... It should therefore be possible to approximate the solution accurately using the Rayleigh-Ritz Galerkin method with a piecewise polynomial ...
DTIC Science & Technology
... obtained. This method is almost as accurate as the simpli- fied set of equations above, except for time-of-flight calculations. It ...
... obtained. This method is almost as accurate as the simplified set of equations above, except for time-of-flight calculations. It ...
The method is based upon molecular line parameters and makes use of a far wing scaling approximation
NASA Technical Reports Server (NTRS)
A method for accurately approximating T-matrix elements in atom-diatom collisions is presented. Calculations are given for hydrogen helium collisions. (AIP)
Energy Citations Database
The construction and the analysis of nonoscillatory shock capturing methods for the approximation of
Some new methods for performing numerical quadrature of an integrable function over a finite interval are described. Each method provides a sequence of approximations of increasing order to the value of the integral. Each approximation makes use of all pr...
National Technical Information Service (NTIS)
A simple yet highly accurate method for approximately calculating spectrum-averaged beta energies and beta spectra for radioactive nuclei is presented. This method should prove useful for users who wish to obtain accurate answers without complicated calcu...
A simple and sufficiently accurate method is proposed for estimating the parameters of shockwave loading of porous materials under conditions of complete compaction of the material to the density of a monolith.
... CsI has a k- edge at approximately 33 and 36 ... for digital mammography, where x-ray beams as ... be accurate, k-fluorescence re-absorption needs to ...
Author(s): Imaoka, Atsushi; Kihara, Masami Abstract: An accurate time transfer method is ... Complex angular momentum approximation to hard-core scattering ...
NASA Website
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 ...
A method for accurate measurement of complex parts that contain no reference points is described. The technique is applied to the production of accurate castings, to their machining, and to their installation. Accuracies of )approximately) 2 mil can be achieved over distances of 7 ft. 3 figs.
A method for accurate measurement of complex parts that contain no reference points is described. The technique is applied to the production of accurate castings, to their machining, and to their installation. Accuracies of /approximately/ 2 mil can be ac...
Saturated groundwater flow can often be described by the law of mass conservation and Darcy's law, i.e. by a potential flow problem. An accurate approximation of the specific discharge can be determined by the mixed finite element method. In this article ...
We show that for large momenta the grand canonical ensemble is not an accurate enough approximation to the phase space integral to be used in calculating inclusive cross sections. In its place we propose a very general method based on the saddle point inversion of the Laplace transform integral. This method is ...
A new approximate projection method is proposed to treat the spurious state problem in the Dyson boson description of nuclear collective motion. In this method, successive orders of approximate projection are used to construct the various physical states in the Dyson boson representation of the shell model. Even in ...
An accurate approximation to calculate atmospheric profiles of transmittance in instrumental spectral intervals is presented. The approximation assumes a known transmittance model; i.e., that the transmittance in the spectral interval of the instrument is...
A procedure for computing saturation vapor by means of a polynomial approximation is presented and evaluated against other methods currently in use. The polynomial procedure is demonstrated to be highly accurate and more economic of computational time requirements than other procedures.
NASA Astrophysics Data System (ADS)
The research program on this grant was to develop new asymptotic and perturbation methods for approximating the performance of queueing systems. This involved obtaining approximations to complicated equations.The approximations provide accurate formulas for the performance measures. Queueing ...
DOE Information Bridge
An accurate analytical approximation to the capacitance transient amplitude measured by deep level transient spectroscopy as a function of the filling pulse duration is derived. The equation includes the influence of a defect concentration profile and the nonexponential trapping in the Debye tail of the depletion region. Because this equation gives an ...
PubMed
The objective of this work was to implement and evaluate a method, derived by D.L. Ermak, for generating skewed random numbers using a combination of uniform random numbers. This method is shown to provide accurate approximations to a Gaussian probability...
This paper presents some new three-stage methods for interpolating and approximating three-dimensional scattered surface data. Error bounds are derived for both the interpolation and approximation methods that are on the order of h/sup k/ where k = 3,4. These methods are shown to be ...
an accurate SASA approximation that uses the same machinery employed by our GB method and requires a small an approximation to the solvent-accessible surface area (SASA) with little additional computational cost. Our new and memory. SASA Approximation With the numerical integration and lookup ...
E-print Network
A reconstruction method of bioluminescence sources is proposed based on a phase approximation model. Compared with the diffuse approximation, this phase approximation model more correctly predicts bioluminescence photon propagation in biological tissues, so that bioluminescence tomography can ...
PubMed Central
The effects of an albedo of dust internal to nebulae on the observable parameters of the nebulae, such as ionization structure and temperature of dust grain have been investigated. We have used the quasi-diffusion method which entails an iterative procedure for solution of the radiative transfer equations to determine the accuracy of less-complicated, but ...
We review several approximate methods for evaluating quantum mechanical partition functions with the goal of obtaining a method that is easy to implement for multidimensional systems but accurately incorporates quantum mechanical corrections to classical partition functions. A particularly promising ...
A discussion is given of the methods of calculating atomic polarizabilities and shielding factors, and the relationships between them are demonstrated. The formulation of the uncoupled Hartree-Fock approximation is presented, and it is shown that the methods are all approximate versions of it. A more ...
The methods of generating group constants have been studied to predict accurately the nuclear characteristics of fast reactors. In resonance energy region, the accuracy of the group constants was investigated, which were calculated by the approximate weig...
The goal of this project is to determine a simpler and possibly more accurate method to estimate live load effect on bridges. The literature on this and related topics is robust and comprehensive. It addresses many approximate methods using many different...
A computationally simple method, based on line-beam response functions, is refined for estimating gamma skyshine dose rates. Critical to this method is the availability of an accurate approximation for the line-beam response function (LBRF). In this study...
Complete eigenvalue spectrum calculations are usually performed for benchmark analysis to compare the accuracy of various approximate methods. In one-speed criticality studies the most accurate methods either rely on analytical techniques (singular eigenf...
An analysis based on the Galerkin method is given of some nonlinear oscillator equations that have been analyzed by several other methods, including harmonic balance and direct variational methods. The present analysis is shown to provide simple yet accurate approximate solutions of these ...
The simulation of problems in electrocardiography using the bidomain model for cardiac tissue often creates issues with satisfaction of the boundary conditions required to obtain a solution. Recent studies have proposed approximate methods for solving such problems by satisfying the boundary conditions only approximately. This paper ...
To obtain energy eigenstates of a two-atom system, it is necessary to separate the wavefunction of the system into nuclear and electronic components. In an adiabatic approximation, the nuclear component is a function of internuclear distance, and the electronic component is a function of electron-nuclear distance. When this approximation is used with the ...
A short review is presented on one of the most successful theories for electronic structure calculations, the pseudopotential approximation, originally introduced by Hans?G.?A. Hellmann in 1934. Recent developments in relativistic quantum theory allow for the accurate adjustment of pseudopotential parameters to valence spectra, producing results for ...
Lagrange distributed approximating functionals (LDAFs) are proposed as the basis for a new, collocation-type method for accurately approximating functions and their derivatives both on and off discrete grids. Example applications are presented to illustrate the use of LDAFs for solving the Schr{umlt o}dinger ...
The frozen-density embedding (FDE) scheme [Wesolowski and Warshel, J. Phys. Chem. 97, 8050 (1993)] relies on the use of approximations for the kinetic-energy component v(T)[rho(1),rho(2)] of the embedding potential. While with approximations derived from generalized-gradient approximation kinetic-energy density functional weak ...
Applying an improved approximation scheme to the centrifugal term, the approximate analytical solutions of the Schr�dinger equation for the Eckart potential are presented. Bound state energy eigenvalues and the corresponding eigenfunctions are obtained in closed forms for the arbitrary radial and angular momentum quantum numbers, and different values of ...
Finding an accurate approximation of a discriminating function in order to evaluate its extrema is a common problem in the field of machine learning. A new type of neural network, the Quantron, generates a complicated wave function whose global maximum value is crucial for classifying patterns. To obtain an analytical approximation of ...
A Discontinuous Galerkin method is applied to hyperbolic systems that contain stiff relaxation terms. We demonstrate that when the relaxation time is unresolved, the method is accurate in the sense that it accurately represents the system's Chapman-Enskog approximation. Results are ...
A method by which a sundial can be used as a moondial has been known for over four centuries. However, since this involved estimating the lunar phase, an error of approximately one hour in time invariably resulted. A proper and accurate lunar equation of time is presented in which no knowledge of the lunar phase is necessary. A ...
The Schr"odinger equation is a pillar of modern science. Numerous methods and techniques have been developed to find an exact or an approximate solution of the SE such as perturbation theory, variational methods, and diagram methods. One widely used approximation is the WKB ...
A constructive method based on the bypass principle and the Pade approximation technique was used for deducing an implicit analytical expression for the Fermi-Dirac integral function. The simple equation has been found to be remarkably accurate in several...
The objective of this study was to modify a previous method, which led to an unacceptably large error for the subject interactions. The derivation of the new approximation was presented, with results that were more accurate.
The parabolic approximation method is widely recognized as useful for accurately analyzing and predicting sound transmission intensity in diverse ocean environments. One reason for its attractiveness is that solutions are marched in range, thereby avoidin...
Numerical methods are investigated for solving a system of continuity equations that contain linear and nonlinear chemistry as source and sink terms. It is shown that implicit, finite-difference approximations, when applied to the chemical kinetic terms, yield accurate results wh...
EPA Science Inventory
A method to determine unsteady solutions of the Navier-Stokes equations was developed and applied. The structural finite-volume, approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate ...
In this paper a new approach combining the features of the homotopy concept with variational approach is proposed to find accurate analytical solutions for nonlinear oscillators with and without a fractional power restoring force. Since the first-order approximation leads to very accurate results, comparisons with other results are ...
The Gaussian effective potential (GEP) is an approximation to quantum mechanics that semiquantitatively estimates quantum effects such as zero-point fluctuations and tunneling. We show how to use the GEP to compute semiclassical eigenvalues. It is well known that the GEP provides very accurate variational approximations to the ...
A scheme for the solution of the time dependent Maxwell's equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell's equations written as a second-order vector wave equation. High-order accurate symmetric difference ...
The influence of nuclear rotation on weak electron binding in the long range field of a linear polar molecule is treated in a way that leads ultimately, with suitable approximation, to the familiar equations for close coupling of electron-nuclear-rotational motions. Subsequently, a conventional pseudopotential approximation is invoked to examine the ...
A new method for the simulation of incompressible diphasic flows in two dimensions is presented, the distinctive features of which are: (1) reformation of the basic equation and specific choices of the finite element approximation of the same; (11) use of a mixed finite elements method, approximating both scalar ...
In this article a method of numerical solution of the Schrodinger equation is proposed. The approach corrects the Ehrenfest approximation by using several trajectories/configurations with their amplitudes coupled within and across configurations, thus making the method formally exact. Accurate results are obtained ...
Recently a method was formulated for treating electron scattering from a potential in a rather strong laser field. The method has now been applied to the case of a local Gaussian potential. The results, reported on here, provide a test of the applicability of the Kroll-Watson soft-photon approximation. This ...
We introduce a method for approximate smoothed inference in a class of switching linear dynamical systems, based on a novel form of Gaussian Sum smoother. This class includes the switching Kalman �Filter � and the more general case of switch transitions dependent on the continuous latent state. The method improves on the standard ...
Recently, we generalized the Delta-Eddington phase function and applied it to the radiative transfer equation for modeling the photon propagation in biological tissue. The resultant phase approximation model was shown to be highly accurate with a wide range of optical properties, including the strongly absorbing and weakly scattering media. In this paper, ...
We present a general framework for performing �bold-line� diagrammatic Monte Carlo calculations using an analytical partial resummation as a starting point for a stochastic summation of all diagrams. As a stringent test case we assess the accuracy of the method by solving the equations of single-site dynamical mean-field theory, using the noncrossing ...
A new method for analysis of an internal friction vs temperature peak to obtain an approximation of the spectrum of relaxation time responsible for the peak is described. This method, referred to as direct spectrum analysis (DSA), is shown to provide an accurate estimate of the distribution of relaxation times. The ...
Based on finite-difference approximations in time and a bilinear finite-element approximation in spatial variables, numerical implementations of a new iterative method with boundary condition splitting are constructed for solving the Dirichlet initial-boundary value problem for the nonstationary Stokes system. The problem is considered ...
We propose two efficient numerical methods of evaluating the luminosity distance in the spatially flat Lambda cold dark matter (?CDM) universe. The first method is based on the Carlson symmetric form of elliptic integrals, which is highly accurate and can replace numerical quadratures. The second method, using a ...
In this paper we present accurate methods for the numerical solution of the Boltzmann equation of rarefied gas. The methods are based on a time splitting technique. The transport is solved by a third order accurate (in space) positive and flux conservative (PFC) method. The collision step is ...
A semiempirical method that yields accurate band gaps and atomic positions in sp{sup 2}-hybridized, organic, semiconducting polymers has been obtained. This method is a tight-binding calculation where most of the parameters are determined via an ab initio local density approximation method ...
A simple power-series method is developed to calculate to large order the Rayleigh-Schr�dinger perturbation expansions for energy levels of a hydrogen atom with a Yukawa-type screened Coulomb potential. Perturbation series for the 1s, 2s, and 2p levels, shown not to be of the Stieltjes type, are calculated to 100th order. Nevertheless, the poles of the Pad� ...
Accurate quantum-mechanical calculations of rate constants for a model of reaction in solution are used as benchmarks for two approximate methods: variational transition-state theory with semiclassical corrections for reaction coordinate motion, and the path-integral centroid density method. The reaction model ...
crack tip to a point of interest h u x = XFEM displacement approximation Iu = nodal degree of freedom is accurately represented. The extended finite element method (XFEM) along with the level set method can be used algorithm are compared. M #12;3 II. Extended Finite Element Method The extended ...
We present a method, CamShift, for the rapid and accurate prediction of NMR chemical shifts from protein structures. The calculations performed by CamShift are based on an approximate expression of the chemical shifts in terms of polynomial functions of interatomic distances. Since these functions are very fast to compute and readily ...
Page 1. Accurate Approximations for European-Style Asian Options ... Let W+ be the final payoff of a European style Asian (call or put) option. ...
In this study we define the continuous height function to investigate the approximation of an interface line and its geometrical properties with the height function method. We show that in each mixed cell the piecewise linear interface reconstruction and the approximation of the derivatives and curvature based on three consecutive ...
This paper derives an explicit series approximation solution for the optimal exercise boundary of an American put option by means of a new analytical method for strongly nonlinear problems, namely the homotopy analysis method (HAM). The Black�Sholes equation subject to the moving boundary conditions for an American put option is ...
A numerical formulation of high-order accuracy, based on variational methods, is proposed for the solution of multi-dimensional diffusion-convection type equations. Accurate solutions are obtained without the difficulties that standard finite difference approximations present. In addition, tests show that very ...
A Discontinuous Galerkin (DG) method is applied to hyperbolic systems that contain stiff relaxation terms. We demonstrate that when the relaxation time is under-resolved, DG is accurate in the sense that the method accurately represents the system's Chapman-Enskog (or ...
We show how spectral functions for quantum impurity models can be calculated very accurately using a complete set of discarded numerical renormalization group eigenstates, recently introduced by Anders and Schiller. The only approximation is to judiciously exploit energy scale separation. Our derivation avoids both the overcounting ambiguities and the ...
A simple method for computing accurate density-dependent dispersion coefficients is presented. The dispersion coefficients are modeled by a generalized gradient-type approximation to Becke and Johnson's exchange hole dipole moment formalism. Our most cost-effective variant, based on a disjoint description of atoms in a molecule, gives ...
We are interested in solving the sparse linear systems, Av = b, that arise from finite difference or finite element approximations to partial differential equations. May iterative methods require solving an easier approximate equation, Pv = b, on each iteration. This is often called preconditioning or operator splitting ...
We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which hold regardless of the inhomogeneity of the string. Working on specific examples we obtain very ...
Performance models of parallel processing in which jobs divide into two or more asynchronous tasks have been developed. Because of the parallelism, the resulting queueing network does not have a product-form solution. An approximate solution method is described which iterates through a sequence of product-form networks. The condition for convergence of ...
Many physical and chemical processes, such as folding of biopolymers, are best described as dynamics on large combinatorial energy landscapes. A concise approximate description of the dynamics is obtained by partitioning the microstates of the landscape into macrostates. Since most landscapes of interest are not tractable analytically, the probabilities of transitions between ...
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 ...
Asymptotic expressions are derived for the two-dimensional incoherent optical transfer function (OTF) of an optical system with defocus and spherical aberration. The two-dimensional stationary phase method is used to evaluate the aberrated OTF at large and moderately large defocus and spherical aberration. For small aberrations, the OTF is approximated by ...
This report describes the shielding model development for the JB-Line Upgrade project. The product of this effort is a simple-to-use but accurate method of estimating the personnel dose expected for various operating conditions on the line. The current techniques for shielding calculations use transport codes such as ANISN which, while ...
... Accession Number : AD0657576. Title : HIGHLY ACCURATE DISCRETE METHODS FOR NONLINEAR PROBLEMS. Descriptive ...
... Title : A METHOD OF ACCURATELY MEASURING DYNAMIC STABILITY DERRIVATIVES IN TRANSONIC AND SUPERSONIC WIND TUNNELS,. ...
This paper is concerned with the accurate analytic solution of the nonlinear pendulum differential equation. Instead of the traditional Taylor series or asymptotic methods, the homotopy analysis technique is used, which does not require a small perturbation parameter or a large asymptotic parameter. It is shown here that such a method ...
... within the limits of the approximations to which (l.1 ... be determined to a first approximation by the ... local intensity of the distorted wave (more accurately ...
... that the approximations are sufficiently accurate, making them useful as tools to aid in the design of electrically short cylindrical monopoles over a ...
We present a class of hybridizable discontinuous Galerkin (HDG) methods for the numerical simulation of wave phenomena in acoustics and elastodynamics. The methods are fully implicit and high-order accurate in both space and time, yet computationally attractive owing to their following distinctive features. First, they reduce the ...
In this paper, we present two methods for accurate gradient estimation from scalar field data sampled on regular lattices. The first method is based on the multidimensional Taylor series expansion of the convolution sum and allows us to specify design criteria such as compactness and approximation power. The second ...
An algorithm for the simulation of unsteady, viscous, stratified compressible flows, which remains valid at all speeds, is presented. The method is second-order accurate in both space and time and is independent of the Mach number. In order to remove the stiffness of the numerical problem due to the large disparity between the flow speed and the acoustic ...
Disclosed are exemplary finite difference methods for electromagnetically simulating planar multilayer structures. The exemplary finite difference methods simulate multilayer planes by combining the admittance matrices of single plane pairs and equivalent circuit models for such single plane pairs based on multilayer finite difference ...
US Patent & Trademark Office Database
The authors present a new multidomain spectral collocation method that uses a staggered grid for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss-Lobatto rule. The method is conservative, free-stream preserving, and exponentially ...
Mathematical solutions to the problem consisting of a partially-full waste tank subjected to seismic loading, embedded in soil, is classically difficult in that one has to address: soil-structure interaction, fluid-structure interaction, non-linear behavior of material, dynamic effects. Separating the problem and applying numerous assumptions will yield approximate solutions. ...
A new method of approximating equivalent load duration curves can help utilities assess the costs associated with power plant expansions. Fast, accurate, and versatile, this technique greatly reduces the number of calculations needed to quantify the effects of customer load demand and unscheduled generator outages on system ...
We present a method by which a quantum-mechanical partition function can be approximated from below by an effective classical partition function. The associated potential is obtained by a simple smearing procedure. For a strongly anharmonic oscillator and a double-well potential, the lowest approximation gives a free energy which is ...
Concentration fields appearing in injection of solutions of radioactive substances into deep-lying strata have been calculated in the zero and first approximations on the basis of solutions constructed by asymptotic methods according to the concept of �exact, on the average,� solutions. The residual term of the expansion has been evaluated; the ...
This paper studies the borrower's optimal strategy to close the mortgage when the volatility of the market investment return is small. Integral equation representation of the mortgage contract value is derived, then used to find the numerical solution of the free boundary. The asymptotic expansions of the free boundary are derived for both small time and large time. Based on these asymptotic ...
When reactivity is a function of time, the one-delayedneutron-group equations can be expressed as a single second order homogeneous differential equation with variable coefficients. Some types of reactivity inputs are such that an accurate solution to this equation can be obtained with the use of "Liouville's Approximation." The ...
Approximate projection methods are useful computational tools for solving the equations of time-dependent incompressible flow.Inthis report we will present a new discretization of the approximate projection in an approximate projection method. The discretizations of divergence and gradient will ...
Synthetic aperture radar (SAR) imagery is now well-known as it is actively used in various remote sensing domains such as oceanography, geology, environment surveillance, cartography, etc. In this paper, we describe a new method for computing an elevation map from a single SAR image. Our method begins by reconstructing an approximate ...
We show that it is possible to construct an accurate approximation to the variational coupled cluster method, limited to double substitutions, from the minimization of a functional that is rigorously extensive, exact for isolated two-electron subsystems and invariant to transformations of the underlying orbital basis. This ...
A reverse phase HPLC method using C18 column has been developed for the quantitative estimation of nicotine in the bulk material and formulations (extended release and immediate release dosage forms). The method is specific to nicotine (RT approximately 4.64 min, asymmetry approximately 1.75), and can resolve ...
Elastic scattering of relativistic electrons and positrons by atoms is considered in the framework of the static field approximation. The scattering field is expressed as a sum of Yukawa terms to allow the use of various approximations. Accurate phase shifts have been computed by combining Buehring's power-series ...
Elastic scattering of relativistic electrons and positrons by atoms is considered in the framework of the static field approximation. The scattering field is expressed as a sum of Yukawa terms to allow the use of various approximations. Accurate phase shifts have been computed by combining B�hring's power-series ...
The cluster variation method (CVM) is an approximation technique which generalizes the mean field approximation and has been widely applied in the last decades, mainly for finding accurate phase diagrams of Ising-like lattice models. Here we discuss in which cases the CVM can yield exact results, considering: (i) ...
Accurate formulations based on finite-element methods are developed for calculating radiant heat transfer among diffuse-gray surfaces in an enclosure. The method of Gebhart is compared with solutions of the rigorous integral equations using these formulations. A Swartz-Wendroff approximation applied to the ...
Many of the current radiosity algorithms create a piecewise constant approximation to the actual radiosity. Through interpolation and extrapolation, a continuous solution is obtained. An accurate solution is found by increasing the number of patches which describe the scene. This has the effect of increasing the computation time as well as the memory ...
Implicit finite difference schemes for solving two dimensional and three dimensional Euler and Navier-Stokes equations will be addressed. The methods are demonstrated in fully vectorized codes for a CRAY type architecture. We shall concentrate on the Beam and Warming implicit approximate factorization algorithm in generalized coordinates. The ...
A method is presented to calculate accurate approximations to the half-life values of elimination systems modelled by one compartment. The major advantage of this method is that only algebraic mathematical operations are required. The results will be of value not only to students beginning the study of elimination ...
ERIC Educational Resources Information Center
We calculate adsorption and desorption isotherms in models of several classes of porous materials using a lattice-gas model solved in the Bethe-Peierls (quasichemical) approximation. Isotherms and fluid density profiles from the Bethe-Peierls and Bragg-Williams approximations are compared with grand-canonical Monte Carlo simulation results. The ...
Two methods have been developed for the computation of resonance integrals in cells containing annular fuel regions. Both are based on rational approximations. One is a generalization of a one-term rational approximation method developed by Segev for a cell with a single fuel annulus. The second modifies the ...
... The concentration of oxygen calculated from ultrasonic data is accurate to approximately 1% over the range of 21 to 95%. ...
... Title : ANALYTIC SOLUTIONS TO THE EQUATIONS OF MOTION ... very accurately by the approximate solutions. An alternate solution for the modal ...
The objective of this work was to implement and evaluate a method for generating skewed random numbers using a combination of uniform random numbers. The method provides a simple and accurate way of generating skewed random numbers from the specified first three moments without an a priori specification of the probability density ...
The accurate simulation of a neuron's ability to integrate distributed synaptic input typically requires the simultaneous solution of tens of thousands of ordinary differential equations. For, in order to understand how a cell distinguishes between input patterns we apparently need a model that is biophysically accurate down to the space scale of a single ...
The accurate simulation of a neuron�s ability to integrate distributed synaptic input typically requires the simultaneous solution of tens of thousands of ordinary differential equations. For, in order to understand how a cell distinguishes between input patterns we apparently need a model that is biophysically accurate down to the space scale of a ...
A radiation source approximation of linear and quadratic interpolation over an optical length is constructed to simplify surface-integral equations of radiative transfer for an absorbing, emitting and linear anisotropic scattering medium. The expressions formulated here for incident radiation and radiative heat flux can be applied easily to various coordinate systems. Test ...
�ecanique 1 (1937), 1�25. 12. Gilbert Strang, Accurate partial difference methods. I. Linear Cauchy problems of the time approximated when t is small enough by Lie or Strang's formula. The Lie formula is given by (1-tA e-tB U0 = t2 R1U0 + t3 R2(t)U0 and then is an approximation of global order 1. The Strang's ...
The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the ...
For the density and kinetic energy density of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential. Turning points produce quantum oscillations leading to energy corrections, which are completely ...
Entropies of Al-Si in layer silicates have been calculated using a series of CVM approximations for the honeycomb lattice. The parameters of the models have been constrained by 29Si NMR data. The results of low order approximations such as ``pair'' and ``star'' have been rejected because of their low accuracy at high Al/(Al+Si) ratios. Reasonably ...
The author proposes a method for analytical solution of the well-known approximate equation for the pair correlation function of systems with a purely repulsive generalized Morse potential. In statistical physics, there are few potentials for which the approximate equations for the pair correlation function are ...
An approach to setting test limits for production processes, based on a simple approximation to the bivariate normal distribution, is presented. Due to measurement errors, producers are typically forced to set test limits well within specification limits. The methods used in practice are rather informal and usually conservative with respect to consumer ...
The radial parts of the Dirac equation between the outer black hole horizon and the cosmological horizon are solved in Reissner-Nordstr�m de Sitter (RNdS) space numerically. An accurate approximation, the polynomial approximation, is used to approximate the modified tortoise coordinate \\hat r_* , which leads to ...
An investigation was conducted to estimate the error when a flat-flux approximation is used to compute the resolved resonance integrals for the cluster- type fuel element embedded in a heavy-water moderator. A more accurate way according to the heterogeneous structure of the cluster as well as to the first collision probability in the different ...
We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the transverse-traceless decomposition and consider perturbations of Schwarzschild black holes caused by boosts and the ...
The general theoretical method for determination of the electrical properties of complex grounding systems embedded in nonuniform soil is adjusted and applied to a frequent practical case of a foundation grounding system surrounded by two-layer soil. The proposed method appears to be considerably more accurate than the only alternative ...
The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line ...
An algorithm and program have been compiled for use on the Nairi-S digital computer. The existing method of calculating carbonizing periods is approximated by a mathematical model in the form of a 1st-order polynomial, which gives results accurate to within +- 3% compared with the existing method. A nomograph has ...
The differential equations describing stellar oscillations are transformed into an algebraic eigenvalue problem. Frequencies of adiabatic oscillations are obtained as the eigenvalues of a banded real symmetric matrix. The Cowling-approximation is employed, i.e. the Eulerian perturbation of the gravitational potential is neglected, and, in order to preserve selfadjointness, it ...
A comparison to Chapman's method is given for the viscosity and heat conductivity of a simple gas. The validity of the conclusion that Kihara's method gives more accurate results than Chapman's second approximation depends on the potential field and temperature range considered. ...
We introduce a new method for simulating colloidal suspensions with spherical colloidal particles of dielectric constant different from the surrounding medium. The method uses an approximate calculation of the Green function to obtain the ion-ion interaction potential in the presence of a dielectric discontinuity at the surface of the ...
A Chebyshev collocation method is presented for solving the spherical harmonics approximation to the equation of radiative transfer in a plane-parallel, homogeneous medium. As a result of test computations performed for Rayleigh and Henyey-Greenstein phase function, it was found that the proposed method can be used to solve transfer ...
A method for computing approximate minimum-mean-square-error estimates of histograms from list-mode data for use in dynamic tracer studies is evaluated. Parameters estimated from these histograms are significantly more accurate than those estimated from histograms computed by a commonly used method.
Vortex methods for inviscid incompressible two-dimensional fluid flow are usually based on blob approximations. This paper presents a vortex method in which the vorticity is approximated by a piecewise polynomial interpolant on a Delaunay triangulation of the vortices. An efficient reconstruction of the Delaunay ...
Vectorial diffraction methods provide accurate analysis of subwavelength diffractive optical elements, but they usually consume a lot of computing time and computer memory. On the other hand, scalar diffraction methods have simpler physical models and cost much less computer resources at the expense of a large numerical error. ...
The relationship between Z vector components and excitation amplitudes is analyzed for several post-Hartree-Fock correlation methods limited to double excitation amplitudes. An analytical formula approximating the Z vector for the coupled cluster doubles method is presented and shown to be quite accurate. This ...
The process of combined conduction and radiation in a large, heat-generating, dry particulate bed in sudden contact with a semi-infinite solid is studied analytically by a successive approximation method and numerically by a finite difference method. The transient behavior of the system, in particular, the behavior of the temperature ...
The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the ...
In this study one of the new techniques is used to solve numerical problems involving integral equations known as Sinc-collocation method. This method has been shown to be a powerful numerical tool for finding accurate solutions. So, in this article, some properties of the Sinc-collocation method required for our ...
Exact calculations of model posterior probabilities or related quantities are often infeasible due to the analytical intractability of predictive densities. Here new approximations to obtain predictive densities are proposed and contrasted with those based on the Laplace method. Our theory and a numerical study indicate that the proposed ...
Semiclassical trajectory methods are tested for electronically nonadiabatic systems with conical intersections. Five triatomic model systems are presented, and each system features two electronic states that intersect via a seam of conical intersections (CIs). Fully converged, full-dimensional quantum mechanical scattering calculations are carried out for all five systems at ...
A method is proposed which allows to efficiently treat elliptic problems on unbounded domains in two and three spatial dimensions in which one is only interested in obtaining accurate solutions at the domain boundary. The method is an extension of the optimal grid approach for elliptic problems, based on optimal rational ...
The friction damper has been widely used to reduce the resonant vibration of blades. The most commonly used methods for studying the dynamic behavior of a blade with a friction damper are direct integration methods. Although the harmonic balance method (HBM) is a well-known method for studying nonlinear vibration ...
BackgroundDermoscopy is one of the major imaging modalities used in the diagnosis of melanoma and other pigmented skin lesions. Due to the di culty and subjectivity of human interpretation, automated analysis of dermoscopy images has become an important research area. Border detection is often the first step in this analysis.MethodsIn this article, we present an ...
Background: Dermoscopy is one of the major imaging modalities used in the diagnosis of melanoma and other pigmented skin lesions. Due to the difficulty and subjectivity of human interpretation, automated analysis of dermoscopy images has become an important research area. Border detection is often the first step in this analysis. Methods: In this article, we present an ...
Recent development of Java's optimization techniques makes Java one of the most useful programming languages for numerical computations. This paper proposes a numerical method of obtaining verified approximate solutions of linear systems. Usual methods for verified computations use switches of rounding modes defined in IEEE standard ...
We show that the inclusion of second-order screened exchange to the random phase approximation allows for an accurate description of electronic correlation in atoms and solids clearly surpassing the random phase approximation, but not yet approaching chemical accuracy. From a fundamental point of view, the method ...
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's), which can be used to estimate a ...
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 ...
We present a family of high-order accurate thin layer approximations for time-domain electromagnetics. The thin layer approximations are valid for metal backed coatings of general isotropic materials and certain classes of anisotropic materials on smooth curvilinear backgrounds. Both dielectric and magnetic materials can be considered. ...
Multidimensional positive definite advection transport algorithm (MPDATA) is an iterative process for approximating the advection equation, which uses a donor cell approximation to compensate for the truncation error of the originally specified donor cell scheme. This step may be repeated an arbitrary number of times, leading to successfully more ...
Three new analytical approximate techniques for addressing nonlinear problems are applied to Jeffery-Hamel flow. Homotopy Analysis Method (HAM), Homotopy Perturbation Method (HPM) and Differential Transformation Method (DTM) are proposed and used in this research. These methods are very useful ...
The approximation error approach has been earlier proposed to handle modelling, numerical and computational errors in inverse problems. The idea of the approach is to include the errors to the forward model and compute the approximate statistics of the errors using Monte Carlo sampling. This can be a computationally tedious task but the key property of the ...
In an attempt to rationalize and improve an approximate exchange perturbation scheme related to the model of Murrell et al., more accurate approximations are introduced eliminating the use of empirical parameters. The total interaction energy was evaluated as the sum of additive electrostatic, exchange, charge transfer, and dispersion ...
We discuss a simple method for milling accurate off-axis parabolic mirrors with a computer-controlled milling machine. For machines with a built-in circle-cutting routine, an exact paraboloid can be milled with few computer commands and without the use of the spherical or linear approximations that have been discussed in other ...
The conceptual basis underlying pressure splitting schemes in fluid mechanics is clarified by deriving a split step scheme using a rational approximation procedure, and it is shown that a modified version of the method provides accurate solutions for both the velocity and the pressure. In the most effective of the algorithms proposed ...
We present a simple and efficient method for calculating symmetrized time correlation functions of neat quantum fluids. Using the pair-product approximation to each complex-time quantum mechanical propagator, symmetrized correlation functions are written in terms of a double integral for each degree of freedom with a purely positive integrand. At moderate ...
The authors consider several methods for solving the linear equations arising from finite difference discretizations of the Stokes equations. The pressure equation method presented here for the first time, apparently, and the method, presented by Bramble and Pasciak, are shown to have computational effort that grows slowly with the ...
Standard shock-capturing numerical methods fail to give accurate solutions to the equations of magnetohydrodynamics (MHD). The essential reason for this failure is that by ignoring the divergence-free constraint on the magnetic field, these methods can be shown to be entropy unstable. In this talk we will briefly review the entropy ...
An approximate but accurate method has been developed for estimating the uncertainty in assembly pressure loss when the loss coefficients are in linear regression form. Although more exact Monte Carlo and convolution integral approaches exist, these approaches require detailed numerical solution and are therefore inappropriate for ...
Maxwell had constructed first approximate solutions of the basic slip problems in the rarefied gas flows by distinguishing between incident and outgoing distributions at a surface. He used a single parameter approximation to the incident distribution and a conservation relation. The method has been improved in the recent past through ...
... The need for numerical methods; Approximate solution of the Dirichlet problem; Approximate solution of the Cauchy problem; Approximate solution ...
A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In ...
The purpose of this paper is to propose a statistical method for determining minimum detectable values in a pulse-counting measurements. The output of x-ray, electron and ion-spectroscopy detectors is a series of pulses that vary in their arrival frequency according to a Poisson distribution. The analysis presented here relates this to a Normal distribution, making it ...
Evaluation of four approximate methods for calculating infrared radiances ... Therefore, results of two simple methods, the absorption approximation and the ...
Since Gelbard introduced the simplified P{sub N} (SPN) equations as an inexpensive approximation to the transport theory, several others 2,3 tested them in multidimensional transport problems. It is reported that the low-order SPA, method was often able to eliminate >80% of the diffusion theory error. Recently, Larsen et al. derived SPN equations from ...
In order to investigate a complicated physical system, it is convenient to consider a simple, easy to solve model, which is chosen to reflect as much physics as possible of the original system, as an ideal approximation. Motivated by this fundamental idea, we propose a novel asymptotic method, the nonsensitive homotopy-Pad� approach. In this ...
In this paper, a Newton-Multigrid method is presented to solve the numerical simulation of the slider air bearing. For each fixed attitude in the specified grid, the Newton method is used to achieve the pressure distribution of the slider by solving the generalized Reynolds equations discretized by the least square finite difference (LSFD) ...
We propose an analytical approximation method for the estimation of multipoint identity by descent (IBD) probabilities in pedigrees containing a moderate number of distantly related individuals. We show that in large pedigrees where cases are related through untyped ancestors only, it is possible to formulate the hidden Markov model of the Lander-Green ...
