Numerical studies towards practical large-eddy simulation

Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral characteristics), and adaptability to complex configurations. First, methods are tested on academic test-cases, in order to abridge with fundamental studies. Consistent results are obtained using adaptable finite volume method, with higher order advection fluxes, implicit grid filtering and "low-cost" shear-improved Smagorinsky model. This analysis particularly focuses on mean flow, fluctuations, two-point correlations and spectra. Moreover, it is shown that exponential averaging is a promising tool for LES implementation in complex geometry with deterministic unsteadiness. Finally, adaptability of the method is demonstrated by application to a configuration representative of blade-tip clearance flow in a turbomachine

Structure of velocity distributions in shock waves in granular gases with extension to molecular gases

International audienceVelocity distributions in normal shock waves obtained in dilute granular flows are studied. These distributions cannot be described by a simple functional shape and are believed to be bimodal. Our results show that these distributions are not strictly bimodal but a trimodal distribution is shown to be sufficient. The usual Mott-Smith bimodal description of these distributions, developed for molecular gases, and based on the coexistence of two subpopulations (a supersonic and a subsonic population) in the shock front, can be modified by adding a third subpopulation. Our experiments show that this additional population results from collisions between the supersonic and subsonic subpopulations. We propose a simple approach incorporating the role of this third intermediate population to model the measured probability distributions and apply it to granular shocks as well as shocks in molecular gases

Big-bounce and future time singularity resolution in Bianchi I: the projective invariant Nieh-Yan case

We extend the notion of the Nieh-Yan invariant to generic metric-affine geometries, where both torsion and nonmetricity are taken into account. Notably, we show that the properties of projective invariance and topologicity can be independently accommodated by a suitable choice of the parameters featuring this new Nieh-Yan term. We then consider a special class of modified theories of gravity able to promote the Immirzi parameter to a dynamical scalar field coupled to the Nieh-Yan form, and we discuss in more detail the dynamics of the effective scalar tensor theory stemming from such a revised theoretical framework. We focus, in particular, on cosmological Bianchi I models and we derive classical solutions where the initial singularity is safely removed in favor of a big-bounce, which is ultimately driven by the non-minimal coupling with the Immirzi field. These solutions, moreover, turn out to be characterized by finite time singularities, but we show that such critical points do not spoil the geodesic completeness and wave regularity of these space-times.Comment: 17 pages, 9 figure

Aerodynamic Noise Prediction for a Rod-Airfoil Configuration using Large Eddy Simulations

Aerodynamic noise produced by aerodynamic interaction between a cylinder (rod) and an airfoil in tandem arrangement is investigated using large eddy simulations. Wake from the rod convects with the flow, impinges of the airfoil to produce unsteady force which acts as a sound source. This rod-airfoil interaction problem is a model problem for noise generation due to inflow or upstream-generated turbulence interacting with a turbomachine bladerow or a wind turbine rotor. The OpenFoam and Charles (developed by Cascade Technologies) solvers are chosen to carry out the numerical simulations. The airfoil is set at zero angle of attack for the simulations. The flow conditions are specified by the Reynolds number (based on the rod diameter), Red = 48 K, and the flow Mach number, M = 0.2. Comparisons with measured data are made for (a) mean and root-mean-squared velocity profiles in the rod and airfoil wakes, (b) velocity spectra in the near field, and (c) far-field pressure spectra and directivity. Near-field flow data (on- and off-surface) is used with the Ffowcs Williams-Hawkings (FW-H) acoustic analogy as well as Amiet’s theory to predict far-field sound

Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology

In the context of the metric-affine Chern-Simons gravity endowed with projective invariance, we derive analytical solutions for torsion and nonmetricity in the homogeneous and isotropic cosmological case, described by a flat Friedmann-Robertson-Walker metric. We describe in some details the general properties of the cosmological solutions in the presence of a perfect fluid, such as dynamical stability and the settling of big bounce points, and we discuss the structure of some specific solutions reproducing de Sitter and power law behaviours for the scale factor. Then, we focus on first-order perturbations in the de Sitter scenario, and we study the propagation of gravitational waves in the adiabatic limit, looking at tensor and scalar polarizations. In particular, we find that metric tensor modes couple to torsion tensor components, leading to the appearance, as in the metric version of Chern-Simons gravity, of birefringence, described by different dispersion relations for the left and right circularized polarization states. As a result, the purely tensor part of torsion propagates like a wave, while nonmetricity decouples and behaves like a harmonic oscillator. Finally, we discuss scalar modes, outlining as they decay exponentially in time and do not propagate.Comment: References adde

More Than 1700 Years of Word Equations

Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So, the title of the present article does not seem to be justified at all. However, a linear Diophantine equation can be viewed as a special case of a system of word equations over a unary alphabet, and, more importantly, a word equation can be viewed as a special case of a Diophantine equation. Hence, the problem WordEquations: "Is a given word equation solvable?" is intimately related to Hilbert's 10th problem on the solvability of Diophantine equations. This became clear to the Russian school of mathematics at the latest in the mid 1960s, after which a systematic study of that relation began. Here, we review some recent developments which led to an amazingly simple decision procedure for WordEquations, and to the description of the set of all solutions as an EDT0L language.Comment: The paper will appear as an invited address in the LNCS proceedings of CAI 2015, Stuttgart, Germany, September 1 - 4, 201

Crack Front Waves and the dynamics of a rapidly moving crack

Crack front waves are localized waves that propagate along the leading edge of a crack. They are generated by the interaction of a crack with a localized material inhomogeneity. We show that front waves are nonlinear entities that transport energy, generate surface structure and lead to localized velocity fluctuations. Their existence locally imparts inertia, which is not incorporated in current theories of fracture, to initially "massless" cracks. This, coupled to crack instabilities, yields both inhomogeneity and scaling behavior within fracture surface structure.Comment: Embedded Latex file including 4 figure

Energy radiation of moving cracks

The energy radiated by moving cracks in a discrete background is analyzed. The energy flow through a given surface is expressed in terms of a generalized Poynting vector. The velocity of the crack is determined by the radiation by the crack tip. The radiation becomes more isotropic as the crack velocity approaches the instability threshold.Comment: 7 pages, embedded figure

Computer vision-based automated peak picking applied to protein NMR spectra

Motivation: A detailed analysis of multidimensional NMR spectra of macromolecules requires the identification of individual resonances (peaks). This task can be tedious and time-consuming and often requires support by experienced users. Automated peak picking algorithms were introduced more than 25 years ago, but there are still major deficiencies/flaws that often prevent complete and error free peak picking of biological macromolecule spectra. The major challenges of automated peak picking algorithms is both the distinction of artifacts from real peaks particularly from those with irregular shapes and also picking peaks in spectral regions with overlapping resonances which are very hard to resolve by existing computer algorithms. In both of these cases a visual inspection approach could be more effective than a ‘blind' algorithm. Results: We present a novel approach using computer vision (CV) methodology which could be better adapted to the problem of peak recognition. After suitable ‘training' we successfully applied the CV algorithm to spectra of medium-sized soluble proteins up to molecular weights of 26 kDa and to a 130 kDa complex of a tetrameric membrane protein in detergent micelles. Our CV approach outperforms commonly used programs. With suitable training datasets the application of the presented method can be extended to automated peak picking in multidimensional spectra of nucleic acids or carbohydrates and adapted to solid-state NMR spectra. Availability and implementation: CV-Peak Picker is available upon request from the authors. Contact: [email protected]; [email protected]; [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin