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Articles 1 - 23 of 23
Full-Text Articles in Physics
Once Upon A Party - An Anecdotal Investigation, Vijay Fafat
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...
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, …
Comforting With Mathematics: A Case Study, Michael J. Goldstein
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.
The Topology Of Absence, Nora E. Culik
The Topology Of Absence, Nora E. Culik
Journal of Humanistic Mathematics
“The Topology of Absence” literalizes triangulations, hyperbeloids, and the concept of the limit in the story of “locating” a lost mother. This story, like “The Physicist’s Basement” in the July 2014 issue, is part of a series that worries about competing notions of mathematics, i.e., mathematics as some sort of disembodied configuration or as emergent in the material reality of human life.
The Physicist's Basement, Nora Culik
The Physicist's Basement, Nora Culik
Journal of Humanistic Mathematics
No abstract provided.
Mathematical And Physical Aspects Of Complex Symmetric Operators, Stephan Ramon Garcia, Emil Prodan, Mihai Putinar
Mathematical And Physical Aspects Of Complex Symmetric Operators, Stephan Ramon Garcia, Emil Prodan, Mihai Putinar
Pomona Faculty Publications and Research
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C-selfadjoint extensions of C-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C-orthonormal vectors, and conjugate-linear symmetric operators. The main results are complemented by a variety of natural examples arising in field theory, quantum physics, and complex variables.
Invisibility: A Mathematical Perspective, Austin G. Gomez
Invisibility: A Mathematical Perspective, Austin G. Gomez
CMC Senior Theses
The concept of rendering an object invisible, once considered unfathomable, can now be deemed achievable using artificial metamaterials. The ability for these advanced structures to refract waves in the negative direction has sparked creativity for future applications. Manipulating electromagnetic waves of all frequencies around an object requires precise and unique parameters, which are calculated from various mathemat- ical laws and equations. We explore the possible interpretations of these parameters and how they are implemented towards the construction of a suitable metamaterial. If carried out correctly, the wave will exit the metamaterial exhibiting the same behavior as when it had entered. …
The Quantum Dialectic, Logan Kelley
The Quantum Dialectic, Logan Kelley
Pitzer Senior Theses
A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part …
Evidence Of The Harmonic Faraday Instability In Ultrasonic Atomization Experiments With A Deep, Inviscid Fluid, Andrew P. Higginbotham '09, Aaron Guillen '11, Nathan C. Jones '10, Thomas D. Donnelly, Andrew J. Bernoff
Evidence Of The Harmonic Faraday Instability In Ultrasonic Atomization Experiments With A Deep, Inviscid Fluid, Andrew P. Higginbotham '09, Aaron Guillen '11, Nathan C. Jones '10, Thomas D. Donnelly, Andrew J. Bernoff
All HMC Faculty Publications and Research
A popular method for generating micron-sized aerosols is to submerge ultrasonic (ω~MHz) piezoelectric oscillators in a water bath. The submerged oscillator atomizes the fluid, creating droplets with radii proportional to the wavelength of the standing wave at the fluid surface. Classical theory for the Faraday instability predicts a parametric instability driving a capillary wave at the subharmonic (ω/2) frequency. For many applications it is desirable to reduce the size of the droplets; however, using higher frequency oscillators becomes impractical beyond a few MHz. Observations are presented that demonstrate that smaller droplets may also be created by …
Coalitions And Cliques In The School Choice Problem, Sinan Aksoy, Alexander Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao, Xinjing Zhu
Coalitions And Cliques In The School Choice Problem, Sinan Aksoy, Alexander Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao, Xinjing Zhu
Pomona Faculty Publications and Research
The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their …
Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering, David Caballero
Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering, David Caballero
CGU Theses & Dissertations
There are many numerical methods to study the quantum mechanical three-body scattering system using the Schrodinger equation. Traditionally, a partial-wave decomposition of the total wave function is carried out first, allowing the scattering system to be solved one partial wave at a time. This is convenient when the interaction is central, causing the total angular momentum to be conserved during the collision process. This is not possible in the presence of a non-central interaction such as a laser field, where the total angular momentum is not conserved during the collision process. The Discrete Variable Representation is a new method for …
Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg
Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg
WM Keck Science Faculty Papers
We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to …
Domain Relaxation In Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Jacob R. Wintersmith '06, Lu Zou
Domain Relaxation In Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Jacob R. Wintersmith '06, Lu Zou
All HMC Faculty Publications and Research
We report on theoretical studies of molecularly thin Langmuir films on the surface of a quiescent subfluid and qualitatively compare the results to both new and previous experiments. The film covers the entire fluid surface, but domains of different phases are observed. In the absence of external forcing, the compact domains tend to relax to circles, driven by a line tension at the phase boundaries. When stretched (by a transient applied stagnation-point flow or by stirring), a compact domain elongates, creating a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape will then relax slowly …
An Experimental Study Of Micron-Scale Droplet Aerosols Produced Via Ultrasonic Atomization, Thomas D. Donnelly, J. Hogan '03, A. Mugler '04, N. Schommer '04, M. Schubmehl '02, Andrew J. Bernoff, B. Forrest '02
An Experimental Study Of Micron-Scale Droplet Aerosols Produced Via Ultrasonic Atomization, Thomas D. Donnelly, J. Hogan '03, A. Mugler '04, N. Schommer '04, M. Schubmehl '02, Andrew J. Bernoff, B. Forrest '02
All HMC Faculty Publications and Research
In the last 10 years, laser-driven fusion experiments performed on atomic clusters of deuterium have shown a surprisingly high neutron yield per joule of input laser energy. Results indicate that the optimal cluster size for maximizing fusion events should be in the 0.01–μm diameter range, but an appropriate source of droplets of this size does not exist. In an attempt to meet this need, we use ultrasonic atomization to generate micron-scale droplet aerosols of high average density, and we have developed and refined a reliable droplet sizing technique based on Mie scattering. Harmonic excitation of the fluid in …
Blowup And Dissipation In A Critical-Case Unstable Thin Film Equation, Thomas P. Witelski, Andrew J. Bernoff, Andrea L. Bertozzi
Blowup And Dissipation In A Critical-Case Unstable Thin Film Equation, Thomas P. Witelski, Andrew J. Bernoff, Andrea L. Bertozzi
All HMC Faculty Publications and Research
We study the dynamics of dissipation and blow-up in a critical-case unstable thin film equation. The governing equation is a nonlinear fourth-order degenerate parabolic PDE derived from a generalized model for lubrication flows of thin viscous fluid layers on solid surfaces. There is a critical mass for blow-up and a rich set of dynamics including families of similarity solutions for finite-time blow-up and infinite-time spreading. The structure and stability of the steady-states and the compactly-supported similarity solutions is studied.
Transformation Of Statistics In Fractional Quantum Hall Systems, John J. Quinn, Arkadiusz Wojs, Jennifer J. Quinn, Arthur T. Benjamin
Transformation Of Statistics In Fractional Quantum Hall Systems, John J. Quinn, Arkadiusz Wojs, Jennifer J. Quinn, Arthur T. Benjamin
All HMC Faculty Publications and Research
A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane’s spherical geometry, the Fermion angular momentum lF is replaced by lB =lF − 1/2 (N −1). The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular …
Transient Anomalous Diffusion In Poiseuille Flow, Marco Latini '01, Andrew J. Bernoff
Transient Anomalous Diffusion In Poiseuille Flow, Marco Latini '01, Andrew J. Bernoff
All HMC Faculty Publications and Research
We revisit the classical problem of dispersion of a point discharge of tracer in laminar pipe Poiseuille flow. For a discharge at the centre of the pipe we show that in the limit of small non-dimensional diffusion, D, tracer dispersion can be divided into three regimes. For small times (t [double less-than sign] D−1/3), diffusion dominates advection yielding a spherically symmetric Gaussian dispersion cloud. At large times (t [dbl greater-than sign] D−1), the flow is in the classical Taylor regime, for which the tracer is homogenized transversely across the pipe and diffuses with …
Stability Of Self-Similar Solutions For Van Der Waals Driven Thin Film Rupture, Thomas P. Witelski, Andrew J. Bernoff
Stability Of Self-Similar Solutions For Van Der Waals Driven Thin Film Rupture, Thomas P. Witelski, Andrew J. Bernoff
All HMC Faculty Publications and Research
Recent studies of pinch-off of filaments and rupture in thin films have found infinite sets of first-type similarity solutions. Of these, the dynamically stable similarity solutions produce observable rupture behavior as localized, finite-time singularities in the models of the flow. In this letter we describe a systematic technique for calculating such solutions and determining their linear stability. For the problem of axisymmetric van der Waals driven rupture (recently studied by Zhang and Lister), we identify the unique stable similarity solution for point rupture of a thin film and an alternative mode of singularity formation corresponding to annular “ring rupture.”
The Legend Of The Apple, Raul A. Simon
The Legend Of The Apple, Raul A. Simon
Humanistic Mathematics Network Journal
No abstract provided.
The Interaction Of A Point Vortex With A Wall-Bounded Vortex Layer, Oliver V. Atassi, Andrew J. Bernoff, Seth Lichter
The Interaction Of A Point Vortex With A Wall-Bounded Vortex Layer, Oliver V. Atassi, Andrew J. Bernoff, Seth Lichter
All HMC Faculty Publications and Research
The interaction of a point vortex with a layer of constant vorticity, bounded below by a wall and above by an irrotational flow, is investigated as a model of vortex–boundary layer interaction. This model calculates both the evolution of the interface which separates the vortex layer from the irrotational flow and the trajectory of the vortex. In order to determine the conditions which lead to sustained unsteady interaction, three cases are investigated where the mutual interaction between the vortex and interface is initially assumed to be weak. (i) When a weak point vortex lies outside the layer, the vortex moves …
Music And Mathematics, Roxanne Kitts
Music And Mathematics, Roxanne Kitts
Humanistic Mathematics Network Journal
No abstract provided.
Advection Of A Passive Scalar By A Vortex Couple In The Small-Diffusion Limit, Joseph F. Lingevitch, Andrew J. Bernoff
Advection Of A Passive Scalar By A Vortex Couple In The Small-Diffusion Limit, Joseph F. Lingevitch, Andrew J. Bernoff
All HMC Faculty Publications and Research
We study the advection of a passive scalar by a vortex couple in the small-diffusion (i.e. large Péclet number, Pe) limit. The presence of weak diffusion enhances mixing within the couple and allows the gradual escape of the scalar from the couple into the surrounding flow. An averaging technique is applied to obtain an averaged diffusion equation for the concentration inside the dipole which agrees with earlier results of Rhines & Young for large times. At the outer edge of the dipole, a diffusive boundary layer of width O(Pe−½) forms; asymptotic matching to the interior …
Modulated, Frequency-Locked, And Chaotic Cross-Waves, William B. Underhill, Seth Lichter, Andrew J. Bernoff
Modulated, Frequency-Locked, And Chaotic Cross-Waves, William B. Underhill, Seth Lichter, Andrew J. Bernoff
All HMC Faculty Publications and Research
Measurements were made of the wave height of periodic, quasi-periodic, and chaotic parametrically forced cross-waves in a long rectangular channel. In general, three frequencies (and their harmonics) may be observed: the subharmonic frequency and two slow temporal modulations — a one-mode instability associated with streamwise variation and a sloshing motion associated with spanwise variation. Their interaction, as forcing frequency, f, and forcing amplitude, a, were varied, produced a pattern of Arnold tongues in which two or three frequencies were locked. The overall picture of frequency-locked and -unlocked regions is explained in terms of the Arnold tongues predicted by …