Kinetic collision detection between two simple polygons

We design a kinetic data structure for detecting collisions between two simple polygons in motion. In order to do so, we create a planar subdivision of the free space between the two polygons, called the external relative geodesic triangulation, which certifies their disjointness. We show how this subdivision can be maintained as a kinetic data structure when the polygons are moving, and analyze its performance in the kinetic setting.     

Laser induced fluorescence line narrowing in iodine

A complementary technique to Lamb dip absorption spectroscopy in gases is described which allows observation of homogeneous linewidths in fluorescence. Hyperline spectra of iodine excited by a single mode argon laser beam at 5145 Å are presented for the 43-13 and 43-11 bands at 5970 and 5830 Å respectively.     

A differential game model of the marketing-operations interface

In the development of their dynamic strategies, the marketing and operations functions within a firm have differing objectives, and conflict between the two functions is common. The strategic interdependence involving marketing and operations decisions is modeled as a noncooperative differential game. Demand is assumed to be a function of price and advertising goodwill, and marketing controls price and advertising to maximize its discounted stream of revenue net of advertising costs. Backlogging is allowed, and operations controls production to minimize its discounted stream of production and backlog costs. A feedback Nash equilibrium is derived for the game, which allows a solution of the system of differential equations for goodwill and backlog, and is analyzed to study the nature of the dynamic strategies for price, advertising, and production.     

Directed self-assembly of microcomponents enabled by laser-activated bubble latching

This article introduces a method for microscale assembly using laser-activated bubble latching. The technique combines the advantages of directed fluidic assembly and surface tension-driven latching to create arbitrarily complex and irregular structures with unique properties. The bubble latches, generated through the laser degradation of the tile material, are created on the fly, reversibly linking components at user-determined locations. Different phases of latching bubble growth are analyzed, and shear force calculations show that each bubble is able to support a tensile force of approximately 0.33 μN. We demonstrate that by exploiting the compressibility of bubbles, assembled objects can be made to switch between rigid and flexible states, facilitating component assembly and transport. Furthermore, we show reconfiguration capabilities through the use of bubble hinging. This novel hybrid approach to the assembly of microscale components offers significant user control while retaining a simplistic design environment.     

Dense Point Sets Have Sparse Delaunay Triangulations or “... But Not Too Nasty”

The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of $n$ points in~$\Real^3$ with spread $\Delta$ has complexity $O(\Delta^3)$. This bound is tight in the worst case for all $\Delta = O(\sqrt{n})$. In particular, the Delaunay triangulation of any dense point set has linear complexity. We also generalize this upper bound to regular triangulations of $k$-ply systems of balls, unions of several dense point sets, and uniform samples of smooth surfaces. On the other hand, for any $n$ and $\Delta = O(n)$, we construct a regular triangulation of complexity $\Omega(n\Delta)$ whose $n$ vertices have spread $\Delta$.     

The nuclear quadrupole interaction in Pr3+:LaF3 — An optical-RF double resonance measurement of the ground electronic state

The nuclear quadrupole hyperfine splittings of Pr³⁺ in LaF₃ have been measured for the ground electronic state using a RF optical resonance technique. A hamiltonian $\text{H}\text{= P[(I}{}^2{}_{\mathrm{z}}\text{?}\text{1}\text{3}\text{I(I+1) + (η/6)(I}{}^2{}_{\mathrm{+}}\text{?I}$²_-)] was fitted to the data with zP=4.185 ± 0.003 MHzandη = 0.105 ± 0.010. Linewidths of 180 kHz were observed.