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- All Subjects: Physics
- Creators: School of Mathematical and Statistical Sciences
- Member of: Barrett, The Honors College Thesis/Creative Project Collection
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Description
We develop the mathematical tools necessary to describe the interaction between a resonant pole and a threshold energy. Using these tools, we analyze the properties an opening threshold has on the resonant pole mass (the "cusp effect"), leading to an effect called "pole-dragging." We consider two models for resonances: a molecular, mesonic model, and a color-nonsinglet diquark plus antidiquark model. Then, we compare the pole-dragging effect due to these models on the masses of the f0(980), the X(3872), and the Zb(10610) and compare the effect's magnitude. We find that, while for lower masses, such as the f 0 (980), the pole-dragging effect that arises from the molecular model is more significant, the diquark model's pole-dragging effect becomes dominant at higher masses such as those of the X(3872) and the Z b (10610). This indicates that for lower threshold energies, diquark models may have less significant effects on predicted resonant masses than mesonic models, but for higher threshold energies, it is necessary to include the pole-dragging effect due to a diquark threshold in high-precision QCD calculations.
ContributorsBlitz, Samuel Harris (Author) / Richard, Lebed (Thesis director) / Comfort, Joseph (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor) / Barrett, The Honors College (Contributor)
Created2015-05
Description
Preliminary feasibility studies for two possible experiments with the GlueX detector, installed in Hall D of Jefferson Laboratory, are presented. First, a general study of the feasibility of detecting the ηC at the current hadronic rate is discussed, without regard for detector or reconstruction efficiency. Second, a study of the use of statistical methods in studying exotic meson candidates is outlined, describing methods and providing preliminary data on their efficacy.
ContributorsPrather, Benjamin Scott (Author) / Ritchie, Barry G. (Thesis director) / Dugger, Michael (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2015-05
Description
We model communication among social insects as an interacting particle system in which individuals perform one of two tasks and neighboring sites anti-mimic one another. Parameters of our model are a probability of defection 2 (0; 1) and relative cost ci > 0 to the individual performing task i. We examine this process on complete graphs, bipartite graphs, and the integers, answering questions about the relationship between communication, defection rates and the division of labor. Assuming the division of labor is ideal when exactly half of the colony is performing each task, we nd that on some bipartite graphs and the integers it can eventually be made arbitrarily close to optimal if defection rates are sufficiently small. On complete graphs the fraction of individuals performing each task is also closest to one half when there is no defection, but is bounded by a constant dependent on the relative costs of each task.
ContributorsArcuri, Alesandro Antonio (Author) / Lanchier, Nicolas (Thesis director) / Kang, Yun (Committee member) / Fewell, Jennifer (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
In this paper, optimal control routines are applied to an existing problem of electron state transfer to determine if spin information can successfully be moved across a chain of donor atoms in silicon. The additional spin degrees of freedom are introduced into the formulation of the problem as well as the control optimization algorithm. We find a timescale of transfer for spin quantum information across the chain fitting with a t > π/A and t > 2π/A transfer pulse time corresponding with rotation of states on the electron Bloch sphere where A is the electron-nuclear coupling constant. Introduction of a magnetic field weakens transfer
efficiencies at high field strengths and prohibits anti-aligned nuclear states from transferring. We also develop a rudimentary theoretical model based on simulated results and partially validate the characteristic transfer times for spin states. This model also establishes a framework for future work including the introduction of a magnetic field.
efficiencies at high field strengths and prohibits anti-aligned nuclear states from transferring. We also develop a rudimentary theoretical model based on simulated results and partially validate the characteristic transfer times for spin states. This model also establishes a framework for future work including the introduction of a magnetic field.
ContributorsMorgan, Eric Robert (Author) / Treacy, Michael (Thesis director) / Whaley, K. Birgitta (Committee member) / Greenman, Loren (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2015-05
Description
In this experiment an Electrodynamic Ion Ring Trap was constructed and tested. Due to the nature of Electrostatic fields, the setup required an oscillating voltage source to stably trap the particles. It was built in a safe manner, The power supply was kept in a project box to avoid incidental contact, and was connected to a small copper wire in the shape of a ring. The maximum voltage that could be experienced via incidental contact was well within safe ranges a 0.3mA. Within minutes of its completion the trap was able to trap small Lycopodium powder spores mass of approximately 1.7*10^{-11}kg in clusters of 15-30 for long timescales. The oscillations of these spores were observed to be roughly 1.01mm at their maximum, and in an attempt to understand the dynamics of the Ion Trap, a concept called the pseudo-potential of the trap was used. This method proved fairly inaccurate, involving much estimation and using a static field estimation of 9.39*10^8 N\C and a charge estimate on the particles of ~1e, a maximum oscillation distance of 1.37m was calculated. Though the derived static field strength was not far off from the field strength required to achieve the correct oscillation distance (Percent error of 9.92%, the small discrepancy caused major calculation errors. The trap's intended purpose however was to eventually trap protein molecules for mapping via XFEL laser, and after its successful construction that goal is fairly achievable. The trap was also housed in a vacuum chamber so that it could be more effectively implemented with the XFEL.
ContributorsNicely, Ryan Joseph (Author) / Kirian, Richard (Thesis director) / Weiterstall, Uwe (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Serge Galams voting systems and public debate models are used to model voting behaviors of two competing opinions in democratic societies. Galam assumes that individuals in the population are independently in favor of one opinion with a fixed probability p, making the initial number of that type of opinion a binomial random variable. This analysis revisits Galams models from the point of view of the hypergeometric random variable by assuming the initial number of individuals in favor of an opinion is a fixed deterministic number. This assumption is more realistic, especially when analyzing small populations. Evolution of the models is based on majority rules, with a bias introduced when there is a tie. For the hier- archical voting system model, in order to derive the probability that opinion +1 would win, the analysis was done by reversing time and assuming that an individual in favor of opinion +1 wins. Then, working backwards we counted the number of configurations at the next lowest level that could induce each possible configuration at the level above, and continued this process until reaching the bottom level, i.e., the initial population. Using this method, we were able to derive an explicit formula for the probability that an individual in favor of opinion +1 wins given any initial count of that opinion, for any group size greater than or equal to three. For the public debate model, we counted the total number of individuals in favor of opinion +1 at each time step and used this variable to define a random walk. Then, we used first-step analysis to derive an explicit formula for the probability that an individual in favor of opinion +1 wins given any initial count of that opinion for group sizes of three. The spatial public debate model evolves based on the proportional rule. For the spatial model, the most natural graphical representation to construct the process results in a model that is not mathematically tractable. Thus, we defined a different graphical representation that is mathematically equivalent to the first graphical representation, but in this model it is possible to define a dual process that is mathematically tractable. Using this graphical representation we prove clustering in 1D and 2D and coexistence in higher dimensions following the same approach as for the voter model interacting particle system.
ContributorsTaylor, Nicole Robyn (Co-author) / Lanchier, Nicolas (Co-author, Thesis director) / Smith, Hal (Committee member) / Hurlbert, Glenn (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
Description
Cryptocurrencies have become one of the most fascinating forms of currency and economics due to their fluctuating values and lack of centralization. This project attempts to use machine learning methods to effectively model in-sample data for Bitcoin and Ethereum using rule induction methods. The dataset is cleaned by removing entries with missing data. The new column is created to measure price difference to create a more accurate analysis on the change in price. Eight relevant variables are selected using cross validation: the total number of bitcoins, the total size of the blockchains, the hash rate, mining difficulty, revenue from mining, transaction fees, the cost of transactions and the estimated transaction volume. The in-sample data is modeled using a simple tree fit, first with one variable and then with eight. Using all eight variables, the in-sample model and data have a correlation of 0.6822657. The in-sample model is improved by first applying bootstrap aggregation (also known as bagging) to fit 400 decision trees to the in-sample data using one variable. Then the random forests technique is applied to the data using all eight variables. This results in a correlation between the model and data of 9.9443413. The random forests technique is then applied to an Ethereum dataset, resulting in a correlation of 9.6904798. Finally, an out-of-sample model is created for Bitcoin and Ethereum using random forests, with a benchmark correlation of 0.03 for financial data. The correlation between the training model and the testing data for Bitcoin was 0.06957639, while for Ethereum the correlation was -0.171125. In conclusion, it is confirmed that cryptocurrencies can have accurate in-sample models by applying the random forests method to a dataset. However, out-of-sample modeling is more difficult, but in some cases better than typical forms of financial data. It should also be noted that cryptocurrency data has similar properties to other related financial datasets, realizing future potential for system modeling for cryptocurrency within the financial world.
ContributorsBrowning, Jacob Christian (Author) / Meuth, Ryan (Thesis director) / Jones, Donald (Committee member) / McCulloch, Robert (Committee member) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Within the context of the Finite-Difference Time-Domain (FDTD) method of simulating interactions between electromagnetic waves and matter, we adapt a known absorbing boundary condition, the Convolutional Perfectly-Matched Layer (CPML) to a background of Drude-dispersive medium. The purpose of this CPML is to terminate the virtual grid of scattering simulations by absorbing all outgoing radiation. In this thesis, we exposit the method of simulation, establish the Perfectly-Matched Layer as a domain which houses a spatial-coordinate transform to the complex plane, construct the CPML in vacuum, adapt the CPML to the Drude medium, and conclude with tests of the adapted CPML for two different scattering geometries.
ContributorsThornton, Brandon Maverick (Author) / Sukharev, Maxim (Thesis director) / Goodnick, Stephen (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
We study two models of a competitive game in which players continuously receive points and wager them in one-on-one battles. In each model the loser of a battle has their points reset, while the points the winner receives is what sets the two models apart. In the knockout model the winner receives no new points, while in the winner-takes-all model the points that the loser had are added to the winner's total. Recurrence properties are assessed for both models: the knockout model is recurrent except for the all-zero state, and the winner-takes-all model is transient, but retains some aspect of recurrence. In addition, we study the population-level allocation of points; for the winner-takes-all model we show explicitly that the proportion of individuals having any number j of points, j=0,1,... approaches a stationary distribution that can be computed recursively. Graphs of numerical simulations are included to exemplify the results proved.
ContributorsVanKirk, Maxwell Joshua (Author) / Lanchier, Nicolas (Thesis director) / Foxall, Eric (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2016-12
Description
A working knowledge of mathematics is a vital requirement for introductory university physics courses. However, there is mounting evidence which shows that many incoming introductory physics students do not have the necessary mathematical ability to succeed in physics. The investigation reported in this thesis used preinstruction diagnostics and interviews to examine this problem in depth. It was found that in some cases, over 75% of students could not solve the most basic mathematics problems. We asked questions involving right triangles, vector addition, vector direction, systems of equations, and arithmetic, to give a few examples. The correct response rates were typically between 25% and 75%, which is worrying, because these problems are far simpler than the typical problem encountered in an introductory quantitative physics course. This thesis uncovered a few common problem solving strategies that were not particularly effective. When solving trigonometry problems, 13% of students wrote down the mnemonic "SOH CAH TOA," but a chi-squared test revealed that this was not a statistically significant factor in getting the correct answer, and was actually detrimental in certain situations. Also, about 50% of students used a tip-to-tail method to add vectors. But there is evidence to suggest that this method is not as effective as using components. There are also a number of problem solving strategies that successful students use to solve mathematics problems. Using the components of a vector increases student success when adding vectors and examining their direction. Preliminary evidence also suggests that repetitive trigonometry practice may be the best way to improve student performance on trigonometry problems. In addition, teaching students to use a wide variety of algebraic techniques like the distributive property may help them from getting stuck when working through problems. Finally, evidence suggests that checking work could eliminate up to a third of student errors.
ContributorsJones, Matthew Isaiah (Author) / Meltzer, David (Thesis director) / Peng, Xihong (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12