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Rose-Hulman Institute of Technology

2018

Articles 1 - 13 of 13

Full-Text Articles in Physical Sciences and Mathematics

Coupling Light Into Siliconwaveguide Using Surface Plasmon Polaritons, Jeong Rok Kim Dec 2018

Coupling Light Into Siliconwaveguide Using Surface Plasmon Polaritons, Jeong Rok Kim

Graduate Theses - Physics and Optical Engineering

No abstract provided.

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Sums Involving The Number Of Distinct Prime Factors Function, Tanay Wakhare Oct 2018

Sums Involving The Number Of Distinct Prime Factors Function, Tanay Wakhare

Rose-Hulman Undergraduate Mathematics Journal

We find closed form expressions for finite and infinite sums that are weighted by $\omega(n)$, where $\omega(n)$ is the number of distinct prime factors of $n$. We then derive general convergence criteria for these series. The approach of this paper is to use the theory of symmetric functions to derive identities for the elementary symmetric functions, then apply these identities to arbitrary primes and values of multiplicative functions evaluated at primes. This allows us to reinterpret sums over symmetric polynomials as divisor sums and sums over the natural numbers.

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Local Warming In Low Latitude Locations: A Time Series Analysis, Ryan Pittman Oct 2018

Local Warming In Low Latitude Locations: A Time Series Analysis, Ryan Pittman

Rose-Hulman Undergraduate Mathematics Journal

Global warming is a well-known and well-studied phenomenon pertaining to a gradual increase of average global temperatures over time. Many global warming mathematical models make certain assumptions regarding the factors that impact global temperature. These assumptions include effects from increased global carbon dioxide levels in the atmosphere and the melting ice sheets, among others. This paper draws conclusions about temperature changes without the assumptions needed for the global warming mathematical models. Instead of using computer models to project temperatures on a global scale, 33 low-latitude locations in the southern United States were individually studied to see if each one has …

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Partial Sum Trigonometric Identities And Chebyshev Polynomials, Sarah Weller Oct 2018

Partial Sum Trigonometric Identities And Chebyshev Polynomials, Sarah Weller

Rose-Hulman Undergraduate Mathematics Journal

Using Euler’s theorem, geometric sums and Chebyshev polynomials, we prove trigonometric identities involving sums and multiplications of cosine.

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Probabilities Involving Standard Trirectangular Tetrahedral Dice Rolls, Rulon Olmstead, Doneliezer Baize Oct 2018

Probabilities Involving Standard Trirectangular Tetrahedral Dice Rolls, Rulon Olmstead, Doneliezer Baize

Rose-Hulman Undergraduate Mathematics Journal

The goal is to be able to calculate probabilities involving irregular shaped dice rolls. Here it is attempted to model the probabilities of rolling standard tri-rectangular tetrahedral dice on a hard surface, such as a table top. The vertices and edges of a tetrahedron were projected onto the surface of a sphere centered at the center of mass of the tetrahedron. By calculating the surface areas bounded by the resultant geodesics, baseline probabilities were achieved. Using a 3D printer, dice were constructed of uniform density and the results of rolling them were recorded. After calculating the corresponding confidence intervals, the …

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A Proof Of The "Magicness" Of The Siam Construction Of A Magic Square, Joshua Arroyo Oct 2018

A Proof Of The "Magicness" Of The Siam Construction Of A Magic Square, Joshua Arroyo

Rose-Hulman Undergraduate Mathematics Journal

A magic square is an n x n array filled with n2 distinct positive integers 1, 2, ..., n2 such that the sum of the n integers in each row, column, and each of the main diagonals are the same. A Latin square is an n x n array consisting of n distinct symbols such that each symbol appears exactly once in each row and column of the square. Many articles dealing with the construction of magic squares introduce the Siam method as a "simple'' construction for magic squares. Rarely, however, does the article actually prove that the …

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On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim, Jackson Bahr, Eric Neyman, Gregory Taylor Oct 2018

On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim, Jackson Bahr, Eric Neyman, Gregory Taylor

Rose-Hulman Undergraduate Mathematics Journal

In this work, we completely characterize by $j$-invariant the number of orders of elliptic curves over all finite fields $F_{p^r}$ using combinatorial arguments and elementary number theory. Whenever possible, we state and prove exactly which orders can be taken on.

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Stranded Cellular Automaton And Weaving Products, Hao Yang Sep 2018

Stranded Cellular Automaton And Weaving Products, Hao Yang

Mathematical Sciences Technical Reports (MSTR)

In order to analyze weaving products mathematically and find out valid weaving products, it is natural to relate them to Cellular Automaton. They are both generated based on specific rules and some initial conditions. Holden and Holden have created a Stranded Cellular Automaton that can represent common weaving and braiding products. Based on their previous findings, we were able to construct a Java program and analyze various aspects of the automaton they created. This paper will discuss the complexity of the Stranded Cellular Automaton, how to determine whether a weaving product holds together or not based on the automaton and …

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Design, Fabrication, And Characterization Of A One-Dimensional Single-Material Polarizing Photonic Crystal, Ehsan Ordouie Jul 2018

Design, Fabrication, And Characterization Of A One-Dimensional Single-Material Polarizing Photonic Crystal, Ehsan Ordouie

Graduate Theses - Physics and Optical Engineering

We examine a multilayered one-dimensional (1D) polarizing photonic crystal designed and fabricated out of a single material. This polarizer is designed for high reflection of the s polarization and low reflection of p polarization at the wavelength of 632.8 nm. This device is fabricated implementing the oblique angle deposition technique to produce six-bilayers of alternating high to low indices of titanium dioxide using e-beam PVD for depositing on top of a fused silica substrate. For modeling, we used transfer-matrix method and numerical finite-difference time-domain analysis to simulate behavior of the 1D photonic bandgap structure. Both model and simulation predict better …

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Gain Modeling Of Erbium-Doped Fiber Amplifiers Pumped At 980nm, Deepak Charles Baskar May 2018

Gain Modeling Of Erbium-Doped Fiber Amplifiers Pumped At 980nm, Deepak Charles Baskar

Graduate Theses - Physics and Optical Engineering

Erbium-Doped Fiber Amplifiers (EDFA) are one of the most widely used optical amplifiers in the field of optical communications and fiber lasers. Theoretical models based on the rate equations, therefore, were developed to predict the performance of such amplifiers. The goal of this thesis is to provide a numerical model for EDFAs and verify its validity through experimental measurements. Two computer programs based on two different numerical methods (the Finite Difference method and the 4th Order Runge-Kutta Method) to solve differential equations were written. The different fiber parameters to build the model including absorption and emission crosssections and scattering losses …

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Branching Matrices For The Automorphism Group Lattice Of A Riemann Surface, Sean A. Broughton Mar 2018

Branching Matrices For The Automorphism Group Lattice Of A Riemann Surface, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

Let S be a Riemann surface and G a large subgroup of Aut(S) (Aut(S) may be unknown). We are particularly interested in regular n-gonal surfaces, i.e., the quotient surface S/G (and hence S/Aut(S)) has genus zero. For various H the ramification information of the branched coverings S/K -> S/H may be captured in a matrix. The ramification information, in particular strong branching, may be then be used in analyzing the structure of Aut(S). The ramification information is conjugation invariant so the matrix's rows and columns may be indexed by conjugacy classes of subgroups. The only required …

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The Convex Body Isoperimetric Conjecture In The Plane, John Berry, Eliot Bongiovanni, Wyatt Boyer, Bryan Brown, Paul Gallagher, David Hu, Alyssa Loving, Zane Martin, Maggie Miller, Byron Perpetua, Sarah Tammen Feb 2018

The Convex Body Isoperimetric Conjecture In The Plane, John Berry, Eliot Bongiovanni, Wyatt Boyer, Bryan Brown, Paul Gallagher, David Hu, Alyssa Loving, Zane Martin, Maggie Miller, Byron Perpetua, Sarah Tammen

Rose-Hulman Undergraduate Mathematics Journal

The Convex Body Isoperimetric Conjecture states that the least perimeter needed to enclose a volume within a ball is greater than the least perimeter needed to enclose the same volume within any other convex body of the same volume in Rn. We focus on the conjecture in the plane and prove a new sharp lower bound for the isoperimetric profile of the disk in this case. We prove the conjecture in the case of regular polygons, and show that in a general planar convex body the conjecture holds for small areas.

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Comparison Of Processed And Non-Processed Biomass Digestion, Richard Bruce Clark Iii Feb 2018

Comparison Of Processed And Non-Processed Biomass Digestion, Richard Bruce Clark Iii

Graduate Theses - Chemistry and Biochemistry

Lignocellulosic ethanol is the main focus of second-generation biofuels [1]. Because cellulose is the most abundant organic material on earth, second-generation biofuels are a more sustainable option than the classical first-generation biofuels that use foodstuffs as the main feedstock in ethanol production [1]. Furthermore, biofuel can be produced not only from unprocessed biomass such as corn husks but also from processed material like paper [1]. Ionic liquids have shown to be quite effective in dissolving naturally occurring, and traditionally insoluble, polymers such as cellulose into solution, and cellulase enzymes have been shown to effectively digest cellulose into simple sugars [2]. …

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