The Gauss-Green theorem in stratified groups

We lay the foundations for a theory of divergence-measure fields in noncommutative stratified nilpotent Lie groups. Such vector fields form a new family of function spaces, which generalize in a sense the $BV$ fields. They provide the most general setting to establish Gauss-Green formulas for vector fields of low regularity on sets of finite perimeter. We show several properties of divergence-measure fields in stratified groups, ultimately achieving the related Gauss-Green theorem.Comment: 69 page

A Dynamical Study of the Non-Star Forming Translucent Molecular Cloud MBM16: Evidence for Shear Driven Turbulence in the Interstellar Medium

We present the results of a velocity correlation study of the high latitude cloud MBM16 using a fully sampled $^{12}$CO map, supplemented by new $^{13}$CO data. We find a correlation length of 0.4 pc. This is similar in size to the formaldehyde clumps described in our previous study. We associate this correlated motion with coherent structures within the turbulent flow. Such structures are generated by free shear flows. Their presence in this non-star forming cloud indicates that kinetic energy is being supplied to the internal turbulence by an external shear flow. Such large scale driving over long times is a possible solution to the dissipation problem for molecular cloud turbulence.Comment: Uses AAS aasms4.sty macros. Accepted for publication in Ap

S-mixing and quantum tunneling of the magnetization in molecular nanomagnets

The role of $S$-mixing in the quantum tunneling of the magnetization in nanomagnets has been investigated. We show that the effect on the tunneling frequency is huge and that the discrepancy (more than 3 orders of magnitude in the tunneling frequency) between spectroscopic and relaxation measurements in Fe$_8$ can be resolved if $S$-mixing is taken into account.Comment: REVTEX, 10 pages, 3 jpg figures, to appear in PR

Power spectral analysis of voltage-gated channels in neurons

This article develops a fundamental insight into the behavior of neuronal membranes, focusing on their responses to stimuli measured with power spectra in the frequency domain. It explores the use of linear and nonlinear (quadratic sinusoidal analysis) approaches to characterize neuronal function. It further delves into the random theory of internal noise of biological neurons and the use of stochastic Markov models to investigate these fluctuations. The text also discusses the origin of conductance noise and compares different power spectra for interpreting this noise. Importantly, it introduces a novel sequential chemical state model, named p2, which is more general than the Hodgkin-Huxley formulation, so that the probability for an ion channel to be open does not imply exponentiation. In particular, it is demonstrated that the p2 (without exponentiation) and n4 (with exponentiation) models can produce similar neuronal responses. A striking relationship is also shown between fluctuation and quadratic power spectra, suggesting that voltage-dependent random mechanisms can have a significant impact on deterministic nonlinear responses, themselves known to have a crucial role in the generation of action potentials in biological neural networks

Unexpected phase locking of magnetic fluctuations in the multi-k magnet USb

The spin waves in the multi-k antiferromagnet USb soften and become quasielastic well below the antiferromagnetic ordering temperature TN. This occurs without a magnetic or structural transition. It has been suggested that this change is in fact due to dephasing of the different multi-k components: a switch from 3-k to 1-k behavior. In this work, we use inelastic neutron scattering with tridirectional polarization analysis to probe the quasielastic magnetic excitations and reveal that the 3-k structure does not dephase. More surprisingly, the paramagnetic correlations also maintain the same clear phase correlations well above TN (up to at least 1.4TN)

Flags and Friends

Our team worked with Orange County’s Special Olympics Flag Football team. We helped coach practices, organized drills, and supported the team at games/tournaments. Through this experience we got the chance to get further involved in our community through doing something we were passionate about. We learned how to apply the different principles of leadership to our mission of fostering an environment that drives inclusion and skill-building. These principles include loving others, extending ourselves, and leading with authority. We went into this experience viewing it as a school project. However, after a few practices, we started developing individual connections with players and coaches and found enjoyment in the overall process. Over the course of our time with the team, we watched their skills improve and friendships strengthen.https://stars.library.ucf.edu/hip-2023fall/1062/thumbnail.jp