An improved algorithm for the automatic determination of root loci by digital computer

1971 ◽  
Vol 41 (8) ◽  
pp. 365 ◽  
Author(s):  
P. Atkinson ◽  
V.S. Dalvi
2000 ◽  
Vol 28 (1-2) ◽  
pp. 237-245 ◽  
Author(s):  
Nasser Hosseini ◽  
Blanka Hejdukova ◽  
Pall E. Ingvarsson ◽  
Bo Johnels ◽  
Torsten Olsson

Author(s):  
Romain Desplats ◽  
Timothee Dargnies ◽  
Jean-Christophe Courrege ◽  
Philippe Perdu ◽  
Jean-Louis Noullet

Abstract Focused Ion Beam (FIB) tools are widely used for Integrated Circuit (IC) debug and repair. With the increasing density of recent semiconductor devices, FIB operations are increasingly challenged, requiring access through 4 or more metal layers to reach a metal line of interest. In some cases, accessibility from the front side, through these metal layers, is so limited that backside FIB operations appear to be the most appropriate approach. The questions to be resolved before starting frontside or backside FIB operations on a device are: 1. Is it do-able, are the metal lines accessible? 2. What is the optimal positioning (e.g. accessing a metal 2 line is much faster and easier than digging down to a metal 6 line)? (for the backside) 3. What risk, time and cost are involved in FIB operations? In this paper, we will present a new approach, which allows the FIB user or designer to calculate the optimal FIB operation for debug and IC repair. It automatically selects the fastest and easiest milling and deposition FIB operations.


2017 ◽  
Vol 80 (16-18) ◽  
pp. 932-940 ◽  
Author(s):  
Raymond Nepstad ◽  
Emlyn Davies ◽  
Dag Altin ◽  
Trond Nordtug ◽  
Bjørn Henrik Hansen

1964 ◽  
Vol 68 (638) ◽  
pp. 111-116 ◽  
Author(s):  
D. J. Bell

SummaryThe problem of maximising the range of a given unpowered, air-launched vehicle is formed as one of Mayer type in the calculus of variations. Eulers’ necessary conditions for the existence of an extremal are stated together with the natural end conditions. The problem reduces to finding the incidence programme which will give the greatest range.The vehicle is assumed to be an air-to-ground, winged unpowered vehicle flying in an isothermal atmosphere above a flat earth. It is also assumed to be a point mass acted upon by the forces of lift, drag and weight. The acceleration due to gravity is assumed constant.The fundamental constraints of the problem and the Euler-Lagrange equations are programmed for an automatic digital computer. By considering the Lagrange multipliers involved in the problem a method of search is devised based on finding flight paths with maximum range for specified final velocities. It is shown that this method leads to trajectories which are sufficiently close to the “best” trajectory for most practical purposes.It is concluded that such a method is practical and is particularly useful in obtaining the optimum incidence programme during the initial portion of the flight path.


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