# Section IV: physics, mathematics, computer science, engineering and technology Bailey Science Center, room 1025 Hasson M. Tavossi, presiding.

1:00 DETERMINING THE VALUE OF A VOTE IN THE UNITED STATES UNDER THE ELECTORAL COLLEGE VOTING SYSTEM USING BINARY INTEGER PROGRAMMING, Joseph M. Cauley', Valdosta State University, Valdosta, GA 31698. The Electoral College system in the United States allows for a leader to be elected to the position of president without the support of the majority of the population by a large margin. In this paper we derive the minimum percentage of registered voters required to elect a president by creating a binary integer programming problem to represent the minimum number of registered voters to win the Electoral College. To find this minimum number, we make some reasonable.1:15 THE SUMMATION OF THE FIRST n INTEGER POWERS [m.sup.k], Maximilian J. Wang * and Sudhir Goel, Valdosta State University. Valdosta, GA 31698. In order to find a limit of Riemann sums in calculus courses, it is necessary to find the sums for many problems: [S.sub.k] (n) = [[SIGMA].sub.m=1.sup.m] [m.sup.k] propose a new approach to derive closed form solutions for Sk(n) using linear algebra. It is simple and efficient for any arbitrary positive integer k. Solutions are modeled as a linear system equation. Gaussian Elimination is used to solve this system. The implementation of computer programing is based on the Backward Substitution algorithm.

1:30 ANALYSIS OF REUSING RANDOM NUMBERS, Timothy J. Daniel *. Valdosta State University. Valdosta, GA 31698. Simulation modeling and programming have come to play a major role in the world today. Random number generation is a large part of that role. How costly is creating this randomness? We discuss and analyze an efficient way to create and reuse random numbers. To show the efficiency, we discuss the Floyd's algorithm and how it is used to determine the quality of the random numbers.

2:00 NUMERICAL SOLUTION OF COMPLEX EQUATIONS AND APPLICATION IN ELECTROMAGNETIC WAVE PROBLEM SOLVING, Jayanti R. Saha *, K.C. Chan and A.K. Saha, Albany State University, Albany, GA 31705. In industries and in many physics problems, solutions of complex equations are necessary. In this research, a general form of complex equation: a +ib = (x + iy)n (where, a & b are known, x & y are unknown and n is either an integer, or a fraction or a function) is considered and an algorithm has been developed to solve this generalized complex equation using MATLAB programming language. A method has also been devised to verify the result using commercially available Wolfram Alpha software, which does not provide a direct and generalized result. Finally, the solution technique is applied to determine the electrical property (complex permittivity) of a piece of Teflon block placing in a rectangular waveguide WR284 and exciting with microwave frequencies from 2.6 to 3.95 GHz from a Vector Network Analyzer E5071C. The validity of the algorithm is verified by using Teflon blocks of different sizes and obtaining the same complex permittivity each time as expected. This work is supported by Albany State University Undergraduate Research Program.

2:15 OSCILLATIONS OF A LONG RECTANGULAR BEAM ON TWO PIVOT POINTS. Matthew Roberts and Tom Colbert. Augusta State University, GA 30904. A long rectangular beam is balanced on a block. The beam is given an angular displacement and set into motion which rotates about one edge of the block and then switches to the other edge. The experiment was motivated by observation that such a system changed its oscillation frequency dramatically as the amplitude decreased. To track the motion, a mirror was placed on the beam at the center of mass and used to observe the deflection of a laser spot as the beam oscillated. The spot was recorded using video and tracker analysis tools. We observed the effect of both decay and increasing frequency. The measured decay rate was 56.11942 half cycles. The system has been modeled by using energy conservation to predict the motion of the oscillating beam. The damping takes place each time the beam hits the block and switches over to the alternate pivot point. The model fits the experimental data very well for many oscillations. In the late time, the model diverges from the experiment significantly, suggesting there are additional energy loss mechanisms which are not yet accounted for.

2:30 TRANSIT OF VENUS, JUNE 2012, Amanda Mashburn *, Bob Powell, Robert Moore, Jr. and Victor Pruett, University of West Georgia. Carrollton, GA 30118. A transit of Venus. the passage of the planet directly between the Earth and the Sun. occurred on June 5, 2012. This was only the eighth transit of Venus since Kepler predicted such events in 1631, since pairs of transits occur eight years apart separated by long gaps of 121.5 years and 105.5 years. In June, 2004, only a few people saw the transit, which ended shortly after the Sun rose. The West Georgia Observatory held an open house on June 5. 2012. Although the sky was partly cloudy, over 300 people saw beginning of the 2012 transit via projections on a screen, with eclipse shades, and through telescopes equipped with solar filters. Photographs of the transit were made through a telescope. This observation of the 2012 transit ended when the Sun sat with the transit still in progress. The next transits of Venus will be in December 2117 and 2125.

2:45 ARRAYS OF THREE DIMENSIONAL FLAT PANEL SOLOR COLLECTORS, Daniel Hartman *. Ben Jenkins and Bob Powell, University of West Georgia, Carrollton, GA 30118. The Massachusetts Institute of Technology has reported that three dimensional photovoltaic structures generate a higher energy density per base area than flat panels. They proposed some designs which support that statement. We have built a simple scale model and have collected data that also supports that work. These data were gathered using a simple geometric arrangement of two solar panels at right angles to each other and two panels in a flat array as a control. Analysis showed reflections from one panel to a second panel help to increase the output when the angle of incidence was greater than 45 degrees. Future work involves more complex designs, including models similar to the one proposed by MIT, and examining the total output during a full day.

3:00 Break

3:15 DEVELOPMENT OF A METHOD TO PREDICT RELATIVE OUTPUT FACTORS OF IRREGULARLY SHAPED ELECTRON FIELDS **, L. Burden * (1), J. Hauger (1), J. Lundeen * (1), J. Newton (1), C. Sailors * (1), R. Slayton (2) and C. Wisnieski (2), (1) Augusta State University, Augusta, GA 30904 and 'Georgia Radiation Therapy Center, Augusta, GA 30912. High energy electron beams delivered from a linear accelerator are often used to treat irregularly shaped superficial lesions. The relative output factor (ROF) is crucial during treatment planning to ensure the proper machine settings are used to deliver the prescribed radiation dose to the lesion. Direct measurement of the ROF for individual patients is time consuming and inefficient. This project will develop an empirical method which can be used to predict the ROF for irregularly shaped electron fields. It will be shown that by dividing the irregular field into wedge-shaped segments the ROF can be calculated by approximating these segments as a fraction of a circular field and summing the dose contribution from each. The ROF of nine circular fields from 2cm to 10cm in increments of 1cm were measured and used as the reference circles for the segment calculations. The measured ROF for several irregular fields will be compared to the predicted ROF.

3:30 SIMULATION OF A VIBRATING BEAM. Daniel Sanchez Carretero ** and Javier E. Hasbun, Department of Physics. University of West Georgia. Carrollton. GA 30118. In this presentation we develop a simulation of a vibrating beam with fixed nodes. The purpose of the simulation is to aid the users in visualizing the beam's vibration and how the dimensional parameters affect the frequency. The simulation is carried out in MATLAB due to its graphical efficiency. The program is capable of graphing frequency versus length, width, height, and density. It finds the frequency of the beam's vibration using the Euler-Bernoulli beam theory and finds the percent error given the experimental measurement as input. The property of the material to resonate is dependent on the material's Young's modulus, density, and physical dimensions. The program assigns the density and Young's modulus depending on the material inputted. The frequency of vibration uses a parameter (P) that's normally obtained from a self-consistent solution of the theory; however, it is possible to improve the agreement between theory and experiment by optimizing the II parameter.

3:45 A NUCLEAR PHYSICS SIMULATION SUITABLE FOR CLASSROOM USE, Benjamin E Hogan * and Javier E. Hasbun, Department of Physics. University of West Georgia, Carrollton, GA 30118. The orbits of a nucleon and its respective parent nucleus about their common center of mass are simulated in an effort to provide a pedagogical approach to the understanding of the structure of atomic nuclei. The nuclear exercise is treated by solving the problem with an effective force on the reduced mass of the system. The potential governing the mean field is modeled by the Woods-Saxon form-factor with parameters that enable it to describe experimental findings. The Woods-Saxon potential is preferred over the infinite well and harmonic oscillator methods because both require infinite separation energies of the nucleons. The results provided by the harmonic oscillator are substituted for a continuum spectrum. Also, a potential resembling the geometric distribution of nuclear density is possible. The simulation is created using Easy Java Simulations (EJS) which is part of the Open Source Physics project and a MATLAB version. The resulting illustration depicts the orbits traced out by the nucleon-core two body system as well as its associated reduced mass.

4:00 INVESTIGATION OF LOW COST BROAD BAND PHOTO-DETECTORS BASED ON LEAD SULFIDE QUANTUM DOTS **, Ryan M. Landry * (1), Ajith DeSilva (1) P. K. D. D. P. Pitigala (2) and A. G. U. Perera (2), (1) University of West Georgia. Carrollton. GA 30118 and (2) Georgia State University, Atlanta, GA 30303. We have developed a non-polar solvent synthesis for lead sulfide (PbS) quantum dots (QDs) in polyvinylcarbazol (PVK). Optical spectroscopy methods of the composites have shown a particle size distribution between 5 and 10 nm with broad optical absorption from 300 to 700 nm, with peak at 480 nm. We study this composite PbS quantum dot (QD) polymer layer as a ultra violet (UV)-infrared (IR) broad band photo-detector. The detector has a configuration of FTO/PVK-PbS QDs/FTO. At room temperature, the device showed a UV-IR spectral response from 300-1300 nm with two response peaks at 470 rim and 635 nm with responsivities of ~0.8 mA/W and ~ 1.1 mA/W respectively, for 4.9 V bias. We use optical spectroscopy, XRD and electrical measurements to characterize the device.

4:15 SIZE DEPENDENT STUDY OF CADMIUM SELENIDE QUANTUM DOTS FABRICATED BY PHOTOLITHOGRAPHY **. Volker Beutner *, Raghuveer R. Gadipalli, Ajith De Silva and Javier E. Hasbun, University of West Georgia. Carrollton. GA 30118. One of the forerunners in nanotechnology is quantum dots (QDs). Quantum dots are nano-sized semiconductor particles whose electronic properties are similar to that of molecules rather than bulk semiconductors. The optical and electronic properties of QDs can be tuned by changing the size of the QDs. We employed wet chemical and photolithography methods to synthesize different sizes of CdSe QDs. Cadmium-perchlorate Hexahydrate and Selenourea salts as precursors and 1-Thioglycerol as a capping agent were used in the chemical process. By varying UV light exposure time, the different sizes of QDs were synthesized. As the exposure time changes from 5 minutes and 100 minutes, the size of QDs were estimated to be in the range from 3 nm to 10 nm. We use a combination of X-ray spectroscopy and optical spectroscopy to determine their chemical composition and the average size.

4:30 A COMPARISON OF TWO DIFFERENT NUMERICAL SOLUTIONS FOR THE TWO DIMENSIONAL ELASTIC WAVE EQUATION **. David C. McCall * and Christian Poppeliers, Georgia Regents University, Augusta, GA 30904. The elastic wave equation describes the evolution of the vector particle motion of a solid material at a point due to the passage of a mechanical wave. We have solved the 2-D elastic wave equation using a well-known finite difference method that is second order accurate in both space and time (O([t.sup.2], [x.sup.2])). The goal of this project is to compare two implementations of this numerical solution using two different computing languages. We find that the (O([t.sup.2], [x.sup.2])) is subject to a high degree of numerical artifacts. Because of this we have started work a (O([t.sup.2], [x.sup.2])) scheme which has a lower degree of numerical artifacts.

4:45 THE EFFECTS OF MEASUREMENT UNCERTAINTY ON SPACT1OAN WAVE GRADIENTS AS ESTIMATED FROM A SEISMIC ARRAY **, C. Elizabeth Johnson. Augusta State University, Augusta, GA 30904. Seismic arrays are used to measure the spatial and temporal changes of a seismic wave field. They do this by recording the wave field in numerous locations on the earth simultaneously. For this project, we analyzed the effects of measurement uncertainties on the estimation of the wave spatial gradients as recorded by a seismic array. Our primary purpose is to determine how the array aperture influences the estimates of the gradients and quantities derived from them given known measurement uncertainties. We constructed a synthetic seismogram and recorded it on a virtual array. The virtual seismometer has known uncertainties in the location and the recorded wave field has known uncertainties in amplitude and phase. We perform a Monte Carlo simulation where the uncertainties are normally distributed and random for each realization of the seismogram. We then compute statistics that indicate that there is an optimal array aperture that minimized the uncertainty in the computed gradients and attributes derived from them for a given amplitude of measurement uncertainties.

5:00 AUTOMATED MEASUREMENT OF FORCES BETWEEN PERMANENT MAGNETS AT ROOM TEMPERATURE AND AT LIQUID NITROGEN TEMPERATURE. Cordell FormyDuval *, Ethan Coley * and Ben de Mayo, University of West Georgia. Carrollton. GA 30118. Permanent magnets are economically important in the electronic technologies of entertainment, medicine, and national defense. In this study an automated system was used to investigate the mechanical forces between two permanent magnets of different shapes, both at room temperature (around 294 K) and at liquid nitrogen temperature (LN2, around 69 K at our altitude). A Vernier Software (VS) Force Sensor (DFS-BTA) and a VS Rotary Motion Sensor (ROT-UU) powered by a motor were used in conjunction with VS's LabPro data acquisition hardware and VS Logger Pro 3 software to move a cubical permanent magnet (strength approximately 58 mT) towards or away from a stationary circular permanent magnet (approximately 43 mT) in a cryostat both when the second magnet was at room temperature and at LN2 temperature. The system was connected to a Mac Mini computer to record and analyze the data. Distances between the magnets varied from approximately 61 mm to 11 mm; about 17,000 measurements were recorded per experimental run. Forces were in the range of 4 to 0.1 Newtons; LN2 temperatures did not affect the magnitude of the inter-magnet forces.

5:15 USING MATLAB TO MEASURE THE POSITION OF AN OBJECT IN A MOVIE **, Ryan Landry and Julie Talbot, University of West Georgia. Carrollton, GA 30118. Movies made with a camera or camcorder can be analyzed using Matlab. After first calibrating the movie using a known length. the Matlab program can determine the x-and y-coordinates of an object's motion, and then graph each coordinate as a function of time. Currently, the program can find the position within 5%. Still in progress is a curve-fitting program that would determine the equation of the trajectory for motion that is more complicated than simple linear or quadratic plots.

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Title Annotation: | FRIDAY PAPER PRESENTATIONS |
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Publication: | Georgia Journal of Science |

Article Type: | Conference notes |

Geographic Code: | 1U5GA |

Date: | Mar 22, 2013 |

Words: | 2630 |

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