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

Intersection Safety

The objectives of this project included a study to determine the safety effects of intersection type (unsignalized, signalized, and interchange) on Nebraska expressway intersections, quantification of the safety effects of a Collision Countermeasure System (CCS), and update of the Nebraska Department of Roads (NDOR) expressway intersection guidelines. The CCS is an Intelligent Transportation Systems (ITS) traffic control device to warn drivers of conflicting cross-traffic at rural, non-signalized intersections. The goal was that if found effective, the CCS will become part of the intersection designer’s options for expressway intersection design (other options being an interchange, traffic signals, and traffic control signs). Analysis results indicated that exposure (measured as total entering traffic) is an important factor affecting expressway intersection safety – expected number of accidents on an intersection approach increase with increasing exposure. While the analysis did not reveal any differences in safety of unsignalized and signalized intersections, the presence of horizontal curves on intersection approaches was found to increase accidents while vertical curves placed through intersections were also found increase accidents on intersection approaches. Expressway approaches with offset left turn lanes were found safer when compared to conventional left turn lanes and expressway approaches with no exclusive left-turn lanes. The above information is recommended for addition to the existing NDOR expressway intersection guidelines to make Nebraska expressway intersections safer. This report also provides directions for future expressway safety investigative research efforts

Intersection Safety

The objectives of this project included a study to determine the safety effects of intersection type (unsignalized, signalized, and interchange) on Nebraska expressway intersections, quantification of the safety effects of a Collision Countermeasure System (CCS), and update of the Nebraska Department of Roads (NDOR) expressway intersection guidelines. The CCS is an Intelligent Transportation Systems (ITS) traffic control device to warn drivers of conflicting cross-traffic at rural, non-signalized intersections. The goal was that if found effective, the CCS will become part of the intersection designer’s options for expressway intersection design (other options being an interchange, traffic signals, and traffic control signs). Analysis results indicated that exposure (measured as total entering traffic) is an important factor affecting expressway intersection safety – expected number of accidents on an intersection approach increase with increasing exposure. While the analysis did not reveal any differences in safety of unsignalized and signalized intersections, the presence of horizontal curves on intersection approaches was found to increase accidents while vertical curves placed through intersections were also found increase accidents on intersection approaches. Expressway approaches with offset left turn lanes were found safer when compared to conventional left turn lanes and expressway approaches with no exclusive left-turn lanes. The above information is recommended for addition to the existing NDOR expressway intersection guidelines to make Nebraska expressway intersections safer. This report also provides directions for future expressway safety investigative research efforts

Multi-Hamiltonian structures for r-matrix systems

For the rational, elliptic and trigonometric r-matrices, we exhibit the links between three "levels" of Poisson spaces: (a) Some finite-dimensional spaces of matrix-valued holomorphic functions on the complex line; (b) Spaces of spectral curves and sheaves supported on them; (c) Symmetric products of a surface. We have, at each level, a linear space of compatible Poisson structures, and the maps relating the levels are Poisson. This leads in a natural way to Nijenhuis coordinates for these spaces. At level (b), there are Hamiltonian systems on these spaces which are integrable for each Poisson structure in the family, and which are such that the Lagrangian leaves are the intersections of the symplective leaves over the Poisson structures in the family. Specific examples include many of the well-known integrable systems.Comment: 26 pages, Plain Te

Rural expressway intersection characteristics that contribute to a reduced safety performance

Expressways have been constructed in many states as a way to increase mobility without the expense of a full access-controlled or grade-separated facility. In most cases, it was assumed that these segments of highway would produce similar mobility and safety characteristics as other access-controlled facilities. However, recent research has found that there are problems with the safety performance of these systems. Although past research has been completed to examine the nature of crashes on these facilities, it is the purpose of this study to continue the research and analyze the common characteristics of the intersections. The intersections studied in this research were located throughout the state of Iowa. The objective of these analyses is to provide an identification of the major contributing factors that create problematic intersections in the state of Iowa. From previous research, it is evident that factors in addition to roadway volume contribute to the safety performance of an at-grade, two-way, stop-controlled expressway intersection. This research identifies common characteristics that may increase or decrease the safety performance of a rural expressway intersection. The methodology used in this research includes the examination of 644 intersections throughout the state of Iowa. Through the use of a statewide database and crash information from 1996 to 2000, we were able to identify the 100 best- and 100 worst-performing intersections based on crash severity rate. With the 200 intersections, a statistical analysis was completed to determine the effects intersection design and surrounding land use have on the intersection\u27s safety performance. The safety performance of intersections located on vertical/horizontal curves, skewed intersections, and varying surrounding land use were studied to determine their effects on rural expressway intersections. Following the completion of the analysis of the 200 intersections, 30 intersections with highest crash severity index rates were selected for more thorough, site-specific analysis. As part of this analysis, we examined the impact of land use adjacent to the intersection and the impact of peaking in hourly traffic volumes. The research identifies attributes that impact crash severity both negatively and positively. Through the identification of these attributes, designers and planners can more adequately address safety concerns on rural expressway intersections

Optimizing double-base elliptic-curve single-scalar multiplication

This paper analyzes the best speeds that can be obtained for single-scalar multiplication with variable base point by combining a huge range of options: • many choices of coordinate systems and formulas for individual group operations, including new formulas for tripling on Edwards curves; • double-base chains with many different doubling/tripling ratios, including standard base-2 chains as an extreme case; • many precomputation strategies, going beyond Dimitrov, Imbert, Mishra (Asiacrypt 2005) and Doche and Imbert (Indocrypt 2006). The analysis takes account of speedups such as S – M tradeoffs and includes recent advances such as inverted Edwards coordinates. The main conclusions are as follows. Optimized precomputations and triplings save time for single-scalar multiplication in Jacobian coordinates, Hessian curves, and tripling-oriented Doche/Icart/Kohel curves. However, even faster single-scalar multiplication is possible in Jacobi intersections, Edwards curves, extended Jacobi-quartic coordinates, and inverted Edwards coordinates, thanks to extremely fast doublings and additions; there is no evidence that double-base chains are worthwhile for the fastest curves. Inverted Edwards coordinates are the speed leader