Ramsey, Scott D. | Engineering Papers

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↗