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

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Levy alpha-stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.Comment: 7 pages, 5 figures, 1 table. Presented at the Conference on Computing in Economics and Finance in Montreal, 14-16 June 2007; at the conference "Modelling anomalous diffusion and relaxation" in Jerusalem, 23-28 March 2008; et

Discovery of a Luminous Quasar in the Nearby Universe

In the course of the Pico dos Dias survey (PDS), we identified the stellar like object PDS456 at coordinates alpha = 17h 28m 19.796s, delta = -14deg 15' 55.87'' (epoch 2000), with a relatively nearby (z = 0.184) and bright (B = 14.69) quasar. Its position at Galactic coordinates l_II = 10.4deg, b_II = +11.2deg, near the bulge of the Galaxy, may explain why it was not detected before. The optical spectrum of PDS456 is typical of a luminous quasar, showing a broad (FWHM ~ 4000 km/s) H_\beta line, very intense FeII lines and a weak [OIII]\lambda5007 line. PDS456 is associated to the infrared source IRAS 17254-1413 with a 60 \mum infrared luminosity L_{60} = 3.8 x 10^{45} erg/s. The relatively flat slopes in the infrared (\alpha(25,60) = -0.33 and \alpha(12,25) = -0.78) and a flat power index in the optical (F_{\nu} \propto \nu^{-0.72}) may indicate a low dust content. A good match between the position of PDS456 and the position of the X-ray source RXS J172819.3-141600 implies an X-ray luminosity L_x = 2.8 x 10^{44} erg/s. The good correlation between the strength of the emission lines in the optical and the X-ray luminosity, as well as the steep optical to X-ray index estimated (\alpha_{ox} = -1.64) suggest that PDS456 is radio quiet. A radio survey previously performed in this region yields an upper limit for radio power at ~ 5 GHz of ~ 2.6 x 10^{30} erg/s/Hz. We estimate the Galactic reddening in this line-of-sight to be A_B \simeq 2.0, implying an absolute magnitude M_B = -26.7 (using H_0 = 75 km s^{-1} Mpc^{-1} and q_0 = 0). In the optical, PDS456 is therefore 1.3 times more luminous than 3C 273 and the most luminous quasar in the nearby (z \leq 0.3) Universe.Comment: 12 pages, LaTeX (aasms4.sty) + 3 figures; accepted for publication in the Astrophysical Journal Letter

The Ehrenfest urn revisited: Playing the game on a realistic fluid model

The Ehrenfest urn process, also known as the dogs and fleas model, is realistically simulated by molecular dynamics of the Lennard-Jones fluid. The key variable is Delta z, i.e. the absolute value of the difference between the number of particles in one half of the simulation box and in the other half. This is a pure-jump stochastic process induced, under coarse graining, by the deterministic time evolution of the atomic coordinates. We discuss the Markov hypothesis by analyzing the statistical properties of the jumps and of the waiting times between jumps. In the limit of a vanishing integration time-step, the distribution of waiting times becomes closer to an exponential and, therefore, the continuous-time jump stochastic process is Markovian. The random variable Delta z behaves as a Markov chain and, in the gas phase, the observed transition probabilities follow the predictions of the Ehrenfest theory.Comment: Accepted by Physical Review E on 4 May 200

HIV-Associated Facial Lipodystrophy: Experience of a Tertiary Referral Center With Fat and Dermis-Fat Compound Graft Transfer

Objectives: HIV-associated lipodystrophy is a common comorbidity in HIV-infected patients, having a profound impact on every aspect of patients' lives, particularly when involving the face. Hence, it is of the utmost importance to evaluate the result of any potential therapies that may help solve HIV-associated facial lipodystrophy. The aim of this article was to evaluate the outcome of patients undergoing facial lipodystrophy correction surgery within our institution. Methods: A retrospective analysis of the clinical charts and iconographic information of patients regarding demographics, morphologic changes, surgical option, postoperative complications, results, and patient satisfaction assessed by a 1- to 10-point scale and by the Assessment of Body Change and Distress questionnaire. Results: Twenty-three patients were operated on from March 2011 to April 2015. Seventy-five percent of cases were treated with fat graft injection, whereas dermis-fat grafts were applied in 25% of patients. The former had their fat harvested more commonly from the abdomen, whereas in the latter case, the graft was harvested mostly from the inner aspect of arms. The mean volume of fat injected on each side of the face was 28.5 ± 22.7 mL. On a scale from 1 to 10, mean patient satisfaction was 7.7 ± 2.8. The Assessment of Body Change and Distress questionnaire revealed statistically significant improvements. Complications occurred in 25% of cases, the most frequent being significant reabsorption. No major complications occurred. Conclusions: Treatment of HIV-associated facial lipodystrophy with autologous fat or dermis-fat compound graft is a safe procedure with long-lasting results and unquestionable aesthetic and social benefits.info:eu-repo/semantics/publishedVersio

Liquid crystal director fluctuations and surface anchoring by molecular simulation

We propose a simple and reliable method to measure the liquid crystal surface anchoring strength by molecular simulation. The method is based on the measurement of the long-range fluctuation modes of the director in confined geometry. As an example, molecular simulations of a liquid crystal in slab geometry between parallel walls with homeotropic anchoring have been carried out using the Monte Carlo technique. By studying different slab thicknesses, we are able to calculate separately the position of the elastic boundary condition, and the extrapolation length

Prognostic relevance of symptoms versus objective evidence of coronary artery disease in diabetic patients

Aim Little is known about the prognostic significance of silent versus symptomatic coronary artery disease (CAD) in diabetic patients. We therefore assessed the incidence of scintigraphic evidence of CAD in diabetic patients without known CAD and the impact of symptoms and scintigraphic findings on prognosis. Methods and results A consecutive series of 1737 diabetic patients without known CAD underwent dual-isotope myocardial perfusion SPECT (MPS) and 1430 were followed-up for a median of 2 (1-8.5) years. Critical events were defined as myocardial infarction or cardiac death. Objective evidence of CAD was found in 39% of 826 asymptomatic diabetic patients, in 51% of 151 diabetic patients with shortness of breath (SOB), and in 44% of 760 diabetic patients with angina. During follow-up, 98 critical events occurred. Annual critical event rates were 2.2% in asymptomatic, 3.2% in angina, and 7.7% in diabetic patients with shortness of breath (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} $p{<}0.001$ \end{document} versus other groups). With MPS evidence of CAD, critical event rates increased to 3.4% (asymptomatic), 5.6% (angina), and 13.2% (SOB) (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} $p{\leqslant}0.009$ \end{document} versus no evidence of CAD). Age, hypertension, shortness of breath, scarring and ischaemia were independent predictors of critical events. MPS findings added incremental information to prescan information regarding outcome prediction. Conclusions In asymptomatic diabetic patients, the rate of objective evidence of CAD and annual critical events were similar to those found in diabetic patients with angina. The outcome was three times worse in diabetic patients with shortness of breath. MPS findings were strongly predictive of outcome and proved valuable for risk stratificatio