The first part of this thesis describes nonlinear dielectric relaxation experiments performed on various molecular glass forming-liquids, with an emphasis on the response at high frequencies (excess wing). A significant nonlinear dielectric effect (NDE) was found to persist in these modes, and the magnitude of this NDE traces the temperature dependence of the activation energy. A time resolved measurement technique monitoring the dielectric loss revealed that for the steady state NDE to develop it would take a very large number of high amplitude alternating current (ac) field cycles. High frequency modes were found to be ‘slaved’ to the average structural relaxation time, contrary to the standard picture of heterogeneity. Nonlinear measurements were also performed on the Johari-Goldstein β-relaxation process. High ac fields were found to modify the amplitudes of these secondary modes. The nonlinear features of this secondary process are reminiscent of those found for the excess wing regime, suggesting that these two contributions to dynamics have common origins.
The second part of this thesis describes the nonlinear effects observed from the application of high direct current (dc) bias fields superposed with a small amplitude sinusoidal ac field. For several molecular glass formers, the application of a dc field was found to slow down the system via reduction in configurational entropy (Adam-Gibbs relation). Time resolved measurements indicated that the rise of the non-linear effect is slower than its decay, as observed in the electro-optical Kerr effect. A model was discussed which quantitatively captures the observed magnitudes and time dependencies of the NDE. Asymmetry in these rise and decay times was demonstrated as a consequence of the quadratic field dependence of the entropy change. It was demonstrated that the high bias field modifies the polarization response to the field, even including the zero field limit.
This paper outlines the design and testing of a z-scan spectrometer capable of measuring the third order refraction index of liquids. The spectrometer underwent multiple redesigns, with each explored in this paper with their benefits and drawbacks discussed. The first design was capable of measuring the third order refraction index for glass, and found a value of 8.43 +- 0.392 x 10^(-16) cm^2/W for the glass sample, with the literature stating glass has a refraction index between 1-100 x 10^(-16) cm^2/W. The second design was capable of measuring the third order refraction index of liquids, and found values of 1.23 $\pm$ 0.121 $\e{-16}$ and 9.43 +- 1.00 x 10^(-17) cm^2/W for water and ethanol respectively, with literature values of 2.7 x 10^(-16) and 5.0 x 10^(-17) cm^2/W respectively. The third design gave inconclusive results due to extreme variability in testing, and and the fourth design outlined has not been tested yet due to time constraints.
This document is a guide that can be used by undergraduate physics students alongside Richard J. Jacob and Professor Emeritus’s Tutorials in the Mathematical Methods of Physics to aid in their understanding of the key mathematical concepts from PHY201 and PHY302. This guide can stand on its own and be used in other upper division physics courses as a handbook for common special functions. Additionally, we have created several Mathematica notebooks that showcase and visualize some of the topics discussed (available from the GitHub link in the introduction of the guide).
investigations into the interactions involving topological defects, such as
magnetic monopoles and strings, that may have been produced in the early
universe. I performed numerical studies on the interactions of twisted
monopole-antimonopole pairs in the 't Hooft-Polyakov model for a range of
values of the scalar to vector mass ratio. Sphaleron solution predicted by
Taubes was recovered, and I mapped out its energy and size as functions of
parameters. I also looked into the production, and decay modes of $U(1)$ gauge
and global strings. I demonstrated that strings can be produced upon evolution
of gauge wavepackets defined within a certain region of parameter space. The
numerical exploration of the decay modes of cosmic string loops led to the
conclusions that string loops emit particle radiation primarily due to kink
collisions, and that their decay time due to these losses is proportional to
$L^p$, where $L$ is the loop length and $p \approx 2$. In contrast, the decay
time due to gravitational radiation scales in proportion to $L$, and I
concluded that particle emission is the primary energy loss mechanism for loops
smaller than a critical length scale, while gravitational losses dominate for
larger loops. In addition, I analyzed the decay of cosmic global string loops
due to radiation of Goldstone bosons and massive scalar ($\chi$) particles.
The length of loops I studied ranges from 200-1000 times the width of the
string core. I found that the lifetime of a loop is approximately $1.4L$. The
energy spectrum of Goldstone boson radiation has a $k^{-1}$ fall off, where $k$
is the wavenumber, and a sharp peak at $k\approx m_\chi/2$, where $m_\chi$ is
the mass of $\chi$. The latter is a new feature and implies a peak at high
energies (MeV-GeV) in the cosmological distribution of QCD axions.