Magnetization structure of a Bloch point singularity

Switching of magnetic vortex cores involves a topological transition characterized by the presence of a magnetization singularity, a point where the magnetization vanishes (Bloch point). We analytically derive the shape of the Bloch point that is an extremum of the free energy with exchange, dipole and the Landau terms for the determination of the local value of the magnetization modulus.Comment: 4 pages, 2 figure

Moving meshes to solve the time-dependent neutron diffusion equation in hexagonal geometry

To simulate the behaviour of a nuclear power reactor it is necessary to be able to integrate the time-dependent neutron diffusion equation inside the reactor core. Here the spatial discretization of this equation is done using a finite element method that permits h-p refinements for different geometries. This means that the accuracy of the solution can be improved refining the spatial mesh (h-refinement) and also increasing the degree of the polynomial expansions used in the finite element method (p-refinement). Transients involving the movement of the control rod banks have the problem known as the rod-cusping effect. Previous studies have usually approached the problem using a fixed mesh scheme defining averaged material properties. The present work proposes the use of a moving mesh scheme that uses spatial meshes that change with the movement of the control rods avoiding the necessity of using equivalent material cross sections for the partially inserted cells. The performance of the moving mesh scheme is tested studying one-dimensional and three-dimensional benchmark problems. (C) 2015 Elsevier B.V. All rights reserved.This work has been partially supported by the Spanish Ministerio de Ciencia e Innovacion under project ENE2011-22823, the Generalitat Valenciana under projects II/2014/08 and ACOMP/2013/237, and the Universitat Politecnica de Valencia under project UPPTE/2012/118.Vidal-Ferràndiz, A.; Fayez Moustafa Moawad, R.; Ginestar Peiro, D.; Verdú Martín, GJ. (2016). Moving meshes to solve the time-dependent neutron diffusion equation in hexagonal geometry. Journal of Computational and Applied Mathematics. 291:197-208. https://doi.org/10.1016/j.cam.2015.03.040S19720829

Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator

We consider the problem of recovering the initial data (or initial state) of infinite-dimensional linear systems with unitary semigroups. It is well-known that this inverse problem is well posed if the system is exactly observable, but this assumption may be very restrictive in some applications. In this paper we are interested in systems which are not exactly observable, and in particular, where we cannot expect a full reconstruction. We propose to use the algorithm studied by Ramdani et al. in (Automatica 46:1616–1625, 2010) and prove that it always converges towards the observable part of the initial state. We give necessary and sufficient condition to have an exponential rate of convergence. Numerical simulations are presented to illustratethe theoretical results

BioPARR:A software system for estimating the rupture potential index for abdominal aortic aneurysms

An abdominal aortic aneurysm (AAA) is a permanent and irreversible dilation of the lower region of the aorta. It is a symptomless condition that, if left untreated, can expand until rupture. Despite ongoing efforts, an efficient tool for accurate estimation of AAA rupture risk is still not available. Furthermore, a lack of standardisation across current approaches and specific obstacles within computational workflows limit the translation of existing methods to the clinic. This paper presents BioPARR (Biomechanics based Prediction of Aneurysm Rupture Risk), a software system to facilitate the analysis of AAA using a finite element analysis based approach. Except semi-automatic segmentation of the AAA and intraluminal thrombus (ILT) from medical images, the entire analysis is performed automatically. The system is modular and easily expandable, allows the extraction of information from images of different modalities (e.g. CT and MRI) and the simulation of different modelling scenarios (e.g. with/without thrombus). The software uses contemporary methods that eliminate the need for patient-specific material properties, overcoming perhaps the key limitation to all previous patient-specific analysis methods. The software system is robust, free, and will allow researchers to perform comparative evaluation of AAA using a standardised approach. We report preliminary data from 48 cases

Finite element model with imposed slip surfaces for earth mass safety evaluation

The study of earth masses requires numerical methods that provide the quantification of the safety factor without requiring detrimental assumptions. For that, equilibrium analysis can perform fast computations but require assumptions that limit its potentiality. Limit analysis does not require detrimental assumptions but are numerically demanding. This work provides a new approach that combines the advantage of both the equilibrium method and the limit analysis. The defined hybrid model allows probabilistic analysis and optimization approaches without the assumption of interslice forces. It is compared with a published case and used to perform probabilistic studies in both a homogeneous and a layered foundation. Analyses show that the shape of the density probability functions is highly relevant when computing the probability of failure, and soil elasticity hardly affects the safety of factor of the earth mass.Programa Operacional Factores de Competitividade—COMPETE, and by Portuguese Funds through FCT–Fundação para a Ciência e a Tecnologia, within the projects PEst –C/MAT/UI0013/2011 and PEst–OE/ECM/UI4047/2011

A Computational Clonal Analysis of the Developing Mouse Limb Bud

A comprehensive spatio-temporal description of the tissue movements underlying organogenesis would be an extremely useful resource to developmental biology. Clonal analysis and fate mappings are popular experiments to study tissue movement during morphogenesis. Such experiments allow cell populations to be labeled at an early stage of development and to follow their spatial evolution over time. However, disentangling the cumulative effects of the multiple events responsible for the expansion of the labeled cell population is not always straightforward. To overcome this problem, we develop a novel computational method that combines accurate quantification of 2D limb bud morphologies and growth modeling to analyze mouse clonal data of early limb development. Firstly, we explore various tissue movements that match experimental limb bud shape changes. Secondly, by comparing computational clones with newly generated mouse clonal data we are able to choose and characterize the tissue movement map that better matches experimental data. Our computational analysis produces for the first time a two dimensional model of limb growth based on experimental data that can be used to better characterize limb tissue movement in space and time. The model shows that the distribution and shapes of clones can be described as a combination of anisotropic growth with isotropic cell mixing, without the need for lineage compartmentalization along the AP and PD axis. Lastly, we show that this comprehensive description can be used to reassess spatio-temporal gene regulations taking tissue movement into account and to investigate PD patterning hypothesis

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations

Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.Comment: 85 pages, 2 figures, book chapte