1,265 research outputs found
Line Patterns in Free Groups
We study line patterns in a free group by considering the topology of the
decomposition space, a quotient of the boundary at infinity of the free group
related to the line pattern. We show that the group of quasi-isometries
preserving a line pattern in a free group acts by isometries on a related space
if and only if there are no cut pairs in the decomposition space.Comment: 35 pages, 22 figures, PDFLatex; v2. finite index requires extra
hypothesis; v3. 37 pages, 24 figures: updated references and add example in
Section 6.3 of a rigid pattern for which the free group is not finite index
in the group of pattern preserving quasi-isometries; v4. 40 pages, 26
figures: improved exposition and add example in Section 6.4 of a rigid
pattern whose cube complex is not a tre
Super cyclically edge connected graphs with two orbits of the same size
对于图,如果是不连通的且至少有两个分支含有圈,则称为图的圈边割.如果图有圈边割,则称其为圈可分的.最小圈边割的基数叫作圈边连通度.如果; 去除任何一个最小圈边割,总存在一分支为最小圈,则图为超圈边连通的.设为双轨道图,最小度,围长且.假设是-正则的,且包含一个长度为的圈,则是超圈边连通的.For a graph , an edge set is a cyclic edge-cut if () is; disconnected and at least two of its components contain cycles. If ; has a cyclic edge-cut, it is said to be cyclically separable. The cyclic; edge-connectivity is cardinality of a minimum cyclic edgecut of . A; graph is super cyclically edge-connected if removal of any minimum; cyclic edge-cut makes a component a shortest cycle. Let be a doubleorbit; graph with minimum degree , girth and . Suppose; is -regular, and contains a; cycle of length , then is super cyclically edge connected.国家自然科学基金资助项
A Scalable Lagrangian Particle Tracking Method
Particle tracking within an underlying flow field is routinely used to analyse both industrial processes and natural phenomena. In a computer code running on a distributed-memory architecture, the different behaviour of fluid-particle systems must be taken into account to properly balance element-particle subdivision among processes. In unsteady simulations, the parallel efficiency is even more critical because it changes over time. Another challenging aspect of a scalable implementation is the initial particle location due to the arbitrary shapes of each subdomain. In this work, an innovative parallel ray tracing particle location algorithm and a two-constrained domain subdivision are presented. The former takes advantage of a global identifier for each particle, resulting in a significant reduction of the overall communication among processes. The latter is designed to mitigate the load unbalance in the particles evolution while maintaining an equal element distribution. A preliminary particle simulation is performed to tag the cells and compute a weight proportional to the probability to be crossed. The algorithm is implemented using MPI distribute memory environment. A cloud droplet impact test case starting from an unsteady flow around a 3D cylinder has been simulated to evaluate the code performances. The tagging technique results in a computational time reduction of up to 78% and a speed up factor improvement of 44% with respect to the common flow-based domain subdivision. The overall scalability is equal to 1.55 doubling the number of cores
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