Variational Multisymplectic Formulations of Nonsmooth Continuum Mechanics

This paper develops the foundations of the multisymplectic formulation of nonsmooth continuum mechanics. It may be regarded as a PDE generalization of previous techniques that developed a variational approach to collision problems. These methods have already proved of value in computational mechanics, particularly in the development of asynchronous integrators and efficient collision methods. The present formulation also includes solid-fluid interactions and material interfaces and, in addition, lays the groundwork for a treatment of shocks

Inclusivity in nurse education.

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A Modified Stern-Gerlach Experiment Using a Quantum Two-State Magnetic Field

The Stern-Gerlach experiment has played an important role in our understanding of quantum behavior. We propose and analyze a modified version of this experiment where the magnetic field of the detector is in a quantum superposition, which may be experimentally realized using a superconducting flux qubit. We show that if incident spin-$1/2$ particles couple with the two-state magnetic field, a discrete target distribution results that resembles the distribution in the classical Stern-Gerlach experiment. As an application of the general result, we compute the distribution for a square waveform of the incident fermion. This experimental setup allows us to establish: (1) the quantization of the intrinsic angular momentum of a spin-$1/2$ particle, and (2) a correlation between EPR pairs leading to nonlocality, without necessarily collapsing the particle's spin wavefunction.Comment: 12 pages, 2 figure

A class of Lorentzian Kac-Moody algebras

We consider a natural generalisation of the class of hyperbolic Kac-Moody algebras. We describe in detail the conditions under which these algebras are Lorentzian. We also construct their fundamental weights, and analyse whether they possess a real principal so(1,2) subalgebra. Our class of algebras include the Lorentzian Kac-Moody algebras that have recently been proposed as symmetries of M-theory and the closed bosonic string.Comment: 40 pages TeX, 5 eps-figure

Nonsmooth Lagrangian mechanics and variational collision integrators

Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Discretizations of this nonsmooth mechanics are developed by using the methodology of variational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically, and the long-time stable energy behavior typical of variational methods is demonstrated

Assessing smoking status in children, adolescents and adults: cotinine cut-points revisited

Aims To reassess saliva cotinine cut-points to discriminate smoking status. Cotinine cut-points that are in use were derived from relatively small samples of smokers and non-smokers 20 or more years ago. It is possible that optimal cut-points may have changed as prevalence and exposure to passive smoking have declined. Design Cross-sectional survey of the general population, with assessment of self-reported smoking and saliva cotinine. Participants A total of 58 791 respondents aged 4 years and older in the Health Survey for England for the years 1996-2004 who provided valid saliva cotinine specimens. Measures Saliva cotinine concentrations, demographic variables, self-reported smoking, presence or absence of smoking in the home, a composite index of social disadvantage derived from occupation, housing tenure and access to a car. Findigns A cut-point of 12 ng/ml performed best overall, with specificity of 96.9% and sensitivity of 96.7% in discriminating confirmed cigarette smokers from never regular smokers. This cut-point also identified correctly 95.8% of children aged 8-15 years smoking six or more cigarettes a week. There was evidence of substantial misreport in claimed ex-smokers, especially adolescents (specificity 72.3%) and young adults aged 16-24 years (77.5%). Optimal cut-points varied by presence (18 ng/ml) or absence (5 ng/ml) of smoking in the home, and there was a gradient from 8 ng/ml to 18 ng/ml with increasing social disadvantage. Conclusions The extent of non-smokers' exposure to other people's tobacco smoke is the principal factor driving optimal cotinine cut-points. A cut-point of 12 ng/ml can be recommended for general use across the whole age range, although different cut-points may be appropriate for population subgroups and in societies with differing levels of exposure to secondhand smoke

Degenerate states of narrow semiconductor rings in the presence of spin orbit coupling: Role of time-reversal and large gauge transformations

The electron Hamiltonian of narrow semiconductor rings with the Rashba and Dresselhaus spin orbit terms is invariant under time-reversal operation followed by a large gauge transformation. We find that all the eigenstates are doubly degenerate when integer or half-integer quantum fluxes thread the quantum ring. The wavefunctions of a degenerate pair are related to each other by the symmetry operation. These results are valid even in the presence of a disorder potential. When the Zeeman term is present only some of these degenerate levels anticross

Imaging Transport Resonances in the Quantum Hall Effect

We use a scanning capacitance probe to image transport in the quantum Hall system. Applying a DC bias voltage to the tip induces a ring-shaped incompressible strip (IS) in the 2D electron system (2DES) that moves with the tip. At certain tip positions, short-range disorder in the 2DES creates a quantum dot island in the IS. These islands enable resonant tunneling across the IS, enhancing its conductance by more than four orders of magnitude. The images provide a quantitative measure of disorder and suggest resonant tunneling as the primary mechanism for transport across ISs.Comment: 4 pages, 4 figures, submitted to PRL. For movies and additional infomation, see http://electron.mit.edu/scanning/; Added scale bars to images, revised discussion of figure 3, other minor change

The Principal Axis of the Virgo Cluster

Using accurate distances to individual Virgo cluster galaxies obtained by the method of Surface Brightness Fluctuations, we show that Virgo's brightest ellipticals have a remarkably collinear arrangement in three dimensions. This axis, which is inclined by 10 to 15 degrees from the line of sight, can be traced to even larger scales where it appears to join a filamentary bridge of galaxies connecting Virgo to the rich cluster Abell 1367. The orientations of individual Virgo ellipticals also show some tendency to be aligned with the cluster axis, as does the jet of the supergiant elliptical M87. These results suggest that the formation of the Virgo cluster, and its brightest member galaxies, have been driven by infall of material along the Virgo-A1367 filament.Comment: 8 pages, 4 figures, accepted for publication in ApJ Letter