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Application of Variational Methods to Transonic Flows With Shock Waves

Description: Note presenting a modification of certain variational methods for the approximate solution of subsonic and transonic flows to compensate for the fact that those methods fail as soon as shock waves occur. By applying a variational principle to the regions of flow behind shock waves and Bateman's original principle to the other regions in the fluid, shock equations can be directly obtained.
Date: November 1951
Creator: Wang, Chi-Teh & Chou, Pei-Chi
Partner: UNT Libraries Government Documents Department

Variational correction to the FERMI beam solution

Description: We consider the time-independent, monoenergetic searchlight problem for a purely scattering, homogeneous slab with a pencil beam of nuclear particles impinging upon one surface. The scattering process is assumed sufficiently peaked in the forward direction so that the Fokker-Planck differential scattering operator can be used. Further, the slab is assumed sufficiently thin so that backscattering is negligibly small. Generally, this problem is approximated by the classic Fermi solution. A number of modifications of Fermi theory, aiming at improved accuracy, have been proposed. Here, we show that the classic Fermi solution (or any approximate solution) can I be improved via a variational formalism.
Date: October 1, 1996
Creator: Su, Bingjing & Pomraning, G.C.
Partner: UNT Libraries Government Documents Department

Covariance Matrices for Direct Dissolution of Vial Insert Samples in DWPF Mock-Up Facility

Description: This report is prepared as part of Technical/QA Task Plan WSRC-RP-97- 351, Rev. 0 which was issued in response to Technical Task Request HLW/DWPF/TTR-970132. The issue to be addressed is the evaluation of a new method for analyzing the feed streams in the Slurry Mix Evaporator (SME) and Melter Feed Tank (MFT) at the Defense Waste Processing Facility (DWPF). The new method involves the direct dissolution (DD) of slurry samples which is intended to replace the more time-consuming current method (CM) of vitrification of slurry samples. A comparison test between the new and current methods, known as DWPF Lab Insert Test, HLWMD-DWPF-005, was performed in the DWPF Analytical Cell Mock-up Facility using PX-7 simulant. This report is concerned with the evaluation of the precision (variability) of the new method in comparison with the current method. This includes determining the number of samples analyzed by the new method that will give equivalent precision to four samples analyzed by the current (vitrification) method. The basis of comparison will be the precision of four feed stream properties: liquidus, viscosity, durability, and homogeneity. A companion report, Harris (1997b), address the issue of bias of the new method with respect to the current method.
Date: September 9, 1997
Creator: Reeve, C.P.
Partner: UNT Libraries Government Documents Department


Description: In this paper the authors present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to a variational approach in the general case they have the solution as a multiresolution (multiscales) expansion on the base of compactly supported wavelet basis. They give an extension of their results to the cases of periodic orbital particle motion and arbitrary variable coefficients. Then they consider more flexible variational method which is based on a biorthogonal wavelet approach. Also they consider a different variational approach, which is applied to each scale.
Date: March 31, 2000
Partner: UNT Libraries Government Documents Department

Recent applications of the stochastic variational method.

Description: The stochastic variational method has proved to be useful in various fields of physics, including atomic, molecular, solid state, nuclear and subnuclear physics. This paper only reviewed a small part of the applications. Other contributions to this volume will show its usefulness in studies related to the structure of the baryons. Its main application is in nuclear physics, which has not been covered here but the interested reader can find examples in the references. We would like to extend its applicability to larger systems and for more complicated interactions. Such developments are under way. This paper overviews the most recent developments and applications of the stochastic variational method for different physical systems.
Date: October 20, 1998
Creator: Varga, K.
Partner: UNT Libraries Government Documents Department

Neutron Transport Methods for Accelerator-Driven Systems

Description: The objective of this project has been to develop computational methods that will enable more effective analysis of Accelerator Driven Systems (ADS). The work is centered at the University of Missouri at Rolla, with a subcontract at Northwestern University, and close cooperation with the Nuclear Engineering Division at Argonne National Laboratory. The work has fallen into three categories. First, the treatment of the source for neutrons originating from the spallation target which drives the neutronics calculations of the ADS. Second, the generalization of the nodal variational method to treat the R-Z geometry configurations frequently needed for scoping calculations in Accelerator Driven Systems. Third, the treatment of void regions within variational nodal methods as needed to treat the accelerator beam tube.
Date: February 9, 2005
Creator: Tsoulfanidis, Nicholas & Lewis, Elmer
Partner: UNT Libraries Government Documents Department


Description: We propose an efficient variational method for Z{sub 2} lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. On the ladder lattice, we identify gauge invariant low-lying states by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian. On the square lattice, the second order phase transition is well reproduced.
Date: July 25, 2005
Creator: SUGIHARA, T.
Partner: UNT Libraries Government Documents Department

Correction of aberrations - past, present and future.

Description: The performance of static rotationally symmetric electron lenses is limited by unavoidable chromatic and spherical aberrations. In 1936, Scherzer demonstrated that the integrands of the integral expressions for the coefficients of these aberrations can be written as a sum of positive quadratic terms. Hence these coefficients can never change sign. This important result is called the Scherzer theorem, the only theorem existing in electron optics. Employing variational methods, Tretner determined the field of magnetic and electrostatic round lenses, which yields the smallest spherical aberration coefficient for particular constraints [2]. Unfortunately, these coefficients are still too large for realistic boundaries to enable sub-Angstrom resolution at medium voltages of about 200 to 300 kV. Therefore, the only possibility to directly reach this limit is the correction of the troublesome aberrations. It was again Scherzer who showed different procedures for canceling these aberrations [3]. The most promising is the incorporation of a corrector consisting of multipole elements or of a tetrode mirror in the case of low voltages. Although the mirror is rotationally symmetric, a non-rotationally symmetric beam splitter is needed to separate the incident beam from the reflected beam.
Date: February 21, 2002
Creator: Rose, H.
Partner: UNT Libraries Government Documents Department

Precise Calculation of Traveling-Wave Periodic Structure

Description: The effects of the round edge beam hole on the frequency and wake field are studied using variational method, which allows for rounded iris disk hole without any approximation in shape treatment. The frequency and wake field of accelerating mode and dipole mode are studied for different edge radius cases, including the flat edge shape that is often used to approximately represent the actual structure geometry. The edge hole shape has weak effect on the frequency, but much effect on the wake field. Our study shows that the amounts of wake fields are not precise enough with the assumption of the flat edge beam hole instead of round edge.
Date: July 6, 2007
Creator: Wang, L.; Li, Z.; Seryi, A. & /SLAC
Partner: UNT Libraries Government Documents Department

The nuclear matter problem

Description: We review the present statiis of the many-body theory of nuclear and pure neutron matter based on realistic models of nuclear forces, The current models of two- and three-nucleon interactions are discussed along with recent results obtained with the Brueckner and variatioual methods. New initiatives in the variational method and quantuni Monte Carlo nicthods to study pure neutron matter are described, and finally, the analytic behavior of the energy of piire neutron matter at low densities is cliscussed.
Date: January 1, 2002
Creator: Carlson, J. A. (Joseph A.); Cowell, S.; Morales, J.; Ravenhall, D. G. & Pandharipande, V. R. (Vijay R.)
Partner: UNT Libraries Government Documents Department

Comparison of simplified and standard spherical harmonics in the variational nodal method

Description: Recently, the variational nodal method has been extended through the use of the Rumyantsev interface conditions to solve the spherical harmonics (P{sub N}) equations of arbitrary odd order. In this paper, the authors generalize earlier x-y geometry work to fit the corresponding simplified spherical harmonics (SP{sub N}) equations into the variational nodal framework. Both P{sub N} and SP{sub N} approximations are implemented in the multigroup VARIANT code at Argonne National Laboratory in two and three dimensional Cartesian and hexagonal geometries. The availability of angular approximations through P{sub 5} and SP{sub 5}, and of flat, linear and quadratic spatial interface approximations allows investigation of both spatial truncation and angular approximation errors. Moreover, the SP{sub 3} approximation offers a cost-effective method for reducing transport errors.
Date: December 31, 1995
Creator: Lewis, E.E. & Palmiotti, G.
Partner: UNT Libraries Government Documents Department

Wavelet approach to accelerator problems. 3: Melnikov functions and symplectic topology

Description: This is the third part of a series of talks in which the authors present applications of methods of wavelet analysis to polynomial approximations for a number of accelerator physics problems. They consider the generalization of the variational wavelet approach to nonlinear polynomial problems to the case of Hamiltonian systems for which they need to preserve underlying symplectic or Poissonian or quasicomplex structures in any type of calculations. They use the approach for the problem of explicit calculations of Arnold-Weinstein curves via Floer variational approach from symplectic topology. The loop solutions are parameterized by the solutions of reduced algebraical problem--matrix Quadratic Mirror Filters equations. Also they consider wavelet approach to the calculations of Melnikov functions in the theory of homoclinic chaos in perturbed Hamiltonian systems.
Date: May 1, 1997
Creator: Fedorova, A.; Zeitlin, M. & Parsa, Z.
Partner: UNT Libraries Government Documents Department

Quantum Monte Carlo calculations for light nuclei

Description: Quantum Monte Carlo calculations of ground and low-lying excited states for nuclei with A {le} 8 have been made using a realistic Hamiltonian that fits NN scattering data. Results for more than two dozen different (J{sup {pi}}, T) p-shell states, not counting isobaric analogs, have been obtained. The known excitation spectra of all the nuclei are reproduced reasonably well. Density and momentum distributions and various electromagnetic moments and form factors have also been computed. These are the first microscopic calculations that directly produce nuclear shell structure from realistic NN interactions.
Date: October 1, 1997
Creator: Wiringa, R.B.
Partner: UNT Libraries Government Documents Department

Monte Carlo calculations of nuclei

Description: Nuclear many-body calculations have the complication of strong spin- and isospin-dependent potentials. In these lectures the author discusses the variational and Green`s function Monte Carlo techniques that have been developed to address this complication, and presents a few results.
Date: October 1, 1997
Creator: Pieper, S.C.
Partner: UNT Libraries Government Documents Department


Description: This four-day workshop focused on the wide variety of approaches to the non-perturbative physics of QCD. The main topic was the formulation of non-Abelian gauge theory in orbit space, but some other ideas were discussed, in particular the possible extension of the Maldacena conjecture to nonsupersymmetric gauge theories. The idea was to involve most of the participants in general discussions on the problem. Panel discussions were organized to further encourage debate and understanding. Most of the talks roughly fell into three categories: (1) Variational methods in field theory; (2) Anti-de Sitter space ideas; (3) The fundamental domain, gauge fixing, Gribov copies and topological objects (both in the continuum and on a lattice). In particular some remarkable progress in three-dimensional gauge theories was presented, from the analytic side by V.P. Nair and mostly from the numerical side by O. Philipsen. This work may ultimately have important implications for RHIC experiments on the high-temperature quark-gluon plasma.
Date: June 1, 2000
Creator: Van Baal, P.; Orland, P. & Pisarski, R.
Partner: UNT Libraries Government Documents Department

Heterogeneous treatment in the variational nodal method

Description: The variational nodal transport method is reduced to its diffusion form and generalized for the treatment of heterogeneous nodes while maintaining nodal balances. Adapting variational methods to heterogeneous nodes requires the ability to integrate over a node with discontinuous cross sections. In this work, integrals are evaluated using composite gaussian quadrature rules, which permit accurate integration while minimizing computing time. Allowing structure within a nodal solution scheme avoids some of the necessity of cross section homogenization, and more accurately defines the intra-nodal flux shape. Ideally, any desired heterogeneity can be constructed within the node; but in reality, the finite set of basis functions limits the practical resolution to which fine detail can be defined within the node. Preliminary comparison tests show that the heterogeneous variational nodal method provides satisfactory results even if some improvements are needed for very difficult, configurations.
Date: June 1, 1995
Creator: Fanning, T.H. & Palmiotti, G.
Partner: UNT Libraries Government Documents Department

Semi-orthogonal wavelets for elliptic variational problems

Description: In this paper the authors give a construction of wavelets which are (a) semi-orthogonal with respect to an arbitrary elliptic bilinear form a({center_dot},{center_dot}) on the Sobolev space H{sub 0}{sup 1}((0, L)) and (b) continuous and piecewise linear on an arbitrary partition of [0, L]. They illustrate this construction using a model problem. They also construct alpha-orthogonal Battle-Lemarie type wavelets which fully diagonalize the Galerkin discretized matrix for the model problem with domain IR. Finally they describe a hybrid basis consisting of a combination of elements from the semi-orthogonal wavelet basis and the hierarchical Schauder basis. Numerical experiments indicate that this basis leads to robust scalable Galerkin discretizations of the model problem which remain well-conditioned independent of {epsilon}, L, and the refinement level K.
Date: April 1, 1998
Creator: Hardin, D.P. & Roach, D.W.
Partner: UNT Libraries Government Documents Department

Tolerance design based on variation transfer function

Description: Tolerance design presented in this paper minimizes the expected quality loss due to system performance variations from the target value and the cost for controlling the tolerances of components and subsystems. The method is based on loss function, variation transfer function (VTF) and design of experiments methodology. The VTF developed in this paper makes it possible to access the variance of system performances for any tolerance levels setting of the components or subsystems based on the data from only one tolerance levels setting with on more experiments or simulations to be conducted. The VTF transfers the variations in the parameters of the components or the subsystems to the variations in the quality characteristic of the system. An optimization model is presented for tolerance design and a method is given to find the coefficients for the VTF. An example is given to demonstrate the method.
Date: February 1, 1996
Creator: Chen, Guangming
Partner: UNT Libraries Government Documents Department

Variational Principle for Optimal Accelerated Neutralized Flow

Description: Minimizing the energy deposited in the electron current in neutralized flows, such as in the Hall thruster, is examined. Modifying the electron current along the channel by inserting emitting electrodes, can enhance the efficiency. By employing variational methods, an optimal electron current distribution is found. The efficiency enhancement due to this effect, however, is shown to be small.
Date: September 1, 2000
Creator: Fruchtman, A. & Fisch, N. J.
Partner: UNT Libraries Government Documents Department

Variational method for adaptive grid generation

Description: A variational method for generating adaptive meshes is described. Functionals measuring smoothness, skewness, orientation, and the Jacobian are minimized to generate a mapping from a rectilinear domain in natural coordinate to an arbitrary domain in physical coordinates. From the mapping, a mesh is easily constructed. In using the method to adaptively zone computational problems, as few as one third the number of mesh points are required in each coordinate direction compared with a uniformly zoned mesh.
Date: January 1, 1983
Creator: Brackbill, J.U.
Partner: UNT Libraries Government Documents Department

Coarse-mesh rebalance methods compatible with the spherical harmonic fictitious source in neutron transport calculations

Description: The coarse-mesh rebalance method, based on neutron conservation, is used in discrete ordinates neutron transport codes to accelerate convergence of the within-group scattering source. Though very powerful for this application, the method is ineffective in accelerating the iteration on the discrete-ordinates-to- spherical-harmonics fictitious sources used for ray-effect elimination. This is largely because this source makes a minimum contribution to the neutron balance equation. The traditional rebalance approach is derived in a variational framework and compared with new rebalance approaches tailored to be compatible with the fictitious source. The new approaches are compared numerically to determine their relative advantages. It is concluded that there is little incentive to use the new methods. (3 tables, 5 figures) (auth)
Date: October 1, 1975
Creator: Miller, W.F. Jr.
Partner: UNT Libraries Government Documents Department