On the Milne Problem and the Hydrodynamic Limit for a Steady Boltzmann Equation Model

For a stationary nonlinear Boltzmann equation in a slab with a particular truncation in the collision operator, the Milne problem for the boundary layer together with a weak type of hydrodynamic behavior in the interior of the slab are studied by nonperturbative methods in the small-mean-free-path limit.     

Boundary Conditions for Scalar Conservation Laws from a Kinetic Point of View

Boundary conditions for multidimensional scalar conservation laws are obtained in the context of hydrodynamic limits from a kinetic point of view. The initial boundary value kinetic problem is well posed since inward and outward characteristics of the domain can be distinguished. The convergence of the first momentum of the distribution function to an entropy solution of the conservation law is established. Boundary conditions are obtained. The equivalence with the Bardos, Leroux, and Nedelec conditions is studied.     

Stability for Rayleigh–Benard Convective Solutions of the Boltzmann Equation

We consider the Boltzmann equation for a gas in a horizontal slab, subject to a gravitational force. The boundary conditions are of diffusive type, specifying the wall temperatures, so that the top temperature is lower than the bottom one (Benard setup). We consider a 2-dimensional convective stationary solution, which for small Knudsen numbers is close to the convective stationary solution of the Oberbeck–Boussinesq equations, near and above the bifurcation point, and prove its stability under 2-d small perturbations, for Rayleigh numbers above and close to the bifurcation point and for small Knudsen numbers.     

Experimental and Numerical Study of the Static Performance of a Hoop-Wrapped CNG Composite Cylinder Considering Its Variable Wall Thickness and Polymer Liner

Mechanics of Composite Materials - The static performance of a composite type 4 CNG cylinder was investigated using a finite-element simulation and experimental validation. This cylinder involved a...     

Hydroelastic Effects of the Camber Ratio on A Ducted Marine Propeller in A Wake Flow

The effects of the camber ratio on the hydrodynamic and structural behaviors of a NACA-based ducted marine propeller in the wake flow behind an underwater axisymmetric body are numerically studied by computational fluid dynamics methods, in particular, the finite element method. The results are presented in terms of the efficiency, deflection, pressure coefficient, and natural frequencies. It is shown that the wake flow strongly affects the performance of the selected propulsion system. It is shown that the distributions of the camber ratio over the blades of the propeller nonlinearly changes its resistance against cavitation occurrence and deflection, and also changes its hydrodynamic performance and vibrational behavior.     

A Cauchy inequality for the Boltzmann equation

The distance to a set of Maxwellians is determined for a family of functions with bounded mass, energy and a small entropy production term. Functions with small masses are close to the null Maxwellian. Functions with masses bounded from below by a constant are approached by functions proportional to the gain term of the Boltzmann operator, taking advantage of its regularity. For these regularizations, the integrands of the entropy production term are small everywhere. Hence classical arguments can be used to obtain the closedness to the set of Maxwellians. Copyright © 2000 John Wiley & Sons, Ltd.     

An Unexpected Role of Carbon Disulfide: A New and Efficient Method for the Synthesis of 2‐Substituted Benzimidazoles

A new and efficient methodology for the synthesis of 2‐substituted benzimidazoles is described. In this procedure, CS₂ unexpectedly facilitated the cyclization reaction between benzene‐1,2‐diamine and benzenecarbaldehydes in CH₂Cl₂ at room temperature. The reactions occur under mild conditions require simpler equipment and easier workup procedures.     

The application of a strain gauge technique to the measurement of the power characteristics of five impellers

The work described in this paper establishes the accuracy with which the power number can be measured within a mixing vessel and presents measurements for five impellers (Rushton, bucket, 45°-pitched blade, 60°-pitched blade and hyperboloid) as a function of rotational speed. The technique uses strain gauges and the telemetric transmission of the strain and is, therefore, more accurate than methods which involve mechanical determination of torque and that allows power measurements to be carried out in relatively small and more cost-effective models of mixing vessels. In the cases where previous data exists the results of this study compare well. This work provides new data for the bucket, 45°-pitched blade and hyperboloid (low Reynolds numbers) impellers and represented a systematic study for all five impellers with one measurement system.The authors would like to acknowledge the financial support of the EPSRC during the course of this work.