Scaling theory of fractal complex networks.

We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes with which we cover the network when determining its box dimension. This approach-grounded in both scaling theory of phase transitions and renormalization group theory-leads to the consistent scaling theory of fractal complex networks, which complements the collection of scaling exponents with several new ones and reveals various relationships between them. We propose the introduction of two classes of exponents: microscopic and macroscopic, characterizing the local structure of fractal complex networks and their global properties, respectively.

Tribological Characterization of Micro Ball Bearings with and without Solid-State Lubrication.

The tribological characteristics of a below 1 mm micro ball bearing comprising steel disc and cages coated with thin copper and silver films were investigated. Electroplating and laser cutting were used to manufacture used elements. Friction was measured using a linear stage and an adapted version of a friction-loop method.

Towards the High Phase Purity of Nanostructured Alluaudite-Type Glass-Ceramics Cathode Materials for Sodium Ion Batteries.

Alluaudite-type materials are systematically attracting more attention as prospective cathode materials for sodium ion batteries. In this paper, we strove to optimize various synthesis parameters of three alluaudite compositions (Na2Fe3(PO4)3-FFF, Na2VFe2(PO4)3-VFF, and Na2VFeMn(PO4)3-VFM) to obtain nanostructured alluaudite-type glass-ceramics with high phase purity. We systematically investigated the role of the chemical reactions, temperature and time of melting, cooling rate, and reducing factors on the quality of the final products.