Method of tracing contour patterns for use in making gradual contour resin matrix composites

The invention relates to methods for making alminate patterns for a resin matrix composite structural component. A sheet of paper is temporarily adhered to a model of the structrual component. A pen is positioned on the paper with a spindle touching the model surface opposite the pen. The pen and spindle are moved along the path that maintains the aforementioned contacts. The resulting line traced on paper is a model constant-thickness locus and provides a pattern for a single lamination of resin-impregnated fabric. The steps are repeated to make other patterns and each time the steps are repeated the distance between the tracer and the spindle is changed to correspond to the thickness of a lamination

Real Options using Markov Chains: an application to Production Capacity Decisions

In this work we address investment decisions using real options. A standard numerical approach for valuing real options is dynamic programming. The basic idea is to establish a discrete-valued lattice of possible future values of the underlying stochastic variable (demand in our case). For most approaches in the literature, the stochastic variable is assumed normally distributed and then approximated by a binomial distribution, resulting in a binomial lattice. In this work, we investigate the use of a sparse Markov chain to model such variable. The Markov approach is expected to perform better since it does not assume any type of distribution for the demand variation, the probability of a variation on the demand value is dependent on the current demand value and thus, no longer constant, and it generalizes the binomial lattice since the latter can be modelled as a Markov chain. We developed a stochastic dynamic programming model that has been implemented both on binomial and Markov models. A numerical example of a production capacity choice problem has been solved and the results obtained show that the investment decisions are different and, as expected the Markov chain approach leads to a better investment policy.Flexible Capacity Investments, Real Options, Markov Chains, Dynamic Programming

Computational results for Constrained Minimum Spanning Trees in Flow Networks

In this work, we address the problem of finding a minimum cost spanning tree on a single source flow network. The tree must span all vertices in the given network and satisfy customer demands at a minimum cost. The total cost is given by the summation of the arc setup costs and of the nonlinear flow routing costs over all used arcs. Furthermore, we restrict the trees of interest by imposing a maximum number of arcs on the longest arc emanating from the single source vertex. We propose a dynamic programming model an solution procedure to solve this problem exactly. Intensive computational experiments were performed using randomly generated test problems and the results obtained are reported. From them we can conclude that the method performance is independent of the type of cost functions considered and improves with the tightness of the constrains.Dynamic programming, network flows, constrained trees, general nonlinear costs

Molding procedure for casting a variety of alloys

General procedure and molding sand composition for preparing molds usable for casting variety of alloys are developed. Molds are prepared from mixture of sand, sodium silicate binder, and organic liquid ester. Castings of radiographic quality are produced from various alloys

Repulsion of an evolving surface on walls with random heights

We consider the motion of a discrete random surface interacting by exclusion with a random wall. The heights of the wall at the sites of $\Z^d$ are i.i.d.\ random variables. Fixed the wall configuration, the dynamics is given by the serial harness process which is not allowed to go below the wall. We study the effect of the distribution of the wall heights on the repulsion speed.Comment: 8 page

Two-Dimensional Scaling Limits via Marked Nonsimple Loops

We postulate the existence of a natural Poissonian marking of the double (touching) points of SLE(6) and hence of the related continuum nonsimple loop process that describes macroscopic cluster boundaries in 2D critical percolation. We explain how these marked loops should yield continuum versions of near-critical percolation, dynamical percolation, minimal spanning trees and related plane filling curves, and invasion percolation. We show that this yields for some of the continuum objects a conformal covariance property that generalizes the conformal invariance of critical systems. It is an open problem to rigorously construct the continuum objects and to prove that they are indeed the scaling limits of the corresponding lattice objects.Comment: 25 pages, 5 figure

The Brownian Web: Characterization and Convergence

The Brownian Web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in ${\mathbb R}\times{\mathbb R}$. We extend the earlier work of Arratia and of T\'oth and Werner by providing characterization and convergence results for the BW distribution, including convergence of the system of all coalescing random walkssktop/brownian web/finale/arXiv submits/bweb.tex to the BW under diffusive space-time scaling. We also provide characterization and convergence results for the Double Brownian Web, which combines the BW with its dual process of coalescing Brownian motions moving backwards in time, with forward and backward paths ``reflecting'' off each other. For the BW, deterministic space-time points are almost surely of ``type'' $(0,1)$ -- {\em zero} paths into the point from the past and exactly {\em one} path out of the point to the future; we determine the Hausdorff dimension for all types that actually occur: dimension 2 for type $(0,1)$, 3/2 for $(1,1)$ and $(0,2)$, 1 for $(1,2)$, and 0 for $(2,1)$ and $(0,3)$.Comment: 52 pages with 4 figure