58,529 research outputs found
Study of a model for the distribution of wealth
An equation for the evolution of the distribution of wealth in a population
of economic agents making binary transactions with a constant total amount of
"money" has recently been proposed by one of us (RLR). This equation takes the
form of an iterated nonlinear map of the distribution of wealth. The
equilibrium distribution is known and takes a rather simple form. If this
distribution is such that, at some time, the higher momenta of the distribution
exist, one can find exactly their law of evolution. A seemingly simple
extension of the laws of exchange yields also explicit iteration formulae for
the higher momenta, but with a major difference with the original iteration
because high order momenta grow indefinitely. This provides a quantitative
model where the spreading of wealth, namely the difference between the rich and
the poor, tends to increase with time.Comment: 12 pages, 2 figure
Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media
We introduce a family of hybrid discretisations for the numerical
approximation of optimal control problems governed by the equations of
immiscible displacement in porous media. The proposed schemes are based on
mixed and discontinuous finite volume element methods in combination with the
optimise-then-discretise approach for the approximation of the optimal control
problem, leading to nonsymmetric algebraic systems, and employing minimum
regularity requirements. Estimates for the error (between a local reference
solution of the infinite dimensional optimal control problem and its hybrid
approximation) measured in suitable norms are derived, showing optimal orders
of convergence
Noncommutative Einstein-Maxwell pp-waves
The field equations coupling a Seiberg-Witten electromagnetic field to
noncommutative gravity, as described by a formal power series in the
noncommutativity parameters , is investigated. A large
family of solutions, up to order one in , describing
Einstein-Maxwell null pp-waves is obtained. The order-one contributions can be
viewed as providing noncommutative corrections to pp-waves. In our solutions,
noncommutativity enters the spacetime metric through a conformal factor and is
responsible for dilating/contracting the separation between points in the same
null surface. The noncommutative corrections to the electromagnetic waves,
while preserving the wave null character, include constant polarization, higher
harmonic generation and inhomogeneous susceptibility. As compared to pure
noncommutative gravity, the novelty is that nonzero corrections to the metric
already occur at order one in .Comment: 19 revtex pages. One refrence suppressed, two references added. Minor
wording changes in the abstract, introduction and conclusio
Free Fermionic Elliptic Reflection Matrices and Quantum Group Invariance
Elliptic diagonal solutions for the reflection matrices associated to the
elliptic matrix of the eight vertex free fermion model are presented. They
lead through the second derivative of the open chain transfer matrix to an XY
hamiltonian in a magnetic field which is invariant under a quantum deformed
Clifford--Hopf algebra.Comment: 9 pages, Late
Efficient reconstruction of CMSSM parameters from LHC data - A case study
We present an efficient method of reconstructing the parameters of the
Constrained MSSM from assumed future LHC data, applied both on their own right
and in combination with the cosmological determination of the relic dark matter
abundance. Focusing on the ATLAS SU3 benchmark point, we demonstrate that our
simple Gaussian approximation can recover the values of its parameters
remarkably well. We examine two popular non-informative priors and obtain very
similar results, although when we use an informative, naturalness-motivated
prior, we find some sizeable differences. We show that a further strong
improvement in reconstructing the SU3 parameters can by achieved by applying
additional information about the relic abundance at the level of WMAP accuracy,
although the expected data from Planck will have only a very limited additional
impact. Further external data may be required to break some remaining
degeneracies. We argue that the method presented here is applicable to a wide
class of low-energy effective supersymmetric models, as it does not require to
deal with purely experimental issues, eg, detector performance, and has the
additional advantages of computational efficiency. Furthermore, our approach
allows one to distinguish the effect of the model's internal structure and of
the external data on the final parameters constraints.Comment: 23 pages, 10 figures - moderate revision: includes naturalness prior.
Matches published versio
Constraints on a mixed inflaton and curvaton scenario for the generation of the curvature perturbation
We consider a supersymmetric grand unified model which naturally solves the
strong CP and mu problems via a Peccei-Quinn symmetry and leads to the standard
realization of hybrid inflation. We show that the Peccei-Quinn field of this
model can act as curvaton. In contrast to the standard curvaton hypothesis,
both the inflaton and the curvaton contribute to the total curvature
perturbation. The model predicts an isocurvature perturbation too which has
mixed correlation with the adiabatic one. The cold dark matter of the universe
is mostly constituted by axions plus a small amount of lightest sparticles. The
predictions of the model are confronted with the Wilkinson microwave anisotropy
probe and other cosmic microwave background radiation data. We analyze two
representative choices of parameters and derive bounds on the curvaton
contribution to the adiabatic perturbation. We find that, for the choice which
provides the best fitting of the data, the curvaton contribution to the
adiabatic amplitude must be smaller than about 67% (at 95% confidence level).
The best-fit power spectra are dominated by the adiabatic part of the inflaton
contribution. We use Bayesian model comparison to show that this choice of
parameters is disfavored with respect to the pure inflaton scale-invariant case
with odds of 50 to 1. For the second choice of parameters, the adiabatic mode
is dominated by the curvaton, but this choice is strongly disfavored relative
to the pure inflaton scale-invariant case (with odds of 10^7 to 1). We conclude
that in the present framework the perturbations must be dominated by the
adiabatic component from the inflaton.Comment: 27 pages including 16 figures, uses Revte
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