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Title: Development of Provably Stable A-Phi Formulation Time Domain Integral Equations.


Abstract not provided.

Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
Report Number(s):
DOE Contract Number:
Resource Type:
Country of Publication:
United States

Citation Formats

Roth, Thomas. Development of Provably Stable A-Phi Formulation Time Domain Integral Equations.. United States: N. p., 2017. Web.
Roth, Thomas. Development of Provably Stable A-Phi Formulation Time Domain Integral Equations.. United States.
Roth, Thomas. 2017. "Development of Provably Stable A-Phi Formulation Time Domain Integral Equations.". United States. doi:.
title = {Development of Provably Stable A-Phi Formulation Time Domain Integral Equations.},
author = {Roth, Thomas},
abstractNote = {Abstract not provided.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 5

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  • The computational power of Feynman path integrals was exploited. Path-integration formalism for the quantum mechanics scattering and classical wave scattering was generalized. Firstly, the standard WKB approximation was generalized to the cases where the critical points of the action functional are degenerate. Three typical semiclassical scattering features served as examples for a classification of degenerate critical points: conservation laws, rainbows, glories. Secondly, the method developed for non-relativistic quantum mechanics scattering was used in the case of classical wave scattering. Scattering by Schwarzschild black holes was chosen as an example, and WKB cross sections for scalar, vector, and tensor fields weremore » worked out. Finally, 2s-th Bessel function behavior of WKB cross section for helicity-s polarized glory scattering in curved space time was proved.« less
  • For theories with first class constraints, phase space path integral is usually defined on the reduced phase space using Faddeev-Popov method. This method consists in defining some gauge conditions that intersect each gauge orbit once and only once. However, there exist theories which do not admit such gauge conditions globally. Moreover, the reduced phase space in general does not have a preferred choice of polarization as compared to the full phase space which normally has a natural vertical polarization. For these reasons, a full phase space formulation is developed in Part I of this dissertation. Phase space path integal formore » cotangent bundles is defined that preserves the vertical polarization. This is then applied to the theories with constraints linear in momenta. Certain conditions on the form of constraints and Hamiltonian are obtained that ensure that wavefunction continues to satisfy the constraints. Full phase space formalism is then applied to three examples - Dirac string theory, a monopole theory without strings and theory of particle with internal spin. The last two examples do not admit a global section of the gauge orbits, and hence Faddeev-Popov method is not applicable to them. in Part II of the dissertation, some aspects of the classical solutions in non-abelian gauge theories are discussed. Axially symmetric multi-instanton solutions for SU(2) gauge theory are obtained by means of a conformal mapping, and these solutions are regularized. Axially symmetric multi-monopole solutions in Yang-Mills-Higgs theory are discussed and certain conditions on the parameters are obtained to ensure the reality of the solutions.« less
  • An algorithm is developed for the optimality analysis of thermal reactor assemblies with a mathematical programming method. The neutron balances of the systems under consideration are transformed into integral equations by using Green's functions. Two-group, two-dimensional Green's functions for the neutron diffusion equations have been derived. A nodal method has been used to transform integral system equations into equivalent matrix eigenvalue problems. A benchmark problem solved with both the nodal method and a finite difference code ''CITATION'' establishes the validity of the integral system equations. Possible ways of improving computed results are discussed. Only 50 mesh points are required inmore » nodal method to obtain one percent error in the eigenvalue in the benchmark calculation. The same accuracy requires 2500 mesh points in the ''CITATION'' code. With the nodal method described above, a two-dimensional maximum power problem for a thermal reactor is solved by treating the fissile material concentration as the controller. Two numerical examples are given.« less