The effects of flow split ratio and flow rate in manifolds

This paper reports a combined experimental and numerical investigation of three-dimensional steady turbulent flows in inlet manifolds of square cross-section. Predictions and measurements of the flows were carried out using computational fluid dynamics and laser Doppler anemometry techniques respectively. The flow structure was characterized in detail and the effects of flow split ratio and inlet flow rate were studied. These were found to cause significant variations in the size and shape of recirculation regions in the branches, and in the turbulence levels. It was then found that there is a significant difference between the flow rates through different branches. The performance of the code was assessed through a comparison between predictions and measurements. The comparison demonstrates that all important features of the flow are well represented by the predictions.     

Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.The work of this author was supported by the National Science Foundation under grants CCR-8802408 and CCR-9101640.The work of this author was supported in part during a visit to Argonne National Laboratory by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under contract W-31-109-Eng-38, and in part during a visit to the Courant Institute by the U.S. Department of Energy under Contract DEFG0288ER25053.     

High-accuracy measurer of complex reflection coefficient of SHF transmission lines

We describe a new method of constructing a device for simultaneous measurement of the relative amplitude and phase difference of microwave signals, using complex phase manipulation of input signals. It is shown that systematic errors of measurement are significantly lower in the proposed amplitude and phase meter. Root-mean-square values are obtained for a system with nonideal elements. A block diagram of the device is presented and its principal characteristics are described. Institute of Radiophysics and Electronics, Armenian Academy of Sciences, Erevan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 9, pp. 1182–1188, September, 1997.     

Static dust sphere in Einstein-Cartan theory

Physically meaningful solutions of the field equations for static spherical dust distributions in the Einstein-Cartan theory have been obtained. There is one in which the spin is zero at the center and another with zero spin at the boundary of the sphere.     

Fast switching anisotropic networks obtained by in situ photopolymerization of liquid crystal molecules

Lightly cross-linked anisotropic networks with uniaxial and π/2 twisted orientations were produced by photopolymerization of monotropic mixtures containing liquid crystal mono and diacrylates. In this way the polymer backbone was immobilized and became decoupled from the motion of the mesogenic side groups. The networks showed very good reversibility and even after becoming isotropic, upon cooling, the initial orientation was recovered. In the same way, in the presence of electric fields the mesogenic groups could be reoriented in the direction of the electric field, reverting back to the initial orientation on removal of the field at a rate comparable with those observed in the monomeric state. Combining viscoelastic measurements with the dielectric behaviour of the monomeric liquid crystal and the anisotropic network, a comparison between the internal and bulk rotational viscosities was also made.     

On the linear relaxation of a one-dimensional bonded fluid model

The linear relaxation of a one-dimensional bonded fluid model is studied in the dynamical mean field approximation at the pair level. The results are compared with simulation data. Relaxation at low temperatures shows a cooperative character that can be understood in terms of a simple diffusion picture.     

Optimal detection of discontinuous changes of signal parameters in discrete time

The problem of optimal detection (discrimination) of signals with random discontinuous parameter changes in discrete time is examined. A recursion algorithm for calculation of the likelihood ratio in real time is obtained. As an example, the problem of optimal detection of a rectangular pulse signal with a random time of appearance, duration, and amplitude is solved. Computer simulation results are presented.