The PSE-3D instability analysis methodology for flows depending strongly on two and weakly on the third spatial dimension

The present contribution discusses the development of a PSE-3D instability analysis algorithm, in which a matrix forming and storing approach is followed. Alternatively to the typically used in stability calculations spectral methods, new stable high-order finitedifference-based numerical schemes for spatial discretization 1 are employed. Attention is paid to the issue of efficiency, which is critical for the success of the overall algorithm. To this end, use is made of a parallelizable sparse matrix linear algebra package which takes advantage of the sparsity offered by the finite-difference scheme and, as expected, is shown to perform substantially more efficiently than when spectral collocation methods are used. The building blocks of the algorithm have been implemented and extensively validated, focusing on classic PSE analysis of instability on the flow-plate boundary layer, temporal and spatial BiGlobal EVP solutions (the latter necessary for the initialization of the PSE-3D), as well as standard PSE in a cylindrical coordinates using the nonparallel Batchelor vortex basic flow model, such that comparisons between PSE and PSE-3D be possible; excellent agreement is shown in all aforementioned comparisons. Finally, the linear PSE-3D instability analysis is applied to a fully three-dimensional flow composed of a counter-rotating pair of nonparallel Batchelor vortices.

Reply to Comment on ``Towards a large deviation theory for strongly correlated systems''

The computational study commented by Touchette opens the door to a desirable generalization of standard large deviation theory for special, though ubiquitous, correlations. We focus on three interrelated aspects: (i) numerical results strongly suggest that the standard exponential probability law is asymptotically replaced by a power-law dominant term; (ii) a subdominant term appears to reinforce the thermodynamically extensive entropic nature of q-generalized rate function; (iii) the correlations we discussed, correspond to Q -Gaussian distributions, differing from Lévy?s, except in the case of Cauchy?Lorentz distributions. Touchette has agreeably discussed point (i), but, unfortunately, points (ii) and (iii) escaped to his analysis. Claiming the absence of connection with q-exponentials is unjustified.

Is the polarity of content producers strongly influenced by the results of the event?

This paper presents an approach to compare two types of data, subjective data (Polarity of Pan American Games 2011 event by country) and objective data (the number of medals won by each participating country), based on the Pearson corre- lation. When dealing with events described by people, knowledge acquisition is difficult because their structure is heterogeneous and subjective. A first step towards knowing the polarity of the information provided by people consists in automatically classifying the posts into clusters according to their polarity. The authors carried out a set of experiments using a corpus that consists of 5600 posts extracted from 168 Internet resources related to a specific event: the 2011 Pan American games. The approach is based on four components: a crawler, a filter, a synthesizer and a polarity analyzer. The PanAmerican approach automatically classifies the polarity of the event into clusters with the following results: 588 positive, 336 neutral, and 76 negative. Our work found out that the polarity of the content produced was strongly influenced by the results of the event with a correlation of .74. Thus, it is possible to conclude that the polarity of content is strongly affected by the results of the event. Finally, the accuracy of the PanAmerican approach is: .87, .90, and .80 according to the precision of the three classes of polarity evaluated.