Limiting entry times distribution for arbitrary null sets SETS

We describe an approach that allows us to deduce the limiting return times distribution for arbitrary sets to be compound Poisson distributed. We establish a relation between the limiting return times distribution and the probability of the cluster sizes, where clusters consist of the portion of points that have finite return times in the limit where random return times go to infinity. In the special case of periodic points we recover the known P\'olya-Aeppli distribution which is associated with geometrically distributed cluster sizes. We apply this method to several examples the most important of which is synchronisation of coupled map lattices. For the invariant absolutely continuous measure we establish that the returns to the diagonal is compound Poisson distributed where the coefficients are given by certain integrals along the diagonal.Comment: 33

The effect of eccentric and concentric training on the size and strength of human skeletal muscle

The objective of this study was to determine if the high forces generated through eccentric contractions, and the subsequent damage sustained, contributes to greater growth and force increase in human skeletal muscle than other contraction types, and whether damage from eccentric exercise effects the increase in torque and muscle size expected after a progressive concentric strength training program. 20 healthy subjects were split into four groups which participated in 3 different training protocols, with one group serving as the control (C). Groups underwent either concentric training (CT), eccentric damage (ED), or a combination of the two protocols (DC) with the non-preferred biceps over a twelve week period. Isometric and concentric force at 50, 90 and 200°/sec was measured weekly with a Cybex isokinetic dynamometer. Upper arm girth was also measured pre and post training. The CT group displayed the greatest increase in peak torque for both isometric and concentric contractions. The groups undergoing eccentric damage (ED & DC) showed a decrease in the ability to generate force in the weeks following damage, and showed only small torque increases over the twelve weeks with DC improving to a greater extent than ED at higher contraction velocities. Eccentric damage appeared to attenuate the increases in peak torque displayed after concentric training. A hypertrophic response from damage may have resulted in a decrease in muscle strength per unit cross-sectional area, and the failure of DC to respond to training may be due to the inability to generate sufficient intramuscular tension required to elicit an adaptive response

The compound Poisson distribution and return times in dynamical systems

Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the limiting distribution is a compound Poissonian distribution. We also derive error terms for the convergence to the limiting distribution. We also prove a very general theorem that can be used to establish compound Poisson distributions in many other settings.Comment: 18 page

The optimal sink and the best source in a Markov chain

It is well known that the distributions of hitting times in Markov chains are quite irregular, unless the limit as time tends to infinity is considered. We show that nevertheless for a typical finite irreducible Markov chain and for nondegenerate initial distributions the tails of the distributions of the hitting times for the states of a Markov chain can be ordered, i.e., they do not overlap after a certain finite moment of time. If one considers instead each state of a Markov chain as a source rather than a sink then again the states can generically be ordered according to their efficiency. The mechanisms underlying these two orderings are essentially different though.Comment: 12 pages, 1 figur

Cost Models for MMC Manufacturing Processes

The quality cost modeling (QCM) tool is intended to be a relatively simple-to-use device for obtaining a first-order assessment of the quality-cost relationship for a given process-material combination. The QCM curve is a plot of cost versus quality (an index indicating microstructural quality), which is unique for a given process-material combination. The QCM curve indicates the tradeoff between cost and performance, thus enabling one to evaluate affordability. Additionally, the effect of changes in process design, raw materials, and process conditions on the cost-quality relationship can be evaluated. Such results might indicate the most efficient means to obtain improved quality at reduced cost by process design refinements, the implementation of sensors and models for closed loop process control, or improvement in the properties of raw materials being fed into the process. QCM also allows alternative processes for producing the same or similar material to be compared in terms of their potential for producing competitively priced, high quality material. Aside from demonstrating the usefulness of the QCM concept, this is one of the main foci of the present research program, namely to compare processes for making continuous fiber reinforced, metal matrix composites (MMC's). Two processes, low pressure plasma spray deposition and tape casting are considered for QCM development. This document consists of a detailed look at the design of the QCM approach, followed by discussion of the application of QCM to each of the selected MMC manufacturing processes along with results, comparison of processes, and finally, a summary of findings and recommendations

Factors affecting the performance of eddy current densification sensors

Hot Isostatic Pressing (HIP) is an increasingly important near net shape process for producing fully dense components from powders [1]. It involves filling a preshaped metal canister with alloy powder, followed by evacuation, and sealing. The can is then placed in a HIP (a furnace that can be pressurized to ~200MPa with an inert gas such as argon). The can is subjected to a heating/pressurization cycle that softens and compacts the powder particles to a fully dense mass and a shape determined by the can shape, the powders initial packing and the thermal-mechanical cycle imposed [2]. Today, many metals, alloys and intermetallics are processed this way (including nickel based superalloys, titanium alloys, NiA1, etc.) and it is increasingly used to produce metal matrix composites