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The reaction times of individuals over consecutive visual stimuli have been studied using spectral analysis and a failure machinery approach. The used tools include the fast Fourier transform and a spectral entropy analysis. The results indicate that the reaction times produced by the independently responding individuals to visual stimuli appear to be correlated. The spectral analysis and the entropy of the spectrum yield that there are features of similarity in the response times of each participant and among them. Furthermore, the analysis of the mistakes made by the participants during the reaction time experiments concluded that they follow a behavior which is consistent with the MTBF (Mean Time Between Failures) model, widely used in industry for the predictive diagnosis of electrical machines and equipment., Comment: 5 figures, 11 pages

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., Comment: arXiv admin note: text overlap with arXiv:1606.03862

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.

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., Comment: 13 pages; 9 figures

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., Comment: Final version

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., Comment: Revised version. Accepted for publication in Israel Journal of Mathematics

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., Comment: 39 pages, 19 figures; substantial revision

Hazrat gave a K-theoretic invariant for Leavitt path algebras as graded algebras. Hazrat conjectured that this invariant classifies Leavitt path algebras up to graded isomorphism, and proved the conjecture in some cases. In this paper, we prove that a weak version of the conjecture holds for all finite essential graphs., Comment: Final version, to appear in Journal of K-Theory. arXiv admin note: text overlap with arXiv:0802.1198 by other authors

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., Comment: 34 pages, 18 figures. All figures are modified; figures 3, 7 and 10 are new. Text thoroughly revised and extended

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., Comment: Final version. To appear in Journal of Algebra

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., Comment: 33 pages, 12 figures

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., Comment: 22 pages, 15 figures; contents extended (sections 3.2 and 4); one new figure (figure 5) and two figures replaced (figures 3 and 8); typos corrected; title changed

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.

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., Comment: Small changes and improvements of previous version

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 $\epsilon_l$ and compared it to existing predictions based on the vortex structure., Comment: 11 figures in 13 files; minor changes after printing proofs

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., Comment: Final version. To appear in J. reine Angew. Math

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph., Comment: Revised version, with added examples. To appear in Proc. Amer. Math. Soc

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., Comment: 21 pages, 12 figures in 15 extra pages/files. Submitted to Physical Review B

We characterize Leavitt path algebras which are exchange rings in terms of intrinsic properties of the graph and show that the values of the stable rank for these algebras are 1, 2 or $\infty$. Concrete criteria in terms of properties of the underlying graph are given for each case.

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., Comment: Final version, to appear in "Algebra and Representation Theory"

In this note, we study the notion of purely infinite simple ring in the case of non-unital rings, and we obtain an analog to Zhang's Dichotomy for $\sigma$-unital purely infinite simple C*-algebras in the purely algebraic context., Comment: Revised version. This paper was accepted for publication in Communications in Algebra

We characterize, in terms of elementary properties, the abelian monoids which are direct limits of finite direct sums of monoids of the form $(Z/nZ)\sqcup\{0\}$ (where 0 is a new zero element), for positive integers $n$. The key properties are the Riesz refinement property and the requirement that each element $x$ has finite order, that is, $(n+1)x=x$ for some positive integer $n$. Such monoids are necessarily semilattices of abelian groups, and part of our approach yields a characterization of the Riesz refinement property among semilattices of abelian groups. Further, we describe the monoids in question as certain submonoids of direct products $\Lambda\times G$ for semilattices $\Lambda$ and torsion abelian groups $G$. When applied to the monoids $V(A)$ appearing in the non-stable K-theory of C*-algebras, our results yield characterizations of the monoids $V(A)$ for C* inductive limits $A$ of sequences of finite direct products of matrix algebras over Cuntz algebras $O_n$. In particular, this completely solves the problem of determining the range of the invariant in the unital case of R{\o}rdam's classification of inductive limits of the above type.

Given an action of a monoid $T$ on a ring $A$ by ring endomorphisms, and an Ore subset $S$ of $T$, a general construction of a fractional skew monoid ring $S^{\rm op} * A * T$ is given, extending the usual constructions of skew group rings and of skew semigroup rings. In case $S$ is a subsemigroup of a group $G$ such that $G=S^{-1}S$, we obtain a $G$-graded ring $S^{\rm op} * A * S$ with the property that, for each $s\in S$, the $s$-component contains a left invertible element and the $s^{-1}$-component contains a right invertible element. In the most basic case, where $G$ is the additive group of integers and $S=T$ is the submonoid of nonnegative integers, the construction is fully determined by a single ring endomorphism $\alpha$ of $A$. If $\alpha $ is an isomorphism onto a proper corner $pAp$, we obtain an analogue of the usual skew Laurent polynomial ring, denoted by $A[t_+,t_-;\alpha]$. Examples of this construction are given, and it is proven that several classes of known algebras, including the Leavitt algebras of type $(1,n)$, can be presented in the form $A[t_+,t_-;\alpha]$. Finally, mild and reasonably natural conditions are obtained under which $S^{\rm op} * A * S$ is a purely infinite simple ring.

The case of a hard type II superconductor in the form of strip with elliptic cross-section when placed in transverse magnetic field is studied. We approach the problem in two steps, both based on the critical-state model. First we calculate numerically the penetrated current profiles that ensure complete shielding in the interior, without assuming an a priori form for the profiles. In the second step we introduce an analytical approximation that asumes that the current profiles are ellipses. Expressions linking the sample magnetization to the applied field are derived covering the whole range of applied fields. The theoretical predictions are tested by the comparison with experimental data for the imaginary part of AC susceptibility., Comment: 12 pages; 3 figures

We extend the notion of a purely infinite simple C*-algebra to the context of unital rings, and we study its basic properties, specially those related to K-Theory. For instance, if $R$ is a purely infinite simple ring, then $K_0(R)^+= K_0(R)$, the monoid of isomorphism classes of finitely generated projective $R$-modules is isomorphic to the monoid obtained from $K_0(R)$ by adjoining a new zero element, and $K_1(R)$ is the abelianization of the group of units of $R$. We develop techniques of construction, obtaining new examples in this class in the case of von Neumann regular rings, and we compute the Grothendieck groups of these examples. In particular, we prove that every countable abelian group is isomorphic to $K_0$ of some purely infinite simple regular ring. Finally, some known examples are analyzed within this framework.