33,763 research outputs found
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
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- 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- 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
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