Chordal graphs are the graphs in which every cycle of length at least four has a chord. A set S is a vertex separator for vertices a and b if the removal of S of the graph separates a and b into distinct connected components. A graph G is chordal if and only if every minimal vertex separator is a clique. We study subclasses of chordal graphs defined by restrictions imposed on the intersections ...

Porous polypropylene (PP) is commonly used as separator materials for lithium ion batteries (LIB). Its mechanical properties, especially critical for abuse tolerance and durability of LIB, are subject to change in different environments. To capture the mechanical responses of a porous PP separator, its microstructure was mapped into separate atomistic models of bulk crystalline phases and orien...

In this paper, a novel light separator with contrast ratio enhancement but maintaining the optical efficiency of the DLP projection system is proposed. The main capability of the novel light separator is to direct the uncontrolled light away from the image system. The working theorem for the novel light separator is derived as well. Uncontrolled light is kept away from the image system by a tot...

The objectives of this experiment were to determine a NE value for pressed beet pulp and the value of concentrated separator by-product (de-sugared molasses) as a ruminal N source in growing and finishing diets for beef cattle. One hundred forty-four cross-bred beef steers (282 +/- 23 kg of initial BW) were used in 2 experiments (growing and finishing). A randomized complete block design was us...

We perform compressive tests of polypropylene battery separator in

This thesis deals with the multi-terminal vertex separator problem. Given a graph G = (V ∪T,E) with V ∪T the set of vertices, where T is a set of terminals, and a weight function w : V → Z, associated with nonterminal nodes, the multi-terminal vertex separator problem consists in partitioning V ∪T into k+1 subsets {S, V1, . . . , Vk} such that there is no edge between two different subsets Vi a...

We develop a new method for deriving a geometric separator for a set of grid points. Our separator has a linear structure, which can effectively partition a grid graph. For example, we prove that for a grid graph G with a set of n points P in a two-dimensional grid, there is a separator with at most 1.129 √ n points in P that partitions G into two disconnected grid graphs each with at most 2n 3...

G. A. Dirac characterized chordal graphs as those in which minimal vertex separators always induce complete subgraphs. I generalize a traditional (2-)vertex separator to a k-vertex separator — meaning a set S of vertices whose removal puts k independent vertices into k separate components. Generalizing Dirac’s theorem, the {P5, 2P3}-free chordal graphs are the graphs in which minimal k-separato...

For undirected graphs G (V, E) and G0 (V0 , E0), say that G is a region intersection graph over G0 if there is a family of connected subsets {Ru ⊆ V0 : u ∈ V} of G0 such that {u , v} ∈ E ⇐⇒ Ru ∩ Rv , ∅. We show if G0 excludes the complete graph Kh as a minor for some h > 1, then every region intersection graph G over G0 with m edges has a balanced separator with at most ch √ m nodes, where ch i...

The characteristics of fluid flow and phase separation in an oil-water separator were numerically analysed as part of the work presented herein. Simulations were performed for different velocities and droplet diameters, and the way this parameters can influence the separator geometry was studied. The simulations were carried out using the software package Fluent 6.2, which is designed for numer...