Elastic instabilities in cone- and -plate flow: Small gap theory

Consider the axisymmetric, inertialess cone- and -plate flow of a viscoelastic fluid. A perturbation method is used to obtain more tractable equations that describe the flow when the gap angle is small. A linear stability analysis of the base viscometric flow shows that there is a loss of stability when an elasticity parameter =DeWe, increases past a critical value. This purely elastic instability is of the oscillatory type. We obtain expressions for the critical elasticity number, frequency and wave number. The critical Deborah number varies as , the wave length as . and the wave speed as , where . is the gap angle. The most unstable mode exhibits infinitely many logarithmically-spaced roll cells which propagate inward towards the apex of the cone. These results are in agreement with experimental and numerical results.     

Convexity preserving interpolation by algebraic curves and surfaces

The problem of interpolation by a convex curve to the vertices of a convex polygon is considered. A natural 1-parameter family ofC algebraic curves solving this problem is presented. This is extended to a solution, of a general Hermite-type problem, in, which the curve also interpolates to one or two prescribedtangents at any desired vertices of the polygon. The construction of these curves is a generalization of well known methods for generatingconic sections. Several properties of this family of algebraic curves are discussed. In addition, the method is generalized to convexC interpolation of strictly convex data sets inR ³ by algebraicsurfaces.     

Dysrhythmias of the respiratory oscillator

Breathing is regulated by a central neural oscillator that produces rhythmic output to the respiratory muscles. Pathological disturbances in rhythm (dysrhythmias) are observed in the breathing pattern of children and adults with neurological and cardiopulmonary diseases. The mechanisms responsible for genesis of respiratory dysrhythmias are poorly understood. The present studies take a novel approach to this problem. The basic postulate is that the rhythm of the respiratory oscillator can be altered by a variety of stimuli. When the oscillator recovers its rhythm after such perturbations, its phase may be reset relative to the original rhythm. The amount of phase resetting is dependent upon stimulus parameters and the level of respiratory drive. The long-range hypothesis is that respiratory dysrhythmias can be induced by stimuli that impinge upon or arise within the respiratory oscillator with certain combinations of strength and timing relative to the respiratory cycle. Animal studies were performed in anesthetized or decerebrate preparations. Neural respiratory rhythmicity is represented by phrenic nerve activity, allowing use of open-loop experimental conditions which avoid negative chemical feedback associated with changes in ventilation.In animal experiments, respiratory dysrhythmias can be induced by stimuli having specific combinations of strength and timing. Newborn animals readily exhibit spontaneous dysrhythmias which become more prominent at lower respiratory drives. In human subjects, swallowing was studied as a physiological perturbation of respiratory rhythm, causing a pattern of phase resetting that is characterized topologically as type 0. Computational studies of the Bonhoeffer-van der Pol (BvP) equations, whose qualitative behavior is representative of many excitable systems, supports a unified interpretation of these experimental findings. Rhythmicity is observed when the BvP model exhibits recurrent periods of excitation alternating with refractory periods. The same system can be perturbed to a state in which amplitude of oscillation is attenuated or abolished. We have characterized critical perturbations which induce transitions between these two states, giving rise to patterns of dysrhythmic activity that are similar to those seen in the experiments. We illustrate the importance of noise in initiation and termination of rhythm, comparable to normal respiratory rhythm intermixed with spontaneous dysrhythmias. In the BvP system the incidence and duration of dysrhythmia is shown to be strongly influenced by the level of noise. These studies should lead to greater understanding of rhythmicity and integrative responses of the respiratory control system, and provide insight into disturbances in control mechanisms that cause apnea and aspiration in clinical disease states. (c) 1995 American Institute of Physics.     

Multiple time scale analysis of two models for the peroxidase-oxidase reaction

A multiple time scale analysis of two four-variable models of the peroxidase-oxidase reaction, the DOP, and the Olsen model, is carried out. It is shown that autonomous limit cycle oscillations are exhibited by the fast subsets of these two models, but only in certain regions of parameter space, confirming the prior suggestion that the slow variable (NADH) is not essential for oscillatory behavior. However, it is found that the slow variable is essential for oscillatory behavior over other ranges of parameter values, and is always essential for complex oscillatory and chaotic behavior. This latter conclusion is based on a study involving driving the fast subset with a sinusoidally varying (NADH). This study suggests the level of coupling between fast and slow variables of an autonomous system necessary to cause the chaos observed in the DOP model. Further study of the driven system allows for the identification of a natural period of the nonoscillatory but bistable fast subsystem and a set of rules for applying a parametric driving in such a way as to generate a more complete Farey sequence from a truncated Farey sequence. These conclusions are used to compare the very similar DOP and Olsen models, which, nevertheless, exhibit quite different Farey sequences and routes to chaos. (c) 1995 American Institute of Physics.     

Error estimates in the determination of rigid body displacements in protein crystals

We report the estimation of random errors in the refinement of the rigid body displacements of the -helices of the enzyme 6-phosphogluconate dehydrogenase. Least-squares refinement of the TLS parameters of the helices has been carried out using X-ray reflection data of 2.1 Å resolution, resulting in anR-factor of 19.5%. Standard deviations were estimated from the normal matrix. The results show that the translational mean-square displacements of nearly all the helices are significant at this resolution. However the libration parameters are only significant when the helices have at least four turns. Screw-rotation tensor values cannot be determined at this resolution.     

OR Utilization in Nigeria: A Sample Survey

The study presents the results of a mail survey on the utilization of Operational Research (OR) techniques in tackling complex operational problems in the private sector in Nigeria. The survey was mailed to OR practitioners in nearly 1000 companies and was aimed at determining the familiarity with, and usage of, OR techniques, background of OR personnel, degree of computer usage, application areas, implementation and contributions of OR, problems attendant in using OR techniques, and future prospects for OR usage.     

Minimax risk overl p -balls forl p -error

Summary Consider estimating the mean vector from dataN _n (, ² I) withl _q norm loss,q1, when is known to lie in ann-dimensionall _p ball,p(0, ). For largen, the ratio of minimaxlinear risk to minimax risk can bearbitrarily large ifp. Obvious exceptions aside, the limiting ratio equals 1 only ifp=q=2. Our arguments are mostly indirect, involving a reduction to a univariate Bayes minimax problem. Whenp, simple non-linear co-ordinatewise threshold rules are asymptotically minimax at small signal-to-noise ratios, and within a bounded factor of asymptotic minimaxity in general. We also give asymptotic evaluations of the minimax linear risk. Our results are basic to a theory of estimation in Besov spaces using wavelet bases (to appear elsewhere).     

The invertibility of the product of unbounded Toeplitz operators

In this note I give necessary and sufficient conditions on outer functionsf andg for the operator to be bounded and invertible on H². I also discuss the relationship of this question to two open questions in operator theory and weighted norm inequalities.     

Moment closure hierarchies for kinetic theories

This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the Euler system, which is based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions. The closure proceeds in two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit. The second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct Navier-Stokes behavior. This is achieved through the introduction of a generalization of the BGK collision operator. The simplest such system in three spatial dimensions is a 14-moment closure, which also recovers the behavior of the Grad 13-moment system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.     

Positivity of entropy production in nonequilibrium statistical mechanics

We analyze different mechanisms of entropy production in statistical mechanics, and propose formulas for the entropy production ratee() in a state . When is steady state describing the long term behavior of a system we show thate()0, and sometimes we can provee()>0.