This paper deals with the implementation of an efficient Arbitrary Lagrangian Eulerian (ALE) formulation for the three dimensional finite element modeling of mode I self-similar dynamic fracture process. Contrary to the remeshing technique, the presented algorithm can continuously advance the crack with the one mesh topology. The uncoupled approach is employed to treat the equations. So, each t...

A graded partially ordered set is Eulerian if every interval has the same number of elements of even rank and of odd rank. Face lattices of convex polytopes are Eulerian. For Eulerian partially ordered sets, the flag vector can be encoded efficiently in the cd-index. The cd-index of a polytope has all positive entries. An important open problem is to give the broadest natural class of Eulerian ...

In this paper, we evaluate the number of Eulerian circuits that can be obtained by an arbitrary rotation in a Markovian string, i.e., corresponding to a given Markovian type. Since all rotations do not result in an Eulerian circuit, but several of them, called Eulerian components; we also investigate the number of Eulerian components that result from a random rotation in a Markovian string. We ...

Any bipartite Eulerian graph, any Eulerian graph with evenly many vertices, and any bipartite graph with evenly many vertices and edges, has an even number of spanning trees. More generally, a graph has evenly many spanning trees if and only if it has an Eulerian edge cut. ∗Work supported in part by NSF grant CCR-9258355 and by matching funds from Xerox Corp.

The main goal of this work is to establish a bijection between Dyck words and a family of Eulerian digraphs. We do so by providing two algorithms implementing such bijection in both directions. The connection between Dyck words and Eulerian digraphs exploits a novel combinatorial structure: a binary matrix, we call Dyck matrix, representing the cycles of an Eulerian digraph. 1. Background, and ...