Universal power law tails of time correlation functions

The universal power law tails of single particle and multi-particle time correlation functions are derived from a unifying point of view, solely using the hydrodynamic modes of the system. The theory applies to general correlation functions, and to systems more general than classical fluids. Moreover it is argued that the collisional transfer part of the stress-stress correlation function in dense classical fluids has the same long time tail $\sim t^{-1-d/2}$ as the velocity autocorrelation function in Lorentz gases.Comment: 10 pages, 0 figures, Revised version: old Eqs(7)-(8) are replaced by new Eqs (7)-(10), based on renormalization of the fluctuating heat conduction equation for systems with quenched disorder. The new power law tail vanishes on a periodic lattice, as it shoul

Theories of Fairness and Reciprocity

Most economic models are based on the self-interest hypothesis that assumes that all people are exclusively motivated by their material self-interest. In recent years experimental economists have gathered overwhelming evidence that systematically refutes the self-interest hypothesis and suggests that many people are strongly motivated by concerns for fairness and reciprocity. Moreover, several theoretical papers have been written showing that the observed phenomena can be explained in a rigorous and tractable manner. These theories in turn induced a new wave of experimental research offering additional exciting insights into the nature of preferences and into the relative performance of competing theories of fairness. The purpose of this paper is to review these recent developments, to point out open questions, and to suggest avenues for future research

Extension of Haff's cooling law in granular flows

The total energy E(t) in a fluid of inelastic particles is dissipated through inelastic collisions. When such systems are prepared in a homogeneous initial state and evolve undriven, E(t) decays initially as t^{-2} \aprox exp[ - 2\epsilon \tau] (known as Haff's law), where \tau is the average number of collisions suffered by a particle within time t, and \epsilon=1-\alpha^2 measures the degree of inelasticity, with \alpha the coefficient of normal restitution. This decay law is extended for large times to E(t) \aprox \tau^{-d/2} in d-dimensions, far into the nonlinear clustering regime. The theoretical predictions are quantitatively confirmed by computer simulations, and holds for small to moderate inelasticities with 0.6< \alpha< 1.Comment: 7 pages, 4 PostScript figures. To be published in Europhysics Letter

On Inequity Aversion - A Reply to Binmore and Shaked

In this paper we reply to Binmore and Shaked’s criticism of the Fehr-Schmidt model of inequity aversion. We put the theory and their arguments into perspective and show that their criticism is not substantiated. Finally, we briefly comment on the main challenges for future research on social preferences

Scaling Solutions of Inelastic Boltzmann Equations with Over-populated High Energy Tails

This paper deals with solutions of the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell models for large times and for large velocities, and the nonuniform convergence to these limits. We demonstrate how the velocity distribution approaches in the scaling limit to a similarity solution with a power law tail for general classes of initial conditions and derive a transcendental equation from which the exponents in the tails can be calculated. Moreover on the basis of the available analytic and numerical results for inelastic hard spheres and inelastic Maxwell models we formulate a conjecture on the approach of the velocity distribution function to a scaling form.Comment: 15 pages, 4 figures. Accepted in J. Statistical Physic

Asymptotic solutions of the nonlinear Boltzmann equation for dissipative systems

Analytic solutions $F(v,t)$ of the nonlinear Boltzmann equation in $d$-dimensions are studied for a new class of dissipative models, called inelastic repulsive scatterers, interacting through pseudo-power law repulsions, characterized by a strength parameter $\nu$, and embedding inelastic hard spheres ($\nu=1$) and inelastic Maxwell models ($\nu=0$). The systems are either freely cooling without energy input or driven by thermostats, e.g. white noise, and approach stable nonequilibrium steady states, or marginally stable homogeneous cooling states, where the data, $v^d_0(t) F(v,t)$ plotted versus $c=v/v_0(t)$, collapse on a scaling or similarity solution $f(c)$, where $v_0(t)$ is the r.m.s. velocity. The dissipative interactions generate overpopulated high energy tails, described generically by stretched Gaussians, $f(c) \sim \exp[-\beta c^b]$ with $0 < b < 2$, where $b=\nu$ with $\nu>0$ in free cooling, and $b=1+{1/2} \nu$ with $\nu \geq 0$ when driven by white noise. Power law tails, $f(c) \sim 1/c^{a+d}$, are only found in marginal cases, where the exponent $a$ is the root of a transcendental equation. The stability threshold depend on the type of thermostat, and is for the case of free cooling located at $\nu=0$. Moreover we analyze an inelastic BGK-type kinetic equation with an energy dependent collision frequency coupled to a thermostat, that captures all qualitative properties of the velocity distribution function in Maxwell models, as predicted by the full nonlinear Boltzmann equation, but fails for harder interactions with $\nu>0$.Comment: Submitted to: "Granular Gas Dynamics", T. Poeschel, N. Brilliantov (eds.), Lecture Notes in Physics, Vol. LNP 624, Springer-Verlag, Berlin-Heidelberg-New York, 200

Adding a Stick to the Carrot? The Interaction of Bonuses and Fines

In this paper we report on a principal-agent experiment where the principal can choose whether to rely on an unenforcable bonus contract or to combine the bonus contract with a fine if the agent’s effort falls below a minimum standard. We show that most principals do not use the fine and that the pure bonus contract is more efficient than the combined contract. Our experiment suggests that principals who are less fair are more likely to choose a combined contract and less likely to actually pay the announced bonus. This offers a new explanation for why explicit and implicit incentives are substitutes rather than complements