Non-Reflecting Boundary Conditions for Traffic Flow Schrödinger Equation

Urban traffic flow can be roughly approximated by a Schrödinger equation. For a simulation of the Schrödinger equation as well as for analytical computations it is usefull that waves of traffic which travel along a road are not reflected at the boundaries of the simulated region. Here, we present the non-reflecting boundary condition for the Schrödinger equation and prove it via numerical computations

A dust cloud around Pluto and Charon

We suggest that Pluto and Charon are immersed in a tenuous dust cloud. The cloud consists of ejecta from Pluto and-especially- Charon, released from their surfaces by impacts of micrometeoroids originating from Edgeworth-Kuiper belt objects. The motion of the ejected grains is dominated by the gravity of Pluto and Charon, which determines a pear-shape of the densest part of the cloud. While the production rates of escaping particles from both sides are comparable, the lifetimes of the Charon particles inside the Hill sphere of Pluto-Charon with respect to the Sun are much longer than of the Pluto ejecta, so that the cloud is composed predominantly of Charon grains. The dust cloud is dense enough to be detected with an in situ dust detector onboard a future space mission to Pluto. The Cloud's maximum optical depth of tau approximate to 3 x 10(-11) is, however, too low to allow remote sensing observations. (C) 2002 Elsevier Science Ltd. All rights reserved

A tenuous dust ring of Jupiter formed by escaping ejecta from the Galilean satellites

[1] This paper focuses on the dust environment between the orbits of the Galilean moons of Jupiter. Recent discovery of dust clouds around the Galilean satellites formed by impact ejecta from hypervelocity impacts of interplanetary micrometeoroids [Kruger et al., 1999d] suggests that a fraction of the ejected particles may escape from the source satellites into circum-Jovian orbits. We estimate production rates and study dynamical evolution of the escaping ejecta, controlled by gravitational, radiation pressure, and electromagnetic forces, to show that grains larger than several tenths of a micrometer in radius are likely to stay in bound orbits around Jupiter for tens or hundreds of years until they either are lost to collisions with the satellites or Jupiter or are ejected to interplanetary space. It is concluded that these small debris form a broad dust ring with number densities up to similar to10(3) km(-3), extending at least from Europa's orbit outward beyond the orbit of Callisto. Our results are consistent with in situ measurements of the Galileo spacecraft. We analyze impact events recorded by the Galileo dust detector from 1996 through 2001 and find more than 200 events outside the orbit of Europa, compatible with impacts of particles orbiting Jupiter in prograde orbits. An empirical dust number density distribution derived from these data agrees quite well with the theoretical one