Characterizing Noise in the Search for the Axion
Axions are theoretical new particles that may help solve large unanswered questions in physics ranging from the nature of dark matter to the Strong-CP problem. The Global Network of Optical Magnetometers (GNOME) is a collaboration searching for evidence of Axion and Axion-like particles by searching for the predicted interaction between the new particles and atomic spins. Magnetometers are highly sensitive instruments traditionally used to measure the magnetic field’s effect on atomic spins, but after drastically reducing the local magnetic field they become an ideal tool to detect the effects of the Axion. We are contributing data from a magnetometer in Lewisburg, and are examining noise characteristics of the data across time and frequency. Gaussianity is one such characteristic, which when estimated can help us to better understand the significance of possible detections and nondetections. We developed a tool to quantify this parameter for GNOME’s magnetometers.

Unveiling the Structure of the Universe for Non-Science Students.
Our research focuses on creating and testing the effectiveness of an introductory astronomy lab activity designed for undergraduate non-science majors. To explore the Hubble Law, the expansion of the universe, and large scale structures, this lab implements the WorldWide Telescope, an interactive multi-perspective visualization tool, analysis of real astronomical data, and tactile models. We conducted a focus group to test the implementation of this new curriculum. Our hope is to fully develop and publish a fun and interesting laboratory experience that can be accessed without economic or social barriers to advanced technological materials.

An LP-based Characterizations Of Solvable Cases Of the Quadratic Assignment Problem

The quadratic assignment problem (QAP) is perhaps the most widely studied nonlinear combinatorial optimization problem. It has many applications in various fields, yet has proven to be extremely difficult to solve. This difficulty has motivated researchers to identify special objective function structures that permit an optimal solution to be found in an efficient manner. Previous work has shown that certain such structures can be explained in terms of the continuous relaxation of a mixed 0-1 linear reformulation of the problem known as the level-1 reformulation-linearization-technique (RLT) form. Specifically, the objective function structures were shown to ensure that a binary optimal extreme point solution exists to the continuous relaxation. This paper extends that work by considering known solvable cases in which the objective function coefficients have special chess-board and graded structures, and similarly characterizing them in terms of the level-1 RLT form. As part of this characterization, we develop a new relaxed version of the level-1 RLT form, the structure of which can be readily exploited to study the special instances under consideration.

Graphs, Adjacency Matrices and Stable Polynomials

Our research concerns the interplay of undirected graphs and stable polynomials. Stable polynomials, which are polynomials with restricted zero sets, are used in a variety of mathematical fields. Here, a stable polynomial p is defined as a two-variable polynomial that satisfies p(z_1,z_2) ≠ 0 for any (z_1,z_2) in the unit disk. In this research, we use adjacency matrices of undirected graphs to construct stable polynomials and investigate the relationships between the shapes of the graphs and the zeros of the polynomials. In a variety of situations, we establish the existence and location of polynomial zeros on the boundary of the unit disk and characterize how the zero set of a stable polynomial could approach those boundary zeros. We also pose and examine conjectures about more generalized and complicated cases. Using our results, one can build polynomials with specific boundary zeros and identify the boundary zeros implied by given polynomial properties.

Analyzing the Impact of Live Staking on Channel and Floodplain Morphology and Soil Carbon Sequestration in a First-Order Stream, Central Pennsylvania

Live staking is a stream restoration technique where live cuttings of riparian trees and woody shrubs are planted into stream banks and floodplains to revegetate degraded areas, decrease erosion and runoff, and provide bank stability. Here we present results from year two of a multi-year study investigating the effects of live staking a post-agricultural, unnamed tributary of Pine Creek located in Woodward, PA. Over 2000 live stakes were planted along the streambanks and floodplain in 2018-2019. In summer 2021, we extracted soil cores along transects perpendicular to the tributary, and we collected high resolution topography along each transect using a Trimble RTK-GPS. We also measured the carbon content of each soil core on a CHN analyzer.
Soil sampling showed that the floodplain mainly consist of silt loam with charcoal, roots, and rusty-colored mottling. There are no major spatial trends in soil characteristics throughout the study site. The mean soil carbon percentage is 1.77% , which is low compared to other published studies of floodplain soil carbon in temperate regions. Channel analysis shows a relatively degraded stream, with low sinuosity and a silt-covered bed that is considerably incised relative to the floodplain elevation.
Compared to baseline data collected in 2020, the average soil carbon increased by 0.1% and channel dimensions have not changed. Overall, these results show that impacts from live staking on channel dimensions and soil properties are not seen after one year, although we hypothesize that soil carbon will increase in the future, given the low baseline values.