Velocity measurements in liquid sodium by means of ultrasound Doppler velocimetry

A successful application of ultrasound Doppler velocimetry in liquid sodium flows is described. To obtain sufficient Doppler signals, different problems had to be solved: the transmission of the ultrasonic beam through the channel wall made of stainless steel, the acoustic coupling between the transducer and the channel wall, and the wetting of the inner surface of the wall by the liquid metal, respectively. A sodium flow in a square duct exposed to a transverse magnetic field is investigated. In accordance with the existing knowledge about MHD channel flows, we found that the velocity profiles modified to a M-shape owing to the effect of an inhomogeneous magnetic field. Received: 12 June 2001/Accepted: 27 October 2001     

Parametric resonance in the problem of a heavy rigid body rolling along a straight line on a plane

The problem of the stability of a heavy rigid body, bounded by the surface of an ellipsoid and with a cavity in the form of a coaxial ellipsoid, rolling along a straight line on a horizontal rough plane is investigated. It is shown that in the case of a body that is close to being dynamically symmetrical, parametric resonance always occurs leading to instability of the rolling. Each ellipsoid has its own “individual” resonance angular velocity. In the general case, regions in which the necessary stability conditions are satisfied can be distinguished in parameter space. The problem of calculating the resonance coefficient corresponding to instability for parametric resonance in a reversible third-order system is solved.     

Necessary Conditions for Differentiability of Distance Functions

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained.     

On iteration semigroups of mean-type mappings and invariant means

Summary. Iteration semigroups of weighted quasi-arithmetic mean-type mappings are considered. Existence and uniqueness of a mean which is invariant with respect to a continuous semigroup of mean-type mapping is proved.     

Rigidity and finiteness under Ricci curvature and volume controls

Consider the class of closed Riemannian manifolds M of dimension dim(M) \geqq 3 \dim(M) \geqq 3 , Ricci curvature Ric(M) \geqq -(n - 1) \textrm{Ric}(M) \geqq -(n - 1) , diameter diam(M) < D and almost maximal volume. We show that the isomorphism types of fundamental groups characterize the diffeomorphism types of manifolds in such a class. In particular, it can be viewed as a generalization of the well-known Mostow‘s rigidity theorem and a finiteness theorem.     

AGE method simulations of a turbulent far‐wake compared to spectral DNS

Turbulent flow simulation methods based on finite differences are attractive for their simplicity, flexibility and efficiency, but not always for accuracy or stability. This paper demonstrates that a good compromise is possible with the advected grid explicit (AGE) method. Starting from the same initial field as a previous spectral DNS, AGE method simulations of a planar turbulent wake were carried out as DNS, and then at three levels of reduced resolution. The latter cases were in a sense large‐eddy simulations (LES), although no specific sub‐grid‐scale model was used. Results for the two DNS methods, including variances and power spectra, were very similar, but the AGE simulation required much less computational effort. Small‐scale information was lost in the reduced resolution runs, but large‐scale mean and instantaneous properties were reproduced quite well, with further large reductions in computational effort. Quality of results becomes more sensitive to the value chosen for one of the AGE method parameters as resolution is reduced, from which it is inferred that the numerical stability procedure controlled by the parameter is acting in part as a sub‐grid‐scale model. Copyright © 2002 John Wiley & Sons, Ltd.