Hamiltonians separable in cartesian coordinates and third-order integrals of motion

We present in this article all Hamiltonian systems in E(2) that are separable in cartesian coordinates and that admit a third-order integral, both in quantum and in classical mechanics. Many of these superintegrable systems are new, and it is seen that there exists a relation between quantum superintegrable potentials, invariant solutions of the Korteweg-De Vries equation and the Painlev\'e transcendents.Comment: 19 pages, Will be published in J. Math. Phy

Fundamental limitations on "warp drive" spacetimes

"Warp drive" spacetimes are useful as "gedanken-experiments" that force us to confront the foundations of general relativity, and among other things, to precisely formulate the notion of "superluminal" communication. We verify the non-perturbative violation of the classical energy conditions of the Alcubierre and Natario warp drive spacetimes and apply linearized gravity to the weak-field warp drive, testing the energy conditions to first and second order of the non-relativistic warp-bubble velocity. We are primarily interested in a secondary feature of the warp drive that has not previously been remarked upon, if it could be built, the warp drive would be an example of a "reaction-less drive". For both the Alcubierre and Natario warp drives we find that the occurrence of significant energy condition violations is not just a high-speed effect, but that the violations persist even at arbitrarily low speeds. An interesting feature of this construction is that it is now meaningful to place a finite mass spaceship at the center of the warp bubble, and compare the warp field energy with the mass-energy of the spaceship. There is no hope of doing this in Alcubierre's original version of the warp-field, since by definition the point in the center of the warp bubble moves on a geodesic and is "massless". That is, in Alcubierre's original formalism and in the Natario formalism the spaceship is always treated as a test particle, while in the linearized theory we can treat the spaceship as a finite mass object. For both the Alcubierre and Natario warp drives we find that even at low speeds the net (negative) energy stored in the warp fields must be a significant fraction of the mass of the spaceship.Comment: 18 pages, Revtex4. V2: one reference added, some clarifying comments and discussion, no physics changes, accepted for publication in Classical and Quantum Gravit

Divide and concur: A general approach to constraint satisfaction

Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin glasses), and satisfiability testing. We present a simple geometric framework to express and solve such problems and apply it to two benchmarks. In the first application (3SAT, a boolean satisfaction problem), the resulting method exhibits similar performance scaling as a leading context-specific algorithm (walksat). In the second application (sphere packing), the method allowed us to find improved solutions to some old and well-studied optimization problems. Based upon its simplicity and observed efficiency, we argue that this framework provides a competitive alternative to stochastic methods such as simulated annealing.Comment: 4 pages, 2 figure

Serologic evidence for the presence in Pteropus bats of a paramyxovirus related to equine morbillivirus.

Two outbreaks of a previously unknown disease in horses and humans occurred in Queensland in 1994. The outbreaks occurred within 1 month of each other in Brisbane and Mackay, which are approximately 1000 km apart. In the Brisbane incident, 21 horses were infected of which 14 died or were euthanized after severe clinical signs of an acute respiratory disease. Two human cases were in patients with less well defined clinical signs; one patient died (1,2). In the Mackay incident two horses became seriously ill and died, and one person also died (3). Although it is now known that the two outbreaks occurred in August and September 1994, knowledge of the Mackay outbreak did not occur until late 1995 when the infected person died of a relapsing encephalitis. The name equine morbillivirus (EMV) has been proposed for a paramyxovirus isolated from four of the Brisbane horses and the first patient who died (2)

Surface stresses on a thin shell surrounding a traversable wormhole

We match an interior solution of a spherically symmetric traversable wormhole to a unique exterior vacuum solution, with a generic cosmological constant, at a junction interface, and the surface stresses on the thin shell are deduced. In the spirit of minimizing the usage of exotic matter we determine regions in which the weak and null energy conditions are satisfied on the junction surface. The characteristics and several physical properties of the surface stresses are explored, namely, regions where the sign of the tangential surface pressure is positive and negative (surface tension) are determined. This is done by expressing the tangential surface pressure as a function of several parameters, namely, that of the matching radius, the redshift parameter, the surface energy density and of the generic cosmological constant. An equation governing the behavior of the radial pressure across the junction surface is also deduced.Comment: 24 pages, 11 figures, LaTeX2e, IOP style files. Accepted for publication in Classical and Quantum Gravity. V2: Four references added, now 25 page

Singularity confinement and algebraic integrability

Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved quantities whereas singularity confinement is associated with the local analysis of singularities. In this paper, the relationship between these two notions is explored for birational autonomous mappings. Two types of results are obtained: first, algebraically integrable mappings are shown to have the singularity confinement property. Second, a proof of the non-existence of algebraic conserved quantities of discrete systems based on the lack of confinement property is given.Comment: 18 pages, no figur

Superintegrability with third order invariants in quantum and classical mechanics

We consider here the coexistence of first- and third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable systems are found that have no classical analog, i.e. the potentials are proportional to \hbar^2, so their classical limit is free motion.Comment: 15 page

Landmine detection and imaging using Micropower Impulse Radar (MIR)

The Lawrence Livermore National Laboratory (LLNL) has developed radar and imaging technologies with potential applications in mine detection by the armed forces and other agencies involved in determining efforts. These new technologies use a patented ultra-wideband (impulse) radar technology that is compact, low-cost, and low power. Designated as Micropower hnpulse Radar, these compact, self-contained radars can easily be assembled into arrays to form complete ground penetrating radar imaging systems. LLNL has also developed tomographic reconstruction and signal processing software capable of producing high-resolution 2-D and 3-D images of objects buried in materials like soil or concrete from radar data. Preliminary test results have shown that a radar imaging system using these technologies has the ability to image both metallic and plastic land mine surrogate targets buried in 5 to 10 cm of moist soil. In dry soil, the system can detect buried objects to a depth of 30 cm and more. This report describes our initial test results and plans for future work

Remarks on the notion of quantum integrability

We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different integrability classes. We end by highlighting some of the expected physical properties associated to models fulfilling the proposed criteria.Comment: 22 pages, no figures, Proceedings of Statphys 2