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Rose-Hulman Institute of Technology

2019

Articles 1 - 22 of 22

Full-Text Articles in Physical Sciences and Mathematics

Repeat Length Of Patterns On Weaving Products, Zhuochen Liu Nov 2019

Repeat Length Of Patterns On Weaving Products, Zhuochen Liu

Mathematical Sciences Technical Reports (MSTR)

Interlacing strands have been used to create artistic weaving patterns. Repeated patterns form aesthetically pleasing products. This research is a mathematical modeling of weaving products in the real world by using Cellular Automata. The research is conducted by observing the evolution of the model to better understand products in the real world. Specifically, this research focuses on the repeat length of a weaving pattern given the rule of generating it and the configuration of the starting row. Previous studies have shown the range of the repeat length in specific situations. This paper will generalize the precise repeat length in one …

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Forward Selection Via Distance Correlation, Ty Adams May 2019

Forward Selection Via Distance Correlation, Ty Adams

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.

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Comparison Between Two Group Signature Schemes, Hao Yang May 2019

Comparison Between Two Group Signature Schemes, Hao Yang

Rose-Hulman Undergraduate Research Publications

Zerocoin is a cryptographic extension to Bitcoin. During its development, the developers decided to make use of group signature schemes to store and verify the coins. In order to compare the performance of Simple Authentication Scheme and the Dynamic Signature Scheme and figure out which one is the optimal choice for the Zerocoin scheme, I implemented them in Java and analyzed them theoretically. This paper will discuss the performance difference between two schemes, the Java implementation of them and the analysis.

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Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang May 2019

Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang

Mathematical Sciences Technical Reports (MSTR)

A cellular automaton is a type of mathematical system that models the behavior of a set of cells with discrete values in progressing time steps. The often complicated behaviors of cellular automata are studied in computer science, mathematics, biology, and other science related fields. Lattice gas cellular automata are used to simulate the movements of particles. This thesis aims to discuss the properties of lattice gas models, including periodicity and invertibility, and to examine their accuracy in reflecting the physics of particles in real life. Analysis of elementary cellular automata is presented to introduce the concept of cellular automata and …

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Effects Of Framing In Exams On Student Performance, Mariana Lane, Eric Reyes May 2019

Effects Of Framing In Exams On Student Performance, Mariana Lane, Eric Reyes

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.

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Modeling And Characterization Of A Ring-Resonator Based Silicon Photonic Sensor On Silicon-On-Insulator (Soi), Gwangho Choi May 2019

Modeling And Characterization Of A Ring-Resonator Based Silicon Photonic Sensor On Silicon-On-Insulator (Soi), Gwangho Choi

Graduate Theses - Physics and Optical Engineering

The purpose of this work is to build silicon photonic devices and verify their functionalities. In particular, the structure of a ring resonator (RR) is analyzed and applied to various silicon photonic application in sensing. Silicon waveguides, grating couplers, directional couplers, and RRs are fabricated on the silicon-on-insulator (SOI) wafer. Geometrical parameters and optical properties of the silicon devices are studied and also applied to the design of the aforementioned devices. The waveguide dimensions and, optical properties of the silicon waveguide such as dispersion and effective-index are examined. The RRs are made of a series of straight and bent waveguides …

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Design, Fabrication, And Characterization Of Multilayer Hyperbolic Metamaterials, James Dilts May 2019

Design, Fabrication, And Characterization Of Multilayer Hyperbolic Metamaterials, James Dilts

Graduate Theses - Physics and Optical Engineering

Hyperbolic metamaterials (HMMs) show extreme anisotropy, acting as metals and dielectrics along orthogonal directions. They are designed using the effective medium theory (EMT) and can be fabricated using standard semiconductor processing techniques. Current techniques used to characterize the optical behavior of HMMs have a high complexity or are unable to robustly determine the complex permittivity tensor. We describe the details of a procedure to obtain a very low mean-squared-error (MSE) for extraction of permittivity from hyperbolic metamaterials using spectroscopic ellipsometry. We have verified our procedure by fabricating three different samples of various materials and fill factors designed to have a …

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Discrete-Position Solar Tracking For Photovoltaic System, Shengnan Hong, Zheng Fu, Richard E. Stamper Apr 2019

Discrete-Position Solar Tracking For Photovoltaic System, Shengnan Hong, Zheng Fu, Richard E. Stamper

Rose-Hulman Undergraduate Research Publications

The purpose of this research is to design a new tracking system for solar panels using the idea of discrete-position tracking. Compared with the traditional fixed solar panel, discrete-position trackers have a higher gain of harvesting solar radiation with smaller misalignment angles. Also, since we are trying to design the a passive tracker with solely mechanical structure to do the kinetics, a discrete-position tracker can decrease the cost of the maintenance to a huge extent in contrast to both one-axis and two-axis continuous tracking systems. The majority of the cost of maintaining a continuous tracker is the motor or hydraulic …

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Monoidal Supercategories And Superadjunction, Dene Lepine Mar 2019

Monoidal Supercategories And Superadjunction, Dene Lepine

Rose-Hulman Undergraduate Mathematics Journal

We define the notion of superadjunction in the context of supercategories. In particular, we give definitions in terms of counit-unit superadjunctions and hom-space superadjunctions, and prove that these two definitions are equivalent. These results generalize well-known statements in the non-super setting. In the super setting, they formalize some notions that have recently appeared in the literature. We conclude with a brief discussion of superadjunction in the language of string diagrams.

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Strengthening Relationships Between Neural Ideals And Receptive Fields, Angelique Morvant Mar 2019

Strengthening Relationships Between Neural Ideals And Receptive Fields, Angelique Morvant

Rose-Hulman Undergraduate Mathematics Journal

Neural codes are collections of binary vectors that represent the firing patterns of neurons. The information given by a neural code C can be represented by its neural ideal JC. In turn, the polynomials in JC can be used to determine the relationships among the receptive fields of the neurons. In a paper by Curto et al., three such relationships, known as the Type 1-3 relations, were linked to the neural ideal by three if-and-only-if statements. Later, Garcia et al. discovered the Type 4-6 relations. These new relations differed from the first three in that they were …

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Triangle Packing On Tripartite Graphs Is Hard, Peter A. Bradshaw Mar 2019

Triangle Packing On Tripartite Graphs Is Hard, Peter A. Bradshaw

Rose-Hulman Undergraduate Mathematics Journal

The problem of finding a maximum matching on a bipartite graph is well-understood and can be solved using the augmenting path algorithm. However, the similar problem of finding a large set of vertex-disjoint triangles on tripartite graphs has not received much attention. In this paper, we define a set of vertex-disjoint triangles as a “tratching.” The problem of finding a tratching that covers all vertices of a tripartite graph can be shown to be NP-complete using a reduction from the three-dimensional matching problem. In this paper, however, we introduce a new construction that allows us to emulate Boolean circuits using …

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Graphs, Random Walks, And The Tower Of Hanoi, Stephanie Egler Mar 2019

Graphs, Random Walks, And The Tower Of Hanoi, Stephanie Egler

Rose-Hulman Undergraduate Mathematics Journal

The Tower of Hanoi puzzle with its disks and poles is familiar to students in mathematics and computing. Typically used as a classroom example of the important phenomenon of recursion, the puzzle has also been intensively studied its own right, using graph theory, probability, and other tools. The subject of this paper is “Hanoi graphs”, that is, graphs that portray all the possible arrangements of the puzzle, together with all the possible moves from one arrangement to another. These graphs are not only fascinating in their own right, but they shed considerable light on the nature of the puzzle itself. …

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Asymptotically Optimal Bounds For (𝑡,2) Broadcast Domination On Finite Grids, Timothy W. Randolph Mar 2019

Asymptotically Optimal Bounds For (𝑡,2) Broadcast Domination On Finite Grids, Timothy W. Randolph

Rose-Hulman Undergraduate Mathematics Journal

Let G = (V,E) be a graph and t,r be positive integers. The signal that a tower vertex T of signal strength t supplies to a vertex v is defined as sig(T, v) = max(t − dist(T,v),0), where dist(T,v) denotes the distance between the vertices v and T. In 2015 Blessing, Insko, Johnson, and Mauretour defined a (t, r) broadcast dominating set, or simply a (t, r) broadcast, on G as a set T ⊆ V such that the sum of all signal received at each vertex v ∈ V from the set of towers T …

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New Experimental Investigations For The 3𝑥+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano Mar 2019

New Experimental Investigations For The 3𝑥+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano

Rose-Hulman Undergraduate Mathematics Journal

The 3x + 1 Problem, or the Collatz Conjecture, was originally developed in the early 1930's. It has remained unsolved for over eighty years. Throughout its history, traditional methods of mathematical problem solving have only succeeded in proving heuristic properties of the mapping. Because the problem has proven to be so difficult to solve, many think it might be undecidable. In this paper we brie y follow the history of the 3x + 1 problem from its creation in the 1930's to the modern day. Its history is tied into the development of the Cosper Algorithm, which maps binary sequences …

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A Generalized Newton-Girard Identity, Tanay Wakhare Mar 2019

A Generalized Newton-Girard Identity, Tanay Wakhare

Rose-Hulman Undergraduate Mathematics Journal

We present a generalization of the Newton-Girard identities, along with some applications. As an addendum, we collect many evaluations of symmetric polynomials to which these identities apply.

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Algorithms To Approximate Solutions Of Poisson's Equation In Three Dimensions, Ray Dambrose Mar 2019

Algorithms To Approximate Solutions Of Poisson's Equation In Three Dimensions, Ray Dambrose

Rose-Hulman Undergraduate Mathematics Journal

The focus of this research was to develop numerical algorithms to approximate solutions of Poisson's equation in three dimensional rectangular prism domains. Numerical analysis of partial differential equations is vital to understanding and modeling these complex problems. Poisson's equation can be approximated with a finite difference approximation. A system of equations can be formed that gives solutions at internal points of the domain. A computer program was developed to solve this system with inputs such as boundary conditions and a nonhomogenous source function. Approximate solutions are compared with exact solutions to prove their accuracy. The program is tested with an …

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Hybrid Optical Integrator Based On Silicon-On-Insulator Platform, Taewon Huh Jan 2019

Hybrid Optical Integrator Based On Silicon-On-Insulator Platform, Taewon Huh

Graduate Theses - Physics and Optical Engineering

A hybrid optical integrator is a recirculating loop that performs oversampling typically for analog input, using the cross-gain modulation (XGM) in a semiconductor optical amplifier (SOA). The modulated input signal changes the gain of the loop through XGM and thus modifies the loop accumulation. This thesis presents hybrid optical integrator for an all-optical analog-to-digital converter based on a silicon photonics platform. The device consists of silicon waveguides of dimension 220 × 500 nm (thick × width) and approximately 5 m optical loop length including fiber length, input and output grating couplers for 1550 nm signal, directional couplers, and external components …

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Tilt Measurements Using A Monolithic Cyclic Interferometer, Joseph Porter Jan 2019

Tilt Measurements Using A Monolithic Cyclic Interferometer, Joseph Porter

Graduate Theses - Physics and Optical Engineering

Measurement applications globally are demanding higher resolution measurements within a smaller footprint. The cyclic interferometer is a proven means of high-resolution tilt measurements while maintaining fringe stability. However, the cyclic interferometer commonly has many optical elements over a large surface area. In this thesis, a monolithic cyclic interferometer has been designed, constructed, and characterized. The monolithic system contains all the functionality of a typical cyclic interferometer, yet the optical elements are contained within a single glass optic. In doing so, the system attains a compact form factor and it is possible to complete measurements within a broader field of application.

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Existence Of A Highest Wave In A Fully Dispersive Two-Way Shallow Water Model, Kyle Claassen, Matthew Johnson, Mats Ehrnstrom Jan 2019

Existence Of A Highest Wave In A Fully Dispersive Two-Way Shallow Water Model, Kyle Claassen, Matthew Johnson, Mats Ehrnstrom

Faculty Publications - Mathematics

No abstract provided.

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On The Fourth Order Schrodinger Equation In Four Dimensions: Dispersive Estimates And Zero Energy Resonances, William Green, Ebru Toprak Jan 2019

On The Fourth Order Schrodinger Equation In Four Dimensions: Dispersive Estimates And Zero Energy Resonances, William Green, Ebru Toprak

Faculty Publications - Mathematics

No abstract provided.

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Nondegeneracy And Stability Of Antiperiodic Bound States For Fractional Nonlinear Schrodinger Equations, Kyle Claassen, Matthew Johnson Jan 2019

Nondegeneracy And Stability Of Antiperiodic Bound States For Fractional Nonlinear Schrodinger Equations, Kyle Claassen, Matthew Johnson

Faculty Publications - Mathematics

No abstract provided.

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Solving Systems Of Differential Equations In The Case Of A Defective Coefficient Matrix, William Green, Sylvia Carlisle Jan 2019

Solving Systems Of Differential Equations In The Case Of A Defective Coefficient Matrix, William Green, Sylvia Carlisle

Faculty Publications - Mathematics

No abstract provided.

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