By means of Monte Carlo simulations and a finite-size scaling analysis, we find a critical line of an n-component Eulerian face-cubic model on the square lattice and the simple cubic lattice in the region v>1, where v is the bond weight. The phase transition belongs to the Ising universality class independent of n. The critical properties of the phase transition can also be captured by the perc...

A Lagrangian-Eulerian numerical scheme for the investigation of bubble motion in turbulent flow is developed. The flow is analyzed in the Eulerian reference frame while the bubble motion is simulated in the Lagrangian one. Finite volume scheme is used, and SIMPLEC algorithm is utilized for the pressure and velocity linkage. The Reynolds stresses are modeled by the RSTM model of Launder. Upwind ...

Labeled graphs, in which edges are labeled by letters from some alphabet Σ, are extensively used to model many types of relations associated with actions, costs, owners, or other properties. Each path in a labeled graph induces a word in Σ∗ – the one obtained by concatenating the letters along the edges in the path. Classical graph-theory problems give rise to new problems that take these words...

This paper deals with parameter identification for traffic models. Two fundamentally different approaches are presented, which are combined to the best advantage. With Eulerian sensing the sensors are spatially stationary, i.e. fixed in place, while with Lagrangian sensing the sensors move with the traffic flow as sensor-vehicles. We present a method to identify model parameters from both metho...

In this article, we generalize the concepts of Eulerian and Hamiltonian digraphs to directed hypergraphs. A dihypergraph H is a pair (V(H), E(H)), where V(H) is a non-empty set of elements, called vertices, and E(H) is a collection of ordered pairs of subsets of V(H), called hyperarcs. It is Eulerian (resp. Hamiltonian) if there is a dicycle containing each hyperarc (resp. each vertex) exactly ...

In this paper we consider mixed volumes of combinations of hypersimplices. These numbers, called “mixed Eulerian numbers”, were first considered by A. Postnikov and were shown to satisfy many properties related to Eulerian numbers, Catalan numbers, binomial coefficients, etc. We give a general combinatorial interpretation for mixed Eulerian numbers and prove the above properties combinatorially...