11 research outputs found
Parking and the visual perception of space
Using measured data we demonstrate that there is an amazing correspondence
among the statistical properties of spacings between parked cars and the
distances between birds perching on a power line. We show that this observation
is easily explained by the fact that birds and human use the same mechanism of
distance estimation. We give a simple mathematical model of this phenomenon and
prove its validity using measured data
Vehicular traffic flow at an intersection with the possibility of turning
We have developed a Nagel-Schreckenberg cellular automata model for
describing of vehicular traffic flow at a single intersection. A set of traffic
lights operating in fixed-time scheme controls the traffic flow. Open boundary
condition is applied to the streets each of which conduct a uni-directional
flow. Streets are single-lane and cars can turn upon reaching to the
intersection with prescribed probabilities. Extensive Monte Carlo simulations
are carried out to find the model flow characteristics. In particular, we
investigate the flows dependence on the signalisation parameters, turning
probabilities and input rates. It is shown that for each set of parameters,
there exist a plateau region inside which the total outflow from the
intersection remains almost constant. We also compute total waiting time of
vehicles per cycle behind red lights for various control parameters.Comment: 8 pages, 17 eps figures, Late
From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond
The discovery of connections between the distribution of energy levels of
heavy nuclei and spacings between prime numbers has been one of the most
surprising and fruitful observations in the twentieth century. The connection
between the two areas was first observed through Montgomery's work on the pair
correlation of zeros of the Riemann zeta function. As its generalizations and
consequences have motivated much of the following work, and to this day remains
one of the most important outstanding conjectures in the field, it occupies a
central role in our discussion below. We describe some of the many techniques
and results from the past sixty years, especially the important roles played by
numerical and experimental investigations, that led to the discovery of the
connections and progress towards understanding the behaviors. In our survey of
these two areas, we describe the common mathematics that explains the
remarkable universality. We conclude with some thoughts on what might lie ahead
in the pair correlation of zeros of the zeta function, and other similar
quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in
Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note:
text overlap with arXiv:0909.491