Physical Sciences and Mathematics Commons^™

Onset Of Superconductivity In Decreasing Fields For General Domains, Andrew J. Bernoff, Peter Sternberg

All HMC Faculty Publications and Research

Ginzburg–Landau theory has provided an effective method for understanding the onset of superconductivity in the presence of an external magnetic field. In this paper we examine the instability of the normal state to superconductivity with decreasing magnetic field for a closed smooth cylindrical region of arbitrary cross-section subject to a vertical magnetic field. We examine the problem asymptotically in the boundary layer limit (i.e., when the Ginzburg–Landau parameter, k, is large). We demonstrate that instability first occurs in a region exponentially localized near the point of maximum curvature on the boundary. The transition occurs at a value of the …

Magnetostratigraphy Of Cueva Del Aleman, Isla De Mona, Puerto Rico And The Species Duration Of Audobon's Shearwater, Bruce C. Panuska, John M. Mylroie, Darrell Armentrout, Donald A. Mcfarlane

WM Keck Science Faculty Papers

Magnetostratigraphic analysis of deposits exposed in Cueva del Aleman shows two reversed and two normal chronozones. The lower normal polarity event is observed in a clastic dike and probably predates initial cave formation. Sediments deposited inside the cave proper show a R-N-R sequence and probably date to at least 1.8 Ma. A fossiliferous clastic dike contains normal polarity with an overlying reversed magnetozone. Audubon’s Shearwater (bird) bones occur in the dike, which is tentatively correlated with the lower N polarity zone predating cave formation. If this correlation is correct, the Audubon’s Shearwater (Puffinus lherminieri) range can be extended back to …

Sorting In Parallel, Ran Libeskind-Hadas

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In 1842, L.F. Menabrea anticipated the benefits of parallel computing in an article that appeared in the Swiss Journal Bibliotheque universelle de Geneve:

When a long series of identical computations is to be performed, such as those required for the formation of numerical tables, the machine can be brought into play so as to give several results at the same time, which will greatly abridge the whole amount of the processes.

Although more than a century passed before Menabrea's vision became a reality, today parallel computers with hundreds and even thousands of processors are used in a broad range …

Tree-Based Multicasting In Wormhole-Routed Irregular Topologies, Ran Libeskind-Hadas, Dominic Mazzoni '99, Ranjith Rajagopalan '99

All HMC Faculty Publications and Research

A deadlock-free tree-based multicast routing algorithm is presented for all direct networks, regardless of interconnection topology. The algorithm delivers a message to any number of destinations using only a single startup phase. In contrast to existing tree-based schemes, this algorithm applies to all interconnection topologies, requires only fixed-sized input buffers that are independent of maximum message length, and uses a single asynchronous flit replication mechanism. The theoretical basis of the technique used here is sufficiently general to develop other tree-based multicasting algorithms for regular and irregular topologies. Simulation results demonstrate that this tree-based algorithm provides a very promising means of …

Design And Design Centers In Engineering Education, Clive L. Dym

All HMC Faculty Publications and Research

This paper is intended to be the opening salvo of the workshop, Computing Futures in Engineering Design (Dym, 1997). Thus, I want to take this privileged moment to ask you to think with me about the role of design in engineering. In particular, I want to reflect upon how design is articulated and how design is taught; about the role of design in engineering education and in the practice of engineering; and about the role that could be played locally and, perhaps, nationally by a center devoted to design education. Because I teach here at Harvey Mudd College (HMC), …

Optimal Contention-Free Unicast-Based Multicasting In Switch-Based Networks Of Workstations, Ran Libeskind-Hadas, Dominic Mazzoni '99, Ranjith Rajagopalan '99

All HMC Faculty Publications and Research

A unicast-based multicasting algorithm is presented for arbitrary interconnection networks arising in switch-based networks of workstations. The algorithm is optimal with respect tot he number of startups incurred and is provably free from depth contention. Specifically, no two constituent unicasts for the same multicast contend for a common channel, even if some unicasts are delayed due to unpredictable variations in latencies. The algorithm uses an underlying partially adaptive deadlock-free unicast routing algorithm. Simulation results indicate that the algorithm behaves as predicted by its theoretical properties and provides a promising approach to unicast-based multicasting.

Positive Solutions For A Concave Semipositone Dirichlet Problem, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

No abstract provided for this article

Average-Case Lower Bounds For Noisy Boolean Decision Trees, William Evans, Nicholas Pippenger

All HMC Faculty Publications and Research

We present a new method for deriving lower bounds to the expected number of queries made by noisy decision trees computing Boolean functions. The new method has the feature that expectations are taken with respect to a uniformly distributed random input, as well as with respect to the random noise, thus yielding stronger lower bounds. It also applies to many more functions than do previous results. The method yields a simple proof of the result (previously established by Reischuk and Schmeltz) that almost all Boolean functions of n arguments require $\Me(n \log n)$ queries, and strengthens this bound from the …

A Minmax Principle, Index Of The Critical Point, And Existence Of Sign Changing Solutions To Elliptic Boundary Value Problems, Alfonso Castro, Jorge Cossio, John M. Neuberger

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In this article we apply the minmax principle we developed in [6] to obtain sign-changing solutions for superlinear and asymptotically linear Dirichlet problems.

We prove that, when isolated, the local degree of any solution given by this minmax principle is +1. By combining the results of [6] with the degree-theoretic results of Castro and Cossio in [5], in the case where the nonlinearity is asymptotically linear, we provide sufficient conditions for:

i) the existence of at least four solutions (one of which changes sign exactly once),

ii) the existence of at least five solutions (two of which change sign), and …

Convergence Of Random Walks On The Circle Generated By An Irrational Rotation, Francis E. Su

All HMC Faculty Publications and Research

Fix . Consider the random walk on the circle which proceeds by repeatedly rotating points forward or backward, with probability , by an angle . This paper analyzes the rate of convergence of this walk to the uniform distribution under ``discrepancy'' distance. The rate depends on the continued fraction properties of the number . We obtain bounds for rates when is any irrational, and a sharp rate when is a quadratic irrational. In that case the discrepancy falls as (up to constant factors), where is the number of steps in the walk. This is the first example of a sharp …

Newton's Cubic Roots, Lisette G. De Pillis

All HMC Faculty Publications and Research

No abstract included in this article

On Multiple Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger

All HMC Faculty Publications and Research

We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.

A Tribute To Karl Menger, Seymour Kass

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Garbage Pizza, Patchwork Quilts, And Math Magic: Stories About Teachers Who Love To Teach And Children Who Love To Learn, By Susan Ohanian, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Resource Review: Research On Children's Learning As A Tool To Improve Math And Science Teaching, Cynthia Hudley

Humanistic Mathematics Network Journal

No abstract provided.

A Situational Pedagogy For Elementary Mathematics, Vincent Haag

Humanistic Mathematics Network Journal

No abstract provided.

Helping Students With Attention Deficit Disorder Succeed In A College Mathematics Class, Pamela E. Matthews

Humanistic Mathematics Network Journal

No abstract provided.

Reflections Of Glenmount Reform Effort, Gail Black, Ruth Miller

Humanistic Mathematics Network Journal

No abstract provided.

The Reform Calculus Debate And The Psychology Of Learning Mathematics, James M. Cargal

Humanistic Mathematics Network Journal

No abstract provided.

Teaching Mathematics Appreciation To Nonscience Majors, Josefina Alvarez

Humanistic Mathematics Network Journal

No abstract provided.

The Object And The Study Of Mathematics, Pinar Karaca

Humanistic Mathematics Network Journal

No abstract provided.

John Dewey, The Math And Science Standards, And The Workplace, Bernard A. Fleishman

Humanistic Mathematics Network Journal

No abstract provided.

Poems, David L. Finn

Humanistic Mathematics Network Journal

No abstract provided.

Inspiration In England, Mary Mcdermott

Humanistic Mathematics Network Journal

No abstract provided.

A Course In Mathematical Ethics, Robert P. Webber

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Nexus: Architecture And Mathematics, Edited By Kim Williams, Joseph Malkevitch

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Ethnomathematics--Challenging Eurocentrism Inmathematics Education, Edited Byarthur B. Powell And Marilyn Frankenstein, Karen Dee Michalowicz

Humanistic Mathematics Network Journal

No abstract provided.

Borsuk-Ulam Implies Brouwer: A Direct Construction, Francis E. Su

All HMC Faculty Publications and Research

No abstract provided in this article.

A Sign-Changing Solution For A Superlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger

All HMC Faculty Publications and Research

We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].

Quasi-Steady Monopole And Tripole Attractors In Relaxing Vortices, Louis F. Rossi, Joseph F. Lingevitch, Andrew J. Bernoff

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Using fully nonlinear simulations of the two-dimensional Navier–Stokes equations at large Reynolds number (Re), we bracket a threshold amplitude above which a perturbed Gaussian monopole will relax to a quasi-steady, rotating tripole, and below which will relax to an axisymmetric monopole. The resulting quasi-steady structures are robust to small perturbations. We propose a means of measuring the decay rate of disturbances to asymptotic vortical structures wherein streamlines and lines of constant vorticity correspond in some rotating or translating frame. These experiments support the hypothesis that small or moderate deviations from asymptotic structures decay through inviscid and viscous mixing.