Analysis of Turbulent Free Convection in a Rectangular Rayleigh-Benard Cell

The present study compares results of direct numerical simulations of thermal convection within a rectangular geometry with Rayleigh-Benard convection in thin fluid layers and cylindrical geometries. It is shown that boundary layer thicknesses show similar tendencies in the rectangular geometry and a thin fluid layer, but the quasi two-dimensional geometry of the container delays the onset of convection significantly. Analysis of the thermal dissipation rates indicates that there are three distinct regimes, of the small scale contribution grows rap-idly as Rayleigh number is increasing, whereas the large scale contribution remains almost constant

Bidding for envy-freeness: A procedural approach to n-player fair-division problems

We develop a procedure for implementing an efficient and envy-free allocation of m objects among n individuals with the possibility of monetary side-payments. The procedure eliminates envy by compensating envious players. It is fully descriptive and says explicitly which compensations should be made, and in what order. Moreover, it is simple enough to be carried out without computer support. We formally characterize the properties of the procedure, show how it establishes envy-freeness with minimal resources, and demonstrate its application to a wide class of fair-division problems.fair-division procedures, envy-freeness

Jamming of Frictional Particles: a Non-equilibrium First Order Phase Transition

We propose a phase diagram for the shear flow of dry granular particles in two dimensions based on simulations and a phenomenological Landau-theory for a nonequilibrium first order phase transition. Our approach incorporates both frictional as well as frictionless particles. The most important feature of the frictional phase diagram is re-entrant flow and a critical jamming point at finite stress. In the frictionless limit the regime of re-entrance vanishes and the jamming transition is continuous with a critical point at zero stress. The jamming phase diagrams derived from the model agree with the experiments of Bi et al. (Nature (2011)) and brings together previously conflicting numerical results