Anomalous statistical properties of the critical current distribution in superconductor containing fractal clusters of a normal phase

TL;DR

This paper investigates how fractal clusters in superconductors affect the distribution of critical currents, revealing conditions for infinite variance and proposing methods to optimize current-carrying capacity.

Contribution

It introduces a new analysis of critical current distribution in fractal-cluster superconductors and proposes a technique to prevent divergence, enhancing superconductor performance.

Findings

Variance and expectation can diverge for certain fractal dimensions.

A truncated distribution technique can avoid divergence.

Optimizing cluster area distribution improves superconductor capacity.

Abstract

Statistical properties of the critical current distribution in superconductor with fractal clusters of a normal phase are considered. It is found that there is the range of fractal dimensions in which the variance and expectation for this distribution increases infinitely. Simple technique of avoiding such a divergence by the use of truncated distributions is proposed. It is suggested that the most current-carrying capability of a superconductor can be achieved by modifying the cluster area distribution in such a way that the regime of giant variance of critical currents will be realized.