A physically based correlation for the effects of power law rheology and inclination on slug bubble rise velocity

A study has been made of the motion of long bubbles in inclined pipes containing viscous Newtonian and non-Newtonian liquids. A semi-theoretical expression for the rise velocity of air bubbles in water is derived on the hypothesis that the dominant factor is the momentum exchange of the bubble underflow, i.e. the bubble nose shape. The correlation calls on empirical inputs from established literature on bubble rise speeds at high Reynolds number. The effects of increasing Newtonian viscosity are analysed with reference to the momentum exchange and it is shown how viscosity reduces the inclination dependence of the bubble Froude number. Results from an experimental survey in seven different non-Newtonian liquids in three different diameter pipes are presented. These data are correlated so as to decouple the effects of surface tension and viscosity. An empirical relation is proposed for the effective shear rate in the fluid travelling around the bubble nose. Our correlation is compared to literature data from a broad range of Reynolds numbers with excellent agreement except at shallow angles.     

Taylor-Galerkin algorithms for viscoelastic flow: Application to a model problem

Coupled and decoupled Taylor-Galerkin algorithms are considered for viscoelastic flow and a model problem—transient startup Poiseuille flow in a channel under a fixed pressure gradient. All algorithms reproduce the steady-state solutions and are stable at high elasticity numbers (E). For a fixed mesh, the coupled and decoupled versions (TGC and TGD) give exceptional time-accuracy at low elasticity numbers [to within O(1%) at E = 1] and reasonable accuracy at high elasticity numbers [to within O(10%) at E = 10, 100]. By definition, the decoupled false-transient scheme (TGF), which uses different time scales for velocity and stress time stepping, provides a poor transient history. Where the main requirement is to compute a steady-state algorithm efficiency is crucial. The TGF scheme attains a steady state between six to eight times faster than does the TGC scheme, and the latter is over twice as fast as the TGD form. © 1994 John Wiley & Sons, Inc.     

PROBING PHOTODYNAMIC DAMAGE IN NUCLEIC ACIDS WITH A DAMAGE-SPECIFIC DNA BINDING PROTEIN: A COMPARISON OF THE B and Z DNA CONFORMATIONS

—We have employed a damage-specific DNA binding protein from human cells as a probe for base damage in polymers irradiated with white light in the presence of methylene blue. Protein-recognizable damage is introduced only into guanine-containing polymers and quenching of damage introduction by H₂O and sodium azide suggest the involvement of a singlet oxygen mechanism. Using poly d(G-m⁵C), we have demonstrated that the left-handed double helical Z conformation is much less susceptible to guanine photooxidation than is the usual B conformation. We speculate that this difference in reactivity may reflect steric hindrance at the purine C-4 position and could provide some insight into the initial steps of the reaction between singlet oxygen and guanine in nucleic acid polymers.     

Hierarchical clustering to measure connectivity in fMRI resting-state data

Low frequency oscillations, which are temporally correlated in functionally related brain regions, characterize the mammalian brain, even when no explicit cognitive tasks are performed. Functional connectivity MR imaging is used to map regions of the resting brain showing synchronous, regional and slow fluctuations in cerebral blood flow and oxygenation. In this study, we use a hierarchical clustering method to detect similarities of low-frequency fluctuations. We describe one measure of correlations in the low frequency range for classification of resting-state fMRI data. Furthermore, we investigate the contribution of motion and hardware instabilities to resting-state correlations and provide a method to reduce artifacts. For all cortical regions studied and clusters obtained, we quantify the degree of contamination of functional connectivity maps by the respiratory and cardiac cycle. Results indicate that patterns of functional connectivity can be obtained with hierarchical clustering that resemble known neuronal connections. The corresponding voxel time series do not show significant correlations in the respiratory or cardiac frequency band.     

Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Thermoresponsive copolymers of methacrylic acid and poly(ethylene glycol) methyl ether methacrylate

Copolymers of methacrylic acid (MAA) and poly(ethylene glycol) methyl ether methacrylate (PEGMA) were prepared and their cloud points in aqueous solution were studied as a function of comonomer ratio, solution pH, and presence of hydrophobic comonomers. Under acidic conditions, the cloud point falls below 0 °C for copolymers with between 25% to 60% ether content, because of the formation of hydrophobic H‐bonded ether–acid complexes. The cloud point also decreases with solution pH. For equivalent ether to acid ratios, the cloud point decreases with decreasing PEG chain length, because of the presence of a larger number of hydrophobic methyl and methacrylate groups. Similarly, the cloud point decreases upon incorporation of hydrophobic comonomers such as butyl, lauryl, or glycidyl methacrylates. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6095–6104, 2005     

Slow visco-elastic flow past a cylinder in a rectangular channel

This paper is concerned with the flow of a visco-elastic liquid through a rectangular channel containing a cylindrical obstruction placed either in a symmetric or asymmetric position with respect to the centre of the channel. Numerical predictions of the flow are obtained using a well established finite element Galerkin mixed formulation. The influence of elasticity on the streamline pattern is found to be negligible, and one only observes changes due to different geometries, i.e. relative positions of cylinder and channel. However, both elasticity and a variable viscosity are found to have significant effects on the forces exerted on the cylinder.     

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (相似文献