Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Series

2009

Claremont Colleges

Discipline
Keyword
Publication

Articles 1 - 30 of 41

Full-Text Articles in Physical Sciences and Mathematics

Voting, The Symmetric Group, And Representation Theory, Zajj Daugherty '05, Alexander K. Eustis '06, Gregory Minton '08, Michael E. Orrison Dec 2009

Voting, The Symmetric Group, And Representation Theory, Zajj Daugherty '05, Alexander K. Eustis '06, Gregory Minton '08, Michael E. Orrison

All HMC Faculty Publications and Research

We show how voting may be viewed naturally from an algebraic perspective by viewing voting profiles as elements of certain well-studied QSn-modules. By using only a handful of simple combinatorial objects (e.g., tabloids) and some basic ideas from representation theory (e.g., Schur's Lemma), this allows us to recast and extend some well-known results in the field of voting theory.

Go to article

Self-Organized Criticality In Sheared Suspensions, L. Corté, Sharon J. Gerbode, W. Man, D. J. Pine Dec 2009

Self-Organized Criticality In Sheared Suspensions, L. Corté, Sharon J. Gerbode, W. Man, D. J. Pine

All HMC Faculty Publications and Research

Recent studies reveal that suspensions of neutrally buoyant non-Brownian particles driven by slow periodic shear can undergo a dynamical phase transition between a fluctuating irreversible steady state and an absorbing reversible state. Using a computer model, we show that such systems exhibit self-organized criticality when a finite particle sedimentation velocity vs is introduced. Under periodic shear, these systems evolve, without external intervention, towards the shear-dependent critical concentration ϕc as vs is reduced. This state is characterized by power-law distributions in the lifetime and size of fluctuating clusters. Experiments exhibit similar behavior and, as vs is reduced, …

Go to article

How Much Can Guided Modes Enhance Absorption In Thin Solar Cells?, Peter N. Saeta, Vivian E. Ferry, Domenico Pacifici, Jeremy N. Munday, Harry A. Atwater Nov 2009

How Much Can Guided Modes Enhance Absorption In Thin Solar Cells?, Peter N. Saeta, Vivian E. Ferry, Domenico Pacifici, Jeremy N. Munday, Harry A. Atwater

All HMC Faculty Publications and Research

Absorption enhancement in thin metal-backed solar cells caused by dipole scatterers embedded in the absorbing layer is studied using a semi-analytical approach. The method accounts for changes in the radiation rate produced by layers above and below the dipole, and treats incoherently the subsequent scattering of light in guided modes from other dipoles. We find large absorption enhancements for strongly coupled dipoles, exceeding the ergodic limit in some configurations involving lossless dipoles. An antireflection-coated 100-nm layer of a-Si:H on Ag absorbs up to 87% of incident above-gap light. Thin layers of both strong and weak absorbers show similar strongly enhanced …

Go to article

On Similarity Classes Of Well-Rounded Sublattices Of Z², Lenny Fukshansky Oct 2009

On Similarity Classes Of Well-Rounded Sublattices Of Z², Lenny Fukshansky

CMC Faculty Publications and Research

A lattice is called well-rounded if its minimal vectors span the corresponding Euclidean space. In this paper we study the similarity classes of well-rounded sublattices of Z2. We relate the set of all such similarity classes to a subset of primitive Pythagorean triples, and prove that it has the structure of a non-commutative infinitely generated monoid. We discuss the structure of a given similarity class, and define a zeta function corresponding to each similarity class. We relate it to Dedekind zeta of Z[i], and investigate the growth of some related Dirichlet series, which reflect on …

Go to article

A Preliminary Mathematical Model Of Skin Dendritic Cell Trafficking And Induction Of T Cell Immunity, Amy H. Lin Erickson, Alison Wise, Stephen Fleming, Margaret Baird, Zabeen Lateef, Annette Molinaro, Miranda Teboh-Ewungkem, Lisette G. De Pillis Sep 2009

A Preliminary Mathematical Model Of Skin Dendritic Cell Trafficking And Induction Of T Cell Immunity, Amy H. Lin Erickson, Alison Wise, Stephen Fleming, Margaret Baird, Zabeen Lateef, Annette Molinaro, Miranda Teboh-Ewungkem, Lisette G. De Pillis

All HMC Faculty Publications and Research

Chronic inflammation is a process where dendritic cells (DCs) are constantly sampling antigen in the skin and migrating to lymph nodes where they induce the activation and proliferation of T cells. The T cells then travel back to the skin where they release cytokines that induce/maintain the inflammatory condition. This process is cyclic and ongoing. We created a differential equations model to reflect the initial stages of the inflammatory process. In particular, we modeled antigen stimulation of DCs in the skin, movement of DCs from the skin to a lymph node, and the subsequent activation of T cells in the …

Go to article

Compression Theorems For Periodic Tilings And Consequences, Arthur T. Benjamin, Alex K. Eustis '06, Mark A. Shattuck Aug 2009

Compression Theorems For Periodic Tilings And Consequences, Arthur T. Benjamin, Alex K. Eustis '06, Mark A. Shattuck

All HMC Faculty Publications and Research

We consider a weighted square-and-domino tiling model obtained by assigning real number weights to the cells and boundaries of an n-board. An important special case apparently arises when these weights form periodic sequences. When the weights of an nm-tiling form sequences having period m, it is shown that such a tiling may be regarded as a meta-tiling of length n whose weights have period 1 except for the first cell (i.e., are constant). We term such a contraction of the period in going from the longer to the shorter tiling as "period compression". It turns out that …

Go to article

Asymptotic Dynamics Of Attractive-Repulsive Swarms, Andrew J. Leverentz '08, Chad M. Topaz, Andrew J. Bernoff Jul 2009

Asymptotic Dynamics Of Attractive-Repulsive Swarms, Andrew J. Leverentz '08, Chad M. Topaz, Andrew J. Bernoff

All HMC Faculty Publications and Research

We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel’s first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly supported population has edges that behave like traveling waves whose speed, density, and slope we calculate. …

Go to article

A Semilinear Wave Equation With Smooth Data And No Resonance Having No Continuous Solution, Jose F. Caicedo, Alfonso Castro Jul 2009

A Semilinear Wave Equation With Smooth Data And No Resonance Having No Continuous Solution, Jose F. Caicedo, Alfonso Castro

All HMC Faculty Publications and Research

We prove that a boundary value problem for a semilinear wave equation with smooth nonlinearity, smooth forcing, and no resonance cannot have continuous solutions. Our proof shows that this is due to the non-monotonicity of the nonlinearity.

Go to article

Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori Jun 2009

Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori

All HMC Faculty Publications and Research

Analysis of acoustic phonons modulated due to the surfaces of a free-standing semiconductor plate and their deformation-potential interaction with electrons are presented. The form factor for electron-modulated acoustic phonon interaction is formulated and analyzed in detail. The form factor at zero in-plane phonon wave vector satisfies sum rules regardless of electron wave function. The form factor is larger than that calculated using bulk phonons, leading to a higher scattering rate and lower electron mobility. When properly normalized, the form factors lie on a universal curve regardless of plate thickness and material.

Go to article

The Initial And Final States Of Electron And Energy Transfer Processes: Diabatization As Motivated By System-Solvent Interactions, Joseph E. Subotnik, Robert J. Cave, Ryan P. Steele, Neil Shenvi Jun 2009

The Initial And Final States Of Electron And Energy Transfer Processes: Diabatization As Motivated By System-Solvent Interactions, Joseph E. Subotnik, Robert J. Cave, Ryan P. Steele, Neil Shenvi

All HMC Faculty Publications and Research

For a system which undergoes electron or energy transfer in a polar solvent, we define the diabatic states to be the initial and final states of the system, before and after the nonequilibrium transfer process. We consider two models for the system-solvent interactions: A solvent which is linearly polarized in space and a solvent which responds linearly to the system. From these models, we derive two new schemes for obtaining diabatic states from ab initio calculations of the isolated system in the absence of solvent. These algorithms resemble standard approaches for orbital localization, namely, the Boys and Edmiston–Ruedenberg (ER) formalisms. …

Go to article

Generation Of Mie Size Microdroplet Aerosols With Applications In Laser-Driven Fusion Experiments, Andrew P. Higginbotham '09, O. Semonin '06, S. Bruce '08, C. Chan '08, M. Maindi '07, Thomas D. Donnelly, M. Maurer, W. Bang, I. Churina, J. Osterholz, I. Kim, A. C. Bernstein, T. Ditmire Jun 2009

Generation Of Mie Size Microdroplet Aerosols With Applications In Laser-Driven Fusion Experiments, Andrew P. Higginbotham '09, O. Semonin '06, S. Bruce '08, C. Chan '08, M. Maindi '07, Thomas D. Donnelly, M. Maurer, W. Bang, I. Churina, J. Osterholz, I. Kim, A. C. Bernstein, T. Ditmire

All HMC Faculty Publications and Research

We have developed a tunable source of Mie scale microdroplet aerosols that can be used for the generation of energetic ions. To demonstrate this potential, a terawatt Ti:Al2O3 laser focused to 2×1019 W/cm2 was used to irradiate heavy water (D2O) aerosols composed of micron-scale droplets. Energetic deuterium ions, which were generated in the laser-droplet interaction, produced deuterium-deuterium fusion with approximately 2×103 fusion neutrons measured per joule of incident laser energy.

Go to article

Topics In Compressed Sensing, Deanna Needell May 2009

Topics In Compressed Sensing, Deanna Needell

CMC Faculty Publications and Research

Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a number of linear measurements much less than its actual dimension. Although in theory it is clear that this is possible, the difficulty lies in the construction of algorithms that perform the recovery efficiently, as well as determining which kind of linear measurements allow for the reconstruction. There have been two distinct major approaches to sparse recovery that each present different benefits and shortcomings. …

Go to article

Noisy Signal Recovery Via Iterative Reweighted L1-Minimization, Deanna Needell Apr 2009

Noisy Signal Recovery Via Iterative Reweighted L1-Minimization, Deanna Needell

CMC Faculty Publications and Research

Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate even in the presence of noise. Recent a modified version of this method, reweighted L1-minimization, has been suggested. Although no provable results have yet been attained, empirical studies have suggested the reweighted version outperforms the standard method. Here we analyze the reweighted L1-minimization method in the noisy case, and provide provable results showing an improvement in the error bound over the standard bounds.

Go to article

Counting On Chebyshev Polynomials, Arthur T. Benjamin, Daniel Walton '07 Apr 2009

Counting On Chebyshev Polynomials, Arthur T. Benjamin, Daniel Walton '07

All HMC Faculty Publications and Research

Chebyshev polynomials have several elegant combinatorial interpretations. Specificially, the Chebyshev polynomials of the first kind are defined by T0(x) = 1, T1(x) = x, and Tn(x) = 2x Tn-1(x) - Tn-2(x). Chebyshev polynomials of the second kind Un(x) are defined the same way, except U1(x) = 2x. Tn and Un are shown to count tilings of length n strips with squares and dominoes, where the tiles are given weights and sometimes color. Using these interpretations, many identities satisfied by Chebyshev polynomials can be given …

Go to article

A Life Cycle Perspective On Online Community Success, Alicia Iriberri '06, Gondy Leroy Feb 2009

A Life Cycle Perspective On Online Community Success, Alicia Iriberri '06, Gondy Leroy

CGU Faculty Publications and Research

Using the information systems lifecycle as a unifying framework, we review online communities research and propose a sequence for incorporating success conditions during initiation and development to increase their chances of becoming a successful community, one in which members participate actively and develop lasting relationships. Online communities evolve following distinctive lifecycle stages and recommendations for success are more or less relevant depending on the developmental stage of the online community. In addition, the goal of the online community under study determines the components to include in the development of a successful online community. Online community builders and researchers will benefit …

Go to article

Thermal Links For The Implementation Of An Optical Refrigerator, John Parker, David Mar, Steven Von Der Porten, John Hankinson, Kevin Byram, Chris Lee, Michael K. Mayeda, Richard C. Haskell, Qimin Yang, Scott R. Greenfield, Richard I. Epstein Jan 2009

Thermal Links For The Implementation Of An Optical Refrigerator, John Parker, David Mar, Steven Von Der Porten, John Hankinson, Kevin Byram, Chris Lee, Michael K. Mayeda, Richard C. Haskell, Qimin Yang, Scott R. Greenfield, Richard I. Epstein

All HMC Faculty Publications and Research

Optical refrigeration has been demonstrated by several groups of researchers, but the cooling elements have not been thermally linked to realistic heat loads in ways that achieve the desired temperatures. The ideal thermal link will have minimal surface area, provide complete optical isolation for the load, and possess high thermal conductivity. We have designed thermal links that minimize the absorption of fluoresced photons by the heat load using multiple mirrors and geometric shapes including a hemisphere, a kinked waveguide, and a tapered waveguide. While total link performance is dependent on additional factors, we have observed net transmission of photons with …

Go to article

An Undescribed Gecko (Gekkonidae: Cyrtodactylus) From Deer Cave, Gunung Mulu National Park, Sarawak, With Comments On The Distribution Of Bornean Cave Geckos, Donald A. Mcfarlane, Joyce Lundberg, Keith Christenson Jan 2009

An Undescribed Gecko (Gekkonidae: Cyrtodactylus) From Deer Cave, Gunung Mulu National Park, Sarawak, With Comments On The Distribution Of Bornean Cave Geckos, Donald A. Mcfarlane, Joyce Lundberg, Keith Christenson

WM Keck Science Faculty Papers

Geckos of the genus Cyrtodactylus are a speciose group in Southeast Asia, with at least nine species known from the island of Borneo (Das & Ismail, 2001; Das, 2006). Of these species, Cyrtodactylus cavernicolus has the smallest known range and is therefore the most vulnerable, a status that is reflected in the species having been designated a Totally Protected Species in Sarawak. Confirmed records of C. cavernicolus are known only from Niah Cave, located in an isolated limestone block known as the Gunung Subis massif, approximately 13 km² in extent. The Niah Cave Gecko is presumed to be dependent on …

Go to article

Bats And Bell Holes: The Microclimatic Impact Of Bat Roosting, Using A Case Study From Runaway Bay Caves, Jamaica, Joyce Lundberg, Donald A. Mcfarlane Jan 2009

Bats And Bell Holes: The Microclimatic Impact Of Bat Roosting, Using A Case Study From Runaway Bay Caves, Jamaica, Joyce Lundberg, Donald A. Mcfarlane

WM Keck Science Faculty Papers

The microclimatic effect of bats roosting in bell holes (blind vertical cylindrical cavities in cave roofs) in Runaway Bay Caves, Jamaica, was measured and the potential impact of their metabolism on dissolution modelled. Rock temperature measurements showed that bell holes with bats get significantly hotter than those without bats during bat roosting periods (by an average of 1.1 °C). The relationship is clearest for bell holes with more than about 300 g aggregate bat body mass and for bell holes that are moderately wide and deep, of W:D ratio between 0.8 and 1.6. Measurement of temperature decay after abandonment showed …

Go to article

Review: A Class Of Solutions To The Quantum Colored Yang-Baxter Equation, Gizem Karaali Jan 2009

Review: A Class Of Solutions To The Quantum Colored Yang-Baxter Equation, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Go to article

Mathematical Model Creation For Cancer Chemo-Immunotherapy, Lisette G. De Pillis, K Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross '08, James Moore '07, Benjamin Preskill '09 Jan 2009

Mathematical Model Creation For Cancer Chemo-Immunotherapy, Lisette G. De Pillis, K Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross '08, James Moore '07, Benjamin Preskill '09

All HMC Faculty Publications and Research

One of the most challenging tasks in constructing a mathematical model of cancer treatment is the calculation of biological parameters from empirical data. This task becomes increasingly difficult if a model involves several cell populations and treatment modalities. A sophisticated model constructed by de Pillis et al., Mixed immunotherapy and chemotherapy of tumours: Modelling, applications and biological interpretations, J. Theor. Biol. 238 (2006), pp. 841–862; involves tumour cells, specific and non-specific immune cells (natural killer (NK) cells, CD8 T cells and other lymphocytes) and employs chemotherapy and two types of immunotherapy (IL-2 supplementation and CD8 T-cell infusion) as treatment modalities. …

Go to article

Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy Jan 2009

Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy

All HMC Faculty Publications and Research

A thin layer of fluid flowing down a solid planar surface has a free surface height described by a nonlinear PDE derived via the lubrication approximation from the Navier Stokes equations. For thin films, surface tension plays an important role both in providing a significant driving force and in smoothing the free surface. Surfactant molecules on the free surface tend to reduce surface tension, setting up gradients that modify the shape of the free surface. In earlier work [12, 13J a traveling wave was found in which the free surface undergoes three sharp transitions, or internal layers, and the surfactant …

Go to article

On The Computational Complexity Of The Reticulate Cophylogeny Reconstruction Problem, Ran Libeskind-Hadas, Michael A. Charleston Jan 2009

On The Computational Complexity Of The Reticulate Cophylogeny Reconstruction Problem, Ran Libeskind-Hadas, Michael A. Charleston

All HMC Faculty Publications and Research

The cophylogeny reconstruction problem is that of finding minimal cost explanations of differences between evolutionary histories of ecologically linked groups of biological organisms. We present a proof that shows that the general problem of reconciling evolutionary histories is NP-complete and provide a sharp boundary where this intractability begins. We also show that a related problem, that of finding Pareto optimal solutions, is NP-hard. As a byproduct of our results, we give a framework by which meta-heuristics can be applied to find good solutions to this problem.

Go to article

Why Did Lagrange "Prove" The Parallel Postulate?, Judith V. Grabiner Jan 2009

Why Did Lagrange "Prove" The Parallel Postulate?, Judith V. Grabiner

Pitzer Faculty Publications and Research

In 1806, Joseph-Louis Lagrange read a memoir "proving" Euclid's parallel postulate to the Institut de France in Paris. The memoir still exists in manuscript, and we’ll look at what it says. We ask why he tried to prove the postulate, and why he attacked the problem in the way that he did. We also look at how the ideas in this manuscript are related to such things as Lagrange’s philosophy of mathematics, artists’ ideas about space, Newtonian mechanics, and Leibniz's Principle of Sufficient Reason. Finally, we reflect on how this episode changes our views about eighteenth-century attitudes toward geometry, space, …

Go to article

Integral Orthogonal Bases Of Small Height For Real Polynomial Spaces, Lenny Fukshansky Jan 2009

Integral Orthogonal Bases Of Small Height For Real Polynomial Spaces, Lenny Fukshansky

CMC Faculty Publications and Research

Let PN(R) be the space of all real polynomials in N variables with the usual inner product < , > on it, given by integrating over the unit sphere. We start by deriving an explicit combinatorial formula for the bilinear form representing this inner product on the space of coefficient vectors of all polynomials in PN(R) of degree ≤ M. We exhibit two applications of this formula. First, given a finite dimensional subspace V of PN(R) defined over Q, we prove the existence of an orthogonal basis for (V, < , >), consisting of polynomials of small height …

Go to article

Search Bounds For Zeros Of Polynomials Over The Algebraic Closure Of Q, Lenny Fukshansky Jan 2009

Search Bounds For Zeros Of Polynomials Over The Algebraic Closure Of Q, Lenny Fukshansky

CMC Faculty Publications and Research

We discuss existence of explicit search bounds for zeros of polynomials with coefficients in a number field. Our main result is a theorem about the existence of polynomial zeros of small height over the field of algebraic numbers outside of unions of subspaces. All bounds on the height are explicit.

Go to article

Persuading Consumers To Form Precise Search Engine Queries, Gondy Leroy Jan 2009

Persuading Consumers To Form Precise Search Engine Queries, Gondy Leroy

CGU Faculty Publications and Research

Today’s search engines provide a single textbox for searching. This input method has not changed in decades and, as a result, consumer search behaviour has not changed either: few and imprecise keywords are used. Especially with health information, where incorrect information may lead to unwise decisions, it would be beneficial if consumers could search more precisely. We evaluated a new user interface that supports more precise searching by using query diagrams. In a controlled user study, using paper-based prototypes, we compared searching with a Google interface with drawing new or modifying template diagrams. We evaluated consumer willingness and ability to …

Go to article

The Pixtalk Communication System A Smartphone Application And Companion Website For The Improvement Of Communication Skills Of Children With Autism, Gondy Leroy, Gianluca De Leo Jan 2009

The Pixtalk Communication System A Smartphone Application And Companion Website For The Improvement Of Communication Skills Of Children With Autism, Gondy Leroy, Gianluca De Leo

CGU Faculty Publications and Research

No abstract provided.

Go to article

The Once And Future Forest Service: Land-Management Policies And Politics In Contemporary America, Char Miller Jan 2009

The Once And Future Forest Service: Land-Management Policies And Politics In Contemporary America, Char Miller

Pomona Faculty Publications and Research

The news from the Far North is not good. In the spring of 2007, University of Alberta scientists reported that portions of the Canadian tundra were transforming into new forests of spruce and shrubs much more rapidly than once was imaginable. "The conventional thinking on treeline dynamics has been that advances are very slow because conditions are so harsh at these high latitudes and altitudes," reported Dr. Ryan Danby, a member of the UA research team. "But what our data indicate is that there was an upslope surge of trees in response to warmer temperatures. It's like [the forest] waited …

Go to article

A Different Pencil Too Good To Be Ignored? A First Look At Wolfram|Alpha, Gizem Karaali, Bruce Yoshiwara Jan 2009

A Different Pencil Too Good To Be Ignored? A First Look At Wolfram|Alpha, Gizem Karaali, Bruce Yoshiwara

Pomona Faculty Publications and Research

So you came across several news pieces about Wolfram|Alpha and you’re wondering what all the fuss is about. Let’s start with the basics.

Go to article

Predicting The Drug Release Kinetics Of Matrix Tablets, Boris Baeumer, Lipika Chatterjee, Peter Hinow, Thomas Rades, Ami E. Radunskaya, Ian Tucker Jan 2009

Predicting The Drug Release Kinetics Of Matrix Tablets, Boris Baeumer, Lipika Chatterjee, Peter Hinow, Thomas Rades, Ami E. Radunskaya, Ian Tucker

Pomona Faculty Publications and Research

In this paper we develop two mathematical models to predict the release kinetics of a water soluble drug from a polymer/excipient matrix tablet. The first of our models consists of a random walk on a weighted graph, where the vertices of the graph represent particles of a drug, excipient and polymer, respectively. The graph itself is the contact graph of a multidisperse random sphere packing. The second model describes the dissolution and the subsequent diffusion of the active drug out of a porous matrix using a system of a partial differential equations. The predictions of both models show good qualitative …

Go to article

Next Last