An atmospheric measurement campaign took place in the spring of 2006 to characterize the emission of particles from an integrated iron and steelmaking site. During the measurement campaign, the PM 10 daily limit value of 50 µg m −3 was not exceeded during any day. However, excursions in PM 10 concentrations occurred over periods of a few hours which were associated with wind passing over the steelworks' site. Measurements with an Aerosol Time-ofFlight Mass Spectrometer (ATOFMS) showed six particle classes associated with emissions from steelmaking processes. Two of these were iron-rich, one showing internal mixing with nitrate, the other internally mixed with phosphate, which subsequent analysis identified as arising from the ironmaking sector and the hot and cold mills as the dominant sources, respectively. Other ATOFMS classes were rich in lead, zinc, and nickel, which were also associated with steelmaking sources. A Micro Orifice Uniform Deposit Impactor (MOUDI), used to measure particle size distributions over periods of 19-42 hours, showed two characteristic size distributions for iron, one bimodal with modes at 0.45 µm and 4 µm, the other unimodal centered at 6 µm. In the former case, the smaller mode exhibited a peak for lead at the same particle size and in the case of the larger mode, phosphate and calcium also showed a peak at 4 µm diameter, consistent with the ATOFMS findings. An additional particle type with a unimodal size distribution centered at about 1.2 µm, with internally mixed Pb, Zn, and Cl but not Fe was also found.

Data were collected on open-grown loblolly pine (Pinustaeda L.), longleaf pine (Pinuspalustris Mill.), and shortleaf pine (Pinusechinata Mill.) and analyzed to provide predictive equations of crown width and maximum potential basal area growth for crown competition and growth and yield models. The measurements were taken on 115 open-grown loblolly pine trees and 76 shortleaf pines in southeastern Arkansas. The longleaf pine data consisted of 81 open-grown trees from southern Alabama, Georgia, and Florida. A circle and an ellipse were tested as geometric models of the vertically projected crown. No significant differences between the tree shapes were found based on analyses of length and azimuth of the largest crown diameter, and the circle was chosen as an appropriate model. This indicated that only the distance between trees, not their orientation to one another, need be included in models of crown competition based on crown contact. Predictive equations of mean crown width based on diameter at breast height were fitted for each species for use in models of crown competition. A Chapman–Richards growth rate function with an intercept term was fit to periodic annual inside-bark basal area growth based on initial inside-bark basal area to provide empirical estimates of maximum basal area growth rates for growth and yield modeling of the given species. Additionally, equations to predict double bark thickness as a function of diameter at breast height were fit for each species to facilitate the use of the equations with outside-bark measurements of diameter.

Abstract. This paper studies systems of partial differential equations modelling laser percussion drilling. The particular phenomenon considered in detail is the ejection of the thin layer of molten material. This thin layer is modelled as an inviscid flow between the fluid surface and fluid/solid interface, both of which are unknown moving boundaries. Through a regular asymptotic expansion, the governing equations are reduced to a combination of the shallow water equations and a two-phase Stefan problem; the key small parameter being the square of the aspect ratio. These leading-order problems exhibit shocks which represents a possible mechanism for the previously unexplained fluid clumping. Approximate formulas and a parameter gronping are derived to predict the rate of melt solidification during ejection. Finally, weak formulations of thp convection-diffusion equation for energy conservation are presented. These weak formulations are novel becanse the energy equation in the fluid contains convection terms. An appropriate extension to the enthalpy method is suggest{~d as a first stage towards numerical calculations.

Large-amplitude oscillations of incompressible viscous drops are studied at small capillary number. On the long viscous time scale, a formal perturbation scheme is developed to determine original modulation equations. These two ordinary differential equations comprise the averaged condition for conservation of energy and the averaged projection of the Navier–Stokes equations onto the vorticity vector. The modulation equations are applied to the free decay of axisymmetric oblate–prolate spheroid oscillations. On the long time scale, only the modulation equation for energy is required. In this example, the results compare well with linear viscous theory, weakly nonlinear inviscid theory and experimental observations. The new results show that previous experimental observations and numerical simulations are all manifestations of a single-valued relationship between dimensionless decay rate and amplitude. Moreover, if the amplitude of the oscillations does not exceed 30% of the drop radius, this decay rate may be approximated by a quadratic. The new results also show that, when the amplitude of the oscillations exceeds 20% of the drop radius, fluid in the inviscid bulk of the drop is undergoing abrupt changes in its acceleration in comparison to the acceleration during small-amplitude deformations.

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A mathematical model describing the coupling of electrical, optical and thermal effects in semiconductor lasers is introduced. Through a systematic asymptotic expansion, the governing system of differential equations is reduced to a single second-order boundary value problem. This highly nonlinear equation describes the time-independent maximum temperature in the boundary layer adjacent to the mirror facet. The solution of the problem is a multi-valued function of current. The graph of the maximum steady-state temperature as a function of current gives a fold-shaped response curve, which indicates that no bounded steady state exists beyond a critical value of current. For certain device parameters and initial conditions, thermal runaway occurs. A mechanism for the sudden mode of semiconductor laser failure is described in terms of thermal runaway.

The asymptotic structure of laminar modulated travelling waves in two-dimensional high-Reynolds-number plane Poiseuille flow is investigated on the upper-energy branch. A finite set of independent slowly varying parameters are identified which parameterize the solution of the Navier-Stokes equations in this subset of the phase space. Our parameterization of the weakly stable modes describes an attracting manifold of maximum-entropy configurations. The complementary modes, which have been neglected in this parameterization, are strongly damped. In order to seek a closure, a countably infinite number of modulation equations are derived on the long viscous time scale: a single equation for averaged kinetic energy and momentum; and the remaining equations for averaged powers of vorticity. Only a finite number of these vorticity modulation equations are required to determine the finite number of unknowns. The new results show that the evolution of the slowly varying amplitude parameters is determined by the vorticity field and that the phase velocity responds to these changes in the amplitude in accordance with the kinetic energy and momentum. The new results also show that the most crucial physical mechanism in the production of vorticity is the interaction between vorticity and kinetic energy, this interaction being responsible for the existence of the attractor.

Rectified diffusion is a bubble growth phenomenon that occurs in acoustic fields. Despite the existence of a well-established spherically symmetric mathematical model, theoretical results have been unsuccessful in reproducing the bubble growth even in the case of a single spherical bubble in the bulk. In the latter case, the influence of surfactants and acoustic microstreaming have been speculated as the explanation for this disagreement. In this article, an exact solution for the leading-order concentration of gas in the liquid is determined. Using this exact solution, the well-established mathematical model is reduced to a system of two ordinary differential equations for the spherical bubble radius and the mass of gas in the bubble. This simplified model predicts the rapid bubble growth observed in experiments of a single spherical bubble in the bulk. The new results show that the bubble growth is asymptotically larger than at later times when the mass flux is limited by the slow diffusion of gas in a much larger region of the liquid surrounding the bubble. The new results also show that this bubble growth is relatively insensitive to a reduction in surface tension.