Physical Sciences and Mathematics Commons^™

Conversion Of Crude Glycerol Using Clostridium Pasteurianum Into Butanol, Stephen Morgan

Summer Community of Scholars Posters (RCEU and HCR Combined Programs)

No abstract provided.

Sea Level Acceleration In The China Seas, Yongcun Cheng, Tal Ezer, Benjamin D. Hamlington

CCPO Publications

While global mean sea level rise (SLR) and acceleration (SLA) are indicators of climate change and are informative regarding the current state of the climate, assessments of regional and local SLR are essential for policy makers responding to, and preparing for, changes in sea level. In this work, three acceleration detection techniques are used to demonstrate the robust SLA in the China Seas. Interannual to multidecadal sea level variations (periods >2 years), which are mainly related to natural internal climate variability and significantly affect estimation of sea level acceleration, are removed with empirical mode decomposition (EMD) analysis prior to the …

Assessing The Impact Of Vertical Land Motion On Twentieth Century Global Mean Sea Level Estimates, B. D. Hamlington, P. Thompson, W. C. Hammond, G. Blewitt, R. D. Ray

CCPO Publications

Near-global and continuous measurements from satellite altimetry have provided accurate estimates of global mean sea level in the past two decades. Extending these estimates further into the past is a challenge using the historical tide gauge records. Not only is sampling nonuniform in both space and time, but tide gauges are also affected by vertical land motion (VLM) that creates a relative sea level change not representative of ocean variability. To allow for comparisons to the satellite altimetry estimated global mean sea level (GMSL), typically the tide gauges are corrected using glacial isostatic adjustment (GIA) models. This approach, however, does …

Modelling The Response Of Ice Shelf Basal Melting To Different Ocean Cavity Environmental Regimes, David E. Gwyther, Eva A. Cougnon, Benjamin K. Galton-Fenzi, Jason L. Roberts, John R. Hunter, Michael S. Dinniman

CCPO Publications

We present simulation results from a version of the Regional Ocean Modeling System modified for ice shelf/ocean interaction, including the parameterisation of basal melting by molecular diffusion alone. Simulations investigate the differences in melting for an idealised ice shelf experiencing a range of cold to hot ocean cavity conditions. Both the pattern of melt and the location of maximum melt shift due to changes in the buoyancy-driven circulation, in a different way to previous studies. Tidal forcing increases both the circulation strength and melting, with the strongest impact on the cold cavity case. Our results highlight the importance of including …

Modeling Ice Shelf/Ocean Interaction In Antarctica: A Review, Michael S. Dinniman, Xylar S. Asay-Davis, Benjamin K. Galton-Fenzi, Paul R. Holland, Adrian Jenkins, Ralph Timmerman

CCPO Publications

The most rapid loss of ice from the Antarctic Ice Sheet is observed where ice streams flow into the ocean and begin to float, forming the great Antarctic ice shelves that surround much of the continent. Because these ice shelves are floating, their thinning does not greatly influence sea level. However, they also buttress the ice streams draining the ice sheet, and so ice shelf changes do significantly influence sea level by altering the discharge of grounded ice. Currently, the most significant loss of mass from the ice shelves is from melting at the base (although iceberg calving is a …

Understanding The Structure And Functioning Of Polar Pelagic Ecosystems To Predict The Impacts Of Change, E. E. Murphy, R. D. Cavanagh, K. F. Drinkwater, S. M. Grant, J. J. Heymans, E. E. Hofmann, G. L. Hunt Jr., N. M. Johnston

CCPO Publications

The determinants of the structure, functioning and resilience of pelagic ecosystems across most of the polar regions are not well known. Improved understanding is essential for assessing the value of biodiversity and predicting the effects of change (including in biodiversity) on these ecosystems and the services they maintain. Here we focus on the trophic interactions that underpin ecosystem structure, developing comparative analyses of how polar pelagic food webs vary in relation to the environment. We highlight that there is not a singular, generic Arctic or Antarctic pelagic food web, and, although there are characteristic pathways of energy flow dominated by …

Impact Of Model Resolution For On-Shelf Heat Transport Along The West Antarctic Peninsula, Jennifer A. Graham, Michael S. Dinniman, John M. Klinck

CCPO Publications

The flux of warm deep water onto Antarctic continental shelves plays a vital role in determining water mass properties adjacent to the continent. A regional model, with two different grid resolutions, has been used to simulate ocean processes along the West Antarctic Peninsula. At both 4 km and 1.5 km resolution, the model reproduces the locations of warm intrusions, as shown through comparison with observations from instrumented seals. However, the 1.5 km simulation shows greater on-shelf heat transport, leading to improved representation of heat content on the shelf. This increased heat transport is associated with increased eddy activity, both at …

Abstractions And Analyses Of Grid Games, Taylor Rowan Boone

Senior Projects Spring 2016

In this paper, we define various combinatorial games derived from the NQueens Puzzle and scrutinize them, particularly the Knights Game, using combinatorial game theory and graph theory. The major result of the paper is an original method for determining who wins the Knights Game merely from the board's dimensions. We also inspect the Knights Game's structural similarities to the Knight's Tour and the Bishops Game, and provide some historical background and real-world applications of the material.

Analyzing Unique-Matching Games Using Elementary Mathematics, Calvin Jongsma, Tom Clark

Faculty Work Comprehensive List

We present here an analysis of the game of Spot It! that can be used as background information for the purpose of leading a math circle around the game. The presentation here follows the progression of solving the puzzle for simple cases first and culminating in the solution of the original game.

Systematic Errors In Intro Lab Video Analysis, John Zwart, Kayt E. Frisch, Tim Martin

Faculty Work Comprehensive List

In video analysis lab experiments, students frequently find large discrepancies between results based on self-filmed videos and expected values (e.g. for g determined by a fit to projectile motion data). These differences are frequently far larger than the uncertainty calculated from their fit. Using an inexpensive point-and-shoot camera with a 4x optical zoom to record video, we investigated two possible causes of this error: the effect of placing the reference meter stick at a different object-to-camera distance and the effect of the motion of interest being in a plane not perpendicular to the camera lens. When we observed these phenomena …

Interactively Cutting And Constraining Vertices In Meshes Using Augmented Matrices, Yu-Hong Yeung, Jessica Crouch, Alex Pothen

Computer Science Faculty Publications

We present a finite-element solution method that is well suited for interactive simulations of cutting meshes in the regime of linear elastic models. Our approach features fast updates to the solution of the stiffness system of equations to account for real-time changes in mesh connectivity and boundary conditions. Updates are accomplished by augmenting the stiffness matrix to keep it consistent with changes to the underlying model, without refactoring the matrix at each step of cutting. The initial stiffness matrix and its Cholesky factors are used to implicitly form and solve a Schur complement system using an iterative solver. As changes …

Asymptotic And Optimal Liouville Properties For Wolff Type Integral Systems, John Villavert

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This article examines the properties of positive solutions to fully nonlinear systems of integral equations involving Hardy and Wolff potentials. The first part of the paper establishes an optimal existence result and a Liouville type theorem for the integral systems. Then, the second part examines the decay rates of positive bound states at infinity. In particular, a complete characterization of the asymptotic properties of bounded and decaying solutions is given by showing that such solutions vanish at infinity with two principle rates: the slow decay rates and the fast decay rates. In fact, the two rates can be fully distinguished …

Stability Analysis And Hopf Bifurcation Of Density-Dependent Predator-Prey Systems With Beddington-Deangelis Functional Response, Xin Jiang, Zhikun She, Zhaosheng Feng

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this article, we study a density-dependent predator-prey system with the Beddington-DeAngelis functional response for stability and Hopf bifurcation under certain parametric conditions. We start with the condition of the existence of the unique positive equilibrium, and provide two sufficient conditions for its local stability by the Lyapunov function method and the Routh-Hurwitz criterion, respectively. Then, we establish sufficient conditions for the global stability of the positive equilibrium by proving the non-existence of closed orbits in the first quadrant R²+. Afterwards, we analyze the Hopf bifurcation geometrically by exploring the monotonic property of the trace of the Jacobean matrix with …

The Complete Classification Of Five-Dimensional Dirichlet–Voronoi Polyhedra Of Translational Lattices, Mathieu Dutour Sikiric, Alexey Garber, Achill Schürmann, Clara Waldmann

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper reports on the full classification of Dirichlet–Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110 244 affine types (L-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet–Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181 394 contraction types are obtained. The paper gives details of the computer-assisted enumeration, which was verified by three independent implementations and a topological mass formula check.

Fusion Of Renewable Ring Resonator Lasers And Ultrafast Laser Inscribed Photonic Waveguides, Hengky Chandrahalim, Stephen C. Rand, Xudong Fan

Faculty Publications

We demonstrated the monolithic integration of reusable and wavelength reconfigurable ring resonator lasers and waveguides of arbitrary shapes to out-couple and guide laser emission on the same fused-silica chip. The ring resonator hosts were patterned by a single-mask standard lithography, whereas the waveguides were inscribed in the proximity of the ring resonator by using 3-dimensional femtosecond laser inscription technology. Reusability of the integrated ring resonator – waveguide system was examined by depositing, removing, and re-depositing dye-doped SU-8 solid polymer, SU-8 liquid polymer, and liquid solvent (toluene). The wavelength reconfigurability was validated by employing Rhodamine 6G (R6G) and 3,3′-Diethyloxacarbocyanine iodide (CY3) …

Unequal A Priori Probability Multiple Hypothesis Testing In Space Domain Awareness With The Space Surveillance Telescope, Tyler J. Hardy, Stephen C. Cain, Travis F. Blake

Faculty Publications

This paper investigates the ability to improve Space Domain Awareness (SDA) by increasing the number of detectable Resident Space Objects (RSOs) from space surveillance sensors. With matched filter based techniques, the expected impulse response, or Point Spread Function (PSF), is compared against the received data. In the situation where the images are spatially undersampled, the modeled PSF may not match the received data if the RSO does not fall in the center of the pixel. This aliasing can be accounted for with a Multiple Hypothesis Test (MHT). Previously, proposed MHTs have implemented a test with an equal a priori prior …

Trade-Offs Between Three Forest Ecosystem Services Across The State Of New Hampshire, Usa: Timber, Carbon, And Albedo, David A. Lutz, Elizabeth A. Burakowski, Mackenzie B. Murphy, Mark E. Borsuk

Dartmouth Scholarship

Forests are more frequently being managed to store and sequester carbon for the purposes of climate change mitigation. Generally, this practice involves long-term conservation of intact mature forests and/or reductions in the frequency and intensity of timber harvests. However, incorporating the influence of forest surface albedo often suggests that long rotation lengths may not always be optimal in mitigating climate change in forests characterized by frequent snowfall. To address this, we investigated trade-offs between three ecosystem services: carbon storage, albedo-related radiative forcing, and timber provisioning. We calculated optimal rotation length at 498 diverse Forest Inventory and Analysis forest sites in …

The Pathology Of Command And Control: A Formal Synthesis, Michael Cox

Dartmouth Scholarship

One of the most important theories in the study of environmental governance and policy is the pathology of command and control, which describes the negative consequences of top-down, technocratic governance of social and ecological systems. However, to date, this theory has been expressed somewhat inconsistently and informally in the literature, even by the seminal works that have established its importance and popularized it. This presents a problem for the sustainability science community if it cannot be sure of the precise details of one of its most important theories. Without such precision, applications and tests of various elements of the theory …

Building Resiliency In Response To Sea Level Rise And Recurrent Flooding: Comprehensive Planning In Hampton Roads, Joshua G. Behr, Rafael Diaz, Molly Mitchell

VMASC Publications

[Introduction]

Over the past few decades, the Hampton Roads region, with its extensive coastline, has been experiencing more frequent flooding from surges and precipitation caused by tropical storms, nor’easters and heavy thunderstorms (Figure 1). Recurrent flooding is “flooding that occurs repeatedly in the same area over time due to precipitation events, high tides or storm surge.”¹ The recurrence of tidal/surge flooding in Hampton Roads has increased from 1.7 days of “nuisance” flooding per year in 1960 to 7.3 days per year in 2014.² Although there is no definitive region-wide data to document the increases in precipitation-induced flooding, there …

Signal Velocity In Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. We first derive necessary and sufficient conditions for asymptotic stability, then derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocities c+>0 and c−f(x−c+t) in the direction …

Voxel Based Morphometry In Optical Coherence Tomography: Validation & Core Findings, Bhavna J. Antony, Min Chen, Aaron Carass, Bruno M. Jedynak, Omar Al-Louzi, Sharon D. Solomon, Shiv Saidha, Peter Calabresi, Jerry L. Prince

Mathematics and Statistics Faculty Publications and Presentations

Optical coherence tomography (OCT) of the human retina is now becoming established as an important modality for the detection and tracking of various ocular diseases. Voxel based morphometry (VBM) is a long standing neuroimaging analysis technique that allows for the exploration of the regional differences in the brain. There has been limited work done in developing registration based methods for OCT, which has hampered the advancement of VBM analyses in OCT based population studies. Following on from our recent development of an OCT registration method, we explore the potential benefits of VBM analysis in cohorts of healthy controls (HCs) and …

Vapor Deposited Cr-Doped Zns Thin Films: Towards Optically Pumped Mid-Infrared Waveguide Lasers, Eric A. Karhu, Charles R. Ildstad, Stefano Poggio, Vedran Furtula, Nikolai Tolstik, Irina T. Sorokina, Joseph J. Belbruno, Ursula J. Gibson

Dartmouth Scholarship

Compact, affordable mid-IR lasers require the development of gain materials in waveguide form. We report on the high vacuum deposition of Cr:ZnS films with concentration ranging from 10¹⁸-10²⁰ dopants/cm³ . At low concentrations, films display well-isolated absorption associated with substitutional Cr²⁺ ions in the lattice. Spatial modulation of the dopant concentration suppresses the absorption associated with this substitution. Lateral crystallite sizes less than 30 nm are associated with the lowest substrate temperatures (<50 °C) used during deposition, and waveguide losses as low as 8dB/cm are observed. These materials are promising candidates as gain media for fabrication of waveguide mid-IR lasers.

Accommodating Retrocausality With Free Will, Yakir Aharonov, Eliahu Cohen, Tomer Shushi

Mathematics, Physics, and Computer Science Faculty Articles and Research

Retrocausal models of quantum mechanics add further weight to the conflict between causality and the possible existence of free will. We analyze a simple closed causal loop ensuing from the interaction between two systems with opposing thermodynamic time arrows, such that each system can forecast future events for the other. The loop is avoided by the fact that the choice to abort an event thus forecasted leads to the destruction of the forecaster's past. Physical law therefore enables prophecy of future events only as long as this prophecy is not revealed to a free agent who can otherwise render it …

Mathematical Frameworks For Consciousness, Menas C. Kafatos, Ashok Narasimhan

Mathematics, Physics, and Computer Science Faculty Articles and Research

If Awareness is fundamental in the universe, mathematical frameworks are better suited to reveal its fundamental aspects than physical models. Awareness operates through three fundamental laws which apply at all levels of reality and is characterized by three universal powers. We explore and summarize in general terms mathematical formalisms that may take us as close as possible to conscious awareness, beginning with the primary relationships between the observer with the observed, using a Hilbert space approach. We also examine insights from category theory, and the calculus of indications or laws of forms. Mathematical frameworks as fundamental languages of our interaction …

Exploring Consciousness Through The Qualitative Content Of Equations, Ashok Narasimhan, Menas C. Kafatos

Mathematics, Physics, and Computer Science Faculty Articles and Research

The majority of the focus on equations in physics has been on the mathematical and computational aspects. Here we focus on the qualitative content of what the relationships expressed in equations imply. In some sense, we are asking foundational questions about the ontology of equations.

Regional Variations Of Optimal Sowing Dates Of Maize For The Southwestern U.S., Boksoon Myoung, Seung Hee Kim, Jinwon Kim, Menas Kafatos

Mathematics, Physics, and Computer Science Faculty Articles and Research

Sowing date (SD) is sensitive to regional climate characteristics; thus, it is critical to systematically examine the effects of SD on crop yields for various temperature regimes. We performed a sensitivity study of SD for maize in the southwestern U.S. using the regionally extended version of the Agricultural Production Systems sIMulator (APSIM) model. The model was run utilizing North American Regional Reanalysis at a 32 km resolution from 1991 to 2011, with an irrigation threshold at 95% of the soil water-holding capacity. Two types of SD optimizations maximizing yield potential (Yp), varying spatially or interannually, revealed that the optimal SD …

Sensitivity Of Maize Yield Potential To Regional Climate In The Southwestern U.S., Seung Hee Kim, Boksoon Myoung, David Stack, Jinwon Kim, Menas Kafatos

Mathematics, Physics, and Computer Science Faculty Articles and Research

The sensitivity of maize yields to the regional climate in the Southwestern U.S. (SWUS) has been investigated by using the Agricultural Production Systems sIMulator (APSIM) model in conjunction with meteorological forcings [daily maximum and minimum temperature (Tmax and Tmin), precipitation, and radiation] from the North American Regional Reanalysis (NARR) dataset. Sensitivity experiments showed that potential crop production responded nonlinearly to variations in Tmax, Tmin, and downwelling solar radiation at the surface. Mean annual yield potential (Yp) was changed by -3.0 and 1.79 Mg ha-1 for the +1 and -1 standard deviations (σ) of Tmax variation for entire the SWUS. The …

The Spectral Theorem For Quaternionic Unbounded Normal Operators Based On The S-Spectrum, Daniel Alpay, Fabrizio Colombo, David P. Kimsey

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The fact that the correct notion of …

Characterizations Of Rectangular (Para)-Unitary Rational Functions, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

We here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle:
(i) through the realization matrix of Schur stable systems,
(ii) the Blaschke-Potapov product, which is then employed to introduce an easy-to-use description of all these functions with dimensions and McMillan degree as parameters,
(iii) through the (not necessarily reducible) Matrix Fraction Description (MFD).
In cases (ii) and (iii) the poles of the rational functions involved may be anywhere in the complex plane, but the unit circle (including both zero and infinity). A special attention is devoted to exploring the gap between the …

Wiener Algebra For The Quaternions, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-Lévy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators.