Physical Sciences and Mathematics Commons^™

A Theoretical Investigation Of The Geometries, Vibrational Frequencies, And Binding Energies Of Several Mixed Alkali Halide Dimers, Robert J. Cave, Ian Ono '94

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Results are presented from ab initio calculations on several mixed alkali halide dimers made up of Li, Na, F, and Cl. All of the dimers are investigated at the restricted Hartree–Fock level to provide ab initio estimates of geometries, vibrational frequencies, and binding energies. The dimer LiNaF2 is then treated using a variety of basis sets at the Hartree–Fock level, as well as at correlated levels (second‐order Møller–Plesset and coupled‐cluster singles and doubles) to examine the sensitivity of the calculations to use of higher levels of theory. The results are then compared to the experimental data available for the LiNaF2 …

Short Terahertz Pulses From Semiconductor Surfaces: The Importance Of Bulk Difference‐Frequency Mixing, Peter N. Saeta, Benjamin I. Greene, Shun Lien Chuang

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The crystallographic orientation dependence of the far‐infrared (FIR) light generated at the (001) surface of a zincblende semiconductor is shown to derive principally from bulk difference‐frequency mixing. A strong modulation is observed for 1‐GW/cm² pulses on InP, which demonstrates that the radiated FIR wave produced by bulk optical rectification is comparable to that generated by the transport of photoinjected carriers. Using the bulk rectification light as a clock, we show that more than 95% of the light produced from an InP (111) crystal by 100‐fs, 100‐μJ pulses is generated in a time shorter than the excitation pulse.

Body Size In Amblyrhiza Inundata (Rodentia, Caviomorpha), An Extinct Megafaunal Rodent From The Anguilla Bank, West Indies: Estimates And Implications, Audrone R. Biknevicius, Donald A. Mcfarlane, Ross D. E. Macphee

WM Keck Science Faculty Papers

Rodent species typically evolve larger mean body sizes when isolated on islands, but the extinct caviomorph Amblyrhiza inundata, known only from Quaternary cave deposits on the islands of Anguilla and St. Martin (northern Lesser Antilles), provides an unusually dramatic example of insular gigantism. Here we report on a series of body mass estimates for Amblyrhiza using predictive equations based on anteroposterior diameters and cortical cross-sectional areas of humeral and femoral diaphyses. Analyses of 14 isolated specimens (5 femoral, 9 humeral), all representing adult or near adult animals, yield body mass estimates ranging from slightly less than 50 kg to more …

The Lazer Mckenna Conjecture For Radial Solutions In The Rn Ball, Alfonso Castro, Sudhasree Gadam

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When the range of the derivative of the nonlinearity contains the first k eigenvalues of the linear part and a certain parameter is large, we establish the existence of 2k radial solutions to a semilinear boundary value problem. This proves the Lazer McKenna conjecture for radial solutions. Our results supplement those in [5], where the existence of k + 1 solutions was proven.

Primary Relaxation Processes At The Band Edge Of Sio₂, Peter N. Saeta, Benjamin I. Greene

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The kinetics of photoinduced defect formation in high-purity silicas has been studied by femtosecond transient absorption spectroscopy in the visible and ultraviolet. Band edge two-photon excitation produces singlet excitons which decay in 0.25 ps into defects with the absorption spectra of nonbridging oxygen hole centers (≡Si-O⋅) and silicon E’ centers (≡Si⋅). We identify these defect pairs with the self-trapped triplet exciton and the 0.25 ps decay with the motion of the photoexcited oxygen atom. Similar results were obtained with both crystalline and amorphous silica samples.

Uniqueness And Stability Of Nonnegative Solutions For Semipositone Problems In A Ball, Ismael Ali, Alfonso Castro, Ratnasingham Shivaji

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We study the uniqueness and stability of nonnegative solutions for classes of nonlinear elliptic Dirichlet problems on a ball, when the nonlinearity is monotone, negative at the origin, and either concave or convex.

A Theoretical Investigation Of The Geometries, Vibrational Frequencies, And Binding Energies Of Several Alkali Halide Dimers, Robert P. Dickey '93, David Maurice '91, Robert J. Cave, Richard J. Mawhorter

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Results are presented from ab initio calculations on the symmetrical alkali halide dimers made up of Li, Na, K, F, and Cl. We examine the sensitivity of representative monomer and dimer geometries to the variation of the basis set with and without polarization and diffuse functions. The geometries are then compared with available experimental results. We have also calculated vibrational frequencies at the restricted Hartree–Fock level and examined the changes in geometry brought about by correlation using second‐order Møller–Plesset perturbation theory. It is found that Hartree–Fock theory in a modest basis set with diffuse and polarization functions yields results comparable …

Properties Of Photon Density Waves In Multiple-Scattering Media, Bruce J. Tromberg, Lars O. Svaasand, Tsong-Tseh Tsay, Richard C. Haskell

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Amplitude-modulated light launched into multiple-scattering media, e.g., tissue, results in the propagation of density waves of diffuse photons. Photon density wave characteristics in turn depend on modulation frequency (ω) and media optical properties. The damped spherical wave solutions to the homogeneous form of the diffusion equation suggest two distinct regimes of behavior: (1) a highfrequency dispersion regime where density wave phase velocity V_p has a ω dependence and (2) a low-frequency domain where V_p is frequency independent. Optical properties are determined for various tissue phantoms by fitting the recorded phase (Φ) and modulation (m) response to …

Tissue Characterization And Imaging Using Photon Density Waves, Lars O. Svaasand, Bruce J. Tromberg, Richard C. Haskell, Tsong-Tseh Tsay, Michael W. Berns

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The optical properties of brain tissues have been evaluated by measuring the phase velocity and attenuation of harmonically modulated light. The phase velocity for photon density waves at 650-nm wavelength has been found to be in the range of 5 to 12% of the corresponding velocity in a nonscattering medium, and the optical penetration depth was in the range 2.9 to 5.2 mm. These results are used to predict the resolution of optical imaging of deep tissue structures by diffusely propagating incoherent photons. The results indicate that structures of a few millimeters in linear dimension can be identified at 10 …

Optimal Leapfrogging, Joel Auslander, Arthur T. Benjamin, Daniel S. Wilkerson

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No abstract provided in this article.

Amblyrhiza And The Vertebrate Paleontology Of Anguillean Caves, Donald A. Mcfarlane, Ross D. E. Macphee

WM Keck Science Faculty Papers

Recorded interest in the caves of Anguilla dates back to the second half of the nineteenth century. The earliest explorations were concerned with the locating phosphatic cave earths, and resulted in the mining of several sites. Incidental to this work, the bones of the largest island rodent ever discovered were collected from Aguillan caves. Whereas the phosphate mining operations were short-lived, the remains of the giant rodent Amblyrhiza have catalyzed a continued interest in the caves of Anguilla. The most recent series of explorations have provided the first adequate documentation of Amhlyrhiza fossil sites, and have started to yield radiometric …

An Elementary Approach To Some Analytic Asymptotics, Nicholas Pippenger

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Fredman and Knuth have treated certain recurrences, such as $M(0) = 1$ and\[M(n + 1) = \mathop {\min }\limits_{0 \leqslant k \leqslant n} (\alpha M(k) + \beta M(n - k)),\] where $\min (\alpha ,\beta ) > 1$, by means of auxiliary recurrences such as \[h(x) = \left\{ {\begin{array}{*{20}c} {0\qquad {\text{if}}0 \leqslant x < 1,} \\ {1 + h({x / \alpha }) + h({x / \beta }){\text{ if}}1 \leq x < \infty .} \\ \end{array} } \right.\] The asymptotic behavior of $h(x)$ as $x \to \infty $ with $\alpha $ and $\beta $ fixed depends on whether ${{\log \alpha } / {\log \alpha }}$ is rational or irrational.

The solution of Fredman and Knuth used analytic methods in both cases, and used in particular the Wiener–Ikehara Tauberian theorem in the irrational case. The author shows that a more explicit solution to these recurrences can be obtained by entirely elementary methods, based on a geometric interpretation of $h(x)$ …

Light-Scattering Technique For The Study Of Dynamic Thickness Fluctuations In Thin Liquid Films, Richard C. Haskell, Daniel C. Petersen, Mark W. Johnson

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The authors describe a light-scattering technique capable of probing the dynamics of thickness fluctuations in lipid bilayers. The technique, which they call reflectance fluctuation spectroscopy (RFS), is keenly sensitive to light scattered from the squeeze modes of motion in a thin liquid film, and insensitive to light scattered from the bend modes. A laser beam is focused to a small spot on the film, and the power in the specularly reflected beam is recorded in real time. Thickness fluctuations associated with the squeeze modes of motion give rise to fluctuations in the power of the specularly reflected light. The frequency …

Light-Scattering Technique For The Study Of Dynamic Thickness Fluctuations In Thin Liquid Films, Richard C. Haskell, Daniel C. Petersen, Mark W. Johnson

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The authors describe a light-scattering technique capable of probing the dynamics of thickness fluctuations in lipid bilayers. The technique, which they call reflectance fluctuation spectroscopy (RFS), is keenly sensitive to light scattered from the squeeze modes of motion in a thin liquid film, and insensitive to light scattered from the bend modes. A laser beam is focused to a small spot on the film, and the power in the specularly reflected beam is recorded in real time. Thickness fluctuations associated with the squeeze modes of motion give rise to fluctuations in the power of the specularly reflected light. The frequency …

A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio

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In this paper we give a sufficient condition on the nonlinear operator N for a point (λ, u) to be a local bifurcation point of equations of the form u + λL^-1(N(u)) = 0, where L is a linear operator in a real Hilbert space, L has compact inverse, and λ ∈ R is a parameter. Our result does not depend on the variational structure of the equation or the multiplicity of the eigenvalue of the linear operator L. Applications are made to systems of differential equations and to the existence of periodic solutions of nonlinear second order …

Topologies And Cotopologies Generated By Sets Of Functions, Alan Dow, Melvin Henriksen, Ralph Kopperman, R. G. Woods

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Let L be either [0, 1] or {0, 1} with the usual order. We study topologies on a set X for which the cozero-sets of certain subfamilies H of L^x form a base, and the properties imposed on such topologies by hypothesizing various order-theoretic conditions on H. We thereby obtain useful generalizations of extremely disconnected spaces, basically disconnected spaces, and F-spaces. In particular we use these tools to study the space of minimal prime ideals of certain commutative rings.

Optimal Blackjack Strategy With "Lucky Bucks", Arthur T. Benjamin, Eric Huggins '91

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In the casino game blackjack or "21," mathematically determined best plays have been calculated by various mathematicians and gambling experts. These optimal playing strategies all assume that the casino pays even money on bets (excluding when the player has a "blackjack"). However, many casinos offer the player "lucky bucks" that pay the player either 3-to-2 or 2-to-1. In the usual game, the player's expected loss is under 1¢ per dollar bet. in this paper, we derive optimal strategies under luck-buck conditions, giving the player an expected gain of 26¢ or 55¢ per dollar bet.