Conditional simulation of random fields by successive residuals

This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

Infusing the use of seasonal climate forecasting into crop management practice in North East Australia using discussion support software

Seasonal climate forecasting offers potential for improving management of crop production risks in the cropping systems of NE Australia. But how is this capability best connected to management practice? Over the past decade, we have pursued participative systems approaches involving simulation-aided discussion with advisers and decision-makers. This has led to the development of discussion support software as a key vehicle for facilitating infusion of forecasting capability into practice. In this paper, we set out the basis of our approach, its implementation and preliminary evaluation. We outline the development of the discussion support software Whopper Cropper, which was designed for, and in close consultation with, public and private advisers. Whopper Cropper consists of a database of simulation output and a graphical user interface to generate analyses of risks associated with crop management options. The charts produced provide conversation pieces for advisers to use with their farmer clients in relation to the significant decisions they face. An example application, detail of the software development process and an initial survey of user needs are presented. We suggest that discussion support software is about moving beyond traditional notions of supply-driven decision support systems. Discussion support software is largely demand-driven and can compliment participatory action research programs by providing cost-effective general delivery of simulation-aided discussions about relevant management actions. The critical role of farm management advisers and dialogue among key players is highlighted. We argue that the discussion support concept, as exemplified by the software tool Whopper Cropper and the group processes surrounding it, provides an effective means to infuse innovations, like seasonal climate forecasting, into farming practice. Crown Copyright (C) 2002 Published by Elsevier Science Ltd. All rights reserved.

Simulation of the load-unload response ratio and critical sensitivity in the lattice solid model

The Load-Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It involves calculating the ratio of a specified energy release measure during loading and unloading where loading and unloading periods are determined from the earth tide induced perturbations in the Coulomb Failure Stress on optimally oriented faults. In the lead-up to large earthquakes, high LURR values are frequently observed a few months or years prior to the event. These signals may have a similar origin to the observed accelerating seismic moment release (AMR) prior to many large earthquakes or may be due to critical sensitivity of the crust when a large earthquake is imminent. As a first step towards studying the underlying physical mechanism for the LURR observations, numerical studies are conducted using the particle based lattice solid model (LSM) to determine whether LURR observations can be reproduced. The model is initialized as a heterogeneous 2-D block made up of random-sized particles bonded by elastic-brittle links. The system is subjected to uniaxial compression from rigid driving plates on the upper and lower edges of the model. Experiments are conducted using both strain and stress control to load the plates. A sinusoidal stress perturbation is added to the gradual compressional loading to simulate loading and unloading cycles and LURR is calculated. The results reproduce signals similar to those observed in earthquake prediction practice with a high LURR value followed by a sudden drop prior to macroscopic failure of the sample. The results suggest that LURR provides a good predictor for catastrophic failure in elastic-brittle systems and motivate further research to study the underlying physical mechanisms and statistical properties of high LURR values. The results provide encouragement for earthquake prediction research and the use of advanced simulation models to probe the physics of earthquakes.

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.

Simulation of the influence of rate- and state-dependent friction on the macroscopic behavior of complex fault zones with the lattice solid model

In order to understand the earthquake nucleation process, we need to understand the effective frictional behavior of faults with complex geometry and fault gouge zones. One important aspect of this is the interaction between the friction law governing the behavior of the fault on the microscopic level and the resulting macroscopic behavior of the fault zone. Numerical simulations offer a possibility to investigate the behavior of faults on many different scales and thus provide a means to gain insight into fault zone dynamics on scales which are not accessible to laboratory experiments. Numerical experiments have been performed to investigate the influence of the geometric configuration of faults with a rate- and state-dependent friction at the particle contacts on the effective frictional behavior of these faults. The numerical experiments are designed to be similar to laboratory experiments by DIETERICH and KILGORE (1994) in which a slide-hold-slide cycle was performed between two blocks of material and the resulting peak friction was plotted vs. holding time. Simulations with a flat fault without a fault gouge have been performed to verify the implementation. These have shown close agreement with comparable laboratory experiments. The simulations performed with a fault containing fault gouge have demonstrated a strong dependence of the critical slip distance D-c on the roughness of the fault surfaces and are in qualitative agreement with laboratory experiments.

Parallel simulation system for earthquake generation: Fault analysis modules and parallel coupling analysis

Solid earth simulations have recently been developed to address issues such as natural disasters, global environmental destruction and the conservation of natural resources. The simulation of solid earth phenomena involves the analysis of complex structures including strata, faults, and heterogeneous material properties. Simulation of the generation and cycle of earthquakes is particularly important, but such simulations require the analysis of complex fault dynamics. GeoFEM is a parallel finite-element analysis system intended for solid earth field phenomena problems. This paper describes recent development in the GeoFEM project for the simulation of earthquake generation and cycles.

An overview of APSIM, a model designed for farming systems simulation

The Agricultural Production Systems Simulator (APSIM) is a modular modelling framework that has been developed by the Agricultural Production Systems Research Unit in Australia. APSIM was developed to simulate biophysical process in farming systems, in particular where there is interest in the economic and ecological outcomes of management practice in the face of climatic risk. The paper outlines APSIM's structure and provides details of the concepts behind the different plant, soil and management modules. These modules include a diverse range of crops, pastures and trees, soil processes including water balance, N and P transformations, soil pH, erosion and a full range of management controls. Reports of APSIM testing in a diverse range of systems and environments are summarised. An example of model performance in a long-term cropping systems trial is provided. APSIM has been used in a broad range of applications, including support for on-farm decision making, farming systems design for production or resource management objectives, assessment of the value of seasonal climate forecasting, analysis of supply chain issues in agribusiness activities, development of waste management guidelines, risk assessment for government policy making and as a guide to research and education activity. An extensive citation list for these model testing and application studies is provided. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.

Effect of vehicle pretreatment on the flux, retention, and diffusion of topically applied penetrants in vitro

Purpose. The flux of a topically applied drug depends on the activity in the skin and the interaction between the vehicle and skin. Permeation of vehicle into the skin can alter the activity of drug and the properties of the skin barrier. The aim of this in vitro study was to separate and quantify these effects. Methods. The flux of four radiolabeled permeants (water, phenol, diflunisal, and diazepam) with log K-oct/water values from 1.4 to 4.3 was measured over 4 h through heat-separated human epidermis pretreated for 30 min with vehicles having Hildebrand solubility parameters from 7.9 to 23.4 (cal/cm(3))(1/2). Results. Enhancement was greatest after pretreatment with the more lipophilic vehicles. A synergistic enhancement was observed using binary mixtures. The flux of diazepam was not enhanced to the same extent as the other permeants, possibly because its partitioning into the epidermis is close to optimal (log K-oct 2.96). Conclusion. An analysis of the permeant remaining in the epidermis revealed that the enhancement can be the result of either increased partitioning of permeant into the epidermis or an increasing diffusivity of permeants through the epidermis.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 1. Methodology for residual generation

For dynamic simulations to be credible, verification of the computer code must be an integral part of the modelling process. This two-part paper describes a novel approach to verification through program testing and debugging. In Part 1, a methodology is presented for detecting and isolating coding errors using back-to-back testing. Residuals are generated by comparing the output of two independent implementations, in response to identical inputs. The key feature of the methodology is that a specially modified observer is created using one of the implementations, so as to impose an error-dependent structure on these residuals. Each error can be associated with a fixed and known subspace, permitting errors to be isolated to specific equations in the code. It is shown that the geometric properties extend to multiple errors in either one of the two implementations. Copyright (C) 2003 John Wiley Sons, Ltd.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 2. Residuals analysis and a case study

In Part 1 of this paper a methodology for back-to-back testing of simulation software was described. Residuals with error-dependent geometric properties were generated. A set of potential coding errors was enumerated, along with a corresponding set of feature matrices, which describe the geometric properties imposed on the residuals by each of the errors. In this part of the paper, an algorithm is developed to isolate the coding errors present by analysing the residuals. A set of errors is isolated when the subspace spanned by their combined feature matrices corresponds to that of the residuals. Individual feature matrices are compared to the residuals and classified as 'definite', 'possible' or 'impossible'. The status of 'possible' errors is resolved using a dynamic subset testing algorithm. To demonstrate and validate the testing methodology presented in Part 1 and the isolation algorithm presented in Part 2, a case study is presented using a model for biological wastewater treatment. Both single and simultaneous errors that are deliberately introduced into the simulation code are correctly detected and isolated. Copyright (C) 2003 John Wiley Sons, Ltd.

Simulation supplements field studies to determine no-till dryland corn population recommendations for semiarid western Nebraska

In a 2-yr multiple-site field study conducted in western Nebraska during 1999 and 2000, optimum dryland corn (Zea mays L.) population varied from less than 1.7 to more than 5.6 plants m(-2), depending largely on available water resources. The objective of this study was to use a modeling approach to investigate corn population recommendations for a wide range of seasonal variation. A corn growth simulation model (APSIM-maize) was coupled to long-term sequences of historical climatic data from western Nebraska to provide probabilistic estimates of dryland yield for a range of corn populations. Simulated populations ranged from 2 to 5 plants m(-2). Simulations began with one of three levels of available soil water at planting, either 80, 160, or 240 mm in the surface 1.5 m of a loam soil. Gross margins were maximized at 3 plants m(-2) when starting available water was 160 or 240 mm, and the expected probability of a financial loss at this population was reduced from about 10% at 160 mm to 0% at 240 mm. When starting available water was 80 mm, average gross margins were less than $15 ha(-1), and risk of financial loss exceeded 40%. Median yields were greatest when starting available soil water was 240 mm. However, perhaps the greater benefit of additional soil water at planting was reduction in the risk of making a financial loss. Dryland corn growers in western Nebraska are advised to use a population of 3 plants m(-2) as a base recommendation.

Structural refinement of systems specified in object-z and CSP

This paper is concerned with methods for refinement of specifications written using a combination of Object-Z and CSP. Such a combination has proved to be a suitable vehicle for specifying complex systems which involve state and behaviour, and several proposals exist for integrating these two languages. The basis of the integration in this paper is a semantics of Object-Z classes identical to CSP processes. This allows classes specified in Object-Z to be combined using CSP operators. It has been shown that this semantic model allows state-based refinement relations to be used on the Object-Z components in an integrated Object-Z/CSP specification. However, the current refinement methodology does not allow the structure of a specification to be changed in a refinement, whereas a full methodology would, for example, allow concurrency to be introduced during the development life-cycle. In this paper, we tackle these concerns and discuss refinements of specifications written using Object-Z and CSP where we change the structure of the specification when performing the refinement. In particular, we develop a set of structural simulation rules which allow single components to be refined to more complex specifications involving CSP operators. The soundness of these rules is verified against the common semantic model and they are illustrated via a number of examples.