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Ramsey, Scott D.

Publications and source records attributed to Ramsey, Scott D..

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Lectures on Lie Group Analysis: Solving Differential Equations Using Symmetries

These notes are meant to be a supplemental reference for the beginner Lie Group Analyst. It is assumed that the reader has a basic concept of the fundamentals of Lie Group Theory (LGT), e.g. has seen the derivation of the infinitesimal generator and understands the mathematical meaning behind invariance. An excellent reference is Albright et al., “Symmetry Analysis of Differential Equations: A Primer,”. The reader is urged to read at least the first three chapters of that document to be able to follow the outset of Chapter 2 of this document. The reader should also have a general understanding of calculus, ordinary differential equations, and partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

IC w22_phadiagractox Highlight: Composition-dependent melting temperature of a compound [Poster]

Figure 1 displays, ambient melting points of the Au-Cu system as a function of Cu atomic percent: present model vs. experimental data from four different sources. Figure 2 displays, ambient melting points of the U-O system as a function of O atomic percent: present model vs. both experiment and quantum molecular dynamics (QMD) simulations on the stoichiometric U-O compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Ambient melting behavior of stoichiometric uranium oxides

As UO 2 is easily oxidized during the nuclear fuel cycle it is important to have a detailed understanding of the structures and properties of the oxidation products. Experimental work over the years has revealed many stable uranium oxides including UO 2 , U 4 O 9 (UO 2.25 ), U 3 O 7 (UO 2.33 ), U 2 O 5 (UO 2.5 ), U 3 O 8 (UO 2.67 ), and UO 3 , all with a number of different polymorphs. These oxides are broadly split into two categories, fluorite-based structures with stoichiometries in the range of UO 2 to UO 2.5 and less dense layered-type structures with stoichiometries in the range of UO 2.5 to UO 3 . While UO 2 is well characterized, both experimentally and computationally, there is a paucity of data concerning higher stoichiometry oxides in the literature. In this work we determine the ambient melting points of all the six stoichiometric uranium oxides listed above and compare them to the available experimental and/or theoretical data. We demonstrate that a family of the six ambient melting points map out a solid-liquid transition boundary consistent with the high-temperature portion of the phase diagram of uranium-oxygen system suggested by Babelot et al.

Burakovsky, Leonid↗
DOE OSTI2022

Analytical Sensitivity Analysis of a Spent Nuclear Fuel Cask

Here, we report nuclear science and engineering is a field increasingly dominated by computational studies resulting from increasingly powerful computational tools. As a result, analytical studies, which previously pioneered nuclear engineering, are increasingly viewed as secondary or unnecessary. However, analytical solutions to reduced-fidelity models can provide important information concerning the underlying physics of a problem and aid in guiding computational studies. Similarly, there is increased interest in sensitivity analysis studies. These studies commonly use computational tools. However, providing a complementary sensitivity study of relevant analytical models can lead to a deeper analysis of a problem. This work provides the analytical sensitivity analysis of the one-dimensional (1D) cylindrical mono-energetic neutron diffusion equation using the forward sensitivity analysis procedure (FSAP) developed by Cacuci. Further, these results are applied to a reduced-fidelity model of a spent nuclear fuel cask, demonstrating how computational analysis might be improved with a complementary analytic sensitivity analysis.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

On the Definition of the Prompt Neutron Lifetime

There are myriad definitions for the mean neutron lifetime, neutron generation time, and other related quantities to characterize a neutron and its progeny’s propagation through an assembly. In this document, we consider lifetime definitions that are associated with eigenvalue forms of the neutron transport equation. Specifically, we focus on the two most widely used eigenvalues: the $\kappa$ eigenvalue and the $\alpha$ eigenvalue. These eigenvalues are used more often than other eigenvalues due to the physical phenomenon they capture. The $\kappa$ eigenvalue allows for the ability to determine if the system can sustain a chain reaction, while the $\alpha$ eigenvalue captures the asymptotic time dependent behavior of the system. An advantage of using these eigenvalues resides in the biorthogonality of the solutions with their adjoint counterpart. This feature allows us to simplify the expressions and to obtain appropriately weighted definitions that highlight important physics and regions of an assembly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A quick introduction to linear transport phenomena

The goal of this report is to provide an introductory-level overview of the linear Boltzmann equation in the context of neutron transport. After deriving the transport equation, we discuss some of its basic applications in reactor theory. Finally, we review several simplifying approximations of the linearized Boltzmann equation that are essential to solving it in many applications. Although the context of neutron transport is called upon to add concreteness to our discussion, many of the concepts and approximations that we discuss remain relevant in other many other phenomena.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Stochastic Neutronics Primer (Volume I)

The purpose of this document is to introduce the elementary concepts and to build a concrete understanding of the stochastic theory of neutron transport to the motivated undergraduate student, the Ph.D. engineer/physicist/mathematician, and the staff scientist or professor learning yet another new skill. The authors understand that there are many learning types- from visual to analytical to repetitive to word-based to analogy-based (and combinations thereof)- and so we have tasked ourselves with providing as many representations as possible within to ensure every reader a fruitful endeavor. This document is written as a set of chapters that continually build upon the previous chapter. In this chapter, we provide the discussion, motivation, and background topics for the remainder of the text.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

On the Symmetry of Blast Waves

This paper presents a brief historical review of G. I. Taylor’s solution of the point blast wave problem which was applied to the Trinity test of the first atomic bomb. Lie group symmetry techniques (also referred to throughout this paper as geometric techniques) are used to derive Taylor’s famous two-fifths law that relates the position of a blast wave to the time after the explosion and the total energy released. The theory of exterior differential systems is combined with the method of characteristics to demonstrate that the solution of the blast wave problem is directly related to the basic relationships that exist between the symmetry (or geometry) and the physics of wave propagation through the equations of motion. The point blast wave model is cast in terms of two exterior differential systems, and both systems are shown to be integrable with local solutions for the velocity, pressure, and density along curves in space and time behind the blast wave. This work is dedicated to the memory of Professor Roy Axford, who introduced many of his students to the topic of symmetry analysis of differential equations.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2021

Lie group analysis of the point-reactor neutron kinetics equations for various reactivity models

This work applies Lie Group Theory to the nonlinear point-reactor neutron kinetics equations for several reactivity feedback and reactivity insertion models. The goal of this work is to connect known analytical solutions to their corresponding Lie groups as well as to obtain new analytical solutions and the circumstances from which they arise. The reactivity models we consider are the Nordheim-Fuchs Model, an arbitrary-order polynomial reactivity insertion model, and the Fuchs Ramp-Insertion Model. In all three models, we generalize the analysis when possible and obtain analytical solutions in every case. For the first two models, we succeed in finding the Lie groups corresponding to classical solutions and find additional solutions that were otherwise unknown. Finally, for the final model, we obtain a reduced-order nonlinear kinetics equation which is not analytically solvable, but by applying a second-order truncation, we find a novel closed-form solution and demonstrate its validity with a numerical example.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Nemchinov-Dyson Solutions of the Two-Dimensional Axisymmetric Inviscid Compressible Flow Equations [Review]

We investigate the two-dimensional (2D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the 2D velocity field is space-time separable and linearly variable in each corresponding spatial coordinate, we proceed to derive an in nite family of elliptic or hyperbolic, uniformly expanding or contracting \gas cloud" solutions. Construction of specific example solutions belonging to this family is dependent on the solution of a system of nonlinear, coupled, second-order ordinary differential equations, and the prescription of an additional physical process of interest (e.g., uniform temperature or uniform entropy flow). The physical and computational implications of these solutions as pertaining to quantitative code verification or model qualification studies are discussed in some detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Analytic Modeling of a Deep Shielding Problem [PowerPoint]

This PhD defense presentation includes how the results assessment methodology identifies physics driving behavior in simulated results using comparison with analytic and reduced-fidelity computational models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Spring 2020 Dissertation Update [Slides]

An update is provided on the dissertation underway and what has been learned thus far. Work thus far: Developed analytic models for each region in the spent fuel cask – Used to identify and explain physical processes which create features in detailed casks; Developed simplified computational models to identify details not seen in analytic models; SC were calculated in the fuel region; The difference in SC’s between the analytic model and the simplified computational model were identified. Outstanding issues: Analysis of analytic models in stainless steel and carbon steel – These materials are thin and have few features (just the slope); Discrepancies between absorption SC’s in fuel; Create a test problem to show the effects of the high energy resonances in the fuel region. Future Work: Sensitivity analysis needs to be continued through the cask – The detailed model will be added to the remaining materials; Sensitivity analysis paper; and, Addressing outstanding issues.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Scale Invariance of the Homentropic Inviscid Euler Equations with Application to the Noh Problem

We investigate the inviscid compressible flow (Euler) equations constrained by an ”isentropic” equation of state (EOS), whose functional form in pressure is an arbitrary function of density alone. Under the aforementioned condition, we interrogate using symmetry methods the scale-invariance of the homentropic inviscid Euler equations. We find that under general conditions, we can reduce the inviscid Euler equations into a system of two coupled ordinary differential equations. To exemplify the utility of these results, we formulate two example scale-invariant, self-similar solutions. The first example includes a shock-free expanding bubble scenario, featuring a modified Tait EOS. The second example features the classical Noh problem, coupled to an arbitrary isentropic EOS. In this case, in order to satisfy the conditions set forth in the classical Noh problem, we find that the solution for the flow is given by a transcendental algebraic equation in the shocked density.

97 MATHEMATICS AND COMPUTING↗