Thickness of the rim of an expanding lamella near the splash threshold

The evolution of the ejected liquid sheet, or lamella, created after impact of a liquid drop onto a solid surface is studied using high-speed video in order to observe the detailed time evolution of the thickness of the rim of the lamella. Since it has been suggested that splashing behavior is set at very early times after impact, we study early times up to D-0/U-0, where D-0 and U-0 are the diameter and speed of the impacting drop, respectively, for different liquid viscosities and impact speeds below the splashing threshold. Within the regime of our experiments, our results are not consistent with the idea that the lamella rim grows similar to the boundary layer thickness. Rather, we find that the rim thickness is always much larger than the boundary layer thickness, and that the rim thickness decreases with increasing impact speed. For lower impact speeds, the increase in the rim thickness is consistent with a root t response over the limited time range available, but the dependence is not simply proportional to root nu, where nu is the kinematic viscosity, and there is a strong dependence of the rim thickness on the impact speed U-0. Scaling of the rim height using a balance of inertial and surface tension forces provides some collapse of the data at lower impact speeds. We also observe an unusual plateau behavior in thickness versus time at higher impact speeds as we approach the splash threshold. (C) 2010 American Institute of Physics. [doi:10.1063/1.3313360

Global Finite-Time Attitude Consensus of Leader-Following Spacecraft Systems Based on Distributed Observers

This paper addresses the leader-following attitude consensus problem for a group of spacecraft when at least one follower can access the leader's attitude and velocity relative to the inertial space. A nonlinear distributed observer is designed to estimate the leader's states for each follower. The observer possesses one important and novel feature of keeping attitude and angular velocity estimation errors on second-order sliding modes, and thus provides finite-time convergent estimates for each follower. Further, quaternion-based hybrid homogeneous controllers recently developed for single spacecraft are extended and then applied, by establishing a separation principle with the proposed observer, to track the leader's attitude motion. As a result, global finite-time attitude consensus is achieved on the entire attitude manifold, with either full-state measurements or attitude-only measurements, as long as the network topology among the followers is undirected and connected. Numerical simulations are presented to demonstrate the performance of the proposed methods.Comment: 13 pages, 12 figure

Applications of integer programming methods to cages

The aim of this paper is to construct new small regular graphs with girth 7 using integer programming techniques. Over the last two decades solvers for integer programs have become more and more powerful and have proven to be a useful aid for many hard combinatorial problems. Despite successes in many related fields, these optimisation tools have so far been absent in the quest for small regular graphs with a given girth. Here we illustrate the power of these solvers as an aid to construct small regular girth 7 graphs from girth 8 cage

Time-dependent, species-specific effects of N:P stoichiometry on grassland plant growth

N and P have different eutrophication effects on grassland communities, yet the underlying mechanisms are poorly understood. To examine plant growth in response to the varying (relative) supply of N and P, we conducted a two-year greenhouse experiment. Five grasses and three herbs were grown with three N:P supply ratios at two overall nutrient supply levels. During the first year the plant growth was relatively low at both high and low N:P supply ratios, whereas during the second year the growth was especially low at a high N:P supply ratio. This second-year low growth was attributed to the high root death rate, which was influenced by a high N:P supply ratio rather than by the nutrient supply level. Species responded differently, especially in P uptake and loss at a high N:P supply ratio. Each species seemed to have a different strategy for P limitation, e.g. an efficient P uptake or a high P resorption rate. Species typical of P-limited grasslands had neither better P uptake nor better P retention at a high N:P supply ratio. This study quantitatively demonstrates an increased plant root death triggered by strong P limitation. This finding indicates a possible extra effect of N eutrophication on ecosystem functioning via changed N:P stoichiometr