Status on development and verification of reactivity initiated accident analysis code for PWR (NODAL3)

A coupled neutronics thermal-hydraulics code NODAL3 has been developed based on the nodal few-group neutron diffusion theory in 3-dimensional Cartesian geometry for a typical pressurized water reactor (PWR) static and transient analyses, especially for reactivity initiated accidents (RIA).The spatial variables are treated by using a polynomial nodal method (PNM) while for the neutron dynamic solver the adiabatic and improved quasi-static methods are adopted. A simple single channel thermal-hydraulics module and its steam table is implemented into the code. Verification works on static and transient benchmarks are being conducted to assess the accuracy of the code. For the static benchmark verification, the IAEA-2D, IAEA-3D, BIBLIS and KOEBERG light water reactor (LWR) benchmark problems were selected, while for the transient benchmark verification, the OECD NEACRP 3-D LWR Core Transient Benchmark and NEA-NSC 3-D/1-D PWR Core Transient Benchmark (Uncontrolled Withdrawal of Control Rods at Zero Power). Excellent agreement of the NODAL3 results with the reference solutions and other validated nodal codes was confirmed

Large-Scale Heterogeneous Computing for 3D Deterministic Particle Transport on Tianhe-2A Supercomputer

Scalable parallel algorithm for particle transport is one of the main application fields in high-performance computing. Discrete ordinate method (Sn) is one of the most popular deterministic numerical methods for solving particle transport equations. In this paper, we introduce a new method of large-scale heterogeneous computing of one energy group time-independent deterministic discrete ordinates neutron transport in 3D Cartesian geometry (Sweep3D) on Tianhe-2A supercomputer. In heterogeneous programming, we use customized Basic Communication Library (BCL) and Accelerated Computing Library (ACL) to control and communicate between CPU and the Matrix2000 accelerator. We use OpenMP instructions to exploit the parallelism of threads based on Matrix 2000. The test results show that the optimization of applying OpenMP on particle transport algorithm modified by our method can get 11.3 times acceleration at most. On Tianhe-2A supercomputer, the parallel efficiency of 1.01 million cores compared with 170 thousand cores is 52%.

Elements of Cartesian Analysis in Saidou Spaces

The objective of this research paper is to follow up on the work already started in order to install a new mathematical analysis, the one we called Cartesian analysis see our previous works[1],[2]. During these last two papers, we started with the definition of cartesian geometry and we defined and introduced to a new Cartesian topology which gave birth to new spaces called Saidou spaces. Thus, and to follow up on this way, we propose to studie the analytical and functional part of this analysis. We will define the notion of a Cartesian function and then its epigraph before to characterize the analytical properties of these functions, for example the continuity and the differentiablity. In an other hand, we will see the relationship between cartesian functions and the convex functions. According to the latest papers and this work we do the asset of the first foundations of the cartesian analysis.

COMPARING THE DISCONTINUOUS GALERKIN AND HIGH-ORDER DIAMOND DIFFERENCING METHODS FOR THE TRANSPORT EQUATION ON A LOZENGE-BASED HEXAGONAL GEOMETRY

This paper presents an implementation and a comparison of two spatial discretisation schemes over a hexagonal geometry for the two-dimensional discrete ordinates transport equation. The methods are a high-order Discontinuous Galerkin (DG) finite element scheme and a high-order Diamond Differencing (DD) scheme. The DG method has been, and is being, studied on the hexagonal geometry, also called a honeycomb mesh – but not the DD method. In this research effort, it was chosen to divide the hexagons into (at least) three lozenges. An affine transformation is then applied onto said lozenges to cast them into the reference quadrilaterals usually studied in finite elements. In practice, this effectively means that the equations used in Cartesian geometry have their terms and operators altered using the Jacobian matrix of the transformation. This was implemented in the discrete ordinates solver of the code DRAGON5. Two 2D benchmark problems were then used for the verification and validation, including one based on the Monju 3D reactor benchmark. It was found that the diamond-differencing scheme seemed better. It converged much faster towards the solution at comparable mesh refinements for first-order expansion of the flux. Even if this difference was not present for second-order, DG was slower, about two to four times slower.

MARIA GAETANA AGNESI, ENFANT PRODIGE, MATEMATICA, PIA NOBILDONNA

Maria Gaetana Agnesi (1718-1799) was a prominent figure in eighteenth-century Milan. A child prodigy, and an attraction in the scientific and philosophical disputes organized in the paternal home, she was the first woman to publish a mathematical treatise, the Instituzioni analitiche ad uso della gioventù italiana (1748), a clear and systematic presentation of both Cartesian geometry and infinitesimal analysis. Among the curves studied in that work is the versiera, (witch) the cubic curve that is still associated with her name. Appointed by Pope Benedict XIV in 1750 on the chair of mathematics at the University of Bologna, she did not accept that assignment. After her father’s death in 1752, she left mathematics to devote herself entirely to pious works, and to taking care of poor and infirm women in the Pio Albergo Trivulzio, where she spent the last fifteen years of life.

The role of strain dependent rheology on formation of divergent plate boundaries

<p>Surface of the Earth is divided into distinct plates that move relative to each other. However, formation and evolution of new plate boundaries is still challenging to numerically produce and predict. In particular, regional lithospheric models as well as large scale convection models lack realistic strike slip plate boundaries that would arise self-consistently in such models. Here, we investigate the role of different rheologies on the inception and dynamic evolution of the new divergent plate boundaries and their offset by strike-slip faulting. We compare visco-plastic rheology and strain dependent rheology and their capacity to localise deformation into narrow plate limits. We use high-resolution 3D thermo-mechanical numerical models in  cartesian geometry to infer the conditions under which realistic divergent plate boundaries develop.</p>

Realistic Mathematic Education: a theoretical- methodological approach to the teaching of mathematics in countryside schools

The movement for a Rural Education still lacks investigations of methodological theoretical assumptions for the didactic field, based on the study of teaching practices that consider the object of knowledge and, at the same time, value the realistic/contextual aspect in which the student is inserted. From this perspective, we investigate the methodological theoretical implications of the theory of Realistic Mathematical Education (EMR) for the teaching of mathematics in the countryside school. Based on a qualitative methodological approach, a hypothetical learning path was elaborated based on the principles of EMR related to the teaching of analytical geometry, from the practice of soil modeling in passion fruit (passiflora edulis) cultivation. Our results point to the EMR as a promising methodological theoretical approach of didactic exploration to the countryside context capable of promoting formal reasoning, concepts in realistic situations, appropriation of mathematical language and potential for the development of concepts in the field of Cartesian geometry.