Alternatives for NASTRAN maintenance, modification and dissemination

Various alternatives to direct NASA support of the program are considered ranging from no support at one end of the spectrum to subsidizing a non profit user's group at the other. Of all the alternatives that are developed, the user group appears to be most viable. NASA's past and future roles in the development of computerized technology are also considered. The need for an institute for computational analysis is identified and NASA's possible involvement is described. The goals of the proposed institute and research funds to support an activity that has the potential of a much larger impact on the technical community are identified

Random trees between two walls: Exact partition function

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that adjacent vertices have labels differing by +1 or -1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p-function with constrained periods. These results are used to analyze the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main modifications in Sect. 5-6 and conclusio

Cosmological constraints on Neutrino - Dark Matter interactions

I summarize the results of a recent analysis where the cosmological effects of interactions of neutrinos with cold Dark Matter (DM) is investigated. This interaction produces diffusion-damped oscillations in the matter power spectrum, analogous to the acoustic oscillations in the baryon-photon fluid. I discuss the bounds from the Sloan Digital Sky Survey on the corresponding opacity defined as the ratio of neutrino-DM scattering cross section over DM mass, and compare with the constraint from observation of neutrinos from supernova 1987A.Comment: Talk given at the Neutrino Oscillation Workshop NOW2006, Otranto, Italy, September 9-16 200

Design of helicopter rotors to noise constraints

Results of the initial phase of a research project to study the design constraints on helicopter noise are presented. These include the calculation of nonimpulsive rotor harmonic and broadband hover noise spectra, over a wide range of rotor design variables and the sensitivity of perceived noise level (PNL) to changes in rotor design parameters. The prediction methodology used correlated well with measured whirl tower data. Application of the predictions to variations in rotor design showed tip speed and thrust as having the most effect on changing PNL

Directed force chain networks and stress response in static granular materials

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the equation. A line of nontrivial fixed point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively.Comment: 18 pages, 12 figures. Minor corrections to one figur

Integrability of graph combinatorics via random walks and heaps of dimers

We investigate the integrability of the discrete non-linear equation governing the dependence on geodesic distance of planar graphs with inner vertices of even valences. This equation follows from a bijection between graphs and blossom trees and is expressed in terms of generating functions for random walks. We construct explicitly an infinite set of conserved quantities for this equation, also involving suitable combinations of random walk generating functions. The proof of their conservation, i.e. their eventual independence on the geodesic distance, relies on the connection between random walks and heaps of dimers. The values of the conserved quantities are identified with generating functions for graphs with fixed numbers of external legs. Alternative equivalent choices for the set of conserved quantities are also discussed and some applications are presented.Comment: 38 pages, 15 figures, uses epsf, lanlmac and hyperbasic

Supersonic flutter of a thermally stressed flat panel with uniform edge loads

Supersonic flutter of thermally stressed flat panel with uniform edge load

Confluence of geodesic paths and separating loops in large planar quadrangulations

We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minimal separating loops, i.e. paths of minimal length among all closed paths passing by one of the three vertices and separating the two others in the quadrangulation. We concentrate on the universal scaling limit of large quadrangulations, also known as the Brownian map, where pairs of geodesic paths or minimal separating loops have common parts of non-zero macroscopic length. This is the phenomenon of confluence, which distinguishes the geometry of random quadrangulations from that of smooth surfaces. We characterize the universal probability distribution for the lengths of these common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding paragraph and one reference added, and several other small correction