Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure

INVESTIGATION OF EFFICIENCY OF GRAY CAST IRON GRAPHITIZING MODIFICATION BY DISPERSION-FILLED CONSUMABLE PATTERN

The key criteria of the process of graphitizing modification of matrix melt silicon concentration and silicon assimilation evaluated were on samples of gray cast iron grade СЧ20 State Standard 1412-85. These criteria of evaluation on the structure and properties of casting ingots proved an efficiency of intra-mold modification of molten gray cast iron by dispersed ferrosilicon grade ФС75 State Standard 1415-93 (ISO 5445-80) using lost-foam casting (LFC-process)