Locally minimal uniformly oriented shortest networks

AbstractThe Steiner problem in a λ-plane is the problem of constructing a minimum length network interconnecting a given set of nodes (called terminals), with the constraint that all line segments in the network have slopes chosen from λ uniform orientations in the plane. This network is referred to as a minimum λ-tree. The problem is a generalization of the classical Euclidean and rectilinear Steiner tree problems, with important applications to VLSI wiring design.A λ-tree is said to be locally minimal if its length cannot be reduced by small perturbations of its Steiner points. In this paper we prove that a λ-tree is locally minimal if and only if the length of each path in the tree cannot be reduced under a special parallel perturbation on paths known as a shift. This proves a conjecture on necessary and sufficient conditions for locally minimal λ-trees raised in [M. Brazil, D.A. Thomas, J.F. Weng, Forbidden subpaths for Steiner minimum networks in uniform orientation metrics, Networks 39 (2002) 186–222]. For any path P in a λ-tree T, we then find a simple condition, based on the sum of all angles on one side of P, to determine whether a shift on P reduces, preserves, or increases the length of T. This result improves on our previous forbidden paths results in [M. Brazil, D.A. Thomas, J.F. Weng, Forbidden subpaths for Steiner minimum networks in uniform orientation metrics, Networks 39 (2002) 186–222]

Downy brome seed bank dynamics in southwestern Saskatchewan

Non-Peer ReviewedIn order to study downy brome seed bank dynamics, a burial experiment was established near Maple Creek in August 1987. Downy brome seed was buried at four depths (2.5 to 20 cm), and placed on the soil surface, in nylon mesh bags. Seed was exhumed at monthly intervals in the fall of 1987 and throughout the 1988 growing season. Seed germination in the field in the fall of 1987 was greatest from the buried seed (almost 50 %) while the surface seed exhibited little germination. This germination occurred in response to fall precipitation. Seed on the soil surface was not in contact with moist soil for a sufficient time to stimulate germination, so 80-90 % of this seed had not germinated by freeze-up in 1987. However the surface collected seed had germination of 34 % when transferred to an incubator in the laboratory, indicating environmentally induced dormancy in the field. There was little recruitment from the seed bank occurred in the spring of 1988 in spite of favorable moisture and temperature conditions. Seed on the soil surface remained viable until the 14th month but the buried seed at all depths had either germinated or deteriorated by the 9th month. This study was repeated in 1988, with similar results to date

Distribution, biology, and control of downy brome (Bromus tectorum L.) in southwestern Saskatchewan

Non-Peer ReviewedDowny brome was likely introduced near Maple Creek in 1960, and has since spread to infest parts of four Agricultural Extension Districts in southwestern Saskatchewan (Maple Creek, Leader, Swift Current, Shaunavon). By 1987, a total of 150 downy brome reports from 72 townships have been confirmed. During the first weed survey of annual crop fields infested with downy brome, 35 fields were visited and the kinds and numbers of weeds were identified according to standardized weed survey procedures. Downy brome density averaged 213 plants per square metre, and associated weeds were Japanese brome, flixweed, green foxtail, and wild buckwheat. Japanese brome was found in 5 fields, and was less abundant than downy brome in the area surveyed. Large numbers of downy brome seeds (50,000 seeds per square metre) were extracted from soil samples. Downy brome seeds buried in soil germinated more rapidly than those seeds on the soil surface. Most downy brome seeds (98 %) buried 2.5, 5.0, 10.0, or 20.0 cm in soil germinated or deteriorated within 3 months. However, a few seeds remained viable in the soil after 3 months. Research is in progress to determine the relative winter hardiness of downy brome and winter wheat, and to develop chemical control methods

Group delay in Bragg grating with linear chirp

An analytic solution for Bragg grating with linear chirp in the form of confluent hypergeometric functions is analyzed in the asymptotic limit of long grating. Simple formulas for reflection coefficient and group delay are derived. The simplification makes it possible to analyze irregularities of the curves and suggest the ways of their suppression. It is shown that the increase in chirp at fixed other parameters decreases the oscillations in the group delay, but gains the oscillations in the reflection spectrum. The conclusions are in agreement with numerical calculations.Comment: 16 pages, 8 figures, submitted to Opt. Com

Capacitive Micromachined Ultrasonic Transducer Array with Pencil Beam Shape and Wide Range Beam Steering

AbstractA capacitive micromachined ultrasonic transducer (CMUT) array is designed as an alternative to conventional piezoelectric transducers. A thin silicon nitride membrane is suspended over a bottom electrode on a silicon wafer. In the immersion mode, the transducer cell shape and dimensions are optimized for an operating frequency of 10MHz. We show that the proposed imager array can generate a pencil shape beam with a ∼1.5° half beam width, enhancing the detector resolution. A phased array technique is employed to excite multiple cells using time-delayed signals to steer the acoustic beam toward the object. This eliminates the need to mechanically move the detector, simplifying the transducer driving system. Moreover, unlike conventional transducers, the pencil beam can be effectively steered over a wide range of angles without producing grating lobes, which minimizes power loss in undesired directions. This can also improve the signal to noise ratio of the imager CMUT array

Anderson transition and thermal effects on electron states in amorphous silicon

I discuss the properties of electron states in amorphous Si based on large scale calculations with realistic several thousand atom models. A relatively simple model for the localized to extended (Anderson) transition is reviewed. Then, the effect of thermal disorder on localized electron states is considered. It is found that under readily accessible conditions, localized (midgap or band tail) states and their conjugate energies may fluctuate dramatically. The possible importance of non-adiabatic atomic dynamics to doped or photo-excited systems is briefly discussed.Comment: Was presented at ICAMS18, Snowbird UT, August 1999. Submitted to J. of Non-Cryst. Solid