A blue sky catastrophe in double-diffusive convection

A global bifurcation of the blue sky catastrophe type has been found in a small Prandtl number binary mixture contained in a laterally heated cavity. The system has been studied numerically applying the tools of bifurcation theory. The catastrophe corresponds to the destruction of an orbit which, for a large range of Rayleigh numbers, is the only stable solution. This orbit is born in a global saddle-loop bifurcation and becomes chaotic in a period doubling cascade just before its disappearance at the blue sky catastrophe.Comment: 4 pages, 6 figures, REVTeX, To be published in Physical Review Letter

Morphologies of three-dimensional shear bands in granular media

We present numerical results on spontaneous symmetry breaking strain localization in axisymmetric triaxial shear tests of granular materials. We simulated shear band formation using three-dimensional Distinct Element Method with spherical particles. We demonstrate that the local shear intensity, the angular velocity of the grains, the coordination number, and the local void ratio are correlated and any of them can be used to identify shear bands, however the latter two are less sensitive. The calculated shear band morphologies are in good agreement with those found experimentally. We show that boundary conditions play an important role. We discuss the formation mechanism of shear bands in the light of our observations and compare the results with experiments. At large strains, with enforced symmetry, we found strain hardening.Comment: 6 pages 5 figures, low resolution figures

Critical packing in granular shear bands

In a realistic three-dimensional setup, we simulate the slow deformation of idealized granular media composed of spheres undergoing an axisymmetric triaxial shear test. We follow the self-organization of the spontaneous strain localization process leading to a shear band and demonstrate the existence of a critical packing density inside this failure zone. The asymptotic criticality arising from the dynamic equilibrium of dilation and compaction is found to be restricted to the shear band, while the density outside of it keeps the memory of the initial packing. The critical density of the shear band depends on friction (and grain geometry) and in the limit of infinite friction it defines a specific packing state, namely the \emph{dynamic random loose packing}

Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment