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...

An interatomic potential based semiclassical theory is proposed to predict the concentration and potential profiles of a Lennard-Jones (LJ) fluid confined in a channel. The inputs to the semiclassical formulation are the LJ parameters of the fluid and the wall, the density of channel wall atoms, and the average concentration of the fluid inside the channel. Using the semiclassical formulation, ...

This paper presents the design and implementation of velocimetry techniques applicable to the analysis of microfluidic systems. The application of both micronresolution particle image velocimetry (micro-PIV) and particle tracking velocimetry (PTV) to the measurement of velocity fields within micromachined fluidic channels is presented. The particle tracking system uses epifluorescent microscopy...

Understanding how landscapes respond to climate dynamics in terms of macroscale (average topographic features) and microscale (landform reorganization) is of interest both for deciphering past climates from today’s landscapes and for predicting future landscapes in view of recent climatic trends. Although several studies have addressed macro-scale response, only a few have focused on quantifyin...

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.

Topological phononics offers numerous opportunities in manipulating elastic waves that can propagate solids without being backscattered. Due to the lack of nanoscale imaging tools aid system design, however, acoustic topological metamaterials have been mostly demonstrated macroscale systems operating at low (kilohertz megahertz) frequencies. Here, we report realization gigahertz valley Hall eff...

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...