# Student Honors Papers

The Student Honors Papers collection represent exemplary work in physics at Illinois Wesleyan University. The Ames Library is proud to archive these and other honors projects in Digital Commons @ IWU, the University's online archive of student, faculty and staff scholarship and creative activity.

Phase Transitions Occurring in Models of Neighborhood Racial Segregation*by Alexander J. Laurie '03*

This thesis is organized as two chapters whose contents are closely related yet quite distinct. The first chapter presents a paper "Role of 'Vision' in Neighborhood Racial Segregation: A Variant of the Schelling Segregation Model," authored by myself and Dr. Jaggi, which has been accepted for publication by the journal Urban Studies and is currently in press (as of April 2003). This chapter introduces the well-known Schelling model of neighborhood segregation, outlines the sociopolitical motivation for our work, and presents the key results that we believe are of interest to social scientists. Chapter two, which ought to be of greater interest to the physics community, presents the results of our investigations into the parallels between the Schelling model and critical phenomena. Our primary extension of the Schelling model was to include social agents who can authentically 'see' their neighbors up to a distance R, called 'vision'. By exploring the consequences of systematically varying R, we have developed an understanding of how vision interacts with racial preferences and minority concentrations and leads to novel, complex segregation behavior. We have discovered three regimes: an unstable regime, where societies invariably segregate; a stable regime, where integrated societies remain stable; and an intermediate regime where a complex behavior is observed. Since the primary audience of Urban Studies consists of sociologists and economists, we have not elaborated in the first chapter upon the phase transition which was strongly suggested by the "complex behavior" in the intermediate regime. The purpose of chapter two then, is to elucidate these additional physically interesting aspects of our model. Melting is a textbook example of first order (discontinuous) phase transitions. These are marked by two central features: a sharp temperature at which the transition occurs, and the coexistence of the two phases at that melting point. One can study the first-order phase transition that ice undergoes when melting into water by observing the ice while continuously raising its temperature. However, if you were only able to view the system at certain discrete temperatures, you would only see a either a piece of ice or a puddle of water during each observation. Thus in order to study the potential phase transition occurring in our model, we must be able to control the governing parameters continuously. However, in our original 'discrete' model, R measures how far an agent sees from its own home as an integer number of houses. Since we can only assign discrete values to R, it is meaningless to speak of a phase transition occurring as a function of this variable. To overcome the limitations of our first model, we introduce a continuous model in chapter two where the range of vision (denoted R2 for notational clarity) can be varied continuously. This model uses a utility function that assigns greater weight to neighbors nearer an evaluating agent. The function used to model this decrease in utility contribution with distance is an exponentially decaying curve. We control the steepness of this curve (and thereby control the agents' vision) using R2. Since R2 can be set to equal any positive real number, we can indeed study the possible phase transition in our simulations' behavior as the function of a continuous variable. Additionally, the continuous model demonstrates the robustness of the sociologically relevant conclusions drawn in chapter one. Our continuous model, a generalization of a model developed by Wasserman and Yohe (2001), is in fact more realistic than our first model. In particular, we were pleased to discover the same three behavioral regimes and all associated trends in both our discrete model and our continuous model. This confirms that our original results were robust and not merely algorithmic artifacts related to the specific treatment of vision used in our discrete model.

Development of a Data Acquisition and Analysis System*by Michael V. Mores '02*

Plasma is the fourth and least understood state of matter. A more complete understanding of this state of matter has numerous practical applications, including fusion energy, space travel, materials synthesis, and thin film deposition. As such, there is an obvious motivation to study this state. To do this, we have constructed a radio-frequency plasma device at Illinois Wesleyan University. I have developed a data acquisition using LabVIEW software that can digitize eight analog signals, saving the data to disk for later analysis. I have also written analysis software using LabVIEW to extract meaningful information from Langmuir Probe Trace.

Photometry of Outer-belt Objects*by Gautham S. Narayan '05*

We present results from multi-wavelength observations of outer-belt asteroid 279 Thule and comet C12002 CE10 (LINEAR). The orbital elements of the second object, formerly classified as asteroid 2002 CE10, at first led to its identification with a group of asteroids called the Damocloids. The Damocloids' orbits are similar to Halley family comets (HFCs), and there is suspicion that the Damocloids are inactive HFC nuclei. Following observations by the 8.2 m Japanese Subaru telescope in August 2003, which determined that 2002 CE IO had a characteristic tail (Takato et al; 2003), it was re-classified as comet C/2002 CE10 (LINEAR). We observed these and other objects with filters close to the Johnson-Kron-Cousins BVRl filters corresponding to the blue, visible, red, and near-IR wavelengths using the 0.9m SMARTS telescope at Cerro-Tololo Inter-American Observatory during October 2003. Using the image reduction routines (imred) of the Image Reduction and Analysis Facility (NOAO Xl IIIRAF), we removed the bias caused by dark currents, and flat fielded the data to improve the signal-to-noise ratio (SNR). Instrumental magnitudes for all objects were extracted using the aperture photometry package (apphot). Landolt standard stars were used to solve the transformation equations and extract extinction coefficients. Photometric calibration routines (photcaI) allowed us to use the extinction coefficients and instrumental magnitudes to determine magnitudes in the Landolt standard system. We computed absolute magnitudes for 279 Thule and C/2002 CE10 (LINEAR) in the VR bands by correcting for the changing geocentric distance, heliocentric distance, and solar phase of the object. 279 Thule was found to have a mean absolute visual magnitude of 8.66±0.OJ and a V-R color of 0.44±0.03, when corrected for solar phase using the standard IAU phase relation (Bowell et al; J989). We discuss the suitability of the standard phase relation for 279 Thule. We place constraints on the size of the objects. We determine the rotation period for 279 Thule to be 7.6±0.5 hrs, using an implementation of the phase dispersion minimization (PDM) algorithm first developed by Stellingwerf (1978). It is likely that observations of C12002 CE lU (LINEAR) have been contaminated by near nucleus coma.

A Novel Technique for Studying the Shear Elastic Properties of Weak Solids*by Jason A. Payne '93*

We have developed a simple, inexpensive, and precise technique to measure the shear elastic modulus of weak solids using electromagnetic and optical tools. This technique can be easily adapted to measure the viscosity of a liquid also. A Helmholtz pair was used to produce a torque on a permanent magnet mounted on the smaller of two concentric cylinders, coupled by the material to be studied. The torque was controlled precisely and measured accurately in terms of the current flowing through the coils of the Helmholtz pair. An optical lever was employed to measure the angular displacement of the inner cylinder as a function of the applied shear stress. The instrument has been validated by making measurements on lemon jello, and agarose gels of varying concentrations. The technique has also been applied to the study of electric field induced "freezing" of electrorheological fluids, a subject of enormous contemporary interest.

Harmonic Oscillation in the Presence of Multiple Damping Forces*by Chris Pelto '97*

The relatively mundane damped harmonic oscillator is found to exhibit interesting motion once under the influence of both a velocity dependent and a Coulombic frictional damping force. Data for the decay of the amplitude as a function of time were collected on a specially prepared torsional oscillator. with a variable electromagnetic damping mechanism. An analytical solution of the appropriate equation of motion was obtained by the method of Laplace transforms. In both the limits of zero Coulombic friction and zero velocity damping, the solution reduces to the well-known answers to the problem. the solution, when plotted with the correct parameters, fits the numerical solution very well. The solution also shows excellent quantitative agreement with the experimental data.