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Method of Successive Approximations for the Solution of Certain Problems in Aerodynamics

Description: A method of successive approximations for the solution of problems in the fields of diffusion, boundary-layer flow, and heat-transfer is illustrated by solving problems in each of these fields. In most of the examples, the approximate solutions are compared with known accurate solutions and the agreement is shown to be good.
Date: April 1951
Creator: Shvets, M. E.
Partner: UNT Libraries Government Documents Department

Highly optimized fourth-order short-time approximation for pathintegrals

Description: We derive a fourth-order short-time approximation for use in imaginary-time path-integral simulations. The short-time approximation converges for all continuous and bounded from below potentials, attains quartic order of convergence for sufficiently smooth potentials, and utilizes statistically independent random variables for its construction. These properties recommend the approximation as a natural replacement of the trapezoidal Trotter-Suzuki approximation for physical systems with continuous distributions.
Date: October 1, 2006
Creator: Predescu, Cristian
Partner: UNT Libraries Government Documents Department

Fourth-Order Method for Numerical Integration of Age- and Size-Structured Population Models

Description: In many applications of age- and size-structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Because quadratures can be designed with any order of accuracy, one can obtain numerical approximations of the solutions with very fast convergence. In this article, we present a general framework and a specific example of a fourth-order method based on composite Newton-Cotes quadratures for a size-structured population model.
Date: January 8, 2008
Creator: Iannelli, M; Kostova, T & Milner, F A
Partner: UNT Libraries Government Documents Department

Orbital-optimized opposite-spin scaled second order correlation: An economical method to improve the description of open-shell molecules

Description: Coupled cluster methods based on Brueckner orbitals are well-known to resolve the problems of symmetry-breaking and spin-contamination that are often associated with Hartree-Fock orbitals. However their computational cost is large enough to prevent application to large molecules. Here they present a simple approximation where the orbitals are optimized with the mean-field energy plus a correlation energy taken as the opposite-spin component of the second order many-body correlation energy, scaled by an empirically chosen parameter (recommended as 1.2 for general applications). This optimized 2nd order opposite spin (abbreviated as O2) method requires fourth order computation on each orbital iteration. O2 is shown to yield predictions of structure and frequencies for closed shell molecules that are very similar to scaled second order Moller-Plesset methods. However it yields substantial improvements for open shell molecules, where problems with spin-contamination and symmetry breaking are shown to be greatly reduced.
Date: January 1, 2007
Creator: Lochan, Rohini C. & Head-Gordon, Martin
Partner: UNT Libraries Government Documents Department

Negative differential mobility of weakly driven particles in models of glass formers

Description: We study the response of probe particles to weak constant driving in kinetically constrained models of glassy systems, and show that the probe's response can be non-monotonic and give rise to negative differential mobility: increasing the applied force can reduce the probe's drift velocity in the force direction. Other significant non-linear effects are also demonstrated, such as the enhancement with increasing force of the probe's fluctuations away from the average path, a phenomenon known in other contexts as giant diffusivity. We show that these results can be explained analytically by a continuous-time random walk approximation where there is decoupling between persistence and exchange times for local displacements of the probe. This decoupling is due to dynamic heterogeneity in the glassy system, which also leads to bimodal distributions of probe particle displacements. We discuss the relevance of our results to experiments.
Date: April 1, 2008
Creator: Jack, Robert L.; Kelsey, David; Garrahan, Juan P. & Chandler, David
Partner: UNT Libraries Government Documents Department

Direction-preserving and Schur-monotonic Semi-separable Approximations of Symmetric Positive Definite Matrices

Description: For a given symmetric positive definite matrix A {element_of} R{sup nxn}, we develop a fast and backward stable algorithm to approximate A by a symmetric positive-definite semi-separable matrix, accurate to any prescribed tolerance. In addition, this algorithm preserves the product, AZ, for a given matrix Z {element_of} R{sup nxd}, where d << n. Our algorithm guarantees the positive-definiteness of the semi-separable matrix by embedding an approximation strategy inside a Cholesky factorization procedure to ensure that the Schur complements during the Cholesky factorization all remain positive definite after approximation. It uses a robust direction-preserving approximation scheme to ensure the preservation of AZ. We present numerical experiments and discuss potential implications of our work.
Date: October 20, 2009
Creator: Gu, Ming; Li, Xiaoye Sherry & Vassilevski, Panayot S.
Partner: UNT Libraries Government Documents Department

Field Flows of Dark Energy

Description: Scalar field dark energy evolving from a long radiation- or matter-dominated epoch has characteristic dynamics. While slow-roll approximations are invalid, a well defined field expansion captures the key aspects of the dark energy evolution during much of the matter-dominated epoch. Since this behavior is determined, it is not faithfully represented if priors for dynamical quantities are chosen at random. We demonstrate these features for both thawing and freezing fields, and for some modified gravity models, and unify several special cases in the literature.
Date: July 8, 2008
Creator: Cahn, Robert N.; de Putter, Roland & Linder, Eric V.
Partner: UNT Libraries Government Documents Department

Update on Electron-Cloud Simulations Using the Package WARP-POSINST

Description: At PAC05[1] and PAC07[2], we presented the package WARP-POSINST for the modeling of the effect of electron clouds on high-energy beams. We present here the latest developments in the package. Three new modes of operations were implemented: (1) a build-up mode where, similarly to POSINST (LBNL) or ECLOUD (CERN), the build-up of electron clouds driven by a legislated bunch train is modeled in one region of an accelerator; (2) a quasistatic mode where, similarly to HEADTAIL (CERN) or QuickPIC (USC/UCLA), the frozen beam approximation is used to split the modeling of the beam and the electrons into two components evolving on their respective time scales; and (3) a Lorentz boosted mode where the simulation is performed in a moving frame where the space and time scales related to the beam and electron dynamics fall in the same range. The implementation of modes (1) and (2) was primary motivated by the need for benchmarking with other codes, while the implementation of mode (3) fulfills the drive toward fully self-consistent simulations of e-cloud effects on the beam including the build-up phase.
Date: April 1, 2009
Creator: Vay, J.-L.; Celata, Christine M.; Furman, Miguel; Venturini, Marco; Sonnad, Kiran G.; Penn, G. et al.
Partner: UNT Libraries Government Documents Department

The Loss Parameters for Very Short Bunches

Description: Semi-empirical formulas for the transverse and longitudinal loss factors generated by cavity and step discontinuities are given in the limit of short bunch length.The parametric transition between the cavity and step approximations is considered.The differences between the impedances offered by periodic structures and isolated single cavities are also discussed.
Date: June 1, 1988
Creator: Yunn, Byung; Bisognano, Joseph & Heifets, Sam
Partner: UNT Libraries Government Documents Department

Normal-reflection image

Description: Common-angle wave-equation migration using the double-square-root is generally less accurate than the common-shot migration because the wavefield continuation equation for thc former involves additional approximations compared to that for the latter. We present a common-angle wave-equation migration that has the same accuracy as common-shot wave-equation migration. An image obtained from common-angle migration is a four- to five-dimensional output volume for 3D cases. We propose a normal-reflection imaging condition for common-angle migration to produce a 3D output volume for 3D migration. The image is closely related to the normal-reflection coefficients at interfaces. This imaging condition will allow amplitude-preserving migration to generate an image with clear physical meaning.
Date: January 1, 2003
Creator: Huang, L. (Lian-Jie) & Fehler, Michael C.
Partner: UNT Libraries Government Documents Department

Kinetic Energy Principle And Neoclassical Toroidal Torque In Tokamaks

Description: It is shown that when tokamaks are perturbed the kinetic energy principle is closely related to the neoclassical toroidal torque by the action invariance of particles. Especially when tokamaks are perturbed from scalar pressure equilibria, the imaginary part of the potential energy in the kinetic energy principle is equivalent to the toroidal torque by the Neoclassical Toroidal Viscosity (NTV). A unified description therefore should be made for both physics. It is also shown in this case that the potential energy operator can be self-adjoint and thus the stability calculation can be simplified by minimizing the potential energy
Date: November 7, 2011
Creator: Park, Jong-Kyu
Partner: UNT Libraries Government Documents Department

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

Description: The maximum entropy analytic continuation (MEAC) method is used to extend the range of accuracy of the linearized semiclassical initial value representation (LSC-IVR)/classical Wigner approximation for real time correlation functions. The LSC-IVR provides a very effective 'prior' for the MEAC procedure since it is very good for short times, exact for all time and temperature for harmonic potentials (even for correlation functions of nonlinear operators), and becomes exact in the classical high temperature limit. This combined MEAC+LSC/IVR approach is applied here to two highly nonlinear dynamical systems, a pure quartic potential in one dimensional and liquid para-hydrogen at two thermal state points (25K and 14K under nearly zero external pressure). The former example shows the MEAC procedure to be a very significant enhancement of the LSC-IVR, for correlation functions of both linear and nonlinear operators, and especially at low temperature where semiclassical approximations are least accurate. For liquid para-hydrogen, the LSC-IVR is seen already to be excellent at T = 25K, but the MEAC procedure produces a significant correction at the lower temperature (T = 14K). Comparisons are also made to how the MEAC procedure is able to provide corrections for other trajectory-based dynamical approximations when used as priors.
Date: August 1, 2008
Creator: Liu, Jian & Miller, William H.
Partner: UNT Libraries Government Documents Department

Semiclassical (SC) Description of Electronically Non-AdiabaticDynamics via the Initial Value Representation (IVR)

Description: The initial value representation (IVR) of semiclassical (SC) theory is used in conjunction with the Meyer-Miller/Stock-Thoss description of electronic degrees of freedom in order to treat electronically non-adiabatic processes. It is emphasized that the classical equations of motion for the nuclear and electronic degrees of freedom that emerge in this description are precisely the Ehrenfest equations of motion (the force on the nuclei is the force averaged over the electronic wavefunction), but that the trajectories given by these equations of motion do not have the usual shortcomings of the traditional Ehrenfest model when they are used within the SC-IVR framework. For example, in the traditional Ehrenfest model (a mixed quantum-classical approach) the nuclear motion emerges from a non-adiabatic encounter on an average potential energy surface (a weighted average according to the population in the various electronic states), while the SC-IVR describes the correct correlation between electronic and nuclear dynamics, i.e., the nuclear motion is on one potential energy surface or the other depending on the electronic state. Calculations using forward-backward versions of SC-IVR theory (FB-IVR) are presented to illustrate this behavior. An even more approximate version of the SC-IVR, the linearized approximation (LSC-IVR), is slightly better than the traditional Ehrenfest model, but since it cannot describe quantum coherence effects, the LSC-IVR is also not able to describe the correct correlation between nuclear and electronic dynamics.
Date: June 22, 2007
Creator: Ananth, V.; Venkataraman, C. & Miller, W.H.
Partner: UNT Libraries Government Documents Department

Using the thermal Gaussian approximation approximation for theBoltzmann Operator in Semiclassical Initial Value Time CorrelationFunctions

Description: The thermal Gaussian approximation (TGA) recently developed by Mandelshtam et al has been demonstrated to be a practical way for approximating the Boltzmann operator exp(-{beta}H) for multidimensional systems. In this paper the TGA is combined with semiclassical (SC) initial value representations (IVRs) for thermal time correlation functions. Specifically, it is used with the linearized SC-IVR (LSC-IVR, equivalent to the classical Wigner model), and the 'forward-backward semiclassical dynamics' (FBSD) approximation developed by Makri et al. Use of the TGA with both of these approximate SC-IVRs allows the oscillatory part of the IVR to be integrated out explicitly, providing an extremely simple result that is readily applicable to large molecular systems. Calculation of the force-force autocorrelation for a strongly anharmonic oscillator demonstrates its accuracy, and of the velocity autocorrelation function (and thus the diffusion coefficient) of liquid neon demonstrates its applicability.
Date: September 6, 2006
Creator: Liu, Jian & Miller, William H.
Partner: UNT Libraries Government Documents Department

Test of the consistency of various linearized semiclassical initial value time correlation functions in application to inelastic neutron scattering from liquid para-hydrogen

Description: The linearized approximation to the semiclassical initial value representation (LSC-IVR) is used to calculate time correlation functions relevant to the incoherent dynamic structure factor for inelastic neutron scattering from liquid para-hydrogen at 14 K. Various time correlations functions were used which, if evaluated exactly, would give identical results, but they do not because the LSC-IVR is approximate. Some of the correlation functions involve only linear operators, and others involve non-linear operators. The consistency of the results obtained with the various time correlation functions thus provides a useful test of the accuracy of the LSC-IVR approximation and its ability to treat correlation functions involving both linear and nonlinear operators in realistic anharmonic systems. The good agreement of the results obtained from different correlation functions, their excellent behavior in the spectral moment tests based on the exact moment constraints, and their semi-quantitative agreement with the inelastic neutron scattering experimental data all suggest that the LSC-IVR is indeed a good short-time approximation for quantum mechanical correlation functions.
Date: March 15, 2008
Creator: Miller, William; Liu, Jian & Miller, William H.
Partner: UNT Libraries Government Documents Department

Spatially-discretized high-temperature approximations and theirO(N) implementation on a grid

Description: We consider the problem of performing imaginary-time propagation of wavefunctions on a grid. We demonstrate that spatially-continuous high-temperature approximations can be discretized in such a way that their convergence order is preserved. Requirements of minimal computational work and reutilization of data then uniquely determine the optimal grid, quadrature technique, and propagation method. It is shown that the optimal propagation technique is O(N) with respect to the grid size. The grid technique is utilized to compare the Monte Carlo efficiency of the Trotter-Suzuki approximation against a recently introduced fourth-order high-temperature approximation, while circumventing the issue of statistical noise, which usually prevents such comparisons from being carried out. We document the appearance of a systematic bias in the Monte Carlo estimators that involve temperature differentiation of the density matrix, bias that is due to the dependence of the eigenvalues on the inverse temperature. This bias is negotiated more successfully by the short-time approximations having higher convergence order, leading to non-trivial computational savings.
Date: October 1, 2006
Creator: Predescu, Cristian
Partner: UNT Libraries Government Documents Department

Real time correlation function in a single phase spaceintegral--beyond the linearized semiclassical initial valuerepresentation

Description: It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the 2nd order WD based on 'Winger trajectories', and the full Donoso-Martens dynamics (full DMD) and the 2nd order DMD based on 'Donoso-Martens trajectories'--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of these four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (non-linear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.
Date: July 10, 2007
Creator: Liu, Jian & Miller, William H.
Partner: UNT Libraries Government Documents Department

Coarse Spaces by Algebraic Multigrid: Multigrid Convergence and Upscaled Error Estimates

Description: We give an overview of a number of algebraic multigrid methods targeting finite element discretization problems. The focus is on the properties of the constructed hierarchy of coarse spaces that guarantee (two-grid) convergence. In particular, a necessary condition known as 'weak approximation property', and a sufficient one, referred to as 'strong approximation property' are discussed. Their role in proving convergence of the TG method (as iterative method) and also on the approximation properties of the AMG coarse spaces if used as discretization tool is pointed out. Some preliminary numerical results illustrating the latter aspect are also reported.
Date: April 30, 2010
Creator: Vassilevski, P S
Partner: UNT Libraries Government Documents Department

Radiation Diffusion: An Overview of Physical and Numerical Concepts

Description: An overview of the physical and mathematical foundations of radiation transport is given. Emphasis is placed on how the diffusion approximation and its transport corrections arise. An overview of the numerical handling of radiation diffusion coupled to matter is also given. Discussions center on partial temperature and grey methods with comments concerning fully implicit methods. In addition finite difference, finite element and Pert representations of the div-grad operator is also discussed
Date: January 14, 2005
Creator: Graziani, F R
Partner: UNT Libraries Government Documents Department

Activity Coefficient Derivatives of Ternary Systems Based on Scatchard's Neutral Electrolyte description

Description: Activity coefficient derivatives with respect to molality are presented for the Scatchard Neutral Electrolyte description of a ternary common-ion electrolyte system. These quantities are needed for the calculation of 'diffusion Onsager coefficients' and in turn for tests of the Onsager Reciprocal Relations in diffusion. The usually-omitted b{sub 23} term is included. The direct SNE binary approximations and a further approximation are discussed. Binary evaluation strategies other than constant ionic strength are considered.
Date: May 16, 2007
Creator: Miller, D G
Partner: UNT Libraries Government Documents Department

A Generalized Eigensolver based on Smoothed Aggregation (GES-SA) for Initializing Smoothed Aggregation Multigrid (SA)

Description: Consider the linear system Ax = b, where A is a large, sparse, real, symmetric, and positive definite matrix and b is a known vector. Solving this system for unknown vector x using a smoothed aggregation multigrid (SA) algorithm requires a characterization of the algebraically smooth error, meaning error that is poorly attenuated by the algorithm's relaxation process. For relaxation processes that are typically used in practice, algebraically smooth error corresponds to the near-nullspace of A. Therefore, having a good approximation to a minimal eigenvector is useful to characterize the algebraically smooth error when forming a linear SA solver. This paper discusses the details of a generalized eigensolver based on smoothed aggregation (GES-SA) that is designed to produce an approximation to a minimal eigenvector of A. GES-SA might be very useful as a standalone eigensolver for applications that desire an approximate minimal eigenvector, but the primary aim here is for GES-SA to produce an initial algebraically smooth component that may be used to either create a black-box SA solver or initiate the adaptive SA ({alpha}SA) process.
Date: May 31, 2007
Creator: Brezina, M; Manteuffel, T; McCormick, S; Ruge, J; Sanders, G & Vassilevski, P S
Partner: UNT Libraries Government Documents Department

Integrated Seismic Event Detection and Location by Advanced Array Processing

Description: The principal objective of this two-year study is to develop and test a new advanced, automatic approach to seismic detection/location using array processing. We address a strategy to obtain significantly improved precision in the location of low-magnitude events compared with current fully-automatic approaches, combined with a low false alarm rate. We have developed and evaluated a prototype automatic system which uses as a basis regional array processing with fixed, carefully calibrated, site-specific parameters in conjuction with improved automatic phase onset time estimation. We have in parallel developed tools for Matched Field Processing for optimized detection and source-region identification of seismic signals. This narrow-band procedure aims to mitigate some of the causes of difficulty encountered using the standard array processing system, specifically complicated source-time histories of seismic events and shortcomings in the plane-wave approximation for seismic phase arrivals at regional arrays.
Date: February 9, 2007
Creator: Kvaerna, T; Gibbons, S J; Ringdal, F & Harris, D B
Partner: UNT Libraries Government Documents Department

Micro-optics for imaging.

Description: This project investigates the fundamental imaging capability of an optic with a physical thickness substantially less than 1 mm. The analysis assumes that post-processing can overcome certain restrictions such as detector pixel size and image degradation due to aberrations. A first order optical analysis quickly reveals the limitations of even an ideal thin lens to provide sufficient image resolution and provides the justification for pursuing an annular design. Some straightforward examples clearly show the potential of this approach. The tradeoffs associated with annular designs, specifically field of view limitations and reduced mid-level spatial frequencies, are discussed and their impact on the imaging performance evaluated using several imaging examples. Additionally, issues such as detector acceptance angle and the need to balance aberrations with resolution are included in the analysis. With these restrictions, the final results present an excellent approximation of the expected performance of the lens designs presented.
Date: September 1, 2010
Creator: Boye, Robert R.
Partner: UNT Libraries Government Documents Department