4,263 research outputs found
Extremal Isolated Horizons: A Local Uniqueness Theorem
We derive all the axi-symmetric, vacuum and electrovac extremal isolated
horizons. It turns out that for every horizon in this class, the induced metric
tensor, the rotation 1-form potential and the pullback of the electromagnetic
field necessarily coincide with those induced by the monopolar, extremal
Kerr-Newman solution on the event horizon. We also discuss the general case of
a symmetric, extremal isolated horizon. In particular, we analyze the case of a
two-dimensional symmetry group generated by two null vector fields. Its
relevance to the classification of all the symmetric isolated horizons,
including the non-extremal once, is explained.Comment: 22 pages, page size changed, typos and equations (142), (143a)
corrected, PACS number adde
The Wilsonian Renormalization Group in Randall-Sundrum 1
We find renormalization group transformations for the compactified
Randall-Sundrum scenario by integrating out an infinitesimal slice of
ultraviolet degrees of freedom near the Planck brane. Under these
transformations the coefficients of operators on the Planck brane experience RG
evolution. The extra-dimensional radius also scales, flowing to zero in the IR.
We find an attractive fixed point in the context of a bulk scalar field theory.
Calculations are simplified in the low energy effective theory as we
demonstrate with the computation of a loop diagram.Comment: 19 pages, typos adde
Spacetimes foliated by Killing horizons
It seems to be expected, that a horizon of a quasi-local type, like a Killing
or an isolated horizon, by analogy with a globally defined event horizon,
should be unique in some open neighborhood in the spacetime, provided the
vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our
paper is to verify whether that intuition is correct. If one can extend a so
called Kundt metric, in such a way that its null, shear-free surfaces have
spherical spacetime sections, the resulting spacetime is foliated by so called
non-expanding horizons. The obstacle is Kundt's constraint induced at the
surfaces by the Einstein or the Einstein-Maxwell equations, and the requirement
that a solution be globally defined on the sphere. We derived a transformation
(reflection) that creates a solution to Kundt's constraint out of data defining
an extremal isolated horizon. Using that transformation, we derived a class of
exact solutions to the Einstein or Einstein-Maxwell equations of very special
properties. Each spacetime we construct is foliated by a family of the Killing
horizons. Moreover, it admits another, transversal Killing horizon. The
intrinsic and extrinsic geometry of the transversal Killing horizon coincides
with the one defined on the event horizon of the extremal Kerr-Newman solution.
However, the Killing horizon in our example admits yet another Killing vector
tangent to and null at it. The geometries of the leaves are given by the
reflection.Comment: LaTeX 2e, 13 page
A search for varying fundamental constants using Hz-level frequency measurements of cold CH molecules
Many modern theories predict that the fundamental constants depend on time,
position, or the local density of matter. We develop a spectroscopic method for
pulsed beams of cold molecules, and use it to measure the frequencies of
microwave transitions in CH with accuracy down to 3 Hz. By comparing these
frequencies with those measured from sources of CH in the Milky Way, we test
the hypothesis that fundamental constants may differ between the high and low
density environments of the Earth and the interstellar medium. For the fine
structure constant we find \Delta\alpha/\alpha = (0.3 +/- 1.1)*10^{-7}, the
strongest limit to date on such a variation of \alpha. For the
electron-to-proton mass ratio we find \Delta\mu/\mu = (-0.7 +/- 2.2) * 10^{-7}.
We suggest how dedicated astrophysical measurements can improve these
constraints further and can also constrain temporal variation of the constants.Comment: 8 pages, 3 figure
Strain localization in a shear transformation zone model for amorphous solids
We model a sheared disordered solid using the theory of Shear Transformation
Zones (STZs). In this mean-field continuum model the density of zones is
governed by an effective temperature that approaches a steady state value as
energy is dissipated. We compare the STZ model to simulations by Shi, et
al.(Phys. Rev. Lett. 98 185505 2007), finding that the model generates
solutions that fit the data,exhibit strain localization, and capture important
features of the localization process. We show that perturbations to the
effective temperature grow due to an instability in the transient dynamics, but
unstable systems do not always develop shear bands. Nonlinear energy
dissipation processes interact with perturbation growth to determine whether a
material exhibits strain localization. By estimating the effects of these
interactions, we derive a criterion that determines which materials exhibit
shear bands based on the initial conditions alone. We also show that the shear
band width is not set by an inherent diffusion length scale but instead by a
dynamical scale that depends on the imposed strain rate.Comment: 8 figures, references added, typos correcte
Normal-superfluid interaction dynamics in a spinor Bose gas
Coherent behavior of spinor Bose-Einstein condensates is studied in the
presence of a significant uncondensed (normal) component. Normal-superfluid
exchange scattering leads to a near-perfect local alignment between the spin
fields of the two components. Through this spin locking, spin-domain formation
in the condensate is vastly accelerated as the spin populations in the
condensate are entrained by large-amplitude spin waves in the normal component.
We present data evincing the normal-superfluid spin dynamics in this regime of
complicated interdependent behavior.Comment: 5 pages, 4 fig
Recurrent Fully Convolutional Neural Networks for Multi-slice MRI Cardiac Segmentation
In cardiac magnetic resonance imaging, fully-automatic segmentation of the
heart enables precise structural and functional measurements to be taken, e.g.
from short-axis MR images of the left-ventricle. In this work we propose a
recurrent fully-convolutional network (RFCN) that learns image representations
from the full stack of 2D slices and has the ability to leverage inter-slice
spatial dependences through internal memory units. RFCN combines anatomical
detection and segmentation into a single architecture that is trained
end-to-end thus significantly reducing computational time, simplifying the
segmentation pipeline, and potentially enabling real-time applications. We
report on an investigation of RFCN using two datasets, including the publicly
available MICCAI 2009 Challenge dataset. Comparisons have been carried out
between fully convolutional networks and deep restricted Boltzmann machines,
including a recurrent version that leverages inter-slice spatial correlation.
Our studies suggest that RFCN produces state-of-the-art results and can
substantially improve the delineation of contours near the apex of the heart.Comment: MICCAI Workshop RAMBO 201
Isolated Horizon, Killing Horizon and Event Horizon
We consider space-times which in addition to admitting an isolated horizon
also admit Killing horizons with or without an event horizon. We show that an
isolated horizon is a Killing horizon provided either (1) it admits a
stationary neighbourhood or (2) it admits a neighbourhood with two independent,
commuting Killing vectors. A Killing horizon is always an isolated horizon. For
the case when an event horizon is definable, all conceivable relative locations
of isolated horizon and event horizons are possible. Corresponding conditions
are given.Comment: 14 pages, Latex, no figures. Some arguments tightened. To appear in
Class. Quant. Gra
- …