Cavitation in liquid cryogens

Cavitation in liquid hydrogen and nitrogen flowing in transparent plastic ventur

Incipient and developed cavitation in liquid cryogens

Cavitational flow of liquid nitrogen and liquid hydrogen in Venturi tub

Thermodynamic depressions within cavities and cavitation inception in liquid hydrogen and liquid nitrogen Final report, 15 Jul. 1964 - 15 Dec. 1967

Thermodynamic depressions within cavities and cavitation inception in liquid hydrogen and nitrogen in transparent plastic venturi tube

Cavitation inception in liquid nitrogen and liquid hydrogen flowing in a venturi Interim report, 15 Jul. 1964 - 15 Jul. 1967

Cavitation characteristics of liquid hydrogen, and liquid nitrogen flow in plastic ventur

Hypergraphic LP Relaxations for Steiner Trees

We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation to other linear relaxations. Our results are the following. Structural results: We extend the technique of uncrossing, usually applied to families of sets, to families of partitions. As a consequence we show that any basic feasible solution to the partition LP formulation has sparse support. Although the number of variables could be exponential, the number of positive variables is at most the number of terminals. Relations with other relaxations: We show the equivalence of the partition LP relaxation with other known hypergraphic relaxations. We also show that these hypergraphic relaxations are equivalent to the well studied bidirected cut relaxation, if the instance is quasibipartite. Integrality gap upper bounds: We show an upper bound of sqrt(3) ~ 1.729 on the integrality gap of these hypergraph relaxations in general graphs. In the special case of uniformly quasibipartite instances, we show an improved upper bound of 73/60 ~ 1.216. By our equivalence theorem, the latter result implies an improved upper bound for the bidirected cut relaxation as well.Comment: Revised full version; a shorter version will appear at IPCO 2010

Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics

A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell's equations reduce to a single equation.Comment: 8 page

Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields in near-linear time solutions as well as upper bounds. Using various computational tools, we get solutions within considerably less than 1% of the optimum. An interesting feature of our approach is that, even though an FWP is hard to compute in theory and Edmonds' algorithm for maximum weighted matching yields a polynomial solution for the MWMP, the practical behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental Algorithms, 200

Spin-dependent phenomena and device concepts explored in (Ga,Mn)As

Over the past two decades, the research of (Ga,Mn)As has led to a deeper understanding of relativistic spin-dependent phenomena in magnetic systems. It has also led to discoveries of new effects and demonstrations of unprecedented functionalities of experimental spintronic devices with general applicability to a wide range of materials. In this article we review the basic material properties that make (Ga,Mn)As a favorable test-bed system for spintronics research and discuss contributions of (Ga,Mn)As studies in the general context of the spin-dependent phenomena and device concepts. Special focus is on the spin-orbit coupling induced effects and the reviewed topics include the interaction of spin with electrical current, light, and heat.Comment: 47 pages, 41 figure