Generative Pre-Trained Physics-Informed Neural Networks Implementation

Steinmetz, A. Modern topics in relativistic spin dynamics and magnetism. PhD dissertation. University of Arizona, 2023.

ME 69700 – Nonlinear Wave Mechanics

The paper commences by examining the geometric properties of de-Sitter space-time, with a specific focus on the isometries generated by Killing vectors.

Symplectic pseudo-spectral solver for (1+1)D nonlinear Klein-Gordon equation with topological solitons, breathers, and Numba acceleration.

Nonlinear MetaMaterials MPI solver

Steinmetz, A., Formanek, M. & Rafelski, J. Magnetic dipole moment in relativistic quantum mechanics. Eur. Phys. J. A 55, 40 (2019).

Python program that solves the dynamic equation of motion of a scalar field in 2+1 dimensions, over a cosmological background, and which comes from a potential that allows the formation of domain walls (double-well potential)

Companion simulation code for the Dynamics of the Hertault Condensate: promoting the Dark Geometry equilibrium constraint to a damped Klein–Gordon equation of motion for the Dark Boson. Reproduces the Hawking temperature; every number generated by the code, none hand-tuned.

The method of stationary phase and the centred-difference approximation are used to generate the finite-difference scheme for solving Klein-Gordon equation in MATLAB.

A novel solution to the Klein-Gordon equation in the presence of a strong rotating electric field

Python scripts for statistical analysis and visualization of nonlinear Klein-Gordon equation solutions generated by the amangkurat solver, including entropy metrics, spatiotemporal evolution plots, and phase space analysis.