The motion, stability and breakup of a stretching liquid bridge with a receding contact line

The complex behavior of drop deposition on a hydrophobic surface is considered by looking at a model problem in which the evolution of a constant-volume liquid bridge is studied as the bridge is stretched. The bridge is pinned with a fixed diameter at the upper contact point, but the contact line at the lower attachment point is free to move on a smooth substrate. Experiments indicate that initially, as the bridge is stretched, the lower contact line slowly retreats inwards. However at a critical radius, the bridge becomes unstable, and the contact line accelerates dramatically, moving inwards very quickly. The bridge subsequently pinches off, and a small droplet is left on the substrate. A quasi-static analysis, using the Young-Laplace equation, is used to accurately predict the shape of the bridge during the initial bridge evolution, including the initial onset of the slow contact line retraction. A stability analysis is used to predict the onset of pinch-off, and a one-dimensional dynamical equation, coupled with a Tanner-law for the dynamic contact angle, is used to model the rapid pinch-off behavior. Excellent agreement between numerical predictions and experiments is found throughout the bridge evolution, and the importance of the dynamic contact line model is demonstrated.Comment: 37 pages, 12 figure

Performance guarantees for greedy maximization of non-submodular controllability metrics

A key problem in emerging complex cyber-physical networks is the design of information and control topologies, including sensor and actuator selection and communication network design. These problems can be posed as combinatorial set function optimization problems to maximize a dynamic performance metric for the network. Some systems and control metrics feature a property called submodularity, which allows simple greedy algorithms to obtain provably near-optimal topology designs. However, many important metrics lack submodularity and therefore lack provable guarantees for using a greedy optimization approach. Here we show that performance guarantees can be obtained for greedy maximization of certain non-submodular functions of the controllability and observability Gramians. Our results are based on two key quantities: the submodularity ratio, which quantifies how far a set function is from being submodular, and the curvature, which quantifies how far a set function is from being supermodular

Collisional relaxation of electrons in a warm plasma and accelerated nonthermal electron spectra in solar flares

Extending previous studies of nonthermal electron transport in solar flares which include the effects of collisional energy diffusion and thermalization of fast electrons, we present an analytic method to infer more accurate estimates of the accelerated electron spectrum in solar flares from observations of the hard X-ray spectrum. Unlike for the standard cold-target model, the spatial characteristics of the flaring region, especially the necessity to consider a finite volume of hot plasma in the source, need to be taken into account in order to correctly obtain the injected electron spectrum from the source-integrated electron flux spectrum (a quantity straightforwardly obtained from hard X-ray observations). We show that the effect of electron thermalization can be significant enough to nullify the need to introduce an {\it ad hoc} low-energy cutoff to the injected electron spectrum in order to keep the injected power in non-thermal electrons at a reasonable value. Rather the suppression of the inferred low-energy end of the injected spectrum compared to that deduced from a cold-target analysis allows the inference from hard X-ray observations of a more realistic energy in injected non-thermal electrons in solar flares.Comment: accepted for publication in Ap

On the variation of solar flare coronal x-ray source sizes with energy

Observations with {\em RHESSI} have enabled the detailed study of the structure of dense hard X-ray coronal sources in solar flares. The variation of source extent with electron energy has been discussed in the context of streaming of non-thermal particles in a one-dimensional cold-target model, and the results used to constrain both the physical extent of, and density within, the electron acceleration region. Here we extend this investigation to a more physically realistic model of electron transport that takes into account the finite temperature of the ambient plasma, the initial pitch-angle distribution of the accelerated electrons, and the effects of collisional pitch-angle scattering. The finite temperature results in the thermal diffusion of electrons, that leads to the observationally-inferred value of the acceleration region volume being an overestimate of its true value. The different directions of the electron trajectories, a consequence of both the non-zero injection pitch-angle and scattering within the target, cause the projected propagation distance parallel to the guiding magnetic field to be reduced, so that a one-dimensional interpretation can overestimate the actual density by a factor of up to $\sim 6$. The implications of these results for the determination of acceleration region properties (specific acceleration rate, filling factor, etc.) are discussed.Comment: 45 pages, 9 figures, accepted for publication in Ap

Flux measurements in the near surface layer over a non-uniform crop surface in China

International audienceEddy covariance measurements were conducted on fluxes of moisture, heat and CO2 in a near-surface layer over a non-uniform crop surface in an agricultural ecosystem in the central plain of China from 10 June to 20 July 2002. During this period, the mean canopy height was about 0.50 m. The study site consisted of grass (10% of area), bean (15%), corn (15%) and rice (60%). Based on footprint analysis, we expected >90% of the measured flux (at a height of 4 m above ground surface) to occur within the nearest 600 m of upwind area. We examined interdiurnal variations in the components of the surface energy balance and in CO2 flux. Results show that the pattern of energy partition had no obvious variation during the season. Daytime absorption of CO2 flux by the crop canopy suddenly increased after thunderstorm events. We examined the energy budget closure and found it to be around 0.85. We compared energy partitioning for all rain-free days, and found energy imbalance was more significant for the 1~3 days after rainy events and energy components almost achieve balance for the other rain-free days. It indicated that the cold or warm rainwater infiltrating into soil made problems

Reduced Order Models for Profiled Steel Diaphragm Panels

The objective of this paper is to provide progress on development and validation of reduced order models for the in plane strength and stiffness of profiled steel panels appropriate for use in structural models of an entire building. Profiled steel panels, i.e, metal deck, often serve as a key distribution element in building lateral force resisting systems. Acting largely as an in-plane shear diaphragm, metal deck as employed in walls, roofs, and floors plays a key role in creating and driving three-dimensional building response. As structural modeling evolves from two-dimensional frameworks to fully three-dimensional buildings, accurate and computationally efficient models of profiled steel panels are needed. Three-dimensional building response is increasingly required by ever-evolving structural standards, particularly in seismic design, and structural efficiency demands that the benefits of three-dimensional response be leveraged in design. Equivalent orthotropic plate models provide a potential reduced order model for profiled steel panels that is investigated in this paper. A recent proposal for the rigidities in such a model are assessed against shell finite element models of profiled steel panels. In addition, the impact of discrete connections and discrete panels, as occurs in an actual roof system, are assessed when applying these reduced order models. Extension of equivalent orthotropic plate models to elastic buckling and strength, in addition to stiffness, both represent work in progress, but initial results are provided. Examples show that equivalent orthotropic plate models must be used with care to yield useful results. This effort is an initial step in developing efficient whole building models that accurately incorporate the behavior of profiled steel panels as diaphragms

Investigation of LED light effects on plant growth in improved protected horticulture system

In controlled environment agriculture, energy is the predominant factor in production costs. Lighting is the one major consumers of energy. Commercial crop production in greenhouses can be enhanced by supplemental lighting which provides low moderate intensity light levels to increase photosynthesis and plant growth. Traditionally, horticultural lights were high-intensity discharge lamps such as high-pressure sodium (HPS), metal-halide (MH), and mercury (HPMV). The disadvantages of these lamps are high-energy costs, heat generation and suboptimal spectrum for photosynthesis