Abstract
The set of weak links connecting superconducting grains of ceramics forms a randomthree-dimensional Josephson net. The temperature and size dependences of the criticalcurrents in bismuth-based and yttrium-based high-temperature superconductingceramic samples consisting of randomly oriented grains have been studied in zeromagnetic field. It is shown that the critical current in samples having variouscross-sectional shapes can be presented as the product of temperature and sizedependent factors. The transport critical current is a homogeneous function ofthe cross-sectional shape dimensions. The size dependent factor is a universalfunction describing properties of the weak link Josephson net. The exponent of thisfunction is independent of the temperature, the type of superconducting material,the existence (or lack) of a Josephson net in the sample, and the method usedfor varying the sample cross-section. The transport critical current density andinduced magnetic field are homogeneous functions of coordinates. It is shownthat the critical current density has a power law dependence on the magneticfield.
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