40,162 research outputs found
Lagrangian Evolution of the Weyl Tensor
We derive the evolution equations for the electric and magnetic parts of the
Weyl tensor for cold dust from both general relativity and Newtonian gravity.
In a locally inertial frame at rest in the fluid frame, the Newtonian equations
agree with those of general relativity. We give explicit expressions for the
electric and magnetic parts of the Weyl tensor in the Newtonian limit. In
general, the magnetic part does not vanish, implying that the Lagrangian
evolution of the fluid is not purely local.Comment: 17 pages, AAS LateX v3.0, submitted to ApJ, MIT-CSR-94-0
Local light-ray rotation
We present a sheet structure that rotates the local ray direction through an
arbitrary angle around the sheet normal. The sheet structure consists of two
parallel Dove-prism sheets, each of which flips one component of the local
direction of transmitted light rays. Together, the two sheets rotate
transmitted light rays around the sheet normal. We show that the direction
under which a point light source is seen is given by a Mobius transform. We
illustrate some of the properties with movies calculated by ray-tracing
software.Comment: 9 pages, 6 figure
A note on dual giant gravitons in
We study some of the properties of dual giant gravitons - D2-branes wrapped
on an - in type IIA string theory on . In particular we confirm that the spectrum of small
fluctuations about the giant is both real and independent of the size of the
graviton. We also extend previously developed techniques for attaching open
strings to giants to this D2-brane giant and focus on two particular limits of
the resulting string sigma model: In the pp-wave limit we quantize the string
and compute the spectrum of bosonic excitations while in the semiclassical
limit, we read off the fast string Polyakov action and comment on the
comparison to the Landau-Lifshitz action for the dual open spin chain.Comment: v3 significantly changed: added coupling to RR 1-form and turned on
worldvolume gauge field, computed gauge field fluctuation, added comments on
closure of the sl(2) sector and re-written to improve clarity. This version
published in JHE
Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit
Volumes of sub-wavelength electromagnetic elements can act like homogeneous
materials: metamaterials. In analogy, sheets of optical elements such as prisms
can act ray-optically like homogeneous sheet materials. In this sense, such
sheets can be considered to be metamaterials for light rays (METATOYs).
METATOYs realize new and unusual transformations of the directions of
transmitted light rays. We study here, in the ray-optics and scalar-wave
limits, the wave-optical analog of such transformations, and we show that such
an analog does not always exist. Perhaps, this is the reason why many of the
ray-optical possibilities offered by METATOYs have never before been
considered.Comment: 10 pages, 3 figures, references update
Comparing D-Bar and Common Regularization-Based Methods for Electrical Impedance Tomography
Objective: To compare D-bar difference reconstruction with regularized linear reconstruction in electrical impedance tomography. Approach: A standard regularized linear approach using a Laplacian penalty and the GREIT method for comparison to the D-bar difference images. Simulated data was generated using a circular phantom with small objects, as well as a \u27Pac-Man\u27 shaped conductivity target. An L-curve method was used for parameter selection in both D-bar and the regularized methods. Main results: We found that the D-bar method had a more position independent point spread function, was less sensitive to errors in electrode position and behaved differently with respect to additive noise than the regularized methods. Significance: The results allow a novel pathway between traditional and D-bar algorithm comparison
Power Spectrum Correlations Induced by Non-Linear Clustering
Gravitational clustering is an intrinsically non-linear process that
generates significant non-Gaussian signatures in the density field. We consider
how these affect power spectrum determinations from galaxy and weak-lensing
surveys. Non-Gaussian effects not only increase the individual error bars
compared to the Gaussian case but, most importantly, lead to non-trivial
cross-correlations between different band-powers. We calculate the
power-spectrum covariance matrix in non-linear perturbation theory (weakly
non-linear regime), in the hierarchical model (strongly non-linear regime), and
from numerical simulations in real and redshift space. We discuss the impact of
these results on parameter estimation from power spectrum measurements and
their dependence on the size of the survey and the choice of band-powers. We
show that the non-Gaussian terms in the covariance matrix become dominant for
scales smaller than the non-linear scale, depending somewhat on power
normalization. Furthermore, we find that cross-correlations mostly deteriorate
the determination of the amplitude of a rescaled power spectrum, whereas its
shape is less affected. In weak lensing surveys the projection tends to reduce
the importance of non-Gaussian effects. Even so, for background galaxies at
redshift z=1, the non-Gaussian contribution rises significantly around l=1000,
and could become comparable to the Gaussian terms depending upon the power
spectrum normalization and cosmology. The projection has another interesting
effect: the ratio between non-Gaussian and Gaussian contributions saturates and
can even decrease at small enough angular scales if the power spectrum of the
3D field falls faster than 1/k^2.Comment: 34 pages, 15 figures. Revised version, includes a clearer explanation
of why the hierarchical ansatz does not provide a good model of the
covariance matrix in the non-linear regime, and new constraints on the
amplitudes Ra and Rb for general 4-pt function configurations in the
non-linear regim
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