tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Let (s n) be a real sequence, let (σ n) denote the sequence of averages of its first n partial sums. Let lim sup n σ n = β and lim inf n σ n = α, where β = α. We prove that lim sup n s n = β and lim inf n s ...

In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-GrossKrook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improveme...

In recent years, multiphase PWMs have been proposed because of their increased efficiency, reduced torque pulsation, improved fault tolerance, and lower power handling requirement by adopting multiphase machines. In the digital implementation, multiphase reference voltages are sampled and fed into the digital modulator to produce gating signals at a constant clock rate f. This means a finite pu...

In this paper we discuss upscaling of immiscible multiphase and miscible multicomponent flow and transport in heterogeneous porous media. The discussion presented in the paper summarizes the results of in Upscaled Modeling in Multiphase Flow Applications by Ginting et al. (2004) and in Upscaling of Multiphase and Multicomponent Flow by Ginting et al. (2006). Perturbation approaches are used to ...

The modern queueing theory is one of the powerful tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. In this paper, we deal with approximations of multiphase queueing systems (tandem queues, queues in series). Multiphase queueing systems are of special interest both in theory and in practical a...

This paper presents a Buckley-Leverett analytical solution for non-Darcy displacement of two immiscible fluids in porous media. The multiphase non-Darcy displacement is described using a Forchheimer equation or other non-Darcy flow correlations under multiphase flow conditions. The analytical solution is used to obtain some insight into the physics of displacement involving non-Darcy flow effec...

A multiphase nanostructured ZrCu-base bulk alloy which showed a unique microstructure consisting of sub-micrometer scale Zr₂Cu solid solution, nano-sized twinned plate-like ZrCu martensite (ZrCu (M)), and retained ZrCu (B2) austenite was fabricated by copper mold casting. The observation of periodic morphology evolution on the fracture surface of the multiphase nanostructured ZrCu-base alloys h...

The interest in multiphase machines for high performance applications has been growing in recent years due to their potential advantages over three-phase machines. One of the possibilities of taking advantage of the additional degrees of freedom that exist in multiphase machines is the series connection of several multiphase machines, with the supply coming from a single multiphase inverter. Th...