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E. Pardo

Publications and source records attributed to E. Pardo.

At least 19 recordsLinked to original sources
arXiv2019

Refinement monoids and adaptable separated graphs

We define a subclass of separated graphs, the class of adaptable separated graphs, and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and we explicitly determine their associated I-systems. We also show that any finitely generated conical refinement monoid can be represented as the monoid of an adaptable separated graph. These results provide the first step toward an affirmative answer to the Realization Problem for von Neumann regular rings, in the finitely generated case.

math.RA↗
arXiv2018

Demagnetization of cubic Gd-Ba-Cu-O bulk superconductor by cross-fields: measurements and 3D modelling

Superconducting bulks, acting as high-field permanent magnets, are promising for many applications. An important effect in bulk permanent magnets is crossed-field demagnetization, which can reduce the magnetic field in superconductors due to relatively small transverse fields. Crossed-field demagnetization has not been studied in sample shapes such as rectangular prisms or cubes. This contribution presents a study based on both 3D numerical modelling and experiments. We study a cubic Gd-Ba-Cu-O bulk superconductor sample of size 6 mm magnetized by field cooling in an external field of around 1.3 T, which is later submitted to crossed-field magnetic fields of up to 164 mT. Modelling results agree with experiments, except at transverse fields 50\% or above of the initial trapped field. The current paths present a strong 3D nature. For instance, at the mid-plane perpendicular to the initial magnetizing field, the current density in this direction changes smoothly from the critical magnitude, ${J_c}$, at the lateral sides to zero at a certain penetration depth. This indicates a rotation of the current density with magnitude ${J_c}$, and hence force free effects like flux cutting are expected to play a significant role.

cond-mat.supr-con↗
arXiv2017

3D Modeling of the Magnetization of Superconducting Rectangular-Based Bulks and Tape Stacks

In recent years, numerical models have become popular and powerful tools to investigate the electromagnetic behavior of superconductors. One domain where this advances are most necessary is the 3D modeling of the electromagnetic behavior of superconductors. For this purpose, a benchmark problem consisting of superconducting cube subjected to an AC magnetic field perpendicular to one of its faces has been recently defined and successfully solved. In this work, a situation more relevant for applications is investigated: a superconducting parallelepiped bulk with the magnetic field parallel to two of its faces and making an angle with the other one without and with a further constraint on the possible directions of the current. The latter constraint can be used to model the magnetization of a stack of high-temperature superconductor tapes, which are electrically insulated in one direction. For the present study three different numerical approaches are used: the Minimum Electro-Magnetic Entropy Production (MEMEP) method, the $H$-formulation of Maxwell's equations and the Volume Integral Method (VIM) for 3D eddy currents computation. The results in terms of current density profiles and energy dissipation are compared, and the differences in the two situations of unconstrained and constrained current flow are pointed out. In addition, various technical issues related to the 3D modeling of superconductors are discussed and information about the computational effort required by each model is provided. This works constitutes a concrete result of the collaborative effort taking place within the HTS numerical modeling community and will hopefully serve as a stepping stone for future joint investigations.

cond-mat.supr-con↗
arXiv2017

Representing finitely generated refinement monoids as graph monoids

Graph monoids arise naturally in the study of non-stable K-theory of graph C*-algebras and Leavitt path algebras. They play also an important role in the current approaches to the realization problem for von Neumann regular rings. In this paper, we characterize when a finitely generated conical refinement monoid can be represented as a graph monoid. The characterization is expressed in terms of the behavior of the structural maps of the associated $I$-system at the free primes of the monoid.

math.RA↗
arXiv2015

Primely generated refinement monoids

We extend both Dobbertin's characterization of primely generated regular refinement monoids and Pierce's characterization of primitive monoids to general primely generated refinement monoids.

math.RA↗
arXiv2014

Ripple field losses in DC biased superconductors: simulations and comparison with measurements

For example in some supercondcuting generators, motors and power transmission cables the superconductor experiences a changing magnetic field in a DC background. Simulating the losses caused by this AC ripple field is an important task from the application design point of view. In this work, we compare two formulations, the $H$-formulation and the minimum magnetic energy variation (the MMEV-formulation), based on the eddy current model (ECM) and the critical state model (CSM), respectively, in simulating ripple field losses in a DC biased coated conductor tape. Furthermore, we compare our simulation results with measurements. We investigate the frequency-dependence of the hysteresis loss predictions of the power law based ECM and verify by a measurement, that in DC use, ECM clearly over-estimates the homogenization of the current density profile in the coated conductor tape: the relaxation of the local current density is not nearly as prominent in the measurement as it is in the simulation. Hence, we suggest that the power law resistivity, used as the \emph{local} relation between the electric field intensity ${\bf E}$ and current density ${\bf J}$ in ECM, is not an intrinsic property of high-temperature superconductors. The difference between the models manifests itself as discrepancies in ripple field loss simulations in very low AC fields with significant DC fields or currents involved. The results also show, however, that for many practical situations, CSM and ECM are both eligible models for ripple field loss simulations.

cond-mat.supr-con↗
arXiv2011

AC loss in ReBCO pancake coils and stacks of them: modelling and measurement

Many applications of ReBCO coated conductors contain stacks of pancake coils. In order to reduce their high AC loss, it is necessary to understand the loss mechanisms. In this article, we measure and simulate the AC loss and the critical current, I_c, in stacks of pancake coils ("pancakes"). We construct stacks of up to 4 pancakes and we measure them by electrical means. We also obtain the anisotropic field dependence of J_c from I_c measurements of the tape. This J_c is the only input to the simulations, together with the coil dimensions. After validating our computations with the measurements, we simulate stacks of many pancakes, up to 32. We found that the AC loss in a stack of (four) pancakes is very high, two orders of magnitude larger than for a single tape. A double pancake behaves as a single one with double width but a stack of more pancakes is very different. Finally, we found that a 2-strand Roebel cable reduces the AC loss in a stack of pancakes but not in a single pancake. In conclusion, the AC loss in stacks of pancakes is too high. However, our simulations are useful to predict the AC loss and optimise the coil design, reducing the AC loss.

cond-mat.supr-con↗
arXiv2011

Flow invariants in the classification of Leavitt path algebras

We analyze in the context of Leavitt path algebras some graph operations introduced in the context of symbolic dynamics by Williams, Parry and Sullivan, and Franks. We show that these operations induce Morita equivalence of the corresponding Leavitt path algebras. As a consequence we obtain our two main results: the first gives sufficient conditions for which the Leavitt path algebras in a certain class are Morita equivalent, while the second gives sufficient conditions which yield isomorphisms. We discuss a possible approach to establishing whether or not these conditions are also in fact necessary. In the final section we present many additional operations on graphs which preserve Morita equivalence (resp., isomorphism) of the corresponding Leavitt path algebras.

math.RA↗
arXiv2008

Theoretical and experimental study of AC loss in HTS single pancake coils

The electromagnetic properties of a pancake coil in AC regime as a function of the number of turns is studied theoretically and experimentally. Specifically, the AC loss, the coil critical current and the voltage signal are discussed. The coils are made of Bi2Sr2Ca2Cu3O10/Ag (BiSCCO) tape, although the main qualitative results are also applicable to other kinds of superconducting tapes, such as coated conductors. The AC loss and the voltage signal are electrically measured using different pick up coils with the help of a transformer. One of them avoids dealing with the huge coil inductance. Besides, the critical current of the coils is experimentally determined by conventional DC measurements. Furthermore, the critical current, the AC loss and the voltage signal are simulated, showing a good agreement with the experiments. For all simulations, the field dependent critical current density inferred from DC measurements on a short tape sample is taken into account.

cond-mat.supr-con↗
arXiv2008

Magnetic flux penetration and AC loss in a composite superconducting wire with ferromagnetic parts

The current distribution and the AC loss in a composite superconducting tape containing a layer from magnetic material is calculated and compared with experiments, showing a very good agreement. The situations of an alternating uniform applied field or a transport current are studied. The newly developed numerical model is an approximation to the critical state model, adapted for the applicability to commercial finite elements codes that solve the vector potential. Substantial feature of this procedure is that it can be carried out in the case when the critical current density in superconductor depends on the magnetic field and the magnetic layer material is non- linear. Additionally, the hysteresis loss in the magnetic material is estimated, based on its measured magnetization loops. Measurements on Bi-2223 multifilamentary tapes covered on edges by nickel confirmed our predictions, showing a substantial ac loss reduction in both the investigated regimes.

cond-mat.supr-con↗
arXiv2008

Isomorphisms between Leavitt algebras and their matrix rings

Let $K$ be any field, let $L_n$ denote the Leavitt algebra of type $(1,n-1)$ having coefficients in $K$, and let ${\rm M}_d(L_n)$ denote the ring of $d \times d$ matrices over $L_n$. In our main result, we show that ${\rm M}_d(L_n) \cong L_n$ if and only if $d$ and $n-1$ are coprime. We use this isomorphism to answer a question posed in \cite{PS} regarding isomorphisms between various C*-algebras. Furthermore, our result demonstrates that data about the $K_0$ structure is sufficient to distinguish up to isomorphism the algebras in an important class of purely infinite simple $K$-algebras.

math.RA↗
arXiv2008

The classification question for Leavitt path algebras

We prove an algebraic version of the Gauge-Invariant Uniqueness Theorem, a result which gives information about the injectivity of certain homomorphisms between ${\mathbb Z}$-graded algebras. As our main application of this theorem, we obtain isomorphisms between the Leavitt path algebras of specified graphs. From these isomorphisms we are able to achieve two ends. First, we show that the $K_0$ groups of various sets of purely infinite simple Leavitt path algebras, together with the position of the identity element in $K_0$, classifies the algebras in these sets up to isomorphism. Second, we show that the isomorphism between matrix rings over the classical Leavitt algebras, established previously using number-theoretic methods, can be reobtained via appropriate isomorphisms between Leavitt path algebras.

math.RA↗
arXiv2007

Prime spectrum and primitive Leavitt path algebras

In this paper a bijection between the set of prime ideals of a Leavitt path algebra $L_K(E)$ and a certain set which involves maximal tails in $E$ and the prime spectrum of $K[x,x^{-1}]$ is established. Necessary and sufficient conditions on the graph $E$ so that the Leavitt path algebra $L_K(E)$ is primitive are also found.

math.RA↗
arXiv2007

Vortex deformation and breaking in superconductors: A microscopic description

Vortex breaking has been traditionally studied for nonuniform critical current densities, although it may also appear due to nonuniform pinning force distributions. In this article we study the case of a high-pinning/low-pinning/high-pinning layered structure. We have developed an elastic model for describing the deformation of a vortex in these systems in the presence of a uniform transport current density $J$ for any arbitrary orientation of the transport current and the magnetic field. If $J$ is above a certain critical value, $J_c$, the vortex breaks and a finite effective resistance appears. Our model can be applied to some experimental configurations where vortex breaking naturally exists. This is the case for YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) low angle grain boundaries and films on vicinal substrates, where the breaking is experienced by Abrikosov-Josephson vortices (AJV) and Josephson string vortices (SV), respectively. With our model, we have experimentally extracted some intrinsic parameters of the AJV and SV, such as the line tension $ε_l$ and compared it to existing predictions based on the vortex structure.

cond-mat.supr-con↗
arXiv2007

Stable rank of Leavitt path algebras

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

math.RA↗
arXiv2006

Nonstable $K$-theory for graph algebras

We compute the monoid $V(L_K(E))$ of isomorphism classes of finitely generated projective modules over certain graph algebras $L_K(E)$, and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of $L_K(E)$ and the lattice of order-ideals of $V(L_K(E))$. When $K$ is the field $\mathbb C$ of complex numbers, the algebra $L_{\mathbb C}(E)$ is a dense subalgebra of the graph $C^*$-algebra $C^*(E)$, and we show that the inclusion map induces an isomorphism between the corresponding monoids. As a consequence, the graph C*-algebra of any row-finite graph turns out to satisfy the stable weak cancellation property.

math.RA↗
arXiv2005

Current distribution and ac loss for a superconducting rectangular strip with in phase alternating current and applied field

The case of ac transport at in-phase alternating applied magnetic fields for a superconducting rectangular strip with finite thickness has been investigated. The applied magnetic field is considered perpendicular to the current flow. We present numerical calculations assuming the critical state model of the current distribution and ac loss for various values of aspect ratio, transport current and applied field amplitude. A rich phenomenology is obtained due to the metastable nature of the critical state. We perform a detailed comparison with the analytical limits and we discuss their applicability for the actual geometry of superconducting conductors. We also define a loss factor which allow a more detailed analysis of the ac behavior than the ac loss. Finally, we compare the calculations with experiments, showing a significant qualitative and quantitative agreement without any fitting parameter.

cond-mat.supr-con↗