Thirty Years of Turnstiles and Transport

To characterize transport in a deterministic dynamical system is to compute exit time distributions from regions or transition time distributions between regions in phase space. This paper surveys the considerable progress on this problem over the past thirty years. Primary measures of transport for volume-preserving maps include the exiting and incoming fluxes to a region. For area-preserving maps, transport is impeded by curves formed from invariant manifolds that form partial barriers, e.g., stable and unstable manifolds bounding a resonance zone or cantori, the remnants of destroyed invariant tori. When the map is exact volume preserving, a Lagrangian differential form can be used to reduce the computation of fluxes to finding a difference between the action of certain key orbits, such as homoclinic orbits to a saddle or to a cantorus. Given a partition of phase space into regions bounded by partial barriers, a Markov tree model of transport explains key observations, such as the algebraic decay of exit and recurrence distributions.Comment: Updated and corrected versio

Program for computing partial pressures from residual gas analyzer data

A computer program for determining the partial pressures of various gases from residual-gas-analyzer data is given. The analysis of the ion currents of 18 m/e spectrometer peaks allows the determination of 12 gases simultaneously. Comparison is made to ion-gage readings along with certain other control information. The output data are presented in both tabular and graphical form

Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface. As an example, we compute the Melnikov function for a perturbation of a three-dimensional map that has a heteroclinic connection between a pair of invariant circles. The intersection curves of the manifolds are shown to undergo bifurcations in homologyComment: LaTex with 10 eps figure

A 2.75-Approximation Algorithm for the Unconstrained Traveling Tournament Problem

A 2.75-approximation algorithm is proposed for the unconstrained traveling tournament problem, which is a variant of the traveling tournament problem. For the unconstrained traveling tournament problem, this is the first proposal of an approximation algorithm with a constant approximation ratio. In addition, the proposed algorithm yields a solution that meets both the no-repeater and mirrored constraints. Computational experiments show that the algorithm generates solutions of good quality.Comment: 12 pages, 1 figur

Resonance Zones and Lobe Volumes for Volume-Preserving Maps

We study exact, volume-preserving diffeomorphisms that have heteroclinic connections between a pair of normally hyperbolic invariant manifolds. We develop a general theory of lobes, showing that the lobe volume is given by an integral of a generating form over the primary intersection, a subset of the heteroclinic orbits. Our definition reproduces the classical action formula in the planar, twist map case. For perturbations from a heteroclinic connection, the lobe volume is shown to reduce, to lowest order, to a suitable integral of a Melnikov function.Comment: ams laTeX, 8 figure

Influence of melt feeding scheme and casting parameters during direct-chill casting on microstructure of an AA7050 billet

© The Minerals, Metals & Materials Society and ASM International 2012Direct-chill (DC) casting billets of an AA7050 alloy produced with different melt feeding schemes and casting speeds were examined in order to reveal the effect of these factors on the evolution of microstructure. Experimental results show that grain size is strongly influenced by the casting speed. In addition, the distribution of grain sizes across the billet diameter is mostly determined by melt feeding scheme. Grains tend to coarsen towards the center of a billet cast with the semi-horizontal melt feeding, while upon vertical melt feeding the minimum grain size was observed in the center of the billet. Computer simulations were preformed to reveal sump profiles and flow patterns during casting under different melt feeding schemes and casting speeds. The results show that solidification front and velocity distribution of the melt in the liquid and slurry zones are very different under different melt feeding scheme. The final grain structure and the grain size distribution in a DC casting billet is a result of a combination of fragmentation effects in the slurry zone and the cooling rate in the solidification range

SNPFile – A software library and file format for large scale association mapping and population genetics studies

<p>Abstract</p> <p>Background</p> <p>High-throughput genotyping technology has enabled cost effective typing of thousands of individuals in hundred of thousands of markers for use in genome wide studies. This vast improvement in data acquisition technology makes it an informatics challenge to efficiently store and manipulate the data. While spreadsheets and at text files were adequate solutions earlier, the increased data size mandates more efficient solutions.</p> <p>Results</p> <p>We describe a new binary file format for SNP data, together with a software library for file manipulation. The file format stores genotype data together with any kind of additional data, using a flexible serialisation mechanism. The format is designed to be IO efficient for the access patterns of most multi-locus analysis methods.</p> <p>Conclusion</p> <p>The new file format has been very useful for our own studies where it has significantly reduced the informatics burden in keeping track of various secondary data, and where the memory and IO efficiency has greatly simplified analysis runs. A main limitation with the file format is that it is only supported by the very limited set of analysis tools developed in our own lab. This is somewhat alleviated by a scripting interfaces that makes it easy to write converters to and from the format.</p