Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function -- the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough.Comment: 12 page

Latent image diffraction from submicron photoresist gratings

Light scattering from latent images in photoresist is useful for lithographic tool characterization, process monitoring, and process control. In particular, closed‐loop control of lithographic processes is critical for high yield, low cost device manufacturing. In this work, we report use of pulsed laser diffraction from photoresist latent images in 0.24 μm pitch distributed feedback laser gratings. Gated detection of pulsed light scattering permits high spatial resolution probing using ultraviolet light without altering the latent image. A correlation between latent image and etched grating diffraction efficiencies is demonstrated and shows the value of "upstream" monitoring

New Hamiltonian formalism and quasi-local conservation equations of general relativity

I describe the Einstein's gravitation of 3+1 dimensional spacetimes using the (2,2) formalism without assuming isometries. In this formalism, quasi-local energy, linear momentum, and angular momentum are identified from the four Einstein's equations of the divergence-type, and are expressed geometrically in terms of the area of a two-surface and a pair of null vector fields on that surface. The associated quasi-local balance equations are spelled out, and the corresponding fluxes are found to assume the canonical form of energy-momentum flux as in standard field theories. The remaining non-divergence-type Einstein's equations turn out to be the Hamilton's equations of motion, which are derivable from the {\it non-vanishing} Hamiltonian by the variational principle. The Hamilton's equations are the evolution equations along the out-going null geodesic whose {\it affine} parameter serves as the time function. In the asymptotic region of asymptotically flat spacetimes, it is shown that the quasi-local quantities reduce to the Bondi energy, linear momentum, and angular momentum, and the corresponding fluxes become the Bondi fluxes. The quasi-local angular momentum turns out to be zero for any two-surface in the flat Minkowski spacetime. I also present a candidate for quasi-local {\it rotational} energy which agrees with the Carter's constant in the asymptotic region of the Kerr spacetime. Finally, a simple relation between energy-flux and angular momentum-flux of a generic gravitational radiation is discussed, whose existence reflects the fact that energy-flux always accompanies angular momentum-flux unless the flux is an s-wave.Comment: 36 pages, 3 figures, RevTex

Photoluminescence from Si nanocrystals exposed to a hydrogen plasma

Si nanocrystals embedded in SiO₂films were exposed to an atomic H plasma at different temperatures. Photoluminescence intensity from the nanocrystals increases with increasing exposure time, followed by saturation that depends on the exposure temperature. The saturation level depends on the final exposure temperature and shows no dependence on the thermal history of exposure. This behavior is shown to be consistent with a model in which the steady-state passivation level is determined by a balance between defect passivation and depassivation by H, with the activation energy for the passivationreaction being larger than that for the depassivation reaction.This work was supported by Research Institute for Basic Science at Kangwon National University

Does noncommutative geometry predict nonlinear Higgs mechanism?

It is argued that the noncommutative geometry construction of the standard model predicts a nonlinear symmetry breaking mechanism rather than the orthodox Higgs mechanism. Such models have experimentally verifiable consequences.Comment: 12 pages, LaTeX file, BI-TP 93/2

An eigenmode analysis of time delays in an acoustically coupled multi-bubble system

The acoustic properties of an inhomogeneous bubbly medium are complex owing to the absorption and re-emission of acoustic energy by the bubbles. This phenomena can be approximated by a globally coupled system of linear oscillators. In previous studies, it has been shown that this simple model can produce results that are in qualitative agreement with experimental data. In order to achieve better quantitative agreement with experimental data, time-delays need to be introduced into the mathematical model. In the present study, the resulting delayed differential equations were solved numerically using a 4th order Runge-Kutta method. The numerical methodology was validated by comparing simplified cases with the solution using analytical methods. The effects of time-delay were assessed by comparing non-timedelayed and time-delayed versions of the mathematical model. Results from numerical simulations were then compared to assess the effects and importance of the inclusion of time-delay in the mathematical model. This study shows that the inclusion of time-delay has a noticeable effect on the lower frequency modes of the model. This effect propagates to the higher frequency modes as the magnitude of the time-delay increases. The results also shows that the time-delay shifts the dominant modes from the lower frequency modes to the higher frequency mode

Instability driven fragmentation of nanoscale fractal islands

Formation and evolution of fragmentation instabilities in fractal islands, obtained by deposition of silver clusters on graphite, are studied. The fragmentation dynamics and subsequent relaxation to the equilibrium shapes are controlled by the deposition conditions and cluster composition. Sharing common features with other materials' breakup phenomena, the fragmentation instability is governed by the length-to-width ratio of the fractal arms.Comment: 5 pages, 3 figures, Physical Review Letters in pres

Hidden Local Symmetry and Infinite Tower of Vector Mesons for Baryons

In an effort to access dense baryonic matter relevant for compact stars in a unified framework that handles both single baryon and multibaryon systems on the same footing, we first address a holographic dual action for a single baryon focusing on the role of the infinite tower of vector mesons deconstructed from five dimensions. To leading order in 't Hooft coupling $\lambda=N_c g_{\rm YM}^2$, one has the Bogomol'nyi-Prasad-Sommerfield (BPS) Skyrmion that results when the warping of the bulk background and the Chern-Simons term in the Sakai-Sugimoto D4/D8-${\bar{\rm D8}}$ model are ignored. The infinite tower was found by Sutcliffe to induce flow to a conformal theory, i.e., the BPS. We compare this structure to that of the SS model consisting of a 5D Yang-Mills action in warped space and the Chern-Simons term in which higher vector mesons are integrated out while preserving hidden local symmetry and valid to $O(\lambda^0)$ and $O(p^4)$ in the chiral counting. We point out the surprisingly important role of the $\omega$ meson that figures in the Chern-Simons term that encodes chiral anomaly in the baryon structure and that may be closely tied to short-range repulsion in nuclear interactions.Comment: 9 pages, REVTeX, to be published in Phys. Rev.