On the Hybrid Minimum Principle On Lie Groups and the Exponential Gradient HMP Algorithm

This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous hybrid systems whose state manifolds constitute Lie groups $(G,\star)$ which are left invariant under the controlled dynamics of the system, and whose switching manifolds are defined as smooth embedded time invariant submanifolds of $G$. The analysis is expressed in terms of extremal (i.e. optimal) trajectories on the cotangent bundle of the state manifold $G$. The Hybrid Maximum Principle (HMP) algorithm introduced in \cite{Shaikh} is extended to the so-called Exponential Gradient algorithm. The convergence analysis for the algorithm is based upon the LaSalle Invariance Principle and simulation results illustrate their efficacy

Exploring Jet Properties in p-p Collisions at 200 GeV with STAR

The mechanisms underlying hadronization are not well understood, both in vacuum and in hot QCD matter. Precise characterization of jet fragmentation to hadrons in p-p collisions will help elucidate the fundamental process of hadronization, and will serve as essential reference to measure the modification of hadronization in heavy ion collisions. We present measurements of fragmentation functions for unidentified particles in jets produced in p-p collisions at 200 GeV using the STAR detector at RHIC. The results from different jet reconstruction algorithms are compared, including variations of the resolution parameter. It is found that the results are largely insensitive to details of the jet-finding algorithm at RHIC energies. Particle production inside and outside of these reconstructed jets will be compared to improve our understanding of the hadronization mechanisms for soft and hard particles in p-p events at RHIC energies.Comment: 4 pages, 7 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennessee Final version after referee's comment