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Register a new userFlux creep in type-II superconductors: self-organized criticality approach
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We consider the current density distribution function of a flux creep regime in type-II superconductors by mapping the flux creep process to the dynamics of a model with a self-organized criticality. We use an extremal Robin Hood type model which evolves to Beens type critical state to treat magnetic flux penetration into a superconductor and derive an analog of the current-voltage characteristics in the flux creep region.
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Pinning and creep determine the current--voltage characteristic of a type II superconductor and thereby its potential for technological applications. The recent development of strong pinning theory provides us with a tool to assess a superconductors electric properties in a quantitative way. Motivated by the observation of typical excess-current characteristics and field-scaling of critical currents, here, we analyze current--voltage characteristics measured on 2H-NbSe$_2$ and $a$-MoGe type II superconductors within the setting provided by strong pinning theory. The experimentally observed shift and rounding of the voltage-onset is consistent with the predictions of strong pinning in the presence of thermal fluctuations. We find the underlying parameters determining pinning and creep and discuss their consistency.
Flux vortices in superconductors can be imaged using transmission electron microscopy because the electron beam is deflected by the magnetic flux associated with the vortices. This technique has a better spatial and temporal resolution than many other imaging techniques and is sensitive to the magnetic flux density within each vortex not simply the fields at the sample surface. Despite these advantages, only two groups have successfully employed the technique using specially adapted instruments. Here we demonstrate that vortices can be imaged with a modern, commercial transmission electron microscope operating at 300 kV equipped with a field emission gun, Lorentz lens and a liquid helium cooled sample holder. We introduce superconductivity for non-specialists and discuss techniques for simulating and optimising images of flux vortices. Sample preparation is discussed in detail as the requirement for samples with very large (>10um), flat areas so that the image is not dominated by diffraction contrast is the main difficulty with the technique. We have imaged vortices in superconducting Bi2Sr2CaCu2O8+d and use correlation functions to investigate the ordered arrangements they adopt as a function of applied magnetic field.
The shape of clouds has proven to be essential for classifying them. Our analysis of images from fair weather cumulus clouds reveals that, besides by turbulence they are driven by self-organized criticality (SOC). Our observations yield exponents that support the fact the clouds, when projected to two dimensions (2D), exhibit conformal symmetry compatible with $c=-2$ conformal field theory (CFT), in contrast to 2D turbulence which has $c=0$ CFT. By using a combination of the Navier-Stokes equation, diffusion equations and a coupled map lattice (CML) we successfully simulated cloud formation, and obtained the same exponents.
A review is given on the theory of vortex-glass phases in impure type-II superconductors in an external field. We begin with a brief discussion of the effects of thermal fluctuations on the spontaneously broken U(1) and translation symmetries, on the global phase diagram and on the critical behaviour. Introducing disorder we restrict ourselves to the experimentally most relevant case of weak uncorrelated randomness which is known to destroy the long-ranged translational order of the Abrikosov lattice in three dimensions. Elucidating possible residual glassy ordered phases, we distinguish betwee positional and phase-coherent vortex glasses. The discussion of elastic vortex glasses, in two and three dimensions occupy the main part of our review. In particular, in three dimensions there exists an elastic vortex-glass phase which still shows quasi-long-range translational order: the `Bragg glass. It is shown that this phase is stable with respect to the formation of dislocations for intermediate fields. Preliminary results suggest that the Bragg-glass phase may not show phase-coherent vortex-glass order. The latter is expected to occur in systems with weak disorder only in higher dimensions. We further demonstrate that the linear resistivity vanishes in the vortex-glass phase. The vortex-glass transition is studied in detail for a superconducting film in a parallel field. Finally, we review some recent developments concerning driven vortex-line lattices moving in a random environment.
Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For the last two decades, considerable experimental evidence accumulated that the mammalian cortex with its diversity in cell types and connections might exhibit SOC. Here we review experimental findings of isolated, layered cortex preparations to self-organize towards four dynamical motifs identified in the cortex in vivo: up-states, oscillations, neuronal avalanches, and coherence potentials. During up-states, the synchronization observed for nested theta/gamma-oscillations embeds scale-invariant neuronal avalanches that exhibit robust power law scaling in size with a slope of -3/2 and a critical branching parameter of 1. This dynamical coordination, tracked in the local field potential (nLFP) and pyramidal neuron activity using 2-photon imaging, emerges autonomously in superficial layers of organotypic cortex cultures and acute cortex slices, is homeostatically regulated, displays separation of time scales, and reveals unique size vs. quiet time dependencies. A threshold operation identifies coherence potentials; avalanches that in addition maintain the precise time course of propagated synchrony. Avalanches emerge under conditions of external driving. Control parameters are established by the balance of excitation and inhibition (E/I) and the neuromodulator dopamine. This rich dynamical repertoire is not observed in dissociated cortex cultures, which lack cortical layers and exhibit dynamics similar to a 1st-order phase transition. The precise interactions between up-states, nested oscillations, avalanches, and coherence potentials in superficial cortical layers provide compelling evidence for SOC in the brain.
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