Step size control for efficient discrete element simulation

The step size determines the accuracy of a discrete element simulation. The position and velocity updating calculation uses a pre-calculated table and hence the control of step size can not use the integration formulas for step size control. A step size control scheme for use with the table driven velocity and position calculation uses the difference between the calculation result from one big step and that from two small steps. This variable time step size method chooses the suitable time step size for each particle at each step automatically according to the conditions. Simulation using fixed time step method is compared with that of using variable time step method. The difference in computation time for the same accuracy using a variable step size (compared to the fixed step) depends on the particular problem. For a simple test case the times are roughly similar. However, the variable step size gives the required accuracy on the first run. A fixed step size may require several runs to check the simulation accuracy or a conservative step size that results in longer run times. (C) 2001 Elsevier Science Ltd. All rights reserved.

Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

A modified discrete random pore model allowing for different initial surface reactivity

We investigate here a modification of the discrete random pore model [Bhatia SK, Vartak BJ, Carbon 1996;34:1383], by including an additional rate constant which takes into account the different reactivity of the initial pore surface having attached functional groups and hydrogens, relative to the subsequently exposed surface. It is observed that the relative initial reactivity has a significant effect on the conversion and structural evolution, underscoring the importance of initial surface chemistry. The model is tested against experimental data on chemically controlled char oxidation and steam gasification at various temperatures. It is seen that the variations of the reaction rate and surface area with conversion are better represented by the present approach than earlier random pore models. The results clearly indicate the improvement of model predictions in the low conversion region, where the effect of the initially attached functional groups and hydrogens is more significant, particularly for char oxidation. It is also seen that, for the data examined, the initial surface chemistry is less important for steam gasification as compared to the oxidation reaction. Further development of the approach must also incorporate the dynamics of surface complexation, which is not considered here.

Applying discrete element modelling to vertical and horizontal shaft impact crushers

The PFC3D (particle flow code) that models the movement and interaction of particles by the DEM techniques was employed to simulate the particle movement and to calculate the velocity and energy distribution of collision in two types of impact crusher: the Canica vertical shaft crusher and the BJD horizontal shaft swing hammer mill. The distribution of collision energies was then converted into a product size distribution for a particular ore type using JKMRC impact breakage test data. Experimental data of the Canica VSI crusher treating quarry and the BJD hammer mill treating coal were used to verify the DEM simulation results. Upon the DEM procedures being validated, a detailed simulation study was conducted to investigate the effects of the machine design and operational conditions on velocity and energy distributions of collision inside the milling chamber and on the particle breakage behaviour. (C) 2003 Elsevier Ltd. All rights reserved.

A parallel implementation of the lattice solid model for the simulation of rock mechanics and earthquake dynamics

The Lattice Solid Model has been used successfully as a virtual laboratory to simulate fracturing of rocks, the dynamics of faults, earthquakes and gouge processes. However, results from those simulations show that in order to make the next step towards more realistic experiments it will be necessary to use models containing a significantly larger number of particles than current models. Thus, those simulations will require a greatly increased amount of computational resources. Whereas the computing power provided by single processors can be expected to increase according to Moore's law, i.e., to double every 18-24 months, parallel computers can provide significantly larger computing power today. In order to make this computing power available for the simulation of the microphysics of earthquakes, a parallel version of the Lattice Solid Model has been implemented. Benchmarks using large models with several millions of particles have shown that the parallel implementation of the Lattice Solid Model can achieve a high parallel-efficiency of about 80% for large numbers of processors on different computer architectures.

Analysis of stirred mill performance using DEM simulation: Part 2 - Coherent flow structures, liner stress and wear, mixing and transport

Stirred Mills are becoming increasingly used for fine and ultra-fine grinding. This technology is still poorly understood when used in the mineral processing context. This makes process optimisation of such devices problematic. 3D DEM simulations of the flow of grinding media in pilot scale tower mills and pin mills are carried out in order to investigate the relative performance of these stirred mills. In the first part of this paper, media flow patterns and energy absorption rates and distributions were analysed to provide a good understanding of the media flow and the collisional environment in these mills. In this second part we analyse steady state coherent flow structures, liner stress and wear by impact and abrasion. We also examine mixing and transport efficiency. Together these provide a comprehensive understanding of all the key processes operating in these mills and a clear understanding of the relative performance issues. (C) 2006 Elsevier Ltd. All rights reserved.

Analysis of stirred mill performance using DEM simulation: Part 1 - Media motion, energy consumption and collisional environment

Stirred mills are becoming increasingly used for fine and ultra-fine grinding. This technology is still poorly understood when used in the mineral processing context. This makes process optimisation of such devices problematic. 3D DEM simulations of the flow of grinding media in pilot scale tower mills and pin mills are carried out in order to investigate the relative performance of these stirred mills. Media flow patterns and energy absorption rates and distributions are analysed here. In the second part of this paper, coherent flow structures, equipment wear and mixing and transport efficiency are analysed. (C) 2006 Published by Elsevier Ltd.

Parallel 3D Simulation of a Fault Gouge using the Lattice Solid Model

Despite the insight gained from 2-D particle models, and given that the dynamics of crustal faults occur in 3-D space, the question remains, how do the 3-D fault gouge dynamics differ from those in 2-D? Traditionally, 2-D modeling has been preferred over 3-D simulations because of the computational cost of solving 3-D problems. However, modern high performance computing architectures, combined with a parallel implementation of the Lattice Solid Model (LSM), provide the opportunity to explore 3-D fault micro-mechanics and to advance understanding of effective constitutive relations of fault gouge layers. In this paper, macroscopic friction values from 2-D and 3-D LSM simulations, performed on an SGI Altix 3700 super-cluster, are compared. Two rectangular elastic blocks of bonded particles, with a rough fault plane and separated by a region of randomly sized non-bonded gouge particles, are sheared in opposite directions by normally-loaded driving plates. The results demonstrate that the gouge particles in the 3-D models undergo significant out-of-plane motion during shear. The 3-D models also exhibit a higher mean macroscopic friction than the 2-D models for varying values of interparticle friction. 2-D LSM gouge models have previously been shown to exhibit accelerating energy release in simulated earthquake cycles, supporting the Critical Point hypothesis. The 3-D models are shown to also display accelerating energy release, and good fits of power law time-to-failure functions to the cumulative energy release are obtained.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Determination of coalescence kernels for high-shear granulation using DEM simulations

Discrete element method (DEM) modeling is used in parallel with a model for coalescence of deformable surface wet granules. This produces a method capable of predicting both collision rates and coalescence efficiencies for use in derivation of an overall coalescence kernel. These coalescence kernels can then be used in computationally efficient meso-scale models such as population balance equation (PBE) models. A soft-sphere DEM model using periodic boundary conditions and a unique boxing scheme was utilized to simulate particle flow inside a high-shear mixer. Analysis of the simulation results provided collision frequency, aggregation frequency, kinetic energy, coalescence efficiency and compaction rates for the granulation process. This information can be used to bridge the gap in multi-scale modeling of granulation processes between the micro-scale DEM/coalescence modeling approach and a meso-scale PBE modeling approach.

XSophe-Sophe-XeprView (R). A computer simulation software suite (v. 1.1.3) for the analysis of continuous wave EPR spectra

The XSophe-Sophe-XeprView((R)) computer simulation software suite enables scientists to easily determine spin Hamiltonian parameters from isotropic, randomly oriented and single crystal continuous wave electron paramagnetic resonance (CW EPR) spectra from radicals and isolated paramagnetic metal ion centers or clusters found in metalloproteins, chemical systems and materials science. XSophe provides an X-windows graphical user interface to the Sophe programme and allows: creation of multiple input files, local and remote execution of Sophe, the display of sophelog (output from Sophe) and input parameters/files. Sophe is a sophisticated computer simulation software programme employing a number of innovative technologies including; the Sydney OPera HousE (SOPHE) partition and interpolation schemes, a field segmentation algorithm, the mosaic misorientation linewidth model, parallelization and spectral optimisation. In conjunction with the SOPHE partition scheme and the field segmentation algorithm, the SOPHE interpolation scheme and the mosaic misorientation linewidth model greatly increase the speed of simulations for most spin systems. Employing brute force matrix diagonalization in the simulation of an EPR spectrum from a high spin Cr(III) complex with the spin Hamiltonian parameters g(e) = 2.00, D = 0.10 cm(-1), E/D = 0.25, A(x) = 120.0, A(y) = 120.0, A(z) = 240.0 x 10(-4) cm(-1) requires a SOPHE grid size of N = 400 (to produce a good signal to noise ratio) and takes 229.47 s. In contrast the use of either the SOPHE interpolation scheme or the mosaic misorientation linewidth model requires a SOPHE grid size of only N = 18 and takes 44.08 and 0.79 s, respectively. Results from Sophe are transferred via the Common Object Request Broker Architecture (CORBA) to XSophe and subsequently to XeprView((R)) where the simulated CW EPR spectra (1D and 2D) can be compared to the experimental spectra. Energy level diagrams, transition roadmaps and transition surfaces aid the interpretation of complicated randomly oriented CW EPR spectra and can be viewed with a web browser and an OpenInventor scene graph viewer.

User guide for shock and blast simulation with the OctVCE code (version 3.5+), Department of Mechanical Engineering Report 2007/13

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel as it is simple to code and sufficient for practical engineering design problems. This also makes the code much more ‘user-friendly’ than structured grid approaches as the gridding process is done automatically. The CFD methodology relies on a finite-volume formulation of the unsteady Euler equations and is solved using a standard explicit Godonov (MUSCL) scheme. Both octree-based adaptive mesh refinement and shared-memory parallel processing capability have also been incorporated. For further details on the theory behind the code, see the companion report 2007/12.

Flow and axial dispersion simulation for traveling axisymmetric Taylor vortices

Numerical experiments using a finite difference method were carried out to determine the motion of axisymmetric Taylor vortices for narrow-gap Taylor vortex flow. When a pressure gradient is imposed on the flow the vortices are observed to move with an axial speed of 1.16 +/- 0.005 times the mean axial flow velocity. The method of Brenner was used to calculate the long-time axial spread of material in the flow. For flows where there is no pressure gradient, the axial dispersion scales with the square root of the molecular diffusion, in agreement with the results of Rosen-bluth et al. for high Peclet number dispersion in spatially periodic flows with a roll structure. When a pressure gradient is imposed the dispersion increases by an amount approximately equal to 6.5 x 10(-4) (W) over bar(2)d(2)/D-m, where (W) over bar is the average axial velocity in the annulus, analogous to Taylor dispersion for laminar flow in an empty tube.

Improving wheat simulation capabilities in Australia from a cropping systems perspective - II. Testing simulation capabilities of wheat growth

To simulate cropping systems, crop models must not only give reliable predictions of yield across a wide range of environmental conditions, they must also quantify water and nutrient use well, so that the status of the soil at maturity is a good representation of the starting conditions for the next cropping sequence. To assess the suitability for this task a range of crop models, currently used in Australia, were tested. The models differed in their design objectives, complexity and structure and were (i) tested on diverse, independent data sets from a wide range of environments and (ii) model components were further evaluated with one detailed data set from a semi-arid environment. All models were coded into the cropping systems shell APSIM, which provides a common soil water and nitrogen balance. Crop development was input, thus differences between simulations were caused entirely by difference in simulating crop growth. Under nitrogen non-limiting conditions between 73 and 85% of the observed kernel yield variation across environments was explained by the models. This ranged from 51 to 77% under varying nitrogen supply. Water and nitrogen effects on leaf area index were predicted poorly by all models resulting in erroneous predictions of dry matter accumulation and water use. When measured light interception was used as input, most models improved in their prediction of dry matter and yield. This test highlighted a range of compensating errors in all modelling approaches. Time course and final amount of water extraction was simulated well by two models, while others left up to 25% of potentially available soil water in the profile. Kernel nitrogen percentage was predicted poorly by all models due to its sensitivity to small dry matter changes. Yield and dry matter could be estimated adequately for a range of environmental conditions using the general concepts of radiation use efficiency and transpiration efficiency. However, leaf area and kernel nitrogen dynamics need to be improved to achieve better estimates of water and nitrogen use if such models are to be use to evaluate cropping systems. (C) 1998 Elsevier Science B.V.