Anisotropic convection model for the earth's mantle

The paper presents a theory for modeling flow in anisotropic, viscous rock. This theory has originally been developed for the simulation of large deformation processes including the folding and kinking of multi-layered visco-elastic rock (Muhlhaus et al. [1,2]). The orientation of slip planes in the context of crystallographic slip is determined by the normal vector - the director - of these surfaces. The model is applied to simulate anisotropic mantle convection. We compare the evolution of flow patterns, Nusselt number and director orientations for isotropic and anisotropic rheologies. In the simulations we utilize two different finite element methodologies: The Lagrangian Integration Point Method Moresi et al [8] and an Eulerian formulation, which we implemented into the finite element based pde solver Fastflo (www.cmis.csiro.au/Fastflo/). The reason for utilizing two different finite element codes was firstly to study the influence of an anisotropic power law rheology which currently is not implemented into the Lagrangian Integration point scheme [8] and secondly to study the numerical performance of Eulerian (Fastflo)- and Lagrangian integration schemes [8]. It turned out that whereas in the Lagrangian method the Nusselt number vs time plot reached only a quasi steady state where the Nusselt number oscillates around a steady state value the Eulerian scheme reaches exact steady states and produces a high degree of alignment (director orientation locally orthogonal to velocity vector almost everywhere in the computational domain). In the simulations emergent anisotropy was strongest in terms of modulus contrast in the up and down-welling plumes. Mechanisms for anisotropic material behavior in the mantle dynamics context are discussed by Christensen [3]. The dominant mineral phases in the mantle generally do not exhibit strong elastic anisotropy but they still may be oriented by the convective flow. Thus viscous anisotropy (the main focus of this paper) may or may not correlate with elastic or seismic anisotropy.

A 2D numerical model for simulating the physics of fault systems

Simulations provide a powerful means to help gain the understanding of crustal fault system physics required to progress towards the goal of earthquake forecasting. Cellular Automata are efficient enough to probe system dynamics but their simplifications render interpretations questionable. In contrast, sophisticated elasto-dynamic models yield more convincing results but are too computationally demanding to explore phase space. To help bridge this gap, we develop a simple 2D elastodynamic model of parallel fault systems. The model is discretised onto a triangular lattice and faults are specified as split nodes along horizontal rows in the lattice. A simple numerical approach is presented for calculating the forces at medium and split nodes such that general nonlinear frictional constitutive relations can be modeled along faults. Single and multi-fault simulation examples are presented using a nonlinear frictional relation that is slip and slip-rate dependent in order to illustrate the model.

Numerical simulation of double-diffusion driven convective flow and rock alteration in three-dimensional fluid-saturated geological fault zones

Numerical methods are used to simulate the double-diffusion driven convective pore-fluid flow and rock alteration in three-dimensional fluid-saturated geological fault zones. The double diffusion is caused by a combination of both the positive upward temperature gradient and the positive downward salinity concentration gradient within a three-dimensional fluid-saturated geological fault zone, which is assumed to be more permeable than its surrounding rocks. In order to ensure the physical meaningfulness of the obtained numerical solutions, the numerical method used in this study is validated by a benchmark problem, for which the analytical solution to the critical Rayleigh number of the system is available. The theoretical value of the critical Rayleigh number of a three-dimensional fluid-saturated geological fault zone system can be used to judge whether or not the double-diffusion driven convective pore-fluid flow can take place within the system. After the possibility of triggering the double-diffusion driven convective pore-fluid flow is theoretically validated for the numerical model of a three-dimensional fluid-saturated geological fault zone system, the corresponding numerical solutions for the convective flow and temperature are directly coupled with a geochemical system. Through the numerical simulation of the coupled system between the convective fluid flow, heat transfer, mass transport and chemical reactions, we have investigated the effect of the double-diffusion driven convective pore-fluid flow on the rock alteration, which is the direct consequence of mineral redistribution due to its dissolution, transportation and precipitation, within the three-dimensional fluid-saturated geological fault zone system. (c) 2005 Elsevier B.V. All rights reserved.

Numerical simulation of dendrite growth during solidification

A comprehensive probabilistic model for simulating dendrite morphology and investigating dendritic growth kinetics during solidification has been developed, based on a modified Cellular Automaton (mCA) for microscopic modeling of nucleation, growth of crystals and solute diffusion. The mCA model numerically calculated solute redistribution both in the solid and liquid phases, the curvature of dendrite tips and the growth anisotropy. This modeling takes account of thermal, curvature and solute diffusion effects. Therefore, it can simulate microstructure formation both on the scale of the dendrite tip length. This model was then applied for simulating dendritic solidification of an Al-7%Si alloy. Both directional and equiaxed dendritic growth has been performed to investigate the growth anisotropy and cooling rate on dendrite morphology. Furthermore, the competitive growth and selection of dendritic crystals have also investigated.

Three-dimensional model for multi-component reactive transport with variable density groundwater flow

PHWAT is a new model that couples a geochemical reaction model (PHREEQC-2) with a density-dependent groundwater flow and solute transport model (SEAWAT) using the split-operator approach. PHWAT was developed to simulate multi-component reactive transport in variable density groundwater flow. Fluid density in PHWAT depends not on only the concentration of a single species as in SEAWAT, but also the concentrations of other dissolved chemicals that can be subject to reactive processes. Simulation results of PHWAT and PHREEQC-2 were compared in their predictions of effluent concentration from a column experiment. Both models produced identical results, showing that PHWAT has correctly coupled the sub-packages. PHWAT was then applied to the simulation of a tank experiment in which seawater intrusion was accompanied by cation exchange. The density dependence of the intrusion and the snow-plough effect in the breakthrough curves were reflected in the model simulations, which were in good agreement with the measured breakthrough data. Comparison simulations that, in turn, excluded density effects and reactions allowed us to quantify the marked effect of ignoring these processes. Next, we explored numerical issues involved in the practical application of PHWAT using the example of a dense plume flowing into a tank containing fresh water. It was shown that PHWAT could model physically unstable flow and that numerical instabilities were suppressed. Physical instability developed in the model in accordance with the increase of the modified Rayleigh number for density-dependent flow, in agreement with previous research. (c) 2004 Elsevier Ltd. All rights reserved.

Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Improving wheat simulation capabilities in Australia from a cropping systems perspective: water and nitrogen effects on spring wheat in a semi-arid environment

Systems approaches can help to evaluate and improve the agronomic and economic viability of nitrogen application in the frequently water-limited environments. This requires a sound understanding of crop physiological processes and well tested simulation models. Thus, this experiment on spring wheat aimed to better quantify water x nitrogen effects on wheat by deriving some key crop physiological parameters that have proven useful in simulating crop growth. For spring wheat grown in Northern Australia under four levels of nitrogen (0 to 360 kg N ha(-1)) and either entirely on stored soil moisture or under full irrigation, kernel yields ranged from 343 to 719 g m(-2). Yield increases were strongly associated with increases in kernel number (9150-19950 kernels m(-2)), indicating the sensitivity of this parameter to water and N availability. Total water extraction under a rain shelter was 240 mm with a maximum extraction depth of 1.5 m. A substantial amount of mineral nitrogen available deep in the profile (below 0.9 m) was taken up by the crop. This was the source of nitrogen uptake observed after anthesis. Under dry conditions this late uptake accounted for approximately 50% of total nitrogen uptake and resulted in high (>2%) kernel nitrogen percentages even when no nitrogen was applied,Anthesis LAI values under sub-optimal water supply were reduced by 63% and under sub-optimal nitrogen supply by 50%. Radiation use efficiency (RUE) based on total incident short-wave radiation was 1.34 g MJ(-1) and did not differ among treatments. The conservative nature of RUE was the result of the crop reducing leaf area rather than leaf nitrogen content (which would have affected photosynthetic activity) under these moderate levels of nitrogen limitation. The transpiration efficiency coefficient was also conservative and averaged 4.7 Pa in the dry treatments. Kernel nitrogen percentage varied from 2.08 to 2.42%. The study provides a data set and a basis to consider ways to improve simulation capabilities of water and nitrogen effects on spring wheat. (C) 1997 Elsevier Science B.V.

Endoscopic Anatomy of the Pterygopalatine Fossa and the Transpterygoid Approach: Development of a Surgical Instruction Model

Introduction: The pterygopalatine fossa (PPF) is a narrow space located between the posterior wall of the antrum and the pterygoid plates. Surgical access to the PPF is difficult because of its protected position and its complex neurovascular anatomy. Endonasal approaches using rod lens endoscopes, however, provide better visualization of this area and are associated with less morbidity than external approaches. Our aim was to develop a simple anatomical model using cadaveric specimens injected with intravascular colored silicone to demonstrate the endoscopic anatomy of the PPF. This model could be used for surgical instruction of the transpterygoid approach. Methods: We dissected six PPF in three cadaveric specimens prepared with intravascular injection of colored material using two different injection techniques. An endoscopic endonasal approach, including a wide nasoantral window and removal of the posterior antrum wall, provided access to the PPF. Results: We produced our best anatomical model injecting colored silicone via the common carotid artery. We found that, using an endoscopic approach, a retrograde dissection of the sphenopalatine artery helped to identify the internal maxillary artery (IMA) and its branches. Neural structures were identified deeper to the vascular elements. Notable anatomical landmarks for the endoscopic surgeon are the vidian nerve and its canal that leads to the petrous portion of the internal carotid artery (ICA), and the foramen rotundum, and V2 that leads to Meckel`s cave in the middle cranial fossa. These two nerves, vidian and V2, are separated by a pyramidal shaped bone and its apex marks the ICA. Conclusion: Our anatomical model provides the means to learn the endoscopic anatomy of the PPF and may be used for the simulation of surgical techniques. An endoscopic endonasal approach provides adequate exposure to all anatomical structures within the PPF. These structures may be used as landmarks to identify and control deeper neurovascular structures. The significance is that an anatomical model facilitates learning the surgical anatomy and the acquisition of surgical skills. A dissection superficial to the vascular structures preserves the neural elements. These nerves and their bony foramina, such as the vidian nerve and V2, are critical anatomical landmarks to identify and control the ICA at the skull base.

Cultural Consonance, a 5HT2A Receptor Polymorphism, and Depressive Symptoms: A Longitudinal Study of Gene x Culture Interaction in Urban Brazil

In this study in urban Brazil we examine, as a predictor of depressive symptoms, the interaction between a single nucleotide polymorphism in the 2A receptor in the serotonin system (-1438G/A) and cultural consonance in family life, a measure of the degree to which an individual perceives her family as corresponding to a widely shared cultural model of the prototypical family. A community sample of 144 adults was followed over a 2-year-period. Cultural consonance in family life was assessed by linking individuals` perceptions of their own families with a shared cultural model of the family derived from cultural consensus analysis. The -1438G/A polymorphism in the 2A serotonin receptor was genotyped using a standard protocol for DNA extracted from leukocytes. Covariates included age, sex, socioeconomic status, and stressful life events. Cultural consonance in family life was prospectively associated with depressive symptoms. In addition, the interaction between genotype and cultural consonance in family life was significant. For individuals with the A/A variant of the -1438G/A polymorphism of the 2A receptor gene, the effect of cultural consonance in family life on depressive symptoms over a 2-year-period was larger (beta = -0.533, P < 0.01) than those effects for individuals with either the G/A (beta = -0.280, P < 0.10) or G/G (beta = -0.272, P < 0.05) variants. These results are consistent with a process in which genotype moderates the effects of culturally meaningful social experience on depressive symptoms. Am. J. Hum. Biol. 21:91-97, 2009. (C) 2008 Wiley-Liss, Inc.

Cultural consonance and adult body composition in urban Brazil

In previous research in Brazil, we found socioeconomic and gender differences in body mass and percent body fat, consistent with a model in which individuals in higher socioeconomic strata, especially women, could achieve a cultural ideal of body size and shape. In this article, using new data, we examine these processes more precisely using measures of cultural consonance. Cultural consonance refers to the degree to which individuals approximate, in their own beliefs and behaviors, the shared prototypes for belief and behavior encoded in cultural models. We have found higher cultural consonance in several domains to be associated with health outcomes. Furthermore, there tends to be a general consistency in cultural consonance across domains. Here we suggest that measures of body composition can be considered indicators of individuals` success in achieving cultural ideals of the body, and that cultural consonance in several domains will be associated with body composition. Using waist circumference as an outcome, smaller waist size was associated with higher cultural consonance in lifestyle (beta = -0.311, P < 0.01) and higher cultural consonance in the consumption of high prestige foods (beta = -0.260, P < 0.01) for women (n = 161), but not for men (n = 106), controlling for age, family income, tobacco use, and dietary intake of protein and carbohydrates. Similar results were obtained using the body mass index and weight as outcomes, while there were no associations with height. These results help to illuminate the cultural mediation of body composition.

A general hazard model for lifetime data in the presence of cure rate

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

Commercialisation of agriculture in Kenya: Case study of urban bias on food availability in farm households

This study investigates the effect of cash cropping on food availability and examines the determinants of the proportion of income allocated for food expenditures in the Nyeri district in Kenya. Using a Tobit model, the results suggest that in general food expenditure allocations suffer due to cash cropping in Kenya as the lump-sum income flows from this may be used for purchases other than food. Food expenditure also suffers when remittances are irregular. On the other hand, earnings from outside employment for married women living with husbands are positively associated with food expenditure allocations. Amounts of non-cash food output as well as ownership of livestock are negatively associated with food expenditure allocations. These findings indicate that lump sum income may not lead to improved welfare of women and children. Thus, there may be social reasons for increasing non-cash food production especially by women, instead of over emphasizing cash cropping as now seems to be so in public policy.

Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma

A mixture model incorporating long-term survivors has been adopted in the field of biostatistics where some individuals may never experience the failure event under study. The surviving fractions may be considered as cured. In most applications, the survival times are assumed to be independent. However, when the survival data are obtained from a multi-centre clinical trial, it is conceived that the environ mental conditions and facilities shared within clinic affects the proportion cured as well as the failure risk for the uncured individuals. It necessitates a long-term survivor mixture model with random effects. In this paper, the long-term survivor mixture model is extended for the analysis of multivariate failure time data using the generalized linear mixed model (GLMM) approach. The proposed model is applied to analyse a numerical data set from a multi-centre clinical trial of carcinoma as an illustration. Some simulation experiments are performed to assess the applicability of the model based on the average biases of the estimates formed. Copyright (C) 2001 John Wiley & Sons, Ltd.

A dynamic model with on-line identification for rotary sugar drying processes

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to reidentified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.place the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.

Model based procedure for scale-up of wet overflow ball mills Part 1: Outline of the methodology

Bond's method for ball mill scale-up only gives the mill power draw for a given duty. This method is incompatible with computer modelling and simulation techniques. It might not be applicable for the design of fine grinding ball mills and ball mills preceded by autogenous and semi-autogenous grinding mills. Model-based ball mill scale-up methods have not been validated using a wide range of full-scale circuit data. Their accuracy is therefore questionable. Some of these methods also need expensive pilot testing. A new ball mill scale-up procedure is developed which does not have these limitations. This procedure uses data from two laboratory tests to determine the parameters of a ball mill model. A set of scale-up criteria then scales-up these parameters. The procedure uses the scaled-up parameters to simulate the steady state performance of full-scale mill circuits. At the end of the simulation, the scale-up procedure gives the size distribution, the volumetric flowrate and the mass flowrate of all the streams in the circuit, and the mill power draw.