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Liquid-liquid-solid systems are becoming increasingly common in everyday life with many possible applications. Here, we focus on a special case of such liquid-liquid-solid systems, namely, capillary suspensions. These capillary suspensions originate from particles that form a network based on capillary forces and are typically composed of solids in a bulk liquid with an added secondary liquid. The structure of particle networks based on capillary bridges possesses unique properties compared with networks formed via other attractive interactions where these differences are inherently related to the properties of the capillary bridges, such as bridge breaking and coalescence between adjacent bridges. Thus, to tailor the mechanical properties of capillary suspensions to specific requirements, it is important to understand the influences on different length scales ranging from the dynamics of the bridges with varying external stimuli to the often heterogeneous network structure. 相似文献
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《Discrete Mathematics》2022,345(1):112659
In a recent paper, Gerbner, Patkós, Tuza and Vizer studied regular F-saturated graphs. One of the essential questions is given F, for which n does a regular n-vertex F-saturated graph exist. They proved that for all sufficiently large n, there is a regular -saturated graph with n vertices. We extend this result to both and and prove some partial results for larger complete graphs. Using a variation of sum-free sets from additive combinatorics, we prove that for all , there is a regular -saturated with n vertices for infinitely many n. Studying the sum-free sets that give rise to -saturated graphs is an interesting problem on its own and we state an open problem in this direction. 相似文献
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Dong Zhang 《Discrete Mathematics》2018,341(1):25-32
In this paper, we reveal the connection between the independent number of a graph and the topological multiplicity of the maximal eigenvalue of the corresponding graph 1-Laplacian. The pseudo independent number of a graph is introduced, which provides a better lower estimate of the topological multiplicity of the maximum eigenvalue. The technique of our proof is based on the localization property of the eigenvector for graph 1-Laplacian, the Krasnoselski genus, and its relation to the topological join. 相似文献
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Palle E.T. Jorgensen Erin P.J. Pearse 《Journal of Mathematical Analysis and Applications》2019,469(2):765-807
Motivated by applications to machine learning, we construct a reversible and irreducible Markov chain whose state space is a certain collection of measurable sets of a chosen l.c.h. space . We study the resulting network (connected undirected graph), including transience, Royden and Riesz decompositions, and kernel factorization. We describe a construction for Hilbert spaces of signed measures which comes equipped with a new notion of reproducing kernels and there is a unique solution to a regularized optimization problem involving the approximation of functions by functions of finite energy. The latter has applications to machine learning (for Markov random fields, for example). 相似文献
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We describe a unified approach for studying book, point-set, and simultaneous embeddability problems of upward planar digraphs. The approach is based on a linear time strategy to compute an upward planar drawing of an upward planar digraph such that all vertices are collinear. Besides having impact in relevant application domains of graph drawing and computational geometry, the presented results open new research directions in the area of upward planarity with constraints of the positions of the vertices. 相似文献