The mixing behavior of the gas-liquid phase in three loop bioreactors was investigated. A gas-induced External Airlift Loop Bioreactor (EALB), a forced-liquid Vertical Tubular Loop Bioreactor (VTLB) and a forced-liquid Horizontal Tubular Loop Bioreactor (HTLB) were used for mixing studies as well as biomass production from natural gas. The effect of design parameters, riser to downcomer cro...

We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the wellknown notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of chain transitive maps. These notions of recurrence are defined using ε-chains, and the minimal lengths of these ε-chains give a way to measure recurrence time (...

Over the past 10 years, geodynamo simulations have grown rapidly in sophistication. However, it is still necessary to make certain approximations in order to maintain numerical stability. In addition, models are forced to make assumptions about poorly known parameters for the Earth’s core. Different magnetic Prandtl numbers have been used and different assumptions about the presence of radiogen...

We establish the eventual regularity of suitably defined weak solutions to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. The existence of a global attractor of the Boussinesq system at large Prandtl number is also presented.

Using direct simulations of hydromagnetic turbulence driven by random polarized waves it is shown that dynamo action is possible over a wide range of magnetic Prandtl numbers from 10−3 to 1. Triply periodic boundary conditions are being used. In the final saturated state the resulting magnetic field has a large-scale component of Beltrami type. For the kinematic phase, growth rates have been de...

In a large class of supersymmetric SO(10) and left-right models, requiring that the effective theory below the scale of SU(2)R breaking be the MSSM implies partial Yukawa unification with Yu = Yd and Ye = YνD . The same result also emerges in models with a horizontal SU(3)H symmetry. As a result, at the tree level, these models lead to vanishing quark mixing angles. We show that the correct mix...