Innovations & Codes Sample Clauses

Innovations & Codes. ‌ There are a number of novel developments detailed in this thesis. The work in Chapter 3 is a follow up on the work by Xxxxxxxx and Xxxxxxxx [147] who first introduced the electron density representation that we describe in the next subsection. This representation was used to calculate total energies alone and was not able to calculate forces. The novelty and my contribution in this chapter was the development of derivatives of the aGPT total energy, and the minor adjustments to the formalism that this requires. Chapter 4 presents a number of new results including new Mg-Ca GPT potentials that were derived in collaboration with Xxxx Xxxxxxxx. These potentials were used to calculate the thermodynamic and mechanical stability of Mg-Ca at different concen- trations. These calculations were done by myself, using several codes that I developed and are currently used by Xxxx. Xxxxxx’x research group. The first of these codes ph.gpt is a phonon code written in Fortran for the GPT/aGPT that calculates band structures, density of states and thermodynamic properties (using tetrahedron integration [80]). The second of these codes md.gpt is a molecular statics/dynamics code for the GPT and aGPT. The molecular statics por- tion of the code is an implementation of the FIRE algorithm [148] using forces derived from the GPT/aGPT potentials. The molecular dynamics portion of the code imple- ments a number of thermostats including the stochastic velocity rescaling thermostat [149] and Xxxxxxxx thermostat [150]. In addition, there is also a barostat optimised for use with these thermostats [151]. Finally, for the special quasirandom structure calculations, I wrote a C++ code called mc.sqs which was designed for larger systems with looser constraints on the matching of the figures to the perfectly random alloy. Chapter 2‌ Electrons in Simple Metals ”Much too complicated to be soluble.” Xxxx X. X. Dirac FRS The physics of metals crosses many length and time scales: from the atomic scale where the nature of the metallic bond is determined [12, 13], to the microscale where the interaction of defects governs the mechanical properties [111]. In this chapter, we seek to build a quantum mechanical description of the fundamental electronic and ionic processes. Such a description will need to be both scalable and accurate. Our starting point is the total many-body Schrödinger equation. This equation governs the dynamics of non-relativistic electrons and nuclei. Whilst even the total ...