8,284 research outputs found
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- 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 regularisation. The Leray principle introduces a {\bfi
smoothed transport velocity} as part of the regularised convective
nonlinearity. The LANS 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
ET-1-induced contraction of renal afferent arterioles of Dahl salt-sensitive rats is impaired by targeted modification of a p66 Shc regulatory phosphorylation site
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 symmetry has
been ascribed to the mode observed at 113 cm in Raman measurements,
discarding a previous B 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
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