In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and ma...

We analyze the macroscale behavior of random lower (and therefore upper) triangular matrices with entries drawn i.i.d. from a distribution nonzero mean and finite variance. show that such matrix behaves like probabilistic version Riemann sum in limit Volterra operator. Specifically, we certain SOT-like WOT-like modes convergence for to scaled close brief discussion moments.

We present a new general framework for designing multiscale methods. Compared with previous work such as Brandt’s systematic up-scaling, the heterogeneous multiscale method and the “equation-free” approach, this new framework has the distinct feature that it does not require reinitializing the microscale model at each macro time step or each macro iteration step. In the new strategy, the macroa...

In this paper, an upscaling study of solid–fluid combustion in porous medium with homogeneous and heterogeneous heat sources is carried out using a volume averaging theory. For the sake of simplicity, the reaction rate is assumed to be of first-order Arrhenius type and convection is not taken into account. Local thermal non-equilibrium is considered between the solid and fluid phases. During th...

A finite element model based on the layerwise theory is developed for the analysis of transverse cracking in cross-ply laminated beams. The numerical model is developed using the layerwise theory of Reddy, and the von Kármán type nonlinear strain field is adopted to accommodate the moderately large rotations of the beam. The finite element beam model is verified by comparing the present numeric...

Editorial Nanofluids, or fluid suspensions of nanometer-sized structures, are research challenges of rare potential but daunting difficulty. The potential comes from both scientific and practical opportunities in many fields. The difficulty reflects the issues related to multiscales. Nanofluids involve at least four relevant scales: the molecular scale, the microscale, the macroscale, and the s...

The microstructure of a dry alpine snowpack is a dynamic environment where microstructural evolution is driven by seasonal density profiles and weather conditions. Notably, temperature gradients on the order of 10–20 K m, or larger, are known to produce a faceted snow microstructure exhibiting little strength. However, while strong temperature gradients are widely accepted as the primary driver...