Computational modes and grid imprinting on five quasi-uniform spherical C-grids

Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations. We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid, despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity.

Modular non-computational-connectionist-hybrid neural network approach to robotic systems

Spiking neural networks are usually limited in their applications due to their complex mathematical models and the lack of intuitive learning algorithms. In this paper, a simpler, novel neural network derived from a leaky integrate and fire neuron model, the ‘cavalcade’ neuron, is presented. A simulation for the neural network has been developed and two basic learning algorithms implemented within the environment. These algorithms successfully learn some basic temporal and instantaneous problems. Inspiration for neural network structures from these experiments are then taken and applied to process sensor information so as to successfully control a mobile robot.

Controlling the computational modes of the arbitrarily structured C-grid

The arbitrarily structured C-grid, TRiSK (Thuburn, Ringler, Skamarock and Klemp, 2009, 2010) is being used in the ``Model for Prediction Across Scales'' (MPAS) and is being considered by the UK Met Office for their next dynamical core. However the hexagonal C-grid supports a branch of spurious Rossby modes which lead to erroneous grid-scale oscillations of potential vorticity (PV). It is shown how these modes can be harmlessly controlled by using upwind-biased interpolation schemes for PV. A number of existing advection schemes for PV are tested, including that used in MPAS, and none are found to give adequate results for all grids and all cases. Therefore a new scheme is proposed; continuous, linear-upwind stabilised transport (CLUST), a blend between centred and linear-upwind with the blend dependent on the flow direction with respect to the cell edge. A diagnostic of grid-scale oscillations is proposed which gives further discrimination between schemes than using potential enstrophy alone and indeed some schemes are found to destroy potential enstrophy while grid-scale oscillations grow. CLUST performs well on hexagonal-icosahedral grids and unrotated skipped latitude-longitude grids of the sphere for various shallow water test cases. Despite the computational modes, the hexagonal icosahedral grid performs well since these modes are easy and harmless to filter. As a result TRiSK appears to perform better than a spectral shallow water model.

Towards data warehousing and mining of protein unfolding simulation data

OBJECTIVES: The prediction of protein structure and the precise understanding of protein folding and unfolding processes remains one of the greatest challenges in structural biology and bioinformatics. Computer simulations based on molecular dynamics (MD) are at the forefront of the effort to gain a deeper understanding of these complex processes. Currently, these MD simulations are usually on the order of tens of nanoseconds, generate a large amount of conformational data and are computationally expensive. More and more groups run such simulations and generate a myriad of data, which raises new challenges in managing and analyzing these data. Because the vast range of proteins researchers want to study and simulate, the computational effort needed to generate data, the large data volumes involved, and the different types of analyses scientists need to perform, it is desirable to provide a public repository allowing researchers to pool and share protein unfolding data. METHODS: To adequately organize, manage, and analyze the data generated by unfolding simulation studies, we designed a data warehouse system that is embedded in a grid environment to facilitate the seamless sharing of available computer resources and thus enable many groups to share complex molecular dynamics simulations on a more regular basis. RESULTS: To gain insight into the conformational fluctuations and stability of the monomeric forms of the amyloidogenic protein transthyretin (TTR), molecular dynamics unfolding simulations of the monomer of human TTR have been conducted. Trajectory data and meta-data of the wild-type (WT) protein and the highly amyloidogenic variant L55P-TTR represent the test case for the data warehouse. CONCLUSIONS: Web and grid services, especially pre-defined data mining services that can run on or 'near' the data repository of the data warehouse, are likely to play a pivotal role in the analysis of molecular dynamics unfolding data.

Black-box decomposition approach for computational hemodynamics: One-dimensional models

Increasing efforts exist in integrating different levels of detail in models of the cardiovascular system. For instance, one-dimensional representations are employed to model the systemic circulation. In this context, effective and black-box-type decomposition strategies for one-dimensional networks are needed, so as to: (i) employ domain decomposition strategies for large systemic models (1D-1D coupling) and (ii) provide the conceptual basis for dimensionally-heterogeneous representations (1D-3D coupling, among various possibilities). The strategy proposed in this article works for both of these two scenarios, though the several applications shown to illustrate its performance focus on the 1D-1D coupling case. A one-dimensional network is decomposed in such a way that each coupling point connects two (and not more) of the sub-networks. At each of the M connection points two unknowns are defined: the flow rate and pressure. These 2M unknowns are determined by 2M equations, since each sub-network provides one (non-linear) equation per coupling point. It is shown how to build the 2M x 2M non-linear system with arbitrary and independent choice of boundary conditions for each of the sub-networks. The idea is then to solve this non-linear system until convergence, which guarantees strong coupling of the complete network. In other words, if the non-linear solver converges at each time step, the solution coincides with what would be obtained by monolithically modeling the whole network. The decomposition thus imposes no stability restriction on the choice of the time step size. Effective iterative strategies for the non-linear system that preserve the black-box character of the decomposition are then explored. Several variants of matrix-free Broyden`s and Newton-GMRES algorithms are assessed as numerical solvers by comparing their performance on sub-critical wave propagation problems which range from academic test cases to realistic cardiovascular applications. A specific variant of Broyden`s algorithm is identified and recommended on the basis of its computer cost and reliability. (C) 2010 Elsevier B.V. All rights reserved.

Performance of balanced two-stage empirical predictors of realized cluster latent values from finite populations: A simulation study

Predictors of random effects are usually based on the popular mixed effects (ME) model developed under the assumption that the sample is obtained from a conceptual infinite population; such predictors are employed even when the actual population is finite. Two alternatives that incorporate the finite nature of the population are obtained from the superpopulation model proposed by Scott and Smith (1969. Estimation in multi-stage surveys. J. Amer. Statist. Assoc. 64, 830-840) or from the finite population mixed model recently proposed by Stanek and Singer (2004. Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 1119-1130). Predictors derived under the latter model with the additional assumptions that all variance components are known and that within-cluster variances are equal have smaller mean squared error (MSE) than the competitors based on either the ME or Scott and Smith`s models. As population variances are rarely known, we propose method of moment estimators to obtain empirical predictors and conduct a simulation study to evaluate their performance. The results suggest that the finite population mixed model empirical predictor is more stable than its competitors since, in terms of MSE, it is either the best or the second best and when second best, its performance lies within acceptable limits. When both cluster and unit intra-class correlation coefficients are very high (e.g., 0.95 or more), the performance of the empirical predictors derived under the three models is similar. (c) 2007 Elsevier B.V. All rights reserved.

Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical simulation of a radial diffuser turbulent airflow

In the present work are presented results from numerical simulations performed with the ANSYS-CFX (R) code. We have studied a radial diffuser flow case, which is the main academic problem used to study the flow behavior on flat plate valves. The radial flow inside the diffuser has important behavior such as the turbulence decay downstream and recirculation regions inside the valve flow channel due to boundary layer detachment. These flow structures are present in compressor reed valve configurations, influencing to a greater extent the compressor efficiency. The main target of the present paper was finding the simulation set-up (computational domain, boundary conditions and turbulence model) that better fits with experimental data published by Tabatabai and Pollard. The local flow turbulence and velocity profiles were investigated using four different turbulence models, two different boundary conditions set-up, two different computational domains and three different flow conditions (Re-in - Reynolds number at the diffuser inlet). We used the Reynolds stress (BSL); the k-epsilon; the RNG k-epsilon; and the shear stress transport (SST) k-omega turbulence models. The performed analysis and comparison of the computational results with experimental data show that the choice of the turbulence model, as well as the choice of the other computational conditions, plays an important role in the results physical quality and accuracy. (c) 2007 Elsevier B.V. All rights reserved.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier B.V. All rights reserved.

Criteria for mixed grids in computational fluid dynamics

The finite volume method is used as a numerical method for solving the fluid flow equations. This method is appropriate to employ under structured and unstructured meshes. Mixed grids, combining both types of grids, are investigated. The coupling of different grids is done by overlapping strategy. The computational effort for the mixed grid is evaluated by the CPU-time, with different percentage of covering area of the unstructured mesh. The present scheme is tested for the driven cavity problem, where the incompressible fluid is integrated by calculating the velocity fields and computing the pressure field in each time step. Several schemes for unstructured grid are examined, and the compatibility condition is applied to check their consistency. A scheme to verify the compatibility condition for the unstructured grids is presented. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.

C-H center dot center dot center dot O and N-H center dot center dot center dot O hydrogen bonds in liquid amides investigated by Monte Carlo simulation

Monte Carlo simulations of liquid formamide, N-methylformamide (MF), and N,N-dimethylformamide (DMF) have been performed in the isothermal and isobaric ensemble at 298 K and 1 atm, aiming to investigate the C-H ... O and N-H ... O hydrogen bonds. The interaction energy was calculated using the classical 6-12 Lennard-Jones pairwise potential plus a Coulomb term on a rigid six-site molecular model with the potential parameters being optimized in this work. Theoretical values obtained for heat of vaporization and liquid densities are in good agreement with the experimental data. The radial distribution function [RDF, g(r)] obtained compare well with R-X diffraction data available. The RDF and molecular mechanics (MM2) minimization show that the C-H ... O interaction has a significant role in the structure of the three liquids. These results are supported by ab initio calculations. This Interaction is particularly important in the structure of MF. The intensity of the N-H ... O hydrogen bond is greater in the MF than formamide. This could explain some anomalous properties verified in MF. (C) 1997 John Wiley & Sons, Inc.

Modeling and simulation of cephalosporin C production in a fed-batch tower-type bioreactor

Immobilized cell utilization in tower-type bioreactor is one of the main alternatives being studied to improve the industrial bioprocess. Other alternatives for the production of beta -lactam antibiotics, such as a cephalosporin C fed-batch p recess in an aerated stirred-tank bioreactor with free cells of Cepha-losporium acremonium or a tower-type bioreactor with immobilized cells of this fungus, have proven to be more efficient than the batch profess. In the fed-batch process, it is possible to minimize the catabolite repression exerted by the rapidly utilization of carbon sources (such as glucose) in the synthesis of antibiotics by utilizing a suitable flow rate of supplementary medium. In this study, several runs for cephalosporin C production, each lasting 200 h, were conducted in a fed-batch tower-type bioreactor using different hydrolyzed sucrose concentrations, For this study's model, modifications were introduced to take into account the influence of supplementary medium flow rate. The balance equations considered the effect of oxygen limitation inside the bioparticles. In the Monod-type rate equations, eel concentrations, substrate concentrations, and dissolved oxygen were included as reactants affecting the bioreaction rate. The set of differential equations was solved by the numerical method, and the values of the parameters were estimated by the classic nonlinear regression method following Marquardt's procedure with a 95% confidence interval. The simulation results showed that the proposed model fit well with the experimental data,and based on the experimental data and the mathematical model an optimal mass flow rate to maximize the bioprocess productivity could be proposed.

Simulation of free surface flows in a distributed memory environment

A parallel technique, for a distributed memory machine, based on domain decomposition for solving the Navier-Stokes equations in cartesian and cylindrical coordinates in two dimensions with free surfaces is described. It is based on the code by Tome and McKee (J. Comp. Phys. 110 (1994) 171-186) and Tome (Ph.D. Thesis, University of Strathclyde, Glasgow, 1993) which in turn is based on the SMAC method by Amsden and Harlow (Report LA-4370, Los Alamos Scientific Laboratory, 1971), which solves the Navier-Stokes equations in three steps: the momentum and Poisson equations and particle movement, These equations are discretized by explicit and 5-point finite differences. The parallelization is performed by splitting the computation domain into vertical panels and assigning each of these panels to a processor. All the computation can then be performed using nearest neighbour communication. Test runs comparing the performance of the parallel with the serial code, and a discussion of the load balancing question are presented. PVM is used for communication between processes. (C) 1999 Elsevier B.V. B.V. All rights reserved.

C - H ⋯ 0 and N - H ⋯ 0 hydrogen bonds in liquid amides investigated by monte carlo simulation

Monte Carlo simulations of liquid formamide, N-methylformamide (MF), and N, N-dimethytformamide (DMF) have been performed in the isothermal and isobaric ensemble at 298 K and 1 atm, aiming to investigate the C-H ⋯ O and N-H ⋯ O hydrogen bonds. The interaction energy was calculated using the classical 6-12 Lennard-Jones pairwise potential plus a Coulomb term on a rigid six-site molecular model with the potential parameters being optimized in this work. Theoretical values obtained for heat of vaporization and liquid densities are in good agreement with the experimental data. The radial distribution function [RDF, g(r)] obtained compare well with R-X diffraction data available. The RDF and molecular mechanics (MM2) minimization show that the C-H ⋯ O interaction has a significant role in the structure of the three liquids. These results are supported by ab initio calculations. This interaction is particularly important in the structure of MF. The intensity of the N - H ⋯ O hydrogen bond is greater in the MF than formamide. This could explain some anomalous properties verified in MF. © 1997 John Wiley & Sons, Inc.