Physical Sciences and Mathematics Commons^™

Enumerative Branching With Less Repetition, Thiago Serra

Faculty Conference Papers and Presentations

We can compactly represent large sets of solutions for problems with discrete decision variables by using decision diagrams. With them, we can efficiently identify optimal solutions for different objective functions. In fact, a decision diagram naturally arises from the branch-and-bound tree that we could use to enumerate these solutions if we merge nodes from which the same solutions are obtained on the remaining variables. However, we would like to avoid the repetitive work of finding the same solutions from branching on different nodes at the same level of that tree. Instead, we would like to explore just one of these …

Applied-Force Oscillations In Avalanche Dynamics, Louis W. Mcfaul, Gregory Sparks, Jordan Sickle, Jonathan T. Uhl, Wendelin J. Wright, Robert Maass, Karin A. Dahmen

Faculty Journal Articles

Until now most studies of discrete plasticity have focused on systems that are assumed to be driven by a monotonically increasing force; in many real systems, however, the driving force includes damped oscillations or oscillations induced by the propagation of discrete events or “slip avalanches.” In both cases, these oscillations may obscure the true dynamics. Here we effectively consider both cases by investigating the effects of damped oscillations in the external driving force on avalanche dynamics. We compare model simulations of slip avalanches under mean-field dynamics with observations in slip-avalanche experiments on slowly compressed micrometer-sized Au specimens using open-loop force …

Introduction To Molecular Dynamics Simulations, Katharina Vollmayr-Lee

Faculty Journal Articles

We provide an introduction to molecular dynamics simulations in the context of the Kob–Andersen model of a glass. We introduce a complete set of tools for doing and analyzing the results of simulations at fixed NVE and NVT. The modular format of the paper allows readers to select sections that meet their needs. We start with an introduction to molecular dynamics independent of the programming language, followed by introductions to an implementation using PYTHON and then the freely available open source software package LAMMPS. We also describe analysis tools for the quick testing of the program during its development and …

Numerical Simulation Of The Trapping Reaction With Mobile And Reacting Traps, Joshua D. Hellerick, Robert C. Rhoades, Benjamin Vollmayr-Lee

Faculty Journal Articles

We study a variation of the trapping reaction, A+B→A, in which both the traps (A) and the particles (B) undergo diffusion, and the traps upon meeting react according to A+A→0 or A. This two-species reaction-diffusion system is known to exhibit a nontrivial decay exponent for the B particles, and recently renormalization group methods have predicted an anomalous dimension in the BB correlation function. To test these predictions, we develop a computer simulation method, motivated by the technique of Mehra and Grassberger [Phys. Rev. E 65, 050101(R) (2002)], that determines the complete probability distribution of the B particles …

Surface Reservoirs Dominate Dynamic Gas-Surface Partitioning Of Many Indoor Air Constituents, Chen Wang, Douglas B. Collins, Caleb Arata, Allen H. Goldstein, James M. Mattila, Delphine K. Farmer, Laura Ampollini, Peter F. Decarlo, Atila Novoselac, Marina E. Vance, William W. Nazaroff, Jonathan P.D. Abbatt

Faculty Journal Articles

Human health is affected by indoor air quality. One distinctive aspect of the indoor environment is its very large surface area that acts as a poorly characterized sink and source of gas-phase chemicals. In this work, air-surface interactions of 19 common indoor air contaminants with diverse properties and sources were monitored in a house using fast-response, on-line mass spectrometric and spectroscopic methods. Enhanced-ventilation experiments demonstrate that most of the contaminants reside in the surface reservoirs and not, as expected, in the gas phase. They participate in rapid air-surface partitioning that is much faster than air exchange. Phase distribution calculations are …

From Dyck Paths To Standard Young Tableaux, Juan B. Gil, Peter R. W. Mcnamara, Jordan O. Tirrell, Michael D. Weiner

Faculty Journal Articles

We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we give Dyck path descriptions for certain SYT of height at most 3, and we introduce a special class of labeled Dyck paths of semilength n that is shown to be in bijection with the set of all SYT with n boxes. In addition, we present bijections from certain classes of Motzkin paths to SYT. As a natural framework for some of our bijections, we introduce a class of set partitions which in some …

Crystalline Architecture And Stratigraphy Of Coral Skeletal Density Banding: A Geobiological Record Of Changing Coral Reef Ecology, Kyle Fouke

Honors Theses

Coral skeletal density banding (CSDB), composed of alternating high density band (HDB) and low density band (LDB) layers that comprise the CaCO₃ (aragonite) skeleton of scleractinian corals, are used as chronometers for global paleoclimatic reconstructions of sea surface temperature (SST). Scleractinian coral skeletons have been intensively studied for centuries with detail analysis of the macro- and microscale skeletal structure to establish taxonomic and evolutionary relationships of coral species, mechanisms of biomineralization, and seafloor physical, chemical and biological alteration (diagenesis) of the skeleton. This study is the first to determine the crystalline architecture of HDBs and CSDB stratigraphic …

Sedimentological, Architectural, And Paleoenvironmental Analysis Of The Fluvial Upper Devonian Catskill Formation, North-Central Pennsylvania, Usa, Matylda Zaklicki

Honors Theses

During the Late Devonian time period, sediments eroded from the Acadian mountains were transported westward and deposited in fluvial environments, but the morphology of the rivers, avulsion style, and controls on basin infilling remain unclear. This study assesses the sedimentology, channel geometry, stratigraphic architecture, and avulsion style of the paleochannels and floodplains of the uppermost 80 meters of the Catskill Formation near Blossburg, Pennsylvania, using field-based lithofacies observations, high-resolution panoramic photographs, and terrestrial lidar scanning.

Upper Catskill Formation strata at Blossburg Middle consist of sandy channel and muddy floodplain deposits. Floodplain deposits were categorized into either proximal floodplain deposits or …

Fluvial Sedimentology And Architecture Of Two Latest Devonian Lower Huntley Mountain Formation Outcrops, North-Central Pennsylvania, Usa, Evan W. Filion

Honors Theses

Thick successions of river deposits accumulated in the north-central Pennsylvania region of the Appalachian foreland basin during Late Devonian time (~380-360 Ma). The properties and morphologies of these paleorivers are not well characterized. Latest Devonian tectonic, climatic, and eustatic controls on river dynamics and basin infilling also remain unclear. This study assesses the sedimentology, facies architecture, paleochannel depths, and grain size of a 133 m thick section of fluvial strata exposed across two outcrops, Blossburg South (older) and Blossburg West (younger), mapped as lower Huntley Mountain Formation near Blossburg, Pennsylvania. Field-based lithofacies observations, high-resolution panoramic photography, terrestrial lidar scanning, and …

Ethics, Privacy And Data Collection: A Complex Intersection, Matthew S. Brown

Honors Theses

The technology around us enables incredible abilities such as high-resolution video calls and the ability to stay connected with everyone we care about through social media. This technology also comes with a hidden cost in the form of data collection.

This work explores what privacy means and how users understand what data social media companies collect and monetize. This thesis also proposes a more ethical business model that addresses privacy concerns from an individual perspective.

Linked-Cluster Expansions For Lattice Spin Models, Yuyi Wan

Honors Theses

Similar to various series expansions that are used to approximate mathematical func- tions, the linked-cluster expansion is an approximation method that allows us to approach the actual values of a very large physical system’s different physical quan- tities by systematically studying smaller systems embedded in this larger system. The main concept in linked-cluster expansion, weight, represents the additional con- tribution to a certain physical quantity by increasing the system size by one unit. These weights are used to eventually build up the result on a larger system. In our case, we focus on the partition function, a quantity that can …

Orthogonal Groups In Characteristic 2 Acting On Polytopes Of High Rank, Peter A. Brooksbank, Dimitri Leemans, John T. Ferrara

Faculty Journal Articles

No abstract provided.

Distribution Of Human Exposure To Ozone During Commuting Hours In Connecticut Using The Cellular Device Network, Owais Gilani, Simon Urbanek, Michael J. Kane

Faculty Journal Articles

Epidemiologic studies have established associations between various air pollutants and adverse health outcomes for adults and children. Due to high costs of monitoring air pollutant concentrations for subjects enrolled in a study, statisticians predict exposure concentrations from spatial models that are developed using concentrations monitored at a few sites. In the absence of detailed information on when and where subjects move during the study window, researchers typically assume that the subjects spend their entire day at home, school, or work. This assumption can potentially lead to large exposure assignment bias. In this study, we aim to determine the distribution of …

Enhancing Models And Measurements Of Traffic-Related Air Pollutants For Health Studies Using Dispersion Modeling And Bayesian Data Fusion, Stuart A. Batterman, Veronica J. Berrocal, Chad Milando, Owais Gilani, Saravanan Arunachalam, K. Max Zhang

Faculty Journal Articles

Research Report 202 describes a study led by Dr. Stuart Batterman at the University of Michigan, Ann Arbor and colleagues. The investigators evaluated the ability to predict traffic-related air pollution using a variety of methods and models, including a line source air pollution dispersion model and sophisticated spatiotemporal Bayesian data fusion methods. Exposure assessment for traffic-related air pollution is challenging because the pollutants are a complex mixture and vary greatly over space and time. Because extensive direct monitoring is difficult and expensive, a number of modeling approaches have been developed, but each model has its own limitations and errors.

Dr. …

On The Ranks Of String C-Group Representations For Symplectic And Orthogonal Groups, Peter A. Brooksbank

Faculty Journal Articles

We determine the ranks of string C-group representations of 4-dimensional projective symplectic groups over a finite field, and comment on those of higher-dimensional symplectic and orthogonal groups.

Exact Sequences Of Inner Automorphisms Of Tensors, Peter A. Brooksbank

Faculty Journal Articles

We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner similar to those, our sequence facilitates inductive reasoning about, and calculation of the groups of symmetries of a tensor. The new insights these methods afford can be applied to problems ranging from understanding algebraic structures to distinguishing entangled states in particle physics.