The turbulent flow of non-Newtonian fluids in the absence of anomalous wall effects

For Newtonian fluids, the engineering predictions for pressure drop in turbulent pipe flow are well established. However, in the case of non-Newtonian liquids, only a few design techniques have been proposed and these do not share a common basis with the approach for Newtonian systems. This present work attempts to provide a common basis for both Newtonian and non-Newtonian systems in situations where anomalous wall effects are absent. Previously published experimental data suggest that if the Reynolds number is calculated on the basis of the apparent viscosity at the wall then the standard Newtonian correlations can be used for the prediction of pressure drop. The use of the wall viscosity in defining the Reynolds number also serves as a test for anomalous behaviour. Any departure of the experimental data from the Newtonian turbulent friction factor correlation indicates anomalous behaviour.     

Combinatorial explosion in model gene networks

The explosive growth in knowledge of the genome of humans and other organisms leaves open the question of how the functioning of genes in interacting networks is coordinated for orderly activity. One approach to this problem is to study mathematical properties of abstract network models that capture the logical structures of gene networks. The principal issue is to understand how particular patterns of activity can result from particular network structures, and what types of behavior are possible. We study idealized models in which the logical structure of the network is explicitly represented by Boolean functions that can be represented by directed graphs on n-cubes, but which are continuous in time and described by differential equations, rather than being updated synchronously via a discrete clock. The equations are piecewise linear, which allows significant analysis and facilitates rapid integration along trajectories. We first give a combinatorial solution to the question of how many distinct logical structures exist for n-dimensional networks, showing that the number increases very rapidly with n. We then outline analytic methods that can be used to establish the existence, stability and periods of periodic orbits corresponding to particular cycles on the n-cube. We use these methods to confirm the existence of limit cycles discovered in a sample of a million randomly generated structures of networks of 4 genes. Even with only 4 genes, at least several hundred different patterns of stable periodic behavior are possible, many of them surprisingly complex. We discuss ways of further classifying these periodic behaviors, showing that small mutations (reversal of one or a few edges on the n-cube) need not destroy the stability of a limit cycle. Although these networks are very simple as models of gene networks, their mathematical transparency reveals relationships between structure and behavior, they suggest that the possibilities for orderly dynamics in such networks are extremely rich and they offer novel ways to think about how mutations can alter dynamics. (c) 2000 American Institute of Physics.     

Lead-free transducer for non-destructive evaluation

Lead-free piezoelectric ceramics with the formula 0.90(Bi_0.5Na_0.5)TiO₃ - 0.05(Bi_0.5K_0.5)TiO₃ - 0.015(Bi_0.5Li_0.5)TiO₃-0.05BaTiO₃ (abbreviated as BNKLBT-1.5) were prepared by a conventional mixed-oxide method. A disc of this material was fabricated and used to construct an ultrasonic transducer suitable for use in non-destructive evaluation (NDE). Using a laser vibrometer, it was observed that both BNKLBT and PZT exhibited a surface displacement pattern indicative of coupling of the radial mode vibration with the thickness mode vibration. This is consistent with the measurements of electrical impedance vs frequency which showed that for both discs a strong radial mode with many harmonics was clearly observed and many (usually undesired) modes existed near the thickness mode resonance frequency. The discs were mounted in stainless steel housings with appropriate electrical connections to form transducers. Tungsten/epoxy backing was incorporated to provide a very short ring-down time, a characteristic required for many NDE applications. The characteristics of the BNKLBT transducer were quite similar to that of a PZT transducer of similar structure, showing that this lead-free material has the potential to replace PZT in transducers for NDE applications. PACS 43.20.Tb; 43.20.Ye; 43.35.Zc; 43.35.Yb; 43.38.Ar; 43.35.Fx     

Non-fickian diffusion in thin polymer films

Diffusion of penetrants through polymers often does not follow the standard Fickian model. Such anomalous behavior can cause difficulty when designing polymer networks for specific uses. One type of non-Fickian behavior that results is so-called case II diffusion, where Fickian-like fronts initially move like √t with a transition to a non-Fickian concentration profile and front speed for moderate time. A mathematical model is presented that replicates this behavior in thin polymer films, and an analysis is performed that yields relevant dimensionless groups for study. An unusual result is derived: In certain parameter ranges, the concentration profile can change concavity, reflecting Fickian behavior for short times and non-Fickian behavior for moderate times. Asymptotic and numerical results are then obtained to characterize the dependence of such relevant quantities as failure time, front speed, and mass transport on these dimensionless groups. This information can aid in the design of effective polymer protectant films. © 1996 John Wiley & Sons, Inc.     

FT-Raman spectroscopic study of calcium-rich and magnesium-rich carbonate minerals

Calcium and magnesium carbonates are important minerals found in sedimentary environments. Although sandstones are the most common rock colonized by endolith organisms, the production of calcium and magnesium carbonates is important in survival strategies of organisms and as a source for the removal of oxalate ions. Extremophile organisms in some situations may convert or destroy carbonates of calcium and magnesium, which gives important information about the conditions under which these organisms can survive. The identification on the surface of Mars of 'White Rock' formations, in Juventae Chasma or Sabaea Terra, as possibly carbonate rocks makes the study of these minerals a prerequisite of remote Martian exploration. Here, we show the protocol for the identification by Raman spectroscopy of different calcium and magnesium carbonates and we present a database of relevance in the search for life, extinct or extant, on Mars; this will be useful for the assessment of data obtained from remote, miniaturized Raman spectrometers now proposed for Mars exploration.