We develop in this paper a moving mesh spectral method for the phase-field model of twophase flows with non-periodic boundary conditions. The method is based on a variational moving mesh PDE for the phase function, coupled with efficient semi-implicit treatments for advancing the mesh function, the phase function and the velocity and pressure in a decoupled manner. Ample numerical results are p...

The dispersion relation is derived for the most general configuration of a passive and reciprocal periodically loaded transmission line in a unique and simple form by introducing two novel parameters. Based on this relation, the phase and group velocities are determined and a simple condition for phase reversal propagation is obtained. The two above mentioned parameters help us to develop a pol...

The aim of upscaling is to determine equivalent homogeneous parameters at a coarse-scale from a spatially oscillating fine-scale parameter distribution. A large variety of upscaling methods is available, among which the homogenization method plays an important role. This paper presents an extension of the classical homogenization method to nonlinear problems as they occur while upscaling parame...

In this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory. MSC 2010 : Primary 34B15; Secondary 34B45

*Correspondence: [email protected] 2School of Mathematics and Computer, Gannan Normal University, Ganzhou, 341000, China Full list of author information is available at the end of the article Abstract In this paper we present some new examples in cone b-metric spaces and prove some fixed point theorems of contractive mappings without the assumption of normality in cone b-metric spaces. The res...