Nonequilibrium noise in electrophoresis: The microion wind

A colloid supported against gravitational settling by means of an imposed electric field behaves, on average, as if it is at equilibrium in a confining potential T. M. Squires, J. Fluid Mech. 443, 403 (2001)]. We show, however, that the effective Langevin equation for the colloid contains a nonequilibrium noise source, proportional to the field, arising from the thermal motion of dissolved ions. The position fluctuations of the colloid show strong, experimentally testable signatures of nonequilibrium behavior, including a highly anisotropic, frequency-dependent ``effective temperature'' obtained from the fluctuation-dissipation ratio.

Turbulence and cooling in galaxy cluster cores

We study the interplay between turbulent heating, mixing, and radiative cooling in an idealized model of cool cluster cores. Active galactic nuclei (AGN) jets are expected to drive turbulence and heat cluster cores. Cooling of the intracluster medium (ICM) and stirring by AGN jets are tightly coupled in a feedback loop. We impose the feedback loop by balancing radiative cooling with turbulent heating. In addition to heating the plasma, turbulence also mixes it, suppressing the formation of cold gas at small scales. In this regard, the effect of turbulence is analogous to thermal conduction. For uniform plasma in thermal balance (turbulent heating balancing radiative cooling), cold gas condenses only if the cooling time is shorter than the mixing time. This condition requires the turbulent kinetic energy to be a parts per thousand(3) the plasma internal energy; such high velocities in cool cores are ruled out by observations. The results with realistic magnetic fields and thermal conduction are qualitatively similar to the hydrodynamic simulations. Simulations where the runaway cooling of the cool core is prevented due to mixing with the hot ICM show cold gas even with subsonic turbulence, consistent with observations. Thus, turbulent mixing is the likely mechanism via which AGN jets heat cluster cores. The thermal instability growth rates observed in simulations with turbulence are consistent with the local thermal instability interpretation of cold gas in cluster cores.

In a hot bubble: why does superbubble feedback work, but isolated supernovae do not?

Using idealized one-dimensional Eulerian hydrodynamic simulations, we contrast the behaviour of isolated supernovae with the superbubbles driven by multiple, collocated supernovae. Continuous energy injection via successive supernovae exploding within the hot/dilute bubble maintains a strong termination shock. This strong shock keeps the superbubble over-pressured and drives the outer shock well after it becomes radiative. Isolated supernovae, in contrast, with no further energy injection, become radiative quite early (less than or similar to 0.1Myr, tens of pc), and stall at scales less than or similar to 100 pc. We show that isolated supernovae lose almost all of their mechanical energy by 1 Myr, but superbubbles can retain up to similar to 40 per cent of the input energy in the form of mechanical energy over the lifetime of the star cluster (a few tens of Myr). These conclusions hold even in the presence of realistic magnetic fields and thermal conduction. We also compare various methods for implementing supernova feedback in numerical simulations. For various feedback prescriptions, we derive the spatial scale below which the energy needs to be deposited in order for it to couple to the interstellar medium. We show that a steady thermal wind within the superbubble appears only for a large number (greater than or similar to 10(4)) of supernovae. For smaller clusters, we expect multiple internal shocks instead of a smooth, dense thermalized wind.

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

Positive isotropic curvature and self-duality in dimension 4

We study a positivity condition for the curvature of oriented Riemannian 4-manifolds: the half-PIC condition. It is a slight weakening of the positive isotropic curvature (PIC) condition introduced by M. Micallef and J. Moore. We observe that the half-PIC condition is preserved by the Ricci flow and satisfies a maximality property among all Ricci flow invariant positivity conditions on the curvature of oriented 4-manifolds. We also study some geometric and topological aspects of half-PIC manifolds.

PolyMage: Automatic Optimization for Image Processing Pipelines

This paper presents the design and implementation of PolyMage, a domain-specific language and compiler for image processing pipelines. An image processing pipeline can be viewed as a graph of interconnected stages which process images successively. Each stage typically performs one of point-wise, stencil, reduction or data-dependent operations on image pixels. Individual stages in a pipeline typically exhibit abundant data parallelism that can be exploited with relative ease. However, the stages also require high memory bandwidth preventing effective utilization of parallelism available on modern architectures. For applications that demand high performance, the traditional options are to use optimized libraries like OpenCV or to optimize manually. While using libraries precludes optimization across library routines, manual optimization accounting for both parallelism and locality is very tedious. The focus of our system, PolyMage, is on automatically generating high-performance implementations of image processing pipelines expressed in a high-level declarative language. Our optimization approach primarily relies on the transformation and code generation capabilities of the polyhedral compiler framework. To the best of our knowledge, this is the first model-driven compiler for image processing pipelines that performs complex fusion, tiling, and storage optimization automatically. Experimental results on a modern multicore system show that the performance achieved by our automatic approach is up to 1.81x better than that achieved through manual tuning in Halide, a state-of-the-art language and compiler for image processing pipelines. For a camera raw image processing pipeline, our performance is comparable to that of a hand-tuned implementation.