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Asymptotic analysis of spatial discretizations in implicit Monte Carlo

Description: We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large. We demonstrate the validity of our analysis with a set of numerical examples.
Date: January 1, 2009
Creator: Densmore, Jeffery D
Partner: UNT Libraries Government Documents Department

Modeling broadband poroelastic propagation using an asymptotic approach

Description: An asymptotic method, valid in the presence of smoothly-varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous Earth models.
Date: May 1, 2009
Creator: Vasco, Donald W.
Partner: UNT Libraries Government Documents Department

Zeroth-order inversion of transient head observations

Description: A high-frequency, asymptotic solution for transient head,appropriate for a medium containing smoothly varying heterogeneity,provides a basis for efficient inverse modeling. The semi analyticsolution is trajectory based, akin to ray methods used in modeling wavepropagation, and may be constructed by post processing the output of anumerical simulator. For high frequencies, the amplitude sensitivities,the relationship between changes in flow properties and changes in headampliude, are dominated by the phase term which may be computed directlyfrom the output of the simulator. Thus, transient head waveforms may beinverted with little more computation than is required to invert arrivaltimes. An applicatino to synthetic head values indicates that thetechnique can be used to improve the fit to waveforms. An application totransient head data from the Migration experiment in Switzerland revealsa narrow, high conductivity pathway within a 0.5 m thick zone offracturing.
Date: August 15, 2007
Creator: Vasco, D.W.
Partner: UNT Libraries Government Documents Department

A numerical study of bunched beam transverse e-p instability based on the centroid model

Description: In a recent theoretical study of the transverse electron-proton (e-p) instability, an asymptotic solution has been found for the equations describing the centroid motion of the traversing proton bunch and the stationary background electrons. It was shown that the combination of finite proton bunch length, non-uniform proton line density, and the single-pass e-p interaction cause the instability to evolve intricately in space and time even in the linear regime. This paper reports a numerical study of the e-p instability based on the same centroid equations. The purpose of the work is to compare the numerical solution with the analytic solution and to use the numerical approach to investigate the early development of the instability not covered by the asymptotic solution. In particular, the instability threshold and the initial growth of the instability are studied for various proton-beam conditions, fraction of charge neutralization, and initial perturbations.
Date: January 1, 2003
Creator: Wang, T. F. (Tai-Sen F.)
Partner: UNT Libraries Government Documents Department

Dynamics of the Ginzburg-Landau equations of superconductivity

Description: This article is concerned with the dynamical properties of solutions of the time-dependent Ginzburg-Landau (TDGL) equations of superconductivity. It is shown that the TDGL equations define a dynamical process when the applied magnetic field varies with time, and a dynamical system when the applied magnetic field is stationary. The dynamical system describes the large-time asymptotic behavior: Every solution of the TDGL equations is attracted to a set of stationary solutions, which are divergence free. These results are obtained in the {open_quotes}{phi} = -{omega}({gradient}{center_dot}A){close_quotes} gauge, which reduces to the standard {close_quotes}{phi} = -{gradient}{center_dot}A{close_quotes} gauge if {omega} = 1 and to the zero-electric potential gauge if {omega} = 0; the treatment captures both in a unified framework. This gauge forces the London gauge, {gradient}{center_dot}A = 0, for any stationary solution of the TDGL equations.
Date: August 1997
Creator: Fleckinger-Pelle, J.; Kaper, H. G. & Takac, P.
Partner: UNT Libraries Government Documents Department

Asymptotic persistence of collective modes in shear flows

Description: A new nonasymptotic method is presented that reveals an unexpected richness in the spectrum of fluctuations sustained by a shear flow with nontrivial arbitrary mean kinematics. The vigor of the method is illustrated by analyzing a two-dimensional, compressible hydrodynamic shear flow. The temporal evolution of perturbations spans a wide range of nonexponential behavior from growth-cum oscillations to monotonic growth. The principal characteristic of the revealed exotic collective modes in their asymptotic persistence. {open_quotes}Echoing{close_quotes} as well as unstable (including parametrically-driven) solutions are displayed. Further areas of application, for both the method and the new physics, are outlined.
Date: March 31, 1998
Creator: Mahajan, S.M. & Rogava, A.D.
Partner: UNT Libraries Government Documents Department

Detonation front theories: Using high-resolution DNS to define extended asymptotic scalings and models

Description: When the detonation reaction-zone length, {eta}{sub r}, is short in comparison to the dimensions of the explosive piece being burnt, the detonation can be viewed as a propagating surface (or front) separating burnt from unburnt material. If the product of the shock curvature, {kappa} and {eta}{sub r} is small (i.e., the scaled shock curvature satisfies the {vert_bar}{kappa}{eta}{sub r}{vert_bar} {much_lt} 1), then to leading order the speed of this surface, D{sub n}({kappa}) is a function only of {kappa}. It is in this limit that the original version of the asymptotic detonation front theory, called detonation shock dynamics (DSD), derives the propagation law, D{sub n}({kappa}). In this lecture, the authors compare D{sub n}({kappa})-theory with the results obtained with high-resolution direct numerical simulations (DNS), and then use the DNS results to guide the development of extended asymptotic front theories with enhanced predictive capabilities.
Date: February 1, 1998
Creator: Aslam, T.D. & Bdzil, J.B.
Partner: UNT Libraries Government Documents Department

Sinuous oscillations and steady warps of polytropic disks

Description: In an asymptotic development of the equations governing the equilibria and linear stability of rapidly rotating polytropes we employed the slender aspect of these objects to reduce the three-dimensional partial differential equations to a somewhat simpler, ordinary integro-differential form. The earlier calculations dealt with isolated objects that were in centrifugal balance, that is the centrifugal acceleration of the configuration was balanced largely by self gravity with small contributions from the pressure gradient. Another interesting situation is that in which the polytrope rotates subject to externally imposed gravitational fields. In astrophysics, this is common in the theory of galactic dynamics because disks are unlikely to be isolated objects. The dark halos associated with disks also provide one possible explanation of the apparent warping of many galaxies. If the axis of the highly flattened disk is not aligned with that of the much less flattened halo, then the resultant torque of the halo gravity on the disk might provide a nonaxisymmetric distortion or disk warp. Motivated by these possibilities we shall here build models of polytropic disks of small but finite thickness which are subjected to prescribed, external gravitational fields. First we estimate how a symmetrical potential distorts the structure of the disk, then we examine its sinuous oscillations to confirm that they freely decay, hence suggesting that a warp must be externally forced. Finally, we consider steady warps of the disk plane when the axis of the disk does not coincide with that of the halo.
Date: May 1, 1995
Creator: Balmforth, N.J. & Spiegel, E.A.
Partner: UNT Libraries Government Documents Department

Application of the Two-Parameter J-A2 Description to Ductile Crack Growth

Description: Typical ASTM fracture testing determines J-integral resistance (J-R) curve or fracture toughness (JIC) based on specimens with high constraint geometry such as those specified in ASTM E1737-96. A three-term asymptotic solution with two parameters J and A2 (a constraint parameter) has been developed for characterizing the constraint effect of various geometries. The present paper extends the J-A2 characterization of a stationary crack tip to the regime of stable crack growth. Similar to the concept of J-controlled crack growth, the J-A2 description can be approximately used to characterize ductile crack growth under certain amount of crack extension. The region of J-A2 controlled crack growth is much larger than that controlled by J-integral alone. From the relationships between A2 and the test data, JIC and tearing modulus (TR), the coefficients used to define a J-R curve can be determined. For non-standard specimens or actual structures, once the constraint parameter A2 is determined, the J-R curves appropriate for these geometries can then be obtained. A procedure of transferring J-R curves determined from the standard ASTM procedure to non-standard specimens or flawed structures is outlined in the paper.
Date: July 8, 1999
Creator: Lam, P.S.
Partner: UNT Libraries Government Documents Department

Scattering of color dipoles: from low to high energies

Description: A dipole-dipole scattering amplitude is calculated exactly in the first two orders of perturbation theory. This amplitude is an analytic function of the relative energy and the dipoles' sizes. The cross section of the dipole-dipole scattering approached the high-energy BFKL asymptotics starting from relatively large rapidity {approx}4.
Date: November 1, 2002
Creator: Babansky, Alexander & Balitsky, Ian
Partner: UNT Libraries Government Documents Department

Axymptotic normality of X/sup 2/ in mxn tables with n large and small cell expectations

Description: Asymptotic normality for chi/sup 2/ used as a test for homogeneity is established under nonstandard conditions. The case of an mxn table with m fixed and the total number of observations proportional to n is studied for n large. Results are obtained under very mild assumptions on the marginal totals.
Date: January 1, 1977
Creator: Cuzick, J.
Partner: UNT Libraries Government Documents Department

Jet fragmentation and MLLA

Description: Recent CDF results in inclusive momentum distributions and multiplicities of particles in restricted cones around jets are compared to predictions using the Modified Leading Log Approximation. The authors found that MLLA gives a very reasonable description of jet fragmentation for a wide range of energies. Model parameters are extracted separately from the multiplicity and from the shape of the momentum distributions and are found to agree. The ratio of charged particle multiplicities in the gluon and quark jets measured in the context of MLLA is compared to the model-independent result and also found to agree.
Date: July 18, 2000
Creator: Safonov, Alexei N.
Partner: UNT Libraries Government Documents Department

Bounds for approximation in total variation distance by quantum circuits

Description: It was recently shown that for reasonable notions of approximation of states and functions by quantum circuits, almost all states and,functions are exponentially hard to approximate. The bounds obtained are asymptotically tight except for the one based on total variation distance (TVD). TVD is the most relevant metric for the performance of a quantum circuit. In this paper we obtain asymptotically tight bounds for TVD. We show that in a natural sense, almost all states are hard to approximate to within a TVD of 2/e -- {epsilon} even for exponentially small {epsilon}. The quantity 2/e -- {epsilon} is asymptotically the average distance to the uniform distribution. Almost all states with probability amplitudes concentrated in a small fraction of the space are hard to approximate to within a TVD of 2 -- {epsilon}. These results imply that non-uniform quantum circuit complexity is non-trivial in any reasonable model. They also reinforce the notion that the relative information distance between states (which is based on the difficulty of transforming one state to another) fully reflects the dimensionality of the space of qubits, not the number of qubits.
Date: September 1, 1995
Creator: Knill, E.
Partner: UNT Libraries Government Documents Department

Asymptotic distribution of a histogram density estimator

Description: Two theorems on the asymptotic distribution of a histogram density estimator based on randomly determined spacings introduced by Van Ryzin in 1973 are stated and proved. One theorem gives conditions for the pointwise asymptotic normality of the density estimator for points in the support of the density at which the density is continuously differentiable. A second theorem gives conditions for the pointwise asymptotic normality of the density estimator with a faster convergence rate for points in the support of the density at which the density is twice continuously differentiable. The results are used to compare the relative asymptotic efficiencies of the histogram estimator with the kernal method of density estimation.
Date: June 1, 1980
Creator: Kim, B K & Van Ryzin, J
Partner: UNT Libraries Government Documents Department

Investigation of an empirical probability measure based test for multivariate normality

Description: Foutz (1980) derived a goodness of fit test for a hypothesis specifying a continuous, p-variate distribution. The test statistic is both distribution-free and independent of p. In adapting the Foutz test for multivariate normality, we consider using chi/sup 2/ and rescaled beta variates in constructing statistically equivalent blocks. The Foutz test is compared to other multivariate normality tests developed by Hawkins (1981) and Malkovich and Afifi (1973). The set of alternative distributions tested include Pearson type II and type VII, Johnson translations, Plackett, and distributions arising from Khintchine's theorem. Univariate alternatives from the general class developed by Johnson et al. (1980) were also used. An empirical study confirms the independence of the test statistic on p even when parameters are estimated. In general, the Foutz test is less conservative under the null hypothesis but has poorer power under most alternatives than the other tests.
Date: January 1, 1984
Creator: Booker, J.M.; Johnson, M.E. & Beckman, R.J.
Partner: UNT Libraries Government Documents Department

The geometry of weak solutions of certain integrable nonlinar PDE`s

Description: We investigate the geometry of new classes of soliton-like weak solutions for integrable nonlinear equations. One example is the class of peakons introduced by Camassa and Holm [1993] for their integrable shallow water equation. Alber, Camassa, Holm and Marsden [1994a] put this shallow water equation into the framework of complex integrable Hamiltonian systems on Riemann surfaces and use special limiting procedures to obtain new solutions such as quasiperiodic solutions, n-solitons, solitons with quasiperiodic background, billiard, and n-peakon solutions and complex angle representations for them. They also obtain explicit formulas for phase shifts of interacting soliton solutions using the method of asymptotic reduction of the corresponding angle representations. The method they use for the shallow water equation also leads to a link between one of the members of the Dym hierarchy and geodesic flow on N-dimensional quadrics. Amongst these geodesics, particularly interesting ones are the umbilic geodesics, which generate the class of umbilic soliton solutions. Umbilic solitons have the property that as the space variable x tends to infinity, the solution tends to a periodic wave, and as x tends to minus infinity, it tends to the same periodic wave with a phase shift. Elliptic billiards may be obtained from the problem of geodesics on quadrics by collapsing along the shortest semiaxis. The corresponding Hamiltonian billiard flows axe associated to new classes of solutions of equations in the Dym hierarchy. Such billiard type solutions have discontinuous spatial derivative and, thus, are weak solutions for this class of PDE`s.
Date: December 31, 1994
Creator: Alder, M. S.; Camassa, R.; Holm, D. D. & Marsden, J. E.
Partner: UNT Libraries Government Documents Department

Preconditioning via asymptotically-defined domain decomposition

Description: Asymptotic analysis is used to derive preconditioners based on operator splitting and domain decomposition for the numerical solution of the advection-diffusion equation. Specifically, asymptotics is used to identify subdomains in which the solution is dominated by a certain operator, and this information is used to construct an effective preconditioner. The authors analyze the one-dimensional case in a function space setting and present numerical results for both one and two dimensions.
Date: June 1, 1994
Creator: Ashby, S. F.; Kelley, C. T.; Scroggs, J. S. & Saylor, P. E.
Partner: UNT Libraries Government Documents Department

Asymptotic analysis, Working Note No. 1: Basic concepts and definitions

Description: In this note we introduce the basic concepts of asymptotic analysis. After some comments of historical interest we begin by defining the order relations O, o, and O{sup {number_sign}}, which enable us to compare the asymptotic behavior of functions of a small positive parameter {epsilon} as {epsilon} {down_arrow} 0. Next, we introduce order functions, asymptotic sequences of order functions and more general gauge sets of order functions and define the concepts of an asymptotic approximation and an asymptotic expansion with respect to a given gauge set. This string of definitions culminates in the introduction of the concept of a regular asymptotic expansion, also known as a Poincare expansion, of a function f : (0, {epsilon}{sub o}) {yields} X, where X is a normed vector space of functions defined on a domain D {epsilon} R{sup N}. We conclude the note with the asymptotic analysis of an initial value problem whose solution is obtained in the form of a regular asymptotic expansion.
Date: July 1, 1993
Creator: Garbey, M. & Kaper, H. G.
Partner: UNT Libraries Government Documents Department

Nonlinear Partial Differential Equations Invariant to a One-Parameter Family of Stretching Groups

Description: Nonlinear partial differential equations (PDEs) in one dependent and two independent variables (call them c, z, and t) occur in many technological applications. Typical PDEs and the contexts in which they arise are the following: c{sub t} = (c{sup n}){sub zz}, which occurs in plasma physics, hydrology, gas flow in porous media, and applied superconductivity; cc{sub t} = c{sub zz}, which describes the expulsion of fluid from a long, slender, heated pipe; c{sub t} = (c{sub z} {sup 13}){sub z}, which describes heat transport in turbulent superfluid He-II; and c{sub tt} = (c{sub zz/2}) {integral} {sub o}{sup 1}c{sub z}{sup 2} dz, which describes the motion of a shock-loaded elastic membrane. All of these equations are invariant to a one-parameter family of one-parameter stretching groups of the form c{prime} = {lambda}{sup a}c, t{prime} = {lambda}{sup {beta}}t, z{prime} = {lambda}z, 0 < {lambda} < {infinity} where {lambda} is the group parameter that labels the individual transformations of a group and {alpha} and {beta} are the parameters that label groups of the family. The parameters {alpha} and {beta} are connected by a linear relation Ma + N{beta} = L where M, N, and L are numbers determined by the structure of the PDE. Similarity solutions are of the PDE that are invariant to one group of the family, say, that for which {alpha} = {alpha}* and {beta} = {beta}*. Such solutions have the form c = t{sup {alpha}*/{beta}*} y(z/t{sup 1/{beta}*}) where y is a function of the single variable x = z/t{sup 1{beta}*}. When substituted into the PDE yields an ordinary differential equation for the function y(x).
Date: June 1, 1994
Creator: Dresner, L.
Partner: UNT Libraries Government Documents Department

Asymptotics of a free boundary problem

Description: This article is concerned with free boundary problems for the differential equations u{double_prime} + (2{nu} + 1)/r u{prime} + u - u{sup q} = 0, r > 0, where 0 {le} q < 1 and {nu} {ge} 0. As was shown by Kaper and Kwong, there exists a unique R > 0, such that the equation admits a classical solution u that is positive and monotone on (0,R) and that satisfies the boundary conditions u{prime}(0) = 0, u(R) = u{prime}(R) = 0. This article is concerned with the behavior of R and u(0) as q {yields} 1.
Date: October 5, 1992
Creator: Atkinson, F. V.; Kaper, H. G. & Kwong, Man Kam
Partner: UNT Libraries Government Documents Department


Description: Starting from analytical properties of high frequency geometric impedance we show how one can accurately calculate short bunch wake-potentials (and even point-charge wakefields) from time domain calculations performed with a much longer bunch. In many practical instances this drastically reduces the need for computer resources, speeds up the calculations, and improves their accuracy. To illustrate this method we give examples for 2D accelerator structures of various complexities. We describe preliminary results of a new method that allows us to accurately obtain longitudinal wakefields of short bunches by adding a long-bunch result from an EM solver and a singular analytical wake model. In the future this work will be generalized to 3D geometries as well. Similarly, the method should be equally applicable to the calculations of transverse wakefields. Periodic structures with a significant number of periods (2 {ge} a{sup 2}/{sigma}L, where L is the period length) have not been considered so far. They have asymptotic wakefields that differ from the examples described above. We believe this method is applicable to such geometries as well, as long as correct asymptotic solutions are used.
Date: March 28, 2011
Creator: Podobedov, B. & Stupakov, G.
Partner: UNT Libraries Government Documents Department

An Order-of-Magnitude Estimation of Benzene Concentration in Saltstone Vault

Description: The contents of Tank 48H that include the tetraphenylborate (TPB) precipitates of potassium and cesium will be grouted and stored in the Saltstone vault. The grouting process is exothermic, which should accelerate the rate of decomposition of TPB precipitates eventually to benzene. Because the vault is not currently outfitted with an active ventilation system, there is a concern that a mixture of flammable gases may form in the vapor space of each cell filled with the curing grout. The purpose of this study was to determine if passive breathing induced by the diurnal fluctuations of barometric pressure would provide any mitigating measure against potential flammability in the cell vapor space. In Revision 0 of this document, a set of algorithms were presented that would predict the equilibrium concentration of benzene in the cell vapor space as a function of benzene generation rate, fill height, and passive breathing rate. The algorithms were derived based on several simplifying assumptions so that order of magnitude estimates could be made quickly for scoping purposes. In particular, it was assumed that passive breathing would occur solely due to barometric pressure fluctuations that were sinusoidal; the resulting algorithm for estimating the rate of passive breathing into or out of each cell is given in Eq. (10). Since Revision 0 was issued, the validity of this critical assumption on the mode of passive breathing was checked against available passive ventilation data for the Hanford waste tanks. It was found that the passive breathing rates estimated from Eq. (10) were on average 50 to 90% lower than those measured for 5 out of 6 Hanford tanks considered in this study (see Table 1); for Tank U-106, the estimated passive breathing rates were on average 20% lower than the measured data. These results indicate that Eq. (10) would most ...
Date: March 20, 2006
Creator: CHOI, A
Partner: UNT Libraries Government Documents Department