Quantum Mechanics with Trajectories: Quantum Trajectories and Adaptive Grids

Although the foundations of the hydrodynamical formulation of quantum mechanics were laid over 50 years ago, it has only been within the past few years that viable computational implementations have been developed. One approach to solving the hydrodynamic equations uses quantum trajectories as the computational tool. The trajectory equations of motion are described and methods for implementation are discussed, including fitting of the fields to gaussian clusters.Comment: Prepared for CiSE, Computing in Science and Engineering IEEE/AIP special issue on computational chemistr

Large amplitude electrothermal waves in a nonequilibrium plasma

Steady, one-dimensional current streamers have been observed in nonequilibrium plasma subjected to crossed E and B fields. Their half-width and amplitude agree with a nonlinear model of electrothermal waves

Shear-free Null Quasi-Spherical Spacetimes

The residual gauge freedom within the null quasi-spherical coordinate condition is studied, for spacetimes admitting an expanding, shear-free null foliation. The freedom consists of a boost and rotation at each coordinate sphere, corresponding to a specification of inertial frame at each sphere. Explicit formulae involving arbitrary functions of two variables are obtained for the accelerated Minkowski, Schwarzschild, and Robinson-Trautman spacetimes. These examples will be useful as test metrics in numerical relativity.Comment: 20 pages, revte

Prepared discussant comments

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Performance of five 30 GHz satellite receivers

Technology development contracts funded by NASA have resulted in five 30 GHz satellite receivers of various design. The results of tests performed at NASA-Lewis to determine the operating characteristics of the receivers and their ability to perform in a digital satellite link are presented and discussed

Matter Bounce in Horava-Lifshitz Cosmology

Horava-Lifshitz gravity, a recent proposal for a UV-complete renormalizable gravity theory, may lead to a bouncing cosmology. In this note we argue that Horava-Lifshitz cosmology may yield a concrete realization of the matter bounce scenario, and thus give rise to an alternative to inflation for producing a scale-invariant spectrum of cosmological perturbations. In this scenario, quantum vacuum fluctuations exit the Hubble radius in the pre-bounce phase and the spectrum is transformed into a scale-invariant one on super-Hubble scales before the bounce because the long wavelength modes undergo squeezing of their wave-functions for a longer period of time than shorter wavelength modes. The scale-invariance of the spectrum of curvature fluctuations is preserved during and after the bounce. A distinctive prediction of this scenario is the amplitude and shape of the bispectrum.Comment: 6 pages, 1 figure, a couple of minor wording change

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist

Multistep self-assembly of heteroleptic magnesium and sodium-magnesium benzamidinate complexes

Reaction of the magnesium bis-alkyl Mg(CH2SiMe3)(2) and the sodium amide NaHMDS (where HMDS = N(SiMe3)(2)) with benzonitrile yields the homometallic heteroleptic complex [PhC(NSiMe3)(2)Mg{mu-NC(CH2SiMe3)Ph}](2) (1). It appears that at least six independent reactions must have occurred in this one-pot reaction to arrive at this mixed benzamidinate ketimido product. Two benzonitrile solvated derivatives of Mg(CH2SiMe3)(2) (5a and 5b) have been synthesized, with 5a crystallographically characterized as a centrosymmetric (MgC)(2) cyclodimer. When, the components of 5a are allowed to react for longer, partial addition of the Mg-alkyl unit across the C N triple bond occurs to yield the trimeric species (Me3SiCH2)(2)Mg-3[mu-N=C(CH2SiMe3)Ph](4)center dot 2N CPh (6), with bridging ketimido groups and terminal alkyl groups. Finally, using the same starting materials as that which produced 1, but altering their order of addition, a magnesium bis-alkyl unit is inserted into the Na-N bonds of a benzamidinate species to yield a new sodium magnesiate complex, PhC(NSiMe3)(2)Mg(mu-CH2SiMe3)(2)Na center dot 2TMEDA (7). The formation of 7 represents a novel (insertion) route to mixed-metal species of this kind and is the first Such example to contain a bidentate terminal anion attached to the divalent metal center. All new species are characterized by H-1 and C-13 NMR spectroscopy and where appropriate by IR spectroscopy. The solid-state structures of complexes 1, 5a, and 7 have also been determined and are disclosed within