Physical Sciences and Mathematics Commons^™

Magnetic Levitation And Noncoalescence Of Liquid Helium, M. A. Weilert, Dwight L. Whitaker, H. J. Maris, G. M. Seidel

Pomona Faculty Publications and Research

We describe experiments in which drops of liquid helium-4, as large as 2 cm in diameter, are magnetically levitated. We have found that, when two or more drops are levitated in the same magnetic trap, the drops often remain in a state of apparent contact without coalescing. It appears that this effect is caused by the slow evaporation of liquid from the drops.

Dynamical Effects Of Partial Orderings In Physical Systems, Adam S. Landsberg, Eric J. Friedman

WM Keck Science Faculty Papers

We demonstrate that many physical systems possess an often overlooked property known as a partial-ordering structure. The detection and analysis of this special geometric property can be crucial for understanding a system's dynamical behavior. We review here the fundamental dynamical features common to all such systems, and describe how the partial ordering imposes interesting restrictions on their possible behavior. We show, for instance, that though such systems are capable of displaying highly complex and even chaotic behaviors, most of their experimentally observable behaviors will be simple. Partial orderings are illustrated with examples drawn from many branches of physics, including solid …

Positive Solutions For A Semilinear Elliptic Problem With Critical Exponent, Ismail Ali, Alfonso Castro

All HMC Faculty Publications and Research

No abstract provided in article.

A Mathematician Among The Molasses Barrels: Maclaurin's Unpublished Memoir On Volumes, Judith V. Grabiner

Pitzer Faculty Publications and Research

Suppose we are given a solid of revolution generated by a conic section. Slice out a frustum of the solid [14, diagrams pp. 77, 80]. Then, construct a cylinder, with the same height as the frustum, whose diameter coincides with the diameter of the frustum at the midpoint of its height. What is the difference between the volume of the frustum and the volume of this cylinder? Does this difference depend on where in the solid the frustum is taken?

The beautiful theorems which answer these questions first appear in a 1735 manuscript by Colin Maclaurin (1698–1746). This …

Methodological And Substantive Issues In Substance Abuse Prevention Research, C. Anderson Johnson, John W. Farquhar, Steve Sussman

CGU Faculty Publications and Research

This article summarizes current issues in drug abuse prevention research through integration of other articles in this journal and by heeding historical trends in prevention science. Recommendations are made for future research directions. For prevention to advance, iterative processes are needed involving both quasi-experimental and experimental designs and involving both small, simple units and large, complex, interactive units. Accuracy of measurement and replication are of paramount importance.

The Structure Of Alkali Halide Dimers: A Critical Test Of Ionic Models And New Ab Initio Results, T. Törring, S. Biermann, J. Hoeft, Richard J. Mawhorter, Robert J. Cave, C. Szemenyei

All HMC Faculty Publications and Research

In semiempirical ionic models a number of adjustable parameters have to be fitted to experimental data of either monomer molecules or crystals. This leads to strong correlations between these constants and prevents a unique test and a clear physical interpretation of the fit parameters. Moreover, it is not clear whether these constants remain unchanged when the model is applied to dimers or larger clusters. It is shown that these correlations can be substantially reduced when reliable information about dimers is available from experiments or ab initio calculations. Starting with Dunham coefficients of the monomer potential determined from microwave measurements, we …

The Interaction Of Intense Laser Pulses With Atomic Clusters, T. Ditmire, Thomas D. Donnelly, A. M. Rubenchik, R. W. Falcone, M. D. Perry

All HMC Faculty Publications and Research

We examine the interaction of intense, femtosecond laser radiation with the large (50–200 Å) clusters produced in pulsed gas jets. Both experiment and simulation show that the plasmas produced during these interactions exhibit electron temperatures far in excess of that predicted by above-threshold ionization theory for a low-density gas. Efficient heating of the clusters by the laser is followed by rapid expansion of the clusters and long-lived x-ray emission from hot, decaying, underdense plasma.

Oscillatory Doubly Diffusive Convection In A Finite Container, Adam S. Landsberg, Edgar Knobloch

WM Keck Science Faculty Papers

Oscillatory doubly diffusive convection in a large aspect ratio Hele-Shaw cell is considered. The partial differential equations are reduced via center-unstable manifold reduction to the normal form equations describing the interaction of even and odd parity standing waves near onset. These equations take the form of the equations for a Hopf bifurcation with approximate D4 symmetry, verifying the conclusions of the preceding paper [A.S. Landsberg and E. Knobloch, Phys. Rev. E 53, 3579 (1996)]. In particular, the amplitude equations differ in the limit of large aspect ratios from the usual Ginzburg-Landau description in having additional nonlinear terms with O(1) coefficients. …

Oscillatory Bifurcation With Broken Translation Symmetry, Adam S. Landsberg, Edgar Knobloch

WM Keck Science Faculty Papers

The effect of distant endwalls on the bifurcation to traveling waves is considered. Previous approaches have treated the problem by assuming that it is a weak perturbation of the translation invariant problem. When the problem is formulated instead in a finite box of length L and the limit L--> [infinity] is taken, one obtains amplitude equations that differ from the usual Ginzburg-Landau description by the presence of an additional nonlinear term. This formulation leads to a description in terms of the amplitudes of the primary box modes, which are odd and even parity standing waves. For large L, the equations …

Determinants Of The Tournaments, Clifford A. Mccarthy '94, Arthur T. Benjamin

All HMC Faculty Publications and Research

No abstract provided in this article.

High Order Harmonic Generation In Atom Clusters, Thomas D. Donnelly, T. Ditmire, K. Neuman, M. D. Perry, R. W. Falcone

All HMC Faculty Publications and Research

We report the generation of short-wavelength, high-order harmonics of intense laser radiation from atom clusters. Clusters containing about 10³ atoms are produced in a high-pressure gas jet. We show them to be a unique nonlinear medium. Compared with monomer gases they yield a higher appearance intensity for a given harmonic order, stronger nonlinear dependence of harmonic signal on laser intensity, higher-order harmonics, and reduced saturation of the harmonic signal at high laser intensity.

Radial Solutions To A Dirichlet Problem Involving Critical Exponents When N=6, Alfonso Castro, Alexandra Kurepa

All HMC Faculty Publications and Research

In this paper we show that, for each λ>0, the set of radially symmetric solutions to the boundary value problem

-Δu(x) = λu(x) + u(x)|u(x)|, x ε B := {x ε R⁶:|x|<1},

u(x) = 0, x ε ∂B

is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.

Remote Ergonomic Research In Space: Spacelab Findings And A Proposal, Stewart I. Donaldson, Harvey Wichman

CGU Faculty Publications and Research

This paper discusses ergonomics research using remotely situated video camerasin spacecraft. Two prototype studies of crewmembers working in the micro-G environments aboard the first two flights of Spacelab are described. Various aspects of crew restraint, stabilization, manipulation of controls, and mobilization were observed, operationally defined, and quantified by observing videotaped scenes of Spacelab crewmembers. In the first study, four performance behaviors were quantified to provide estimates of their frequency of occurrence and variation over the course of each of the flights. The behaviors and their mean percent of observed times were: Hand-Hold 32.2%, Foot Restraint 35.3%, Translation 9.4%, and Struggle …

The Steady Boundary Layer Due To A Fast Vortex, Andrew J. Bernoff, Harald J. H. M. Van Dongen, Seth Lichter

All HMC Faculty Publications and Research

A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherently unsteady. Here we show that for a vortex convected by a uniform shear flow, there is a steady solution when the speed of the vortex c_v is sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (c_v→∞) and numerically …

Combinatorics And Campus Security, Arthur T. Benjamin

All HMC Faculty Publications and Research

One day I received electronic mail from our director of campus security [Gilbraith 1993]:

"I have a puzzle for you that has practical applications for me. I need to know how many different combinations there are for our combination locks. A lock has 5 buttons. In setting the combination you can use only 1button or as many as 5. Buttons may be pressed simultaneously and / or successively, but the same button cannot be used more than once in the same combination.

I had a student (obviously not a math major) email me that there are only 120 possibilities, but …

Existence Results For Semipositone Systems, V. Anuradha, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We study existence of positive solutions to the coupled-system of boundary value problems of the form

-Δu(x) = λf(x,u,v); x ∈ Ω

-Δv(x) = λg(x,u,v); x ∈ Ω

u(x) = 0 = v(x); x ∈ ∂Ω

where λ > 0 is a parameter, Ω is a bounded domain in R^N; N ≥ 1 with a smooth boundary ∂Ω and f,g are C^1 function with at least one of f(x_0,0,0) or g(x_0,0,0) being negative for some x_0 ∈ Ω (semipositone). We establish our existence results using the method of sub-super solutions. We also discuss non-existence results for λ small.

Experimental And Theoretical Investigation Of Recombination Pumped X-Ray Lasers Driven By High-Intensity, Short Pulse Lasers, Thomas D. Donnelly, L. Da Silva, R. W. Lee, S. Mrowka, M. Hofer, R. W. Falcone

All HMC Faculty Publications and Research

We have experimentally investigated a recombination-pumped soft-x-ray laser on a Lyman-α transition (135 Å) of hydrogenlike lithium. Furthermore, we have modeled the dynamics of this system, including the effects of the multipeaked electron distribution function that is obtained from the sequential, optical-field ionization of an atom. We compare the predictions of our model and our experimental results.

An Nmr Investigation Of The Effect Of Hydrogen Bonding On The Rates Of Rotation About The C-N Bonds In Urea And Thiourea, Karl A. Haushalter, Janice Lau, John D. Roberts

All HMC Faculty Publications and Research

The interaction between urea and tetrabutylammonium acetate was investigated in dimethylformamide/ dimethyl sulfoxide solutions using ¹H and 15^N NMR. The chemical-shift behavior of the urea protons is consistent with a urea-acetate hydrogen-bonded complex involving both carboxylate oxygens and the urea hydrogens trans to the carbonyl oxygen with K_assoc = 120 ± 10. Line shape analysis of the temperature-dependent ¹H NMR spectra show that ∆G^‡ for rotation about the C-N bond of urea changes only slightly from 11.0 ± 0.1 to 11.2 ± 0.1 kcal/mol on 1:1 molar addition of tetrabutylammonium acetate to a dilute solution of urea. A parallel investigation …

Intraocular Lens Case Designs, Donald S. Remer, Stephen S. Davis, Michael Bak '95, Ken Kalafus, Ilan Sabar, Khannan Suntharam, William Washington, Yu-Tung Wong

All HMC Faculty Publications and Research

IOLAB Corporation makes two types of intraocular lenses for the replacement of cataracts: one from polymethyl methacrylate (PMMA) and a newer one from silicone. IOLAB ships the lens to the doctor in a two-piece case made from polycarbonate. At a price of $0.53 per case, IOLAB spends about $270,000 per year on lens cases (based on 1994 purchases of 500,000 cases). IOLAB asked us to reduce the cost of the existing lens case and to design a new case to protect and fold the silicone lens. We designed three items.

Meyer Jerison, 1922-1995, Leonard Gillman, Melvin Henriksen

All HMC Faculty Publications and Research

Memories and biography of mathematician Meyer Jerison (b. November 28, 1922 - d. March 19, 1995).

Modular Spaces And K-Widths, Asuman Güven Aksoy, Grzegorz Lewicki

CMC Faculty Publications and Research

In this paper, we show that the ball measure of noncompactness of a modular space X_p is equal to the limit of its K -widths when p is a left continuous, s-convex modular function, without any ∆₂-condition. We also obtain a similar result for SF-spaces, when the SF-norm N is uniformly continuous.

Syllogism Solving Under Time Pressure, Gondy Leroy, Koen Lamberts

CGU Faculty Publications and Research

No abstract provided.