
Photovoltaics: An Investigation into the Origins of Efficiency on All Scales
Jeremy Bannister
This project is comprised of a set of parallel investigations, which share the common motivation of increasing the e ciency of photovoltaics. Firstly, the reader is introduced to core concepts of photovoltaic energy conversion via a semiclassical description of the physical system. Secondly, a key player in photovoltaic e ciency calculations, the exciton, is discussed in greater quantum mechanical detail. The reader will be taken through a numerical derivation of the lowenergy exciton states in various geometries, including a line segment, a circle and a sphere. These numerical calculations are done using Wolfram Mathematica, a computer program which is widely regarded as the goldstandard for computational physics, and the instructions for replicating the calculations are provided. Finally, the reader will be introduced to the experimentation I performed throughout the year, involving the purchasing, assembling and testing of miniature solar cells, culminating in a demonstration of the cosine law of solar incidence. In reading this paper, the reader will begin to gain an understanding of the landscape of photovoltaics and the factors that a↵ect their e ciency, as well as the avenues by which we might hope to achieve an increase in that e ciency in the near future.

Well, It's About Time
Dan Gagne
A clock can be thought of as anything that oscillates with a known and stable
frequency, and is able to count its oscillations. Multivibrators are examples of such a
device. Multivibrators resonate with a calculable resonant frequency, and this frequency
is stable enough to be a standard by which time is kept. Though we assume clocks to be
perfect timekeepers, however, this is not the case. All clocks have imperfections which
lead to variations in timekeeping, and this project will explore the severity of those
imperfections on a multivibrator's timekeeping.

32 Engineering (Columbia U.)
Bill Nguyen

An Exploration of Chaotic Behavior in Electrical Circuits
Ryan O'Connell
This senior project investigates chaotic behavior and controlled chaos in electrical circuits. It primarily focuses on two types of circuits using a varicap diode and an operational amplifier based Chua diode as the nonlinear elements that produce chaotic behavior in the voltage outputs. Attempts to get the circuits to function correctly were not successful, but the project includes a theoretical investigation of the chaotic behavior of the circuits through bifurcations and period doubling, as well as ways this behavior could theoretically be controlled.

Analogy: A Decomposition of Space and Time
D. J. Shoemaker
The written part of this project is divided into two sections, with the first section focusing on the human eye as a biological tool for gathering and processing physical information. The second section strives to provide a model of human vision by utilizing Fourier Analysis. Out of this model came a focus on Fourier Analysis as not only a model, but as a methodology that can be applied in a variety of ways. The Fourier methodology provided a conceptual bridge that allowed me to more thoroughly explore art, physics, and how these two fields can contribute to each other.

Gaussian Cosmology: A New Model for the Accelerated Expansion of the Universe
Brian Strigel
In this paper I lay the groundwork for an alternative model for the contemporary expansion of the universe. The current model states that the universe is growing exponentially due to the vacuum of space pulling on it. This model states that the growth rate of the universe is linear in time. However in 1998, researchers suggested that the expansion rate of the universe is accelerating. This means the universe is expanding logarithmically, not linearly. In my model, I lay the groundwork for future research and suggest that the universe develops in time in accordance to a Gaussian scale factor and gives a contemporary inflation. This theoretical change has many consequences. It may seem that the universe should continue to expand at an accelerating rate forever; however, my paper suggests that after expanding the universe will eventually slow, stop, and reverse, and compress back into a single point after expanding. Second, my paper claims that the scalar field driven by dark energy is the causal mechanism for the universe’s inflation. This scalar field is homogeneous and grows linearly in time. Finally, my paper claims that primordial inflation fits within my model, as it can predict CMB temperature fluctuations. My model challenges the theory that vacuum energy drives the universe’s current expansion and that quantum perturbations drive primordial inflation.

Quantized Conductance in Transport Experiments: The LandauerBüttiker Perspective
Clark Travaglini
Graphene is a singleatom thick allotrope of carbon that has earned an enormous amount of interest in condensed matter physics due to its unique properties. These properties are studied in the context of electronic transport, which has a rich tradition of interplay between theoretical predictions and concrete experiments. In this thesis we discuss various models that are used to model transport behavior, with a strong emphasis on the LandauerBüttiker formalism. We describe a proposed transport experiment to measure the quantum Hall effect in a hybrid graphene system and discuss fabrication and measurement techniques. We conclude the thesis by presenting an analysis of experimental results we observed while attempting these measurements.

Midlatitude Storm Dynamics: Testing the Eady Model
Maya Weingrod Sandor
The midlatitude storm track, approximately 3070 degrees north or south latitude, is where the majority of longlasting storms happen on earth. The Eady model was developed to predict the behavior of these storms. Although the Eady model yields mathematically solvable solutions, it does so by making simplifying assumptions that may not match well to real storms. My project analyzes winter storms in the northern midlatitudes from January 1958 to December 2001 to test the accuracy of the Eady model at predicting midlatitude storm behavior.

Construction of a Nuclear Shell Model
Emily Conant, Ph.D. Student (Texas A&M, Physics)
Nuclear experimental data has suggested that like electrons, nuclei are arranged in shells. Developed by Maria Goeppert Mayer and J. Hans D. Jensen, the nuclear shell model is a phenomenological model, which uses shell closure as an explanation for the unique stability that occurs when the nucleon number is equal to: 2, 8, 20, 28, 50, 82, and 126. Nuclei are spinhalf fermions that exhibit wave behavior and are thus treated quantum mechanically. In this thesis, we analytically solve the Schrödinger equation in onedimension, twodimensions and three dimensions for an infinite square well and harmonic oscillator potential to acquire the proper tools needed to tackle a more complicated problem. We then implement a more accurate mean field potential for nuclei, known as the WoodsSaxon potential, which must be solved numerically. We transform this continuous secondorder differential equation into a difference equation, which approximates the second derivative by a quartic fit method and calculates the curvature of points in space. We build a computational model that calculates the energy eigenvalues for a specific nucleus and incorporates the spinorbit interaction, which is responsible for energy level splitting. We construct an energy level diagram, experiment with different values for the proportionality factor in the spinorbit interaction, and use the factors that produce the most optimal scheme, thus allowing us to derive the magic numbers. We speculate about the possibility of a new magic number as well as evaluate the strengths and weaknesses of the nuclear shell model.

Effects of Atmospheric Thermodynamics on Satellite Rain Detection
Michael DiRosa
The goal of this thesis is to provide a better analysis framework towards understanding the effects of thermodynamic variables of the atmosphere on satellite precipitation detection. Satellite precipitation data from the Global Precipitation Measurement mission (GPM) is compared with concurrent data from the National Mosaic and Qualitative Precipitation Estimate system (NMQ). The need for improvement in satellite precipitation detection comes from a dearth in extremee weather forecasting throughout impoverished and developing parts of the world, as well as oceans and places of scarce coverage. The Global Precipitation Measurement mission, which launched in February 2014, holds much promise in providing near worldwide coverage. GPM uses a microwave radiometer as well as a dual frequency radar to detect precipitation, while NMQ uses a bevy of ground based radars and rain gauges. The imprecisions of GPM's microwave radiometer are tested against surface temperature and relative humidity measurements in the Poughkeepsie, NY area. This analysis structure is developed to be able to find dependence between poor correlation of the two datasets (NMQ and GPM) and the thermodynamic environment of the present atmosphere.

Concept and Application of a VerticalAxis Wind Turbine
Leo Kaupert
Wind power is one of the most appealing shortterm solutions to the evergrowing energy crisis, seeing as much of the infrastructure for this technology is already in place. This enterprise currently places an emphasis on horizontalaxis wind turbines, but are they really the most efficient kind? Certain aspects of verticalaxis turbine design show promise over the traditional horizontal design, however, this technology has not been explored nearly enough to know if it is viable for commercial use. In this project I designed and constructed a prototype wind turbine of the vertical design. I tested the efficiency of the design for converting wind energy into electrical power. The results for these tests are presented in the thesis, and the lessons learned through the investigation, concerning what works and what does not, will hopefully provide insight for future improvements of verticalaxis wind turbine technology.

Photoconductivity of Graphene in a Magnetic Field
Trevor LaMountain, Ph.D. Student (Northwestern U., Applied Physics)
Graphene is a singleatomthick allotrope of carbon that displays a variety of novel physical behavior due to its geometry. Graphene is referred to as a “twodimensional material’’ since electrons in the material are confined to one atomic plane. This spatial confinement gives graphene its unique properties, which are both interesting from a purely scientific position and promising for technological applications. A better understanding of graphene’s electronic and optoelectronic properties helps shed light on the physics of this novel material, and informs the development of graphenebased technologies. In this project, we investigate photoresponse of graphene under the influence of high magnetic fields. We seek to better understand the current body knowledge in this field through a review of relevant literature. This body of knowledge is further developed through the nanofabrication of two grapheneonboronnitride devices for a future photoconductivity measurement at the National High Magnetic Field Laboratory. These devices are customdesigned to meet specific requirements and restrictions of the measurement setup.

The Collective Cyclotron Motion of the Relativistic Plasma in Graphene: A Hydrodynamic Study
Andres Martinez de Velasco
Particles in clean graphene have been found to behave as a relativistic electronhole plasma with a certain universal, quantum critical behavior when the dominant parameter of the system is the rate of electronelectron scattering. The high scattering rate allows this plasma to be described through relativistic hydrodynamics. Plasma behavior is expected to occur at a relatively high temperature and small carrier density. The thermoelectric response functions of this system are expected to have a resonant frequency when subjected to small magnetic fields and to an external AC electric field in the microwave frequency range. The magnetic field induces a collective cyclotron motion and the electric field establishes a longitudinal current across the sample. This system is expected to exhibit interesting quantum phase transitions from the Fermiliquid, disorderdominated regime to the quantumcritical, hydrodynamic, relativistic regime. These transitions may be induced through changes in the carrier density which is the critical tuning parameter of this system. At small or large values of carrier density, we expect Fermiliquid behavior and at a critical density value, where the system is close to the particlehole symmetric Dirac point, we expect relativistic plasma behavior. This thesis is an exploration of such a system. It reflects both research in the literature and experimental work. The motivating ideas behind this project are the proposal that the particles in graphene could behave like a relativistic plasma, condensing into a true manybody system with diffusive currents of conserved quantities, as opposed to exhibiting Fermiliquid behavior, determined by noninteracting particles where only those particles at the Fermilevel affect the physics of the system. In addition, this hydrodynamic system offers the opportunity to explore quantum criticality beyond absolute zero temperature and to gain another perspective on the purported universal, materialindependent conductivity which it is thought to display.

Spinor Parallel Transport in Spacetime
Eli Regen, M.S. Student (IIT, Physics)
The four fundamental interactions can be described with modern geometry. Gauge theory says that the three interactions of subatomic physics, the strong force, the weak force, and electromagnetism must exist in order to maintain a symmetry of Lagrangians called local gauge invariance. The fourth interaction, gravity, is different amongst the fundamental interactions because in General Relativity (GR) the geometry of spacetime itself is responsible for the dynamics, while the other three take place in fixed Minkowski spacetime. In GR the paths of test particles are calculated with the geodesic equation employing the LeviCivita connection. Since all massive particles that cause and are affected by gravity are fermions, which are represented by spinors, this project explores the parallel transportation of spinors through spacetime.

Quantum Optical Coherence Tomography Variations with Polarization Sensitivity
Clara Sekowski, M.S. Student (Boston U., Physics)
Quantum optical coherence tomography is a technique used as an improvement on classical optical coherence tomography that takes advantage of the entangled nature of photons to encode information. By spontaneously down converting light and placing a material within an interferometer, one can create a polarizationsensitive spatial map of reflective layers within the sample in addition to measuring the dispersive characteristics of the material in between. While it certainly resembles OCT, the coincidence interferogram differs from normal intensity readings by accessing greater depths with the benefit of zero group velocity dispersion, at twice the resolution. This technique could have a huge impact on bioimaging with further optimization, particularly with cancer detection. Apart from being scientifically sneaky, the noninvasiveness makes QOCT an attractive model for understanding the ways light interacts with matter and what it can tell us about its' nature. This paper seeks to understand the improvements that QOCT makes upon traditional bioimaging techniques on a fundamental level.

A Study of Charge Transport Properties of SingleMolecule Junctions using Density Functional Theory
Ingrid Stolt, Ph.D. Student (Northwestern U., Physics)
Density functional theory (DFT) is a computational method for modeling multielectron systems, such as atoms and molecules, using a quantum mechanical approach. Here we use DFT to investigate the relationship between electronic structure and charge transport in an organic compound known as 4,4’bipyridine (BPD) when it is held between conducting metal leads to form a metalmoleculemetal junction. It has been shown that when a very small voltage is applied across such a system BPD can act as a functional circuit element in that it allows a current to flow through the junction. The electronic behavior of BPD nanojunctions formed with gold (Au) electrodes has been widely investigated and is relatively well known; however, the conductance properties of BPD junctions formed with other metals have not been studied in detail. Therefore, the goal of this project is to determine the charge transport characteristics of BPD junctions when alternative metals, such as aluminum (Al), are used as leads. The dependence of the system conductance on electrode identity is discussed.

Constructing the Quantum Steering Ellipsoid Using State Measurement of Biphotons
Carter Vanderbilt
This paper investigates a recently discovered geometric representation of twoqubit states, the Quantum Steering Ellipsoid, by taking quantum state measurements on pairs of polarizationentangled photons produced using spontaneous parametric down conversion (SPDC). Measurements of the signal photon that are conditioned on observations of the idler photon demonstrate all possible Bloch Vectors that the signal photon can be collapsed to by way of "steering," which is only possible due to the nonlocal nature of entangled systems. Using these data, we experimentally verify the Quantum Steering Ellipsoid and its potential uses for analyzing entanglement as a geometric classification of quantum states.

Cloudgazing: A Phenomenological Methodology
Daniel Waldo
The aim of this project was, first, to provisionally circumscribe the domain of knowable things, and second, to do science within those boundaries. In the first half, the project begins by examining the conceptions of science presented by various authors, including Francis Bacon, Edmund Husserl, and Michio Kaku. Using these resources, it sketches an epistemology based in, and not exceeding, experience. In order to tie this epistemology to a method of scientific practice, it surveys ethics, which is the domain of actions. Finally, a scientific methodology is proposed which does not conflict with the epistemology or ethics. In the second half, this methodology is demonstrated using for its example nephology, the study of clouds. Various exercises are proposed with an eye toward educating the reader on clouds and many of the phenomena associated with them.

Observation and Recollection: Reconstructing Michael Faraday’s Discovery of Electromagnetic Induction
Charlotte Ames
Michael Faraday is well known in physics for his vivid experiments and public demonstrations still used today as well as work which is credited with leading to the emergence of field theory. His lack of a formal education led him to design experiments and lectures focused only on qualitative observation and careful manipulation of natural phenomena, and his methods of collecting data and documenting his theories have allowed his peers, and us, full view into his work. This project seeks to reconstruct Faraday’s famous iron ring induction experiment by exploring the scientific historical context, the multitude of documents he left, and a recreation of the experiment while applying a modern understanding of electrodynamics. An analysis of the interaction of these elements reveals the historic and scientific significance in contrast with popular understanding.

The Hofstadter Butterfly and IR Spectroscopy of High Mobility Graphene
Eames Bennett, Ph.D. Student (Texas A&M, Physics)
Graphene is an atomicallythin sheet of carbon atoms with a hexagonal lattice structure. The material's remarkable electronic properties make it ideal for testing the physics of mescoscopic systems in two dimensions. Known as a zero bandgap semiconductor, graphene displays a characteristic linear dispersion relation at low energies. Two sheets of graphene stacked together, referred to as bilayer graphene, exhibit a second, unique hyperbolic dispersion relation. These electronic characteristics produce quantum effects that differ dramatically from their threedimensional counterparts.
In this thesis we present the foundational theory behind lowdimensional semiconductors and graphene as well as preliminary results of research on highmobility bilayer graphene. The initial goal for this research was to directly measure Landau level transitions using Fourier Transform Infrared (FTIR) spectroscopy. While the device was too small to detect signal from FTIR spectroscopy, we found the device exhibited a selfsimilar recursive energy spectrum characteristic of interference from a moiré superlattice. Known as Hofstadter's butterfly, this recursive energy spectrum is one of the first fractals attributable to quantum effects. We analyze the resulting transport data and verify the Hofstadter spectrum in bilayer graphene.

Representation Theory and Its Application in Particle Physics
Yan Chu, Ph.D. Student (Duke, Mathematics)
The Lagrangian is an essential tool in the formulation of many physical theories. On the subatomic level the Lagrangian for fundamental particles is known to be symmetric under certain gauge transformations. Such transformations can be described by special unitary groups. In this project I study the representation of these groups and their associated algebras and extend them to a hypothetical tetraquark system, whose existence was recently confirmed by research conducted at the Large Hadron Collider. My results include the calculation of all the possible states for the tetraquark system in their fourfold product representation and their classification into 9 multiplets.

Quantum Hall Effect in Hybrid Graphene
Gavin Myers, Ph.D. Student (Boston College, Physics)
This research is an investigation of a twodimensional electronic effect in connected one and twoatomsthick carbon sheets, known as hybrid graphene. In particular, the phenomenon studied is known as the quantum Hall effect, which describes the unusual motion of electrons in twodimensional materials when placed in a magnetic field, and gives rise to quantized electrical resistance. An extensive nanofabrication process was used to produce a microcircuit which would allow for various different connections to the sample for testing. Hybrid graphene was measured at magnetic fields strengths up to 9 Tesla (about 2,000 times stronger than the average refrigerator magnet), at a temperature 1.4 degrees above absolute zero, both necessary conditions for resolving such a fragile effect. While rather extensive research has previously been done on the quantum Hall effect on homogeneous oneatomthick graphene, the addition of a twolayer region, however small, introduces a novel and notable effect on the way the system responds to the magnetic field.

Fabrication and Characterization of GrapheneBoron Nitride van der Waals Heterostructure
Min Kyung Shinn, Ph.D. Student (Washington U. of St. Louis, Physics)
In an effort to measure the electronic transport properties of hybrid graphene, a combination one and twolayer thick carbon lattice, we have constructed van der Waals heterostructures by layering hexagonal boron nitride (hBN) and hybride graphene. The development of the quantum Hall effect of hybrid graphene is impeded by its usual substrate silicon dioxide, and the new BN substrate allows us to observe the effect more clearly. The electronic properties measurement of the heterostructure at low temperature and high magnetic field, up to 9 T, yielded improved quality of the quantum Hall resistance data. As the visibility of graphene is compromised with the new BN substrate, the second part of this project is to investigate spectroscopic methods to locate graphene using a home built Raman microscope.

A Model of Charge Transport in a DyeSensitized Solar Cell
Emily Carlson, Postbaccalaureate Fellow (American Museum of Natural History)
Renewable energy sources continue to play a crucial role in the conversation about global warming and alternate energy sources. Solar cells are widely recognized as a promising energy source, and photovoltaic solar cells (PV) are the most commonly used type of solar cell. However, dyesensitized solar cells (DSSC) can be produced at a lower cost and have several other attributes that make them a favorable alternative to simple PV solar cells. This paper will discuss the physics behind PV and DSSC as well as the differential equations which describe the movement of charge carrier concentration called transport equations. These transport equations for a DSSC form a system of ODEs, which we reduce to one equation by making linear approximations of two of the species concentrations. Newton’s Shooting Method and RungeKutta are used in order to numerically solve these transport equations.

The Deformation of a ZnSn Alloy
Kierstin Daviau, Ph.D. Student (Yale U., Geophysics)
The deeper you journey towards the center of planet Earth the more mysteries you find. The structure of the inner Earth in not yet known in detail and the reasons behind this perceived structure are even more elusive. This paper considers the torsional deformation properties of a crystalline ZnSn alloy as a standin for the Fe material predicted to make up Earth's inner core. I will first acquaint the reader with the reasons to pursue this investigation, then arm them with an arsenal of background information to clarify the physics behind it. I will then discuss a simplified model of the possible deformations the ZnSn crystal could undergo and finish with a description of the deformation experiment being done at Bard College at Simon's Rock.

Directional Quorum Sensing and Hydrogel Diffusion Studies Within Microfluidic Devices
Jose Falla, Ph.D. Student (U. of Colorado, Chemistry)
Microfluidic devices have emerged as a novel technique for studies in the micro to femto liter range, with applications in cellular biophysics, microbial behavior and molecular biology. These devices have aided our investigation of directional quorum sensing between E. coli. The E. coli have been transformed into a set containing the LuxI gene, which codes for the production of Acyl Homoserine Lactone (AHL), and a set containing the LuxR gene, which upon detection of AHL increases Green Fluorescent Protein (GFP) production. These sets of bacteria have been encapsulated in a photopolymerized hydrogel within a microfluidic device where the creation of directional flow is possible. It is yet unclear whether communication between hydrogelentrapped E. coli is possible within a microfluidic device. Current efforts are directed towards the optimization of the photolithographic techniques and cell viability within the hydrogel and microfluidic device, as well as understanding diffusion and transport through the hydrogel, experimentally and through mathematical models.

Acoustic Analysis of Gamelan Bars
Sun Bin Kim
A study of the metallophones of the Balinese gamelan gong kebyar is described here, in which the relationship between their acoustic properties and their sense of pitch are investigated. First, acoustic recordings of the gamelan metallophones were made to analyze their spectral qualities—specifically, the ratios of overtone frequencies to the fundamental and their relative amplitudes. To compare the measured values to theoretical predictions, physical measurements of one of these instruments were also made, the dimensions of the bars supplying values for the frequency equation for transverse waves in a bar.
Results showed that the gamelan metallophones have a distribution of overtones close to that predicted for transverse waves in a straight solid bar, with ratios similar to those in a western glockenspiel. Since the modes of vibrations form nonharmonic overtones and thus do not provide “support” to the fundamental pitch as in a string or a pipe, pitch in gamelan metallophones must be reinforced by other means. Two properties are hypothesized to work in tandem: amplification by bamboo resonators underneath each bar, and the Balinese practice of pairing instruments detuned from each other in such a way that the two pitches are perceived as one (the socalled “chorus effect”).
To test these factors, additional recordings were made in which, respectively, the resonators were covered with felt, and the two paired instruments were played simultaneously. Results showed that resonators significantly strengthen the fundamental pitch, particularly in the metallophones struck with hard mallets. Spectral analysis of the paired recordings reveal that the two “peaks” from the fundamental of each member actually merge into one, with the result that the listener hears one “averaged” pitch with shimmering interference beats that enrich the overall timbre.

Frustrated Total Internal Reflection of Microwaves
Andres Medina, B.S. Student (Columbia U., Electrical Engineering)
At the interface between two different dielectric media, waves generally undergo reflection and refraction. However, for sufficiently large angles of incidence, transmission of a wave into the medium of greater speed of propagation will be completely suppressed. Instead, total internal reflection (TIR) takes place. In this case, the transmitted wave is replaced by an evanescent wave that decays exponentially with increasing distance from the interface. The aim of this project is to investigate the evanescent wave, using a microwave setup. Starting from Maxwell’s equations in a dielectric material, we analyze the reflection and transmission of electromagnetic waves at a boundary, and obtain a theoretical description of the evanescent microwave field near the surface of the medium. To investigate this phenomenon experimentally, we built a set of circular prisms from polyethylene sheets, and devised a setup to verify the existence of the evanescent wave, and to measure its range and properties.

Two Dimensional Shape Reconstruction By Optical Diffuse Imaging Using Monte Carlo
Jose Mendez, B.S. Student (Columbia U., Mechanical Engineering)
The project involves a simulated optics designed relating the light phenomena of diffusion and scattering. The purpose of this project is to investigate a simple method that can simulate and reconstruct a two dimensional image from diffuse scattering off of an unknown object in a medium. By analyzing the light diffusion properties, I want to track the paths of the photons from specific boundary conditions that will be determined depending the medium and possible scattering objects. Using a Monte Carlo simulation program done in Matlab language, I approximate the random walks in which the photons undergo in passing through a medium. As a result of this method, I obtain data sets relating the “weight” or intensity of the photons after scattering. The aim is to describe any modifications in the photons’ distribution due to interaction with a barrier by studying the relationship of the intensity with respect to the exiting position.

Supersymmetry and NonRelativistic Quantum Mechanics
Mark Neznansky, MSc Student (Bernstein Center, Berlin, Computational Neuroscience)
Elementary particles are classified according to their spin either as bosons, obeying BoseEinstein statistics, or as fermions, obeying FermiDirac statistics. In quantum mechanics, the Schrödinger equation describes the nonrelativistic evolution of a boson, and the KleinGordon equation is an analogous relativistic formulation. The Dirac equation describes the evolution of a fermion while also obeying special relativity, and the LévyLeblond equation is its adaptation to nonrelativistic settings. Although the two kinds of particles behave very differently, there’s a proposed symmetry that associates pairs of bosons and fermions differing only in their spin, called supersymmetry.
In this project we introduce the idea of supersymmetry and the mathematical tools it had engendered. We begin with a method to factorize the onedimensional timeindependent Schrödinger equation, and obtain a symmetry between pairs of Hamiltonian operators with matching spectra. After looking at a supersymmetric description of harmonic oscillations, we construct and present the Lie algebraic structure of the symmetries that leave the solutions of the time dependent freeparticle Schrödinger and LévyLeblond equations in one spatial dimension invariant. We then construct a d+s “superspace” combining d spacetime dimensions and s anticommuting dimensions, and introduce a single supersymmetric superfield in the 2+2 dimensional superspace from which both fermionic and bosonic equations of motions can be extracted. Lastly, we show that using a Fourier transformation the symmetry group of the nonrelativistic equations can be extended to represent the symmetries of the relativistic threedimensional bosonic and fermionic fields obeying the KleinGordon and Dirac equations for a free massless particle, while the supersymmetric algebra can be extended to the quite extensive algebra behind the massless relativistic superfield in a 3+2 dimensional superspace.

Convective Available Potential Energy Through the Years and Above Southwestern Oklahoma
Nolan Reece
Global warming is a term that refers to the humaninduced alterations of weather patterns resulting from an increase in the Earth's atmospheric temperature. A possible consequence of such an increase is the likelihood of instability in the atmosphere, and thus for severe weather. The Convective Available Potential Energy (CAPE) of a region in the sky is a reliable indicator of such severe weather. The following is a general analysis of a region of the troposphere above southwestern Oklahoma over 40 years. Data has been taken from the four previous decades during the months of March through June, the height of tornado season, over roughly 100 square miles of a region notorious for its tornadic activity. The results will show if there is any upward or downward trend of CAPE during the time in which Global Warming has become a relevant concern.

Electronic Transport in Graphene: Measuring the Integer Quantum Hall Effect in LargeArea, Monolayer Samples
Jonah Richard, B.S. Student (Columbia U., Chemical Engineering)
Graphene, a recently discovered allotrope of carbon, is the first purely twodimensional material to be experimentally isolated to date. It possesses unprecedented electrical, mechanical, optical and thermal properties, providing boundless opportunities for environmental and technological applications; thinner than paper, stronger than steel, lighter than a feather, more conductive than copper and practically invisible, graphene has been deemed a wonder material. Even a decade after its isolation, it continues to fascinate the scientific world. Confining a material to two dimensions imposes certain restrictions on electronic transport that stimulate unconventional properties; in graphene, these qualities are revealed through, and explained by, its function as a zerogap semiconductor with massless Dirac fermions as charge carriers. This thesis investigates the curious electronic properties expressed by this new material in both a theoretical and experimental manner; a theoretical framework is provided with the purpose of providing a basis for understanding how graphene's electronic properties can be determined experimentally via the integer quantum Hall effect (IQHE). A measurement of the IQHE is then conducted and acts to supplement the theories originally presented. The data obtained through the quantum Hall measurement demonstrates signs of the quantized resistance/conductance characteristic of the IQHE, but does not manifest the entirety of the expected results. Experimental methods, including fabrication process and initial laboratory setup, are explained, along with a discussion of the experimental results and possible reasons for the data's deviation from original predictions.

An Exploration of Window Films: Optical and Thermal Properties
Frank Stortini, MAT Student (Bard)
A window film is a mylar based foil designed to stabilize the temperature within a room by altering the flux of visible light and infrared radiation through the window thereby reducing heating and cooling costs. This project reviews key mathematical equations behind the physics of black body radiation and develops experimental methods for testing the effectiveness of window films. Two identical thermally insulated boxes featuring a window are constructed and serve as models for buildings. These boxes are then used to perform systematic tests to gauge the effectiveness of the window films at rejecting electromagnetic radiation of different wavelengths from the external environment as well as their ability to insulate and prevent radiation from exiting the internal environment through the glass. An analysis of the data in combination with physical characterizations of the material properties of the films reveals differences between various products. In a head to head comparison of two samples, the more expensive film outperforms its counterpart; however, determining which film is better for specific applications to various substrates is not so clear cut.

Electricity in Two Dimensions: Measuring Electrical Interface Effects of Single and Bilayer Graphene
Oliver Switzer, Programmer (HowAboutWe)
Graphene is a twodimensional carbon allotrope that has gained a significant amount of attention in the world of condensed matter physics since its discovery in 2004. Through mechanical exfoliation, it is possible to isolate these one atomthick layers of carbon from bulk graphite. Graphene is one of the few conductive, twodimensional materials that exist today, and is often called a "zerogap semiconductor" because of its unique band structure. Having an unusual dispersion relationship, charges in the material exhibit interesting and drastically different quantum mechanical behavior than what is seen in threedimensional materials.
For this project, electrically coupled monolayer and bilayer graphene devices were fabricated to measure the quantum Hall effect. The focus of this research was centered around measuring the effects of Landau quantization on charge transport through the interface of monolayer and bilayer graphene. While it could not be concluded whether the measured quantum Hall effect corresponded to monolayer or bilayer graphene, the data collected for the monobilayer device exhibited traces of the quantum Hall effect at high magnetic fields in the longitudinal resistance measurements, but did not exhibit these features in the collected data for transverse resistance. These measurements ultimately show that the quantum Hall effect can be observed in hybridized graphene devices.

32 Engineering (Columbia U.)
Jun Tian, MBA Student (Carnegie Mellon)

Sustainable Energy Design: Cutting Energy Consumption Due to Heating
Nadedja Artiomenco, Department Member (New School, Economics)
In an age of increasing concerns over energy consumption and green house gas emission, improving the performance of our built environment in both regards should be a priority. Although buildings account for as much as 45% of global energy consumption, with the resulting carbon emissions substantially more than those in the transportation sector, the importance of buildings in cutting energy consumption and greenhouse gas emissions has been underemphasized and that needs to change if countries are to achieve energy security and manage climate change. While the supply side of the energy equation is an important aspect of sustainable building, with growing opportunities to utilize renewable noncarbon energy sources, the focus of this paper is to scrutinize the sources of energy consumption of buildings during their operation, specifically due to heating demands, and to subsequently explore the potential of direct energy savings.
One way to cut the energy consumption of a building is to reduce the energy cost of heating. This can be achieved by reducing the contributions of the three elements implied in the heating demand of a building: its heat loss coefficient or ‘leakiness,’ the temperature difference between the indoors and the environment, and the inefficiency of the heating system. This paper compares the impact of a more efficient heating system on the energy performance of a building depending on the climate zone, which provides an insight into the significance of locationspecific solutions for the most effective strategy in cutting the energy consumption of a building. The results also show that altering the temperature difference alone can reduce the energy expenditures due to heating dramatically, which becomes even more relevant for an alreadybuilt structure, while the opportunity for reducing the heat loss parameters of the building’s fabric is limited.

An Experimental Investigation of the Directivity of Violin Sound Radiation
Rachel Becker, Student (Violin Making School of America)
An experimental method for measuring the directivity of violin sound radiation is described, along with detailed derivations of the key mathematical and physical concepts involved. The test violin is mounted on a turntable and excited by a mechanical oscillator at a variety of frequencies. A microphone detects the resulting sound, which is processed using the Fast Fourier Transform to isolate individual frequencies. Measurements are taken at many points around the instrument and graphed on a polar plot to visualize the directivity. Theories as to the possible sources of the directivity are discussed.

Supersymmetric Gauge Theory
Ke Cai, Ph.D. Student (U. of Texas, Mathematics)
All elementary particles can be categorized into two kinds (fermions and bosons). Fermions, such as electrons, are the buildingblocks of matter, whereas bosons, such as photons, are usually force carriers that mediate fundamental interactions. Supersymmetry says that every fermion has a corresponding boson, and every boson has a corresponding fermion. Relations between bosons and fermions in a supersymmetric theory are described by operators that we call Q's, which are square roots of derivatives.
In a gauge theory, all physical quantities are invariant under a group of continuous transformations on the system. Gauge theories form the basis of The Standard Model, the currently employed model of particle physics. We study the simplest gauge theory, electricity and magnetism, in the context of supersymmetry in n spatial (n = 3; 2; 1; 0) and one temporal dimensions. The bosons and fermions of our interest are, respectively, photons and their supersymmetric partners, photinos. We show that a supersymmetric gauge theory of photons and photinos does not exist in a world of one spatial and one temporal dimensions.

Measuring Planck’s Constant Using Lightemitting Diodes
Andrew HoffmanPatalona, MAT (Bard)
The goal of this project was to calculate an accurate value of Planck's constant, h, using the principles of how lightemitting diodes work. After a simple working device was built, I made a more substantial apparatus to help Modern Physics students replicate the same experiment in the future. The experiment itself revolves around what is known about diodes, LEDs, and electron energies to compare the threshold voltage of an LED to the energy of the diode's band gap. Measurements of the band gap, and thus the emitted photon energy, for a series of different colored LEDs then provides a measurement for h. In this paper, I will explain the relevant concepts and theory behind diodes and LEDs, take the reader through the procedure, and describe how I came to my conclusions, as well as the difficulties and snags I faced involving the experiment. A description of the actual device to replicate the experiment is included, as well as instructions on how students can use it effectively.

An Exploration of Various Topics of Mechanics, Motors, Motor Control
Anirban Joy, Physicist (1st Detect Mass Spectrometers)
The project started with the aim of designing a dynamically stabilized bicycle. Experiments were carried out, based on a seminal paper on bicycle stability by David E.H. Jones. Two extension springs were attached to the ends of the handle bar of a bicycle. THz bicycle was pedaled up to a certain speed and both the springs were pulled to a certain extent. Each spring can now apply force in only one direction; if the right hand spring is pulled, the handle bar is pulled right, if the left had sprig is pulled, the handle bar is pulled left. The direction of the torques was noticed when the bicycle is going on a straight line, turning, or leaning. The forces on the bicycle were compared with the forces suggested by Jones. Finally, a flow chart was drawn.

Quantum Codes and Computation
Sankalpa Khadka, Neurology Lab Technician (Yale U.)
In 1982, Richard Feynman first suggested that in order to simulate quantum mechanical system one needs quantum computer. In classical computer, data are store in the form of binary digits called bits. In quantum computer, information is stored in the form of quantum bit or qubit which lives in two dimensional complex vector space. Similarly, a classical computer uses logical gates to manipulate bits. Quantum analog of classical gates are unitary transformations which manipulate qubits.
The project presents quantum codes and computation process for error correction and quantum algorithms. The project focuses especially on Deutsch's algorithm which was proposed by David Deutsch in 1985 as an example of quantum algorithm that is significantly faster than classical algorithm for a system involving single qubit. Deutsch's Problem determines whether a function is contanst or not for a single qubit system. The project extends Deutsch's algorithm for multiple qubits and explores properties of various unitary tranformations and information they encode.

Electron Scattering in Crossed Electric and Magnetic Fields: A Semiclassical Study
Alexandros Fragkopoulos, Ph.D. Student (Georgia Tech, Physics)
We studied the classical and quantum dynamics of electrons emitted from a point source into a twodimensional layer subject to perpendicular homogeneous electric and magnetic fields. We solved the classical problem and found that individual trajectories feature a simple combination of drift and circular motion. However, a more complicated picture arises if one examines whole fields of trajectories emitted from a range of angles. Trajectories trace out a set of caustics that confine the classical motion as well as a series of focal points, images of the source. In general, electrons travel on several different paths from the source to a given destination. We use numerical methods to establish these paths.
In the quantum picture, the electrons propagate as waves. We construct an approximate quantum solution by means of the semiclassical method, and assign a wave to each classical trajectory. Interference of the individual waves modifies the classical distribution of the electrons and their associated electric current. We developed software that computes the semiclassical wavefunction and generates images of the current density for different strengths of the electric and magnetic fields. Using a related method, we estimate the total current emitted by the source.
A quantum mechanical calculation asserts that the total current is exponentially suppressed for an extended set of parameters. This surprising prediction is confirmed by the semiclassical study; our simulations show almost complete destructive interference of the electron waves everywhere in the plane of motion. This result may be relevant for the unusual behavior of charges observed in the Quantum Hall Effect.

Identification of Magnetic Activity from Solar Spectral Analysis
Leandra Merola, Salesperson (Skygroup Realty)
For this project I looked at the Ca II K spectral line to better understand the magnetic fluctuations within the sun. While the sun radiates a broad spectrum of energy, elements within the sun absorb and emit very specific wavelengths of energy as the electrons in that element are excited. Knowledge of the properties of different elements and the spectral or absorption lines they form within the electromagnetic radiation spectrum allows for studies of spectral lines that appear when looking at the radiation spectrum of the sun. I first learned about the atomic properties that cause the formation of absorption lines and was then able to compare properties of a specific spectral line of calcium with the solar cycle. The solar cycle is an elevenyear cycle that corresponds to a change in the number of sunspots and magnetic activity on the sun. I found that certain properties of the Ca II K line were correlated with the solar cycle. This study was conducted alongside intense research to better my understanding of what is known about the sun and how it works.

MUSCLE: A Simulation Toolkit Modeling Low Energy Muon Beam Transport in Crystals
Nazmus Saquib, M.S. (U. of Utah, Computational Engineering & Science), Ph.D. Student (MIT, Media Lab)
The project involves the development of MUSCLE (MUonS Cascade at Low Energy), a collection of programs written in C++ and Mathematica to numerically simulate the passage of low energy muon beams through crystals. Monte Carlo methods employing binary collision approximation calculations and appropriate molecular dynamics algorithms are implemented to construct the trajectories and determine the spatial distribution of stopped muons in single crystals. Channeling of muon particles along certain crystal planes are also found. Binary collision approximation and molecular dynamics algorithms are compared and the possible effect of channeling is discussed.

A Mathematical Exploration of Lowdimensional Black Holes
Abigail Stevens, MSc (U. of Alberta, Physics), Ph.D. Student (U. of Amsterdam, Astronomy)
In this paper we will be mathematically exploring lowdimensional gravitational physics and, more specifically, what it tells us about lowdimensional black holes and if there exists a Schwarzschild solution to Einstein's field equation in 2+1 dimensions. We will be starting with an existing solution in 3+1 dimensions, and then reconstructing the classical and relativistic arguments for 2+1 dimensions. Our conclusion is that in 2+1 dimensions, the Schwarzschild solution to Einstein's field equation is nonsingular, and therefore it does not yield a black hole. While we still arrive at conic orbits, the relationship between Minkowskilike and Newtonian forces, energies, and geodesics in 2+1 dimensions is different than the relationship between Schwarzschild and Newtonian forces, energies, and geodesics in 3+1 dimensions.

Aeroelasticity and Vibration of Composite Aircraft Wings: Transverse Oscillation of Composite Wings Modeled as Simple Beams
Paulos Ashebir, Ph.D. (UC Irvine, Transportation Science)
Poised to succeed the traditional use of metals like aluminum for aircraft bodies, composite materials have been making a profound impact in the aerospace industry. Carbon Fiber Reinforced Plastics (CFRP), which are preferred for their ideal strength to weight ratio, are composites widely used in structural components of large passenger carriers such as the new Airbus A380 and the Boeing 787.
In light of the aerospace industry’s pressing concern on safety, stability and control, this study aims to address key issues concerning the vibration, aeroelasticity, and flutter of composite material aircraft wings. This will be done by investigating the vibration characteristics of aircraft wings modeled as simple beams. Solutions for transverse vibration modes and frequencies of these simple beams are evaluated analytically and numerically using computational tools. The solutions that model the vibration of simple beams are then expanded to approximate the vibration characteristics of a Boeing 7878 wing. A similar study, prepared for NASA’s Marshall Space Flight Center, is used to compare vibration characteristics of the retired B57 Canberra’s wing to the Boeing 7878’s wing. The comparison will address the basic assumptions and simplifications made in the simple beam model while suggesting improvements for vibration analysis of composite material aircraft wings. Structural Health Monitoring will also be discussed as part of the new wave of structural engineering studies that have been triggered by the increased application of composite materials in aerospace structures.

32 Engineering (Columbia U.)
Mathias Bahlke, Ph.D. (MIT, Electrical Engineering)

An Exploration of Thermodynamic and Electromagnetic Phenomena in Plasmas
Taposhi Biswas, MAT (Stony Brook), Science & Math Teacher (Cambridge School of Weston)
This project aims to use statistical mechanics and thermodynamics in conjunction with electrodynamics to create a reasonable model of a plasma. The introduction of particle interactions into the ideal gas model seems to produce some difficulties, which we try to resolve in this project. This is primarily done through the use of kinetic theory, and the use of experimentally determined quantities to check the realism of the physics. Some attempts to model the system numerically are also made. These results are then examined, and an intuitive physical explanation for each result is offered.

Sustainable Energy: A Solar Solution
Srijna Jha, M.S. (Humboldt U., Sustainability)
In Fall 2008, The Bard Solar Recharging Station project started as an idea initiated by Laurie Husted, the college's Environmental Resources Auditor. The project would serve two objectives. First, it would raise energy conservation awareness on campus and second, it would use solar panels to provide the electricity for recharging the two electric cars that are used by the Buildings & Grounds and the Security departments at Bard. I was contacted by Laurie about the project, it had my interest immediately and from that email the idea today has evolved to become an ongoing solar charging project in the Ludlow parking lot and these pages of in depth research done over a period of two semesters . It has grown organically, textually and has been revised, rewritten and updated several times before presenting itself.
In this thesis I have defined and explained the underlying physics parallel to the discussion and development of the Bard Recharging Unit (BRU). Furthermore, having taken a central role in the currently ongoing construction and research process and after understanding the mechanism of production of Solar energy first hand, I have discussed strategies and modifications to the design which will lead to a higher productivity/efficiency. The thesis may be useful as a manual to setup future solar recharging stations at Bard. It will give the reader a comprehensive understanding of photovoltaic systems designs and installations by covering all class room, lab and outdoor work.

Planet Building 101: An Introduction on How to Play God
Leila Makdisi, M.A. (U. of Chicago, History & Philosophy of Physics), Mission Specialist (Adler Planetarium)
An investigation into the classical and thermodynamical modeling equations that describe the equilibrium states of gaseous, rocky and liquid planets. The project details the functions which dictate the structure of gas planets using the LaneEmden and Spherical Bessel Equations, specifically for the case of an ideal adiabatic polytrope of n = 1. This is followed by a series of forays into the search for the maximum radius using arguments from the LaneEmden Equation, internal atomic and central pressure constraints, and the equipartition of energies from the Virial Theorem. Comparisons are drawn between the framework of polytropes of solar composition and stellar bodies. This work includes derivations of firstorder solid and liquid models and poses hypothesis as to modeling with regard to layered planetary cores and the addition of atmospheres. Extensions of these theoretical examinations are explored as tools for detailed datafitting models of extrasolar planets.

The Quantum Wheel
Shafat Mubin, Ph.D. Student (Penn State, Physics)
Under the laws of quantum mechanics, a spinning wheel possessing properties analogous to an ordinary classical wheel will undergo phenomena different from the ones predicted by classical physics. The interactions of such a wheel with a potential step and barrier are studied here. The impacts of constant and fluid friction on the wheel are also analysed. Some attempt is made to predict practical analogues of a quantum wheel and the factors which may have significant influence on such models.

An Investigation of Inflationary Cosmology
Marjorie Schillo, Ph.D. (NYU, Physics), Postdoctoral Researcher (KU Leuven)
This project is an investigation of inflationary cosmology. We begin with the background material necessary to build the theory of inflation. Some knowledge of differential geometry and/or general relativity will be necessary to follow all computations. However, we have attempted to present all concepts in a readable manner that does not require much background knowledge. We will define all of the terms that will appear in the Einstein field equation, then use the field equation to find the more utilitarian Friedmann and Einstein equations. From here we will introduce the standard model of cosmology and its shortcomings. These will then serve as the motivation for inflation as a plausible cosmological model. We will discuss the technical requirements of an inflationary epoch, and how different models have been constructed. Finally we propose possible inflationary potentials and discuss the advantages and difficulties of implementing them.

Theoretical Investigations in the Field of Thermoelectricity
Miroslav Stodic
In this work I investigate theories of solidstate physics that explain the two physical effects which underlie the field of thermoelectricity: the Seebeck and Peltier effect: When two slabs of dissimilar metals or semiconductors are joined together at both ends to form a thermocouple, and the two junctions are held at different temperatures, a voltage develops between the two materials. This is the Seebeck effect. Conversely, when an electrical current is driven across one of the thermocouple, heat is either absorbed or released, depending on the direction of the electrical current flow. This is known as the Peltier effect. By harnessing the power of the Seebeck effect, thermoelectric devices can be created which work as thermoelectric power generators, converting heat into electricity. Analogously, the Peltier effect is used for thermoelectric refrigeration, or as a heat pump. Currently, the efficiency of these thermoelectric materials, which in either mode depends on a parameter known as the figureofmerit or ZT, is low, and thermoelectric devices have only found niche applications. Hence, my investigation of the physical mechanisms behind the thermoelectric effects aims at clues how to design thermoelectric materials of higher efficiency. I conclude with a survey of prospective types of thermoelectric materials that are currently actively investigated. Some suggested uses of highefficient thermoelectric materials are the conversion of the waste heat of car engines into useful electrical power, and the cooling of transistors in computers and other electronic devices in order to increase their performance.

Active Noise Control: Me and My Acoustic Shadow
Ani Toncheva, Construction Consultant (Wilson Ihrig & Associates)
Passive methods of noise control, such as sound insulation, are often expensive and ineffective at low frequencies. Alternatively, active methods have been developed since the 1930s, using destructive interference. Until recently, active noise control has dealt with a fairly limited range of noise problems, due to limitations in digital signal processing. Current research shows potential uses for ANC to reduce environmental noise in the free field. A noise source may not be canceled globally with active methods. However, we can design basic systems that attenuate sound over a sufficiently large complaint area. This paper outlines the principles of active noise control in free field and explores some basic examples of ANC systems and these acoustic shadows.

An Investigation into Improving the Efficiency of Solar Cells
Junhao Zhou, Ph.D. Student (U. of Texas, Geosystems & Chemical Engineering)
The first time that human beings used solar collection technology was in the 7th Century B.C. and various techniques have been used ever since. Solar energy is renewable; as long as the sun continues to irradiate, we are able to obtain sunshine on the earth and put it to use. Over the last decade, the use of photovoltaic cells to convert sunlight in to electrical energy has emerged to become an application of recognized potential and has attracted the interest of increasing number of researchers. However, the current solar energy consumption is still very low compared with other forms of energy. In this study, the history of solar technology development is presented with an emphasis on photovoltaics, as the advantages and disadvantages of utilizing solar photovoltaic energy are examined. The physics behind the function of existing photovoltaic cell design and different proposed improved types of photovoltaic cells are looked at closely. Several ways to improve the efficiency of photovoltaic cells are discussed.

Analysis of Heterogeneous Patterns and Social Dynamics in Human Communication
Zhechao Zhou, M.S. (U. of Michigan, Applied Math), M.S. (CUNY, Financial Engineering), Quantitative Researcher (ITG)
Vertex connectivities in complex networks are widely recognized to display a scalefree powerlaw distribution generated by network growth and node preferential attachment. Observation of the powerlaw distribution of tie weights together with the overrepresentation of network motifs in social networks suggests the existence of nontrivial network mechanisms beyond node level. This project investigates the existing social network theories and proposes a stochastic model for weighted scalefree networks in which highweight ties are more likely to grow using continuous random walk as an approach. The model reproduces the observed scalefree weight distributions from a pure dyad perspective and concavity of the distribution curve as the consequence of triad embeddedness. Computer simulations of both processes confirm the theoretical predictions with the statistical analysis of a communication network among millions of individuals. This project, as part of an ongoing NSFfunded social network study, contributes to the dynamic analysis of processes of tie formation, stability and change at the dyad and triad level and leads to a systematic understanding of the fundamental processes and interdependencies underlying social network dynamics that has deep implications in largescale human interaction.

Temperature Dependence of Magnetic Susceptibility in Eu ^{3+} Compounds
Lisa Downward, Ph.D. (UC Santa Cruz, Physics), Analytics Engineer (Lattice Engines)
An attempt was made to characterize the nature of the temperature dependence of the magnetic susceptibility in Eu 3+ compounds. Initial measurements produced perplexing results and led to several design modifications; difficulties involving the accuracy and consistency of measurements had to be overcome. In the end, the magnetic susceptibility of Eu 3+ was obtained in relatively good agreement with literature values, thought he temperature dependence was much smaller than expected. An investigation of the magnetic susceptibility of potassium ferricyanide was also included, though no literature values were available for comparison.

A Numerical Model for the NavierStokes Equation
Ivan Dramaliev, M.S. (UC Santa Cruz, Computer Science), Independent Computer Software Professional
This project is an attempt to study the behavior of fluids. In particular, an attempt was made to build a computer model that would realistically simulate such behavior. Discussed are some properties of fluids associated with the equations that govern fluid dynamics – the NavierStokes equation. A description of the numerical solution is then provided, implemented, and analyzed.

Cello String Dynamics
Amanda Holt, Ph.D. (UC Santa Cruz, Physics), Postdoc (Penn)
The strings used for musical instruments do not behave as ideal elastic oscillators. Internal stiffness, composite materials, means of production, methods of excitation, and boundary condition all affect the sound of a string and may lead to certain kinds of pitch distortion. Cello strings are more prone to distortion than others because of their size and composition. Different distortions were studied experimentally and by computer modeling. Attempts to measure inharmonicity and pitch distortion over time were unsuccessful, but the dynamics of a nonrigid bridge was successfully modeled using Mathematica. Also, quantitative studies were made concerning the difference between light and heavy gauge strings and between two different brands of strings.

Potential Energy Differences between Rotamers in 1,2dihaloethanes
Melanie Pender, Senior Health Information Consultant (WellPoint)
Energy differences between the trans and gauche rotamers of 1,2dibromoethane, 1,2dibromoethaned4, and 1bromo2chloroethane are determined using FTIR spectroscopy. Assignment of trans and gauche absorbance bands are based on literature citations. Gasphase IR spectra, taken over a temperature range from 35ºC to 250ºC at 5ºC intervals yield conformer population ratios. The ratios are plott4ed against inverse temperature to give the energy difference between the conformers in accordance with the Boltzmann distribution law. These energy differences are lower than reported results using a grating IR spectrophotometer. The energy difference between 1,2dibromoethane conformers is (6.74 ± 0.17) kJ/mol while reported values range from 6.07 ) kJ/mol to (7.41 ± 0.63) kJ/mol. The energy difference between the 1bromo2chloroethane conformers is (5.53 ± 0.14) kJ/mol whole reported values range from (6.0 ± 0.4) kJ/mol to (6.11 ± 0.13) kJ/mol. The energy difference between the 1,2dibromoethaned4 conformers is (6.18 ± 0.10) kJ/mol; no previous results have been found for 1,2dibromoethaned4. The differences in experimental and literature values could be due to an unknown compound that contaminated the gauche peaks in all three compounds.

Physical, Physiological, and Neurological Components of Human Touch Reception
Lynne Purvis, Environmental Activist
Beginning with an overview of the physical, physiological, and neurological components of human touch reception and the main tenets of elastic and viscoelastic mechanics, I outline a model of a human finger in contact with a rigid spherical object. I model finger pad skin as an isotropic, homogeneous, dissipative, nonlinear viscoelastic material characterized by a relaxation function and a nonlinear relaxed modulus of elasticity. The elasticity modulus is dependent upon the depth of indentation , which is changing with time. The depth of indentation however is dependent on the elastic modulus of the skin. I solve for the depth of indentation as a function of time for a constant stimulus force, which I found to be: d(τ ) = 3.99 ( 1 – e –20.36 τ ) + 1.78 ( 1 – e –.855 τ ). This allows for solving the stresses and strains within the skin, which may then be used to calculate a neural firing rate from the skin’s touch receptors.