Physical Sciences and Mathematics Commons^™

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

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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.

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

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No abstract provided in this article.

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

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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.

Calculation Of Electronic Coupling Matrix Elements For Ground And Excited State Electron Transfer Reactions: Comparison Of The Generalized Mulliken–Hush And Block Diagonalization Methods, Robert J. Cave, Marshall D. Newton

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Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (Hab) for electron transfer reactions using ab initio electronic structure theory. The first is based on the generalized Mulliken–Hush (GMH) model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization (BD) approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for (a) several states of the system Zn2OH2+ and (b) the low-lying states of the benzene–Cl atom complex and its contact ion pair. Generally …

Optimization Of Plasmas For Recombination-Pumped Short-Wavelength Lasers, M. Murphy, C. Glasheen, F. A. Moscatelli, Thomas D. Donnelly

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We report on experiments investigating the optimization of laser-ablated plasmas which are used to produce recombination-pumped, short-wavelength lasers. We evaluate the density of electrons and neutral atoms in laser ablated lithium and carbon plasmas as a function of time and distance away from the ablated target surface. We use an interferometric technique which can reveal information about the temperature of the plasma electrons. We find that the cold electrons which result in gain in recombination-pumped lithium lasers on the Lyman-α transition are produced by the high-intensity pump pulse rather than the lower intensity ablating pulse.

Photoluminescence Properties Of Silicon Quantum-Well Layers, Peter N. Saeta, A. C. Gallagher

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Nanometer-scale crystal silicon films surrounded by SiO₂ were prepared by oxidizing silicon-on-insulator substrates prepared from SIMOX (separation by implantation of oxygen) and crystallized hydrogenated amorphous silicon films. Average silicon layer thickness was determined from reflection spectra. When sufficiently thin (<2 >nm), all layers emitted red photoluminescence under blue and UV cw excitation, with a spectrum that did not depend on the mean layer thickness. The spectrum was roughly Gaussian with a peak energy of 1.65 eV, which is lower than for most porous silicon spectra. The time scale for the luminescence decay was ~35 μs at room temperature and …

Adaptive Multicast Routing In Wormhole Networks, Ran Libeskind-Hadas, Tom Hehre '96, Andrew Hutchings '98, Mark Reyes '98, Kevin Watkins '97

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Multicast communication has applications in a number of fundamental operations in parallel computing. An effective multicast routing algorithm must be free from both livelock and deadlock while minimizing communication latency. We describe two classes of multicast wormhole routing algorithms that employ the multi-destination wormhole hardware mechanism proposed by Lin et al. [12] and Panda et al. [17]. Specific examples of these classes of algorithms are described and experimental results suggests that such algorithms enjoy low communication latencies across a range of network loads.

The Interaction Of A Point Vortex With A Wall-Bounded Vortex Layer, Oliver V. Atassi, Andrew J. Bernoff, Seth Lichter

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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 …

Positive Solution Curves Of Semipositone Problems With Concave Nonlinearities, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji

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We consider the positive solutions to the semilinear equation:

-Δu(x) = λf(u(x)) for x ∈ Ω

u(x) = 0 for x ∈ ∂Ω

where Ω denotes a smooth bounded region in R^N (N > 1) and λ > 0. Here f :[0, ∞)→R is assumed to be monotonically increasing, concave and such that f(0) < 0 (semipositone). Assuming that f'(∞) ≡ lim t→∞ f'(t) > 0, we establish the stability and uniqueness of large positive solutions in terms of (f(t)/t)'. When Ω is a ball, we determine the exact number of positive solutions for each λ > 0. We also obtain the geometry of the branches of positive solutions completely and establish how …