1,265 research outputs found

    Line Patterns in Free Groups

    Full text link
    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

    Get PDF
    对于图GG,如果G;FG -; F是不连通的且至少有两个分支含有圈,则称FF为图GG的圈边割.如果图GG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GG为超圈边连通的.设G=(G1,G2,(;V1,V2))G = \left( {{G_1},{G_2},\left(; {{V_1},{V_2}} \right)} \right)为双轨道图,最小度δ(G);4\delta \left( G \right) \ge; 4,围长g(G)6g\left( G \right) \ge 6V1=V2;\left| {{V_1}} \right| = \left| {{V_2}}; \right|.假设Gi{G_i}ki{k_i}-正则的,k1;k2{k_1} \le; {k_2}G1{{G_1}}包含一个长度为gg的圈,则GG是超圈边连通的.For a graph GG, an edge set FF is a cyclic edge-cut if (GFG - F) is; disconnected and at least two of its components contain cycles. If GG; has a cyclic edge-cut, it is said to be cyclically separable. The cyclic; edge-connectivity is cardinality of a minimum cyclic edgecut of GG. A; graph is super cyclically edge-connected if removal of any minimum; cyclic edge-cut makes a component a shortest cycle. Let G=(;G1,G2,(V1,V2))G = \left(; {{G_1},{G_2},\left( {{V_1},{V_2}} \right)} \right) be a doubleorbit; graph with minimum degree δ(G)4\delta \left( G \right) \ge 4, girth g;6g \ge; 6 and V1=V2\left| {{V_1}} \right| = \left| {{V_2}} \right|. Suppose; Gi{G_i} is ki{k_i}-regular, k1k2{k_1} \le {k_2} and G1{{G_1}} contains a; cycle of length gg, then GG is super cyclically edge connected.国家自然科学基金资助项

    A Scalable Lagrangian Particle Tracking Method

    Get PDF
    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
    corecore