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Retention of sprays on plants is a critical component influencing the effectiveness of agrichemical applications. Previous simulations of s pray retention by plants gave poor agreement for hard-to-wet species when compared with actual measured retention. A new model is developed here that accounts for: species wettability, impaction angle, droplet bounce, partial retention on shatter, a variable time to shatter, and the number of daughter droplets produced. The aim of this study was to compare predictions from the new model with data obtained by spraying five mixtures via five nozzles onto easy-to-wet cotton ( Gossypium hirsutum L.), and hard-to-wet wheat ( Triticum aestivum L.) and fat hen ( Chenopodium album L.). The new model correctly predicts retention to be highest on cotton and lowest on wheat. The trend in both measured data and the model predictions is for retention to decrease with increasing droplet size, on all three plant species. Formulation is correctly predicted to have little influence on retention by easy-to-wet cotton plants and to enhance retention by the harder-to-wet wheat and fat hen plants. The parameters that describe partial retention on shatter and variable time to shatter have a substantial influence on retention, as they affect primary or secondary droplet capture. A better understanding of the kinetic energy effects and the interactions between the formulation and the leaf surface are needed to refine their input values. [ABSTRACT FROM AUTHOR]

Realistic virtual models of leaf surfaces are important for several applications in the plant sciences, such as modelling agrichemical spray droplet movement and spreading on the surface. In this context, the virtual surfaces are required to be smooth enough to facilitate the use of the mathematical equations that govern the motion of the droplet. Although an effective approach is to apply discrete smoothing D[sup 2]-spline algorithms to reconstruct the leaf surfaces from three-dimensional scanned data, difficulties arise when dealing with wheat (Triticum aestivum L.) leaves, which tendtotwist and bend. To overcome this topological difficulty, we develop a parameterisation technique that rotates and translates the original data, allowing the surface to be fitted using the discrete smoothing D[sup 2]-spline methods in the new parameter space. Our algorithm uses finite element methods to represent the surface as a linear combination of compactly supported shape functions. Numerical results confirm that the parameterisation, along with the use of discrete smoothing D[sup 2]-spline techniques, produces realistic virtual representations of wheat leaves. [ABSTRACT FROM AUTHOR]

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modeling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D²-splines [R. Arcangéli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, New York, 2004], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, SIAM J. Numer. Anal., 1 (2003), pp. 208-234], and the radial basis function Clough-Tocher method [M. N. Oqielat, I. W. Turner, and J. A. Belward, Appl. Math. Model., 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D²-splines produce reconstructed leaf surfaces which better represent the original physical leaf. [ABSTRACT FROM AUTHOR]

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results obtained by a forced KdV equation are also presented, as are numerical solutions of the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely [ABSTRACT FROM AUTHOR]

Focuses on approximation techniques in tank calibration. Interpolation, approximation and geometry; Choice of interpolation schemes; Volume as a function of height; Quality of a cubic-spline approximation near a singularity.

A curvilinear thin film model is used to simulate the motion of droplets on a virtual leaf surface, with a view to better understand the retention of agricultural sprays on plants. The governing model, adapted from Roy et al. (2002 J. Fluid Mech. 454, 235-261 (doi:10.1017/S0022112001007133)) with the addition of a disjoining pressure term, describes the gravity- and curvature-driven flow of a small droplet on a complex substrate: a cotton leaf reconstructed from digitized scan data. Coalescence is the key mechanism behind spray coating of foliage, and our simulations demonstrate that various experimentally observed coalescence behaviours can be reproduced qualitatively. By varying the contact angle over the domain, we also demonstrate that the presence of a chemical defect can act as an obstacle to the droplet's path, causing break-up. In simulations on the virtual leaf, it is found that the movement of a typical spray size droplet is driven almost exclusively by substrate curvature gradients. It is not until droplet mass is sufficiently increased via coalescence that gravity becomes the dominating force.