Three regularization models of the Navier-Stokes equations

We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as SGS models are also shown by examining their effects on superfilter-scale properties. Numerical solutions of the Clark-alpha model are compared to two previously employed regularizations, LANS-alpha and Leray-alpha (at Re ~ 3300, Taylor Re ~ 790) and to a DNS. We derive the Karman-Howarth equation for both the Clark-alpha and Leray-alpha models. We confirm one of two possible scalings resulting from this equation for Clark as well as its associated k^(-1) energy spectrum. At sub-filter scales, Clark-alpha possesses similar total dissipation and characteristic time to reach a statistical turbulent steady-state as Navier-Stokes, but exhibits greater intermittency. As a SGS model, Clark reproduces the energy spectrum and intermittency properties of the DNS. For the Leray model, increasing the filter width decreases the nonlinearity and the effective Re is substantially decreased. Even for the smallest value of alpha studied, Leray-alpha was inadequate as a SGS model. The LANS energy spectrum k^1, consistent with its so-called "rigid bodies," precludes a reproduction of the large-scale energy spectrum of the DNS at high Re while achieving a large reduction in resolution. However, that this same feature reduces its intermittency compared to Clark-alpha (which shares a similar Karman-Howarth equation). Clark is found to be the best approximation for reproducing the total dissipation rate and the energy spectrum at scales larger than alpha, whereas high-order intermittency properties for larger values of alpha are best reproduced by LANS-alpha.Comment: 21 pages, 8 figure

Leray and LANS-α\alpha modeling of turbulent mixing

Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply existence and uniqueness of strong solutions to the corresponding modelled system of equations. We will consider the large eddy interpretation of two such mathematical regularisation principles, i.e., Leray and LANS$-\alpha$ regularisation. The Leray principle introduces a {\bfi smoothed transport velocity} as part of the regularised convective nonlinearity. The LANS$-\alpha$ principle extends the Leray formulation in a natural way in which a {\bfi filtered Kelvin circulation theorem}, incorporating the smoothed transport velocity, is explicitly satisfied. These regularisation principles give rise to implied subgrid closures which will be applied in large eddy simulation of turbulent mixing. Comparison with filtered direct numerical simulation data, and with predictions obtained from popular dynamic eddy-viscosity modelling, shows that these mathematical regularisation models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure

Distributed utterances

I propose an apparatus for handling intrasentential change in context. The standard approach has problems with sentences with multiple occurrences of the same demonstrative or indexical. My proposal involves the idea that contexts can be complex. Complex contexts are built out of (“simple”) Kaplanian contexts by ordered n-tupling. With these we can revise the clauses of Kaplan’s Logic of Demonstratives so that each part of a sentence is taken in a different component of a complex context. I consider other applications of the framework: to agentially distributed utterances (ones made partly by one speaker and partly by another); to an account of scare-quoting; and to an account of a binding-like phenomenon that avoids what Kit Fine calls “the antinomy of the variable.

Highly turbulent solutions of LANS-alpha and their LES potential

We compute solutions of the Lagrangian-Averaged Navier-Stokes alpha-model (LANS) for significantly higher Reynolds numbers (up to Re 8300) than have previously been accomplished. This allows sufficient separation of scales to observe a Navier-Stokes (NS) inertial range followed by a 2nd LANS inertial range. The analysis of the third-order structure function scaling supports the predicted l^3 scaling; it corresponds to a k^(-1) scaling of the energy spectrum. The energy spectrum itself shows a different scaling which goes as k^1. This latter spectrum is consistent with the absence of stretching in the sub-filter scales due to the Taylor frozen-in hypothesis employed as a closure in the derivation of LANS. These two scalings are conjectured to coexist in different spatial portions of the flow. The l^3 (E(k) k^(-1)) scaling is subdominant to k^1 in the energy spectrum, but the l^3 scaling is responsible for the direct energy cascade, as no cascade can result from motions with no internal degrees of freedom. We verify the prediction for the size of the LANS attractor resulting from this scaling. From this, we give a methodology either for arriving at grid-independent solutions for LANS, or for obtaining a formulation of a LES optimal in the context of the alpha models. The fully converged grid-independent LANS may not be the best approximation to a direct numerical simulation of the NS equations since the minimum error is a balance between truncation errors and the approximation error due to using LANS instead of the primitive equations. Furthermore, the small-scale behavior of LANS contributes to a reduction of flux at constant energy, leading to a shallower energy spectrum for large alpha. These small-scale features, do not preclude LANS to reproduce correctly the intermittency properties of high Re flow.Comment: 37 pages, 17 figure

LAPW frozen-phonon calculation, shell model lattice dynamics and specific-heat measurement of SnO

An ab-initio Linear Augmented Plane-Wave (LAPW) calculation of the zone-centered phonon frequencies of SnO has been performed. E$_g$ symmetry has been ascribed to the mode observed at 113 cm$^{-1}$ in Raman measurements, discarding a previous B$_{1g}$ assignement. The other phonon modes measured by Raman spectroscopy are also well reproduced. A new shell-model has also been developed, that gives good agreement of the zone-centered frequencies compared to the measured data and the LAPW results. Specific heat measurements have been performed between 5 K and 110 K. Computation of the specific heat and the M\"{o}ssbauer recoilless fraction with the improved shell-model shows a good agreement with the experimental data as a function of temperature.Comment: 11 pages, 1 figure. to appear in Phys. Rev. B (November 1999

Modeling and simulation of phase-transitions in multicomponent aluminum alloy casting

The casting process of aluminum products involves the spatial distribution of alloying elements. It is essential that these elements are uniformly distributed in order to guarantee reliable and consistent products. This requires a good understanding of the main physical mechanisms that affect the solidification, in particular the thermodynamic description and its coupling to the transport processes of heat and mass that take place. The continuum modeling is reviewed and methods for handling the thermodynamics component of multi-element alloys are proposed. Savings in data-storage and computing costs on the order of 100 or more appear possible, when a combination of data-reduction and data-representation methods is used. To test the new approach a simplified model was proposed and shown to qualitatively capture the evolving solidification front

Advances in understanding gray matter pathology in multiple sclerosis: Are we ready to redefine disease pathogenesis?

The purpose of this special issue in BMC Neurology is to summarize advances in our understanding of the pathological, immunological, imaging and clinical concepts of gray matter (GM) pathology in patients with multiple sclerosis (MS). Review articles by Lucchinetti and Popescu, Walker and colleagues, Hulst and colleagues and Horakova and colleagues summarize important recent advances in understanding GM damage and its implications to MS pathogenesis. They also raise a number of important new questions and outline comprehensive approaches to addressing those questions in years to come. In the last decade, the use of immunohistochemistry staining methods and more advanced imaging techniques to detect GM lesions, like double inversion recovery, contributed to a surge of studies related to cortical and subcortical GM pathology in MS. It is becoming more apparent from recent biopsy studies that subpial cortical lesions in early MS are highly inflammatory. The mechanisms responsible for triggering meningeal inflammation in MS patients are not yet elucidated, and they should be further investigated in relation to their role in initiating and perpetuating the disease process. Determining the role of antigens, environmental and genetic factors in the pathogenesis of GM involvement in MS is critical. The early involvement of cortical and subcortical GM damage in MS is very intriguing and needs to be further studied. As established in numerous cross-sectional and longitudinal studies, GM damage is a better predictor of physical disability and cognitive impairment than WM damage. Monitoring the evolution of GM damage is becoming an important marker in predicting future disease course and response to therapy in MS patients