16,305 research outputs found
Apparatus for changing the orientation and velocity of a spinning body traversing a path Patent
Development of method and apparatus for spinning satellite about selected axis after reaching predetermined orientatio
How do random Fibonacci sequences grow?
We study two kinds of random Fibonacci sequences defined by and
for , (linear case) or (non-linear case), where each sign is independent and
either + with probability or - with probability (). Our
main result is that the exponential growth of for (linear
case) or for (non-linear case) is almost surely given by
where is an explicit
function of depending on the case we consider, and is an
explicit probability distribution on \RR_+ defined inductively on
Stern-Brocot intervals. In the non-linear case, the largest Lyapunov exponent
is not an analytic function of , since we prove that it is equal to zero for
. We also give some results about the variations of the largest
Lyapunov exponent, and provide a formula for its derivative
Training a perceptron in a discrete weight space
On-line and batch learning of a perceptron in a discrete weight space, where
each weight can take different values, are examined analytically and
numerically. The learning algorithm is based on the training of the continuous
perceptron and prediction following the clipped weights. The learning is
described by a new set of order parameters, composed of the overlaps between
the teacher and the continuous/clipped students. Different scenarios are
examined among them on-line learning with discrete/continuous transfer
functions and off-line Hebb learning. The generalization error of the clipped
weights decays asymptotically as / in the case of on-line learning with binary/continuous activation
functions, respectively, where is the number of examples divided by N,
the size of the input vector and is a positive constant that decays
linearly with 1/L. For finite and , a perfect agreement between the
discrete student and the teacher is obtained for . A crossover to the generalization error ,
characterized continuous weights with binary output, is obtained for synaptic
depth .Comment: 10 pages, 5 figs., submitted to PR
Spin-1 gravitational waves
Gravitational fields invariant for a 2-dimensional Lie algebra of Killing
fields [ X,Y] =Y, with Y of light type, are analyzed. The conditions for them
to represent gravitational waves are verified and the definition of energy and
polarization is addressed; realistic generating sources are described.Comment: 18 pages, no figures. A section on possible sources has been added.
Version accepted for publication in Int. J. Mod. Phys.
Geodetic, teleseismic, and strong motion constraints on slip from recent southern Peru subduction zone earthquakes
We use seismic and geodetic data both jointly and separately to constrain coseismic slip from the 12 November 1996 M_w 7.7 and 23 June 2001 M_w 8.5 southern Peru subduction zone earthquakes, as well as two large aftershocks following the 2001 earthquake on 26 June and 7 July 2001. We use all available data in our inversions: GPS, interferometric synthetic aperture radar (InSAR) from the ERS-1, ERS-2, JERS, and RADARSAT-1 satellites, and seismic data from teleseismic and strong motion stations. Our two-dimensional slip models derived from only teleseismic body waves from South American subduction zone earthquakes with M_w > 7.5 do not reliably predict available geodetic data. In particular, we find significant differences in the distribution of slip for the 2001 earthquake from models that use only seismic (teleseismic and two strong motion stations) or geodetic (InSAR and GPS) data. The differences might be related to postseismic deformation or, more likely, the different sensitivities of the teleseismic and geodetic data to coseismic rupture properties. The earthquakes studied here follow the pattern of earthquake directivity along the coast of western South America, north of 5°S, earthquakes rupture to the north; south of about 12°S, directivity is southerly; and in between, earthquakes are bilateral. The predicted deformation at the Arequipa GPS station from the seismic-only slip model for the 7 July 2001 aftershock is not consistent with significant preseismic motion
A WZW model based on a non-semi-simple group
We present a conformal field theory which desribes a homogeneous four
dimensional Lorentz-signature space-time. The model is an ungauged WZW model
based on a central extension of the Poincar\'e algebra. The central charge of
this theory is exactly four, just like four dimensional Minkowski space. The
model can be interpreted as a four dimensional monochromatic plane wave. As
there are three commuting isometries, other interesting geometries are expected
to emerge via duality.Comment: 8 pages, phyzzx, IASSNS-HEP-93/61 Texable versio
Robustness of Sound Speed and Jet Quenching for Gauge/Gravity Models of Hot QCD
We probe the effectiveness and robustness of a simple gauge/gravity dual
model of the QCD fireball that breaks conformal symmetry by constructing a
family of similar geometries that solve the scalar/gravity equations of motion.
This family has two parameters, one of which is associated to the temperature.
We calculate two quantities, the speed of sound and the jet-quenching
parameter. We find the speed of sound to be universal and robust over all the
geometries when appropriate units are used, while the jet-quenching parameter
varies significantly away from the conformal limit. We note that the overall
structure of the jet-quenching depends strongly on whether the running scalar
is the dilaton or not. We also discuss the variation of the scalar potential
over our family of solutions, and truncate our results to where the associated
error is small.Comment: 21 pages, 9 figures, LaTeX. v2:references added, minor correction to
speed of sound; conclusions unchange
On a class of invariant coframe operators with application to gravity
Let a differential 4D-manifold with a smooth coframe field be given. Consider
the operators on it that are linear in the second order derivatives or
quadratic in the first order derivatives of the coframe, both with coefficients
that depend on the coframe variables. The paper exhibits the class of operators
that are invariant under a general change of coordinates, and, also, invariant
under the global SO(1,3)-transformation of the coframe. A general class of
field equations is constructed. We display two subclasses in it. The subclass
of field equations that are derivable from action principles by free variations
and the subclass of field equations for which spherical-symmetric solutions,
Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the
resulting metric is computed. Invoking the Geodesic Postulate, we find all the
equations that are experimentally (by the 3 classical tests) indistinguishable
from Einstein field equations. This family includes, of course, also Einstein
equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool
employed in the paper is an invariant formulation reminiscent of Cartan's
structural equations. The article sheds light on the possibilities and
limitations of the coframe gravity. It may also serve as a general procedure to
derive covariant field equations
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