On the stability of Riemannian manifold with parallel spinors

Inspired by the recent work [HHM03], we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result says that Ricci flat metrics which also admit nonzero parallel spinors are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Our second result, which is a local version of the first one, shows that any metric of positive scalar curvature cannot lie too close to a metric with nonzero parallel spinor. We also prove a rigidity result for special holonomy metrics. In the case of SU(m) holonomy, the rigidity result implies that scalar flat deformations of Calabi-Yau metric must be Calabi-Yau. Finally we explore the connection with a positive mass theorem of [D03], which presents another approach to proving these stability and rigidity results. Dedicated to Jeff Cheeger for his sixtieth birthday     

Amplifiers and Lasers in PCF Configurations

In this paper we will present an overview of the use of photonic crystal fibers as fiber amplifiers. We will describe the basic concepts of optical amplification, and how to do numerical modelling of such components. We will then identify advantages and disadvantages of amplifiers based on PCF technology compared to conventional fibers, and then go into greater detail on some of these specific applications, such as low pump power amplifiers, and high-power double-clad amplifiers and lasers.     

An Efficient Numerical Model for Planar Spiral Inductor On-Chip

In this paper, a very useful numerical technique has been developed for analyzing the transient characteristics of a planar-spiral inductor on-chip. A locally conformal technique and an alternating-direction implicit scheme are applied to the finite-difference time-domain method. A formulation for solving three dimensional Maxwell’s equations is proposed. Using the proposed method, various parameters of the planar-spiral inductors have been analyzed and an equivalent circuit, which includes frequency-independent circuit elements, has been introduced. Highly computational efficiency is implemented. Numerical results show excellent agreement with the measured data over a wide frequency range.     

Rain Attenuation at 103 GHz in Millimeter Wave Ranges

We have conducted a millimeter wave propagation experiment at 103 GHz (2.9 mm) on a propagation path of 390 m. The results were compared with the rain attenuation calculations from the Marshall-Palmer, Best, Joss-Thomas-Waldvogel and Weibull distributions for raindrop-size. It has been shown that the Weibull distribution has a good agreement with the experiments.     

Structure of solid monolayers and multilayers of n -hexane on graphite

We present all-atom molecular dynamics simulations ofn-hexane on the basal plane of graphite at monolayer and multilayer coverages. In keeping with experimental data, we find the presence of ordered adsorbed layers both at single monolayer coverage and when the adsorbed layer coexists with excess liquid adsorbate. Using a simulation method that does not impose any particular periodicity on the adsorbed layer, we quantitatively compare our results to the results of neutron diffraction experiments and find a structural transition from a uniaxially incommensurate lattice to a fully commensurate structure on increasing the coverage from a monolayer to a multilayer. The zig-zag backbone planes of all the alkane molecules lie parallel to the graphite surface at the multilayer coverage, while a few molecules are observed to attain the perpendicular orientation at monolayer coverage. Dedicated to Professor C N R Rao on his 70th birthday     

From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation

   Abstract. We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature.     

A Dominated Theorem on 5L(2, R) and Its Application

In this paper, we give the following dominated theorem: Let φ(g) ∈ L1(G//K),φε(t)=ε> 0, and the least radical decreasing dominatedfunction φ(t) = sup |φ(y)| ∈L1(G//K). If shtφ(t) is monotonically decreasingon (0, ∞), then for any f∈L1loc(G//K) , the following inequality holds:sup |φε * f(x)| ≤ Cmf(x),where mf(x) is the Hardy-Littlewood maximal function of f, and C = ||φ||1.An application of this dominated theorem is also given.