Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the Eulerian polynomials and the shifted Eulerian polynomials are moment sequences for a simple family of orthogonal polynomials. The coefficient arrays of these families of orthogonal polynomials are shown to be exponential Riordan arrays. Using the theory of orthogonal polynomials we are then able t...

Subcooled flow boiling in multi-microchannels can be used as an efficient thermal management approach in compact electrical devices. Highly subcooled flow boiling of HFE 7100 is studied in two microchannel heat sinks to choose a proper numerical model for simulating boiling flows in microchannels. Results of five different numerical models, including Volume of Fluid (VOF), Eulerian boiling, Eul...

A poset P is called k-Eulerian if every interval of rank k is Eulerian. The class of k-Eulerian posets interpolates between graded posets and Eulerian posets. It is a straightforward observation that a 2k-Eulerian poset is also (2k+1)-Eulerian. We prove that the ab-index of a (2k+1)Eulerian poset can be expressed in terms of c = a + b, d = ab + ba and e2k+1 = (a − b)2k+1. The proof relies upon ...

Abstract In this paper, we explore the interrelationship between Eulerian numbers and B splines. Specifically, using B splines, we give the explicit formulas of the refined Eulerian numbers, and descents polynomials. Moreover, we prove that the coefficients of descent polynomials D d (t) are logconcave. This paper also provides a new approach to study Eulerian numbers and descent polynomials.

A novel 3D computational model was developed for the turbulent particulate two-phase flow simulation in rectangular channel. The is based on Eulerian approach applied to Reynolds-averaged Navier–Stokes modeling and statistical Probability Distribution Function method. uniqueness of method lies direct calculation normal transverse components Reynolds stresses both gas particles. Two cases were e...

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 ...

In this research the separation efficiency of deoiling hydrocyclone is evaluated using three-dimensional simulation of multiphase flow based on Eulerian-Eulerian finite volume method. The mixture approach of Reynolds Stress Model is also employed to capture the features of turbulent multiphase swirling flow. The obtained separation efficiency of Colman's design is compared with available experi...