Physical Sciences and Mathematics Commons^™

Existence Of Well-Defined Pointer Observable Selects Tensor Product Factorizations Of Quantum Systems, Brian Lee

CMC Senior Theses

In the decoherence account of quantum mechanics, a choice of particular tensor product structure (a particular partition of system into subsystems) is assumed. We explore whether it is possible to relax this arbitrary choice by requiring that a valid tensor product structure admits a quasi-classical description. Such tensor product structures are said to be quasi-classical or decoherence-selected tensor product structures. This project generalizes a 2-qubit quasi-classical tensor product structure selection algorithm to an n-qubit selection algorithm, which allows us to, for the first time, consider the relationship between decoherence-selected tensor product structures and locality-selected tensor product structures. To generalize the …

Using Computational Fluid Dynamics And Optical Sensor Technology To Scale Cell Culture Platforms, Mandar Makwana

KGI Theses and Dissertations

Different cell culture vessels ranging from micro scale to laboratory scale to commercial scale play critical role in upstream process development for biologics manufacturing. Based on the mode of operation, cell culture vessels have different hydrodynamic environments, making it challenging to scale. Integrated approaches using computational tools supported by experimental studies can overcome these challenges. Computational Fluid Dynamics (CFD) is one such tool that can simulate hydrodynamics within the cell culture vessels and can provide insights at macro and micro-scale. Accuracy of a CFD model significantly depends on the fluid model and assumptions. Traditionally, simple two-equation fluid models were developed …

Analysis Of Biologically Effective Dose For Retroactive Yttrium-90 Trans-Arterial Radioembolization Treatment Optimization, Mj Lindsey

CMC Senior Theses

Trans-arterial radioembolization (TARE) is a protracted modality of radiation therapy where radionuclides labeled with Yttrium-90 (⁹⁰Y) are inserted inside a patient's hepatic artery to treat hepatocellular carcinoma (HCC). While TARE has been shown to be a clinically effective and safe treatment, there is little understanding of the radiobiological relationship between absorbed dose and tissue response, and thus there is no dosimetric standard for treatment planning. The Biologically Effective Dose (BED) formalism, derived from the Linear-Quadratic model of radiobiology, is used to weigh the absorbed dose by the time pattern of delivery. BED is a virtual dose that can …

Modeling Self-Diffusiophoretic Janus Particles In Fluid, Kausik Das

HMC Senior Theses

We explore spherical Janus particles in which a chemical reaction occurs on one face, depleting a substrate in the suspending fluid, while no reaction occurs on the other face. The steady state concentration field is governed by Laplace’s equation with mixed boundary conditions. We use the collocation method to obtain numerical solutions to the equation in spherical coordinates. The asymmetry of the reaction gives rise to a slip velocity that causes the particle to move spontaneously in the fluid through a process known as self-diffusiophoresis. Using the Lorentz reciprocal theorem, we obtain the swimming velocity of the particle. We extend …

Can The Xy+Z Heisenberg Model Be Compressed Using The Yang-Baxter Equation? An Exploration Of The Compression Of Quantum Time Dynamic Circuits Describing Heisenberg Spin Chains, Miriam Caron, Bo Peng Dr., Scott Gould Dr., Kevin Setter Dr., Niranjan Govind Dr.

Pitzer Senior Theses

Quantum computing is currently deployed on noisy intermediate-scale quantum (NISQ) devices, which are only able to simulate circuits reliably on shallow depth quantum circuits. A promising problem on near-term quantum computers is quantum time dynamics (QTD). However, QTD circuits grow with increasing time simulations making them difficult to simulate on NISQ devices. This thesis project explores QTD simulations in variations of 1D Heisenberg spin chains with nearest-neighbor and transverse external field interactions with an eye towards studying the dynamics in broader classes of spin models. I first study the quantum Yang-Baxter equation (YBE) and how it has been shown to …

Optical Tweezers: Exerting Force With Light, Gabriella Seifert

Scripps Senior Theses

Photons carry momentum. When a tightly-focused beam of photons hit a particle, they transfer some of their momentum to the particle, exerting a force. Optical tweezers take advantage of this phenomenon to trap (or “tweeze”) a spherical bead just after the focus of a diverging laser beam, creating a potential well that pulls in beads. In this thesis, I predict the force exerted on trapped beads and measure the actual force using an optical tweezers setup that I built. To predict the force, I follow the path of all possible rays from a diverging beam incident on a spherical bead …

Data-Driven Methods For Low-Energy Nuclear Theory, Jordan M.R. Fox

CGU Theses & Dissertations

The term data-driven describes computational methods for numerical problem solvingwhich have been developed by the field of data science; these are at the intersection of computer science,mathematics, and statistics. When applied to a domain science like nuclear physics, especially with the goalof deepening scientific insight, data-driven methods form a core pillar of the computational science endeavor.In this dissertation I explore two problems related to theoretical nuclear physics: one in the framework of numerical statistics, and the other in the framework of machine learning. I) Historically our understanding of the structure of the atomic nucleus, the quantum many-body problem, has been …

Using Powder Diffraction To Give Insight Into Structures Of Ir2(Diisocyanomenthane)4x2 [Dimen] (X = Cl; Pf6; Bph4), Mairead Brownell

Scripps Senior Theses

Ir2(dimen)42+ (dimen = 1,8-diisocyanomenthane) has been studied extensively as model compound to better understand catalysis of photochemical reactions. Although Ir2(dimen)42+ has been used primarily to observe the photophysical changes of metal-metal transitions, it gives great insight into the transitions that allow other d8-d8 metal complexes to undergo photochemical processes and generate hydrogen gas. The large visible range by which Ir2(dimen)42+ (1) can be electronically excited in solution is indicative of its two solution phase ground states, which interestingly have been hypothesized to resemble two unique packing structures observed in the powder state. In this study, the powder diffraction patterns of …

The Effects Of "Sticky Stuff" On The Spin Rate And Break Of A Baseball Pitch, Natalie Dale

Scripps Senior Theses

In June 2021, Major League Baseball cracked down on the use of foreign substances by pitchers on the ball (Castrovince, 2021a). It is believed the sticky substances give the pitchers an unfair advantage over batters since they increase spin rate, consequently, through the Magnus Effect, creating more movement or “break” in the pitch, making it harder to hit. There are existing gaps in empirical research on this topic, thus the goal of this project was to determine the effect the banned substances have on the spin rate and related break of the pitches. By using pitch tracking technology, two types …

Parallels Of Quantum Mechanics And Mahāyāna Buddhist Philosophy: An Argument For Relational Quantum Mechanics, Axel I. Palapa

CMC Senior Theses

Western orthodoxy philosophy is based on the principle of noncontradiction and thus, the philosophy of science is as well. The most prominent interpretations of quantum mechanics, since its inception, have followed this principle. In this paper, two quantum phenomena, the Observer Problem (measurement problem) and quantum entanglement will be analyzed from a Mahayana Buddhism ontological perspective. I will analyze the mathematical and philosophical arguments proposed by Graham Priest and Jay Garfield, based on dialethism, pertaining to Nagarjuna and the Net of Indra. Demonstrating the parallels and adaptability of the arguments to further the philosophical groundwork for Carlo Reveille’s Relational Quantum …

Once Upon A Party - An Anecdotal Investigation, Vijay Fafat

Journal of Humanistic Mathematics

Mathematicians and Physicists attending let-your-hair-down parties behave exactly like their own theories. They live by their theorems, they jive by their theorems. Life imitates their craft, and we must simply observe the deep truths hiding in their party-going behavior...

A Detailed X-Ray Analysis Of The Cold Front In Relics Cluster A2163, Anne Poy

CMC Senior Theses

Galaxy clusters are the largest gravitationally bound objects in the Universe. Studying them can teach us about how they merge and grow, which in turn provides unparalleled information about the history of the evolution of the Universe. X-ray observations of galaxy clusters have uncovered substructure in the hot, X-ray emitting gas known as the intracluster mediums (ICM). Substructure indicates that the ICM has been churned up, possibly by a significant off-axis merger event. This substructure includes cold fronts, sloshing spirals, and shocks. We present deep Chandra observations of the merging cluster Abell 2163. We investigate the global spectrum and find …

Computationally Recovering Preferred Factorizations Of Quantum Hilbert Space, Louisa Cornelis

Scripps Senior Theses

This thesis addresses the question of the preferred factorization of the quantum mechanical Hilbert Space into sub parts. Specifically, I computationally implement streamlined aspects of the recent “in principle” proposal of Carroll and Singh in their paper Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics. The goal is to link the selection of a preferred tensor product factorization to the appearance of quasi-classical behavior in this preferred factorization. Carroll and Singh quantify quasi-classical behavior through the criteria of “robustness” and “predictability” using the purity and pointer entropies. This work tests whether it is necessary to use both entropies …

Drawing Parallels In Art Science For Collaborative Learning: A Case Study, Karen Westland

The STEAM Journal

This research paper explores drawing as a tool to facilitate interdisciplinary practice. Outlined is the personal experience of PhD researcher [name removed] in their physics/craft research project, combined with thoughts and opinions from collaborators gathered through group discursive interviews. Interdisciplinary projects face interpersonal and conceptually ambiguous challenges which can be addressed through adopting drawing techniques for educational purposes. Findings highlight that drawing can assist across a breadth of applications as a learning tool for everyone, regardless of drawing ability, to improve the functionality of collaborative projects. Specifically, drawing combined with other communication techniques develops a performative communicative approach that enriches …

Modeling Residence Time Distribution Of Chromatographic Perfusion Resin For Large Biopharmaceutical Molecules: A Computational Fluid Dynamic Study, Kevin Vehar

KGI Theses and Dissertations

The need for production processes of large biotherapeutic particles, such as virus-based particles and extracellular vesicles, has risen due to increased demand in the development of vaccinations, gene therapies, and cancer treatments. Liquid chromatography plays a significant role in the purification process and is routinely used with therapeutic protein production. However, performance with larger macromolecules is often inconsistent, and parameter estimation for process development can be extremely time- and resource-intensive. This thesis aimed to utilize advances in computational fluid dynamic (CFD) modeling to generate a first-principle model of the chromatographic process while minimizing model parameter estimation's physical resource demand. Specifically, …

Decay And Dissipation: Finding Energy Level Jumps In A Harmonic Oscillator System Using Fortran And Fourier Analysis, Clara Chilton

Scripps Senior Theses

In this paper, I will look at a mass-spring system that can be described by a Hamiltonian. In most systems described by a Hamiltonian, the energy levels will be quantized, and the system will be able to jump between them. However, many methods of finding these jumps aren’t well-suited to numerical analysis. I’ll use a Markovian approximation (The Liouville von Neuman Equation), which allows me to use only the last time step to find the current one. Using this, I will analyze the system to find the time evolution of the probability density matrix – whose diagonal shows the probability …

Electrodynamics Modeling Of Plasmonic-Organic Hybrid Waveguides, Marcus Michel

Pomona Senior Theses

Optical fibers have multiple advantages over conventional electrical connections, such as lower energy losses and higher bandwidth. To use optics for chip-to-chip communication, electro-optic (EO) modulators need to be scaled down to be incorporated on integrated circuits. This size reduction has been accomplished using plasmonic-organic hybrid (POH) waveguides, which make use of nonlinear organic EO materials and surface plasmon polaritons to achieve light modulation in devices with lengths on the micron scale. As these devices are just starting to be developed, there are many avenues for their potential optimization. In order to streamline and reduce the cost of the optimization …

Characterizing Solar Cells, Katheryn R. Kornegay

Pomona Senior Theses

Perovskite solar cells and organic photovoltaics are both attractive because of their potential flexibility, tunable material properties, and low cost. Though perovskite solar cells have reached efficiencies comparable to conventional silicon solar cells, these have only occurred with lab-scale devices. Organic photovoltaics have much lower operating efficiencies than both perovskite and silicon solar cells, often due to non-uniformities and defects. In this thesis, we use two different techniques to better characterize these two types of solar cells. For perovskite solar cells, we use a drift-diffusion model, to characterize the transition between different doped states in its hole-transport layer, Spiro-OMeTAD, and …

Complex Ciliary Flows Around Stentor Polymorphus In Solutions Of 2% Buttermilk And Chlamydomonas Reinhardtii, Eliana B. Smithstein

Scripps Senior Theses

Stentor are large, unicellular ciliates of the Heterotricha order. They live in both freshwater and marine habitats and are mostly found in ponds. I studied Stentor polymorphus, which is a species of Stentor only recently discovered to be lab culturable. They range from 0.5-1.5mm in length and are unusual because they live with endosymbiotic algae and are much more likely than other, more widely studied, species of Stentor to form aggregates while they are eating. There are three main components to this thesis: First, I established protocols for keeping a viable S. polymorphus culture, since no protocols had been …

Gravity-Drawing Flexible Silicone Filaments As Fiber Optics And Model Foldamers, Katherine Snell

CMC Senior Theses

Here, we present a method of gravity-drawing polydimethylsiloxane (PDMS) silicone fibers with application as fiber optics and as model foldamers. Beginning as a viscous liquid, PDMS is cured using heat until its measured viscosity reaches 4000 mPa•s. The semi-cured elastomer is then extruded through a tube furnace to produce thin (diameters on the order of hundred micrometers) filaments with scalable lengths. PDMS is biocompatible, gas-permeable, flexible, and hydrophobic. Additionally, the PDMS surface hydrophobicity can be modified via UV exposure, O2 plasma, and corona discharge. We demonstrate the patternibility (i.e patterns of hydrophobicity) of PDMS fibers, adding complexity to potential foldamer …

Comforting With Mathematics: A Case Study, Michael J. Goldstein

Journal of Humanistic Mathematics

Death by suicide often leaves behind grieving family members with unanswered questions. Of these concerns, fear that their loved one suffered or felt regret is common. When the method of suicide was jumping from height, that answer can easily be determined using basic kinematics. Despite the perception that mathematics is a cold, calculating field, it can provide a clear, definitive answer and comfort those left behind.

@Yourlocation: A Spatial Analysis Of Geotagged Tweets In The Us, Ocean Mckinney

CMC Senior Theses

This project examines the spatial network properties observable from geo-located tweet data. Conventional exploration examines characteristics of a variety of network attributes, but few employ spatial edge correlations in their analysis. Recent studies have demonstrated the improvements that these correlations contribute to drawing conclusions about network structure. This thesis expands upon social network research utilizing spatial edge correlations and presents processing and formatting techniques for JSON (JavaScript Object Notation) data.

Giardia Lamblia Growth In Viscoelastic Fluids, Kelly Watanabe

CMC Senior Theses

Giardia lamblia is a single-celled protozoan parasite that when ingested, causes diarrheal disease and infects 33% of people in developing countries. Previous studies observe Giardia in water-like fluids, but Giardia's infectious environment consists of viscoelastic mucus in the small intestine. Therefore, Giardia was cultured in viscoelastic fluids, and its population growth was observed in vitro. To create shear-thinning viscoelastic fluids, 0.2% and 0.4% long-chain polyacrylamide (LCPAM) was added to cell culture media. Giardia was cultured in control media, 0.2% LCPAM, and 0.4% LCPAM, and population growth was quantitatively determined over time. Increasing LCPAM concentration resulted in a solution with …

Pursuing Natural Unity, Consciousness Included, Rowen Cox-Rubien

Scripps Senior Theses

An ontological exploration of consciousness and how it is related to the body and other aspects of physical reality. Framed by David Chalmers' conception of "The Hard Problem", we begin from a physicalist perspective to discuss the problem of mental causation, which is the inquiry of how the mind communicates and interacts with the body. From here we examine the employment of identity reduction to functionalize and therefore physically explain mentality. We find that reductionist methods, the backbone of scientific investigation, do not work to explain conscious experience, because conscious experience is not quantifiable--it is qualitative. Thus we are left …

Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter

Scripps Senior Theses

Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.

Hyperthermia As A Cancer Treatment- From Theory To Practice, Graham Fullerton

CMC Senior Theses

Using iron super-paramagnetic and ferromagnetic nanoparticles composed of Fe₃O₄ molecules, scientists analyze the effectiveness and practicality of this new treatment theory, hyperthermia. The problems of magnetic particle density, isothermal barriers/cellular cooling thresholds, and nanoparticle specific targeting are addressed in this review.

Iron magnetic nanoparticles were chosen due to their relatively low biological reactivates and lack of subsequent cellular toxicity. However, there are significant heating problems associated with these magnetic nanoparticles due to their relative size and short thermal time constants or thermal half-lives. Effectively, these aforementioned issues create a phenomenon where cancerous cells, surrounded by unheated healthy …

Can A Comprehensive Transition Plan To Barefoot Running Be The Solution To The Injury Epidemic In American Endurance Runners?, Michael A. Scarlett

CMC Senior Theses

Fossils belonging to the genus Homo, dating as far back as two million years ago, exhibit uniquely efficient features suggesting that early humans had evolved to become exceptional endurance runners. Although they did not have the cushion or stability-control features provided in our modern day running shoes, our early human ancestors experienced far less of the running-related injuries we experience today. The injury rate has been estimated as high as 90% annually for Americans training for a marathon and as high as 79% annually for all American endurance runners. There is an injury epidemic in conventionally shod populations that …

Maximal Lelm Distinguishability Of Qubit And Qutrit Bell States Using Projective And Non-Projective Measurements, Nathaniel Leslie

HMC Senior Theses

Many quantum information tasks require measurements to distinguish between different quantum-mechanically entangled states (Bell states) of a particle pair. In practice, measurements are often limited to linear evolution and local measurement (LELM) of the particles. We investigate LELM distinguishability of the Bell states of two qubits (two-state particles) and qutrits (three-state particles), via standard projective measurement and via generalized measurement, which allows detection channels beyond the number of orthogonal single-particle states. Projective LELM can only distinguish 3 of 4 qubit Bell states; we show that generalized measurement does no better. We show that projective LELM can distinguish only 3 of …

Quantum Foundations With Astronomical Photons, Calvin Leung

HMC Senior Theses

Bell's inequalities impose an upper limit on correlations between measurements of two-photon states under the assumption that the photons play by a set of local rules rather than by quantum mechanics. Quantum theory and decades of experiments both violate this limit.

Recent theoretical work in quantum foundations has demonstrated that a local realist model can explain the non-local correlations observed in experimental tests of Bell's inequality if the underlying probability distribution of the local hidden variable depends on the choice of measurement basis, or ``setting choice''. By using setting choices determined by astrophysical events in the distant past, it is …

Jaguar Sun, Anya Nadal

The STEAM Journal

Cymatics, is derived from a Greek word, meaning "wave", is a subset of modal vibrational phenomena. The term was coined by Hans Jenny, a Swiss follower of the philosophical school known as anthroposophy. This is a visual representation of the frequency field. I created this piece from acrylic on canvas based on the subtle energies I can see and feel.