15,718 research outputs found
Asymptotics of Relativistic Spin Networks
The stationary phase technique is used to calculate asymptotic formulae for
SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives
the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For
the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical
calculations of the Spin Network evaluation. Finally we discuss the asymptotics
of the SO(3,1) 10j-symbol.Comment: 31 pages, latex. v3: minor clarification
Electric field formulation for thin film magnetization problems
We derive a variational formulation for thin film magnetization problems in
type-II superconductors written in terms of two variables, the electric field
and the magnetization function. A numerical method, based on this formulation,
makes it possible to accurately compute all variables of interest, including
the electric field, for any value of the power in the power law current-voltage
relation characterizing the superconducting material. For high power values we
obtain a good approximation to the critical state model solution. Numerical
simulation results are presented for simply and multiply connected films, and
also for an inhomogeneous film.Comment: 15 p., submitte
On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables
We discuss various features and details of two versions of the Barrett-Crane
spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian
model and second of the SL(2,C)-symmetric Lorentzian version in which all
tetrahedra are space-like. Recently, Livine and Oriti proposed to introduce a
causal structure into the Lorentzian Barrett--Crane model from which one can
construct a path integral that corresponds to the causal (Feynman) propagator.
We show how to obtain convergent integrals for the 10j-symbols and how a
dimensionless constant can be introduced into the model. We propose a `Wick
rotation' which turns the rapidly oscillating complex amplitudes of the Feynman
path integral into positive real and bounded weights. This construction does
not yet have the status of a theorem, but it can be used as an alternative
definition of the propagator and makes the causal model accessible by standard
numerical simulation algorithms. In addition, we identify the local symmetries
of the models and show how their four-simplex amplitudes can be re-expressed in
terms of the ordinary relativistic 10j-symbols. Finally, motivated by possible
numerical simulations, we express the matrix elements that are defined by the
model, in terms of the continuous connection variables and determine the most
general observable in the connection picture. Everything is done on a fixed
two-complex.Comment: 22 pages, LaTeX 2e, 1 figur
On the feasibility of radiation sterilization of planetary spacecraft Final report
Feasibility study for X-ray or gamma ray sterilization of spacecraft - radiation effect
Handbook of space environmental effects on solar cell power systems
Space environmental effects on solar cell power systems for earth satellite
Asymptotics of 10j symbols
The Riemannian 10j symbols are spin networks that assign an amplitude to each
4-simplex in the Barrett-Crane model of Riemannian quantum gravity. This
amplitude is a function of the areas of the 10 faces of the 4-simplex, and
Barrett and Williams have shown that one contribution to its asymptotics comes
from the Regge action for all non-degenerate 4-simplices with the specified
face areas. However, we show numerically that the dominant contribution comes
from degenerate 4-simplices. As a consequence, one can compute the asymptotics
of the Riemannian 10j symbols by evaluating a `degenerate spin network', where
the rotation group SO(4) is replaced by the Euclidean group of isometries of
R^3. We conjecture formulas for the asymptotics of a large class of Riemannian
and Lorentzian spin networks in terms of these degenerate spin networks, and
check these formulas in some special cases. Among other things, this conjecture
implies that the Lorentzian 10j symbols are asymptotic to 1/16 times the
Riemannian ones.Comment: 25 pages LaTeX with 8 encapsulated Postscript figures. v2 has various
clarifications and better page breaks. v3 is the final version, to appear in
Classical and Quantum Gravity, and has a few minor corrections and additional
reference
Optimal learning rules for discrete synapses
There is evidence that biological synapses have a limited number of discrete weight states. Memory storage with such synapses behaves quite differently from synapses with unbounded, continuous weights, as old memories are automatically overwritten by new memories. Consequently, there has been substantial discussion about how this affects learning and storage capacity. In this paper, we calculate the storage capacity of discrete, bounded synapses in terms of Shannon information. We use this to optimize the learning rules and investigate how the maximum information capacity depends on the number of synapses, the number of synaptic states, and the coding sparseness. Below a certain critical number of synapses per neuron (comparable to numbers found in biology), we find that storage is similar to unbounded, continuous synapses. Hence, discrete synapses do not necessarily have lower storage capacity
Finiteness and Dual Variables for Lorentzian Spin Foam Models
We describe here some new results concerning the Lorentzian Barrett-Crane
model, a well-known spin foam formulation of quantum gravity. Generalizing an
existing finiteness result, we provide a concise proof of finiteness of the
partition function associated to all non-degenerate triangulations of
4-manifolds and for a class of degenerate triangulations not previously shown.
This is accomplished by a suitable re-factoring and re-ordering of integration,
through which a large set of variables can be eliminated. The resulting
formulation can be interpreted as a ``dual variables'' model that uses
hyperboloid variables associated to spin foam edges in place of representation
variables associated to faces. We outline how this method may also be useful
for numerical computations, which have so far proven to be very challenging for
Lorentzian spin foam models.Comment: 15 pages, 1 figur
Area Regge Calculus and Discontinuous Metrics
Taking the triangle areas as independent variables in the theory of Regge
calculus can lead to ambiguities in the edge lengths, which can be interpreted
as discontinuities in the metric. We construct solutions to area Regge calculus
using a triangulated lattice and find that on a spacelike hypersurface no such
discontinuity can arise. On a null hypersurface however, we can have such a
situation and the resulting metric can be interpreted as a so-called refractive
wave.Comment: 18 pages, 1 figur
Graviton propagator from background-independent quantum gravity
We study the graviton propagator in euclidean loop quantum gravity, using the
spinfoam formalism. We use boundary-amplitude and group-field-theory
techniques, and compute one component of the propagator to first order, under a
number of approximations, obtaining the correct spacetime dependence. In the
large distance limit, the only term of the vertex amplitude that contributes is
the exponential of the Regge action: the other terms, that have raised doubts
on the physical viability of the model, are suppressed by the phase of the
vacuum state, which is determined by the extrinsic geometry of the boundary.Comment: 6 pages. Substantially revised second version. Improved boundary
state ansat
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