The spatial dependence of Lagrangian displacement and velocity statistics is studied in the context of a data assimilating numerical model of the Gulf Mexico. In the active eddy region of the Western Gulf, a combination of Eulerian and Lagrangian measures are used to locate strongly hyperbolic regions of the flow. The statistics of the velocity field sampled by sets of drifters launched specifi...

Arbitrary Lagrangian Eulerian (ALE) methods have existed for several decades. However, three-dimensional multi-material arbitrary Lagrangian Eulerian (MMALE) methods for unstructured grids are relatively new. MMALE algorithms provide the framework to model sections of a simulation as either Lagrangian, ALE, or Eulerian. In addition, sections of a simulation can switch in time between mesh motio...

Let G = (V, A) be an Eulerian directed graph with an arclabeling. In this work we study the problem of finding an Eulerian circuit of lexicographically minimal label among all Eulerian circuits of the graph. We prove that this problem is NP-hard by showing a reduction from the Directed-Hamiltonian-Circuit problem. If the labeling of the arcs is such that arcs going out from the same vertex have...

Stembridge, J.R., Eulerian numbers, tableaux, and the Betti numbers of a toric variety, Discrete Mathematics 99 (1992) 307-320. Let Z denote the Coxeter complex of S,, and let X(X) denote the associated toric variety. Since the Betti numbers of the cohomology of X(Z) are Eulerian numbers, the additional presence of an &-module structure permits the definition of an isotypic refinement of these ...

In this thesis we consider two sets of combinatorial structures defined on an Eulerian graph: the Eulerian orientations and Euler tours. We are interested in the computational problems of counting (computing the number of elements in the set) and sampling (generating a random element of the set). Specifically, we are interested in the question of when there exists an efficient algorithm for cou...