Rice morphogenesis and plant architecture: Measurement, specification and the reconstruction of structural development by 3D architectural modelling

Background and Aims The morphogenesis and architecture of a rice plant, Oryza sativa, are critical factors in the yield equation, but they are not well studied because of the lack of appropriate tools for 3D measurement. The architecture of rice plants is characterized by a large number of tillers and leaves. The aims of this study were to specify rice plant architecture and to find appropriate functions to represent the 3D growth across all growth stages. Methods A japonica type rice, 'Namaga', was grown in pots under outdoor conditions. A 3D digitizer was used to measure the rice plant structure at intervals from the young seedling stage to maturity. The L-system formalism was applied to create '3D virtual rice' plants, incorporating models of phenological development and leaf emergence period as a function of temperature and photoperiod, which were used to determine the timing of tiller emergence. Key Results The relationships between the nodal positions and leaf lengths, leaf angles and tiller angles were analysed and used to determine growth functions for the models. The '3D virtual rice' reproduces the structural development of isolated plants and provides a good estimation of the fillering process, and of the accumulation of leaves. Conclusions The results indicated that the '3D virtual rice' has a possibility to demonstrate the differences in the structure and development between cultivars and under different environmental conditions. Future work, necessary to reflect both cultivar and environmental effects on the model performance, and to link with physiological models, is proposed in the discussion.

Determination of lifter design, speed and filling effects in AG mills by 3D DEM

The power required to operate large gyratory mills often exceeds 10 MW. Hence, optimisation of the power consumption will have a significant impact on the overall economic performance and environmental impact of the mineral processing plant. In most of the published models of tumbling mills (e.g. [Morrell, S., 1996. Power draw of wet tumbling mills and its relationship to charge dynamics, Part 2: An empirical approach to modelling of mill power draw. Trans. Inst. Mining Metall. (Section C: Mineral Processing Ext. Metall.) 105, C54-C62. Austin, L.G., 1990. A mill power equation for SAG mills. Miner. Metall. Process. 57-62]), the effect of lifter design and its interaction with mill speed and filling are not incorporated. Recent experience suggests that there is an opportunity for improving grinding efficiency by choosing the appropriate combination of these variables. However, it is difficult to experimentally determine the interactions of these variables in a full scale mill. Although some work has recently been published using DEM simulations, it was basically. limited to 2D. The discrete element code, Particle Flow Code 3D (PFC3D), has been used in this work to model the effects of lifter height (525 cm) and mill speed (50-90% of critical) on the power draw and frequency distribution of specific energy (J/kg) of normal impacts in a 5 m diameter autogenous (AG) mill. It was found that the distribution of the impact energy is affected by the number of lifters, lifter height, mill speed and mill filling. Interactions of lifter design, mill speed and mill filling are demonstrated through three dimensional distinct element methods (3D DEM) modelling. The intensity of the induced stresses (shear and normal) on lifters, and hence the lifter wear, is also simulated. (C) 2004 Elsevier Ltd. All rights reserved.

Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.

Computer simulations of coupled problems in geological and geochemical systems

The finite element method is used to simulate coupled problems, which describe the related physical and chemical processes of ore body formation and mineralization, in geological and geochemical systems. The main purpose of this paper is to illustrate some simulation results for different types of modelling problems in pore-fluid saturated rock masses. The aims of the simulation results presented in this paper are: (1) getting a better understanding of the processes and mechanisms of ore body formation and mineralization in the upper crust of the Earth; (2) demonstrating the usefulness and applicability of the finite element method in dealing with a wide range of coupled problems in geological and geochemical systems; (3) qualitatively establishing a set of showcase problems, against which any numerical method and computer package can be reasonably validated. (C) 2002 Published by Elsevier Science B.V.

Numerical modelling of chemical effects of magma solidification problems in porous rocks

The solidification of intruded magma in porous rocks can result in the following two consequences: (1) the heat release due to the solidification of the interface between the rock and intruded magma and (2) the mass release of the volatile fluids in the region where the intruded magma is solidified into the rock. Traditionally, the intruded magma solidification problem is treated as a moving interface (i.e. the solidification interface between the rock and intruded magma) problem to consider these consequences in conventional numerical methods. This paper presents an alternative new approach to simulate thermal and chemical consequences/effects of magma intrusion in geological systems, which are composed of porous rocks. In the proposed new approach and algorithm, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with the proposed mass source and physically equivalent heat source. The major advantage in using the proposed equivalent algorithm is that a fixed mesh of finite elements with a variable integration time-step can be employed to simulate the consequences and effects of the intruded magma solidification using the conventional finite element method. The correctness and usefulness of the proposed equivalent algorithm have been demonstrated by a benchmark magma solidification problem. Copyright (c) 2005 John Wiley & Sons, Ltd.

Modelling the size of the crushed zone around a blasthole

A new model to predict the extent of crushing around a blasthole is presented. The model is based on the back-analysis of a comprehensive experimental program that included the direct measurement of the zone of crushing from 92 blasting tests on concrete blocks using two commercial explosives. The concrete blocks varied from low, medium to high strength and measured 1.5 in in length, 1.0 m in width and 1.1 m in height. A dimensionless parameter called the crushing zone index (CZI) is introduced. This index measures the crushing potential of a charged blasthole and is a function of the borehole pressure, the unconfined compressive strength of the rock material, dynamic Young's modulus and Poisson's ratio. It is shown that the radius of crushing is a function of the CZI and the blasthole radius. A good correlation between the new model and measured results was obtained. A number of previously proposed models could not approximate the conditions measured in the experimental work and there are noted discrepancies between the different approaches reviewed, particularly for smaller diameter holes and low strength rock conditions. The new model has been verified with full scale tests reported in the literature. Results from this validation and model evaluations show its applicability to production blasting. (C) 2003 Elsevier Science Ltd. All rights reserved.

3D information visualisation: An historical perspective

The use of 3D visualisation of digital information is a recent phenomenon. It relies on users understanding 3D perspectival spaces. Questions about the universal access of such spaces has been debated since its inception in the European Renaissance. Perspective has since become a strong cultural influence in Western visual communication. Perspective imaging assists the process of experimenting by the sketching or modelling of ideas. In particular, the recent 3D modelling of an essentially non-dimensional Cyber-space raises questions of how we think about information in general. While alternate methods clearly exist they are rarely explored within the 3D paradigm (such as Chinese isometry). This paper seeks to generate further discussion on the historical background of perspective and its role in underpinning this emergent field. © 2005 IEEE.

An anisotropic viscous representation of Mohr-Coulomb failure for use is modelling coupled mantle-continent dynamics

In mantle convection models it has become common to make use of a modified (pressure sensitive, Boussinesq) von Mises yield criterion to limit the maximum stress the lithosphere can support. This approach allows the viscous, cool thermal boundary layer to deform in a relatively plate-like mode even in a fully Eulerian representation. In large-scale models with embedded continental crust where the mobile boundary layer represents the oceanic lithosphere, the von Mises yield criterion for the oceans ensures that the continents experience a realistic broad-scale stress regime. In detailed models of crustal deformation it is, however, more appropriate to choose a Mohr-Coulomb yield criterion based upon the idea that frictional slip occurs on whichever one of many randomly oriented planes happens to be favorably oriented with respect to the stress field. As coupled crust/mantle models become more sophisticated it is important to be able to use whichever failure model is appropriate to a given part of the system. We have therefore developed a way to represent Mohr-Coulomb failure within a code which is suited to mantle convection problems coupled to large-scale crustal deformation. Our approach uses an orthotropic viscous rheology (a different viscosity for pure shear to that for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation - neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane which is formally equivalent in any symmetric formulation. It is also important to allow strain-weakening of the material. The material should remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-Integration-point finite element code and will show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion, and comparisons between mantle convection models using the von Mises versus the Mohr-Coulomb yield criteria. The formulation itself is general and applies to 2D and 3D problems, although it is somewhat more complicated to identify the slip plane in 3D.

Weibull model selection for reliability modelling

A large number of models have been derived from the two-parameter Weibull distribution and are referred to as Weibull models. They exhibit a wide range of shapes for the density and hazard functions, which makes them suitable for modelling complex failure data sets. The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these models are suitable for modelling a given data set. This paper deals with this topic.

Variants of temporal defeasible logics for modelling norm modifications

This paper proposes some variants of Temporal Defeasible Logic (TDL) to reason about normative modifications. These variants make it possible to differentiate cases in which, for example, modifications at some time change legal rules but their conclusions persist afterwards from cases where also their conclusions are blocked.

Embedded Voxel Colouring

The reconstruction of a complex scene from multiple images is a fundamental problem in the field of computer vision. Volumetric methods have proven to be a strong alternative to traditional correspondence-based methods due to their flexible visibility models. In this paper we analyse existing methods for volumetric reconstruction and identify three key properties of voxel colouring algorithms: a water-tight surface model, a monotonic carving order, and causality. We present a new Voxel Colouring algorithm which embeds all reconstructions of a scene into a single output. While modelling exact visibility for arbitrary camera locations, Embedded Voxel Colouring removes the need for a priori threshold selection present in previous work. An efficient implementation is given along with results demonstrating the advantages of posteriori threshold selection.

Air Bubble Entrainment in Hydraulic Jumps: Physical Modelling and Scale Effects

A hydraulic jump is characterised by strong energy dissipation and air entrainment. In the present study, new air-water flow measurements were performed in hydraulic jumps with partially-developed flow conditions in relatively large-size facilities with phase-detection probes. The experiments were conducted with identical Froude numbers, but a range of Reynolds numbers and relative channel widths. The results showed drastic scale effects at small Reynolds numbers in terms of void fraction and bubble count rate distributions. The void fraction distributions implied comparatively greater detrainment at low Reynolds numbers leading to a lesser overall aeration of the jump roller, while dimensionless bubble count rates were drastically lower especially in the mixing layer. The experimental results suggested also that the relative channel width had little effect on the air-water flow properties for identical inflow Froude and Reynolds numbers.