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We study the limit distribution of eigenvalues of a Ruelle operator (which is also called the Thurston pushforward operator) for the dynamical system $z \mapsto z^2+c$ when $c<-2$ and tends to $-2$.

We report the data on magnetization losses and critical current of multifilament copper stabilized coated conductors. Eight centimeters long samples of copper stabilized YBa2Cu3O7-x (YBCO) coated conductors manufactured commercially were subdivided into superconducting filaments by near-IR laser micromachining. The width of the superconducting stripes was varied from 0.2 mm to 0.04 mm. Some of the samples were striated leaving superconducting bridges for current sharing between the filaments. The AC losses were measured at different sweep rates of the magnetic field up to 14 T/s. We will present the results for the hysteresis and coupling losses and discuss the means to reduce the coupling loss by changing the processing parameters of micromachining and by post-ablation treatment., Comment: In the first version of this preprint the value of copper resistivity used for calculating eddy current losses was ten times lower than the actual value. Please don't ask how that could have happened. Correspondingly, the conclusions described in the first column on page 4 were wrong and are now corrected

We have measured the magnetoresistance of stretched sheets of carbon nanotubes in temperatures ranging from 2 K to 300 K and in magnetic fields up to 9 T, oriented either perpendicular or parallel to the plane of the sheets. The samples have been partially aligned by post-fabrication stretching, such that the direction of stretching was either parallel or perpendicular to the direction of applied electric current. We have observed large differences between the magnetoresistance measured under the two field orientations, most pronounced at the lowest temperatures, highest fields, and for the laterally-aligned sample. Treatment of the sheets with nitric acid affects this anisotropy. We analyzed the results within the theoretical framework of weak and strong localization and concluded that the anisotropy bears the mark of a more unusual phenomenon, possibly magnetically-induced mechanical strain., Comment: 34 pages, 10 figures

We examine energy transport in an ensemble of closed quantum systems driven by stochastic perturbations. One can show that the probability and energy fluxes can be described in terms of quantum advection modes (QAM) associated with the off-diagonal elements of the density matrix. These QAM play the role of Landauer channels in a system with discrete energy spectrum and the eigenfunctions that cannot be described as plane waves. In order to determine the type of correlations that exist between the direction and magnitudes of each QAM and the average direction of energy and probability fluxes we have numerically solved the time-dependent Schr\"{o}dinger equation describing a single particle trapped in a parabolic potential well which is perturbed by stochastic 'ripples'. The ripples serve as a localized energy source and are offset to one side of the potential well. As the result a non-zero net energy flux flows from one part of the potential well to another across the symmetry center of the potential. We find that some modes exhibit positive correlation with the direction of the energy flow. Other modes, that carry a smaller energy per unit of the probability flux, anticorrelate with the energy flow and thus provide a backflow of the probability. The overall picture of energy transport that emerges from our results is very different from the conventional one based on a system with continuous energy spectrum., Comment: 12 pages, 6 figures and one table. To be published in Phys. Rev. E

We present the results of numerical analysis of normal zone propagation in a stack of $YBa_2Cu_3O_{7-x}$ coated conductors which imitates a pancake coil. Our main purpose is to determine whether the quench protection quality of such coils can be substantially improved by increased contact resistance between the superconducting film and the stabilizer. We show that with increased contact resistance the speed of normal zone propagation increases, the detection of a normal zone inside the coil becomes possible earlier, when the peak temperature inside the normal zone is lower, and stability margins shrink. Thus, increasing contact resistance may become a viable option for improving the prospects of coated conductors for high $T_c$ magnets applications., Comment: 9 pages, 4 figures

This paper reports the results of an experimental investigation of the performance of two types of magnetic screens assembled from YBa2Cu3O7-d (YBCO) coated conductors. Since effective screening of the axial DC magnetic field requires the unimpeded flow of an azimuthal persistent current, we demonstrate a configuration of a screening shell made out of standard YBCO coated conductor capable to accomplish that. The screen allows the persistent current to flow in the predominantly azimuthal direction at a temperature of 77 K. The persistent screen, incorporating a single layer of superconducting film, can attenuate an external magnetic field of up to 5 mT by more than an order of magnitude. For comparison purposes, another type of screen which incorporates low critical temperature quasi-persistent joints was also built. The shielding technique we describe here appears to be especially promising for the realization of large scale high-Tc superconducting screens., Comment: 8 pages, 3 figures

We present the results of numerical analysis of a model of normal zone propagation in coated conductors. The main emphasis is on the effects of increased contact resistance between the superconducting film and the stabilizer on the speed of normal zone propagation, the maximum temperature rise inside the normal zone, and the stability margins. We show that with increasing contact resistance the speed of normal zone propagation increases, the maximum temperature inside the normal zone decreases, and stability margins shrink. This may have an overall beneficial effect on quench protection quality of coated conductors. We also briefly discuss the propagation of solitons and development of the temperature modulation along the wire., Comment: To be published in Superconductor Science and Technology. This preprint contains one animated figure (Fig. 6(a)). when asked whether you want to play the content, click "Play". Acrobat Reader (Windows and Mac, but not Linux) will play embedded flash movies. In the printed copy Fig. 6(b) will show the temperature profile at gamma t=150

We discuss the emergence of a spontaneous temperature and critical current spatial modulation in current-carrying high temperature superconducting wire. The modulation of the critical current along the wire on a scale of 3 - 10 mm forces a fraction of the transport current to crisscross the resistive interface between the superconducting film and normal metal stabilizer attached to it. This generates additional heat that allows such a structure to be self sustainable. Stability and the conditions for experimental observation of this phenomenon are also discussed., Comment: To be published in Phys. Rev. E (in section Chaos and Pattern Formation)

We report the magnetization losses in an experimental multifilament coated conductor. A 4 mm wide and 10 cm long YBCO coated conductor was subdivided into eight 0.5 mm wide filaments by laser ablation and subjected to post-ablation treatment. As the result, the hysteresis loss was reduced, as expected, in proportion to the width of the filaments. However, the coupling loss was reduced dramatically, and became practically negligible, in the range of a sweep rate up to 20 T/s. This represents a drastic improvement on previous multifilament conductors in which often the coupling losses became equal to the hysteresis loss at a sweep rate as low as 3-4 T/s. These results demonstrate that there is an effective and practical way to suppress coupling losses in coated multifilament conductors., Comment: This paper is based on a talk given at 2006 Applied Superconductivity Conference in Seattle, WA (August 27-September 1, 2006). To be published in IEEE Trans. Appl. Superconductivity

We report an experimental approach to making multifilament coated conductors with low losses in applied time-varying magnetic field. Previously, the multifilament conductors obtained for that purpose by laser ablation suffered from high coupling losses. Here we report how this problem can be solved. When the substrate metal in the grooves segregating the filaments is exposed to oxygen, it forms high resistivity oxides that electrically insulate the stripes from each other and from the substrate. As the result, the coupling loss has become negligible over the entire range of tested parameters (magnetic field amplitudes B and frequencies f) available to us., Comment: Submitted to Appl. Phys. Lett. 10 pages, 3 figures

We studied the magnetization losses of four different types of filamentary YBCO coated conductors. A 10 mm wide YBCO coated conductor was subdivided into 20 filaments by laser cutting. The separation of coupling loss from the total is possible because the energy loss per cycle in samples with electrically insulated filaments has a very small frequency dependence. We measured the frequency dependence of the total losses in the frequency range between 0.1 Hz and 500 Hz. The coupling loss was obtained from the total by subtracting the hysteresis loss. The latter was measured at low frequencies since only hysteresis loss is non-negligible at frequencies below 1 Hz. The transverse resistivity was determined from the coupling losses; it was assumed that the sample length is equal to half of the twist pitch. The values of transverse resistivity deduced from the loss data were compared with those obtained by the four-point measurements with current flowing perpendicular to the filaments. Preliminary results indicate that the current method of laser ablation creates electrical contacts between the superconducting filaments and the substrate. This was also confirmed by the Hall probe mapping of the magnetic field in the vicinity of the tape. The measured transverse resistivity was close to the resistivity of the substrate (Hastelloy)., Comment: This paper was presented at 2005 EUCAS Conference

We report the results of a magnetization losses study in experimental multifilament, multiply connected coated superconductors exposed to time-varying magnetic field. In these samples, the superconducting layer is divided into parallel stripes segregated by non-superconducting grooves. In order to facilitate the current sharing between the stripes and thus increase the reliability of the striated conductors, a sparse network of superconducting bridges is superimposed on the striated film. We find that the presence of the bridges does not substantially increase the magnetization losses, both hysteresis and coupling, as long as the number of bridges per length of the sample is not large. These results indicate that it is possible to find a reasonable compromise between the competing requirements of connectivity and loss reduction in an ac-tolerant version of the high temperature coated conductors specifically designed for ac power applications., Comment: 19 pages, 12 figures to be published in J. Appl. Phys

The implementation of the 2nd generation high-Tc superconductors in power applications, such as electrical transformers, motors and generators requires superconducting wires that are superior to copper Litz wires at cryogenic temperatures in terms of losses in time-varying magnetic field, as well as in engineering current density. Another problem is to find a way to make practical coils and armatures out of flat tape-like conductors with low bending strain tolerance. We discuss several novel approaches to the construction of coils and armatures based specifically on the properties of coated conductors manufactured today.

The possibility of a substantial reduction of weight and size of electrical generators is the main incentive behind the effort to develop superconducting armature windings based on coated conductors in the form of wide tapes with large aspect ratio. The main obstacle to the application of coated superconductors in stator windings is the large losses incurred due to the ac magnetic field produced by the rotor's dc coils of the field windings. In the range of frequencies typical for aircraft generators, the hysteretic losses in wide tapes are unacceptably high. They can be reduced by dividing the superconducting layer into multiple filaments separated by non-superconducting barriers. However, the lack of current sharing between the filaments makes the conductor vulnerable to the localized defects, so that a single blockage can impede the flow of transport current through the whole length of a given filament. We present estimates of reliability as well as the magnetization losses in multiply connected superconductors. In this type of superconducting tape, a sparse network of superconducting bridges, which allows for current sharing, connects the filaments. The trade-off between the different types of losses and the connectivity requirement imposes restrictions on the number of filaments and properties of the network of bridges., Comment: 4 pages, 3 figures

We report the results of a study of the magnetization losses in experimental multifilament, as well as control (uniform), coated superconductors exposed to time-varying magnetic field of various frequencies. Both the hysteresis loss, proportional to the sweep rate of the applied magnetic field, and the coupling loss, proportional to the square of the sweep rate, have been observed. A scaling is found that allows us to quantify each of these contributions and extrapolate the results of the experiment beyond the envelope of accessible field amplitude and frequency. The combined loss in the multifilament conductor is reduced by about 90% in comparison with the uniform conductor at full field penetration at sweep rate as high as 3T/s.

We report magnetoresistivity measurements on strongly underdoped YBa_2Cu_3O_x (x=6.25, 6.36) single crystals in applied magnetic fields H || c-axis. We identify two different contributions to both in-plane and out-of-plane magnetoresistivities. The first contribution has the same sign as the temperature coefficient of the resistivity \partial ln(\rho_i)/\partial T (i={c,ab}). This contribution reflects the incoherent nature of the out-of-plane transport. The second contribution is positive, quadratic in field, with an onset temperature that correlates to the antiferromagnetic ordering., Comment: 4 pages, 3 figures

We report magnetoconductivity measurements on YBa_2Cu_3O_x (x=6.25 and 6.36) single crystals. Our main result is that both the in-plane Delta_sigma_ab and out-of-plane Delta_sigma_c magnetoconductivities exhibit the field dependence characteristic of "two-dimensional" quantum interference in applied magnetic fields H parallel to the c-axis. Namely, Delta_sigma_c,ab are proportional to ln(H/H_0), with Delta_sigma_c/sigma_c substantially greater than Delta_sigma_ab/sigma_ab. We interpret this result as evidence of interlayer incoherence in these crystals, so that the phase-coherent trajectories are mostly confined to one bilayer., Comment: 9 pages, 5 figures

We present an overview of the capabilities of a new software developed for use with multiterminal measurements. The program supports two configurations of current and voltage contacts known in the parlance of the field as "flux transformer" and " I$\|$c" geometries. The problem of instability of the results obtained by the multiterminal method and the ways to overcome it is also discussed., Comment: 2 pages; more information on http://www.virtinst.com

Transport as well as magnetic relaxation properties of the mixed state were studied on strongly underdoped Y_1-xPr_xBa_2Cu_3O_7-d crystals. We observed two correlated phenomena - a coupling transition and a transition to quantum creep. The distribution of transport current below the coupling transition is highly nonuniform, which facilitates quantum creep. We speculate that in the mixed state below the coupling transition, where dissipation is nonohmic, the current distribution may be unstable with respect to self-channeling resulting in the formation of very thin current-carrying layers., Comment: 11 pages, 9 figures, Submitted to Phys. Rev. B

The large ($10^2 - 10^5$) and strongly temperature dependent resistive anisotropy $\eta = (\sigma_{ab}/\sigma_c)^{1/2}$ of cuprates perhaps holds the key to understanding their normal state in-plane $\sigma_{ab}$ and out-of-plane $\sigma_{c}$ conductivities. It can be shown that $\eta$ is determined by the ratio of the phase coherence lengths $\ell_i$ in the respective directions: $\sigma_{ab}/\sigma_c = \ell_{ab}^2/\ell_{c}^2$. In layered crystals in which the out-of-plane transport is incoherent, $\ell_{c}$ is fixed, equal to the interlayer spacing. As a result, the T-dependence of $\eta$ is determined by that of $\ell_{ab}$, and vice versa, the in-plane phase coherence length can be obtained directly by measuring the resistive anisotropy. We present data for hole-doped $YBa_2Cu_3O_y$ ($6.3 < y < 6.9$) and $Y_{1-x}Pr_xBa_2Cu_3O_{7-\delta }$ ($0 < x \leq 0.55$) and show that $\sigma_{ab}$ of crystals with different doping levels can be well described by a two parameter universal function of the in-plane phase coherence length. In the electron-doped $Nd_{2-x}Ce_{x}CuO_{4-y}$, the dependence $\sigma_{ab}(\eta)$ indicates a crossover from incoherent to coherent transport in the c-direction., Comment: 5 pages, 2 figures

We present a novel approach to the analysis of the normal state in-plane $\sigma_{ab}$ and out-of-plane $\sigma_{c}$ conductivities of anisotropic layered crystals such as oxygen deficient $YBa_{2}Cu_{3}O_{x}$. It can be shown that the resistive anisotropy is determined by the ratio of the phase coherence lengths in the respective directions; i.e., $\sigma_{ab}/\sigma_c=\ell_{ab}^2/\ell_c^2$. From the idea that at all doping levels and temperatures $T$ the out-of-plane transport in these crystals is incoherent, follows that $\ell_c$ is T-independent, equal to the spacing $\ell_0$ between the neighboring bilayers. Thus, the T-dependence of $\ell_{ab}$ is given by the measured anisotropy, and $\sigma_{ab}(\ell_{ab})$ dependence is obtained by plotting $\sigma_{ab}$ vs $\ell=(\sigma_{ab}/\sigma_c)^{1/2}\ell_0$. The analysis of several single crystals of $YBa_{2}Cu_{3}O_{x}$ ($6.35

We show that the resistive anisotropy of an anisotropic medium is determined by the ratio of the phase coherence lengths. In layered crystals in which the interlayer transport is incoherent, the out-of-plane phase coherence length is fixed and temperature independent. This leads to a temperature dependent resistive anisotropy and to the coexistence of metallic in-plane and non-metallic out-of-plane conductivities. Our approach provides a description of the c-axis conductivity in the highly nonclassical regime, characteristic of layered cuprates., Comment: 5 pages and 1 figure

We report transport and magnetic relaxation measurements in the mixed state of strongly underdoped Y_{1-x}Pr_{x}Ba_{2}Cu_{3}O_{7} crystals. A transition from thermally activated flux creep to temperature independent quantum flux creep is observed in both transport and magnetic relaxation at temperatures T * 5 K. Flux transformer measurements indicate that the crossover to quantum creep is preceded by a coupling transition. Based on these observations we argue that below the coupling transition the current is confined within a very narrow layer beneath the current contacts., Comment: 5 Pages, 3 figures