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Unstable equilibrium solutions in a homogeneous shear flow with sinuous symmetry are numerically found in large-eddy simulations (LES) with no kinetic viscosity. The small-scale properties are determined by the mixing length scale $l_S$ used to define eddy viscosity, and the large-scale motion is induced by the mean shear at the integral scale, which is limited by the spanwise box dimension $L_z$. The fraction $ R_S= L_z/l_S$, which plays the role of a Reynolds number, is used as a numerical continuation parameter. It is shown that equilibrium solutions appear by a saddle-node bifurcation as $R_S$ increases, and that they resemble those in plane Couette flow with the same symmetry. The vortical structures of both lower- and upper-branch solutions become spontaneously localised in the vertical direction. The lower-branch solution is an edge state at low $R_S$, and takes the form of a thin critical layer as $R_S$ increases, as in the asymptotic theory of generic shear flow at high-Reynolds numbers. On the other hand, the upper-branch solutions are characterised by a tall velocity streak with multi-scale multiple vortical structures. At the higher end of $R_S$, an incipient multiscale structure is found. The LES turbulence occasionally visits vertically localised states whose vortical structure resembles the present vertically localised LES equilibria.

In this article we present Miuz, a robustness index for complex networks. Miuz measures the impact of disconnecting a node from the network while comparing the sizes of the remaining connected components. Strictly speaking, Miuz for a node is defined as the inverse of the size of the largest connected component divided by the sum of the sizes of the remaining ones. We tested our index in attack strategies where the nodes are disconnected in decreasing order of a specified metric. We considered Miuz and other well-known centrality measures such as betweenness, degree , and harmonic centrality. All of these metrics were compared regarding the behavior of the robust-ness (R-index) during the attacks. In an attempt to simulate the internet backbone, the attacks were performed in complex networks with power-law degree distributions (scale-free networks). Preliminary results show that attacks based on disconnecting a few number of nodes Miuz are more dangerous (decreasing the robustness) than the same attacks based on other centrality measures. We believe that Miuz, as well as other measures based on the size of the largest connected component, provides a good addition to other robustness metrics for complex networks., Comment: in 34th International Conference of the Chilean Computer Science Society (SCCC), Nov 2015, Santiago, Chile. 2015. arXiv admin note: substantial text overlap with arXiv:1601.02465

The turbulent/non-turbulent interface is analysed in a direct numerical simulation of a boundary layer in the range $Re_\theta=2800-6600$, with emphasis on the behaviour of the relatively large-scale fractal intermittent region. This requires the introduction of a new definition of the distance between a point and a general surface, which is compared with the more usual vertical distance to the top of the layer. Interfaces are obtained by thresholding the enstrophy field and the magnitude of the rate-of-strain tensor, and it is concluded that, while the former are physically relevant features, the latter are not. By varying the threshold, a topological transition is identified as the interface moves from the free stream into the turbulent core. A vorticity scale is defined that collapses that transition for different Reynolds numbers, roughly equivalent to the root-mean-squared vorticity at the edge of the boundary layer. Conditionally averaged flow variables are analysed as functions of the new distance, both within and outside the interface. It is found that the interface contains a nonequilibrium layer whose thickness scales well with the Taylor microscale, enveloping a self-similar layer spanning a fixed fraction of the boundary-layer thickness. Interestingly, the straining structure of the flow is similar in both regions. Irrotational pockets within the turbulent core are also studied. They form a self-similar set whose size decreases with increasing depth, presumably due to break-up by the turbulence, but the rate of viscous diffusion is independent of the pocket size. The raw data used in the analysis are freely available from our web page (http://torroja.dmt.upm.es)., Comment: 46 pages, 25 figures

It is remarked that fluxes in conservation laws, such as the Reynolds stresses in the momentum equation of turbulent shear flows, or the spectral energy flux in isotropic turbulence, are only defined up to an arbitrary solenoidal field. While this is not usually significant for long-time averages, it becomes important when fluxes are modelled locally in large-eddy simulations, or in the analysis of intermittency and cascades. As an example, a numerical procedure is introduced to compute fluxes in scalar conservation equations in such a way that their total integrated magnitude is minimised. The result is an irrotational vector field that derives from a potential, thus minimising sterile flux `circuits'. The algorithm is generalised to tensor fluxes and applied to the transfer of momentum in a turbulent channel. The resulting instantaneous Reynolds stresses are compared with their traditional expressions, and found to be substantially different.

Whether as telecommunications or power systems, networks are very important in everyday life. Maintaining these networks properly functional and connected, even under attacks or failures, is of special concern. This topic has been previously studied with a whole network robustness perspective,modeling networks as undirected graphs (such as roads or simply cables). This perspective measures the average behavior of the network after its last node has failed. In this article we propose two alternatives to well-known studies about the robustness of the backbone Internet: to use a supply network model and metrics for its representation (we called it the Go-Index), and to use robustness metrics that can be calculated while disconnections appear. Our research question is: if a smart adversary has a limited number of strikes to attack the Internet, how much will the damage be after each one in terms of network disconnection? Our findings suggest that in order to design robust networks it might be better to have a complete view of the robustness evolution of the network, from both the infrastructure and the users perspective., Comment: 6 pages, 7 figures. arXiv admin note: text overlap with arXiv:1601.02465

In this article we present the Hayastan Shakarian (HS), a robustness index for complex networks. HS measures the impact of a network disconnection (edge) while comparing the sizes of the remaining connected components. Strictly speaking, the Hayastan Shakarian index is defined as edge removal that produces the maximal inverse of the size of the largest connected component divided by the sum of the sizes of the remaining ones. We tested our index in attack strategies where the nodes are disconnected in decreasing order of a specified metric. We considered using the Hayastan Shakarian cut (disconnecting the edge with max HS) and other well-known strategies as the higher betweenness centrality disconnection. All strategies were compared regarding the behavior of the robustness (R-index) during the attacks. In an attempt to simulate the internet backbone, the attacks were performed in complex networks with power-law degree distributions (scale-free networks). Preliminary results show that attacks based on disconnecting using the Hayastan Shakarian cut are more dangerous (decreasing the robustness) than the same attacks based on other centrality measures. We believe that the Hayastan Shakarian cut, as well as other measures based on the size of the largest connected component, provides a good addition to other robustness metrics for complex networks., Comment: 4 pages, 8 figures, short paper submitted to DRCN 2016

Statistically stationary and homogeneous shear turbulence (SS-HST) is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, long-term simulations of HST are `minimal' in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, $L_z$, which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large $(L_x\gtrsim 2L_z$, $L_y \gtrsim L_z$) to prevent other directions to be constrained as well. It is also found that very long boxes, $L_x \gtrsim 2 L_y$, couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wall-bounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, $\sim 20 S^{-1}$, and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general., Comment: Published in Physics of Fluids; the supplemental appendices are merged in the article

The perspective of statistical state dynamics (SSD) has recently been applied to the study of mechanisms underlying turbulence in various physical systems. An example implementation of SSD is the second order closure referred to as stochastic structural stability theory (S3T), which has provided insight into the dynamics of wall turbulence and specifically the emergence and maintenance of the roll/streak structure. This closure eliminates nonlinear interactions among the perturbations has been removed, restricting nonlinearity in the dynamics to that of the mean equation and the interaction between the mean and perturbation covariance. Here, this quasi-linear restriction of the dynamics is used to study the structure and dynamics of turbulence in plane Poiseuille flow at moderately high Reynolds numbers in a closely related dynamical system, referred to as the restricted nonlinear (RNL) system. RNL simulations reveal that the essential features of wall-turbulence dynamics are retained. Remarkably, the RNL system spontaneously limits the support of its turbulence to a small set of streamwise Fourier components giving rise to a naturally minimal representation of its turbulence dynamics. Although greatly simplified, this RNL turbulence exhibits natural-looking structures and statistics. Surprisingly, even when further truncation of the perturbation support to a single streamwise component is imposed the RNL system continues to produce self-sustaining turbulent structure and dynamics. RNL turbulence at the Reynolds numbers studied is dominated by the roll/streak structure in the buffer layer and similar very-large-scale structure (VLSM) in the outer layer. Diagnostics of the structure, spectrum and energetics of RNL and DNS turbulence are used to demonstrate that the roll/streak dynamics supporting the turbulence in the buffer and logarithmic layer is essentially similar in RNL and DNS., Comment: published in J. Fluid Mech., 26 pages, 15 figures. arXiv admin note: text overlap with arXiv:1401.7816

Place recognition is one of the most challenging problems in computer vision, and has become a key part in mobile robotics and autonomous driving applications for performing loop closure in visual SLAM systems. Moreover, the difficulty of recognizing a revisited location increases with appearance changes caused, for instance, by weather or illumination variations, which hinders the long-term application of such algorithms in real environments. In this paper we present a convolutional neural network (CNN), trained for the first time with the purpose of recognizing revisited locations under severe appearance changes, which maps images to a low dimensional space where Euclidean distances represent place dissimilarity. In order for the network to learn the desired invariances, we train it with triplets of images selected from datasets which present a challenging variability in visual appearance. The triplets are selected in such way that two samples are from the same location and the third one is taken from a different place. We validate our system through extensive experimentation, where we demonstrate better performance than state-of-art algorithms in a number of popular datasets.

A temporal study of energy transfer across length scales is performed in 3D numerical simulations of homogeneous shear flow and isotropic turbulence. The average time taken by perturbations in the energy flux to travel between scales is measured and shown to be additive. Our data suggests that the propagation of disturbances in the energy flux is independent of the forcing and that it defines a `velocity' that determines the energy flux itself. These results support that the cascade is, on average, a scale-local process where energy is continuously transmitted from one scale to the next in order of decreasing size., Comment: Accepted for publication as a Letter in Physics of Fluids