Elasticity Equations with High Contrast Parameters

This chapter presents some recent results on the elasticity equations with high contrast coefficients. It first sets up the problems for finite and extreme moduli before discussing the incompressible limit of elasticity equations. It then provides a complete asymptotic expansion with respect to the compressional modulus and considers the limiting cases of holes and hard inclusions. It proves that the energy functional is uniformly bounded and demonstrates that the potentials on the boundary of the inclusion are also uniformly bounded. It also shows that these potentials converge as the bulk and shear moduli tend to their extreme values and that similar boundedness and convergence result holds true for the boundary value problem.

Improved Green’s functions for passive-source structural studies

Over the past two decades, teleseismic receiver functions have proved to be a useful tool to investigate crustal structure. Because they represent a first-order approximation to the [Formula: see text]-wave component of the teleseismic-[Formula: see text] Green’s function, receiver functions provide valuable information on physical properties related to shear modulus. However, the implicit use of the [Formula: see text]-component seismogram as a proxy for the source precludes the recovery of information on discontinuous structure involving contrasts in compressional modulus. By deconvolving improved estimates of complex source time functions generated by earthquakes, one may move beyond the conventional receiver function paradigm to a more accurate approximation of the earth’s Green’s function. Using a new deconvolution method, we present estimates of the [Formula: see text]-component of the teleseismic-[Formula: see text] Green’s functions at several stations of the Canadian National Seismic Network (CNSN) that clearly show the receiver-side pure [Formula: see text]-wave crustal multiple. The identification and characterization of these signals in studies of the lithosphere will afford better constraints on subsurface lithology and represent a narrowing of the gap between active- and passive-source seismic imaging.

Scanning Probe Microscope Study of Mixed Chain-Length Phase-Segregated Langmuir-Blodgett Monolayers

ABSTRACTUsing a scanning probe microscope, the influence of adhesion on measured film height of mixed-chain-length fatty acid Langmuir-Blodgett monolayers was investigated. A 1:1 mixture of CH3[CH2]22COOH and CH3[CH2]14COOH, was deposited in which the long chain-length acid, C24, was segregated from the short chain-length acid, C16. Two experiments were performed, contact scanning and force curve mapping. From both experiments, the film height difference measured between the C16 and C24 regions was larger than expected. Adhesion of the tip was 20% larger over the C16 acid regions. Using a compressional modulus derived from film pressure vs. area isotherms of the pure components, the adhesion difference and apparent filmheight difference over the two regions can be understood.