Efficient modeling of high temperature superconductors surrounded by magnetic components using a reduced H-ϕ\phi formulation

Although the H-formulation has proven to be one of the most versatile formulations used to accurately model superconductors in the finite element method, the use of vector dependent variables in non-conducting regions leads to unnecessarily long computation times. Additionally, in some applications of interest, the combination of multiple magnetic components interacting with superconducting bulks and/or tapes leads to large domains of simulation. In this work, we separate the magnetic field into a source and reaction field and use the H-$\phi$ formulation to efficiently simulate a superconductor surrounded by magnetic bodies. We model a superconducting cube between a pair of Helmholtz coils and a permanent magnet levitating above a superconducting pellet. In both cases, we find excellent agreement with the H-formulation, while the computation times are reduced by factors of nearly three and four in 2-D and 3-D, respectively. Finally, we show that the H-$\phi$ formulation is more accurate and efficient than the H-A formulation in 2-D

Validation de la reproductibilité d’outils de mesure de la fraction d’éjection du ventricule gauche en médecine nucléaire

La fraction d’éjection du ventricule gauche est un excellent marqueur de la fonction cardiaque. Plusieurs techniques invasives ou non sont utilisées pour son calcul : l’angiographie, l’échocardiographie, la résonnance magnétique nucléaire cardiaque, le scanner cardiaque, la ventriculographie radioisotopique et l’étude de perfusion myocardique en médecine nucléaire. Plus de 40 ans de publications scientifiques encensent la ventriculographie radioisotopique pour sa rapidité d’exécution, sa disponibilité, son faible coût et sa reproductibilité intra-observateur et inter-observateur. La fraction d’éjection du ventricule gauche a été calculée chez 47 patients à deux reprises, par deux technologues, sur deux acquisitions distinctes selon trois méthodes : manuelle, automatique et semi-automatique. Les méthodes automatique et semi-automatique montrent dans l’ensemble une meilleure reproductibilité, une plus petite erreur standard de mesure et une plus petite différence minimale détectable. La méthode manuelle quant à elle fournit un résultat systématiquement et significativement inférieur aux deux autres méthodes. C’est la seule technique qui a montré une différence significative lors de l’analyse intra-observateur. Son erreur standard de mesure est de 40 à 50 % plus importante qu’avec les autres techniques, tout comme l’est sa différence minimale détectable. Bien que les trois méthodes soient d’excellentes techniques reproductibles pour l’évaluation de la fraction d’éjection du ventricule gauche, les estimations de la fiabilité des méthodes automatique et semi-automatique sont supérieures à celles de la méthode manuelle.Left ventricular ejection fraction is an excellent indicator of cardiac function. Many invasive and non-invasive techniques can be used for its assessment: angiography, echocardiography, cardiac MRI, computed tomography of the heart, multigated radionuclide angiography and myocardial perfusion imaging. More than 40 years of scientific publication praise the multigated radionuclide angiography for its execution speed, its availability, its low cost and intrarater and interrater reproducibility. The left ventricular ejection fraction was calculated twice for 47 patients, using two raw data acquisitions, two technologists and three software platforms: one fully manual, one semi-automatic and one fully automatic. In general, the automatic and semi-automatic methods showed greater reproducibility, a smaller standard error of measurement and minimal detectable change than the manual method, whereas the manual method systematically gave a significantly lower quality of result. It was the only technique that showed significant intrarater difference, and its standard error of measurement and minimal detectable change were 40% to 50% higher than those of automatic and semi-automatic methods. Even though all three techniques are all excellent and reliable options, reliability coefficient estimations were superior using automatic and semi-automatic methods as compared to the manual method

DHA Improves Cognition and Prevents Dysfunction of Entorhinal Cortex Neurons in 3xTg-AD Mice

Defects in neuronal activity of the entorhinal cortex (EC) are suspected to underlie the symptoms of Alzheimer's disease (AD). Whereas neuroprotective effects of docosahexaenoic acid (DHA) have been described, the effects of DHA on the physiology of EC neurons remain unexplored in animal models of AD. Here, we show that DHA consumption improved object recognition (↑12%), preventing deficits observed in old 3xTg-AD mice (↓12%). Moreover, 3xTg-AD mice displayed seizure-like akinetic episodes, not detected in NonTg littermates and partly prevented by DHA (↓50%). Patch-clamp recording revealed that 3xTg-AD EC neurons displayed (i) loss of cell capacitance (CC), suggesting reduced membrane surface area; (ii) increase of firing rate versus injected current (F-I) curve associated with modified action potentials, and (iii) overactivation of glutamatergic synapses, without changes in synaptophysin levels. DHA consumption increased CC (↑12%) and decreased F-I slopes (↓21%), thereby preventing the opposite alterations observed in 3xTg-AD mice. Our results indicate that cognitive performance and basic physiology of EC neurons depend on DHA intake in a mouse model of AD

H-phi formulation for the efficient simulation of superconductors

International audienceThis work shows how to implement the H-φ formulation in a commercial finite element framework for efficiently modeling the electromagnetic behavior of high critical temperature superconductors. We show that the results obtained with the H-φ and H formulations are in good agreement in both 2-D and 3-D, but the H-φ formulation is much faster

H-phi formulation for the efficient simulation of superconductors

International audienceThis work shows how to implement the H-φ formulation in a commercial finite element framework for efficiently modeling the electromagnetic behavior of high critical temperature superconductors. We show that the results obtained with the H-φ and H formulations are in good agreement in both 2-D and 3-D, but the H-φ formulation is much faster

Implementation of the H-ϕ formulation in COMSOL Multiphysics for simulating the magnetization of bulk superconductors and comparison with the H-formulation

The H-formulation, used abundantly for the simulation of high temperature superconductors, has shown to be a very versatile and easily implementable way of modeling electromagnetic phenomena involving superconducting materials. However, the simulation of a full vector field in current-free domains unnecessarily adds degrees of freedom to the model, thereby increasing computation times. In this contribution, we implement the well known H-$\phi$ formulation in COMSOL Multiphysics in order to compare the numerical performance of the H and H-$\phi$ formulations in the context of computing the magnetization of bulk superconductors. We show that the H-$\phi$ formulation can reduce the number of degrees of freedom and computation times by nearly a factor of two for a given relative error. The accuracy of the magnetic fields obtained with both formulations are demonstrated to be similar. The computational benefits of the H-$\phi$ formulation are shown to far outweigh the added complexity of its implementation, especially in 3-D. Finally, we identify the ideal element orders for both H and H-$\phi$ formulations to be quartic in 2-D and cubic in 3-D, corresponding to the highest element orders implementable in COMSOL

COMSOL implementation of the H-ϕ-Formulation with thin cuts for modeling superconductors with transport currents

Despite the acclaimed success of the magnetic field (H) formulation for modeling the electromagnetic behavior of superconductors with the finite element method, the use of vector-dependent variables in non-conducting domains leads to unnecessarily long computation times. In order to solve this issue, we have recently shown how to use a magnetic scalar potential together with the H-formulation in the COMSOL Multiphysics environment to efficiently and accurately solve for the magnetic field surrounding superconducting domains. However, from the definition of the magnetic scalar potential, the non-conducting domains must be made simply connected in order to obey Ampere's law. In this work, we use thin cuts to apply a discontinuity in $\phi$ and make the non-conducting domains simply connected. This approach is shown to be easily implementable in the COMSOL Multiphysics finite element program, already widely used by the applied superconductivity community. We simulate three different models in 2-D and 3-D using superconducting filaments and tapes, and show that the results are in very good agreement with the H-A and H-formulations. Finally, we compare the computation times between the formulations, showing that the H-$\phi$-formulation can be up to seven times faster than the standard H-formulation in certain applications of interest