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Colby College

Honors Theses

Theses/Dissertations

2022

Articles 1 - 8 of 8

Full-Text Articles in Physical Sciences and Mathematics

Challenges Of Constructing Entrainment Map For Arbitrary Circadian Models, Yuxuan (Nelson) Wu Jan 2022

Challenges Of Constructing Entrainment Map For Arbitrary Circadian Models, Yuxuan (Nelson) Wu

Honors Theses

The entrainment map, developed by Dr.Diekman and Dr.Bose, is claimed to be a 1-dimensional map that produces a better prediction for phase-locking than methods than the phase response curve for circadian models. In his paper, he constructs the entrainment map for the two-dimensional circadian model, the Novak-Tyson model, and the other two higher-dimensional circadian models. For this thesis, we concentrate on exploring if it is viable to construct the entrainment map for other circadian models that are not included in his paper: the Becker-Weimann model and the Relogio model. In addition, we discuss the challenges of constructing the entrainment map …

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Apparatus Improvement And Characterisation For Experiments On Ultra-Cold Plasmas., Jakub Bystrický Jan 2022

Apparatus Improvement And Characterisation For Experiments On Ultra-Cold Plasmas., Jakub Bystrický

Honors Theses

Apparatus for creating ultra-cold neutral plasmas (UNPs) was improved and data on plasma expansion was collected. We increase the trapping efficiency of a quadrupole magneto-optical trap (MOT) by installing a tapered amplifier to increase the power of the cooling laser used to trap atoms. We achieve an improvement in density of trapped atoms from 1 x 1010 cm-3 to 2.5 - 4.5 x 1010 cm-3. In addition, to improve precision and decrease systematic error, the magnetic field induced by inductive current in the MOT's anti-helmholtz coils was suppressed. This was achieved by installing a KEPCO …

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Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa Jan 2022

Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa

Honors Theses

In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …

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"It's Not About The Polar Bears": Evangelical Christian Arguments For Environmentalism, Teresa D. White Jan 2022

"It's Not About The Polar Bears": Evangelical Christian Arguments For Environmentalism, Teresa D. White

Honors Theses

In recent history, white conservative evangelical Christians have formed an influential voting bloc of the Republican party in United States politics. Historically, conservatives have often denied the reality of human-induced climate change and have opposed climate change action and many environmental regulations. However, a number of conservative evangelical Christians have split from their traditionally conservative political views and have accepted the reality of climate change, becoming strong advocates for climate change action. This paper examines the arguments often presented by such advocates. I argue that evangelical environmental advocates craft specific arguments to convince fellow evangelicals to care for the environment …

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Nft Sneaker Marketplace Design, Testing, And Challenges, Chris Zhu Jan 2022

Nft Sneaker Marketplace Design, Testing, And Challenges, Chris Zhu

Honors Theses

This paper introduces the preliminary background and implementation of the NFT sneaker marketplace. Specifically, we build sneaker NFTs on top of ERC-20 within the Ethereum network and use a top-to-bottom design mechanism. Our website performs well in its functionality, compatibility, and performance. We discuss possible future steps for security implementation. In particular, we recommend using a cold wallet for clients' transactions and implementing multi-signature contracts to avoid spoofing and repudiation. Introducing the sneaker NFT marketplace will vastly reduce the costs of transactions and delivery time in the physical sneaker marketplace. We hope investors in the physical asset space can find …

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Analyzing The Free Energy Of Ions Sampling A Voltage Gated Sodium Ion Channel, Isabel Varghese Jan 2022

Analyzing The Free Energy Of Ions Sampling A Voltage Gated Sodium Ion Channel, Isabel Varghese

Honors Theses

Voltage gated sodium ion channels are implicated in cardiac diseases, seizures, etc., and they play a role in maintaining ionic homeostasis in cells. Computational studies use prokaryotic model because they are simpler but function similarly to human voltage gated sodium ion channels. This study uses molecular dynamics (MD) to study three specific questions regarding voltage gated sodium ion channels of Magnetococcus marinus. The first question in this study is how the free energy of sodium diffusion compares to that of calcium ion diffusion. We were not able to find any physically significant information due to poor sampling and a lack …

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Representation Theory And Its Applications In Physics, Jakub Bystrický Jan 2022

Representation Theory And Its Applications In Physics, Jakub Bystrický

Honors Theses

Representation theory is a branch of mathematics that allows us to represent elements of a group as elements of a general linear group of a chosen vector space by means of a homomorphism. The group elements are mapped to linear operators and we can study the group using linear algebra. This ability is especially useful in physics where much of the theories are captured by linear algebra structures. This thesis reviews key concepts in representation theory of both finite and infinite groups. In the case of finite groups we discuss equivalence, orthogonality, characters, and group algebras. We discuss the importance …

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Decomposing Manifolds In Low-Dimensions: From Heegaard Splittings To Trisections, Suixin "Cindy" Zhang Jan 2022

Decomposing Manifolds In Low-Dimensions: From Heegaard Splittings To Trisections, Suixin "Cindy" Zhang

Honors Theses

The decomposition of a topological space into smaller and simpler pieces is useful for understanding the space. In 1898, Poul Heegaard introduced the concept of a Heegaard splitting, which is a bisection of a 3-manifold. Heegaard diagrams, which describe Heegaard splittings combinatorially, have been recognized as a powerful tool for classifying 3-manifolds and producing important invariants of 3-manifolds. Handle decomposition, invented by Stephen Smale in 1962, describes how an n-manifold can be constructed by successively adding handles. In 2012, Gay and Kirby introduced trisections of 4-manifold, which are a four-dimensional analogues of Heegaard splittings in dimension three. Trisection diagrams give …

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