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

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

Design and fabrication of a radiative actively cooled honeycomb sandwich structural panel for a hypersonic aircraft

The panel assembly consisted of an external thermal protection system (metallic heat shields and insulation blankets) and an aluminum honeycomb structure. The structure was cooled to temperature 442K (300 F) by circulating a 60/40 mass solution of ethylene glycol and water through dee shaped coolant tubes nested in the honeycomb and adhesively bonded to the outer skin. Rene'41 heat shields were designed to sustain 5000 cycles of a uniform pressure of + or - 6.89kPa (+ or - 1.0 psi) and aerodynamic heating conditions equivalent to 136 kW sq m (12 Btu sq ft sec) to a 422K (300 F) surface temperature. High temperature flexible insulation blankets were encased in stainless steel foil to protect them from moisture and other potential contaminates. The aluminum actively cooled honeycomb sandwich structural panel was designed to sustain 5000 cycles of cyclic in-plane loading of + or - 210 kN/m (+ or - 1200 lbf/in.) combined with a uniform panel pressure of + or - 6.89 kPa (?1.0 psi)

Scaling in Gravitational Clustering, 2D and 3D Dynamics

Perturbation Theory (PT) applied to a cosmological density field with Gaussian initial fluctuations suggests a specific hierarchy for the correlation functions when the variance is small. In particular quantitative predictions have been made for the moments and the shape of the one-point probability distribution function (PDF) of the top-hat smoothed density. In this paper we perform a series of systematic checks of these predictions against N-body computations both in 2D and 3D with a wide range of featureless power spectra. In agreement with previous studies, we found that the reconstructed PDF-s work remarkably well down to very low probabilities, even when the variance approaches unity. Our results for 2D reproduce the features for the 3D dynamics. In particular we found that the PT predictions are more accurate for spectra with less power on small scales. The nonlinear regime has been explored with various tools, PDF-s, moments and Void Probability Function (VPF). These studies have been done with unprecedented dynamical range, especially for the 2D case, allowing in particular more robust determinations of the asymptotic behaviour of the VPF. We have also introduced a new method to determine the moments based on the factorial moments. Results using this method and taking into account the finite volume effects are presented.Comment: 13 pages, Latex file, 9 Postscript Figure

Wind models for flight simulator certification of landing and approach guidance and control systems

The definition of a model suitable for certification was the main objective of this report. The model was designed to simplify and reduce the wind model parameters to enable evaluation of a large number of aircraft and control system design parameters. Analytical descriptions of wind phenomena were presented. For those parameters defying analytic description, probabilistic descriptions were sought. A brief analysis of the effects of wind on aircraft motion was conducted. The axes transformations required between wind and turbulence components in their inherent axis system and in the airplane's axis system were shown. Techniques of providing a random process on computers for the representation of turbulence were presented. A simulation model was presented that combines all the foregoing components

On the arithmetic of Krull monoids with infinite cyclic class group

Let $H$ be a Krull monoid with infinite cyclic class group $G$ and let $G_P \subset G$ denote the set of classes containing prime divisors. We study under which conditions on $G_P$ some of the main finiteness properties of factorization theory--such as local tameness, the finiteness and rationality of the elasticity, the structure theorem for sets of lengths, the finiteness of the catenary degree, and the existence of monotone and of near monotone chains of factorizations--hold in $H$. In many cases, we derive explicit characterizations

A Study of the Use of the Phrase Faithful is God in the New Testament Writings

The concept of God\u27s faithfulness is implicit in all of the Sacred Scripture; indeed, one could say that the Bible is, in a sense, the story of God\u27s faithfulness. But only comparatively seldom does this attribute of God come to the surface explicitly. The purpose of this thesis is to study those passages and their context in the New Testament where it is specifically mentioned. Each of those passages is like a facet of a diamond, revealing a new aspect of God\u27s faithfulness, high lighting another element of it, making our conception of it richer and deeper

A Probe for Characterization of Natural Phenomena Using the Modulated Scattering Technique

This project aims to provide students and researchers with low cost, low power, lightweight probes for characterizing natural phenomena. To achieve this, the probes are designed using the modulated scattering technique, which in this application provides a system somewhat analogous to a hybrid radar and RFID system. The achieved design is one square inch in area, less than 10 grams, and easily has a battery life of over 20 days using two CR2032 batteries in series