1,476 research outputs found
The Height of a Giraffe
A minor modification of the arguments of Press and Lightman leads to an
estimate of the height of the tallest running, breathing organism on a
habitable planet as the Bohr radius multiplied by the three-tenths power of the
ratio of the electrical to gravitational forces between two protons (rather
than the one-quarter power that Press got for the largest animal that would not
break in falling over, after making an assumption of unreasonable brittleness).
My new estimate gives a height of about 3.6 meters rather than Press's original
estimate of about 2.6 cm. It also implies that the number of atoms in the
tallest runner is very roughly of the order of the nine-tenths power of the
ratio of the electrical to gravitational forces between two protons, which is
about 3 x 10^32.Comment: 12 pages, LaTe
Numerical computation of real or complex elliptic integrals
Algorithms for numerical computation of symmetric elliptic integrals of all
three kinds are improved in several ways and extended to complex values of the
variables (with some restrictions in the case of the integral of the third
kind). Numerical check values, consistency checks, and relations to Legendre's
integrals and Bulirsch's integrals are included
Matrix product representation of gauge invariant states in a Z_2 lattice gauge theory
The Gauss law needs to be imposed on quantum states to guarantee gauge
invariance when one studies gauge theory in hamiltonian formalism. In this
work, we propose an efficient variational method based on the matrix product
ansatz for a Z_2 lattice gauge theory on a spatial ladder chain. Gauge
invariant low-lying states are identified by evaluating expectation values of
the Gauss law operator after numerical diagonalization of the gauge
hamiltonian.Comment: 15 pages, 6 figures, minor corrections, accepted for publication in
JHE
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Customized design of hearing aids using statistical shape learning
3D shape modeling is a crucial component of rapid prototyping systems
that customize shapes of implants and prosthetic devices to a patientâs
anatomy. In this paper, we present a solution to the problem of customized 3D
shape modeling using a statistical shape analysis framework. We design a novel
method to learn the relationship between two classes of shapes, which are related
by certain operations or transformation. The two associated shape classes are
represented in a lower dimensional manifold, and the reduced set of parameters
obtained in this subspace is utilized in an estimation, which is exemplified by a
multivariate regression in this paper.We demonstrate our method with a felicitous
application to estimation of customized hearing aid devices
Superradiant instabilities of rotating black branes and strings
Black branes and strings are generally unstable against a certain sector of
gravitational perturbations. This is known as the Gregory-Laflamme instability.
It has been recently argued that there exists another general instability
affecting many rotating extended black objects. This instability is in a sense
universal, in that it is triggered by any massless field, and not just
gravitational perturbations. Here we investigate this novel mechanism in
detail. For this instability to work, two ingredients are necessary: (i) an
ergo-region, which gives rise to superradiant amplification of waves, and (ii)
``bound'' states in the effective potential governing the evolution of the
particular mode under study. We show that the black brane Kerr_4 x R^p is
unstable against this mechanism, and we present numerical results for
instability timescales for this case. On the other hand, and quite
surprisingly, black branes of the form Kerr_d x R^p are all stable against this
mechanism for d>4. This is quite an unexpected result, and it stems from the
fact that there are no stable circular orbits in higher dimensional black hole
spacetimes, or in a wave picture, that there are no bound states in the
effective potential. We also show that it is quite easy to simulate this
instability in the laboratory with acoustic black branes.Comment: 19 pages, 10 figures. v2: Enlarged discussion on the necessary
conditions for the existence of instabilit
Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field
This paper continues a study on Choptuik scaling in gravitational collapse of
a complex scalar field at the threshold for black hole formation. We perform a
linear perturbation analysis of the previously derived complex critical
solution, and calculate the critical exponent for black hole mass, . We also show that this critical solution is unstable via a
growing oscillatory mode.Comment: 15 pages of latex/revtex; added details of numerics, in press in Phys
Rev D; 1 figure included, or available by anonymous ftp to
ftp://ftp.itp.ucsb.edu/figures/nsf-itp-95-58.ep
Towards the realistic fermion masses with a single family in extra dimensions
In a class of multidimensional models, topology of a thick brane provides
three chiral fermionic families with hierarchical masses and mixings in the
effective four-dimensional theory, while the full model contains a single
vector-like generation. We carry out numerical simulations and reproduce all
known Standard Model fermion masses and mixings in one of these models.Comment: 12 pages, 2 figures, uses JHEP3.cls. Some minor corrections are mad
Is the present expansion of the universe really accelerating?
The current observations are usually explained by an accelerating expansion
of the present universe. However, with the present quality of the supernovae Ia
data, the allowed parameter space is wide enough to accommodate the
decelerating models as well. This is shown by considering a particular example
of the dark energy equation-of-state ,
which is equivalent to modifying the \emph{geometrical curvature} index of
the standard cosmology by shifting it to where is a
constant. The resulting decelerating model is consistent with the recent CMB
observations made by WMAP, as well as, with the high redshift supernovae Ia
data including SN 1997ff at . It is also consistent with the newly
discovered supernovae SN 2002dc at and SN 2002dd at which
have a general tendency to improve the fit.Comment: Replaced with the accepted version to appear in MNRA
Choosing integration points for QCD calculations by numerical integration
I discuss how to sample the space of parton momenta in order to best perform
the numerical integrations that lead to a calculation of three jet cross
sections and similar observables in electron-positron annihilation.Comment: 25 pages with 8 figure
Numerical study of the shape and integral parameters of a dendrite
We present a numerical study of sidebranching of a solidifying dendrite by
means of a phase--field model. Special attention is paid to the regions far
from the tip of the dendrite, where linear theories are no longer valid. Two
regions have been distinguished outside the linear region: a first one in which
sidebranching is in a competition process and a second one further down where
branches behave as independent of each other. The shape of the dendrite and
integral parameters characterizing the whole dendrite (contour length and area
of the dendrite) have been computed and related to the characteristic tip
radius for both surface tension and kinetic dominated dendrites. Conclusions
about the different behaviors observed and comparison with available
experiments and theoretical predictions are presented.Comment: 10 pages, 7 figures, Accepted for publication in Phys. Rev.
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