Physical Sciences and Mathematics Commons^™

The Surface Diffusion And The Willmore Flow For Uniformly Regular Hypersurfaces, Jeremy Lecrone, Yuanzhen Shao, Gieri Simonett

Department of Math & Statistics Faculty Publications

We consider the surface diffusion and Willmore flows acting on a general class of (possibly non–compact) hypersurfaces parameterized over a uniformly regular reference manifold possessing a tubular neighborhood with uniform radius. The surface diffusion and Willmore flows each give rise to a fourth–order quasilinear parabolic equation with nonlinear terms satisfying a specific singular structure. We establish well–posedness of both flows for initial surfaces that are C^1+α–regular and parameterized over a uniformly regular hypersurface. For the Willmore flow, we also show long–term existence for initial surfaces which are C^1+α–close to a sphere, and we prove …

Asymptotically-Optimal Topological Nearest-Neighbor Filtering, Read Sandström, Jory Denny, Nancy M. Amato

Department of Math & Statistics Faculty Publications

Nearest-neighbor finding is a major bottleneck for sampling-based motion planning algorithms. The cost of finding nearest neighbors grows with the size of the roadmap, leading to a significant computational bottleneck for problems which require many configurations to find a solution. In this work, we develop a method of mapping configurations of a jointed robot to neighborhoods in the workspace that supports fast search for configurations in nearby neighborhoods. This expedites nearest-neighbor search by locating a small set of the most likely candidates for connecting to the query with a local plan. We show that this filtering technique can preserve asymptotically-optimal …

Topology-Guided Roadmap Construction With Dynamic Region Sampling, Read Sandström, Diane Uwacu, Jory Denny, Nancy M. Amato

Department of Math & Statistics Faculty Publications

Many types of planning problems require discovery of multiple pathways through the environment, such as multi-robot coordination or protein ligand binding. The Probabilistic Roadmap (PRM) algorithm is a powerful tool for this case, but often cannot efficiently connect the roadmap in the presence of narrow passages. In this letter, we present a guidance mechanism that encourages the rapid construction of well-connected roadmaps with PRM methods. We leverage a topological skeleton of the workspace to track the algorithm's progress in both covering and connecting distinct neighborhoods, and employ this information to focus computation on the uncovered and unconnected regions. We demonstrate …

Systems Of Meaning In Place Attachment, Emily Routman

Geography and the Environment Capstone Projects

Numerous scholars agree that contact with natural landscapes has benefits for the landscape and the person experiencing them, including increased environmentally-responsible behaviors as well as psychological, cognitive, physiological, and social benefits. People develop a sense of place in outdoor landscapes while experiencing the physical environment, and sense of place is strengthened by place attachment – one’s emotional ties to a place. According to Williams and Patterson (1999), place attachment is perceived through four systems of meaning: 1) aesthetic/inherent, 2) goal-directed/instrumental, 3) cultural/symbolic, and 4) individual/expressive. The present study sought to understand which of these four systems of meaning are the …

Tree Removal Analysis Of The 2018-2019 Gambles Mill Eco-Corridor Restoration, Zach Harrell

Environmental Studies Senior Seminar Projects

Trees have been extensively researched, and it has been concluded that they are useful not only useful tools in enhancing biofiltration, as well as managing stormwater and retaining sediment, but they also benefit the health of the ecosystem as a whole. But as the University of Richmond’s Gambles Mill Eco-corridor was restored between 2018 and 2019 in order limit to the amount of phosphorus, nitrogen, and other sediment flowing into the Little Westham Creek; many of the trees that combat these problems were removed. The following research intends to analyze the number of trees actually removed throughout the restoration, as …

Stream Restoration As A Method Of Improving Local Water Quality, Emily George

Environmental Studies Senior Seminar Projects

Projects of stream restoration are a known Best Management Practice (BMP) to approach stormwater management, and have been adopted globally as a means of improving local hydrology. Urbanization has led to an increase in impervious surfaces, resulting in deteriorated streams, many of which are subject to stream restoration. Stormwater control measures (SCM), such as stream restoration, are considered to be a subset of green infrastructure as a method to reconnect streams with surrounding riparian areas, revitalize original hydrology, and support the local ecosystems. This paper looks into the viability of stream restoration as a way of improving water quality, focusing …

Cost Benefit Analysis And Beyond: Stream Restoration In Richmond, Virginia, Claire Powell

Environmental Studies Senior Seminar Projects

This research assessed the costs and benefits of six recent stream restoration projects in Richmond, Virginia within the context of the Chesapeake Bay Total Maximum Daily Load (CB TMDL) pollutant reduction requirements. In order to meet these requirements, state and local governments promoted stream restoration as an important way to reduce Bay-wide inputs of nitrogen, phosphorus, and total suspended solids. The overall intention of this paper was to holistically evaluate the risks and positive impacts associated with stream restoration, with a focus on Little Westham Creek, a stream restoration project located on the University of Richmond campus. I hypothesized that …

Step Pools: Examining The Flow Resistance And Stability Of Artificial Step Pools In Comparison With Their Natural Counterparts, Quinn Kirkpatrick

Environmental Studies Senior Seminar Projects

This study looked at step pool stream studies, reports, and field data in five catchment areas. The areas of interest include the Rio Cordon catchment area in Italy, the Cascade Mountain Range in Washington, the Siuslaw National Forest in Oregon, various areas in California, the University of Richmond in Virginia, and the Arkansas River Basin in Colorado. The purpose of this study was to compare the flow resistance and stability after large flooding events of artificial and natural step pool sequences to potentially provide information to improve monitoring of newly installed step pools and the design of future step pool …

Exploring Options For Mussel Restoration, Henry Hurt

Environmental Studies Senior Seminar Projects

This paper seeks to explore the feasibility and possible procedures of restoring freshwater mussels to the Little Westham Creek (LWC) as a way to reduce excess organic pollutants such as nitrogen and phosphorus coming from upstream. To this end, the use of mussels in bioremediation and restoration procedures found in scientific literature were reviewed with the goal of creating a guideline of how such a project would be carried out at the Gambles Mill Eco- Corridor. Based on the results of past literature, water data collected by students in this seminar, and data from RES, it was estimated that a …

The Generality Of The Guga Mrci Approach In Columbus For Treating Complex Quantum Chemistry, Hans Lischka, Ron Shepard, Thomas Müller, Peter G. Szalay, Russell M. Pitzer, Adelia J. A. Aquino, Carol A. Parish, Et Al.

Chemistry Faculty Publications

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calcu- lations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of dia- batization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully vari- ational …

A Template For Success: Celebrating The Work Of Judith Grabiner, Della Dumbaugh, Adrian Rice

Department of Math & Statistics Faculty Publications

Judith Grabiner is a mathematician who specializes in the history of mathematics. She is currently the Flora Sanborn Pitzer Professor Emerita of Mathematics at Pitzer College, one of the Claremont Colleges in Claremont, California. She has authored more than forty articles, as well as three books: The Origins of Cauchy’s Rigorous Calculus (1981), The Calculus as Algebra: J.-L. Lagrange, 1736–1813 (1990), and A Historian Looks Back: The Calculus as Algebra and Selected Writings (2010), which won the Beckenbach Prize from the Mathematical Association of America in 2014. She deliv- ered an invited address titled “The Centrality of Mathemat- ics in …

On Quasilinear Parabolic Equations And Continuous Maximal Regularity, Jeremy Lecrone, Gieri Simonett

Department of Math & Statistics Faculty Publications

We consider a class of abstract quasilinear parabolic problems with lower–order terms exhibiting a prescribed singular structure. We prove well–posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global existence of solutions and we extend the generalized principle of linearized stability to settings with initial values in critical spaces. These general results are applied to the surface diffusion flow in various settings.

Aromatic Ouroboroi: Heterocycles Involving A Sigma-Donor-Acceptor Bond And 4n+2 Pi-Electrons, Kelling J. Donald, William Tiznado, Rodrigo Baez-Grez, Diego Inostroza

Chemistry Faculty Publications

The aromaticity and dynamics of a set of recently proposed neutral 5- and 6-membered heterocycles that are closed by dative (donor–acceptor) or multi-center s bonds, and have resonance forms with a Hu¨ckel number of p-electrons, are examined. The donors and acceptors in the rings include N, O, and F, and B, Be, and Mg, respectively. The planar geometry of the rings, coupled with evidence from different measures of aromaticity, namely the NICSzz, and NICSpzz components of the conventional nucleus independent chemical shifts (NICS), and ring current strengths (RCS), indicate non-trivial degrees of aromaticity in certain cases, including the cyclic C3B2OH6 …

One-Pot Silyl Ketene Imine Formation-Nucleophilic Addition Reactions Of Acetonitrile With Acetals And Nitrones, C. Wade Downey, Grace Ann L. Robertson, Jhonmattew Santa, Kari R. Flicker, William M. Stith

Chemistry Faculty Publications

Trimethylsilyl trifluoromethanesulfonate (TMSOTf) and a trialkylamine base promote the conversion of acetonitrile to its silyl ketene imine in situ when acetonitrile is employed as solvent. Residual TMSOTf acts as a Lewis acid catalyst to activate acetals and nitrones in the reaction mixture, yielding β-methoxynitriles and β-(silyloxy)aminonitriles, respectively. Some reaction products undergo elimination under the reaction conditions to provide the α,β-unsaturated nitrile directly.

Score Following With Hidden Tempo Using A Switching State-Space Model, Yucong Jiang, Chris Raphael

Department of Math & Statistics Faculty Publications

A score-following program traces the notes in a musical score during a performance. This capability is essential to many meaningful applications that synchronize audio with a score in an on-line fashion. Existing algorithms often stumble on certain difficult cases, one of which is piano music. This paper presents a new method to tackle such cases. The method treats tempo as a variable rather than a constant (with constraints), allowing the program to adapt to live performance variations. This is first expressed by a Kalman filter model at the note level, and then by an almost equivalent switching state-space model at …

Spider's Guide To Sustainable Living, Office For Sustainability

Guides

Thank you for checking out this guide to caring for our future and ourselves. We're glad you did, because we need you. From the climate emergency to emerging health crises to social unrest, the need for change is all around us. The UR Sustainability Plan envisions "a future where sustainability is woven into the fabric of the University" in which we cultivate a culture of caring for people and the natural world. Consider this your invitation to join the movement to make this vision a reality.

Throughout the Spiders Guide to Sustainable Living, we will point out actions you can …

Assessing Inequitable Urban Heat Islands And Air Pollution Disparities With Low-Cost Sensors In Richmond, Virginia, Andre M. Eanes, Todd R. Lookingbill, Jeremy S. Hoffman, Kelly C. Saverino, Stephen S. Fong

Geography and the Environment Faculty Publications

Air pollution and the urban heat island effect are consistently linked to numerous respiratory and heat-related illnesses. Additionally, these stressors disproportionately impact low-income and historically marginalized communities due to their proximity to emissions sources, lack of access to green space, and exposure to other adverse environmental conditions. Here, we use relatively low-cost stationary sensors to analyze PM_2.5 and temperature data throughout the city of Richmond, Virginia, on the ten hottest days of 2019. For both hourly means within the ten hottest days of 2019 and daily means for the entire record for the year, the temperature was found to …

Landscapes Of War Permanently Altered Topography Is One Of The Casualties Of War, But Battlefields Can Also Be Of "Collateral Value", Todd R. Lookingbill, Peter D. Smallwood

Geography and the Environment Faculty Publications

But the rationale for creating battlefield parks has changed over the past 100 years, as have attitudes about battlefield conservation with a related emphasis on the physical landscapes themselves, leading to their management for multiple, layered assets through principles of constructive conservation. Existing battlefield parks provide perhaps the longest-standing examples of the evolution of landscapes of war toward generators of multiple ecosystem benefits. Moving from battlefield parks that, in some cases, have not seen warfare for hundreds of years, we examined landscapes of more recent conflict and considered the future collateral values that could be attained by establishing parks at …