Tracer Dispersion in a Self-Organized Critical System

We have studied experimentally transport properties in a slowly driven granular system which recently was shown to display self-organized criticality [Frette {\em et al., Nature} {\bf 379}, 49 (1996)]. Tracer particles were added to a pile and their transit times measured. The distribution of transit times is a constant with a crossover to a decaying power law. The average transport velocity decreases with system size. This is due to an increase in the active zone depth with system size. The relaxation processes generate coherently moving regions of grains mixed with convection. This picture is supported by considering transport in a $1D$ cellular automaton modeling the experiment.Comment: 4 pages, RevTex, 1 Encapsulated PostScript and 4 PostScript available upon request, Submitted to Phys. Rev. Let

Flame heights and charring on a particle board – An experimental study

Vertically oriented particle-board samples were exposed to external venting flames to study the fire spread and charring behaviour along a timber façade. Variation in flame height and the height, volume, area, density, and depth of the char layer were studied to determine the impact of heat-release rate and experiment duration. There was a peak flame height after which the flame returned to steady height approximately equal to the value before the ignition of the particle board and flame heights with inert panels. Flames did not spread to the top of the panel with increased experiment duration. Char height and area were found to increase with heat-release rate but were not affected significantly by experiment duration. Char depth and volume increased with both experiment duration and heat-release rates. Char density decreased with increased experiment duration and heat-release rate.publishedVersio

The average velocity in a queue

A number of cars drive along a narrow road that does not allow overtaking. Each driver has a certain maximum speed at which he or she will drive if alone on the road. As a result of slower cars ahead, many cars are forced to drive at speeds lower than their maximum ones. The average velocity in the queue offers a non-trivial example of a mean value calculation. Approximate and exact results are obtained using sampling, enumeration and calculations. The geometrical nature of the problem as well as the separate levels of averaging involved are emphasized. Further problems suitable for exploration in student projects are outlined

Velocity and cluster distributions in a bottleneck system

Velocity and cluster distributions for particles with unidirectional motion in one dimension are studied. The particles never pass each other, like cars on a narrow road that does not allow overtaking. As a result, particles cluster behind slow particles queues are formed behind slow cars . Thus, the actual velocity of each particle is to a large extent determined by slow particles further ahead. Considering all possible permutations of N particles with initial velocities vi , the average number of particles with actual velocity vi is N+1 / i i+1 in the sequence vi , the initial velocities are listed with monotonically increasing values . For i large and vi i the average number of actual velocities is thus a power law in vi, even though the average cluster density is found to be independent of cluster size, L. On the other hand, the cluster density varies significantly with cluster velocity; we obtain N−i ! N−L ! / N·N! N−L−i+1 ! . The average velocity at a given position in the sequence of N particles, and the average global velocity are determined. Explicit results for several distributions of the initial velocities show that the global velocity depends sensitively on the form of this distribution

Lip Height Effects in Quadrangular Steel Containers

The reduction in the mass-loss rate as a function of lip height is investigated through 90 experiments with hydrocarbon pool fires in quadrangular containers of size 10 cm, 20 cm, and 30 cm. The results show a reduction in the mass loss rate of 30-55 percent for 7 cm initial lip height compared with pool fires with no initial lip height

Lip-height effect in diffusive pool fires

A freeboard, lip height, from the container rim to the fuel surface affects the mass-loss rate of a pool fire. Experiments where heptane was burned in circular containers with diameter 10, 20 and 30 cm have been conducted. The results showed a decrease of up to 36% in the mass-loss rate for lip heights larger than zero. The mass-loss rate per unit area is affected by the lip height enough for it to surpass the effect of the diameter: a large-diameter pool fire with a high lip height may have lower mass-loss rate per unit area than a pool fire with smaller diameter and lower lip height. An analysis of the energy distribution for one experiment, showed that 35% of the received energy was lost to the surroundings; 30% was stored, and 35% was spent on evaporating fuel

Lorentzian-geometry-based analysis of airplane boarding policies highlights “slow passengers first” as better

We study airplane boarding in the limit of a large number of passengers using geometric optics in a Lorentzian metric. The airplane boarding problem is naturally embedded in a (1+1)-dimensional space-time with a flat Lorentzian metric. The duration of the boarding process can be calculated based on a representation of the one-dimensional queue of passengers attempting to reach their seats in a two-dimensional space-time diagram. The ability of a passenger to delay other passengers depends on their queue positions and row designations. This is equivalent to the causal relationship between two events in space-time, whereas two passengers are timelike separated if one is blocking the other and spacelike if both can be seated simultaneously. Geodesics in this geometry can be utilized to compute the asymptotic boarding time, since space-time geometry is the many-particle (passengers) limit of airplane boarding. Our approach naturally leads to the introduction of an effective refractive index that enables an analytical calculation of the average boarding time for groups of passengers with different aisle-clearing time distribution. In the past, airline companies attempted to shorten the boarding times by trying boarding policies that allow either slow or fast passengers to board first. Our analytical calculations, backed by discrete-event simulations, support the counterintuitive result that the total boarding time is shorter with the slow passengers boarding before the fast passengers. This is a universal result, valid for any combination of the parameters that characterize the problem: the percentage of slow passengers, the ratio between aisle-clearing times of the fast and the slow group, and the density of passengers along the aisle. We find an improvement of up to 28% compared with the fast-first boarding policy. Our approach opens up the possibility to unify numerous simulation-based case studies under one framework