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 $\theta^{\alpha\beta}$, is investigated. A large family of solutions, up to order one in $\theta^{\alpha\beta}$, 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 $\theta^{\alpha\beta}$.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 $R$ 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