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Abstract. This article presents MassMov2D, a two-dimensional model of mud and debris flow dynamics over complex topography, based on a numerical integration of the depth-averaged motion equations using a shallow water approximation. The core part of the model was implemented using the GIS scripting language PCRaster. This environment provides visualization of the results through map animations and time series, and a user-friendly interface. The constitutive equations and the numerical solution adopted in MassMov2D are presented in this article. The model was applied to two field case studies of mud flows on torrential alluvial fans, one in the Austrian Tyrol (Wartschenbach torrent) and the other in the French Alps (Faucon torrent). Existing data on the debris flow volume, input discharge and deposits were used to back-analyze those events and estimate the values of the leading parameters. The results were compared with modeling codes used by other authors for the same case studies. The results obtained with MassMov2D matched well with the observed debris flow deposits, and are in agreement with those obtained using alternative codes.

We present a new structure-preserving numerical scheme for solving the Euler-Poincaré Differential (EPDiff) equation on arbitrary triangle meshes. Unlike existing techniques, our method solves the difficult non-linear EPDiff equation by constructing energy preserving, yet fully explicit, update rules. Our approach uses standard differential operators on triangle meshes, allowing for a simple and efficient implementation. Key to the structure-preserving features that our method exhibits is a novel numerical splitting scheme. Namely, we break the integration into three steps which rely on linear solves with a fixed sparse matrix that is independent of the simulation and thus can be pre-factored. We test our method in the context of simulating concentrated reconnecting wavefronts on flat and curved domains. In particular, EPDiff is known to generate geometrical fronts which exhibit wave-like behavior when they interact with each other. In addition, we also show that at a small additional cost, we can produce globally-supported periodic waves by using our simulated fronts with wavefronts tracking techniques. We provide quantitative graphs showing that our method exactly preserves the energy in practice. In addition, we demonstrate various interesting results including annihilation and recreation of a circular front, a wave splitting and merging when hitting an obstacle and two separate fronts propagating and bending due to the curvature of the domain. ; We would like to thank Eric Yudin for his help with rendering the figures in this work. The first author acknowledges an Adams Fellowship. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement No 714776.

AbstractMath relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across grades 1–6. In grades 1–2, children's ability to judge the relative magnitude of numerical symbols was most predictive of early arithmetic skills. The unique contribution of children's ability to assess ordinality in numerical symbols steadily increased across grades, overtaking all other predictors by grade 6. We found no evidence that children's ability to judge the relative magnitude of approximate, nonsymbolic numbers was uniquely predictive of arithmetic ability at any grade. Overall, symbolic number processing was more predictive of arithmetic ability than nonsymbolic number processing, though the relative importance of symbolic number ability appears to shift from cardinal to ordinal processing.

The 12th Workshop on Synthesis And System Integration of Mixed Information technologies (SASIMI2004), Oct. 18-19, 2004, Kanazawa, Japan, pp.422-429. ; This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted. ; The availability of large, inexpensive memory has made it possible to realize numerical functions, such as the reciprocal, square root, and trigonometric functions, using a look-up table. This is much faster than by software. However, a naive look-up method requires unreasonably large memory. In this paper, we show the use of a look-up table (LUT) cascade to realize a piecewise linear approximation to the given function. Our approach yields memory of reasonable size and significant accuracy.

It is important to know the mechanical and micromechanical characteristics of conventional dental implants in order to design and develop novel dental implants and surface treatments that ensure a good biomechanical stability and almost fully replace the biological tissue. A successful integration of the implant depends on its chemical, mechanical and physical properties and the quality of the bone tissue. Considering these facts, we developed two novel variants of dental implant stems with an anti-rotational geometrical solution. On these variants, we have then performed numerical analyses of static strength. Outcomes of simulations vary depending on the type of the implant and load mode.

The numerical integration of the pulsation equation is reduced to the resolution of a set of linear algebraic equations by considering the star as composed of discrete shells submitted to the appropriate pressure and gravity forces. The method has been applied to three models with encouraging results although further improvements are needed to reach the precision of standard numerical integration procedures.

We present a method for computing the stochastic operational matrix of integration to advance the study of stochastic Volterra-Fredholm integral equations (SVFIEs) based on delay arguments. First, the method evaluates the combined effects of the delay and its parameters on the accuracy improvement of the convergence rate. Our results can be applied to SVFIEs, with the operational delay matrices of the block pulse function simplified to algebraic ones. Numerical calculations were performed on a PC using Python 3 programs. Results also demonstrate the accuracy of approximate solutions; arithmetic operations are carried out without the need for derivation or integration.

The error estimate of Borgonovo's moment‐independent index is considered, and it shows that the possible computational complexity of is mainly due to the probability density function (PDF) estimate because the PDF estimate is an ill‐posed problem and its convergence rate is quite slow. So it reminds us to compute Borgonovo's index using other methods. To avoid the PDF estimate, , which is based on the PDF, is first approximatively represented by the cumulative distribution function (CDF). The CDF estimate is well posed and its convergence rate is always faster than that of the PDF estimate. From the representation, a stable approach is proposed to compute with an adaptive procedure. Since the small probability multidimensional integral needs to be computed in this procedure, a computational strategy named asymptotic space integration is introduced to reduce a high‐dimensional integral to a one‐dimensional integral. Then we can compute the small probability multidimensional integral by adaptive numerical integration in one dimension with an improved convergence rate. From the comparison of numerical error analysis of some examples, it can be shown that the proposed method is an effective approach to uncertainty importance measure computation.

71 82 18 1 ; OJS ; Bladé, E.; Cea, L.; Corestein, G. (2014). Modelización numérica de inundaciones fluviales. Ingeniería del agua. 18(1):71-82. https://doi.org/10.4995/ia.2014.3144 ; [EN] At the present time there is a strong demand from policy makers for reliable predictions of the effects of climate and land use changes on inundation risk, in order to meet the targets specified in the EU Water Framework Directive. Numerical models are a valuable predictive tool to support decision-making related to the implementation of water and flood risk management strategies. While a decade ago one-dimensional modelling was the most commonly used tool in inundation studies, at the present time the application of two-dimensional models to river inundation modelling is generalized. Combined with GIS tools, the water depth and velocity results of a 2D model can be efficiently combined with land use data in order to quantify the potential damages caused by a certain inundation. Nevertheless, in order to improve the reliability of the numerical predictions, a number of challenges should be addressed in current models, as: modelling the interaction between hydrodynamics, solid loads, and morphologic changes during extreme flood events; a correct characterisation of head losses and flow through bridges with complex geometries; the integration of hydrological and hydraulic models for a better consideration of boundary conditions; and the implementation of efficient parallelization techniques in order to reduce the computational time and increase the scale of the problems which can be addressed with 2D and 3D models. Bladé, E., Gómez-Valentín, M., Dolz, J., Aragón-Hernández, J. L., Corestein, G., and Sánchez-Juny, M. (2012). "Integration of 1D and 2D Finite Volume Schemes for Computations of Water Flow in Natural Channels." Advances in Water Resources, 42, 17-29. Cea, L., Stelling, G., and Zijlema, M. (2009). "Non-hydrostatic 3D free surface layer-structured finite volume model for short wave propagation." International Journal for ...

A closed-form expression is derived for the numerical dispersion relation of the 2-D locally one-dimensional finite-difference time-domain (LOD-FDTD) method in lossy media. In contrast to the lossless formulation, we found that transverse-electric (TEz ) and transverse-magnetic (TMz ) waves in lossy media exhibit different numerical dispersion relations. Moreover, when the material relaxation-time constant is not well resolved by the integration time-step, the TMz case shows much worse accuracy than the TEz case. To remove this limitation, a split-field LOD-FDTD formulation for TMz waves is then considered, which exhibits the same dispersion relation as the LOD-FDTD method for TEz waves. The validity of the theoretical results is illustrated through numerical simulations. ; This work was supported in part by the Spanish Government (MINECO) and the European Commission (ERDF) under Research Projects TEC2014-55463-C3-2-P and TEC2014-55463-C3-3-P.

In this paper, we have modified the stress integration scheme proposed by Choi and Yoon [1]; which is based on the numerical approximation of the yield function gradients, to implement in the finite element code ABAQUS three elastic isotropic, plastic anisotropic constitutive models with yielding described by Yld2004-18p [2], CPB06ex2 [3] and Yld2011-27p [4] criteria, respectively. We have developed both VUMAT and UMAT subroutines for the three constitutive models, and have carried out cylindrical cup deep drawing test simulations and calculations of dynamic necking localization under plane strain tension, using explicit and implicit analyses. An original feature of this paper is that these finite element simulations are systematically compared with additional calculations performed using (i) the numerical approximation scheme developed by Choi and Yoon [1]; and (ii) the analytical computation of the first and second order yield functions gradients. This comparison has shown that the numerical approximation of the yield function gradients proposed in this paper facilitates the implementation of the constitutive models, and in the case of the implicit analyses, it leads to a significant decrease of the computational time without impairing the accuracy of the finite element results. In addition, we have demonstrated that there is a critical loading rate below which the dynamic implicit analyses are computationally more efficient than the explicit calculations. ; The research leading to these results has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme. Project PURPOSE, grant agreement 758056.