Method to obtain nonuniformity information from field emission behavior

Copyright © 2010 American Vacuum Society / American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Vacuum Science and Technology Part B: Microelectronics and Nanometer Structures, 28(3), Article number 441 and may be found at http://scitation.aip.org/content/avs/journal/jvstb/28/3/10.1116/1.3327928.This article describes the characterization of field emission from a planar cathode to a spherical anode with the approach curve method (ACM). In such a diode configuration the electric field strength at the cathode surface is nonuniform. This nonuniformity gives an extra degree of freedom and it allows the interpretation of the current-voltage and voltage-distance (V×d) curves in terms of nonuniformity. The authors apply the ACM to Cu emitters to explain the nonlinearity of the V×d curve in ACM measurements. This analysis provides a good insight into field emission phenomena, supporting a method for nonuniformity characterization based on field emission behavior

Incremental and Decremental Maintenance of Planar Width

We present an algorithm for maintaining the width of a planar point set dynamically, as points are inserted or deleted. Our algorithm takes time O(kn^epsilon) per update, where k is the amount of change the update causes in the convex hull, n is the number of points in the set, and epsilon is any arbitrarily small constant. For incremental or decremental update sequences, the amortized time per update is O(n^epsilon).Comment: 7 pages; 2 figures. A preliminary version of this paper was presented at the 10th ACM/SIAM Symp. Discrete Algorithms (SODA '99); this is the journal version, and will appear in J. Algorithm

Lift-and-Round to Improve Weighted Completion Time on Unrelated Machines

We consider the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times. Our main result is a $(3/2-c)$-approximation algorithm for some fixed $c>0$, improving upon the long-standing bound of 3/2 (independently due to Skutella, Journal of the ACM, 2001, and Sethuraman & Squillante, SODA, 1999). To do this, we first introduce a new lift-and-project based SDP relaxation for the problem. This is necessary as the previous convex programming relaxations have an integrality gap of $3/2$. Second, we give a new general bipartite-rounding procedure that produces an assignment with certain strong negative correlation properties.Comment: 21 pages, 4 figure