Cycles of Sums of Integers

We study the period of the linear map $T:\textbf{Z}_m^n\rightarrow \textbf{Z}_m^n:(a_0,\dots,a_{n-1})\mapsto(a_0+a_1,\dots,a_{n-1}+a_0)$ as a function of $m$ and $n$, where $\textbf{Z}_m$ stands for the ring of integers modulo $m$. This map being a variant of the Ducci map, several known results are adapted in the context of $T$. The main theorem of this paper states that the period modulo $m$ can be deduced from the prime factorization of $m$ and the periods of its prime factors. We give some other interesting properties.Comment: Submitted March 8 201

Multiscale Finite Element Modeling of Nonlinear Magnetoquasistatic Problems Using Magnetic Induction Conforming Formulations

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and many mesoscale problems defined on finely-meshed small areas around some points of interest of the macroscale mesh (e.g. numerical quadrature points). The exchange of information between these macro and meso problems is thoroughly explained in this paper. For the sake of validation, we consider a two-dimensional geometry of an idealized periodic soft magnetic composite.Comment: Paper accepted for publication in the SIAM MMS journa

Numerical simulation of the magnetization of high-temperature superconductors: 3D finite element method using a single time-step iteration

We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects associated with currents that are not perpendicular to the local magnetic induction. We consider samples that are subjected to a uniform magnetic field varying linearly with time. Their magnetization is calculated by means of a weak formulation in the magnetostatic approximation of the Maxwell equations (A-phi formulation). An implicit method is used for the temporal resolution (Backward Euler scheme) and is solved in the open source solver GetDP. Picard iterations are used to deal with the power law conductivity of HTS. The finite element formulation is validated for an HTS tube with large pinning strength through the comparison with results obtained with other well-established methods. We show that carrying the calculations with a single time-step (as opposed to many small time-steps) produce results with excellent accuracy in a drastically reduced simulation time. The numerical method is extended to the study of the trapped magnetization of cylinders that are drilled with different arrays of columnar holes arranged parallel to the cylinder axis

Subproblem h-Conform Formulation for Accurate Thin Shell Models Between Conducting and Nonconducting Regions

peer reviewedA subproblem method (SPM) with h-formulation is developed for correcting the inaccuracies near edges and corners that arise from using thin shell (TS) models to replace thin volume regions by surfaces. The developed surface-to-volume correction problem is defined as a step of multiple SPs, with inductors and magnetic or conducting regions, some of them being thin. The TS model assumes that the fields in the thin regions are approximated by a priori 1-D analytical distributions along the shell thickness (C. Geuzaine et al., “Dual formulations for the modeling of thin electromagnetic shells using edge elements,” IEEE Trans. Magn., vol. 36, no. 4, pp. 799–802, 2000). Their interior is not meshed and ratherextracted from the studied domain, which is reduced to a zero-thickness double layer with interface conditions (ICs) linked to 1-D analytical distributions that however neglect end and curvature effects. This leads to inaccuracies near edges and corners that increase with the thickness. To cope with these difficulties, the authors have recently proposed a SPM based on the h-formulation for a thin region located between non-conducting regions (Vuong Q. Dang et al., “Subproblem Approach for Thin Shell Dual Finite Element Formulations”, IEEE Trans. Magn., vol. 48, no. 2, pp. 407–410, 2012). The magnetic field h is herein defined in nonconducting regions by means of a magnetic scalar potential , i.e. h = -grad{\phi} , with discontinuities of through the TS. In this paper, the SPM is extended to account for thin regions located between conducting regions or between conducting and nonconducting regions, in the general case of multiply connected regions. In these regions, the potential is not defined anymore on both sides of the TS and the problem has to be expressed in terms of the discontinuities of h, possibly involving on one side only, to be strongly defined via an IC through the TS. In the proposed SP strategy, a reduced problem with only inductors is first solved on a simplified mesh without thin and volume regions. Its solution gives surface sources (SSs) as ICs for added TS regions, and volume sources (VSs) for possible added volume regions. The TS solution is further improved by a volume correction via SSs and VSs that overcome the TS assumptions, respectively suppressing the TS model and adding the volume model. Each SP has its own separate mesh, which increases the computational efficiency. Details on the proposed method will be given in the extended paper, with practical applications

Finite element models for studying the capacitive behaviour of wound components

peer reviewedFinite element models of increasing accuracy are proposed for the study of the capacitive behaviour of wound magnetic components. Simple models, which are based on the classical assumption of a decoupling between electric and magnetic fields, are first described. Formulations which enable such a coupling are then presented. The models are tested on various coreless inductors, made of round conductors or copper sheets. The results are discussed and compared with experimental data measured with an impedance analyzer

Experimental Investigation of the Cavitation Effects on the Heat Generation in a Closed Loop Pumping System

A series of tests were carried out in the cavitation tunnel of the Laboratory for Water and Turbine Machines of the University of Ljubljana in order to investigate the effects of cavitation in the water heating process of closed loop pumping systems. For that, the water temperature was measured at the low pressure reservoir during runs of about 10 minutes. As expected, a constant temperature increase was observed which was proportional to the pump’s rotation speed. Then, the results obtained while keeping the same pump operating point and flow conditions with and without cavitation in the Venturi test section were compared. Surprisingly, it was found that the temperature increase rate was slightly higher when cavitation is present in the system. Moreover, the heat power was always higher than the hydraulic one for all the tests up to a certain cavitation level. However, this trend was inversed for higher cavitation numbers and lower hydraulic powers. Both results seem to prove that there is a clear influence of cavitation in heat generation process. Therefore, a new test rig will be built in Barcelona by the Spanish company Condorchem Envitech, S. L. with the help of Universitat Politècnica de Catalunya BarcelonaTech to continue the current researchPostprint (published version

The microbiology of cryopedogenic soils of the subarctic with particular reference to the Churchill region

Soil materials taken from sampling sites in the Churchill and Inuvik areas were examined in an attempt to determine the role of various micro-organisms contributing to cryopedogenesis. Examination of the samples taken during September 1964 and 1965 included a critical study of the physico-chemical, microbiological and general biological characteristics. The findings suggest that soil development in the area is typical of that proceeding in other cryopedogenic regions in North America... These soils, further, are characterized as harbouring considerable population of bacteria, fungi and actinomycetes which, in general, tend to decrease abruptly (in a numberical sense) with depth. Soils are biologically active and are comparable to temperate soils in terms of their potential biological activity as determined by respiration intensity, mineralization of organic nitrogen and other enzymic activities... Microbial population in the areas consists mainly of cold-adapted native species similar in many respects to those forms prevalent in more temperate regions. Among the actinomycetes and fungi, the total number of genera encountered was low but, where present, these constituted a significant proportion of the total microbial population... A large number of quite different microbial isolates were found to be capable of growing under nitrogen-fixing conditions. Although they were mainly bacterial in type, some nitrogen-fixing species of fungi, yeasts and actinomycetes were noted. Counts of nitrogen-fixers ranged from several tens of thousands to several millions per gram of soil. The significance of these findings in terms of cryopedogenesis is discussed

Homogenization of nonlocal wire metamaterial via a renormalization approach

It is well known that defining a local refractive index for a metamaterial requires that the wavelength be large with respect to the scale of its microscopic structure (generally the period). However, the converse does not hold. There are simple structures, such as the infinite, perfectly conducting wire medium, which remain non-local for arbitrarily large wavelength-to-period ratios. In this work we extend these results to the more realistic and relevant case of finite wire media with finite conductivity. In the quasi-static regime the metamaterial is described by a non-local permittivity which is obtained analytically using a two-scale renormalization approach. Its accuracy is tested and confirmed numerically via full vector 3D finite element calculations. Moreover, finite wire media exhibit large absorption with small reflection, while their low fill factor allows considerable freedom to control other characteristics of the metamaterial such as its mechanical, thermal or chemical robustness.Comment: 8 pages on two columns, 7 figures, submitted to Phys. Rev.