Static mapping is the assignment of parallel processes to the processing elements (PEs) of a parallel system, where the assignment does not change during the application's lifetime. In our scenario we model an application's computations and their dependencies by an application graph. This graph is first partitioned into (nearly) equally sized blocks. These blocks need to communicate at block boundaries. To assign the processes to PEs, our goal is to compute a communication-efficient bijective mapping between the blocks and the PEs. This approach of partitioning followed by bijective mapping has many degrees of freedom. Thus, users and developers of parallel applications need to know more about which choices work for which application graphs and which parallel architectures. To this end, we not only develop new mapping algorithms (derived from known greedy methods). We also perform extensive experiments involving different classes of application graphs (meshes and complex networks), architectures of parallel computers (grids and tori), as well as different partitioners and mapping algorithms. Surprisingly, the quality of the partitions, unless very poor, has little influence on the quality of the mapping. More importantly, one of our new mapping algorithms always yields the best results in terms of the quality measure maximum congestion when the application graphs are complex networks. In case of meshes as application graphs, this mapping algorithm always leads in terms of maximum congestion and maximum dilation, another common quality measure. (a) (b) c e (c) Fig. 1. (a) Application graph Ga with 4-way partition indicated by colors. (b) Communication graph Gc induced by Ga and the partition. Gc expresses the neighborhood relations of Ga's blocks. Edge weights (shown through width) indicate communication volumes between blocks. (c) Processor graph Gp. Nodes and edges represent the PEs and the communication links, respectively. Communication between the green and the red block in Gc, i. e. via ec, requires two hops in Gp.Motivation. Communication costs are crucial for the scalability of many parallel applications. Static mapping, in turn, is crucial when it comes to keeping communication costs under control through (i) providing a partitioning with few edges between blocks and (ii) mapping nearby blocks onto nearby PEs: due to the sparse nature of many large-scale parallel computers, communication costs may vary by several orders of magnitude depending on the distance between the PEs involved [2]. Also, numerous recent applications involve massive complex networks such as social networks or web graphs [3]. These networks usually lead to denser communication graphs and make improved mapping strategies even more desirable. Contribution. We investigate numerous algorithms for static mapping, the scenario being that an application graph is first partitioned into blocks, followed by a bijective mapping of the blocks onto the nodes of a processor graph. The graph partitioners we employ are the state-of-the-art packages M...

Submitted for the DFD11 Meeting of The American Physical Society Pore-scale Analysis of the effects of Contact Angle Hysteresis on Blob Mobilization in a Pore Doublet SHAO-YIU HSU, ROLAND GLANTZ, MARKUS HILPERT, Johns Hopkins University-The mobilization of residual oil blobs in porous media is of major interest to the petroleum industry. We studied the Jamin effect, which hampers the blob mobilization, experimentally in a pore doublet model and explain the Jamin effect through contact angle hysteresis. A liquid blob was trapped in one of the tubes of the pore doublet model and then subjected to different pressure gradients. We measured the contact angles (in 2D and 3D) as well as the mean curvatures of the blob. Due to gravity effects and hysteresis, the contact angles of the blob were initially (zero pressure gradient) nonuniform and exhibited a pronounced altitude dependence. As the pressure gradient was increased, the contact angles became more uniform and the altitude dependence of the contact angle decreased. At the same time, the mean curvature of the drainage interface increased, and the mean curvature of the imbibition interface decreased. The pressure drops across the pore model, which we inferred with our theory from the measured contact angles and mean curvatures, were in line with the directly measured pressure data. We not only show that a trapped blob can sustain a finite pressure gradient but also develop methods to measure the contact angles and mean curvatures in 3D.

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