squared differences and 0 ≤ η ≤ 1 is a real and positive parameter. Expanding neutrino oscillation probabilities in terms of α ≡ Δ21 /Δ∗, we demonstrate that the analytical formulas can be remarkably simplified for η = cos2 θ 12, with θ 12 being the solar mixing angle. As a by-product, the mapping from neutrino oscillation parameters in vacuum to their counterparts in matter is obtained at the order of O({α}^2) . Finally, we show that our approximate formulas are not only valid for an arbitrary neutrino energy and any baseline length, but also still maintaining a high level of accuracy.
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, 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.
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.
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
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 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(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.
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)
Rakhmanov, E. A.
2016-09-01
The Gonchar-Stahl ρ^2-theorem characterizes the rate of convergence of best uniform (Chebyshev) rational approximations (with free poles) for one basic class of analytic functions. The theorem itself, modifications and generalizations of it, methods involved in its proof and other related details constitute an important subfield in the theory of rational approximations of analytic functions and complex analysis. This paper briefly outlines the essentials of the subfield. The fundamental contributions of A. A. Gonchar and H. Stahl are at the heart of the exposition. Bibliography: 70 titles.
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
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
Accurate Sloshing Modes Modeling: A New Analytical Solution and its Consequences on Control
NASA Astrophysics Data System (ADS)
Gonidou, Luc-Olivier; Desmariaux, Jean
2014-06-01
This study addresses the issue of sloshing modes modeling for GNC analyses purposes. On European launchers, equivalent mechanical systems are commonly used for modeling sloshing effects on launcher dynamics. The representativeness of such a methodology is discussed here. First an exact analytical formulation of the launcher dynamics fitted with sloshing modes is proposed and discrepancies with equivalent mechanical system approach are emphasized. Then preliminary comparative GNC analyses are performed using the different models of dynamics in order to evaluate the impact of the aforementioned discrepancies from GNC standpoint. Special attention is paid to system stability.
NASA Technical Reports Server (NTRS)
Mostrel, M. M.
1988-01-01
New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.
Analytical Grid Generation for accurate representation of clearances in CFD for Screw Machines
NASA Astrophysics Data System (ADS)
Rane, S.; Kovačević, A.; Stošić, N.
2015-08-01
One of the major factors affecting the performance prediction of twin screw compressors by use of computational fluid dynamics (CFD) is the accuracy with which the leakage gaps are captured by the discretization methods. The accuracy of mapping leakage flows can be improved by increasing the number of grid points on the profile. However, this method faces limitations when it comes to the complex deforming domains of a twin screw compressor because the computational time increases tremendously. In order to address this problem, an analytical grid distribution procedure is formulated that can independently refine the region of high importance for leakage flows in the interlobe space. This paper describes the procedure of analytical grid generation with the refined mesh in the interlobe area and presents a test case to show the influence of the mesh refinement in that area on the performance prediction. It is shown that by using this method, the flow domains in the vicinity of the interlobe gap and the blowhole area are refined which improves accuracy of leakage flow predictions.
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.
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
An Approximate Analytical Model of Shock Waves from Underground Nuclear Explosions
1990-12-01
Technical Information Service (NTIS). Qualified requestors may obtain additional copies from the Defense Technical Information Center. All others should...apply to the National Technical Information Service. If your address has changed, or .if you wish to be removed from the mailing list, or if the addressee...NUMBERS An Approximate Analvtlial Model of Shock Waves from Contract Underground Nuclear Explosions F19628-88-K-0040
NASA Astrophysics Data System (ADS)
Reed, Shad A.
Hard coatings, such as magnesium aluminate spinel, offer the potential to satisfy the damping requirements of turbine engine components. Unfortunately, the characterization of these materials is complicated by several nonlinearities thus making it difficult to qualify the materials for use in an engine. An experimental and computational research program was initiated with the hope answering some of the questions surrounding these materials. The major contributions of this research program are a new experimental apparatus and method that is able to more accurately determine the nonlinear material properties of these materials, an exhaustive set of material properties data at higher strain levels than previously tested, and, for the first time, a quantification of the effect of strain history on material properties. The use of a reduced order computational model provided several important and unique insights. Specifically, this portion of the research proved that the log decrement method is able to more accurately predict the damping of a nonlinear reduced order frictional model. Additionally, the behavior of the reduced order model indicates that internal friction is the dominant, but not sole, mechanism responsible for the nonlinearities in magnesium aluminate spinel. Finally, modifications of the reduced order model were suggested to include a dependence on the initial conditions of the model, a trend seen in the experiment but not present in the original reduced order model.
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.
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.
NASA Astrophysics Data System (ADS)
Lloyd, N. S.; Bouman, C.; Horstwood, M. S.; Parrish, R. R.; Schwieters, J. B.
2010-12-01
This presentation describes progress in mass spectrometry for analysing very small analyte quantities, illustrated by example applications from nuclear forensics. In this challenging application, precise and accurate (‰) uranium isotope ratios are required from 1 - 2 µm diameter uranium oxide particles, which comprise less than 40 pg of uranium. Traditionally these are analysed using thermal ionisation mass spectrometry (TIMS), and more recently using secondary ionisation mass spectrometry (SIMS). Multicollector inductively-coupled plasma mass spectrometry (MC-ICP-MS) can offer higher productivity compared to these techniques, but is traditionally limited by low efficiency of analyte utilisation (sample through to ion detection). Samples can either be introduced as a solution, or sampled directly from solid using laser ablation. Large multi-isotope ratio datasets can help identify provenance and intended use of anthropogenic uranium and other nuclear materials [1]. The Thermo Scientific NEPTUNE Plus (Bremen, Germany) with ‘Jet Interface’ option offers unparalleled MC-ICP-MS sensitivity. An analyte utilisation of c. 4% has previously been reported for uranium [2]. This high-sensitivity configuration utilises a dry high-capacity (100 m3/h) interface pump, special skimmer and sampler cones and a desolvating nebuliser system. Coupled with new acquisition methodologies, this sensitivity enhancement makes possible the analysis of micro-particles and small sample volumes at higher precision levels than previously achieved. New, high-performance, full-size and compact discrete dynode secondary electron multipliers (SEM) exhibit excellent stability and linearity over a large dynamic range and can be configured to simultaneously measure all of the uranium isotopes. Options for high abundance-sensitivity filters on two ion beams are also available, e.g. for 236U and 234U. Additionally, amplifiers with high ohm (1012 - 1013) feedback resistors have been developed to
Semiconductor quantum wells with BenDaniel-Duke boundary conditions: approximate analytical results
NASA Astrophysics Data System (ADS)
Barsan, Victor; Ciornei, Mihaela-Cristina
2017-01-01
The Schrödinger equation for a particle moving in a square well potential with BenDaniel-Duke boundary conditions is solved. Using algebraic approximations for trigonometric functions, the transcendental equations of the bound states energy are transformed into tractable, algebraic equations. For the ground state and the first excited state, they are cubic equations; we obtain simple formulas for their physically interesting roots. The case of higher excited states is also analysed. Our results have direct applications in the physics of type I and type II semiconductor heterostructures.
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
Analytical approximations for spatial stochastic gene expression in single cells and tissues.
Smith, Stephen; Cianci, Claudia; Grima, Ramon
2016-05-01
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.
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.
NASA Astrophysics Data System (ADS)
Franssens, Ghislain; de Maziére, Martine; Fonteyn, Dominique
2000-08-01
A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz s model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.
Franssens, G; De Maziére, M; Fonteyn, D
2000-08-20
A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz's model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.
Sugden, Isaac; Adjiman, Claire S; Pantelides, Constantinos C
2016-12-01
The global search stage of crystal structure prediction (CSP) methods requires a fine balance between accuracy and computational cost, particularly for the study of large flexible molecules. A major improvement in the accuracy and cost of the intramolecular energy function used in the CrystalPredictor II [Habgood et al. (2015). J. Chem. Theory Comput. 11, 1957-1969] program is presented, where the most efficient use of computational effort is ensured via the use of adaptive local approximate model (LAM) placement. The entire search space of the relevant molecule's conformations is initially evaluated using a coarse, low accuracy grid. Additional LAM points are then placed at appropriate points determined via an automated process, aiming to minimize the computational effort expended in high-energy regions whilst maximizing the accuracy in low-energy regions. As the size, complexity and flexibility of molecules increase, the reduction in computational cost becomes marked. This improvement is illustrated with energy calculations for benzoic acid and the ROY molecule, and a CSP study of molecule (XXVI) from the sixth blind test [Reilly et al. (2016). Acta Cryst. B72, 439-459], which is challenging due to its size and flexibility. Its known experimental form is successfully predicted as the global minimum. The computational cost of the study is tractable without the need to make unphysical simplifying assumptions.
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.
Liu, Jie; Herbert, John M
2015-07-21
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.
NASA Astrophysics Data System (ADS)
Hollingshead, Kyle B.; Jain, Avni; Truskett, Thomas M.
2013-10-01
We study whether fine discretization (i.e., terracing) of continuous pair interactions, when used in combination with first-order mean-spherical approximation theory, can lead to a simple and general analytical strategy for predicting the equilibrium structure and thermodynamics of complex fluids. Specifically, we implement a version of this approach to predict how screened electrostatic repulsions, solute-mediated depletion attractions, or ramp-shaped repulsions modify the radial distribution function and the potential energy of reference hard-sphere fluids, and we compare the predictions to exact results from molecular simulations.
Analytical approximations for the long-term decay behavior of spent fuel and high-level waste
Malbrain, C.M.; Deutch, J.M.; Lester, R.K.
1982-05-01
Simple analytical approximations are presented that describe the radioactivity and radiogenic decay heat behavior of high-level wastes (HLWs) from various nuclear fuel cycles during the first 100,000 years of waste life. The correlations are based on detailed computations of HLW properties carried out with the isotope generation and depletion code ORIGEN 2. The ambiguities encountered in using simple comparisons of the hazards posed by HLWs and naturally occurring mineral deposits to establish the longevity requirements for geologic waste disposal schemes are discussed.
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.
NASA Technical Reports Server (NTRS)
Hinata, S.
1989-01-01
An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations is obtained. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field is incorporated into the model. To single out the effect of the Lorentz force on the omega-effect, the effect of the Lorentz force on the alpha-effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo number N. The amplitude is proportional to N - 1, while the period is almost exactly the same as the dissipation time of the unstable mode (proportional to N).
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.
An analytical fit to an accurate ab initio ( 1A 1) potential surface of H 2O
NASA Astrophysics Data System (ADS)
Redmon, Michael J.; Schatz, George C.
1981-01-01
The accurate ab initio MBPT quartic force field of Bartlett, Shavitt and Purvis has been fit to an analytical function using a method developed by Sorbie and Murrell (SM). An analysis of this surface indicates that it describes most properties of the H 2O molecule very accurately, including an exact fit to the MBPT force field, and very close to the correct energy difference between linear and equilibrium H 2O. The surface also reproduces the correct diatomic potentials in all dissociative regions, but some aspects of it in the "near asymptotic" O( 1D) + H 2 region are not quantitatively described. For example, the potential seems to be too attractive at long range for O + H 2 encounters, although it does have the correct minimum energy path geometry and correctly exhibits no barrier to O atom insertion. Comparisons of this surface with one previously developed by SM indicates generally good agreement between the two, especially after some of the SM parameters were corrected, using a numerical differentiation algorithm to evaluate them. A surface developed by Schinke and Lester (SL) is more realistic than outs in the O( 1D) + H 2 regions, but less quantitative in its description of the H 2O molecule. Overall, the present fit appears to be both realistic and quantitative for energy displacements up to 3-4; eV from H 2O equilibrium, and should therefore be useful for spectroscopic and collision dynamics studies involving H 2O.
NASA Astrophysics Data System (ADS)
Dodin, Amro; Tscherbul, Timur V.; Brumer, Paul
2016-06-01
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 = /1 2 ( γ 1 + γ 2) / Δ p , where γi are the radiative decay rates of the excited levels i = 1, 2, and Δ p = √{ Δ 2 + ( 1 - p 2) γ 1 γ 2 } 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 + > = /1 √{ r 1 + r 2 } ( √{ r 1 } | e 1 > + √{ r 2 } | e 2 >) , 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.
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.
NASA Astrophysics Data System (ADS)
Neese, Frank; Wennmohs, Frank; Hansen, Andreas
2009-03-01
Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Møller-Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50-100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few kcal mol-1. Extended numerical test calculations demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500
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.
Boothroyd, A.I. ); Dove, J.E.; Keogh, W.J. ); Martin, P.G. ); Peterson, M.R. )
1991-09-15
The interaction potential energy surface (PES) of H{sub 4} is of great importance for quantum chemistry, as a test case for molecule--molecule interactions. It is also required for a detailed understanding of certain astrophysical processes, namely, collisional excitation and dissociation of H{sub 2} in molecular clouds, at densities too low to be accessible experimentally. Accurate {ital ab} {ital initio} energies were computed for 6046 conformations of H{sub 4}, using a multiple reference (single and) double excitation configuration interaction (MRD-CI) program. Both systematic and random'' errors were estimated to have an rms size of 0.6 mhartree, for a total rms error of about 0.9 mhartree (or 0.55 kcal/mol) in the final {ital ab} {ital initio} energy values. It proved possible to include in a self-consistent way {ital ab} {ital initio} energies calculated by Schwenke, bringing the number of H{sub 4} conformations to 6101. {ital Ab} {ital initio} energies were also computed for 404 conformations of H{sub 3}; adding {ital ab} {ital initio} energies calculated by other authors yielded a total of 772 conformations of H{sub 3}. (The H{sub 3} results, and an improved analytic PES for H{sub 3}, are reported elsewhere.) {ital Ab} {ital initio} energies are tabulated in this paper only for a sample of H{sub 4} conformations; a full list of all 6101 conformations of H{sub 4} (and 772 conformations of H{sub 3} ) is available from Physics Auxiliary Publication Service (PAPS), or from the authors.
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.
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.
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)
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.
Schuemann, J; Giantsoudi, D; Grassberger, C; Paganetti, H
2015-06-15
Purpose: To estimate the clinical relevance of approximations made in analytical dose calculation methods (ADCs) used for treatment planning on tumor coverage and tumor control probability (TCP) in proton therapy. Methods: We compared dose distributions planned with ADC to delivered dose distributions (as determined by TOPAS Monte Carlo (MC) simulations). We investigated 10 patients per site for 5 treatment sites (head-and-neck, lung, breast, prostate, liver). We evaluated differences between the two dose distributions analyzing dosimetric indices based on the dose-volume-histograms, the γ-index and the TCP. The normal tissue complication probability (NTCP) was estimated for the bladder and anterior rectum for the prostate patients. Results: We find that the target doses are overestimated by the ADC by 1–2% on average for all patients considered. All dosimetric indices (the mean dose, D95, D50 and D02, the dose values covering 95%, 50% and 2% of the target volume, respectively) are predicted within 5% of the delivered dose. A γ-index with a 3%/3mm criteria had a passing rate for target volumes above 96% for all patients. The TCP predicted by the two algorithms was up to 2%, 2.5%, 6%, 6.5%, and 11% for liver and breast, prostate, head-and-neck and lung patients, respectively. Differences in NTCP for anterior-rectum and bladder for prostate patients were less than 3%. Conclusion: We show that ADC provide adequate dose distributions for most patients, however, they can Result in underdosage of the target by as much as 5%. The TCP was found to be up to 11% lower than predicted. Advanced dose-calculation methods like MC simulations may be necessary in proton therapy to ensure target coverage for heterogeneous patient geometries, in clinical trials comparing proton therapy to conventional radiotherapy to avoid biases due to systematic discrepancies in calculated dose distributions, and, if tighter range margins are considered. Fully funded by NIH grants.
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
NASA Astrophysics Data System (ADS)
Barry, D. A.; Parlange, J.-Y.; Li, L.; Jeng, D.-S.; Crapper, M.
2005-10-01
The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 × 10 -5%. This error is orders of magnitude lower than any existing analytical approximations.
Gai, Litao; Bilige, Sudao; Jie, Yingmo
2016-01-01
In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.
NASA Astrophysics Data System (ADS)
Mohammed, Ziad; Saghafifar, Hossein
2014-02-01
An analytical model based on the rate equations of strongly pumped Yb-doped double-clad fiber laser (DCFLs) is presented. The output power and the distributed laser along the whole fiber have been found. In this paper, most parameters affecting the laser performance have been considered. The influences of scattering losses, pump reflection, output reflectivity, doping concentration and fiber length have been studied. It is shown that for wide ranges of the previous parameters and large variations of the input powers for all types of pumping (forward, backward and two-end), the maximum relative error of the output power would be less than 2.72% when the results are compared with the numerical model. Depending on our analytical model, a simple optimization method has been illustrated for high-power laser oscillators.
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..
NASA Technical Reports Server (NTRS)
Schlesinger, Robert E.
1990-01-01
Results are presented from a linear Lagrangian entraining parcel model of an overshooting thunderstorm cloud top. The model, which is similar to that of Adler and Mack (1986), gives analytic exact solutions for vertical velocity and temperature by representing mixing with Rayleigh damping instead of nonlinearly. Model results are presented for various combinations of stratospheric lapse rate, drag intensity, and mixing strength. The results are compared to those of Adler and Mack.
NASA Astrophysics Data System (ADS)
Cumpson, Peter J.; Hedley, John
2003-12-01
Calibration of atomic force microscope (AFM) cantilevers is necessary for the measurement of nanonewton and piconewton forces, which are critical to analytical applications of AFM in the analysis of polymer surfaces, biological structures and organic molecules at nanoscale lateral resolution. We have developed a compact and easy-to-use reference artefact for this calibration, using a method that allows traceability to the SI (Système International). Traceability is crucial to ensure that force measurements by AFM are comparable to those made by optical tweezers and other methods. The new non-contact calibration method measures the spring constant of these artefacts, by a combination of electrical measurements and Doppler velocimetry. The device was fabricated by silicon surface micromachining. The device allows AFM cantilevers to be calibrated quite easily by the 'cantilever-on-reference' method, with our reference device having a spring constant uncertainty of around ± 5% at one standard deviation. A simple substitution of the analogue velocimeter used in this work with a digital model should reduce this uncertainty to around ± 2%. Both are significant improvements on current practice, and allow traceability to the SI for the first time at these nanonewton levels.
NASA Astrophysics Data System (ADS)
Chandra, R.; Johansson, A. J.
An analytical model for estimating the link loss for the on-body wave propagation around the torso is presented. The model is based on the attenuation of the creeping waves over an elliptical approximation of the human torso and includes the influence of the arms. The importance of including the arms' effect for a proper estimation of the link loss is discussed. The model is validated by the full-wave electromagnetic simulations on a numerical phantom.
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.
NASA Astrophysics Data System (ADS)
Alsing, P. M.; Fanto, M. L.
2016-01-01
We present an analytical formulation of the recent one-shot decoupling model of Bràdler and Adami (2015 arXiv:1505.0284) and compute the resulting 'Page information' curves, for the reduced density matrices for the evaporating black hole (BH) internal degrees of freedom, and emitted Hawking radiation pairs entangled across the horizon. We argue that BH evaporation/particle production has a very close analogy to the laboratory process of spontaneous parametric down conversion, when the pump is allowed to deplete.
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).
Shahbazi, Mohammad; Saranlı, Uluç; Babuška, Robert; Lopes, Gabriel A D
2016-12-05
This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of non-negligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.
NASA Astrophysics Data System (ADS)
Choudhury, Raja Roy; Choudhury, Arundhati Roy; Ghose, Mrinal Kanti
2013-09-01
To characterize nonlinear optical fiber, a semi-analytical formulation using variational principle and the Nelder-Mead Simplex method for nonlinear unconstrained minimization is proposed. The number of optimizing parameters in order to optimize core parameter U has been increased to incorporate more flexibility in the formulation of an innovative form of fundamental modal field. This formulation provides accurate analytical expressions for modal dispersion parameter (g) of optical fiber with Kerr nonlinearity. The minimization of core parameter (U), which involves Kerr nonlinearity through the nonstationary expression of propagation constant, is carried out by the Nelder-Mead Simplex method of nonlinear unconstrained minimization, suitable for problems with nonsmooth functions as the method does not require any derivative information. This formulation has less computational burden for calculation of modal parameters than full numerical methods.
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 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.
Sugden, Isaac; Adjiman, Claire S.; Pantelides, Constantinos C.
2016-01-01
The global search stage of crystal structure prediction (CSP) methods requires a fine balance between accuracy and computational cost, particularly for the study of large flexible molecules. A major improvement in the accuracy and cost of the intramolecular energy function used in the CrystalPredictor II [Habgood et al. (2015 ▸). J. Chem. Theory Comput. 11, 1957–1969] program is presented, where the most efficient use of computational effort is ensured via the use of adaptive local approximate model (LAM) placement. The entire search space of the relevant molecule’s conformations is initially evaluated using a coarse, low accuracy grid. Additional LAM points are then placed at appropriate points determined via an automated process, aiming to minimize the computational effort expended in high-energy regions whilst maximizing the accuracy in low-energy regions. As the size, complexity and flexibility of molecules increase, the reduction in computational cost becomes marked. This improvement is illustrated with energy calculations for benzoic acid and the ROY molecule, and a CSP study of molecule (XXVI) from the sixth blind test [Reilly et al. (2016 ▸). Acta Cryst. B72, 439–459], which is challenging due to its size and flexibility. Its known experimental form is successfully predicted as the global minimum. The computational cost of the study is tractable without the need to make unphysical simplifying assumptions. PMID:27910837
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.
Asgharzadeh, Hafez; Borazjani, Iman
2017-02-15
diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.
NASA Astrophysics Data System (ADS)
Asgharzadeh, Hafez; Borazjani, Iman
2017-02-01
diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.
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.
NASA Astrophysics Data System (ADS)
Wan, X.; Tse, P. W.; Xu, G. H.; Tao, T. F.; Zhang, Q.
2016-04-01
Most previous studies on nonlinear Lamb waves are conducted using mode pairs that satisfying strict phase velocity matching and non-zero power flux criteria. However, there are some limitations in existence. First, strict phase velocity matching is not existed in the whole frequency bandwidth; Second, excited center frequency is not always exactly equal to the true phase-velocity-matching frequency; Third, mode pairs are isolated and quite limited in number; Fourth, exciting a single desired primary mode is extremely difficult in practice and the received signal is quite difficult to process and interpret. And few attention has been paid to solving these shortcomings. In this paper, nonlinear S0 mode Lamb waves at low-frequency range satisfying approximate phase velocity matching is proposed for the purpose of overcoming these limitations. In analytical studies, the secondary amplitudes with the propagation distance considering the fundamental frequency, the maximum cumulative propagation distance (MCPD) with the fundamental frequency and the maximum linear cumulative propagation distance (MLCPD) using linear regression analysis are investigated. Based on analytical results, approximate phase velocity matching is quantitatively characterized as the relative phase velocity deviation less than a threshold value of 1%. Numerical studies are also conducted using tone burst as the excitation signal. The influences of center frequency and frequency bandwidth on the secondary amplitudes and MCPD are investigated. S1-S2 mode with the fundamental frequency at 1.8 MHz, the primary S0 mode at the center frequencies of 100 and 200 kHz are used respectively to calculate the ratios of nonlinear parameter of Al 6061-T6 to Al 7075-T651. The close agreement of the computed ratios to the actual value verifies the effectiveness of nonlinear S0 mode Lamb waves satisfying approximate phase velocity matching for characterizing the material nonlinearity. Moreover, the ratios derived from
Bieniasz, L K
2003-07-01
Accurate calculation of concentration gradients at the boundaries is crucial in electrochemical kinetic simulations, owing to the frequent occurrence of gradient-dependent boundary conditions, and the importance of the gradient-dependent electric current. By using the information about higher spatial derivatives of the concentrations, contained in the time-dependent, kinetic reaction-diffusion partial differential equation(s) in one-dimensional space geometry, under appropriate assumptions it is possible to increase the accuracy orders of the conventional, one-sided n-point finite-difference formulae for the concentration gradients at the boundaries, without increasing n. In this way a new class of high order accurate gradient approximations is derived, and tested in simulations of potential-step chronoamperometric and current-step chronopotentiometric transients for the Reinert-Berg system. The new formulae possess advantages over the conventional gradient approximations. For example, they allow one to obtain a third order accuracy by using two space points only, or fourth order accuracy by using three points, and yet they yield smaller errors than the conventional four-point, or five-point formulae, respectively. Needing fewer points, for approximating the gradients with a given accuracy, simplifies also the solution of the linear algebraic equations arising from the application of implicit time integration schemes.
Larson, Jeffrey S.; Goodman, Laurie J.; Tan, Yuping; Defazio-Eli, Lisa; Paquet, Agnes C.; Cook, Jennifer W.; Rivera, Amber; Frankson, Kristi; Bose, Jolly; Chen, Lili; Cheung, Judy; Shi, Yining; Irwin, Sarah; Kiss, Linda D. B.; Huang, Weidong; Utter, Shannon; Sherwood, Thomas; Bates, Michael; Weidler, Jodi; Parry, Gordon; Winslow, John; Petropoulos, Christos J.; Whitcomb, Jeannette M.
2010-01-01
We report here the results of the analytical validation of assays that measure HER2 total protein (H2T) and HER2 homodimer (H2D) expression in Formalin Fixed Paraffin Embedded (FFPE) breast cancer tumors as well as cell line controls. The assays are based on the VeraTag technology platform and are commercially available through a central CAP-accredited clinical reference laboratory. The accuracy of H2T measurements spans a broad dynamic range (2-3 logs) as evaluated by comparison with cross-validating technologies. The measurement of H2T expression demonstrates a sensitivity that is approximately 7–10 times greater than conventional immunohistochemistry (IHC) (HercepTest). The HERmark assay is a quantitative assay that sensitively and reproducibly measures continuous H2T and H2D protein expression levels and therefore may have the potential to stratify patients more accurately with respect to response to HER2-targeted therapies than current methods which rely on semiquantitative protein measurements (IHC) or on indirect assessments of gene amplification (FISH). PMID:21151530
NASA Astrophysics Data System (ADS)
Moldabekov, Zh A.; Ramazanov, T. S.; Gabdullin, M. T.
2016-11-01
In this work, using recently obtained expansion of the dielectric function in the long wave length limit by Moldabekov et al (2015 Phys. Plasmas 22 102104), we extended previously obtained formulas for the equation of state of the semiclassical dense plasma from Ramazanov et al (2015 Phys. Rev. E 92 023104) to the quantum case. Inner energy and contribution to the pressure due to plasma non-ideality derived for both Coulomb pair interaction and quantum pair interaction potentials. Obtained analytical result for the equation of state reproduces the Montroll-Ward contribution, which corresponds to the quantum ring sum. It was shown that the obtained results are consistent with the Thomas-Fermi approximation with the first order gradient correction. Additionally, the generalization of the quantum Deutsch potential to the case of the degenerate electrons is discussed. Obtained results will be useful for understanding of the physics of dense plasmas as well as for further development of the dense plasma simulation on the basis of the quantum potentials.
NASA Astrophysics Data System (ADS)
Sarkar, Vaskar; Dutta, Aloke K.
2006-11-01
A novel approach of defining the threshold voltage for long channel MOSFETs has been presented in this paper, where it has been proposed that it corresponds to the gate-to-source voltage for which the drift and diffusion components of the total drain current become equal to each other. In order to avoid the greater computation time associated with the numerical solution of these two components, an analytical expression of the surface potential, corresponding to the threshold condition, is given here, which has the same functional form as the one proposed by Tsividis. The fuzzy parameter n, appearing in this expression of the surface potential, is expressed as a function of the substrate doping density ( NA) and the oxide thickness ( tox). The threshold voltage values, obtained analytically from the relation between the surface potential at the threshold condition and the closed-form technology-mapped expression of the fuzzy parameter n, show an excellent match with those obtained from SILVACO simulations for a wide range of NA and tox, with the maximum error being only about 4%. The comparison of the percent error values of the threshold voltage obtained from this proposed model with those obtained from the other two recently proposed methods, all with respect to SILVACO simulation results, further verifies the validity of our completely analytical, mathematically simple, and straight-forward approach, proposed in this work here.
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.
Bozkaya, Uğur
2014-10-14
An efficient implementation of analytic energy gradients and spin multiplicities for the density-fitted orbital-optimized second-order perturbation theory (DF-OMP2) [Bozkaya, U. J. Chem. Theory Comput. 2014, 10, 2371-2378] is presented. The DF-OMP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the cost of single point analytic gradient computations with the orbital-optimized MP2 with the resolution of the identity approach (OO-RI-MP2) [Neese, F.; Schwabe, T.; Kossmann, S.; Schirmer, B.; Grimme, S. J. Chem. Theory Comput. 2009, 5, 3060-3073]. Our results demonstrate that the DF-OMP2 method provides substantially lower computational costs for analytic gradients than OO-RI-MP2. On average, the cost of DF-OMP2 analytic gradients is 9-11 times lower than that of OO-RI-MP2 for systems considered. We also consider aromatic bond dissociation energies, for which MP2 provides poor reaction energies. The DF-OMP2 method exhibits a substantially better performance than MP2, providing a mean absolute error of 2.5 kcal mol(-1), which is more than 9 times lower than that of MP2 (22.6 kcal mol(-1)). Overall, the DF-OMP2 method appears very helpful for electronically challenging chemical systems such as free radicals or other cases where standard MP2 proves unreliable. For such problematic systems, we recommend using DF-OMP2 instead of the canonical MP2 as a more robust method with the same computational scaling.
Araujo, G.L.; Castano, J.; Luque, A.; Sanchez, E.
1983-12-01
The current-voltage characteristics of p/sup +/-i-n/sup +/ solar cells is analyzed and an approximated two-exponential model for the dark and J /SUB sc/ -V /SUB oc/ operation is presented. It is shown that this two-exponential model and the superposition principle can be used as a first approximation and as a means of attaining further insight on the basic mechanisms actually occurring in the cell. However, some care should be taken when trying to determine the physical solar cell parameters from experimental data through fitting techniques. All this facts are illustrated and confirmed with theoretical examples and measured currentvoltage characteristics of six different devices.
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.
Karton, Amir; Tarnopolsky, Alex; Lamère, Jean-François; Schatz, George C; Martin, Jan M L
2008-12-18
We present a number of near-exact, nonrelativistic, Born-Oppenheimer reference data sets for the parametrization of more approximate methods (such as DFT functionals). The data were obtained by means of the W4 ab initio computational thermochemistry protocol, which has a 95% confidence interval well below 1 kJ/mol. Our data sets include W4-08, which are total atomization energies of over 100 small molecules that cover varying degrees of nondynamical correlations, and DBH24-W4, which are W4 theory values for Truhlar's set of 24 representative barrier heights. The usual procedure of comparing calculated DFT values with experimental atomization energies is hampered by comparatively large experimental uncertainties in many experimental values and compounds errors due to deficiencies in the DFT functional with those resulting from neglect of relativity and finite nuclear mass. Comparison with accurate, explicitly nonrelativistic, ab initio data avoids these issues. We then proceed to explore the performance of B2x-PLYP-type double hybrid functionals for atomization energies and barrier heights. We find that the optimum hybrids for hydrogen-transfer reactions, heavy-atoms transfers, nucleophilic substitutions, and unimolecular and recombination reactions are quite different from one another: out of these subsets, the heavy-atom transfer reactions are by far the most sensitive to the percentages of Hartree-Fock-type exchange y and MP2-type correlation x in an (x, y) double hybrid. The (42,72) hybrid B2K-PLYP, as reported in a preliminary communication, represents the best compromise between thermochemistry and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochemistry and the DBH24-W4 data set, however, we find a new (36,65) hybrid which we term B2GP-PLYP. At a slight expense in performance for hydrogen-transfer barrier heights and nucleophilic substitutions, we
Makowski, Mariusz; Liwo, Adam; Scheraga, Harold A
2007-03-22
A physics-based model is proposed to derive approximate analytical expressions for the cavity component of the free energy of hydrophobic association of spherical and spheroidal solutes in water. The model is based on the difference between the number and context of the water molecules in the hydration sphere of a hydrophobic dimer and of two isolated hydrophobic solutes. It is assumed that the water molecules touching the convex part of the molecular surface of the dimer and those in the hydration spheres of the monomers contribute equally to the free energy of solvation, and those touching the saddle part of the molecular surface of the dimer result in a more pronounced increase in free energy because of their more restricted mobility (entropy loss) and fewer favorable electrostatic interactions with other water molecules. The density of water in the hydration sphere around a single solute particle is approximated by the derivative of a Gaussian centered on the solute molecule with respect to its standard deviation. On the basis of this approximation, the number of water molecules in different parts of the hydration sphere of the dimer is expressed in terms of the first and the second mixed derivatives of the two Gaussians centered on the first and second solute molecules, respectively, with respect to the standard deviations of these Gaussians, and plausible analytical expressions for the cavity component of the hydrophobic-association energy of spherical and spheroidal solutes are introduced. As opposed to earlier hydration-shell models, our expressions reproduce the desolvation maxima in the potentials of mean force of pairs of nonpolar solutes in water, and their advantage over the models based on molecular-surface area is that they have continuous gradients in the coordinates of solute centers.
Progress toward post-adiabatic EMRI waveforms using the multiscale approximation
NASA Astrophysics Data System (ADS)
Moxon, Jordan; Flanagan, Eanna; Hinderer, Tanja; Pound, Adam
2017-01-01
I present updates on an analytic approximation method for use in computing orbits and waveforms for Extreme Mass Ratio Inspirals (EMRIs). EMRIs are of particular interest for future space-based gravitational wave detectors, such as (e)LISA. Such gravitational wave detectors will depend on precise predictions of the waveform to take full advantage of the available data. The analytic approximation method for which I present new developments is based on second order self force methods, improved by use of the two-timescale approximation method. Once complete, this method will allow efficient computations of highly accurate EMRI waveforms.
Spline methods for approximating quantile functions and generating random samples
NASA Technical Reports Server (NTRS)
Schiess, J. R.; Matthews, C. G.
1985-01-01
Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.
Schulz, Andreas S.; Shmoys, David B.; Williamson, David P.
1997-01-01
Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science. PMID:9370525
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.
Signal Approximation with a Wavelet Neural Network
1992-12-01
specialized electronic devices like the Intel Electronically Trainable Analog Neural Network (ETANN) chip. The WNN representation allows the...accurately approximated with a WNN trained with irregularly sampled data. Signal approximation, Wavelet neural network .
The delta-Eddington approximation for radiative flux transfer
NASA Technical Reports Server (NTRS)
Joseph, J. H.; Wiscombe, W. J.; Weinman, J. A.
1976-01-01
Simple approximations, like the Eddington, are often incapable of coping with the highly asymmetric phase functions typical of particulate scattering. A simple yet accurate method called the delta-Eddington approximation is proposed for determining monochromatic radiative fluxes in an absorbing-scattering atmosphere. In this method, the governing phase function is approximated by a Dirac delta function forward scatter peak and a two-term expansion of the phase function. The fraction of scattering into the truncated forward peak is taken proportional to the square of the phase function asymmetry factor, which distinguishes the delta-Eddington approximation from others of similar nature. The transmission, reflection, and absorption predicted by the delta-Eddington approximation are compared with doubling method calculations for realistic ranges of optical depth, single-scattering albedo, surface albedo, sun angle and asymmetry factor. The approximation is shown to provide an accurate and analytically simple parameterization of radiation to replace the empirism currently encountered in many general circulation and climate models.
A new approximate solution for chlorine concentration decay in pipes.
Yeh, Hund-Der; Wen, Shi-Bin; Chang, Ya-Chi; Lu, Chung-Sying
2008-05-01
Biswas et al. (1993. A model for chlorine concentration decay in pipes. Water Res. 27(12), 1715-1724) presented an analytical solution of a two-dimensional (2-D) steady-state chlorine transport equation in a pipe under the turbulent condition and employed fractional error function and regression technique to develop an approximate solution. However, their approximate solution may not give a good result if the wall decay parameter is large. This paper provides a more accurate approximate solution of the 2-D steady-state chlorine transport equation under the turbulent condition. This new approximate solution has advantages of easy evaluation and good accuracy when compared with the approximate solution given by Biswas et al. (1993). In addition, this paper also develops a methodology that combines simulated annealing (SA) with this new approximate solution to determine the wall decay parameter. Two cases are chosen to demonstrate the application of the present approximate solution and methodology. The first case is to use this new approximate solution in simulating chlorine decay in pipes with the experiment-observed data given by Rossman (2006. The effect of advanced treatment on chlorine decay in metallic pipes. Water Res. 40(13), 2493-2502), while the second case presents the determination of the wall consumption at the end of the pipe network.
A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation
NASA Astrophysics Data System (ADS)
Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.
2014-02-01
This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.
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.
Efficient and accurate computation of the incomplete Airy functions
NASA Technical Reports Server (NTRS)
Constantinides, E. D.; Marhefka, R. J.
1993-01-01
The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high-frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals with such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. In this paper a convergent series solution for the incomplete Airy functions is derived. Asymptotic expansions involving several terms are also developed and serve as large argument approximations. The combination of the series solution with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data.
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
Accurate and precise zinc isotope ratio measurements in urban aerosols.
Gioia, Simone; Weiss, Dominik; Coles, Barry; Arnold, Tim; Babinski, Marly
2008-12-15
We developed an analytical method and constrained procedural boundary conditions that enable accurate and precise Zn isotope ratio measurements in urban aerosols. We also demonstrate the potential of this new isotope system for air pollutant source tracing. The procedural blank is around 5 ng and significantly lower than published methods due to a tailored ion chromatographic separation. Accurate mass bias correction using external correction with Cu is limited to Zn sample content of approximately 50 ng due to the combined effect of blank contribution of Cu and Zn from the ion exchange procedure and the need to maintain a Cu/Zn ratio of approximately 1. Mass bias is corrected for by applying the common analyte internal standardization method approach. Comparison with other mass bias correction methods demonstrates the accuracy of the method. The average precision of delta(66)Zn determinations in aerosols is around 0.05 per thousand per atomic mass unit. The method was tested on aerosols collected in Sao Paulo City, Brazil. The measurements reveal significant variations in delta(66)Zn(Imperial) ranging between -0.96 and -0.37 per thousand in coarse and between -1.04 and 0.02 per thousand in fine particular matter. This variability suggests that Zn isotopic compositions distinguish atmospheric sources. The isotopic light signature suggests traffic as the main source. We present further delta(66)Zn(Imperial) data for the standard reference material NIST SRM 2783 (delta(66)Zn(Imperial) = 0.26 +/- 0.10 per thousand).
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.
Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)
Peskin, M
2004-04-22
I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.
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.
On the calculation of resonances by means of analytic continuation in coupling constant
NASA Astrophysics Data System (ADS)
Horáček, J.; Paidarová, I.
2010-11-01
The method of analytic continuation in the coupling constant in combination with the use of statistical Padé approximation designed to determine resonance parameters is introduced. It is shown that standard quantum chemistry codes provide accurate data which can be used for the process of analytic continuation in coupling constant. Resonance parameters, both the energy and the width, can be inferred for real molecules with accuracy comparable to other more elaborated methods.
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
Accurate spectral color measurements
NASA Astrophysics Data System (ADS)
Hiltunen, Jouni; Jaeaeskelaeinen, Timo; Parkkinen, Jussi P. S.
1999-08-01
Surface color measurement is of importance in a very wide range of industrial applications including paint, paper, printing, photography, textiles, plastics and so on. For a demanding color measurements spectral approach is often needed. One can measure a color spectrum with a spectrophotometer using calibrated standard samples as a reference. Because it is impossible to define absolute color values of a sample, we always work with approximations. The human eye can perceive color difference as small as 0.5 CIELAB units and thus distinguish millions of colors. This 0.5 unit difference should be a goal for the precise color measurements. This limit is not a problem if we only want to measure the color difference of two samples, but if we want to know in a same time exact color coordinate values accuracy problems arise. The values of two instruments can be astonishingly different. The accuracy of the instrument used in color measurement may depend on various errors such as photometric non-linearity, wavelength error, integrating sphere dark level error, integrating sphere error in both specular included and specular excluded modes. Thus the correction formulas should be used to get more accurate results. Another question is how many channels i.e. wavelengths we are using to measure a spectrum. It is obvious that the sampling interval should be short to get more precise results. Furthermore, the result we get is always compromise of measuring time, conditions and cost. Sometimes we have to use portable syste or the shape and the size of samples makes it impossible to use sensitive equipment. In this study a small set of calibrated color tiles measured with the Perkin Elmer Lamda 18 and the Minolta CM-2002 spectrophotometers are compared. In the paper we explain the typical error sources of spectral color measurements, and show which are the accuracy demands a good colorimeter should have.
Heat pipe transient response approximation.
Reid, R. S.
2001-01-01
A simple and concise routine that approximates the response of an alkali metal heat pipe to changes in evaporator heat transfer rate is described. This analytically based routine is compared with data from a cylindrical heat pipe with a crescent-annular wick that undergoes gradual (quasi-steady) transitions through the viscous and condenser boundary heat transfer limits. The sonic heat transfer limit can also be incorporated into this routine for heat pipes with more closely coupled condensers. The advantages and obvious limitations of this approach are discussed. For reference, a source code listing for the approximation appears at the end of this paper.
An improved approximation scheme for the centrifugal term and the Hulthén potential
NASA Astrophysics Data System (ADS)
Ikhdair, S. M.
2009-03-01
We present a new approximation scheme for the centrifugal term to solve the Schrödinger equation with the Hulthén potential for any arbitrary l -state by means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound-state energy eigenvalues and the normalized corresponding eigenfunctions expressed in terms of the Jacobi polynomials or hypergeometric functions for a particle exposed to this potential field. Our numerical results of the energy eigenvalues are found to be in high agreement with those results obtained by using the program based on a numerical integration procedure. The s -wave ( l = 0analytic solution for the binding energies and eigenfunctions of a particle are also calculated. The physical meaning of the approximate analytical solution is discussed. The present approximation scheme is systematic and accurate.
Approximating spatially exclusive invasion processes
NASA Astrophysics Data System (ADS)
Ross, Joshua V.; Binder, Benjamin J.
2014-05-01
A number of biological processes, such as invasive plant species and cell migration, are composed of two key mechanisms: motility and reproduction. Due to the spatially exclusive interacting behavior of these processes a cellular automata (CA) model is specified to simulate a one-dimensional invasion process. Three (independence, Poisson, and 2D-Markov chain) approximations are considered that attempt to capture the average behavior of the CA. We show that our 2D-Markov chain approximation accurately predicts the state of the CA for a wide range of motility and reproduction rates.
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.
Interpolation and Approximation Theory.
ERIC Educational Resources Information Center
Kaijser, Sten
1991-01-01
Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH)
Liu, Fang; Lin, Lin; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F.; Sharifzadeh, Sahar; Jornada, Felipe H. da; Deslippe, Jack; Yang, Chao; and others
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.
NASA Astrophysics Data System (ADS)
Zhu, Ting-Lei; Zhao, Chang-Yin; Zhang, Ming-Jiang
2017-04-01
This paper aims to obtain an analytic approximation to the evolution of circular orbits governed by the Earth's J2 and the luni-solar gravitational perturbations. Assuming that the lunar orbital plane coincides with the ecliptic plane, Allan and Cook (Proc. R. Soc. A, Math. Phys. Eng. Sci. 280(1380):97, 1964) derived an analytic solution to the orbital plane evolution of circular orbits. Using their result as an intermediate solution, we establish an approximate analytic model with lunar orbital inclination and its node regression be taken into account. Finally, an approximate analytic expression is derived, which is accurate compared to the numerical results except for the resonant cases when the period of the reference orbit approximately equals the integer multiples (especially 1 or 2 times) of lunar node regression period.
An Analytic Model of Dusty, Stratified, Spherical H II Regions
NASA Astrophysics Data System (ADS)
Rodríguez-Ramírez, J. C.; Raga, A. C.; Lora, V.; Cantó, J.
2016-12-01
We study analytically the effect of radiation pressure (associated with photoionization processes and with dust absorption) on spherical, hydrostatic H ii regions. We consider two basic equations, one for the hydrostatic balance between the radiation-pressure components and the gas pressure, and another for the balance among the recombination rate, the dust absorption, and the ionizing photon rate. Based on appropriate mathematical approximations, we find a simple analytic solution for the density stratification of the nebula, which is defined by specifying the radius of the external boundary, the cross section of dust absorption, and the luminosity of the central star. We compare the analytic solution with numerical integrations of the model equations of Draine, and find a wide range of the physical parameters for which the analytic solution is accurate.
Gaussian phase distribution approximations for oscillating gradient spin echo diffusion MRI
NASA Astrophysics Data System (ADS)
Ianuş, Andrada; Siow, Bernard; Drobnjak, Ivana; Zhang, Hui; Alexander, Daniel C.
2013-02-01
Oscillating gradients provide an optimal probe of small pore sizes in diffusion MRI. While sinusoidal oscillations have been popular for some time, recent work suggests additional benefits of square or trapezoidal oscillating waveforms. This paper presents analytical expressions of the free and restricted diffusion signal for trapezoidal and square oscillating gradient spin echo (OGSE) sequences using the Gaussian phase distribution (GPD) approximation and generalises existing similar expressions for sinusoidal OGSE. Accurate analytical models are necessary for exploitation of these pulse sequences in imaging studies, as they allow model fitting and parameter estimation in reasonable computation times. We evaluate the accuracy of the approximation against synthesised data from the Monte Carlo (MC) diffusion simulator in Camino and Callaghan's matrix method and we show that the accuracy of the approximation is within a few percent of the signal, while providing several orders of magnitude faster computation. Moreover, since the expressions for trapezoidal wave are complex, we test sine and square wave approximations to the trapezoidal OGSE signal. The best approximations depend on the gradient amplitude and the oscillation frequency and are accurate to within a few percent. Finally, we explore broader applications of trapezoidal OGSE, in particular for non-model based applications, such as apparent diffusion coefficient estimation, where only sinusoidal waveforms have been considered previously. We show that with the right apodisation, trapezoidal waves also have benefits by virtue of the higher diffusion weighting they provide compared to sinusoidal gradients.
Approximate probability distributions of the master equation.
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.
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.
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.
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
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.
Selecting MODFLOW cell sizes for accurate flow fields.
Haitjema, H; Kelson, V; de Lange, W
2001-01-01
Contaminant transport models often use a velocity field derived from a MODFLOW flow field. Consequently, the accuracy of MODFLOW in representing a ground water flow field determines in part the accuracy of the transport predictions, particularly when advective transport is dominant. We compared MODFLOW ground water flow rates and MODPATH particle traces (advective transport) for a variety of conceptual models and different grid spacings to exact or approximate analytic solutions. All of our numerical experiments concerned flow in a single confined or semiconfined aquifer. While MODFLOW appeared robust in terms of both local and global water balance, we found that ground water flow rates, particle traces, and associated ground water travel times are accurate only when sufficiently small cells are used. For instance, a minimum of four or five cells are required to accurately model total ground water inflow in tributaries or other narrow surface water bodies that end inside the model domain. Also, about 50 cells are needed to represent zones of differing transmissivities or an incorrect flow field and (locally) inaccurate ground water travel times may result. Finally, to adequately represent leakage through aquitards or through the bottom of surface water bodies it was found that the maximum allowable cell dimensions should not exceed a characteristic leakage length lambda, which is defined as the square root of the aquifer transmissivity times the resistance of the aquitard or stream bottom. In some cases a cell size of one-tenth of lambda is necessary to obtain accurate results.
Accurate modelling of unsteady flows in collapsible tubes.
Marchandise, Emilie; Flaud, Patrice
2010-01-01
The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.
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.
On the dynamics of approximating schemes for dissipative nonlinear equations
NASA Technical Reports Server (NTRS)
Jones, Donald A.
1993-01-01
Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.
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.
Zhang, D.S.; Wei, G.W.; Kouri, D.J. ); Hoffman, D.K. ); Gorman, M.; Palacios, A. ); Gunaratne, G.H. The Institute of Fundamental Studies, Kandy )
1999-09-01
An algorithm is presented to integrate nonlinear partial differential equations, which is particularly useful when accurate estimation of spatial derivatives is required. It is based on an analytic approximation method, referred to as distributed approximating functionals (DAF[close quote]s), which can be used to estimate a function and a finite number of derivatives with a specified accuracy. As an application, the Kuramoto-Sivashinsky (KS) equation is integrated in polar coordinates. Its integration requires accurate estimation of spatial derivatives, particularly close to the origin. Several stationary and nonstationary solutions of the KS equation are presented, and compared with analogous states observed in the combustion front of a circular burner. A two-ring, nonuniform counter-rotating state has been obtained in a KS model simulation of such a burner. [copyright] [ital 1999] [ital The American Physical Society
NASA Astrophysics Data System (ADS)
Milton, Graeme W.
2016-11-01
The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer p. If p takes its maximum value, then we have a complete analytic material. Otherwise, it is incomplete analytic material of rank p. For two-dimensional materials, further progress can be made in the identification of analytic materials by using the well-known fact that a 90° rotation applied to a divergence-free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.
Milton, Graeme W
2016-11-01
The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer p. If p takes its maximum value, then we have a complete analytic material. Otherwise, it is incomplete analytic material of rank p. For two-dimensional materials, further progress can be made in the identification of analytic materials by using the well-known fact that a 90(°) rotation applied to a divergence-free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.
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.}
A useful approximation for the flat surface impulse response
NASA Technical Reports Server (NTRS)
Brown, Gary S.
1989-01-01
The flat surface impulse response (FSIR) is a very useful quantity in computing the mean return power for near-nadir-oriented short-pulse radar altimeters. However, for very small antenna beamwidths and relatively large pointing angles, previous analytical descriptions become very difficult to compute accurately. An asymptotic approximation is developed to overcome these computational problems. Since accuracy is of key importance, a condition is developed under which this solution is within 2 percent of the exact answer. The asymptotic solution is shown to be in functional agreement with a conventional clutter power result and gives a 1.25-dB correction to this formula to account properly for the antenna-pattern variation over the illuminated area.
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.
A study of Gaussian approximations of fluorescence microscopy PSF models
NASA Astrophysics Data System (ADS)
Zhang, Bo; Zerubia, Josiane; Olivo-Marin, Jean-Christophe
2006-02-01
Despite the availability of rigorous physical models of microscopy point spread functions (PSFs), approximative PSFs, particularly separable Gaussian approximations are widely used in practical microscopic data processing. In fact, compared with a physical PSF model, which usually involves non-trivial terms such as integrals and infinite series, a Gaussian function has the advantage that it is much simpler and can be computed much faster. Moreover, due to its special analytical form, a Gaussian PSF is often preferred to facilitate the analysis of theoretical models such as Fluorescence Recovery After Photobleaching (FRAP) process and of processing algorithms such as EM deconvolution. However, in these works, the selection of Gaussian parameters and the approximation accuracy were rarely investigated. In this paper, we present a comprehensive study of Gaussian approximations for diffraction-limited 2D/3D paraxial/non-paraxial PSFs of Wide Field Fluorescence Microscopy (WFFM), Laser Scanning Confocal Microscopy (LSCM) and Disk Scanning Confocal Microscopy (DSCM) described using the Debye integral. Besides providing an optimal Gaussian parameter for the 2D paraxial WFFM PSF case, we further derive nearly optimal parameters in explicit forms for each of the other cases, based on Maclaurin series matching. Numerical results show that the accuracy of the 2D approximations is very high (Relative Squared Error (RSE) < 2% in WFFM, < 0.3% in LSCM and < 4% in DSCM). For the 3D PSFs, the approximations are average in WFFM (RSE ~= 16-20%), accurate in DSCM (RSE~= 3-6%) and nearly perfect in LSCM (RSE ~= 0.3-0.5%).
An Approximate Approach to Automatic Kernel Selection.
Ding, Lizhong; Liao, Shizhong
2016-02-02
Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
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.
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.
NASA Astrophysics Data System (ADS)
Ghanbarian, Behzad; Daigle, Hugh; Hunt, Allen G.; Ewing, Robert P.; Sahimi, Muhammad
2015-01-01
Understanding and accurate prediction of gas or liquid phase (solute) diffusion are essential to accurate prediction of contaminant transport in partially saturated porous media. In this study, we propose analytical equations, using concepts from percolation theory and the Effective Medium Approximation (EMA) to model the saturation dependence of both gas and solute diffusion in porous media. The predictions of our theoretical approach agree well with the results of nine lattice Boltzmann simulations. We find that the universal quadratic scaling predicted by percolation theory, combined with the universal linear scaling predicted by the EMA, describes diffusion in porous media with both relatively broad and extremely narrow pore size distributions.
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.
An approximate compact analytical expression for the Blasius velocity profile
NASA Astrophysics Data System (ADS)
Savaş, Ö.
2012-10-01
A single-term, two-parameter, hyperbolic tangent function is presented to describe the flow profiles in the Blasius boundary layer, which reproduces the streamwise velocity profile within 0.003 (0.3% of free stream velocity) of its numerical exact solution throughout the flow. The function can be inverted for an implicit description of the velocity profile.
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.
Bronchopulmonary segments approximation using anatomical atlas
NASA Astrophysics Data System (ADS)
Busayarat, Sata; Zrimec, Tatjana
2007-03-01
Bronchopulmonary segments are valuable as they give more accurate localization than lung lobes. Traditionally, determining the segments requires segmentation and identification of segmental bronchi, which, in turn, require volumetric imaging data. In this paper, we present a method for approximating the bronchopulmonary segments for sparse data by effectively using an anatomical atlas. The atlas is constructed from a volumetric data and contains accurate information about bronchopulmonary segments. A new ray-tracing based image registration is used for transferring the information from the atlas to a query image. Results show that the method is able to approximate the segments on sparse HRCT data with slice gap up to 25 millimeters.
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.
Radiative transport in the delta-P1 approximation for semi-infinite turbid media
Seo, InSeok; Hayakawa, Carole K.; Venugopalan, Vasan
2012-01-01
We have developed an analytic solution for spatially resolved diffuse reflectance within the δ-P1 approximation to the radiative transport equation for a semi-infinite homogeneous turbid medium. We evaluate the performance of this solution by comparing its predictions with those provided by Monte Carlo simulations and the standard diffusion approximation. We demonstrate that the δ-P1 approximation provides accurate estimates for spatially resolved diffuse reflectance in both low and high scattering media. We also develop a multi-stage nonlinear optimization algorithm in which the radiative transport estimates provided by the δ-P1 approximation are used to recover the optical absorption (μa), reduced scattering ( μs′), and single-scattering asymmetry coefficients (g1) of liquid and solid phantoms from experimental measurements of spatially resolved diffuse reflectance. Specifically, the δ-P1 approximation can be used to recover μa, μs′, and g1 with errors within ±22%, ±18%, and ±17%, respectively, for both intralipid-based and siloxane-based tissue phantoms. These phantoms span the optical property range 4<(μs′/μa)<117. Using these same measurements, application of the standard diffusion approximation resulted in the recovery of μa and μs′ with errors of ±29% and ±25%, respectively. Collectively, these results demonstrate that the δ-P1 approximation provides accurate radiative transport estimates that can be used to determine accurately the optical properties of biological tissues, particularly in spectral regions where tissue may display moderate/low ratios of reduced scattering to absorption ( μs′/μa). PMID:18383690
Approximating Confidence Intervals for Factor Loadings.
ERIC Educational Resources Information Center
Lambert, Zarrel V.; And Others
1991-01-01
A method is presented that eliminates some interpretational limitations arising from assumptions implicit in the use of arbitrary rules of thumb to interpret exploratory factor analytic results. The bootstrap method is presented as a way of approximating sampling distributions of estimated factor loadings. Simulated datasets illustrate the…
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.
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.
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.
Accurate ab Initio Spin Densities.
Boguslawski, Katharina; Marti, Konrad H; Legeza, Ors; Reiher, Markus
2012-06-12
We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as a basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insight into chemically interesting features of the molecule under study such as the distribution of α and β electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput.2011, 7, 2740].
Intrinsic Nilpotent Approximation.
1985-06-01
RD-A1II58 265 INTRINSIC NILPOTENT APPROXIMATION(U) MASSACHUSETTS INST 1/2 OF TECH CAMBRIDGE LAB FOR INFORMATION AND, DECISION UMCLRSSI SYSTEMS C...TYPE OF REPORT & PERIOD COVERED Intrinsic Nilpotent Approximation Technical Report 6. PERFORMING ORG. REPORT NUMBER LIDS-R-1482 7. AUTHOR(.) S...certain infinite-dimensional filtered Lie algebras L by (finite-dimensional) graded nilpotent Lie algebras or g . where x E M, (x,,Z) E T*M/O. It
Anomalous diffraction approximation limits
NASA Astrophysics Data System (ADS)
Videen, Gorden; Chýlek, Petr
It has been reported in a recent article [Liu, C., Jonas, P.R., Saunders, C.P.R., 1996. Accuracy of the anomalous diffraction approximation to light scattering by column-like ice crystals. Atmos. Res., 41, pp. 63-69] that the anomalous diffraction approximation (ADA) accuracy does not depend on particle refractive index, but instead is dependent on the particle size parameter. Since this is at odds with previous research, we thought these results warranted further discussion.
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
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.
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.
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.
NASA Astrophysics Data System (ADS)
Horáček, J.; Mach, P.; Urban, J.
2010-09-01
The method of analytic continuation in the coupling constant in combination with use of the statistical Padé approximation is applied to the determination of resonance energy and width of the 2Πg state of N2-. It is shown that standard quantum chemistry codes provide accurate data which can be used for analytic continuation in the coupling constant, and the resonance energy and width can be inferred with an accuracy comparable to other more elaborate methods.
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.
BIOACCESSIBILITY TESTS ACCURATELY ESTIMATE ...
Hazards of soil-borne Pb to wild birds may be more accurately quantified if the bioavailability of that Pb is known. To better understand the bioavailability of Pb to birds, we measured blood Pb concentrations in Japanese quail (Coturnix japonica) fed diets containing Pb-contaminated soils. Relative bioavailabilities were expressed by comparison with blood Pb concentrations in quail fed a Pb acetate reference diet. Diets containing soil from five Pb-contaminated Superfund sites had relative bioavailabilities from 33%-63%, with a mean of about 50%. Treatment of two of the soils with P significantly reduced the bioavailability of Pb. The bioaccessibility of the Pb in the test soils was then measured in six in vitro tests and regressed on bioavailability. They were: the “Relative Bioavailability Leaching Procedure” (RBALP) at pH 1.5, the same test conducted at pH 2.5, the “Ohio State University In vitro Gastrointestinal” method (OSU IVG), the “Urban Soil Bioaccessible Lead Test”, the modified “Physiologically Based Extraction Test” and the “Waterfowl Physiologically Based Extraction Test.” All regressions had positive slopes. Based on criteria of slope and coefficient of determination, the RBALP pH 2.5 and OSU IVG tests performed very well. Speciation by X-ray absorption spectroscopy demonstrated that, on average, most of the Pb in the sampled soils was sorbed to minerals (30%), bound to organic matter 24%, or present as Pb sulfate 18%. Ad
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.
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.
Multicriteria approximation through decomposition
Burch, C.; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E.
1998-06-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of their technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. Their method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) the authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing; (2) they also show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
Multicriteria approximation through decomposition
Burch, C. |; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E. |
1997-12-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
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…
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…
Capacity of the circular plate condenser: analytical solutions for large gaps between the plates
NASA Astrophysics Data System (ADS)
Rao, T. V.
2005-11-01
A solution of Love's integral equation (Love E R 1949 Q. J. Mech. Appl. Math. 2 428), which forms the basis for the analysis of the electrostatic field due to two equal circular co-axial parallel conducting plates, is considered for the case when the ratio, τ, of distance of separation to radius of the plates is greater than 2. The kernel of the integral equation is expanded into an infinite series in odd powers of 1/τ and an approximate kernel accurate to {\\cal O}(\\tau^{-(2N+1)}) is deduced therefrom by terminating the series after an arbitrary but finite number of terms, N. The approximate kernel is rearranged into a degenerate form and the integral equation with this kernel is reduced to a system of N linear equations. An explicit analytical solution is obtained for N = 4 and the resulting analytical expression for the capacity of the circular plate condenser is shown to be accurate to {\\cal O}(\\tau^{-9}) . Analytical expressions of lower orders of accuracy with respect to 1/τ are deduced from the four-term (i.e., N = 4) solution and predictions (of capacity) from the expressions of different orders of accuracy (with respect to 1/τ) are compared with very accurate numerical solutions obtained by solving the linear system for large enough N. It is shown that the {\\cal O}(\\tau^{-9}) approximation predicts the capacity extremely well for any τ >= 2 and an {\\cal O}(\\tau^{-3}) approximation gives, for all practical purposes, results of adequate accuracy for τ >= 4. It is further shown that an approximate solution, applicable for the case of large distances of separation between the plates, due to Sneddon (Sneddon I N 1966 Mixed Boundary Value Problems in Potential Theory (Amsterdam: North-Holland) pp 230-46) is accurate to {\\cal O}(\\tau^{-6}) for τ >= 2.
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.
Sensitivity and Approximation of Coupled Fluid-Structure Equations by Virtual Control Method
Murea, Cornel Marius Vazquez, Carlos
2005-08-15
The formulation of a particular fluid-structure interaction as an optimal control problem is the departure point of this work. The control is the vertical component of the force acting on the interface and the observation is the vertical component of the velocity of the fluid on the interface. This approach permits us to solve the coupled fluid-structure problem by partitioned procedures. The analytic expression for the gradient of the cost function is obtained in order to devise accurate numerical methods for the minimization problem. Numerical results arising from blood flow in arteries are presented. To solve the optimal control problem numerically, we use a quasi-Newton method which employs the analytic gradient of the cost function and the approximation of the inverse Hessian is updated by the Broyden, Fletcher, Goldforb, Shano (BFGS) scheme. This algorithm is faster than fixed point with relaxation or block Newton methods.
Frozen Gaussian approximation for 3-D seismic wave propagation
NASA Astrophysics Data System (ADS)
Chai, Lihui; Tong, Ping; Yang, Xu
2017-01-01
We present a systematic introduction on applying frozen Gaussian approximation (FGA) to compute synthetic seismograms in 3-D earth models. In this method, seismic wavefield is decomposed into frozen (fixed-width) Gaussian functions, which propagate along ray paths. Rather than the coherent state solution to the wave equation, this method is rigorously derived by asymptotic expansion on phase plane, with analysis of its accuracy determined by the ratio of short wavelength over large domain size. Similar to other ray-based beam methods (e.g. Gaussian beam methods), one can use relatively small number of Gaussians to get accurate approximations of high-frequency wavefield. The algorithm is embarrassingly parallel, which can drastically speed up the computation with a multicore-processor computer station. We illustrate the accuracy and efficiency of the method by comparing it to the spectral element method for a 3-D seismic wave propagation in homogeneous media, where one has the analytical solution as a benchmark. As another proof of methodology, simulations of high-frequency seismic wave propagation in heterogeneous media are performed for 3-D waveguide model and smoothed Marmousi model, respectively. The second contribution of this paper is that, we incorporate the Snell's law into the FGA formulation, and asymptotically derive reflection, transmission and free surface conditions for FGA to compute high-frequency seismic wave propagation in high contrast media. We numerically test these conditions by computing traveltime kernels of different phases in the 3-D crust-over-mantle model.
Frozen Gaussian approximation for three-dimensional seismic wave propagation
NASA Astrophysics Data System (ADS)
Chai, Lihui; Tong, Ping; Yang, Xu
2016-09-01
We present a systematic introduction on applying frozen Gaussian approximation (FGA) to compute synthetic seismograms in three-dimensional earth models. In this method, seismic wavefield is decomposed into frozen (fixed-width) Gaussian functions, which propagate along ray paths. Rather than the coherent state solution to the wave equation, this method is rigorously derived by asymptotic expansion on phase plane, with analysis of its accuracy determined by the ratio of short wavelength over large domain size. Similar to other ray-based beam methods (e.g. Gaussian beam methods), one can use relatively small number of Gaussians to get accurate approximations of high-frequency wavefield. The algorithm is embarrassingly parallel, which can drastically speed up the computation with a multicore-processor computer station. We illustrate the accuracy and efficiency of the method by comparing it to the spectral element method for a three-dimensional (3D) seismic wave propagation in homogeneous media, where one has the analytical solution as a benchmark. As another proof of methodology, simulations of high-frequency seismic wave propagation in heterogeneous media are performed for 3D waveguide model and smoothed Marmousi model respectively. The second contribution of this paper is that, we incorporate the Snell's law into the FGA formulation, and asymptotically derive reflection, transmission and free surface conditions for FGA to compute high-frequency seismic wave propagation in high contrast media. We numerically test these conditions by computing traveltime kernels of different phases in the 3D crust-over-mantle model.
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.
NASA Technical Reports Server (NTRS)
Merrill, W. C.
1978-01-01
The Routh approximation technique for reducing the complexity of system models was applied in the frequency domain to a 16th order, state variable model of the F100 engine and to a 43d order, transfer function model of a launch vehicle boost pump pressure regulator. The results motivate extending the frequency domain formulation of the Routh method to the time domain in order to handle the state variable formulation directly. The time domain formulation was derived and a characterization that specifies all possible Routh similarity transformations was given. The characterization was computed by solving two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given. Additional computational problems are discussed, including an optimization procedure that can improve the approximation accuracy by taking advantage of the transformation characterization.
Topics in Metric Approximation
NASA Astrophysics Data System (ADS)
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
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.
Approximate Qualitative Temporal Reasoning
2001-01-01
i.e., their boundaries can be placed in such a way that they coincide with the cell boundaries of the appropriate partition of the time-line. (Think of...respect to some appropriate partition of the time-line. For example, I felt well on Saturday. When I measured my temperature I had a fever on Monday and on...Bittner / Approximate Qualitative Temporal Reasoning 49 [27] I. A. Goralwalla, Y. Leontiev , M. T. Özsu, D. Szafron, and C. Combi. Temporal granularity for
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.
Approximation methods in gravitational-radiation theory
NASA Astrophysics Data System (ADS)
Will, C. M.
1986-02-01
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. The author summarizes recent developments in two areas in which approximations are important: (1) the quadrupole approximation, 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 (2) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
Semiclassical approximations to quantum time correlation functions
NASA Astrophysics Data System (ADS)
Egorov, S. A.; Skinner, J. L.
1998-09-01
Over the last 40 years several ad hoc semiclassical approaches have been developed in order to obtain approximate quantum time correlation functions, using as input only the corresponding classical time correlation functions. The accuracy of these approaches has been tested for several exactly solvable gas-phase models. In this paper we test the accuracy of these approaches by comparing to an exactly solvable many-body condensed-phase model. We show that in the frequency domain the Egelstaff approach is the most accurate, especially at high frequencies, while in the time domain one of the other approaches is more accurate.
Factorized Diffusion Map Approximation.
Amizadeh, Saeed; Valizadegan, Hamed; Hauskrecht, Milos
2012-01-01
Diffusion maps are among the most powerful Machine Learning tools to analyze and work with complex high-dimensional datasets. Unfortunately, the estimation of these maps from a finite sample is known to suffer from the curse of dimensionality. Motivated by other machine learning models for which the existence of structure in the underlying distribution of data can reduce the complexity of estimation, we study and show how the factorization of the underlying distribution into independent subspaces can help us to estimate diffusion maps more accurately. Building upon this result, we propose and develop an algorithm that can automatically factorize a high dimensional data space in order to minimize the error of estimation of its diffusion map, even in the case when the underlying distribution is not decomposable. Experiments on both the synthetic and real-world datasets demonstrate improved estimation performance of our method over the standard diffusion-map framework.
Factorized Diffusion Map Approximation
Amizadeh, Saeed; Valizadegan, Hamed; Hauskrecht, Milos
2013-01-01
Diffusion maps are among the most powerful Machine Learning tools to analyze and work with complex high-dimensional datasets. Unfortunately, the estimation of these maps from a finite sample is known to suffer from the curse of dimensionality. Motivated by other machine learning models for which the existence of structure in the underlying distribution of data can reduce the complexity of estimation, we study and show how the factorization of the underlying distribution into independent subspaces can help us to estimate diffusion maps more accurately. Building upon this result, we propose and develop an algorithm that can automatically factorize a high dimensional data space in order to minimize the error of estimation of its diffusion map, even in the case when the underlying distribution is not decomposable. Experiments on both the synthetic and real-world datasets demonstrate improved estimation performance of our method over the standard diffusion-map framework. PMID:25309676
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
Saddlepoint approximations for small sample logistic regression problems.
Platt, R W
2000-02-15
Double saddlepoint approximations provide quick and accurate approximations to exact conditional tail probabilities in a variety of situations. This paper describes the use of these approximations in two logistic regression problems. An investigation of regression analysis of the log-odds ratio in a sequence or set of 2x2 tables via simulation studies shows that in practical settings the saddlepoint methods closely approximate exact conditional inference. The double saddlepoint approximation in the test for trend in a sequence of binomial random variates is also shown, via simulation studies, to be an effective approximation to exact conditional inference.
Approximation to the Probability Density at the Output of a Photmultiplier Tube
NASA Technical Reports Server (NTRS)
Stokey, R. J.; Lee, P. J.
1983-01-01
The probability density of the integrated output of a photomultiplier tube (PMT) is approximated by the Gaussian, Rayleigh, and Gamma probability densities. The accuracy of the approximations depends on the signal energy alpha: the Gamma distribution is accurate for all alpha, the Raleigh distribution is accurate for small alpha (approximate or less than 1 photon) and the Gaussian distribution is accurate for large alpha (approximate or greater than 10 photons).
An analytic Pade-motivated QCD coupling
Martinez, H. E.; Cvetic, G.
2010-08-04
We consider a modification of the Minimal Analytic (MA) coupling of Shirkov and Solovtsov. This modified MA (mMA) coupling reflects the desired analytic properties of the space-like observables. We show that an approximation by Dirac deltas of its discontinuity function {rho} is equivalent to a Pade(rational) approximation of the mMA coupling that keeps its analytic structure. We propose a modification to mMA that, as preliminary results indicate, could be an improvement in the evaluation of low-energy observables compared with other analytic couplings.
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.
Boluda-Ruiz, Rubén; García-Zambrana, Antonio; Castillo-Vázquez, Carmen; Castillo-Vázquez, Beatriz
2016-10-03
A novel accurate and useful approximation of the well-known Beckmann distribution is presented here, which is used to model generalized pointing errors in the context of free-space optical (FSO) communication systems. We derive an approximate closed-form probability density function (PDF) for the composite gamma-gamma (GG) atmospheric turbulence with the pointing error model using the proposed approximation of the Beckmann distribution, which is valid for most practical terrestrial FSO links. This approximation takes into account the effect of the beam width, different jitters for the elevation and the horizontal displacement and the simultaneous effect of nonzero boresight errors for each axis at the receiver plane. Additionally, the proposed approximation allows us to delimit two different FSO scenarios. The first of them is when atmospheric turbulence is the dominant effect in relation to generalized pointing errors, and the second one when generalized pointing error is the dominant effect in relation to atmospheric turbulence. The second FSO scenario has not been studied in-depth by the research community. Moreover, the accuracy of the method is measured both visually and quantitatively using curve-fitting metrics. Simulation results are further included to confirm the analytical results.
Application of approximate entropy on dynamic characteristics of epileptic absence seizure☆
Zhou, Yi; Huang, Ruimei; Chen, Ziyi; Chang, Xin; Chen, Jialong; Xie, Lingli
2012-01-01
Electroencephalogram signals are time-varying complex electrophysiological signals. Existing studies show that approximate entropy, which is a nonlinear dynamics index, is not an ideal method for electroencephalogram analysis. Clinical electroencephalogram measurements usually contain electrical interference signals, creating additional challenges in terms of maintaining robustness of the analytic methods. There is an urgent need for a novel method of nonlinear dynamical analysis of the electroencephalogram that can characterize seizure-related changes in cerebral dynamics. The aim of this paper was to study the fluctuations of approximate entropy in preictal, ictal, and postictal electroencephalogram signals from a patient with absence seizures, and to improve the algorithm used to calculate the approximate entropy. The approximate entropy algorithm, especially our modified version, could accurately describe the dynamical changes of the brain during absence seizures. We could also demonstrate that the complexity of the brain was greater in the normal state than in the ictal state. The fluctuations of the approximate entropy before epileptic seizures observed in this study can form a good basis for further study on the prediction of seizures with nonlinear dynamics. PMID:25745446
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.
Countably QC-Approximating Posets
Mao, Xuxin; Xu, Luoshan
2014-01-01
As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σc(L)op of all σ-Scott-closed subsets of L is weakly generalized countably approximating. PMID:25165730
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.
An improved 3D MoF method based on analytical partial derivatives
NASA Astrophysics Data System (ADS)
Chen, Xiang; Zhang, Xiong
2016-12-01
MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.
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)
Sago, Norichika; Fujita, Ryuichi; Nakano, Hiroyuki
2016-05-01
We revisit the accuracy of the post-Newtonian (PN) approximation and its region of validity for quasicircular orbits of a point particle in the Kerr spacetime, by using an analytically known highest post-Newtonian order gravitational energy flux and accurate numerical results in the black hole perturbation approach. It is found that regions of validity become larger for higher PN order results although there are several local maximums in regions of validity for relatively low-PN order results. This might imply that higher PN order calculations are also encouraged for comparable-mass binaries.
A New Analytic Alignment Method for a SINS.
Tan, Caiming; Zhu, Xinhua; Su, Yan; Wang, Yu; Wu, Zhiqiang; Gu, Dongbing
2015-11-04
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.
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.
Analytical Born Completion of Inelastic Differential Cross Sections
NASA Astrophysics Data System (ADS)
Boydstun, Olen E., Jr.; Morrison, Michael A.
1998-05-01
To calculate accurate differential cross sections (DCS) for electron scattering from atoms and molecules, one must include a huge number of partial waves in the expansion of the scattering amplitude in spherical harmonics.(D. G. Thompson, Proc. Roy. Soc. A294), 160 (1966). The required number far exceeds the number of low-order partial waves included in, for example, a coupled state solution of the Schrödinger equation. By extending the method developed Isaacs & Morrison for elastic electron-molecule scattering,(William A. Isaacs and Michael A. Morrison, Phys. Rev. A 53), 4215 (1996). we have used the Born approximation to analytically complete the infinite sum over partial waves for vibrationally inelastic scattering. This method allows accurate approximation of the infinity of high-order partial waves without the computational cost of evaluating these terms numerically. We shall demonstrate the importance of this approximation for vibrationally inelastic scattering of electrons from H2 and N_2, both near and well above the excitation thresholds.
Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.
Chao, Fa-An; Byrd, R Andrew
2017-02-04
The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C(α), H(α), etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain.
Application of geometric approximation to the CPMG experiment: Two- and three-site exchange
NASA Astrophysics Data System (ADS)
Chao, Fa-An; Byrd, R. Andrew
2017-04-01
The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C‧, Cα, Hα, etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain.
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.
A non-grey analytical model for irradiated atmospheres. II. Analytical vs. numerical solutions
NASA Astrophysics Data System (ADS)
Parmentier, Vivien; Guillot, Tristan; Fortney, Jonathan J.; Marley, Mark S.
2015-02-01
Context. The recent discovery and characterization of the diversity of the atmospheres of exoplanets and brown dwarfs calls for the development of fast and accurate analytical models. Aims: We wish to assess the goodness of the different approximations used to solve the radiative transfer problem in irradiated atmospheres analytically, and we aim to provide a useful tool for a fast computation of analytical temperature profiles that remains correct over a wide range of atmospheric characteristics. Methods: We quantify the accuracy of the analytical solution derived in paper I for an irradiated, non-grey atmosphere by comparing it to a state-of-the-art radiative transfer model. Then, using a grid of numerical models, we calibrate the different coefficients of our analytical model for irradiated solar-composition atmospheres of giant exoplanets and brown dwarfs. Results: We show that the so-called Eddington approximation used to solve the angular dependency of the radiation field leads to relative errors of up to ~5% on the temperature profile. For grey or semi-grey atmospheres (i.e., when the visible and thermal opacities, respectively, can be considered independent of wavelength), we show that the presence of a convective zone has a limited effect on the radiative atmosphere above it and leads to modifications of the radiative temperature profile of approximately ~2%. However, for realistic non-grey planetary atmospheres, the presence of a convective zone that extends to optical depths smaller than unity can lead to changes in the radiative temperature profile on the order of 20% or more. When the convective zone is located at deeper levels (such as for strongly irradiated hot Jupiters), its effect on the radiative atmosphere is again on the same order (~2%) as in the semi-grey case. We show that the temperature inversion induced by a strong absorber in the optical, such as TiO or VO is mainly due to non-grey thermal effects reducing the ability of the upper
Accurate Evaluation of Quantum Integrals
NASA Technical Reports Server (NTRS)
Galant, D. C.; Goorvitch, D.; Witteborn, Fred C. (Technical Monitor)
1995-01-01
Combining an appropriate finite difference method with Richardson's extrapolation results in a simple, highly accurate numerical method for solving a Schrodinger's equation. Important results are that error estimates are provided, and that one can extrapolate expectation values rather than the wavefunctions to obtain highly accurate expectation values. We discuss the eigenvalues, the error growth in repeated Richardson's extrapolation, and show that the expectation values calculated on a crude mesh can be extrapolated to obtain expectation values of high accuracy.
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.
Complex source beam: A tool to describe highly focused vector beams analytically
Orlov, S.; Peschel, U.
2010-12-15
The scalar-complex-source model is used to develop an accurate description of highly focused radially, azimuthally, linearly, and circularly polarized monochromatic vector beams. We investigate the power and full beam widths at half maximum of vigorous Maxwell equation solutions. The analytical expressions are employed to compare the vector complex source beams with the real beams produced by various high-numerical-aperture (NA) focusing systems. We find a parameter set for which the spatial extents of the analytical beams are the same as those of experimentally realized ones. We ensure the same shape of the considered beams by investigating an overlap of the complex source beams with high-NA beams. We demonstrate that the analytical expressions are good approximations for realistic highly focused beams.
Evaluation of higher order PMD effects using Jones matrix analytical models: a comparative study
NASA Astrophysics Data System (ADS)
Ferreira, M. F.
2006-04-01
A comparative study among the Jones matrix analytical models with high-order PMD is presented. The models that make use of an exponential expansion arrested up to second order or consider the dispersion vector as a Taylor series expansion do not give good results in the approximation of high-order PMD effects, because of the nonlimited behavior with respect to frequency of the modulus of their dispersion vectors. On the other hand, the analytical model which describes the dispersion vector as rotating on a circumference in the Stokes space is found to be the most accurate. Moreover, it can be used to obtain an analytical expression of the pulse broadening, which is often chosen as a quality-system parameter.
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.
Dkp Equation Under a Vector HULTHÉN-TYPE Potential:. AN Approximate Solution
NASA Astrophysics Data System (ADS)
Zarrinkamar, S.; Rajabi, A. A.; Rahimov, H.; Hassanabadi, H.
Approximate analytical solutions of Duffin-Kemmer-Petiau equation are obtained for a vector Hulthén potential. The solutions are reported for any J-state using an elegant approximation and methodology of supersymmetry quantum mechanics.
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.
Rapid Non-Linear Uncertainty Propagation via Analytical Techniques
NASA Astrophysics Data System (ADS)
Fujimoto, K.; Scheeres, D. J.
2012-09-01
Space situational awareness (SSA) is known to be a data starved problem compared to traditional estimation problems in that observation gaps per object may span over days if not weeks. Therefore, consistent characterization of the uncertainty associated with these objects including non-linear effects is crucial in maintaining an accurate catalog of objects in Earth orbit. Simultaneously, the motion of satellites in Earth orbit is well-modeled in that it is particularly amenable to having their solution and their uncertainty described through analytic or semi-analytic techniques. Even when stronger non-gravitational perturbations such as solar radiation pressure and atmospheric drag are encountered, these perturbations generally have deterministic components that are substantially larger than their time-varying stochastic components. Analytic techniques are powerful because time propagation is only a matter of changing the time parameter, allowing for rapid computational turnaround. These two ideas are combined in this paper: a method of analytically propagating non-linear orbit uncertainties is discussed. In particular, the uncertainty is expressed as an analytic probability density function (pdf) for all time. For a deterministic system model, such pdfs may be obtained if the initial pdf and the system states for all time are also given analytically. Even when closed-form solutions are not available, approximate solutions exist in the form of Edgeworth series for pdfs and Taylor series for the states. The coefficients of the latter expansion are referred to as state transition tensors (STTs), which are a generalization of state transition matrices to arbitrary order. Analytically expressed pdfs can be incorporated in many practical tasks in SSA. One can compute the mean and covariance of the uncertainty, for example, with the moments of the initial pdf as inputs. This process does not involve any sampling and its accuracy can be determined a priori. Analytical
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.
DALI: Derivative Approximation for LIkelihoods
NASA Astrophysics Data System (ADS)
Sellentin, Elena
2015-07-01
DALI (Derivative Approximation for LIkelihoods) is a fast approximation of non-Gaussian likelihoods. It extends the Fisher Matrix in a straightforward way and allows for a wider range of posterior shapes. The code is written in C/C++.
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.
Analytical Relativity of Black Holes
NASA Astrophysics Data System (ADS)
Damour, Thibault
The successful detection and analysis of gravitational wave (GW) signals from coalescing binary black holes necessitates the accurate prior knowledge of the form of the GW signals. This knowledge can be acquired through a synergy between Analytical Relativity (AR) methods and Numerical Relativity (NR) ones. We describe here the most promising AR formalism for describing the motion and radiation of coalescing binary black holes, the Effective One Body (EOB) method, and discuss its comparison with NR simulations.
Taylor Approximations and Definite Integrals
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2007-01-01
We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)
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
Analytical chemistry of nitric oxide.
Hetrick, Evan M; Schoenfisch, Mark H
2009-01-01
Nitric oxide (NO) is the focus of intense research primarily because of its wide-ranging biological and physiological actions. To understand its origin, activity, and regulation, accurate and precise measurement techniques are needed. 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 the picomolar-to-micromolar range in physiological milieus, 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 a focus on the underlying mechanism of each technique and on approaches that have been coupled with modern analytical measurement tools to create novel NO sensors.
An approximate classical unimolecular reaction rate theory
NASA Astrophysics Data System (ADS)
Zhao, Meishan; Rice, Stuart A.
1992-05-01
We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.
Approximate Solution to the Generalized Boussinesq Equation
NASA Astrophysics Data System (ADS)
Telyakovskiy, A. S.; Mortensen, J.
2010-12-01
The traditional Boussinesq equation describes motion of water in groundwater flows. It models unconfined groundwater flow under the Dupuit assumption that the equipotential lines are vertical, making the flowlines horizontal. The Boussinesq equation is a nonlinear diffusion equation with diffusivity depending linearly on water head. Here we analyze a generalization of the Boussinesq equation, when the diffusivity is a power law function of water head. For example polytropic gases moving through porous media obey this equation. Solving this equation usually requires numerical approximations, but for certain classes of initial and boundary conditions an approximate analytical solution can be constructed. This work focuses on the latter approach, using the scaling properties of the equation. We consider one-dimensional semi-infinite initially empty aquifer with boundary conditions at the inlet in case of cylindrical symmetry. Such situation represents the case of an injection well. Solutions would propagate with the finite speed. We construct an approximate scaling function, and we compare the approximate solution with the direct numerical solutions obtained by using the scaling properties of the equations.
ANALYTICAL GALAXY PROFILES FOR PHOTOMETRIC AND LENSING ANALYSIS
Spergel, David N.
2010-11-15
This article introduces a family of analytical functions of the form x {sup {nu}} K {sub {nu}}(x), where K {sub {nu}} is the incomplete Bessel function of the third kind. This family of functions can describe the density profile, projected and integrated light profiles, and the gravitational potentials of galaxies. For the proper choice of parameters, these functions accurately approximate Sersic functions over a range of indices and are good fits to galaxy light profiles. With an additional parameter corresponding to a galaxy core radius, these functions can fit galaxy like M87 over a factor of 10{sup 5} in radius. Unlike Sersic profiles, these functions have simple analytical two-dimensional and three-dimensional Fourier transforms, so they are easily convolved with spatially varying point-spread function (PSF) and are well suited for photometric and lensing analysis. We use these functions to estimate the effects of seeing on lensing measurements and show that high S/N measurements, even when the PSF is larger than the galaxy effective radius, should be able to recover accurate estimates of lensing distortions by weighting light in the outer isophotes that are less affected by seeing.
Cosmic shear covariance: the log-normal approximation
NASA Astrophysics Data System (ADS)
Hilbert, S.; Hartlap, J.; Schneider, P.
2011-12-01
Context. Accurate estimates of the errors on the cosmological parameters inferred from cosmic shear surveys require accurate estimates of the covariance of the cosmic shear correlation functions. Aims: We seek approximations to the cosmic shear covariance that are as easy to use as the common approximations based on normal (Gaussian) statistics, but yield more accurate covariance matrices and parameter errors. Methods: We derive expressions for the cosmic shear covariance under the assumption that the underlying convergence field follows log-normal statistics. We also derive a simplified version of this log-normal approximation by only retaining the most important terms beyond normal statistics. We use numerical simulations of weak lensing to study how well the normal, log-normal, and simplified log-normal approximations as well as empirical corrections to the normal approximation proposed in the literature reproduce shear covariances for cosmic shear surveys. We also investigate the resulting confidence regions for cosmological parameters inferred from such surveys. Results: We find that the normal approximation substantially underestimates the cosmic shear covariances and the inferred parameter confidence regions, in particular for surveys with small fields of view and large galaxy densities, but also for very wide surveys. In contrast, the log-normal approximation yields more realistic covariances and confidence regions, but also requires evaluating slightly more complicated expressions. However, the simplified log-normal approximation, although as simple as the normal approximation, yields confidence regions that are almost as accurate as those obtained from the log-normal approximation. The empirical corrections to the normal approximation do not yield more accurate covariances and confidence regions than the (simplified) log-normal approximation. Moreover, they fail to produce positive-semidefinite data covariance matrices in certain cases, rendering them
Approximation techniques of a selective ARQ protocol
NASA Astrophysics Data System (ADS)
Kim, B. G.
Approximations to the performance of selective automatic repeat request (ARQ) protocol with lengthy acknowledgement delays are presented. The discussion is limited to packet-switched communication systems in a single-hop environment such as found with satellite systems. It is noted that retransmission of errors after ARQ is a common situation. ARQ techniques, e.g., stop-and-wait and continuous, are outlined. A simplified queueing analysis of the selective ARQ protocol shows that exact solutions with long delays are not feasible. Two approximation models are formulated, based on known exact behavior of a system with short delays. The buffer size requirements at both ends of a communication channel are cited as significant factor for accurate analysis, and further examinations of buffer overflow and buffer lock-out probability and avoidance are recommended.
Understanding Business Analytics
2015-01-05
Business Analytics, Decision Analytics, Business Intelligence, Advanced Analytics, Data Science. . . to a certain degree, to label is to limit - if only... Business Analytics. 2004 2006 2008 2010 2012 2014 Figure 1: Google trending of daily searches for various analytic disciplines “The limits of my
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.
NASA Technical Reports Server (NTRS)
Cheatwood, F. M.; Dejarnette, F. R.
1992-01-01
An approximate axisymmetric method has been developed which can reliably calculate nonequilibrium fully viscous hypersonic flows over blunt-nosed bodies. By substituting Maslen's second-order pressure expression for the normal momentum equation, a simplified form of the viscous shock layer (VSL) equations is obtained. This approach can solve both the subsonic and supersonic regions of the shock layer without a starting solution for the shock shape. This procedure is significantly faster than the parabolized Navier-Stokes and VSL solvers and would be useful in a preliminary design environment. Solutions have been generated for air flows over several analytic body shapes. Surface heat transfer and pressure predictions are comparable to VSL results. Computed heating rates are in good agreement with experimental data. The present technique generates its own shock shape as part of its solution, and therefore could be used to provide more accurate initial shock shapes for higher-order procedures which require starting solutions.
NASA Technical Reports Server (NTRS)
Murphy, P. C.
1984-01-01
An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm.
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.
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.
Analytical solution for aquifer decontamination by pumping
NASA Astrophysics Data System (ADS)
Chen, Chia-Shyun; Woodside, Greg D.
1988-08-01
Rehabilitation of polluted aquifers is an important issue in groundwater study. The use of withdrawal wells to extract dissolved solutes from contaminated aquifers is a possible mechanical remedial technique. A mathematical model dealing with aquifer decontamination by pumping is developed. The pumping well with a constant flow rate is taken into account as a mathematical sink located at the center of the plume to be removed. This plume is assumed to have a circular geometry inside which the solute concentration is axial symmetric with respect to the well and is incorporated into the model as an initial condition that can be formulated in an analytic or a sectionally continuous function capable of representing a wide range of uniform or nonuniform profiles. It assumes advection and longitudinal mechanical dispersion to be the transport mechanisms on a radially converging groundwater flow field. The analytical solution detecting concentration variation inside the aquifer is determined in closed forms with the Green's function approach and the Laplace transform technique. Using the field data presented by Pickens and Grisak (1981), the analytical solution obtained very accurately reproduces the reported concentration history at the well during the withdrawal phase of the single-well injection-withdrawal tracer test. It is found that if the initial conditions are expressed in functions presenting noticeable concentration gradients at the plume boundary, adverse dispersion against the converging groundwater movement would cause spreading of solutes beyond the original extent of plume during pumping. If the initial conditions gradually decrease to zero concentration at the plume boundary where negligible concentration gradients exist, concentration distributions do not extend beyond the initial condition envelopes during the withdrawal process. Since the well is placed at the center of the plume where maximum concentration occurs, the analytical solution evaluated at
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.
1983-01-01
The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.
Combining global and local approximations
NASA Technical Reports Server (NTRS)
Haftka, Raphael T.
1991-01-01
A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.
Combining global and local approximations
Haftka, R.T. )
1991-09-01
A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model. 6 refs.
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.
Accurate and fast computation of transmission cross coefficients
NASA Astrophysics Data System (ADS)
Apostol, Štefan; Hurley, Paul; Ionescu, Radu-Cristian
2015-03-01
Precise and fast computation of aerial images are essential. Typical lithographic simulators employ a Köhler illumination system for which aerial imagery is obtained using a large number of Transmission Cross Coefficients (TCCs). These are generally computed by a slow numerical evaluation of a double integral. We review the general framework in which the 2D imagery is solved and then propose a fast and accurate method to obtain the TCCs. We acquire analytical solutions and thus avoid the complexity-accuracy trade-off encountered with numerical integration. Compared to other analytical integration methods, the one presented is faster, more general and more tractable.
Simple analytic expressions for correcting the factorizable formula for Compton
NASA Astrophysics Data System (ADS)
Lajohn, L. A.; Pratt, R. H.
2016-05-01
The factorizable form of the relativistic impulse approximation (RIA) expression for Compton scattering doubly differential cross sections (DDCS) becomes progressively less accurate as the binding energy of the ejected electron increases. This expression, which we call the RKJ approximation, makes it possible to obtain the Compton profile (CP) from measured DDCS. We have derived three simple analytic expressions, each which can be used to correct the RKJ error for the atomic K-shell CP obtained from DDCS for any atomic number Z. The expression which is the most general is valid over a broad range of energy ω and scattering angle θ, a second expression which is somewhat simpler is valid at very high ω but over most θ, and the third which is the simplest is valid at small θ over a broad range of ω. We demonstrate that such expressions can yield a CP accurate to within a 1% error over 99% of the electron momentum distribution range of the Uranium K-shell CP. Since the K-shell contribution dominates the extremes of the whole atom CP (this is where the error of RKJ can exceed an order of magnitude), this region can be of concern in assessing the bonding properties of molecules as well as semiconducting materials.
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
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.
NASA Astrophysics Data System (ADS)
Mamedov, Bahtiyar Akber; Copuroglu, Ebru
2017-02-01
By using the Löwdin-α function method, we have analytically calculated the two-center kinetic energy integrals over Slater type orbitals (STOs). The two-center kinetic energy integrals are presented in terms of the two-center overlap integrals. A new approach is applicable to accurate calculations of two-center kinetic energy integral over STOs for arbitrary values of scaling parameters and interatomic distances. Obtained results show that the proposed method is easy to apply to the real systems, and has better calculation CPU time with compared to the existing approximations.
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.
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.
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.
Ellipsoidal-mirror reflectometer accurately measures infrared reflectance of materials
NASA Technical Reports Server (NTRS)
Dunn, S. T.; Richmond, J. C.
1967-01-01
Reflectometer accurately measures the reflectance of specimens in the infrared beyond 2.5 microns and under geometric conditions approximating normal irradiation and hemispherical viewing. It includes an ellipsoidal mirror, a specially coated averaging sphere associated with a detector for minimizing spatial and angular sensitivity, and an incident flux chopper.
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.
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"…
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.
Simple analytic model for astrophysical S factors
Yakovlev, D. G.; Beard, M.; Gasques, L. R.; Wiescher, M.
2010-10-15
We propose a physically transparent analytic model of astrophysical S factors as a function of a center-of-mass energy E of colliding nuclei (below and above the Coulomb barrier) for nonresonant fusion reactions. For any given reaction, the S(E) model contains four parameters [two of which approximate the barrier potential, U(r)]. They are easily interpolated along many reactions involving isotopes of the same elements; they give accurate practical expressions for S(E) with only several input parameters for many reactions. The model reproduces the suppression of S(E) at low energies (of astrophysical importance) due to the shape of the low-r wing of U(r). The model can be used to reconstruct U(r) from computed or measured S(E). For illustration, we parametrize our recent calculations of S(E) (using the Sao Paulo potential and the barrier penetration formalism) for 946 reactions involving stable and unstable isotopes of C, O, Ne, and Mg (with nine parameters for all reactions involving many isotopes of the same elements, e.g., C+O). In addition, we analyze astrophysically important {sup 12}C+{sup 12}C reaction, compare theoretical models with experimental data, and discuss the problem of interpolating reliably known S(E) values to low energies (E < or approx. 2-3 MeV).
Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations
Obermayer, Klaus
2017-01-01
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons. PMID:28095421
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.
Strong washout approximation to resonant leptogenesis
NASA Astrophysics Data System (ADS)
Garbrecht, Björn; Gautier, Florian; Klaric, Juraj
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 ɛ=Xsin(2varphi)/(X2+sin2varphi), where X=8πΔ/(|Y1|2+|Y2|2), Δ=4(M1-M2)/(M1+M2), varphi=arg(Y2/Y1), and M1,2, Y1,2 are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y1,2|2gg 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.
Accurate Analysis of Array References
1992-09-22
This thesis addresses the problem of data dependence analysis, the base step in detecting loop level parallelism in scientific programs. Traditional...data dependence analysis research has concentrated on the simpler problem of affine memory disambiguation. Many algorithms have been developed that...can devise an experiment to test the effectiveness of affine memory disambiguation at approximating the full dependence problem. We discover that the
Condensed phase electron transfer beyond the Condon approximation
NASA Astrophysics Data System (ADS)
Mavros, Michael G.; Hait, Diptarka; Van Voorhis, Troy
2016-12-01
Condensed phase electron transfer problems are often simplified by making the Condon approximation: the approximation that the coupling connecting two charge-transfer diabatic states is a constant. Unfortunately, the Condon approximation does not predict the existence of conical intersections, which are ubiquitous in both gas-phase and condensed-phase photochemical dynamics. In this paper, we develop a formalism to treat condensed-phase dynamics beyond the Condon approximation. We show that even for an extremely simple test system, hexaaquairon(ii)/hexaaquairon(iii) self-exchange in water, the electronic coupling is expected to fluctuate rapidly and non-Condon effects must be considered to obtain quantitatively accurate ultrafast nonequilibrium dynamics. As diabatic couplings are expected to fluctuate substantially in many condensed-phase electron transfer systems, non-Condon effects may be essential to quantitatively capture accurate short-time dynamics.
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.
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.)
Approximating subtree distances between phylogenies.
Bonet, Maria Luisa; St John, Katherine; Mahindru, Ruchi; Amenta, Nina
2006-10-01
We give a 5-approximation algorithm to the rooted Subtree-Prune-and-Regraft (rSPR) distance between two phylogenies, which was recently shown to be NP-complete. This paper presents the first approximation result for this important tree distance. The algorithm follows a standard format for tree distances. The novel ideas are in the analysis. In the analysis, the cost of the algorithm uses a "cascading" scheme that accounts for possible wrong moves. This accounting is missing from previous analysis of tree distance approximation algorithms. Further, we show how all algorithms of this type can be implemented in linear time and give experimental results.
Discontinuous Galerkin method based on non-polynomial approximation spaces
Yuan Ling . E-mail: lyuan@dam.brown.edu; Shu Chiwang . E-mail: shu@dam.brown.edu
2006-10-10
In this paper, we develop discontinuous Galerkin (DG) methods based on non-polynomial approximation spaces for numerically solving time dependent hyperbolic and parabolic and steady state hyperbolic and elliptic partial differential equations (PDEs). The algorithm is based on approximation spaces consisting of non-polynomial elementary functions such as exponential functions, trigonometric functions, etc., with the objective of obtaining better approximations for specific types of PDEs and initial and boundary conditions. It is shown that L {sup 2} stability and error estimates can be obtained when the approximation space is suitably selected. It is also shown with numerical examples that a careful selection of the approximation space to fit individual PDE and initial and boundary conditions often provides more accurate results than the DG methods based on the polynomial approximation spaces of the same order of accuracy.
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…
An approximation method for fractional integro-differential equations
NASA Astrophysics Data System (ADS)
Emiroglu, Ibrahim
2015-12-01
In this work, an approximation method is proposed for fractional order linear Fredholm type integrodifferential equations with boundary conditions. The Sinc collocation method is applied to the examples and its efficiency and strength is also discussed by some special examples. The results of the proposed method are compared to the available analytic solutions.
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
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 ...
Dual approximations in optimal control
NASA Technical Reports Server (NTRS)
Hager, W. W.; Ianculescu, G. D.
1984-01-01
A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.
Zillich, Robert E.
2015-11-15
We construct an accurate imaginary time propagator for path integral Monte Carlo simulations for heterogeneous systems consisting of a mixture of atoms and molecules. We combine the pair density approximation, which is highly accurate but feasible only for the isotropic interactions between atoms, with the Takahashi–Imada approximation for general interactions. We present finite temperature simulations results for energy and structure of molecules–helium clusters X{sup 4}He{sub 20} (X=HCCH and LiH) which show a marked improvement over the Trotter approximation which has a 2nd-order time step bias. We show that the 4th-order corrections of the Takahashi–Imada approximation can also be applied perturbatively to a 2nd-order simulation.
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
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
NASA Astrophysics Data System (ADS)
Hinds, Arianne T.
2011-09-01
Spatial transformations whose kernels employ sinusoidal functions for the decorrelation of signals remain as fundamental components of image and video coding systems. Practical implementations are designed in fixed precision for which the most challenging task is to approximate these constants with values that are both efficient in terms of complexity and accurate with respect to their mathematical definitions. Scaled architectures, for example, as used in the implementations of the order-8 Discrete Cosine Transform and its corresponding inverse both specified in ISO/IEC 23002-2 (MPEG C Pt. 2), can be utilized to mitigate the complexity of these approximations. That is, the implementation of the transform can be designed such that it is completed in two stages: 1) the main transform matrix in which the sinusoidal constants are roughly approximated, and 2) a separate scaling stage to further refine the approximations. This paper describes a methodology termed the Common Factor Method, for finding fixed-point approximations of such irrational values suitable for use in scaled architectures. The order-16 Discrete Cosine Transform provides a framework in which to demonstrate the methodology, but the methodology itself can be employed to design fixed-point implementations of other linear transformations.
NASA Astrophysics Data System (ADS)
Chaikovskaya, L.; Dubovik, O.; Litvinov, P.; Grudo, J.; Lopatsin, A.; Chaikovsky, A.; Denisov, S.
2015-01-01
Inversion algorithms and program packages recently created for processing data of the ground-based radiometer spectral measurements along with lidar multi-wavelength measurements are extremely multiparametric. Therefore, it is very important to develop an efficient program module for computations of functions modeling measurements by a sun-radiometer in the inversion procedure. In this paper, we present the analytical version of such efficient algorithm and analytical code on C++ designed for performance of algorithm testing. The code computes multiple scattering of the Sun light in the atmosphere. Data output are the radiance and linear polarization parameters angular patterns at a preselected altitude. The atmosphere model with mixed aerosol and molecular scattering is given approximately as the homogeneous atmosphere model. The algorithm testing has been carried out by comparison of computed data with accurate data obtained on the base of the discrete-ordinate code. Errors of estimates of downward radiance above the Earth surface turned out to be within 10%-15%.. The analytical solution construction concept has taken from the scalar task of solar radiation transfer in the atmosphere where an approximate analytical solution was developed. Taking into account the fact that aerosol phase functions are highly forward elongated, the multi-component method of solving vector transfer equations and small-angle approximation have been used. Generalization of the scalar approach to the polarization parameters is described.
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.
Approximating Densities of States with Gaps
NASA Astrophysics Data System (ADS)
Haydock, Roger; Nex, C. M. M.
2011-03-01
Reconstructing a density of states or similar distribution from moments or continued fractions is an important problem in calculating the electronic and vibrational structure of defective or non-crystalline solids. For single bands a quadratic boundary condition introduced previously [Phys. Rev. B 74, 205121 (2006)] produces results which compare favorably with maximum entropy and even give analytic continuations of Green functions to the unphysical sheet. In this paper, the previous boundary condition is generalized to an energy-independent condition for densities with multiple bands separated by gaps. As an example it is applied to a chain of atoms with s, p, and d bands of different widths with different gaps between them. The results are compared with maximum entropy for different levels of approximation. Generalized hypergeometric functions associated with multiple bands satisfy the new boundary condition exactly. Supported by the Richmond F. Snyder Fund.
On numerically accurate finite element
NASA Technical Reports Server (NTRS)
Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.
1974-01-01
A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.
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.
Adiabatic approximation and fluctuations in exciton-polariton condensates
NASA Astrophysics Data System (ADS)
Bobrovska, Nataliya; Matuszewski, Michał
2015-07-01
We study the relation between the models commonly used to describe the dynamics of nonresonantly pumped exciton-polariton condensates, namely the ones described by the complex Ginzburg-Landau equation, and by the open-dissipative Gross-Pitaevskii equation including a separate equation for the reservoir density. In particular, we focus on the validity of the adiabatic approximation and small density fluctuations approximation that allow one to reduce the coupled condensate-reservoir dynamics to a single partial differential equation. We find that the adiabatic approximation consists of three independent analytical conditions that have to be fulfilled simultaneously. By investigating stochastic versions of the two corresponding models, we verify that the breakdown of these approximations can lead to discrepancies in correlation lengths and distributions of fluctuations. Additionally, we consider the phase diffusion and number fluctuations of a condensate in a box, and show that self-consistent description requires treatment beyond the typical Bogoliubov approximation.
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
Analytical and numerical modeling of non-collinear shear wave mixing at an imperfect interface
NASA Astrophysics Data System (ADS)
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 excess 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.
Comparison of distance measures in spatial analytical modeling for health service planning
2009-01-01
Background Several methodological approaches have been used to estimate distance in health service research. In this study, focusing on cardiac catheterization services, Euclidean, Manhattan, and the less widely known Minkowski distance metrics are used to estimate distances from patient residence to hospital. Distance metrics typically produce less accurate estimates than actual measurements, but each metric provides a single model of travel over a given network. Therefore, distance metrics, unlike actual measurements, can be directly used in spatial analytical modeling. Euclidean distance is most often used, but unlikely the most appropriate metric. Minkowski distance is a more promising method. Distances estimated with each metric are contrasted with road distance and travel time measurements, and an optimized Minkowski distance is implemented in spatial analytical modeling. Methods Road distance and travel time are calculated from the postal code of residence of each patient undergoing cardiac catheterization to the pertinent hospital. The Minkowski metric is optimized, to approximate travel time and road distance, respectively. Distance estimates and distance measurements are then compared using descriptive statistics and visual mapping methods. The optimized Minkowski metric is implemented, via the spatial weight matrix, in a spatial regression model identifying socio-economic factors significantly associated with cardiac catheterization. Results The Minkowski coefficient that best approximates road distance is 1.54; 1.31 best approximates travel time. The latter is also a good predictor of road distance, thus providing the best single model of travel from patient's residence to hospital. The Euclidean metric and the optimal Minkowski metric are alternatively implemented in the regression model, and the results compared. The Minkowski method produces more reliable results than the traditional Euclidean metric. Conclusion Road distance and travel time
Minimax rational approximation of the Fermi-Dirac distribution
Moussa, Jonathan E.
2016-10-27
Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ–1)) poles to achieve an error tolerance ϵ at temperature β–1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. Furthermore, this is particularly beneficial when Δ >> Δocc, such as in electronic structure calculations that use a large basis set.
Minimax rational approximation of the Fermi-Dirac distribution
Moussa, Jonathan E.
2016-10-27
Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ^{–1})) poles to achieve an error tolerance ϵ at temperature β^{–1} over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δ_{occ}, the occupied energy interval. Furthermore, this is particularly beneficial when Δ >> Δ_{occ}, such as in electronic structure calculations that use a large basis set.
Finite difference methods for approximating Heaviside functions
NASA Astrophysics Data System (ADS)
Towers, John D.
2009-05-01
We present a finite difference method for discretizing a Heaviside function H(u(x→)), where u is a level set function u:Rn ↦ R that is positive on a bounded region Ω⊂Rn. There are two variants of our algorithm, both of which are adapted from finite difference methods that we proposed for discretizing delta functions in [J.D. Towers, Two methods for discretizing a delta function supported on a level set, J. Comput. Phys. 220 (2007) 915-931; J.D. Towers, Discretizing delta functions via finite differences and gradient normalization, Preprint at http://www.miracosta.edu/home/jtowers/; J.D. Towers, A convergence rate theorem for finite difference approximations to delta functions, J. Comput. Phys. 227 (2008) 6591-6597]. We consider our approximate Heaviside functions as they are used to approximate integrals over Ω. We prove that our first approximate Heaviside function leads to second order accurate quadrature algorithms. Numerical experiments verify this second order accuracy. For our second algorithm, numerical experiments indicate at least third order accuracy if the integrand f and ∂Ω are sufficiently smooth. Numerical experiments also indicate that our approximations are effective when used to discretize certain singular source terms in partial differential equations. We mostly focus on smooth f and u. By this we mean that f is smooth in a neighborhood of Ω, u is smooth in a neighborhood of ∂Ω, and the level set u(x)=0 is a manifold of codimension one. However, our algorithms still give reasonable results if either f or u has jumps in its derivatives. Numerical experiments indicate approximately second order accuracy for both algorithms if the regularity of the data is reduced in this way, assuming that the level set u(x)=0 is a manifold. Numerical experiments indicate that dependence on the placement of Ω with respect to the grid is quite small for our algorithms. Specifically, a grid shift results in an O(hp) change in the computed solution
Finite difference approximation of hedging quantities in the Heston model
NASA Astrophysics Data System (ADS)
in't Hout, Karel
2012-09-01
This note concerns the hedging quantities Delta and Gamma in the Heston model for European-style financial options. A modification of the discretization technique from In 't Hout & Foulon (2010) is proposed, which enables a fast and accurate approximation of these important quantities. Numerical experiments are given that illustrate the performance.
Approximate and exact numerical integration of the gas dynamic equations
NASA Technical Reports Server (NTRS)
Lewis, T. S.; Sirovich, L.
1979-01-01
A highly accurate approximation and a rapidly convergent numerical procedure are developed for two dimensional steady supersonic flow over an airfoil. Examples are given for a symmetric airfoil over a range of Mach numbers. Several interesting features are found in the calculation of the tail shock and the flow behind the airfoil.
Temporal Learning Analytics for Adaptive Assessment
ERIC Educational Resources Information Center
Papamitsiou, Zacharoula; Economides, Anastasios A.
2014-01-01
Accurate and early predictions of student performance could significantly affect interventions during teaching and assessment, which gradually could lead to improved learning outcomes. In our research, we seek to identify and formalize temporal parameters as predictors of performance ("temporal learning analytics" or TLA) and examine…
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
Rational approximations for tomographic reconstructions
NASA Astrophysics Data System (ADS)
Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas
2013-06-01
We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp-Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image.
Gadgets, approximation, and linear programming
Trevisan, L.; Sudan, M.; Sorkin, G.B.; Williamson, D.P.
1996-12-31
We present a linear-programming based method for finding {open_quotes}gadgets{close_quotes}, i.e., combinatorial structures reducing constraints of one optimization problems to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method we present a number of new, computer-constructed gadgets for several different reductions. This method also answers a question posed by on how to prove the optimality of gadgets-we show how LP duality gives such proofs. The new gadgets improve hardness results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 60/61 and 44/45 respectively is N P-hard. We also use the gadgets to obtain an improved approximation algorithm for MAX 3SAT which guarantees an approximation ratio of .801. This improves upon the previous best bound of .7704.
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
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.
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
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.
Second Approximation to Conical Flows
1950-12-01
Public Release WRIGHT AIR DEVELOPMENT CENTER AF-WP-(B)-O-29 JUL 53 100 NOTICES ’When Government drawings, specifications, or other data are used V...so that the X, the approximation always depends on the ( "/)th, etc. Here the second approximation, i.e., the terms in C and 62, are computed and...the scheme shown in Fig. 1, the isentropic equations of motion are (cV-X2) +~X~C 6 +- 4= -x- 1 It is assumed that + Ux !E . $O’/ + (8) Introducing Eqs
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.
Exact and Approximate Sizes of Convex Datacubes
NASA Astrophysics Data System (ADS)
Nedjar, Sébastien
In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.
Allen, Jeffrey S
2003-05-15
An analytical solution to the capillary equation of Young and Laplace is derived that allows determination of the static contact angle based on the volume of a sessile drop and the wetted area of the substrate. This solution does not require numerical integration to determine the drop profile and accounts for surface deformation due to gravitational effects. Calculation of the static contact angle by this method is remarkably simple and accurate when the contact angle is less than 30 degrees. A natural scaling arises in the solution, which provides indication of when a drop is small enough so as to neglect gravitational influences on the surface shape which, for small contact angles, is generally less than 1 microl. The technique described has the simplicity of the spherical cap approximation but remains accurate for any size of sessile drop.
NASA Astrophysics Data System (ADS)
Pommé, S.
2009-06-01
An analytical model is presented to calculate the total detection efficiency of a well-type radiation detector for photons, electrons and positrons emitted from a radioactive source at an arbitrary position inside the well. The model is well suited to treat a typical set-up with a point source or cylindrical source and vial inside a NaI well detector, with or without lead shield surrounding it. It allows for fast absolute or relative total efficiency calibrations for a wide variety of geometrical configurations and also provides accurate input for the calculation of coincidence summing effects. Depending on its accuracy, it may even be applied in 4π-γ counting, a primary standardisation method for activity. Besides an accurate account of photon interactions, precautions are taken to simulate the special case of 511 keV annihilation quanta and to include realistic approximations for the range of (conversion) electrons and β -- and β +-particles.
Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen; Ringler, Todd
2012-01-04
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.
An Analytic Approach to Perturbative QCD
NASA Astrophysics Data System (ADS)
Magradze, B. A.
The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q2-plane is established. The corresponding analytic coupling is reconstructed via a dispersion relation. We also consider some other approximations to the QCD β-function, when the corresponding couplings are solved in terms of the Lambert function. The Landau gauge gluon propagator has been considered in the renormalization group invariant analytic approach (IAA). It is shown that there is a nonperturbative ambiguity in determination of the anomalous dimension function of the gluon field. Several analytic solutions for the propagator at the one-loop order are constructed. Properties of the obtained analytical solutions are discussed.
Quench in superconducting magnets. 2: Analytic solution
NASA Astrophysics Data System (ADS)
Shajii, A.; Freidberg, J. P.
1994-09-01
A set of analytic solutions for the Quencher model, as described in Part 1 (Shajii and Freidberg, 1994), is presented in this paper. These analytic solutions represent the first such results that remain valid for the long time scales of interest during a quench process. The assumptions and the resulting simplifications that lead to the analytic solutions are discussed, and the regimes of validity of the various approximations are specified. The predictions of the analytic results are shown to be in very good agreement with numerical as well as experimental results. Important analytic scaling relations are verified by such comparisons, and the consequences of some of these scalings on currently designed superconducting magnets are discussed.
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.
Recent advances in approximation concepts for optimum structural design
NASA Technical Reports Server (NTRS)
Barthelemy, Jean-Francois M.; Haftka, Raphael T.
1991-01-01
The basic approximation concepts used in structural optimization are reviewed. Some of the most recent developments in that area since the introduction of the concept in the mid-seventies are discussed. The paper distinguishes between local, medium-range, and global approximations; it covers functions approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It also appears that some new methodologies are emerging which could greatly benefit from the introduction of new computer architecture.
Approximation methods for combined thermal/structural design
NASA Technical Reports Server (NTRS)
Haftka, R. T.; Shore, C. P.
1979-01-01
Two approximation concepts for combined thermal/structural design are evaluated. The first concept is an approximate thermal analysis based on the first derivatives of structural temperatures with respect to design variables. Two commonly used first-order Taylor series expansions are examined. The direct and reciprocal expansions are special members of a general family of approximations, and for some conditions other members of that family of approximations are more accurate. Several examples are used to compare the accuracy of the different expansions. The second approximation concept is the use of critical time points for combined thermal and stress analyses of structures with transient loading conditions. Significant time savings are realized by identifying critical time points and performing the stress analysis for those points only. The design of an insulated panel which is exposed to transient heating conditions is discussed.
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.
An approximate projection method for incompressible flow
NASA Astrophysics Data System (ADS)
Stevens, David E.; Chan, Stevens T.; Gresho, Phil
2002-12-01
This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139-1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40-65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency.A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake.
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…
Lopes, J S; Arenas, M; Posada, D; Beaumont, M A
2014-03-01
The estimation of parameters in molecular evolution may be biased when some processes are not considered. For example, the estimation of selection at the molecular level using codon-substitution models can have an upward bias when recombination is ignored. Here we address the joint estimation of recombination, molecular adaptation and substitution rates from coding sequences using approximate Bayesian computation (ABC). We describe the implementation of a regression-based strategy for choosing subsets of summary statistics for coding data, and show that this approach can accurately infer recombination allowing for intracodon recombination breakpoints, molecular adaptation and codon substitution rates. We demonstrate that our ABC approach can outperform other analytical methods under a variety of evolutionary scenarios. We also show that although the choice of the codon-substitution model is important, our inferences are robust to a moderate degree of model misspecification. In addition, we demonstrate that our approach can accurately choose the evolutionary model that best fits the data, providing an alternative for when the use of full-likelihood methods is impracticable. Finally, we applied our ABC method to co-estimate recombination, substitution and molecular adaptation rates from 24 published human immunodeficiency virus 1 coding data sets.
Lopes, J S; Arenas, M; Posada, D; Beaumont, M A
2014-01-01
The estimation of parameters in molecular evolution may be biased when some processes are not considered. For example, the estimation of selection at the molecular level using codon-substitution models can have an upward bias when recombination is ignored. Here we address the joint estimation of recombination, molecular adaptation and substitution rates from coding sequences using approximate Bayesian computation (ABC). We describe the implementation of a regression-based strategy for choosing subsets of summary statistics for coding data, and show that this approach can accurately infer recombination allowing for intracodon recombination breakpoints, molecular adaptation and codon substitution rates. We demonstrate that our ABC approach can outperform other analytical methods under a variety of evolutionary scenarios. We also show that although the choice of the codon-substitution model is important, our inferences are robust to a moderate degree of model misspecification. In addition, we demonstrate that our approach can accurately choose the evolutionary model that best fits the data, providing an alternative for when the use of full-likelihood methods is impracticable. Finally, we applied our ABC method to co-estimate recombination, substitution and molecular adaptation rates from 24 published human immunodeficiency virus 1 coding data sets. PMID:24149652
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
2016-12-01
Students not familiar with chemistry tend to misinterpret analytical chemistry as some kind of the sorcery where analytical chemists working as modern wizards handle magical black boxes able to provide fascinating results. However, this approach is evidently improper and misleading. Therefore, the position of modern analytical chemistry among sciences and in the contemporary world is discussed. Its interdisciplinary character and the necessity of the collaboration between analytical chemists and other experts in order to effectively solve the actual problems of the human society and the environment are emphasized. The importance of the analytical method validation in order to obtain the accurate and precise results is highlighted. The invalid results are not only useless; they can often be even fatal (e.g., in clinical laboratories). The curriculum of analytical chemistry at schools and universities is discussed. It is referred to be much broader than traditional equilibrium chemistry coupled with a simple description of individual analytical methods. Actually, the schooling of analytical chemistry should closely connect theory and practice.
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…
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.
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
2016-05-07
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
Accurate method for computing correlated color temperature.
Li, Changjun; Cui, Guihua; Melgosa, Manuel; Ruan, Xiukai; Zhang, Yaoju; Ma, Long; Xiao, Kaida; Luo, M Ronnier
2016-06-27
For the correlated color temperature (CCT) of a light source to be estimated, a nonlinear optimization problem must be solved. In all previous methods available to compute CCT, the objective function has only been approximated, and their predictions have achieved limited accuracy. For example, different unacceptable CCT values have been predicted for light sources located on the same isotemperature line. In this paper, we propose to compute CCT using the Newton method, which requires the first and second derivatives of the objective function. Following the current recommendation by the International Commission on Illumination (CIE) for the computation of tristimulus values (summations at 1 nm steps from 360 nm to 830 nm), the objective function and its first and second derivatives are explicitly given and used in our computations. Comprehensive tests demonstrate that the proposed method, together with an initial estimation of CCT using Robertson's method [J. Opt. Soc. Am. 58, 1528-1535 (1968)], gives highly accurate predictions below 0.0012 K for light sources with CCTs ranging from 500 K to 10^{6} K.
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.
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)
Stable computations with flat radial basis functions using vector-valued rational approximations
NASA Astrophysics Data System (ADS)
Wright, Grady B.; Fornberg, Bengt
2017-02-01
One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are 'flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vector-valued analytic functions with the property that all components of the vector share the same singularities. This new algorithm (RBF-RA) is more accurate, robust, and easier to implement than the Contour-Padé method, which is similarly based on vector-valued rational approximation. In contrast to the stable RBF-QR and RBF-GA algorithms, which are based on finding a better conditioned base in the same RBF-space, the new algorithm can be used with any type of smooth radial kernel, and it is also applicable to a wider range of tasks (including calculating Hermite type implicit RBF-FD stencils). We present a series of numerical experiments demonstrating the effectiveness of this new method for computing RBF interpolants in the flat regime. We also demonstrate the flexibility of the method by using it to compute implicit RBF-FD formulas in the flat regime and then using these for solving Poisson's equation in a 3-D spherical shell.
Bauer, Jaroslaw H.
2011-03-15
In the recent work of Vanne and Saenz [Phys. Rev. A 75, 063403 (2007)] the quasistatic limit of the velocity gauge strong-field approximation describing the ionization rate of atomic or molecular systems exposed to linearly polarized laser fields was derived. It was shown that in the low-frequency limit the ionization rate is proportional to the laser frequency {omega} (for a constant intensity of the laser field). In the present work I show that for circularly polarized laser fields the ionization rate is proportional to {omega}{sup 4} for H(1s) and H(2s) atoms, to {omega}{sup 6} for H(2p{sub x}) and H(2p{sub y}) atoms, and to {omega}{sup 8} for H(2p{sub z}) atoms. The analytical expressions for asymptotic ionization rates (which become nearly accurate in the limit {omega}{yields}0) contain no summations over multiphoton contributions. For very low laser frequencies (optical or infrared) these expressions usually remain with an order-of-magnitude agreement with the velocity gauge strong-field approximation.
A simple analytical description of the non-stationary dynamics in Ising spin systems
NASA Astrophysics Data System (ADS)
Domínguez Vázquez, Eduardo; Del Ferraro, Gino; Ricci-Tersenghi, Federico
2017-03-01
The analytical description of the dynamics in models with discrete variables (e.g. Ising spins) is a notoriously difficult problem, which can only be tackled under some approximation. Recently a novel variational approach to solve the stationary dynamical regime has been introduced by Pelizzola (2013 Eur. Phys. J. B 86 120), where simple closed equations are derived under mean-field approximations based on the cluster variational method. Here we propose to use the same approximation based on the cluster variational method also for the non-stationary regime, which has not been considered up to now within this framework. We check the validity of this approximation in describing the non-stationary dynamical regime of several Ising models defined on Erdős–Rényi random graphs: we study ferromagnetic models with symmetric and partially asymmetric couplings, models with random fields and also spin glass models. A comparison with the actual Glauber dynamics, solved numerically, shows that one of the two studied approximations (the so-called ‘diamond’ approximation) provides very accurate results in all the systems studied. Only for the spin glass models do we find some small discrepancies in the very low temperature phase, probably due to the existence of a large number of metastable states. Given the simplicity of the equations to be solved, we believe the diamond approximation should be considered as the ‘minimal standard’ in the description of the non-stationary regime of Ising-like models: any new method pretending to provide a better approximate description to the dynamics of Ising-like models should perform at least as good as the diamond approximation.
Accurate orbit propagation with planetary close encounters
NASA Astrophysics Data System (ADS)
Baù, Giulio; Milani Comparetti, Andrea; Guerra, Francesca
2015-08-01
We tackle the problem of accurately propagating the motion of those small bodies that undergo close approaches with a planet. The literature is lacking on this topic and the reliability of the numerical results is not sufficiently discussed. The high-frequency components of the perturbation generated by a close encounter makes the propagation particularly challenging both from the point of view of the dynamical stability of the formulation and the numerical stability of the integrator. In our approach a fixed step-size and order multistep integrator is combined with a regularized formulation of the perturbed two-body problem. When the propagated object enters the region of influence of a celestial body, the latter becomes the new primary body of attraction. Moreover, the formulation and the step-size will also be changed if necessary. We present: 1) the restarter procedure applied to the multistep integrator whenever the primary body is changed; 2) new analytical formulae for setting the step-size (given the order of the multistep, formulation and initial osculating orbit) in order to control the accumulation of the local truncation error and guarantee the numerical stability during the propagation; 3) a new definition of the region of influence in the phase space. We test the propagator with some real asteroids subject to the gravitational attraction of the planets, the Yarkovsky and relativistic perturbations. Our goal is to show that the proposed approach improves the performance of both the propagator implemented in the OrbFit software package (which is currently used by the NEODyS service) and of the propagator represented by a variable step-size and order multistep method combined with Cowell's formulation (i.e. direct integration of position and velocity in either the physical or a fictitious time).
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.
Ab initio dynamical vertex approximation
NASA Astrophysics Data System (ADS)
Galler, Anna; Thunström, Patrik; Gunacker, Patrik; Tomczak, Jan M.; Held, Karsten
2017-03-01
Diagrammatic extensions of dynamical mean-field theory (DMFT) such as the dynamical vertex approximation (DΓ A) allow us to include nonlocal correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an Ab initio DΓ A approach (AbinitioDΓ A ) for electronic structure calculations of materials. The starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare nonlocal Coulomb interaction and all local vertex corrections. From this, we calculate the full nonlocal vertex and the nonlocal self-energy through the Bethe-Salpeter equation. The AbinitioDΓ A approach naturally generates all local DMFT correlations and all nonlocal G W contributions, but also further nonlocal correlations beyond: mixed terms of the former two and nonlocal spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO3.
Potential of the approximation method
Amano, K.; Maruoka, A.
1996-12-31
Developing some techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph with m vertices: For 5 {le} s {le} m/4, a monotone circuit computing CLIQUE(m, s) contains at least (1/2)1.8{sup min}({radical}s-1/2,m/(4s)) gates: If a non-monotone circuit computes CLIQUE using a {open_quotes}small{close_quotes} amount of negation, then the circuit contains an exponential number of gates. The former is proved very simply using so called bottleneck counting argument within the framework of approximation, whereas the latter is verified introducing a notion of restricting negation and generalizing the sunflower contraction.
Nonlinear Filtering and Approximation Techniques
1991-09-01
Shwartz), Academic Press (1991). [191 M.Cl. ROUTBAUD, Fiting lindairc par morceaux avec petit bruit d’obserration, These. Universit6 de Provence ( 1990...Kernel System (GKS), Academic Press (1983). 181 H.J. KUSHNER, Probability methods for approximations in stochastic control and for elliptic equations... Academic Press (1977). [9] F. LE GLAND, Time discretization of nonlinear filtering equations, in: 28th. IEEE CDC, Tampa, pp. 2601-2606. IEEE Press (1989
Reliable Function Approximation and Estimation
2016-08-16
Journal on Mathematical Analysis 47 (6), 2015. 4606-4629. (P3) The Sample Complexity of Weighted Sparse Approximation. B. Bah and R. Ward. IEEE...solving systems of quadratic equations. S. Sanghavi, C. White, and R. Ward. Results in Mathematics , 2016. (O5) Relax, no need to round: Integrality of...Theoretical Computer Science. (O6) A unified framework for linear dimensionality reduction in L1. F Krahmer and R Ward. Results in Mathematics , 2014. 1-23
Approximate Counting of Graphical Realizations.
Erdős, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos
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.
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
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.
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.
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
Improved measurement of the rotor temperature in analytical ultracentrifugation.
Zhao, Huaying; Balbo, Andrea; Metger, Howard; Clary, Robert; Ghirlando, Rodolfo; Schuck, Peter
2014-04-15
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 showed that external calibration of the scan time, radial magnification, and temperature is critically important for accurate measurements (Anal. Biochem. 440 (2013) 81-95). To achieve accurate temperature calibration, we introduced the use of an autonomous miniature temperature logging integrated circuit (Maxim Thermochron iButton) that can be inserted into an ultracentrifugation cell assembly and spun at low rotor speeds. In the current 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 allowing for a direct temperature measurement of the spinning rotor during high-speed sedimentation velocity experiments up to 60,000rpm. We demonstrated the sensitivity of this approach by monitoring the adiabatic cooling due to rotor stretching during rotor acceleration and the reverse process on rotor deceleration. Based on this, we developed a procedure to approximate isothermal rotor acceleration for better temperature control.
NASA Astrophysics Data System (ADS)
Gessese, A.; Heining, C.; Sellier, M.; Mc Nish, R.; Rack, W.
2015-01-01
Glaciers are an important component of the climate system that respond sensitively to climate change. Small glaciers respond more quickly to changing weather patterns compared to large polar ice sheets and ice caps that make them ideal to study climate variability. This study relates to the numerical reconstruction of the glacier bed in order to generate basal boundary data for ice flow models. Bedrock elevation is a paramount input parameter in glacier flow modeling to accurately capture its flow dynamics but is difficult to measure. We present an easy to implement direct numerical and analytical methodology to infer the bedrock geometry under glacial ice from the knowledge of the free surface elevation or the free surface velocity in one space dimension. The numerical and analytical methods are both based on the shallow ice approximation and require the time series of the surface mass balance distribution. Moreover, the analytical method requires the knowledge of the glacier thickness at one arbitrary location. Numerical benchmark test cases are used to verify the suitability and applicability of the algorithms, and a sensitivity analysis demonstrates the robustness of the method.
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.
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
NASA Astrophysics Data System (ADS)
Comfort, R. H.; Baugher, C. R.; Chappell, C. R.
1982-07-01
A procedure for analyzing low-energy (less than approximately 100 eV) ion data from the plasma composition experiment on ISEE 1 is set forth. The method is based on a derived analytic expression for particle flux to a limited aperture retarding potential analyzer (RPA) in the thin sheath approximation, which makes allowance for some effects of a charged spacecraft on plasma particle trajectories. Calculations using simulated data are employed in testing the efficacy and accuracy of the technique. On the basis of an analysis of these calculation results and the mathematical model, the method is seen as being able to provide accurate ion temperatures from all good plasmaspheric RPA data. It is noted that corresponding densities and spacecraft potentials should be accurate when spacecraft potentials are negative but that they are subject to error for positive spacecraft potentials, particularly when ion Mach numbers are much less than 1. An analysis of data from a representative ISEE 1 pass produces a plasmasphere temperature profile that is consistent in overall structure with previous observations.
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.
Plasmon Pole Approximations within a GW Sternheimer implementation
NASA Astrophysics Data System (ADS)
Gosselin, Vincent; Cote, Michel
We use an implementation of the GW approximation that exploits a Sternheimer equation and a Lanczos procedure to circumvent the resource intensive sum over all bands and inversion of the dielectric matrix. I will present further improvement of the method that uses Plasmon Pole approximations to evaluate the integral over all frequencies analytically. A comparison study between the von Linden-Horsh and Engel-Farid approaches for energy levels of various molecules along with benchmarking of the computational ressources needed by the method will be discussed.
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.
Analytical phase diagrams for colloids and non-adsorbing polymer.
Fleer, Gerard J; Tuinier, Remco
2008-11-04
We review the free-volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett. 20 (1992) 559] for the phase behavior of colloids in the presence of non-adsorbing polymer and we extend this theory in several aspects: (i) We take the solvent into account as a separate component and show that the natural thermodynamic parameter for the polymer properties is the insertion work Pi(v), where Pi is the osmotic pressure of the (external) polymer solution and v the volume of a colloid particle. (ii) Curvature effects are included along the lines of Aarts et al. [J. Phys.: Condens. Matt. 14 (2002) 7551] but we find accurate simple power laws which simplify the mathematical procedure considerably. (iii) We find analytical forms for the first, second, and third derivatives of the grand potential, needed for the calculation of the colloid chemical potential, the pressure, gas-liquid critical points and the critical endpoint (cep), where the (stable) critical line ends and then coincides with the triple point. This cep determines the boundary condition for a stable liquid. We first apply these modifications to the so-called colloid limit, where the size ratio q(R)=R/a between the radius of gyration R of the polymer and the particle radius a is small. In this limit the binodal polymer concentrations are below overlap: the depletion thickness delta is nearly equal to R, and Pi can be approximated by the ideal (van't Hoff) law Pi=Pi(0)=phi/N, where phi is the polymer volume fraction and N the number of segments per chain. The results are close to those of the original Lekkerkerker theory. However, our analysis enables very simple analytical expressions for the polymer and colloid concentrations in the critical and triple points and along the binodals as a function of q(R). Also the position of the cep is found analytically. In order to make the model applicable to higher size ratio's q(R) (including the so-called protein limit where q(R)>1) further extensions are needed. We
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, 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...
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, 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, 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...
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.
NASA Astrophysics Data System (ADS)
Kong, Dali; Zhang, Keke; Schubert, Gerald
2017-02-01
It is expected that the Juno spacecraft will provide an accurate spectrum of the Jovian zonal gravitational coefficients that would be affected by both the deep zonal flow, if it exists, and the basic rotational distortion. We derive the first analytical solution, under the spheroidal-shape approximation, for the density anomaly induced by an internal zonal flow in rapidly rotating Jupiter-like planets. We compare the density anomaly of the analytical solution to that obtained from a fully numerical solution based on a three-dimensional finite element method; the two show excellent agreement. We apply the analytical solution to a rapidly rotating Jupiter-like planet and show that there exists a close relationship between the spatial structure of the zonal flow and the spectrum of zonal gravitational coefficients. We check the accuracy of the spheroidal-shape approximation by computing both the spheroidal and non-spheroidal solutions with exactly the same physical parameters. We also discuss implications of the new analytical solution for interpreting the future high-precision gravitational measurements of the Juno spacecraft.
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…
Fermion tunneling beyond semiclassical approximation
Majhi, Bibhas Ranjan
2009-02-15
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in R. Banerjee and B. R. Majhi, J. High Energy Phys. 06 (2008) 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.
Improved non-approximability results
Bellare, M.; Sudan, M.
1994-12-31
We indicate strong non-approximability factors for central problems: N{sup 1/4} for Max Clique; N{sup 1/10} for Chromatic Number; and 66/65 for Max 3SAT. Underlying the Max Clique result is a proof system in which the verifier examines only three {open_quotes}free bits{close_quotes} to attain an error of 1/2. Underlying the Chromatic Number result is a reduction from Max Clique which is more efficient than previous ones.
Approximate transferability in conjugated polyalkenes
NASA Astrophysics Data System (ADS)
Eskandari, Keiamars; Mandado, Marcos; Mosquera, Ricardo A.
2007-03-01
QTAIM computed atomic and bond properties, as well as delocalization indices (obtained from electron densities computed at HF, MP2 and B3LYP levels) of several linear and branched conjugated polyalkenes and O- and N-containing conjugated polyenes have been employed to assess approximate transferable CH groups. The values of these properties indicate the effects of the functional group extend to four CH groups, whereas those of the terminal carbon affect up to three carbons. Ternary carbons also modify significantly the properties of atoms in α, β and γ.
A stochastic approximation method for assigning values to calibrators.
Schlain, B
1998-04-01
A new procedure is provided for transferring analyte concentration values from a reference material to production calibrators. This method is robust to calibration curve-fitting errors and can be accomplished using only one instrument and one set of reagents. An easily implemented stochastic approximation algorithm iteratively finds the appropriate analyte level of a standard prepared from a reference material that will yield the same average signal response as the new production calibrator. Alternatively, a production bulk calibrator material can be iteratively adjusted to give the same average signal response as some prespecified, fixed reference standard. In either case, the outputted value assignment of the production calibrator is the analyte concentration of the reference standard in the final iteration of the algorithm. Sample sizes are statistically determined as functions of known within-run signal response precisions and user-specified accuracy tolerances.
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.
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.
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.
Analytical solutions of moisture flow equations and their numerical evaluation
Gibbs, A.G.
1981-04-01
The role of analytical solutions of idealized moisture flow problems is discussed. Some different formulations of the moisture flow problem are reviewed. A number of different analytical solutions are summarized, including the case of idealized coupled moisture and heat flow. The evaluation of special functions which commonly arise in analytical solutions is discussed, including some pitfalls in the evaluation of expressions involving combinations of special functions. Finally, perturbation theory methods are summarized which can be used to obtain good approximate analytical solutions to problems which are too complicated to solve exactly, but which are close to an analytically solvable problem.
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.
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.
Laguerre approximation of random foams
NASA Astrophysics Data System (ADS)
Liebscher, André
2015-09-01
Stochastic models for the microstructure of foams are valuable tools to study the relations between microstructure characteristics and macroscopic properties. Owing to the physical laws behind the formation of foams, Laguerre tessellations have turned out to be suitable models for foams. Laguerre tessellations are weighted generalizations of Voronoi tessellations, where polyhedral cells are formed through the interaction of weighted generator points. While both share the same topology, the cell curvature of foams allows only an approximation by Laguerre tessellations. This makes the model fitting a challenging task, especially when the preservation of the local topology is required. In this work, we propose an inversion-based approach to fit a Laguerre tessellation model to a foam. The idea is to find a set of generator points whose tessellation best fits the foam's cell system. For this purpose, we transform the model fitting into a minimization problem that can be solved by gradient descent-based optimization. The proposed algorithm restores the generators of a tessellation if it is known to be Laguerre. If, as in the case of foams, no exact solution is possible, an approximative solution is obtained that maintains the local topology.
Analytical Chemistry in Russia.
Zolotov, Yuri
2016-09-06
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)
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.
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.
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES
Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.; Vassilevski, Panayot S.
2016-01-22
The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
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.
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.
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.
Second-order Born approximation for the scattering phase shifts: Application to the Friedel sum rule
NASA Astrophysics Data System (ADS)
Nersisyan, Hrachya B.; Fernández-Varea, José M.
2013-09-01
Screening effects are important to understand various aspects of ion-solid interactions and, in particular, play a crucial role in the stopping of ions in solids. In this paper the phase shifts and scattering amplitudes for the quantum-mechanical elastic scattering within up to the second-order Born (B2) approximation are revisited for an arbitrary spherically-symmetric electron-ion interaction potential. The B2 phase shifts and scattering amplitudes are then used to derive the Friedel sum rule (FSR) involving the second-order Born corrections. This results in a simple equation for the B2 perturbative screening parameter of an impurity ion immersed in a fully degenerate electron gas which, as expected, turns out to depend on the ion atomic number Z1 unlike the first-order Born (B1) screening parameter reported earlier by some authors. Furthermore, our analytical results for the Yukawa, hydrogenic, Hulthén, and Mensing potentials are compared, for both positive and negative ions and a wide range of one-electron radii, to the exact screening parameters calculated self-consistently by imposing the FSR requirement. It is shown that the B2 screening parameters agree excellently with the exact values at large and moderate densities of the degenerate electron gas, while at lower densities they progressively deviate from the exact numerical solutions but are nevertheless more accurate than the prediction of the B1 approximation. In addition, a simple Padé approximant to the Born series has been developed that improves the performance of the perturbative FSR for any negative ion as well as for Z1=+1.
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.
Machine-learned approximations to Density Functional Theory Hamiltonians
NASA Astrophysics Data System (ADS)
Hegde, Ganesh; Bowen, R. Chris
2017-02-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
Machine-learned approximations to Density Functional Theory Hamiltonians.
Hegde, Ganesh; Bowen, R Chris
2017-02-15
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
Machine-learned approximations to Density Functional Theory Hamiltonians
Hegde, Ganesh; Bowen, R. Chris
2017-01-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. PMID:28198471
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…
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.
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…
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)
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)
Evaluating the Accuracy of Hessian Approximations for Direct Dynamics Simulations.
Zhuang, Yu; Siebert, Matthew R; Hase, William L; Kay, Kenneth G; Ceotto, Michele
2013-01-08
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.
High accurate interpolation of NURBS tool path for CNC machine tools
NASA Astrophysics Data System (ADS)
Liu, Qiang; Liu, Huan; Yuan, Songmei
2016-09-01
Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level without sacrificing the computing efficiency at present. In order to solve this problem, a high accurate interpolation method for NURBS tool path is proposed. The proposed method can efficiently reduce the feedrate fluctuation by forming a quartic equation with respect to the curve parameter increment, which can be efficiently solved by analytic methods in real-time. Theoretically, the proposed method can totally eliminate the feedrate fluctuation for any 2nd degree NURBS curves and can interpolate 3rd degree NURBS curves with minimal feedrate fluctuation. Moreover, a smooth feedrate planning algorithm is also proposed to generate smooth tool motion with considering multiple constraints and scheduling errors by an efficient planning strategy. Experiments are conducted to verify the feasibility and applicability of the proposed method. This research presents a novel NURBS interpolation method with not only high accuracy but also satisfying computing efficiency.
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
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.
When Density Functional Approximations Meet Iron Oxides.
Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong
2016-10-11
Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe2O3, Fe3O4, and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.
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.
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.
New literal approximations for the longitudinal dynamic characteristics of flexible flight vehicles
NASA Technical Reports Server (NTRS)
Livneh, Rafael; Schmidt, David K.
1992-01-01
The goal of the literal approximation method is to obtain simple literal (analytical) approximations for key dynamic characteristics of flexible flight vehicles. A basic question regarding the method is its usefulness as an additional design tool for existing design and simulation procedures. Two aspects of this question are: (1) ease of derivation and use of the literal approximations, and (2) the suitability of one set of literal approximations to describe the dynamics of a large set of significantly different vehicles. These issues are addressed by incorporating symbolic manipulation software into the literal approximation method for the analysis of a fifth order model of the longitudinal dynamics of a flexible flight vehicle. The automated literal approximation generated in this fashion reduces the manual derivation time by an approximate factor of four. A single set of literal approximations is shown to provide adequate approximations for the dynamics of significantly different flight vehicles configurations, such as an aircraft, a missile, and a hypersonic vehicle.
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) .
Femtolensing: Beyond the semiclassical approximation
NASA Technical Reports Server (NTRS)
Ulmer, Andrew; Goodman, Jeremy
1995-01-01
Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.