An Entropy Stable Discontinuous Galerkin Finite-Element Moment Method for the Boltzmann Equation

This paper presents a numerical approximation technique for the Boltzmann equation based on a moment system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure relation for the moment systems derives from minimization of a suitable {\phi}-divergence. This divergence-based closure yields a hierarchy of tractable symmetric hyperbolic moment systems that retain the fundamental structural properties of the Boltzmann equation. The resulting combined discontinuous Galerkin moment method corresponds to a Galerkin approximation of the Boltzmann equation in renormalized form. We present a new class of numerical flux functions, based on the underlying renormalized Boltzmann equation, that ensure entropy dissipation of the approximation scheme. Numerical results are presented for a one-dimensional test case.Comment: arXiv admin note: substantial text overlap with arXiv:1503.0518

Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation

This paper presents an a-posteriori goal-oriented error analysis for a numerical approximation of the steady Boltzmann equation based on a moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element (DGFE) approximation in position dependence. We derive computable error estimates and bounds for general target functionals of solutions of the steady Boltzmann equation based on the DGFE moment approximation. The a-posteriori error estimates and bounds are used to guide a model adaptive algorithm for optimal approximations of the goal functional in question. We present results for one-dimensional heat transfer and shock structure problems where the moment model order is refined locally in space for optimal approximation of the heat flux.Comment: arXiv admin note: text overlap with arXiv:1602.0131

WRF-ARW based systems for nowcasting and very-short range forecasts at the Meteorological Service of Catalonia

Póster presentado en: 3rd European Nowcasting Conference, celebrada en la sede central de AEMET en Madrid del 24 al 26 de abril de 2019

A conservative Galerkin solver for the quasilinear diffusion model in magnetized plasmas

The quasilinear theory describes the resonant interaction between particles and waves with two coupled equations: one for the evolution of the particle probability density function (pdf), the other for the wave spectral energy density (sed). In this paper, we propose a conservative Galerkin scheme for the quasilinear model in three-dimensional momentum space and three-dimensional spectral space, with cylindrical symmetry. We construct an unconditionally conservative weak form, and propose a discretization that preserves the unconditional conservation property, by “unconditional” we mean that conservation is independent of the singular transition probability. The discrete operators, combined with a consistent quadrature rule, will preserve all the conservation laws rigorously. The technique we propose is quite general: it works for both relativistic and non-relativistic systems, for both magnetized and unmagnetized plasmas, and even for problems with time-dependent dispersion relations. We represent the particle pdf by continuous basis functions, and use discontinuous basis functions for the wave sed, thus enabling the application of a positivity-preserving technique. The marching simplex algorithm, which was initially designed for computer graphics, is adopted for numerical integration on the resonance manifold. We introduce a semi-implicit time discretization, and discuss the stability condition. In addition, we present numerical examples with a “bump on tail” initial configuration, showing that the particle-wave interaction results in a strong anisotropic diffusion effect on the particle pdf.</p

A Conservative Galerkin Solver for the Quasilinear Diffusion Model in Magnetized Plasmas

Arising from averaging and linearizing over the original Vlasov-Maxwell system for magnetized plasmas, the quasilinear theory describes the resonant interaction between particles and waves. Such a model reduction in weak turbulence regime results in a kinetic diffusion process in momentum space for the particle probability density function(pdf ), where the diffusion coefficients are determined by the wave spectral energy density(sed). Meanwhile, a reaction equation in spectral space governs the time dynamics of the wave sed, with growth rates linearly dependent on the particle pdf. We propose a conservative Galerkin scheme for the quasilinear diffusion model in three-dimensional momentum space and three-dimensional spectral space, with cylindrical symmetry. The conservation laws are preserved by adopting the conservative discrete integro-differential operators and a consistent quadrature rule. We introduce a semi-implicit time discretization, and the stability condition is discussed. Numerical examples with applications in the electron runaway problem are provided, they show that the particle-wave interaction results in a strong anisotropic diffusion effect on the particle pdf.Comment: 20 pages, 3 figure

Effect of compost and urea nitrogen on growth and yield of sweet pepper (Capsicum annuum L.) and on some properties of the Gezira soil

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Compost is stable humus like product resulting from biological decomposition of organic matter under controlled conditions. The objective of this study was to investigate the combined effect of compost with urea nitrogen on some soil properties, growth and yield of sweet pepper. This study comprised a number of experimentations conducted over two consecutive seasons (2009/10-2010/11) at the Experimental Farm of the Faculty of Agricultural Sciences, University of Gezira and laboratories of CIRAD in France. Compost was applied at 0, 10 and 20 t ha-1 combined with N at 0, 43 and 86 kg ha-1 in the form of urea. The results showed that application of compost alone or in combination with urea nitrogen improved soil properties and hence growth and yield of sweet pepper. Improvement of those parameters was more pronounced when the urea and compost were combined, especially at the higher rates. Combination of urea and compost presumably improved availability of nitrogen from the organic source to sweet pepper and, therefore, positively affected growth and yield of the crop. The extent of improvement was less when urea nitrogen and organic manures were applied in the same season. Hence, it could be recommended to fertilize sweet pepper with compost and urea at the rate of 86 kg N/ ha

Imaging of hydrothermal altered zones in Wadi Al-Bana, in southern Yemen, using remote sensing techniques and very low frequency–electromagnetic data

© 2019, Saudi Society for Geosciences. Economic mineralization and hydrothermally altered zones are areas of great economic interests. This study focusses on hydrothermal altered zones of high mineralization potentials in Wadi Al-Bana, in southern Yemen. An azimuthal very low frequency–electromagnetic (AVLF-EM) data acquisition was conducted in search for mineralization in the study area. The study integrated observations from geophysical field data with others extracted from object-oriented principal component analysis (PCA) to better map and understand mineralization in the investigated area. This technique was applied to two data sets, ASTER and Landsat 8 Operational Land Imager (OLI) imagery. The results of PCA revealed high accuracy in detecting alteration minerals and for mapping zones of high concentration of these minerals. The PCA-based distribution of selected alteration zones correlated spatially with high conductivity anomalies in the subsurface that were detected by VLF measurements. Finally, a GIS model was built and successfully utilized to categorize the resulted altered zones, into three levels. [Figure not available: see fulltext.]

The perceived impact of location privacy: A web-based survey of public health perspectives and requirements in the UK and Canada

<p>Abstract</p> <p>Background</p> <p>The "place-consciousness" of public health professionals is on the rise as spatial analyses and Geographic Information Systems (GIS) are rapidly becoming key components of their toolbox. However, "place" is most useful at its most precise, granular scale – which increases identification risks, thereby clashing with privacy issues. This paper describes the views and requirements of public health professionals in Canada and the UK on privacy issues and spatial data, as collected through a web-based survey.</p> <p>Methods</p> <p>Perceptions on the impact of privacy were collected through a web-based survey administered between November 2006 and January 2007. The survey targeted government, non-government and academic GIS labs and research groups involved in public health, as well as public health units (Canada), ministries, and observatories (UK). Potential participants were invited to participate through personally addressed, standardised emails.</p> <p>Results</p> <p>Of 112 invitees in Canada and 75 in the UK, 66 and 28 participated in the survey, respectively. The completion proportion for Canada was 91%, and 86% for the UK. No response differences were observed between the two countries. Ninety three percent of participants indicated a requirement for personally identifiable data (PID) in their public health activities, including geographic information. Privacy was identified as an obstacle to public health practice by 71% of respondents. The overall self-rated median score for knowledge of privacy legislation and policies was 7 out of 10. Those who rated their knowledge of privacy as high (at the median or above) also rated it significantly more severe as an obstacle to research (<it>P </it>< 0.001). The most critical cause cited by participants in both countries was bureaucracy.</p> <p>Conclusion</p> <p>The clash between PID requirements – including granular geography – and limitations imposed by privacy and its associated bureaucracy require immediate attention and solutions, particularly given the increasing utilisation of GIS in public health. Solutions include harmonization of privacy legislation with public health requirements, bureaucratic simplification, increased multidisciplinary discourse, education, and development of toolsets, algorithms and guidelines for using and reporting on disaggregate data.</p

Explicit expressions for the estimation of the elastic constants of lamellar bone as a function of the volumetric mineral content using a multi-scale approach

[EN] In this work, explicit expressions to estimate all the transversely isotropic elastic constants of lamellar bone as a function of the volumetric bone mineral density (BMD) are provided. The methodology presented is based on the direct homogenization procedure using the finite element method, the continuum approach based on the Hill bounds, the least-square method and the mean field technique. Firstly, a detailed description of the volumetric content of the different components of bone is provided. The parameters defined in this step are related to the volumetric BMD considering that bone mineralization process occurs at the smallest scale length of the bone tissue. Then, a thorough description provides the details of the numerical models and the assumptions adopted to estimate the elastic behaviour of the forward scale lengths. The results highlight the noticeable influence of the BMD on the elastic modulus of lamellar bone. Power law regressions fit the Young's moduli, shear stiffness moduli and Poisson ratios. In addition, the explicit expressions obtained are applied to the estimation of the elastic constants of cortical bone. At this scale length, a representative unit cell of cortical bone is analysed including the fibril orientation pattern given by Wagermaier et al. (Biointerphases 1:1-5, 2006) and the BMD distributions observed by Granke et al. (PLoS One 8:e58043, 2012) for the osteon. Results confirm that fibril orientation arrangement governs the anisotropic behaviour of cortical bone instead of the BMD distribution. The novel explicit expressions obtained in this work can be used for improving the accuracy of bone fracture risk assessment.The authors acknowledge the Ministerio de Economia y Competitividad for the financial support received through the project DPI2013-46641-R and to the Generalitat Valenciana for Programme PROMETEO 2016/007. The authors declare that they have no conflict of interestVercher Martínez, A.; Giner Maravilla, E.; Belda, R.; Aigoun, A.; Fuenmayor Fernández, F. (2018). Explicit expressions for the estimation of the elastic constants of lamellar bone as a function of the volumetric mineral content using a multi-scale approach. Biomechanics and Modeling in Mechanobiology. 17(2):449-464. https://doi.org/10.1007/s10237-017-0971-xS449464172Akiva U, Wagner HD, Weiner S (1998) Modelling the three-dimensional elastic constants of parallel-fibred and lamellar bone. J Mater Sci 33:1497–1509Ascenzi A, Bonucci E (1967) The tensile properties of single osteons. Ana Rec 158:375–386Barbour KE, Zmuda JM, Strotmeyer ES, Horwitz MJ, Boudreau R, Evans RW, Ensrud K, Petit MA, Gordon CL, Cauley JA (2013) Correlates of trabecular and cortical volumetric bone mineral density of the radius and tibia older men: the osteoporotic fractures in men study. J Bone Miner Res 25(5):1017–1028Bar-On B, Wagner HD (2013) Structural motifs and elastic properties of hierarchical biological tissues—a review. J Struct Biol 183:149–164Cowin SC (2000) How is a tissue built? J Biomech Eng 122:553–569Cowin SC (2001) Bone mechanics handbook, 2nd edn. CRC Press, Boca RatonCurrey JD (1986) Power law models for the mechanical properties of cancellous bone. Eng Med 15(3):153–154Currey JD (1988) The effect of porosity and mineral content on the Young’s modulus of elasticity of compact bone. J Biomech 21:131–139Daszkiewicz K, Maquer G, Zysset PK (2017) The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements. Biomech Model Mechanobiol 16:731–742Faingold A, Sidney RC, Wagner HD (2012) Nanoindentation of osteonal bone lamellae. J Mech Biomech Materials 9:198–206Fratzl P, Fratzl-Zelman N, Klaushofer K, Vogl G, Koller K (1991) Nucleation and growth of mineral crystals in bone studied by small-angle X-ray scattering. Calcif Tissue Int 48:407–413Fritsch A, Hellmich C (2007) ’Universal’ microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity. J Theo Biol 24:597–620Grampp S, Genant HK, Mathur A, Lang P, Jergas M, Takada M, Glüer CC, Lu Y, Chavez M (1997) Comparisons of noninvasive bone mineral measurements in assessing age-related loss, fracture discrimination and diagnostic classification. J Bone Miner Res 12:697–711Grant CA, Langton C, Schuetz MA, Epari DR (2011) Determination of the material properties of ovine cortical bone. Poster No. 2226, 57th Orthopaedic Research Society (ORS) Annual meeting, Long Beach, CaliforniaGranke M, Gourrier A, Rupin F, Raum K, Peyrin F, Burghammer M, Saïd A, Laugier P (2012) Microfibril orientation dominates the microelastic properties of human bone tissue at the lamellar length scale. PLoS One 8:e58043Gurtin ME (1972) The linear theory of elasticity. Handbuch del Physik VIa 2:1–296Hamed E, Jasiuk I (2012) Elastic modeling of bone at nanostructural level. Mat Sci Eng R73:27–49Hernández CJ, Beaupré GS, Keller TS, Carter DR (2001a) The influence of bone volume fraction and ash fraction on bone strength and modulus. Bone 29:74–78Hill R (1952) The elastic behaviour of a crystalline aggregate. Proc Phys Soc Sec A 65:349–354Hodge AJ, Petruska JA (1963) Recent studies with the electron microscope on ordered aggregates of the tropocollagen macromolecule. In: Ramachandran GN (ed) Aspects of protein structure. Academic Press, New York, pp 289–300Jäger I, Fratzl P (2000) Mineralized collagen: a mechanical model with a staggered arrangement of mineral particles. Biophys J 78:1737–1746Kuhn JL, Goldstein SA, Choi K, London M, Feldkamp LA, Matthews LS (1989) Comparison of the trabecular and cortical tissue moduli from human iliac crests. J Orthop Res 7:876–884Landis WJ, Song MJ, Leith A, McEwen L, McEwen BF (1993) Mineral and organic matrix interaction in normally calcifying tendon visualized in three dimensions by high-voltage electron microscopic tomography and graphic image reconstruction. J Struct Biol 110:39–54Lees S, Heeley JD, Cleary PF (1979) A study of some properties of a sample of bovine cortical bone using ultrasound. Calcif Tissue Int 29:107–117Lekhnitskii SG (1963) Theory of elasticity of anisotropic elastic body. Holden-Day, San Francisco, pp 1–73Lempriere BM (1968) Poisson’s ratio in orthotropic materials. Am Inst Aeronaut Astronaut J J6:2226–2227Liu Y, Kim YK, Dai L, Li N, Khan SO, Pashley DH, Tay FR (2011) Hierarchical and non-hierarchical mineralization of collagen. Biomater 32:1291–1300Majumdar S, Kothari M, Augat P, Newitt DC, Link TM, Lin JC, Lang T, Lu Y, Genant HK (1998) High-resolution magnetic resonance imaging: three-dimensional trabecular bone architecture and biomechanical properties. Bone 22(5):445–454Martínez-Reina J, Domínguez J, García-Aznar JM (2011) Effect of porosity and mineral content on the elastic constants of cortical bone: a multiscale approach. Biomech Model Mechanobiol 10:309–322Nobakhti S, Limbert G, Thurner PJ (2014) Cement lines and interlamellar areas in compact bone as strain amplifiers—Contributors to elasticity, fracture toughness and mechanotransduction. J Mech Behav Biomed Mater 29:235–251Orgel JPRO, Irving TC, Miller A, Wess TJ (2006) Microfibrillar structure of type I collagen in situ. PNAS USA 103:9001–9005Reisinger AG, Pahr DH, Zysset PK (2010) Sensitivity analysis and parametric study of elastic properties of unidirectional mineralized bone fibril-array using mean field methods. Biomech Model Mechanobiol 9:499–510Reisinger AG, Pahr DH, Zysset PK (2011) Elastic anisotropy of bone lamellae as a function of fibril orientation pattern. Biomech Model Mechanobiol 10:67–77Rho JY, Kuhn-Spearing L, Zioupos P (1998) Mechanical properties and the hierarchical structure of bone. Med Eng Phys 20:92–102Robinson RA, Rochester MD (1952) An electron-microscopic study of the crystalline inorganic component of bone and its relationship to the organic matrix. J Bone Joint Surg 34–a:389–435Roque WL, Arcaro K, Alberich-Bayarri A (2013) Mechanical competence of bone: a new parameter to grade trabecular bone fragility from tortuosity and elasticity. IEEE Trans Bio Eng 60:1363–1370Rubin MA, Jasiuk I, Taylor J, Rubin J, Ganey T, Apkarian RP (2003) TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone. Bone 33:270–282Sasaki N, Tagami A, Goto T, Taniguchi M, Nakata M, Hikichi K (2002) Atomic force microscopic studies on the structure of bovine femoral cortical bone at the collagen fibril-mineral level. J Mater Sci Mater Med 13(3):333–337Schaffler MB, Burr DB (1988) Stiffness of compact bone: effects of porosity and density. J Biomech 21:13–16Silver FH, Landis WJ (2011) Deposition of apatite in mineralizing vertebrate extracellular matrices: a model of possible nucleation sites on type I collagen. Connect Tissue Res 52:242–254Tommasini SM, Nasser P, Hu B, Jepsen KJ (2008) Biological co-adaptation of morphological and composition traits contributes to mechanical functionality and skeletal fragility. J Bone Miner Res 23:236–246Ulrich D, Rietbergen B, Weinans H, Rüegsegger P (1998) Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech 31:1187–1192Ulrich D, Rietbergen B, Laib A, Rüegsegger P (1999) The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone. Bone 25:55–60Vercher A, Giner E, Arango C, Tarancón JE, Fuenmayor FJ (2014) Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models. Biomech Model Mechanobiol 13:437–449Vercher-Martínez A, Giner E, Arango C, Fuenmayor FJ (2015) Influence of the mineral staggering on the elastic properties of the mineralized collagen fibril in lamellar bone. J Mech Behav Biomed Mater 42:243–256Wagermaier W, Gupta HS, Gourrier A, Burghammer M, Roschger P, Fratzl P (2006) Spiral twisting of fiber orientation inside bone lamellae. Biointerphases 1:1–5Weiner S, Traub W (1986) Organization of hydroxiapatite within collagen fibrils. FEBS Lett 206:262–266Weiner S, Wagner HD (1998) The material bone: structure-mechanical function relations. Annu Rev Mater Sci 28:271–298Yang L, Palermo L, Black DM, Eastell R (2014) Prediction of incident hip fracture with the estimated femoral strength by finite element analysis of DXA scans in the study of osteoporotic fractures. JBMR 29:2594–2600Yuan YJ, Cowin SC (2008a) The estimated elastic constants for a single bone osteonal lamella. Biomech Model Mechanobiol 7:1–11Yu W, Glüer CC, Grampp S, Jergas M, Fuerst T, Wu CY, Lu Y, Fan B, Genant HK (1995) Spinal bone mineral assessment in postmenopausal women: a comparison between dual X-ray absorptiometry and quantitative computed tomography. Osteoporos Int 5:433–439Yang L, Palermo L, Black DM, Eastell R (2014) Prediction of incident hip fracture with the estimated femoral strength by finite element analysis of DXS Scans in the study of osteoporotic fractures. J Bone Miner Res 29(12):2594–2600Yuan F, Stock SR, Haeffner DR, Almer JD, Dunand DC, Brinson LC (2011) A new model to simulate the elastic properties of mineralized collagen fibril. Biomech Model Mechanobiol 10:147–16