36,713 research outputs found
Technology and Urban Management. Semiannual Report, October 1, 1967 through March 31, 1968
The projects under Technology and Urban Management (TAUM) have continued during the last few months with considerable success. The individual studies conducted in the City of Oakland and the progress made are described in this report
Chiral Green's Functions in Superconformal Field Theory
By solving the Ward identities in a superconformal field theory we find the
unique three-point Green's functions composed of chiral superfields for N =
1,2,3,4 supersymmetry. We show that the N=1 four-point function with R-charge
equal to one is uniquely determined by the Ward identities up to the
specification of four constants. We discuss why chiral Green's functions above
three-points, with total R-charge greater than N, are not uniquely determined.Comment: 32 pages, no figures, LaTeX2e forma
Variational integrators, the Newmark scheme, and dissipative systems
Variational methods are a class of symplectic-momentum integrators for ODEs. Using
these schemes, it is shown that the classical Newmark algorithm is structure preserving in a
non-obvious way, thus explaining the observed numerical behavior. Modifications to variational
methods to include forcing and dissipation are also proposed, extending the advantages
of structure preserving integrators to non-conservative systems
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
Computationally Efficient Nonparametric Importance Sampling
The variance reduction established by importance sampling strongly depends on
the choice of the importance sampling distribution. A good choice is often hard
to achieve especially for high-dimensional integration problems. Nonparametric
estimation of the optimal importance sampling distribution (known as
nonparametric importance sampling) is a reasonable alternative to parametric
approaches.In this article nonparametric variants of both the self-normalized
and the unnormalized importance sampling estimator are proposed and
investigated. A common critique on nonparametric importance sampling is the
increased computational burden compared to parametric methods. We solve this
problem to a large degree by utilizing the linear blend frequency polygon
estimator instead of a kernel estimator. Mean square error convergence
properties are investigated leading to recommendations for the efficient
application of nonparametric importance sampling. Particularly, we show that
nonparametric importance sampling asymptotically attains optimal importance
sampling variance. The efficiency of nonparametric importance sampling
algorithms heavily relies on the computational efficiency of the employed
nonparametric estimator. The linear blend frequency polygon outperforms kernel
estimators in terms of certain criteria such as efficient sampling and
evaluation. Furthermore, it is compatible with the inversion method for sample
generation. This allows to combine our algorithms with other variance reduction
techniques such as stratified sampling. Empirical evidence for the usefulness
of the suggested algorithms is obtained by means of three benchmark integration
problems. As an application we estimate the distribution of the queue length of
a spam filter queueing system based on real data.Comment: 29 pages, 7 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
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
Generalised geometry, eleven dimensions and E11
We construct the non-linear realisation of E11 and its first fundamental
representation in eleven dimensions at low levels. The fields depend on the
usual coordinates of space-time as well as two form and five form coordinates.
We derive the terms in the dynamics that contain the three form and six form
fields and show that when we restricted their field dependence to be only on
the usual space-time we recover the correct self-duality relation. Should this
result generalise to the gravity fields then the non-linear realisation is an
extension of the maximal supergravity theory, as previously conjectured. We
also comment on the connections between the different approaches to generalised
geometry.Comment: 17 pages, Trivial typos corrected in version one and a substantial
note added which gives the equation of motion relating the gravity field to
its dua
Coulomb Oscillations in Antidots in the Integer and Fractional Quantum Hall Regimes
We report measurements of resistance oscillations in micron-scale antidots in
both the integer and fractional quantum Hall regimes. In the integer regime, we
conclude that oscillations are of the Coulomb type from the scaling of magnetic
field period with the number of edges bound to the antidot. Based on both
gate-voltage and field periods, we find at filling factor {\nu} = 2 a tunneling
charge of e and two charged edges. Generalizing this picture to the fractional
regime, we find (again, based on field and gate-voltage periods) at {\nu} = 2/3
a tunneling charge of (2/3)e and a single charged edge.Comment: related papers at http://marcuslab.harvard.ed
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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