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Schaper numbers, palindrome partitions, and symmetric functions, with applications to characters of the symmetric group
Get PDFFinding the decomposition numbers for the symmetric group is a difficult problem and has led to many different research directions. For a given Specht module, the Schaper sum formula can be refined with knowledge of the Schaper number for the particular partition to give more precise information about the decomposition numbers. In Chapter 2, we give a combinatorial formula for the Schaper number when the partition has at most two columns. At the end, we provide a conjecture for the Schaper number for the partition of shaper (3^n).
Chapter 3 covers the joint work with my advisor, David Hemmer, and is published in the Ramanujan Journal. There is a well-known bijection between finite binary sequences and integer partitions. Sequences of length r correspond to partitions of perimeter r+1. Motivated by work on rational numbers in the Calkin-Wilf tree, we classify partitions whose corresponding binary sequence is a palindrome. We give a generating function that counts these partitions and describe how to efficiently generate all of them. Atypically for partition generating functions, we find an unusual significance to prime degrees. Specifically, we prove there are nontrivial palindrome partitions of n except when n=3 or n+1 is prime. We find an interesting new ``branching diagram for partitions, similar to Young\u27s lattice, with an action of the Klein four group corresponding to natural operations on the binary sequences.
Symmetric functions show up in several areas of mathematics including enumerative combinatorics and representation theory. Tewodros Amdeberhan conjectures equalities of symmetric group characters sums over a new set called Ev(\lambda). In Chapter 4, I share my results from investigating an alternating sum of characters for Ev(\lambda) written in terms of the inner product of Schur functions and power sum symmetric functions. I found an equality between the alternating sum of power-sum symmetric polynomials and a product of monomial symmetric polynomials. As a consequence, a special case of an alternating sum of symmetric group characters over the set Ev(\lambda) equals 0
ThermalTrack Dataset - Validation Labels
Get PDFWe present a wheel track detection system that leverages RGB-Thermal (RGB-T) imaging, where thermal channels reveal critical temperature differentials between compacted tracks and loose snow - tracks exhibit higher thermal inertia and lower reflectivity, emitting stronger radiation signatures even in visually homogeneous conditions. By fusing these distinctive thermal patterns with RGB spatial information, our method reliably identifies navigable tracks, enabling robust path-following in complete white-out conditions where snow textures and terrain features become indistinguishable
Carbon Footprint and Energy Analysis of a Mixed Metal Oxide Thermochemical Energy Storage Technology
No full textStrategies to decarbonize electricity generation and distribution require energy storage technologies that deliver power during periods of downtime in variable renewable energy sources, such as wind and solar PV. Ideally, energy storage technologies should not add significantly to the carbon footprint of the renewable electricity grid. In this study, we determine the carbon footprint and cumulative energy demand for a new thermochemical energy storage technology using an environmental life cycle assessment (LCA). The technology is based on abundant mixed metal oxide energy storage material that operates over a 20-year lifetime with periodic renewal of the storage material. This energy storage technology can deliver power over a time that is intermediate in the range between short- and long-duration energy storage. Input data for the operation were derived from industry demonstration trials and engineering calculations. The results indicate that the contribution of the process infrastructure and energy storage material manufacture and recycle contribute 36.2 kg CO2 eq/MWh-e delivered to the grid, a value on par or lower compared to Li-ion battery and vanadium redox flow battery storage, and much lower than conventional fossil-based power (US coal 1090: US natural gas 736: US grid 502.6 kg CO2 eq/MWh-e). Technology performance parameters such as round-trip efficiency and efficiency loss factor significantly affected the LCA results, shining a light on areas for improvement
Enhancing flotation separation of spodumene from feldspar using sodium N-oleoyl-L-alaninate
No full textSodium oleate (NaOL), as a traditional collector for spodumene, shows suboptimal flotation performance in industrial applications. To overcome this limitation, in this study sodium N-oleoyl-L-alaninate (SNOA) was first introduced as an innovative and more efficient collector for spodumene flotation. Flotation experiments revealed that SNOA possessed stronger collecting ability and superior selectivity in comparison to NaOL. Advanced analytical techniques such as AFM, Zeta potential, FTIR, and XPS indicated that NOA−, the active component of SNOA, was efficiently adsorbed on the spodumene surface activated by Ca2+, forming dense multilayers via robust electrostatic and chemical interactions. In comparison, NOA− exhibited limited adsorption on the feldspar surface activated by Ca2+, resulting in minimal monolayer formation through weak interactions. DFT calculations demonstrated that the adsorption energy of NOA−, which contains amide and carboxyl groups, on activated spodumene was significantly higher compared to its adsorption on activated feldspar. This is attributed to the stronger ionic interactions formed between the functional groups of NOA− and the active sites (Al and Ca) of activated spodumene surface. Therefore, SNOA was proven to be a high-efficiency collector for spodumene, demonstrating substantial potential for future industrial applications
Exploring the impact of surface topography on Rayleigh-Bénard dry convection in the Pi cloud chamber using OpenFOAM: In cylindrical and rectangular geometries
No full textThe Pi convection-cloud chamber can generate steady-state turbulence in both rectangular and cylindrical shapes via Rayleigh-Bénard convection (RBC) by maintaining warm bottom and cold top surfaces. Although most experiments in the Pi chamber were conducted in cylindrical shapes, all previous Pi chamber simulations were conducted in a rectangular shape due to the limitations of those models to discretize a cylindrical domain when using the finite difference method therein. Here, we use OpenFOAM, an open-source finite-volume-based Computational Fluid Dynamics (CFD) software package, to conduct Large-Eddy Simulation (LES) of dry RBC in the Pi chamber at high Rayleigh numbers (108 to 109). Results show that large-scale circulation (LSC) direction varies in the chamber with a constant side wall temperature. Imposing a slight temperature imbalance at the side wall ranging from 0.1 to 0.7 degrees can lock the LSC, aligning better with Pi chamber observations, particularly at higher Rayleigh numbers. In addition, we examine the impact of surface topography on LSC and heat transfer in RBC systems within cylindrical and rectangular shapes under varying conditions. Results show that roughing top/bottom surfaces by adding bars of a few tens millimeters height can strengthen thermal plumes and enhance temperature fluctuations in the chamber. Furthermore, we observe that different bar height configurations lead to notable changes in LSC orientation and thermal stratification, highlighting the complex interactions between surface features and convection patterns. This finding highlights how surface topography and chamber geometry affect Rayleigh-Bénard convection, improving understanding of turbulent heat transfer and atmospheric boundary-layer processes. Direct Numerical Simulations (DNS) are also conducted to validate LES results. While LES effectively captures qualitative behaviors seen in DNS, it tends to underestimate velocity variances near walls, illustrating a trade-off between computational efficiency and accuracy
Design and Validation of Edge Case Test Artifact for Evaluation of Automated Driving LiDAR and Radar Sensors
No full textWith the advent of technologies to support autonomous vehicles (AVs), there is a proliferation of different AV technologies from a variety of companies and organizations. With this increase in options comes the need to evaluate the operation of AV technologies to ensure safety and accuracy. Of particular note for physical evaluation involves the perception systems of AVs. However, there is a lack of standard methods to physically evaluate the perception system of AVs. A set of test artifacts can be used to compare the performances of perception systems, but the artifacts must be usable with different types of perception sensors. This article presents the development of an artifact that has both undetectable and detectable edge cases for light detection and ranging (LiDAR) and radar sensors. Specifically, different physical properties were investigated to design the proposed artifact with the desired capabilities of achieving detectable and undetectable edge cases under different conditions. With rigorous testing, a final design for the test artifact was completed where its detectable component reflects at least 7.47 times more radio wave energy and results in at least 1.92 times the amount of LiDAR points as compared with the undetectable component. The test artifact was further tested in outdoor conditions in addition to misaligned positions to demonstrate the versatility and potential weakness of the test artifact, respectively. The demonstrated test artifact in this research can therefore be used to compare the performance of different LiDAR and radar models within AV perception systems
Tourism, trade, energy, and economic development: Drivers of ecological footprint in the World\u27s top tourist destinations
Get PDFEcological sustainability, energy consumption, tourism, and economic growth interact in complex ways, a pressing concern for modern policy and study. Using data from 1999 to 2023, this study looks at the top 10 tourist destinations to see how these variables relate to their environmental impact. The primary regression analysis employs the Driscoll-Kraay Standard Errors (DKSE) approach, while Feasible Generalized Least Squares (FGLS) and Panel-Corrected Standard Errors (PCSE) are used for robustness checks. The DKSE results show that a 1 % increase in economic development reduces the ecological footprint by 0.775 %. Similarly, renewable energy minimizes the EFP by 0.140 %, and trade openness shows the most substantial effect, reducing it by 1.503 %. On the contrary, tourism and gross fixed capital formation raise EFP by 0.003 % and 0.905 %, respectively. All results are statistically significant at the 1 % level and verified by FGLS and PCSE robustness checks. The findings highlight the importance of sustainable trade policy, energy-efficient technology adoption, and sustainable tourist practices to reduce negative environmental consequences without sacrificing economic development
Assessing carbon and nitrogen economics in temperate forests through the relationship between foliar nutrient resorption and root production
No full textPlants both respond to and influence their immediate soil environment, which can yield divergent predictions regarding plant economics and trait coordination. Tree species with high foliar nitrogen (N) resorption efficiency (NRE)—an important N conservation strategy—may invest less carbon (C) belowground to acquire soil-derived N. This “tree perspective” hypothesis predicts a negative relationship between NRE and root production. Alternatively, high NRE reduces litter N concentrations, which can reduce soil N availability, requiring trees to invest more C belowground to get N. This “soil perspective” hypothesis predicts a positive relationship between NRE and root production. We test these hypotheses and then examine how NRE relates to foliar and litter N in three natural forests (~ 80–120-year-old trees; 12 species) and one common garden (~ 25-year-old trees; 9 species) in the eastern U.S. NRE was weakly and positively related to root production at the common garden, supporting our “soil perspective” hypothesis that litter–soil nutrient feedbacks drive a positive relationship between NRE and root production. There was no relationship between NRE and root production at the natural forest sites, providing no evidence for our “tree perspective” hypothesis, which purports that NRE is negatively related to root production given competition between roots and leaves for C. NRE was positively related to foliar N but negatively related to litter N, illustrating that NRE is an important physiological trait linking aboveground nutrient use with litter–soil nutrient feedbacks. These findings suggest that plant economics and the cost of soil N acquisition contribute to local-scale nutrient cycling in temperate forests
An intercomparison of wall fluxes in a turbulent thermal convection chamber: Direct numerical simulations and wall-modeled large-eddy simulations enhanced by machine learning
Get PDFThermal convection in a closed chamber is driven by a warm bottom, a cold top, and side walls at various temperatures. Although wall fluxes are the source of convection energy, accurately modeling these fluxes (i.e., the wall model) is challenging. In large-eddy simulations (LESs), many wall models are traditionally derived from the canonical boundary layer, which may be unsuitable for thermal convection bounded by both horizontal and vertical walls. This study conducts a model intercomparison of dry convection in a cubic-meter chamber using three direct numerical simulations (DNSs) and four LESs with different wall models. The LESs employ traditional wall models, a new wall model employing physics-aware neural networks, and a refined grid near the walls. The experiment involves four cases with varying sidewall temperatures. Our results show that LESs capture the main flow features and the trends of mean fluxes. The physics-aware neural networks and refined wall grids can improve the temporally averaged local fluxes when the large-scale circulation has a preferred direction. Even without the local improvement of wall fluxes, the LES flow quantities (temperature and velocities) can still largely match those in DNSs, provided the mean flux largely matches the DNSs. Additionally, DNSs reveal that a variation in corner treatments has minimal impacts on the flow quantities away from corners. Finally, LESs underestimate the mean fluxes of the entire wall due to their inability to resolve corner regions, but their mean flux away from the corner can better match DNS
Rapid riparian ecosystem decline in Rocky Mountain National Park
Get PDFUnderstanding the drivers of ecosystem collapse is critical for resource management, particularly for protected areas mandated to preserve biodiversity. In Rocky Mountain National Park, Colorado, tall willows (Salix spp.) dominated riparian vegetation, and a beaver-willow state was the natural ecosystem type in the Colorado River headwaters. However, willows comprise a portion of elk diets and are a preferred food for recently introduced moose, and the vegetation structure has changed dramatically since the early 2000s. To assess ecosystem changes, we analyzed time-series data on willow height from 1997 to 2021 inside and outside 3 exclosures built to exclude ungulates, area of tall willows in 1999 and 2019, area of open water from 1953 to 2019, vegetation composition in 1998 and 2021, groundwater depth from 1996 to 2021, surface water flow from 1953 to 2023, and climate from 1950 to 2023. Tall willow coverage and open water area declined by \u3e90% from 1999 to 2019. Willow height outside the ungulate exclosures declined by more than 75% since the 1990s; yet, within exclosures that were formerly browsed, willow height increased by up to 500%. Tall willow communities have largely been replaced by grasslands. Browsing by elk and moose likely played a pivotal role in triggering a collapse of the beaver-willow state and the formation of an alternative moose-elk-grassland state that appears stable and may be difficult to reverse without direct human action. Restoration efforts will depend on a reduction in herbivory and reconnection of the river with its floodplain