A local multiple proper generalized decomposition based on the partition of unity

It is well known that model order reduction techniques that project the solution of the problem at hand onto a low-dimensional subspace present difficulties when this solution lies on a nonlinear manifold. To overcome these difficulties (notably, an undesirable increase in the number of required modes in the solution), several solutions have been suggested. Among them, we can cite the use of nonlinear dimensionality reduction techniques or, alternatively, the employ of linear local reduced order approaches. These last approaches usually present the difficulty of ensuring continuity between these local models. Here, a new method is presented, which ensures this continuity by resorting to the paradigm of the partition of unity while employing proper generalized decompositions at each local patch

The energy budget in Rayleigh-Benard convection

It is shown using three series of Rayleigh number simulations of varying aspect ratio AR and Prandtl number Pr that the normalized dissipation at the wall, while significantly greater than 1, approaches a constant dependent upon AR and Pr. It is also found that the peak velocity, not the mean square velocity, obeys the experimental scaling of Ra^{0.5}. The scaling of the mean square velocity is closer to Ra^{0.46}, which is shown to be consistent with experimental measurements and the numerical results for the scaling of Nu and the temperature if there are strong correlations between the velocity and temperature.Comment: 5 pages, 3 figures, new version 13 Mar, 200

Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data

Engineering is evolving in the same way than society is doing. Nowadays, data is acquiring a prominence never imagined. In the past, in the domain of materials, processes and structures, testing machines allowed extract data that served in turn to calibrate state-of-the-art models. Some calibration procedures were even integrated within these testing machines. Thus, once the model had been calibrated, computer simulation takes place. However, data can offer much more than a simple state-of-the-art model calibration, and not only from its simple statistical analysis, but from the modeling and simulation viewpoints. This gives rise to the the family of so-called twins: the virtual, the digital and the hybrid twins. Moreover, as discussed in the present paper, not only data serve to enrich physically-based models. These could allow us to perform a tremendous leap forward, by replacing big-data-based habits by the incipient smart-data paradigm

Cavitation pressure in liquid helium

Recent experiments have suggested that, at low enough temperature, the homogeneous nucleation of bubbles occurs in liquid helium near the calculated spinodal limit. This was done in pure superfluid helium 4 and in pure normal liquid helium 3. However, in such experiments, where the negative pressure is produced by focusing an acoustic wave in the bulk liquid, the local amplitude of the instantaneous pressure or density is not directly measurable. In this article, we present a series of measurements as a function of the static pressure in the experimental cell. They allowed us to obtain an upper bound for the cavitation pressure P_cav (at low temperature, P_cav < -2.4 bar in helium 3, P_cav < -8.0 bar in helium 4). From a more precise study of the acoustic transducer characteristics, we also obtained a lower bound (at low temperature, P_cav > -3.0 bar in helium 3, P_cav > - 10.4 bar in helium 4). In this article we thus present quantitative evidence that cavitation occurs at low temperature near the calculated spinodal limit (-3.1 bar in helium 3 and -9.5 bar in helium 4). Further information is also obtained on the comparison between the two helium isotopes. We finally discuss the magnitude of nonlinear effects in the focusing of a sound wave in liquid helium, where the pressure dependence of the compressibility is large.Comment: 11 pages, 9 figure

Wall roughness induces asymptotic ultimate turbulence

Turbulence is omnipresent in Nature and technology, governing the transport of heat, mass, and momentum on multiple scales. For real-world applications of wall-bounded turbulence, the underlying surfaces are virtually always rough; yet characterizing and understanding the effects of wall roughness for turbulence remains a challenge, especially for rotating and thermally driven turbulence. By combining extensive experiments and numerical simulations, here, taking as example the paradigmatic Taylor-Couette system (the closed flow between two independently rotating coaxial cylinders), we show how wall roughness greatly enhances the overall transport properties and the corresponding scaling exponents. If only one of the walls is rough, we reveal that the bulk velocity is slaved to the rough side, due to the much stronger coupling to that wall by the detaching flow structures. If both walls are rough, the viscosity dependence is thoroughly eliminated in the boundary layers and we thus achieve asymptotic ultimate turbulence, i.e. the upper limit of transport, whose existence had been predicted by Robert Kraichnan in 1962 (Phys. Fluids {\bf 5}, 1374 (1962)) and in which the scalings laws can be extrapolated to arbitrarily large Reynolds numbers

The joy of ruling: an experimental investigation on collective giving

We analyse team dictator games with different voting mechanisms in the laboratory. Individuals vote to select a donation for all group members. Standard Bayesian analysis makes the same prediction for all three mechanisms: participants should cast the same vote regardless of the voting mechanism used to determine the common donation level. Our experimental results show that subjects fail to choose the same vote. We show that their behaviour is consistent with a joy of ruling: individuals get an extra utility when they determine the voting outcome

FIDEL—a retrovirus-like retrotransposon and its distinct evolutionary histories in the A- and B-genome components of cultivated peanut

In this paper, we describe a Ty3-gypsy retrotransposon from allotetraploid peanut (Arachis hypogaea) and its putative diploid ancestors Arachis duranensis (A-genome) and Arachis ipaënsis (B-genome). The consensus sequence is 11,223 bp. The element, named FIDEL (Fairly long Inter-Dispersed Euchromatic LTR retrotransposon), is more frequent in the A- than in the B-genome, with copy numbers of about 3,000 (±950, A. duranensis), 820 (±480, A. ipaënsis), and 3,900 (±1,500, A. hypogaea) per haploid genome. Phylogenetic analysis of reverse transcriptase sequences showed distinct evolution of FIDEL in the ancestor species. Fluorescent in situ hybridization revealed disperse distribution in euchromatin and absence from centromeres, telomeric regions, and the nucleolar organizer region. Using paired sequences from bacterial artificial chromosomes, we showed that elements appear less likely to insert near conserved ancestral genes than near the fast evolving disease resistance gene homologs. Within the Ty3-gypsy elements, FIDEL is most closely related with the Athila/Calypso group of retrovirus-like retrotransposons. Putative transmembrane domains were identified, supporting the presence of a vestigial envelope gene. The results emphasize the importance of FIDEL in the evolution and divergence of different Arachis genomes and also may serve as an example of the role of retrotransposons in the evolution of legume genomes in general