On the relation between viscoelastic and magnetohydrodynamic flows and their instabilities

We demonstrate a close analogy between a viscoelastic medium and an electrically conducting fluid containing a magnetic field. Specifically, the dynamics of the Oldroyd-B fluid in the limit of large Deborah number corresponds to that of a magnetohydrodynamic (MHD) fluid in the limit of large magnetic Reynolds number. As a definite example of this analogy, we compare the stability properties of differentially rotating viscoelastic and MHD flows. We show that there is an instability of the Oldroyd-B fluid that is physically distinct from both the inertial and elastic instabilities described previously in the literature, but is directly equivalent to the magnetorotational instability in MHD. It occurs even when the specific angular momentum increases outwards, provided that the angular velocity decreases outwards; it derives from the kinetic energy of the shear flow and does not depend on the curvature of the streamlines. However, we argue that the elastic instability of viscoelastic Couette flow has no direct equivalent in MHD.Comment: 21 pages, 3 figures, to be published in J. Fluid Mec

Neural regulation of the protein composition of saliva

Fluid and protein secretion from salivary glands are primarily regulated by efferent parasympathetic and sympathetic nerves respectively. The protein concentration of saliva, which is made up of a number of functionally important proteins, can vary depending on the impulse traffic arriving from these nerves. The composition of the proteins secreted by a salivary gland with a mixed population of secretory cells can vary with different secretory stimuli and intensities of stimuli, according to how the individual cell populations respond. Most of the published evidence suggests that the protein composition of saliva secreted form the parotid gland, which has an apparently homogeneous secretory cell population, appears to be similar regardless of the type of nerve stimulus. It is likely that salivary secretory cells can secrete protein by a constitutive route, not involving storage granules, in addition to the regulated secretion of protein from storage granules, and that the constitutive route may operate during parasympathetic nerve stimulation. However the functional significance of this type of protein secretion is as yet unknown. In the longer-term the composition of proteins secreted from salivary glands also depends upon the rates of synthesis of individual proteins. Levels of secretory proteins show differing dependencies on specific nerve-mediated stimuli as shown by the changing compositions of proteins secreted following denervation or chronic pharmacological blockade. The levels of secreted proteins appear to be regulated at both the transcriptional and translational levels of protein synthesis. In rodent salivary glands there is a dependency of secretory proline-rich protein synthesis on β-adrenergically mediated stimuli which is dependent upon putative cAMP regulatory sequences of nucleotides in the gene. Although N-linked glycosylation has been shown to be regulated by β-adrenergically mediated stimuli, it is not known if the composition of sugars on proteins varies with neural stimuli.Biomedical Reviews 1993; 2: 47-56

The function of salivary proteins and the regulation of their secretion by salivary glands

Salivary glycoproteins give saliva its characteristic physical properties and enable it to form a thin film over hard and soft tissues in the mouth. Oral health and homeostasis are dependent upon the functions performed by the salivary film and most of these functions, including lubrication, barrier function and microbial interactions, are in turn dependent upon salivary proteins. Some salivary proteins appear to fulfil more than one function and some functions are performed by a number of different proteins. There are relatively great variations in amounts of different proteins present in salivas from different subjects. However, subjects with low levels of particular proteins do not appear to suffer terms of oral health and this may be due to functional compensation by other proteins. Salivary protein secretion by salivary glands is dependent upon stimuli mediated by sympathetic and parasympathetic nerves and both acinar and ductal cells make a contribution to protein secretion. In addition to the well-characterized storage granule exocytosis pathway of protein secretion, salivary cells can secrete proteins by vesi cular, non-storage granule pathways. These include direct secretion of newly synthesized proteins to saliva and to the glandular matrix and to circulation, and transcytosis of polymeric immunoglobulin A into saliva following secretion by glandular plasma cells. Recent data indicate that all ofthese pathways are subject to regulation by autonomic ner ves. Resynthesis of some salivary proteins following secretion also shows a dependency upon nerve-mediated stimuli. The distal intracellular mechanisms coupling stimulation to synthesis are uncertain although the proximal events appear to be similar to those coupling stimulation to exocytosis. The synthesis of some salivary proteins can be upregulated by cy-tokines released from inflammatory cells and this can lead to increased salivary levels of antimicrobial proteins including lactoferrin and immunoglobulin A.Biomedical Reviews 1998; 9: 3-15

Spectral isolation of naturally reductive metrics on simple Lie groups

We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ on a compact simple Lie group $G$, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.Comment: 19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact symmetric spaces must be finite, to appear Math Z. (published online Dec. 2009

Vicious walkers, friendly walkers and Young tableaux II: With a wall

We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial descriptions of symmetric functions. For the problem of $n$-friendly walkers, we derive exact asymptotics for the number of stars and watermelons both in the absence of a wall and in the presence of a wall.Comment: 35 pages, AmS-LaTeX; Definitions of n-friendly walkers clarified; the statement of Theorem 4 and its proof were correcte

Linking Performance and Asset Management - A White Paper Produced by the Federal Highway Administration Transportation Asset Management Expert Task Group

DTFH61-13-A-00005This paper examines how the transportation asset management processes in 23 CFR 515, the transportation performance management processes in 23 CFR 490, and the planning requirements in 23 CFR 450 increase the linkage between asset management and performance management