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In this paper, the influence of different dimensionless distance on heat transfer characteristics in a rectangular enclosure is studied using lattice Boltzmann method (LBM). It is shown that the relation between the Rayleigh number (Ra) and the Nusselt number (Nu) using LBM is in promising agreement with that of the previous experimental data by Corvaro and Paroncini [Appl. Therm. Eng.28 (2007) 25]. It is found that the characteristic of heat transport is closely related to the dimensionless distance of heat source. Special attention is paid to investigate the relation between Ra and Nu. Some relations between Ra and Nu for different dimensionless distance are approximately established in natural convection. It is further found that the heat transport is enhanced with the increase of dimensionless distance.

Averaging-normalization, applied to weakly nonlinear wave equations provides a tool for identification of slow manifolds in these infinite-dimensional systems. After discussing the general procedure we demonstrate its effectiveness for a Rayleigh wave equation to find low-dimensional invariant manifolds.

Having long been the realm of molecular chemistry, astronomy, and plasma diagnostics, the upper millimeter-wave band (∼100 to 300 GHz) and the THz region above it have recently become the subject of heightened activity in the engineering community because of exciting new technology (e.g., sub-picosecond optoelectronics) and promising new “terrestrial” applications (e.g., counter-terrorism and medical imaging). The most challenging of these applications are arguably those that demand remote sensing at a stand-off of roughly 10 m or more between the target and the sensor system. As in any other spectral region, remote sensing in the THz region brings up the complex issues of sensor modality and architecture, free-space electromagnetic effects and components, transmit and receive electronics, signal processing, and atmospheric propagation. Unlike other spectral regions, there is not much literature that addresses these issues from a conceptual or system-engineering viewpoint. So a key theme of this chapter is to review or derive the essential engineering concepts in a comprehensive fashion, starting with fundamental principles of electromagnetics, quantum mechanics, and signal processing, and building up to trade-off formulations using system-level metrics such as noiseequivalent power and receiver operating characteristics. A secondary theme is to elucidate aspects of the THz region and its incumbent technology that are unique, whether advantageous or disadvantageous, relative to other spectral regions. The end goal is to provide a useful tutorial for graduate students or practicing engineers considering the upper mm-wave or THz regions for system research or development.