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Some Effective Properties of the Periodic Structure: a Homogenization Theory Study
Prof. Ying-Hong Liu ( Research Center for Applied Sciences, Academia Sinica )

2008 - 05 - 16 (Fri.)
11:10 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

In this study, we apply the homogenization theory to periodic structures and two main characteristics of that are addressed. First, we investigate band structures of phononic crystals with particular emphasis on the effects of the mass density ratio and of the contrast of elastic constants. It is shown that the density ratio rather than the contrast of elastic constants is the dominant factor that opens up phononic band gaps. Then we aimed to study propagating modes of acoustic wave in periodic solid layers in ideal or viscous fluids. In particular, at long wavelength limit, a three-scale homogenization analysis is developed to derive the effective group velocities in analytical forms for the shear-vertical (SV) as well as for the longitudinal-shear horizontal (P- SH) waves. It is found that propagating modes, i.e., modes with real group velocities may be supported even if the fluid phase is viscous. The physical background of these observations is explained by applying the theory of homogenization to investigate the group velocities of the low-frequency bands at the center of symmetry Γ.

Time:March 7, 2008 - January 31, 2009
Room:
Organizer:I-Liang Chern ( Department of Mathematics, National Taiwan University )

Available Talk List

2008-03-07 (Fri.)		Causality of Wave Propagation (I)
2008-03-14 (Fri.)		Multiscale modeling, asymptotic analysis, and their applications in finance (I,II)
2008-04-11 (Fri.)		Average performance of the sparsest approximation using a dictionary
2008-04-25 (Fri.)		Anomalous Dispersion and Superluminal Propagation
2008-05-09 (Fri.)		Imaging of Multiple Targets in Rician/Rayleigh Fading Media
2008-05-09 (Fri.)		What are networks？
2008-05-16 (Fri.)		Some Effective Properties of the Periodic Structure: a Homogenization Theory Study
2008-05-23 (Fri.)		生物運動力學的若干研究
2008-09-26 (Fri.)		Introduction to Homogenization Theory I, II
2008-10-03 (Fri.)		Two-Scale Convergence and Homogenization of Periodic Structures
2008-10-17 (Fri.)		Homogenization Theory for the Elasticity I, II
2008-10-31 (Fri.)		Memory Effects and Homogenization
2008-11-14 (Fri.)		Maxmizing Band Gaps in 2-D Photonic Crystals
2008-11-21 (Fri.)		What is weak convergence?
2008-11-27 (Thu.)		What is weak convergence?
2008-12-26 (Fri.)		Solving Guided Wave Modes in Plasmonic Crystals
2009-01-09 (Fri.)		Solving Guided Wave Modes in Plasmonic Crystals II
2009-01-16 (Fri.)		Band Gap Optimization for Photonic Crystals -Part I: Introduction
2009-02-20 (Fri.)		Investigation of Transport and Mixing in Microchannel Driven by Capillary Pumping
2009-02-27 (Fri.)		Band Gap Optimization for Photonic Crystals (Part II: Result and Discussion)
2009-03-06 (Fri.)		Analytical solution of electro-osmotic flow in a periodic structure of the filter
2009-03-13 (Fri.)		Homogenization Theory and Its Application
2009-03-20 (Fri.)		Review of achieving transparency with plasmonic and metamaterial coatings
2009-05-01 (Fri.)		Revisiting the aerodynamics of hovering flight using simple models
2009-05-22 (Fri.)		Electro-osmotic flow in a micro-channel with corrugated walls:coherence between the electric potential and the wall shape function
2012-12-05 (Wed.)		SSS