Response to "The invalidity of a Mach probe model" [Phys. Plasmas 9, 1832 (2002)]

Hutchinson gives a nice analysis of the (in)validity of Hudis and Lidsky’s unmagnetized Mach probe theory.(1) We agree with his main assertions, which are that (1) a one-dimensional model is incapable of properly describing unmagnetized ion collection by a Mach probe and (2) any experimental agreement with theories based on Hudis and Lidsky should not be interpreted as physical validation of their model

A Laboratory Plasma Experiment for Studying Magnetic Dynamics of Accretion Discs and Jets

This work describes a laboratory plasma experiment and initial results which should give insight into the magnetic dynamics of accretion discs and jets. A high-speed multiple-frame CCD camera reveals images of the formation and helical instability of a collimated plasma, similar to MHD models of disc jets, and also plasma detachment associated with spheromak formation, which may have relevance to disc winds and flares. The plasmas are produced by a planar magnetized coaxial gun. The resulting magnetic topology is dependent on the details of magnetic helicity injection, namely the force-free state eigenvalue alpha_gun imposed by the coaxial gun.Comment: accepted for publication in MNRA

Study of magnetic helicity injection via plasma imaging using a high-speed digital camera

The evolution of a plasma generated by a novel planar coaxial gun is photographed using a state-of-the-art digital camera, which captures eight time-resolved images per discharge. This experiment is designed to study the fundamental physics of magnetic helicity injection, which is an important issue in fusion plasma confinement, as well as solar and astrophysical phenomena such as coronal mass ejections and accretion disk dynamics. The images presented in this paper are not only beautiful but provide a powerful way to understand the global dynamics of the plasma

A Model of R&D Valuation and the Design of Research Incentives

We develop a real options model of R&D valuation, which takes into account the uncertainty in the quality of the research output, the time and cost to completion, and the market demand for the R&D output. The model is then applied to study the problem of pharmaceutical under-investment in R&D for vaccines to treat diseases affecting the developing regions of the world. To address this issue, world organizations and private foundations are willing to sponsor vaccine R&D, but there is no consensus on how to administer the sponsorship effectively. Different research incentive contracts are examined using our valuation model. Their effectiveness is measured in the following four dimensions: cost to the sponsor, the probability of development success, the consumer surplus generated and the expected cost per person successfully vaccinated. We find that, in general, purchase commitment plans (pull subsidies) are more effective than cost subsidy plans (push subsidies), while extending patent protection is completely ineffective. Specifically, we find that a hybrid subsidy constructed from a purchase commitment combined with a sponsor co-payment feature produces the best results in all four dimensions of the effectiveness measure.

Clustering in Hilbert space of a quantum optimization problem

The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground state subspace of a certain quantum optimization problem. This involves extending the notion of clustering to Hilbert space, where the classical Hamming distance is not immediately useful. Quantum clusters correspond to macroscopically distinct subspaces of the full quantum ground state space which grow with the system size. We explicitly demonstrate that such clusters arise in the solution space of random quantum satisfiability (3-QSAT) at its satisfiability transition. We estimate both the number of these clusters and their internal entropy. The former are given by the number of hardcore dimer coverings of the core of the interaction graph, while the latter is related to the underconstrained degrees of freedom not touched by the dimers. We additionally provide new numerical evidence suggesting that the 3-QSAT satisfiability transition may coincide with the product satisfiability transition, which would imply the absence of an intermediate entangled satisfiable phase.Comment: 11 pages, 6 figure