Polygon triangulation inO(n log logn) time with simple data structures

We give a newO(n log logn)-time deterministic algorithm for triangulating simplen-vertex polygons, which avoids the use of complicated data structures. In addition, for polygons whose vertices have integer coordinates of polynomially bounded size, the algorithm can be modified to run inO(n log*n) time. The major new techniques employed are the efficient location of horizontal visibility edges that partition the interior of the polygon into regions of approximately equal size, and a linear-time algorithm for obtaining the horizontal visibility partition of a subchain of a polygonal chain, from the horizontal visibility partition of the entire chain. The latter technique has other interesting applications, including a linear-time algorithm to convert a Steiner triangulation of a polygon into a true triangulation.This research was partially supported by the following grants: NSERC 583584, NSERC 580485, ONR-N00014-87-0467, and by DIMACS, an NSF Science and Technology Center (NSF-STC88-09648).     

A compact piecewise-linear voronoi diagram for convex sites in the plane

In the plane the post-office problem, which asks for the closest site to a query site, and retraction motion planning, which asks for a one-dimensional retract of the free space of a robot, are both classically solved by computing a Voronoi diagram. When the sites arek disjoint convex sets we give a compact representation of the Voronoi diagram, usingO (k) line segments, that is sufficient for logarithmic time post-office location queries and motion planning. If these sets are polygons withn total vertices given in standard representations, we compute this diagram optimally in Θ (k logn) deterministic time for the Euclidean metric and inO (k logn logm) deterministic time for the convex distance function defined by a convexm-gon. This work was supported by NSERC in the form of a Graduate Scholarship and two Research Grants.     

Reactive surface micropatterning by wet stamping

Hydrogel stamps are used to reactively micropattern various types of substrates. The method, called reactive wet stamping (r-WETS), is general in nature and overcomes several limitations of conventional soft-lithographic techniques. Illustrative applications of r-WETS in surface wettability modification, deposition of metallic microstructures, preparation of supports for electrostatic self-assembly, and multistep reactive patterning are discussed.     

A study of the reaction 2H(π±, p)X

We have studied the excitation function of the reaction ²H(π^±, p)X at a fixed proton angle of 90° for several fixed proton momenta of the detected proton as a function of the incident pion energy. No signal was found for a previous candidate for a dibaryon resonance around a mass of 2.23 GeV. The general trend of the data is reproduced by a multiple scattering theory     

Studying the mechanical behavior of a plastic, shock-resisting, antitank landmine

Modal behavior in landmines has recently become a topic of interest for acoustic landmine detection. It is well known that landmines exhibit mechanical resonance behavior that enhances the soil velocity over a buried landmine. Recent experimental work by Zagrai et al. [A. Zagrai, D. Donskoy, and A. Ekimov, J. Acoust. Soc. Am. 118 (6), 3619-3628 (2005)] demonstrates the existence of structural modes in several landmines. The work reported herein parallels the work of Zagrai et al. in studying the structural modes of the pressure plate of a plastic, cylindrically symmetric, antitank landmine. The pressure plate is considered to act as an elastically supported thin elastic plate. An observed perturbation of the first symmetric mode of the pressure plate is caused by the landmine's shock-resisting mechanism. This is validated by a lumped element model for the first symmetric mode coupled to the shock-resisting mechanism.     

Capillary filling of anodized alumina nanopore arrays

The filling behavior of a room temperature solvent, perfluoromethylcyclohexane, in approximately 20 nm nanoporous alumina membranes was investigated in situ with small angle x-ray scattering. Adsorption in the pores was controlled reversibly by varying the chemical potential between the sample and a liquid reservoir via a thermal offset, DeltaT. The system exhibited a pronounced hysteretic capillary filling transition as liquid was condensed into the nanopores. These results are compared with Kelvin-Cohan theory, with a modified Derjaguin approximation, as well as with predictions by Cole and Saam.     

Hydration, swelling, interlayer structure, and hydrogen bonding in organolayered double hydroxides: insights from molecular dynamics simulation of citrate-intercalated hydrotalcite

Molecular dynamics (MD) simulation of the Mg/Al (3:1) layered double hydroxide (LDH), hydrotalcite (HT), containing citrate, C6H5O7(3-), as the charge balancing interlayer anion provides new molecular scale insight into the interlayer structure, hydrogen bonding, and energetics of the hydration and consequent swelling of LDH compounds containing organic and biomolecules. Citrate-HT exhibits affinity for water up to very high hydration levels, in contrast to the preferred low hydration states of most LDHs intercalated with small, inorganic anions. This result is consistent with the recent experimental observation of the delamination of lactate-HT. The high water affinity is rationalized in terms of the preference of citrate ion for hydrogen bonds (H-bonds) donated from water molecules rather than from the hydroxyl groups of the metal hydroxide layer and the need to develop an integrated interlayer H-bond network among the citrate ions, water, and -OH groups of the hydroxide layers. The changes in the orientation of citrate molecules with progressive hydration are also intimately related to its preference to accept hydrogen bonds from water.     

Pd-Xantphos-catalyzed direct arylation of nucleosides

Direct arylation of the exocyclic amino groups of nucleosides represents a simple approach to N-aryl nucleoside derivatives. To date, one limitation has been that only electron-deficient aryl bromides and triflates possessed adequate reactivity for efficient, direct N-arylation of nucleosides. We demonstrate herein that Pd-Xantphos catalytic systems lead to successful N-arylation of suitably protected 2'-deoxyadenosine and 2'-deoxyguanosine with a wide range of aryl bromides.