Pattern Formation in Certain Classical and Quantum Systems

<p>My research predominantly focuses on micromagnetic simulations of cobalt nanoparticles. These simulations are carried out by using the Object-Oriented MicroMagnetic Framework: OOMMF) distributed by the National Institute of Standards and Technology: NIST). In performing these simulations, observations of skyrmionic states were observed for large enough nanoparticles. Skyrmions are magnetic vortex states which have a core that is antiparallel with the outermost local magnetic moments. These states are being explored as an exciting branch of research that are applicable in many applications including, but not limited to, magnetic storage devices. Most simulations were carried out using a hemispherical geometry because collaborators at the University of Tennessee, Knoxville use laser-induced dewetting to create arrays of hemispheres on the nanometer scale. In conjunction with these simulations, we have performed analytical and numerical calculations of the demagnetizing factor of a hemispherical particle. The demagnetizing factor of a system is a parameter that characterizes shape anisotropy and is useful in calculating the energy of a uniformly magnetized body. Demagnetizing factors have been calculated for different geometries, but never for a hemisphere.</p><p>Other projects that my research includes research into rogue waves and a mapping between classical and quantum systems. The rogue wave work deals with analysis of the Nonlinear Schr"{o}dinger Equation and developing new forms of rogue wave solutions. This process includes focussing on the time-reversal invariance of the Nonlinear Shr"{o}dinger Equation and also generalizes a wave form known as compactons to generate approximate, traveling wave solutions that are like a rogue wave in nature. These can be applied to oceanic, optical, and even economical situations. The mapping that we have generalized here indicates that classical and quantum correlation functions can be calculated from one another simply by allowing time to go to imaginary time, and taking the real part of the expression. This is partially based on previous work in a more specific version of this mapping, but generalizes it to any operator rather than specifically the density operator.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date.available

2012

Author dc:creator

• Johnson, Patrick Greenleaf Hart

Contributors dc:contributor

• Zohar Nussinov

Language dc:language

English (en)

DOI

https://doi.org/10.7936/K7Q81B58

OAI identifier oai:identifier

oai:openscholarship.wustl.edu:etd-1963