A speckle-shearing interferometer: A tool for measuring derivatives of surface displacements

A speckle-shearing interferometer is developed using a sheared Michelson interferometer. The tool, like speckle interferometry, utilizes the speckle effect of coherent light. However, while speckle interferometry measures surface displacements, the speckle-shearing interferometer determines the derivatives of the surface displacements. Hence, it eliminates the necessity of differentiating the measured displacements to obtain strain.     

Derivation of the Euler Equations from Quantum Dynamics

We derive the Euler equations from quantum dynamics for a class of fermionic many-body systems. We make two types of assumptions. The first type are physical assumptions on the solution of the Euler equations for the given initial data. The second type are a number of reasonable conjectures on the statistical mechanics and dynamics of the Fermion Hamiltonian.©2003 B. Nachtergaele and H.-T. Yau. This article may be reproduced in its entirety for non-commercial purposes.Research partially supported by NSF # DMS-0070774.Research partially supported by NSF # DMS-0072098, the Veblen Fund from the Institute for Advanced Study and a Fellowship from the MacArthur Foundation.     

Amphoteric refraction exhibited by anisotropic crystals

Amphoteric refraction of light ray at the interface between isotropic materials and anisotropic materials is analyzed. Depending on the incident angle, the refractive light ray can either refract positively or negatively. This amphoteric refraction phenomenon can be quite prevalent when the difference of the two principal refractive indices is large. The reflectance under various incident angles has also been calculated, and an experimental demonstration with a calcite crystal in air is presented.     

Bulk universality for Wigner matrices

We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e^?U(x). We prove that the eigenvalue statistics in the bulk are given by the Dyson sine kernel provided that U ∈ C⁶( \input amssym $\Bbb R$ ) with at most polynomially growing derivatives and ν(x) ≥ Ce^?C|x| for x large. The proof is based upon an approximate time reversal of the Dyson Brownian motion combined with the convergence of the eigenvalue density to the Wigner semicircle law on short scales. © 2010 Wiley Periodicals, Inc.     

Mutually pumped phase conjugator using a BaTiO3 crystal having two inclined faces

A pentagon-shaped undoped BaTiO₃ crystal was used to construct a high-quality mutually pumped phase conjugator. It yields two very stable phase-conjugate outputs (ǃ.7% fluctuation in intensity) with high reflectivity (the highest ᅝ%) when the two incident beams are of equal intensities. The response time of the conjugator is rather fast (ƻ s) and the tolerance of the acceptance angle is large too (걄°). Fine structures (35 7m) in an image, after passing through a phase aberrator, can be recovered by the conjugate waves yielded by this conjugator.     

Fundamentals of Computational Conformal Geometry

Computational conformal geometry is an inter-disciplinary field between mathematics and computer science. This work introduces the fundamentals of computational conformal geometry, including theoretic foundation, computational algorithms, and engineering applications. Two computational methodologies are emphasized, one is the holomorphic differentials based on Riemann surface theory and the other is surface Ricci flow from geometric analysis.     

Early cure behavior of a liquid dicyanate ester resin

The early cure behavior of 4,4‐dicyanato 1,1‐diphenolethane resin with and without incorporating Cr(acac)₃, Co(acac)₃, and Cu(acac)₂, respectively, as catalysts was investigated by gel permeation chromatography. The curing intermediates were separated by the column elution method and characterized by Fourier transform infrared, ¹H, and ³C NMR spectroscopies. The results indicated that the formed dimer in the early cure stage is a straight chain containing a primary amino group. The formed triazine ring in the trimer has a strong catalytic effect on the remaining cyanate groups so that the reactivity of the trimers was significantly increased. The reactivities of the curing intermediates decreased with molecular size until 7‐mer was reached. The initial monomer consumption is described by second‐order‐rate kinetics. In the presence of metal acetylacetonates, the curing reactions may be accelerated, but they did not change the reaction path and preceding sequence of reactivities. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3085–3092, 2001