Comparison of DEM and experiment for a scale model SAG mill

Predictions of flow patterns in a 600-mm scale model SAG mill made using four classes of discrete element method (DEM) models are compared to experimental photographs. The accuracy of the various models is assessed using quantitative data on shoulder, toe and vortex center positions taken from ensembles of both experimental and simulation results. These detailed comparisons reveal the strengths and weaknesses of the various models for simulating mills and allow the effect of different modelling assumptions to be quantitatively evaluated. In particular, very close agreement is demonstrated between the full 3D model (including the end wall effects) and the experiments. It is also demonstrated that the traditional two-dimensional circular particle DEM model under-predicts the shoulder, toe and vortex center positions and the power draw by around 10 degrees. The effect of particle shape and the dimensionality of the model are also assessed, with particle shape predominantly affecting the shoulder position while the dimensionality of the model affects mainly the toe position. Crown Copyright (C) 2003 Published by Elsevier Science B.V. All rights reserved.

The lattice solid model to simulate the physics of rocks and earthquakes: Incorporation of friction

The particle-based lattice solid model developed to study the physics of rocks and the nonlinear dynamics of earthquakes is refined by incorporating intrinsic friction between particles. The model provides a means for studying the causes of seismic wave attenuation, as well as frictional heat generation, fault zone evolution, and localisation phenomena. A modified velocity-Verlat scheme that allows friction to be precisely modelled is developed. This is a difficult computational problem given that a discontinuity must be accurately simulated by the numerical approach (i.e., the transition from static to dynamical frictional behaviour). This is achieved using a half time step integration scheme. At each half time step, a nonlinear system is solved to compute the static frictional forces and states of touching particle-pairs. Improved efficiency is achieved by adaptively adjusting the time step increment, depending on the particle velocities in the system. The total energy is calculated and verified to remain constant to a high precision during simulations. Numerical experiments show that the model can be applied to the study of earthquake dynamics, the stick-slip instability, heat generation, and fault zone evolution. Such experiments may lead to a conclusive resolution of the heat flow paradox and improved understanding of earthquake precursory phenomena and dynamics. (C) 1999 Academic Press.

Growth regime map for liquid-bound granules: further development and experimental validation

An attempt was made to quantify the boundaries and validate the granule growth regime map for liquid-bound granules recently proposed by Iveson and Litster (AlChE J. 44 (1998) 1510). This regime map postulates that the type of granule growth behaviour is a function of only two dimensionless groups: the amount of granule deformation during collision (characterised by a Stokes deformation number, St(def)) and the maximum granule pore saturation, s(max). The results of experiments performed with a range of materials (glass ballotini, iron ore fines, copper chalcopyrite powder and a sodium sulphate and cellulose mixture) using both drum and high shear mixer granulators were examined. The drum granulation results gave good agreement with the proposed regime map. The boundary between crumb and steady growth occurs at St(def) of order 0.1 and the boundary between steady and induction growth occurs at St(def) of order 0.001. The nucleation only boundary occurs at pore saturations that increase from 70% to 80% with decreasing St(def). However, the high shear mixer results all had St(def) numbers which were too large. This is most likely to be because the chopper tip-speed is an over-estimate of the average impact velocity granules experience and possibly also due to the dynamic yield strength of the materials being significantly greater than the yield strengths measured at low strain rates. Hence, the map is only a useful tool for comparing the granulation behaviour of different materials in the same device. Until we have a better understanding of the flow patterns and impact velocities in granulators, it cannot be used to compare different types of equipment. Theoretical considerations also revealed that several of the regime boundaries are also functions of additional parameters not explicitly contained on the map, such as binder viscosity. (C) 2001 Elsevier Science B.V. All rights reserved.

Simulation of the micro-physics of rocks using LSMearth

The particle-based Lattice Solid Model (LSM) was developed to provide a basis to study the physics of rocks and the nonlinear dynamics of earthquakes (MORA and PLACE, 1994; PLACE and MORA, 1999). A new modular and flexible LSM approach has been developed that allows different microphysics to be easily included in or removed from the model. The approach provides a virtual laboratory where numerical experiments can easily be set up and all measurable quantities visualised. The proposed approach provides a means to simulate complex phenomena such as fracturing or localisation processes, and enables the effect of different micro-physics on macroscopic behaviour to be studied. The initial 2-D model is extended to allow three-dimensional simulations to be performed and particles of different sizes to be specified. Numerical bi-axial compression experiments under different confining pressure are used to calibrate the model. By tuning the different microscopic parameters (such as coefficient of friction, microscopic strength and distribution of grain sizes), the macroscopic strength of the material and can be adjusted to be in agreement with laboratory experiments, and the orientation of fractures is consistent with the theoretical value predicted based on Mohr-Coulomb diagram. Simulations indicate that 3-D numerical models have different macroscopic properties than in 2-D and, hence, the model must be recalibrated for 3-D simulations. These numerical experiments illustrate that the new approach is capable of simulating typical rock fracture behaviour. The new model provides a basis to investigate nucleation, rupture and slip pulse propagation in complex fault zones without the previous model limitations of a regular low-level surface geometry and being restricted to two-dimensions.

Modelling pre-clearing vegetation distribution using GIS-integrated statistical, ecological and data models: A case study from the wet tropics of Northeastern Australia

Traditional vegetation mapping methods use high cost, labour-intensive aerial photography interpretation. This approach can be subjective and is limited by factors such as the extent of remnant vegetation, and the differing scale and quality of aerial photography over time. An alternative approach is proposed which integrates a data model, a statistical model and an ecological model using sophisticated Geographic Information Systems (GIS) techniques and rule-based systems to support fine-scale vegetation community modelling. This approach is based on a more realistic representation of vegetation patterns with transitional gradients from one vegetation community to another. Arbitrary, though often unrealistic, sharp boundaries can be imposed on the model by the application of statistical methods. This GIS-integrated multivariate approach is applied to the problem of vegetation mapping in the complex vegetation communities of the Innisfail Lowlands in the Wet Tropics bioregion of Northeastern Australia. The paper presents the full cycle of this vegetation modelling approach including sampling sites, variable selection, model selection, model implementation, internal model assessment, model prediction assessments, models integration of discrete vegetation community models to generate a composite pre-clearing vegetation map, independent data set model validation and model prediction's scale assessments. An accurate pre-clearing vegetation map of the Innisfail Lowlands was generated (0.83r(2)) through GIS integration of 28 separate statistical models. This modelling approach has good potential for wider application, including provision of. vital information for conservation planning and management; a scientific basis for rehabilitation of disturbed and cleared areas; a viable method for the production of adequate vegetation maps for conservation and forestry planning of poorly-studied areas. (c) 2006 Elsevier B.V. All rights reserved.

Implementation of particle-scale rotation in the 3-d Lattice Solid Model

In this study, 3-D Lattice Solid Model (LSMearth or LSM) was extended by introducing particle-scale rotation. In the new model, for each 3-D particle, we introduce six degrees of freedom: Three for translational motion, and three for orientation. Six kinds of relative motions are permitted between two neighboring particles, and six interactions are transferred, i.e., radial, two shearing forces, twisting and two bending torques. By using quaternion algebra, relative rotation between two particles is decomposed into two sequence-independent rotations such that all interactions due to the relative motions between interactive rigid bodies can be uniquely decided. After incorporating this mechanism and introducing bond breaking under torsion and bending into the LSM, several tests on 2-D and 3-D rock failure under uni-axial compression are carried out. Compared with the simulations without the single particle rotational mechanism, the new simulation results match more closely experimental results of rock fracture and hence, are encouraging. Since more parameters are introduced, an approach for choosing the new parameters is presented.

A generalised dynamic model for char particle gasification with structure evolution and peripheral fragmentation

A generalised model for the prediction of single char particle gasification dynamics, accounting for multi-component mass transfer with chemical reaction, heat transfer, as well as structure evolution and peripheral fragmentation is developed in this paper. Maxwell-Stefan analysis is uniquely applied to both micro and macropores within the framework of the dusty-gas model to account for the bidisperse nature of the char, which differs significantly from the conventional models that are based on a single pore type. The peripheral fragmentation and random-pore correlation incorporated into the model enable prediction of structure/reactivity relationships. The occurrence of chemical reaction within the boundary layer reported by Biggs and Agarwal (Chem. Eng. Sci. 52 (1997) 941) has been confirmed through an analysis of CO/CO2 product ratio obtained from model simulations. However, it is also quantitatively observed that the significance of boundary layer reaction reduces notably with the reduction of oxygen concentration in the flue gas, operational pressure and film thickness. Computations have also shown that in the presence of diffusional gradients peripheral fragmentation occurs in the early stages on the surface, after which conversion quickens significantly due to small particle size. Results of the early commencement of peripheral fragmentation at relatively low overall conversion obtained from a large number of simulations agree well with experimental observations reported by Feng and Bhatia (Energy & Fuels 14 (2000) 297). Comprehensive analysis of simulation results is carried out based on well accepted physical principles to rationalise model prediction. (C) 2001 Elsevier Science Ltd. AH rights reserved.

Exact form factors for the Josephson tunneling current and relative particle number fluctuations in a model of two coupled Bose-Einstein condensates

Form factors are derived for a model describing the coherent Josephson tunneling between two coupled Bose-Einstein condensates. This is achieved by studying the exact solution of the model within the framework of the algebraic Bethe ansatz. In this approach the form factors are expressed through determinant representations which are functions of the roots of the Bethe ansatz equations.

Impulse-response function of splanchnic circulation with model-independent constraints: theory and experimental validation

Modeling physiological processes using tracer kinetic methods requires knowledge of the time course of the tracer concentration in blood supplying the organ. For liver studies, however, inaccessibility of the portal vein makes direct measurement of the hepatic dual-input function impossible in humans. We want to develop a method to predict the portal venous time-activity curve from measurements of an arterial time-activity curve. An impulse-response function based on a continuous distribution of washout constants is developed and validated for the gut. Experiments with simultaneous blood sampling in aorta and portal vein were made in 13 anesthetized pigs following inhalation of intravascular [O-15] CO or injections of diffusible 3-O[ C-11] methylglucose (MG). The parameters of the impulse-response function have a physiological interpretation in terms of the distribution of washout constants and are mathematically equivalent to the mean transit time ( T) and standard deviation of transit times. The results include estimates of mean transit times from the aorta to the portal vein in pigs: (T) over bar = 0.35 +/- 0.05 min for CO and 1.7 +/- 0.1 min for MG. The prediction of the portal venous time-activity curve benefits from constraining the regression fits by parameters estimated independently. This is strong evidence for the physiological relevance of the impulse-response function, which includes asymptotically, and thereby justifies kinetically, a useful and simple power law. Similarity between our parameter estimates in pigs and parameter estimates in normal humans suggests that the proposed model can be adapted for use in humans.

Critical behavior of one-particle spectral weights in the transverse Ising model

We investigate the critical behavior of the spectral weight of a single quasiparticle, one of the key observables in experiment, for the particular case of the transverse Ising model. Series expansions are calculated for the linear chain and the square and simple cubic lattices. For the chain model, a conjectured exact result is discovered. For the square and simple cubic lattices, series analyses are used to estimate the critical exponents. The results agree with the general predictions of Sachdev [Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999)].

Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern

Strain localisation is a widespread phenomenon often observed in shear and compressive loading of geomaterials, for example, the fault gouge. It is believed that the main mechanisms of strain localisation are strain softening and mismatch between dilatancy and pressure sensitivity. Observations show that gouge deformation is accompanied by considerable rotations of grains. In our previous work as a model for gouge material, we proposed a continuum description for an assembly of particles of equal radius in which the particle rotation is treated as an independent degree of freedom. We showed that there exist critical values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-surface layers of the fault, even in the absence of inelasticity. Here, we generalise the model to the case of finite deformations characteristic for the gouge deformation. We derive objective constitutive relationships relating the Jaumann rates of stress and moment stress to the relative strain and curvature rates, respectively. The model suggests that the pattern of localisation remains the same as in the linear case. However, the presence of the Jaumann terms leads to the emergence of non-zero normal stresses acting along and perpendicular to the shear layer (with zero hydrostatic pressure), and localised along the mid-line of the gouge; these stress components are absent in the linear model of simple shear. These additional normal stresses, albeit small, cause a change in the direction in which the maximal normal stresses act and in which en-echelon fracturing is formed.