Parameters affecting the performance of wetting and drying in a two-dimensional finite element long wave hydrodynamic model

The marsh porosity method, a type of thin slot wetting and drying algorithm in a two-dimensional finite element long wave hydrodynamic model, is discussed and analyzed to assess model performance. Tests, including comparisons to simple examples and theoretical calculations, examine the effects of varying the marsh porosity parameters. The findings demonstrate that the wetting and drying concept of marsh porosity, often used in finite element hydrodynamic modeling, can behave in a more complex manner than initially expected.

An FDTD model for calculation of gradient-induced eddy currents in MRI system

In most magnetic resonance imaging (MRI) systems, pulsed magnetic gradient fields induce eddy currents in the conducting structures of the superconducting magnet. The eddy currents induced in structures within the cryostat are particularly problematic as they are characterized by long time constants by virtue of the low resistivity of the conductors. This paper presents a three-dimensional (3-D) finite-difference time-domain (FDTD) scheme in cylindrical coordinates for eddy-current calculation in conductors. This model is intended to be part of a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The singularity apparent in the governing equations is removed by using a series expansion method and the conductor-air boundary condition is handled using a variant of the surface impedance concept. The numerical difficulty due to the asymmetry of Maxwell equations for low-frequency eddy-current problems is circumvented by taking advantage of the known penetration behavior of the eddy-current fields. A perfectly matched layer absorbing boundary condition in 3-D cylindrical coordinates is also incorporated. The numerical method has been verified against analytical solutions for simple cases. Finally, the algorithm is illustrated by modeling a pulsed field gradient coil system within an MRI magnet system. The results demonstrate that the proposed FDTD scheme can be used to calculate large-scale eddy-current problems in materials with high conductivity at low frequencies.

The comprehensive osteoarthritis test: a simple index for measurement of treatment effects in clinical trials

Objective. To assess the measurement properties of a simple index of symptom severity in osteoarthritis (OA) of the hips and knees. Methods. Both the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) and the proposed new Comprehensive Osteoarthritis Test (COAT) instrument were completed weekly by 125 subjects in the context of a randomized, 12-week, 3 parallel-arm clinical trial. The reliabilities of the various scales were assessed on a weekly basis by use of Cronbach's alpha coefficients. The validity of the COAT total scale was assessed by correlation with the WOMAC total scale on a weekly basis with correlation coefficients, and in terms of the correlations between subject-level intercepts and slopes over time. The relative responsiveness of the WOMAC and COAT total scales was assessed using a multilevel (longitudinal) multivariate (WOMAC, COAT) linear model. Results. The WOMAC and COAT total scales were highly reliable (mean over weeks: WOMAC alpha = 0.98; COAT alpha = 0.97). The correlations between the WOMAC and COAT scales were very high (mean over weeks = 0.92; subject-level intercepts = 0.91, slopes = 0.88). The COAT total scale was significantly more responsive than the WOMAC total scale in the active treatment (34.8% improvement vs 26.8%; p = 0.002). Conclusion. The COAT total scale is simple to administer, reliable, valid, and responsive to treatment effects.

A simulation model of cereal-legume intercropping systems for semi-arid regions I. Model development

Cereal-legume intercropping plays an important role in subsistence food production in developing countries, especially in situations of limited water resources. Crop simulation can be used to assess risk for intercrop productivity over time and space. In this study, a simple model for intercropping was developed for cereal and legume growth and yield, under semi-arid conditions. The model is based on radiation interception and use, and incorporates a water stress factor. Total dry matter and yield are functions of photosynthetically active radiation (PAR), the fraction of radiation intercepted and radiation use efficiency (RUE). One of two PAR sub-models was used to estimate PAR from solar radiation; either PAR is 50% of solar radiation or the ratio of PAR to solar radiation (PAR/SR) is a function of the clearness index (K-T). The fraction of radiation intercepted was calculated either based on Beer's Law with crop extinction coefficients (K) from field experiments or from previous reports. RUE was calculated as a function of available soil water to a depth of 900 mm (ASW). Either the soil water balance method or the decay curve approach was used to determine ASW. Thus, two alternatives for each of three factors, i.e., PAR/SR, K and ASW, were considered, giving eight possible models (2 methods x 3 factors). The model calibration and validation were carried out with maize-bean intercropping systems using data collected in a semi-arid region (Bloemfontein, Free State, South Africa) during seven growing seasons (1996/1997-2002/2003). The combination of PAR estimated from the clearness index, a crop extinction coefficient from the field experiment and the decay curve model gave the most reasonable and acceptable result. The intercrop model developed in this study is simple, so this modelling approach can be employed to develop other cereal-legume intercrop models for semi-arid regions. (c) 2004 Elsevier B.V. All rights reserved.

Functional-structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function

This paper presents a new method for producing a functional-structural plant model that simulates response to different growth conditions, yet does not require detailed knowledge of underlying physiology. The example used to present this method is the modelling of the mountain birch tree. This new functional-structural modelling approach is based on linking an L-system representation of the dynamic structure of the plant with a canonical mathematical model of plant function. Growth indicated by the canonical model is allocated to the structural model according to probabilistic growth rules, such as rules for the placement and length of new shoots, which were derived from an analysis of architectural data. The main advantage of the approach is that it is relatively simple compared to the prevalent process-based functional-structural plant models and does not require a detailed understanding of underlying physiological processes, yet it is able to capture important aspects of plant function and adaptability, unlike simple empirical models. This approach, combining canonical modelling, architectural analysis and L-systems, thus fills the important role of providing an intermediate level of abstraction between the two extremes of deeply mechanistic process-based modelling and purely empirical modelling. We also investigated the relative importance of various aspects of this integrated modelling approach by analysing the sensitivity of the standard birch model to a number of variations in its parameters, functions and algorithms. The results show that using light as the sole factor determining the structural location of new growth gives satisfactory results. Including the influence of additional regulating factors made little difference to global characteristics of the emergent architecture. Changing the form of the probability functions and using alternative methods for choosing the sites of new growth also had little effect. (c) 2004 Elsevier B.V. All rights reserved.

Edge-to-edge matching and its applications - Part I. Application to the simple HCP/BCC system

The edge-to-edge matching crystallographic model has been used to predict all the orientation relationships (OR) between crystals that have simple hexagonal close packed (HCP) and body-centered cubic (BCC) structures. Using the critical values for the interatomic spacing misfit along the matching directions and the cl-value mismatch between matching planes, the model predicted all the four common ORs, namely the Burgers OR, the Potter OR, the Pitsch-Schrader OR and the Rong Dunlop OR, together with the corresponding habit planes. Taking the c(H)/a(H) and a(H)/a(B) ratios as variables, where H and B denote the HCP and BCC structures respectively, the model also predicted the relationship between these variables and the four ORs. These predictions are perfectly consistent with the published experimental results. As was the case in the FCC/BCC system, the edge-to-edge matching model has been shown to be a powerful tool for predicting the crystallographic features of diffusion-controlled phase transformations. (C) 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Optimization of a transplant model to assess skin reconstitution from stem cell-enriched primary human keratinocyte populations

Given that an important functional attribute of stem cells in vivo is their ability to sustain tissue regeneration, we set out to establish a simple and easy technique to assess this property from candidate populations of human keratinocyte stem cells in an in vivo setting. Keratinocytes were inoculated into devitalized rat tracheas and transplanted subcutaneously into SCID mice, and the epithelial lining regenerated characterized to establish the validity of this heterotypic model. Furthermore, the rate and quality of epidermal tissue reconstitution obtained from freshly isolated unfractionated vs. keratinocyte stem cell-enriched populations was tested as a function of (a) cell numbers inoculated; and (b) the inclusion of irradiated support keratinocytes and dermal cells. Rapid and sustained epidermal tissue regeneration from small numbers of freshly isolated human keratinocyte stem cells validates the utilization of this simple and reliable model system to assay for enrichment of epidermal tissue-reconstituting cells.

Application of a coupled ground-surface water flow model to simulate periodic groundwater flow influenced by a sloping boundary, capillarity and vertical flows

Theoretical developments as well as field and laboratory data have shown the influence of the capillary fringe on water table fluctuations to increase with the fluctuation frequency. The numerical solution of a full, partially saturated flow equation can be computationally expensive. In this paper, the influence of the capillary fringe on water table fluctuations is simplified through its parameterisation into the storage coefficient of a fully-saturated groundwater flow model using the complex effective porosity concept [Nielsen, P., Perrochet, P., 2000. Water table dynamics under capillary fringes: experiments and modelling. Advances in Water Resources 23 (1), 503-515; Nielsen, P., Perrochet, P., 2000. ERRATA: water table dynamics under capillary fringes: experiments and modelling (Advances in Water Resources 23 (2000) 503-515). Advances in Water Resources 23, 907-908]. The model is applied to sand flume observations of periodic water table fluctuations induced by simple harmonic forcing across a sloping boundary, analogous to many beach groundwater systems. While not providing information on the moisture distribution within the aquifer, this approach can reasonably predict the water table fluctuations in response to periodic forcing across a sloping boundary. Furthermore, he coupled ground-surface water model accurately predicts the extent of the seepage face formed at the sloping boundary. (C) 2005 Elsevier Ltd. All rights reserved.

Estimation of water retention curve from mercury intrusion porosimetry and van Genuchten model

The water retention curve (WRC) is a hydraulic characteristic of concrete required for advanced modeling of water (and thus solute) transport in variably saturated, heterogeneous concrete. Unfortunately, determination by a direct experimental method (for example, measuring equilibrium moisture levels of large samples stored in constant humidity cells) is a lengthy process, taking over 2 years for large samples. A surrogate approach is presented in which the WRC is conveniently estimated from mercury intrusion porosimetry (MIP) and validated by water sorption isotherms: The well-known Barrett, Joyner and Halenda (BJH) method of estimating the pore size distribution (PSD) from the water sorption isotherm is shown to complement the PSD derived from conventional MIP. This provides a basis for predicting the complete WRC from MIP data alone. The van Genuchten equation is used to model the combined water sorption and MIP results. It is a convenient tool for describing water retention characteristics over the full moisture content range. The van Genuchten parameter estimation based solely on MIP is shown to give a satisfactory approximation to the WRC, with a simple restriction on one. of the parameters.

Simple approach to estimating the van der Waals interaction between carbon nanotubes

The van der Waals (vdW) interactions between carbon nanotubes (CNTs) were studied based on the continuum Lennard-Jones model. It was found that all the vdW potentials between two arbitrary CNTs fall on the same curve when plotted in terms of certain reduced parameters, the well depth, and the equilibrium vdW gap. Based on this observation, an approximate approach is developed to obtain the vdW potential between two CNTs without time-consuming computations. The vdW potential estimated by this approach is close to that obtained from complex integrations. Therefore, the developed approach can greatly simplify the calculation of vdW interactions between CNTs.

A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays

Motivation: An important problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive. Results: By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The usefulness of our approach is demonstrated on three real datasets.

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)].

Leading coordinate analysis of reaction pathways in proton chain transfer: Application to a two-proton transfer model for the green fluorescent protein

The ‘leading coordinate’ approach to computing an approximate reaction pathway, with subsequent determination of the true minimum energy profile, is applied to a two-proton chain transfer model based on the chromophore and its surrounding moieties within the green fluorescent protein (GFP). Using an ab initio quantum chemical method, a number of different relaxed energy profiles are found for several plausible guesses at leading coordinates. The results obtained for different trial leading coordinates are rationalized through the calculation of a two-dimensional relaxed potential energy surface (PES) for the system. Analysis of the 2-D relaxed PES reveals that two of the trial pathways are entirely spurious, while two others contain useful information and can be used to furnish starting points for successful saddle-point searches. Implications for selection of trial leading coordinates in this class of proton chain transfer reactions are discussed, and a simple diagnostic function is proposed for revealing whether or not a relaxed pathway based on a trial leading coordinate is likely to furnish useful information.

Network topology and the evolution of dynamics in an artificial genetic regulatory network model created by whole genome duplication and divergence

Topological measures of large-scale complex networks are applied to a specific artificial regulatory network model created through a whole genome duplication and divergence mechanism. This class of networks share topological features with natural transcriptional regulatory networks. Specifically, these networks display scale-free and small-world topology and possess subgraph distributions similar to those of natural networks. Thus, the topologies inherent in natural networks may be in part due to their method of creation rather than being exclusively shaped by subsequent evolution under selection. The evolvability of the dynamics of these networks is also examined by evolving networks in simulation to obtain three simple types of output dynamics. The networks obtained from this process show a wide variety of topologies and numbers of genes indicating that it is relatively easy to evolve these classes of dynamics in this model. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.