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Mathematical Modeling: Lights Out!

Description

Lights Out is a puzzle game where the goal is to turn off all the lights on a nxn board starting from a random configuration. In order to find the solution of a configuration, the game is constructed using a matrix basis in the span of the field Z mod…

Lights Out is a puzzle game where the goal is to turn off all the lights on a nxn board starting from a random configuration. In order to find the solution of a configuration, the game is constructed using a matrix basis in the span of the field Z mod 2.This the game can be modeled by the system Ap=s which will be the center of the investigation when determining the solvability for any n×n board since A is not always invertable leading to some interesting cases. The goal of this thesis was to construct a model that will allow the player to solve for the pushes to attain the zero-state for an nxn system. Constructing the model gave a procedure that will allow to solve the puzzle game. The procedure presented here first uses a simple clearing technique (valid for any board size) to turn off all the lights except in the last row, which we call the standard-clear. The heart of the technique, is to give a way to use the information about which lights remain lit in the last row to determine which switches in the first row need to be pushed before the standard-clear. This part of the solution algorithm we call the first row adjustment, and it depends heavily on the specific board size n of the problem. Finally, after these first row pushes are made, the standard clear will now turn off all the lights including (seemingly magically) the last row. Thus the solution to the Lights Out puzzle of a given size is reduced to finding a first row adjustment for that size. (Please refer to the actual thesis for the full abstract)

ContributorsBarraza, Jay Romeo (Author) / Vaz, Paul (Thesis director) / Paupert, Julien (Committee member) / Civil, Environmental and Sustainable Engineering Programs (Contributor) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)

Created2015-05

Collaborative Thesis: Supplier Tool Selection

Description

The goal of this thesis was to provide in depth research into the semiconductor wet-etch market and create a supplier analysis tool that would allow Company X to identify the best supplier partnerships. Several models were used to analyze the wet etch market including Porter's Five Forces and SWOT analyses.…

The goal of this thesis was to provide in depth research into the semiconductor wet-etch market and create a supplier analysis tool that would allow Company X to identify the best supplier partnerships. Several models were used to analyze the wet etch market including Porter's Five Forces and SWOT analyses. These models were used to rate suppliers based on financial indicators, management history, market share, research and developments spend, and investment diversity. This research allowed for the removal of one of the four companies in question due to a discovered conflict of interest. Once the initial research was complete a dynamic excel model was created that would allow Company X to continually compare costs and factors of the supplier's products. Many cost factors were analyzed such as initial capital investment, power and chemical usage, warranty costs, and spares parts usage. Other factors that required comparison across suppliers included wafer throughput, number of layers the tool could process, the number of chambers the tool has, and the amount of space the tool requires. The demand needed for the tool was estimated by Company X in order to determine how each supplier's tool set would handle the required usage. The final feature that was added to the model was the ability to run a sensitivity analysis on each tool set. This allows Company X to quickly and accurately forecast how certain changes to costs or tool capacities would affect total cost of ownership. This could be heavily utilized during Company X's negotiations with suppliers. The initial research as well the model lead to the final recommendation of Supplier A as they had the most cost effective tool given the required demand. However, this recommendation is subject to change as demand fluctuates or if changes can be made during negotiations.

ContributorsSchmitt, Connor (Co-author) / Rickets, Dawson (Co-author) / Castiglione, Maia (Co-author) / Witten, Forrest (Co-author) / Simonson, Mark (Thesis director) / Hertzel, Michael (Committee member) / Department of Finance (Contributor) / Department of Economics (Contributor) / Department of Information Systems (Contributor) / Department of Supply Chain Management (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Accountancy (Contributor) / WPC Graduate Programs (Contributor) / Barrett, The Honors College (Contributor)

Created2016-12

Branching Worlds: Quantum Mechanics and Hugh Everett's Many-Worlds Interpretation

Description

This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal…

This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.

ContributorsSecrest, Micah (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)

Created2021-05

Entanglement, Locality, and Hidden Variables

Description

The purpose of this paper is to provide an analysis of entanglement and the particular problems it poses for some physicists. In addition to looking at the history of entanglement and non-locality, this paper will use the Bell Test as a means for demonstrating how entanglement works, which measures the…

The purpose of this paper is to provide an analysis of entanglement and the particular problems it poses for some physicists. In addition to looking at the history of entanglement and non-locality, this paper will use the Bell Test as a means for demonstrating how entanglement works, which measures the behavior of electrons whose combined internal angular momentum is zero. This paper will go over Dr. Bell's famous inequality, which shows why the process of entanglement cannot be explained by traditional means of local processes. Entanglement will be viewed initially through the Copenhagen Interpretation, but this paper will also look at two particular models of quantum mechanics, de-Broglie Bohm theory and Everett's Many-Worlds Interpretation, and observe how they explain the behavior of spin and entangled particles compared to the Copenhagen Interpretation.

ContributorsWood, Keaten Lawrence (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)

Created2021-05

Mathematical Modeling of Neuron and Network Dynamics

Description

The Morris-Lecar two-dimensional conductance-based model for an excitable membrane can be used to simulate neurons, and these neuron models can be connected to model neuronal networks. In this work, we analyze the dynamics of the Morris-Lecar model using phase plane analysis, and we simulate the model with different parameter regimes.…

The Morris-Lecar two-dimensional conductance-based model for an excitable membrane can be used to simulate neurons, and these neuron models can be connected to model neuronal networks. In this work, we analyze the dynamics of the Morris-Lecar model using phase plane analysis, and we simulate the model with different parameter regimes. We also develop and simulate a two-cell model network, as well as larger networks composed of 17 cells. We show that the bifurcation type and the parameters for the synaptic connections between model neurons affect the model network dynamic behavior. In particular, we look at the synchronization of networks of identical, repetitively firing neurons.

ContributorsSchlichting, Nicolas Jordan (Author) / Crook, Dr. Sharon (Thesis director) / Baer, Dr. Steven (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)

Created2019-12

Precision Temperature Control of CXFEL Linear Accelerator Cavities

Description

The ASU Compact X-ray Free Electron Laser (CXFEL) is a first of its kind instrument that will illuminate the processes of life and allow scientists to create more effective treatments for disease. The dimensions of the linear accelerator (LINAC) cavities must remain stable during operation, for a change in the…

The ASU Compact X-ray Free Electron Laser (CXFEL) is a first of its kind instrument that will illuminate the processes of life and allow scientists to create more effective treatments for disease. The dimensions of the linear accelerator (LINAC) cavities must remain stable during operation, for a change in the geometry alters the standing wave microwave energy resonance within the cavities and leads to reflected rather than coupled and useful microwave energy to electric field coupling. This disturbs the electron bunch acceleration dynamics critical to the ultimate generation of x-ray pulses. Cooling water must be supplied to the electron generating RF-GUN, and linear accelerator (LINAC) structures at unique flowrate and temperature setpoints that are specific to the operating mode of the CXFEL. Design specifications for the water supply to the RF-GUN and three LINACs and were made for the nominal operating mode, which adds a 3 kW heat load to the water. To maintain steady cavity dimensions, water must be supplied to each device under test at 30.0 ºC ± 0.06 ºC. The flowrate of water must be 3.5 GPM to the RF-GUN and 2.5 GPM to each of the three LINACs with ± 0.01 GPM flowrate resolution. The primary function of the Dedicated-Precision Thermal Trim Unit (D-PTTU) is to control the flowrate and temperature of water supply to each device under test. A simplified model of the system was developed to select valves that would meet our design specifications for flowrate and temperature control. After using this model for valve selection, a detailed system model was created to simulate relevant coupled-domain physics of the integrated system. The detailed system model was used to determine the critical sensitivities of the system and will be used to optimize the performance of the system in the future. Before the detailed system model can be verified and tuned with experiments, the sensors were calibrated in an ice-bath to ensure the sensors measure accurate and precise values. During initial testing, the D-PTTU was able to achieve ± 0.02 ºC temperature resolution, which exceeds the design specification by a factor of three.

ContributorsGardeck, Alex John (Author) / Holl, Mark (Thesis director) / Smith, Dean (Committee member) / Department of Physics (Contributor) / Mechanical and Aerospace Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)

Created2020-05

Data-driven Modeling of TRPM8 Ion Channel Kinetics

Description

Ion channels in the membranes of cells in the body allow for the creation of action potentials from external stimuli, allowing us to sense our surroundings. One particular channel, TRPM8, is a trans-membrane ion channel believed to be the primary cold sensor in humans. Despite this important biological role and…

Ion channels in the membranes of cells in the body allow for the creation of action potentials from external stimuli, allowing us to sense our surroundings. One particular channel, TRPM8, is a trans-membrane ion channel believed to be the primary cold sensor in humans. Despite this important biological role and intense study of the channel, TRPM8 is not fully understood mechanistically and has not been accurately modeled. Existing models of TRPM8 fail to account for menthol activation of the channel. In this paper we re-implement an established whole cell model for TRPM8 with gating by both voltage and temperature. Using experimental data obtained from the Van Horn lab at Arizona State University, we refined the model to represent more accurately the dynamics of the human TRPM8 channel and incorporate the channel activation through menthol agonist binding. Our new model provides a large improvement over preexisting models, and serves as a basis for future incorporation of other channel activators of TRPM8 and for the modeling of other channels in the TRP family.

ContributorsAckerman, David (Author) / Crook, Sharon (Thesis director) / Van Horn, Wade (Committee member) / School of Earth and Space Exploration (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)

Created2019-05

Votes that Count: Building a Tool to Facilitate Understanding of the Effects of Voting Procedure on Electoral Outcomes

Description

The goal of this project was to develop a prototype for an educational tool that will help users understand how the voting system deployed by a government can affect the outcomes of elections. This tool was developed in Java SE, consisting of a model for the simulation of elections capable…

The goal of this project was to develop a prototype for an educational tool that will help users understand how the voting system deployed by a government can affect the outcomes of elections. This tool was developed in Java SE, consisting of a model for the simulation of elections capable of supporting various voting systems, along with a variety of fairness measures, and educational and explanatory material. While a completed version of this tool would ideally be fully self-contained, easily accessible in-browser, and provide detailed visualizations of the simulated elections, the current prototype version consists of a GitHub repository containing the code, with the educational material and explanations contained within the thesis paper. Ultimately, the goal of this project was to be a stepping stone on the path to create a tool that will instill a measure of systemic skepticism in the user; to give them cause to question why our systems are built the way they are, and reasons to believe that they could be changed for the better. In undertaking this project, I hope to help in providing people with the political education needed to make informed decisions about how they want the government to function. The GitHub repository containing all the code can be found at, https://github.com/SpencerDiamond/Votes_that_Count

ContributorsDiamond, Spencer (Author) / Sarjoughian, Hessam (Thesis director) / Hines, Taylor (Committee member) / Barrett, The Honors College (Contributor) / Department of Physics (Contributor) / Department of English (Contributor) / School of Mathematical and Statistical Sciences (Contributor)

Created2022-05

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