Analysis and computations for a model of quasi-static deformation of a thinning sheet arising in superplastic forming

We consider a mathematical model for the quasi-static deformation of a thinning sheet. The model couples a first-order equation for the thickness of the sheet to a prescribed curvature equation for the displacement of the sheet. We prove a local in time existence and uniqueness theorem for this system when the sheet can be written as a graph. A contact problem is formulated for a sheet constrained to be above a mould. Finally we present some computational results

Phase Separation of Saturated and Mono-unsaturated Lipids as determined from a Microscopic Model

A molecular model is proposed of a bilayer consisting of fully saturated DPPC and mono unsaturated DOPC. The model not only encompasses the constant density within the hydrophobic core of the bilayer, but also the tendency of chain segments to align. It is solved within self-consistent field theory. A model bilayer of DPPC undergoes a main chain transition to a gel phase, while a bilayer of DOPC does not do so above zero degrees centigrade because of the double bond which disrupts order. We examine structural and thermodynamic properties of these membranes and find our results in reasonable accord with experiment. In particular, order-parameter profiles are in good agreement with NMR experiments. A phase diagram is obtained for mixtures of these lipids in a membrane at zero tension. The system undergoes phase separation below the main-chain transition temperature of the saturated lipid. Extensions to the ternary DPPC, DOPC, and cholesterol system are outlined.Comment: 29 pages, 4 figures, 1 table. revised versio

Bearing detection in the presence of two sources of varying coherence using the complex cepstrum

The effect of the presence of two acoustic sources (one, the primary, whose location is to be detected) of varying coherence on a cepstral bearing finding procedure is experimentally studied. The coherence between the acoustic sources was altered by adding random noise of various SNR (signal-to-noise ratio) to the input signal of the primary source; the same base signal being fed to both sources. The results demonstrate that, when block liftering is used, the primary source bearing is reliably estimated for coherences as low as gamma sup 2 greater than or approx equal to 0.5. The results also imply that background noise (unreflected) of SNR greater than or approx equal to 10 dB will not markedly affect the accuracy of the bearing estimation algorithm

Convex Multivariable Trace Functions

For any densely defined, lower semi-continuous trace \tau on a C*-algebra A with mutually commuting C*-subalgebras A_1, A_2, ... A_n, and a convex function f of n variables, we give a short proof of the fact that the function (x_1, x_2, ..., x_n) --> \tau (f(x_1, x_2, ..., x_n)) is convex on the space \bigoplus_{i=1}^n (A_i)_{self-adjoint}. If furthermore the function f is log-convex or root-convex, so is the corresponding trace function. We also introduce a generalization of log-convexity and root-convexity called \ell-convexity, show how it applies to traces, and give a few examples. In particular we show that the trace of an operator mean is always dominated by the corresponding mean of the trace values.Comment: 13 pages, AMS TeX, Some remarks and results adde

Dynamic characteristics of far-field radiation of current modulated phase-locked diode laser arrays

A versatile and powerful streak camera/frame grabber system for studying the evolution of the near and far field radiation patterns of diode lasers was assembled and tested. Software needed to analyze and display the data acquired with the steak camera/frame grabber system was written and the total package used to record and perform preliminary analyses on the behavior of two types of laser, a ten emitter gain guided array and a flared waveguide Y-coupled array. Examples of the information which can be gathered with this system are presented