Under proper hypotheses, we rigorously derive the Plateau angle conditions at triple junctions of diffused interfaces in three dimensions, starting from the vector-valued Allen-Cahn equation with a triple-well potential. Our derivation is based on an application of the divergence theorem using the divergence-free form of the equation via an associated stress tensor.

No abstract

No abstract

Azure SQL Database and the upcoming release of SQL Server introduce a novel database recovery mechanism that combines traditional ARIES recovery with multi-version concurrency control to achieve database recovery in constant time, regardless of the size of user transactions. Additionally, our algorithm enables continuous transaction log truncation, even in the presence of long running transactions, thereby allowing large data modifications using only a small, constant amount of log space. These capabilities are particularly important for any Cloud database service given a) the constantly increasing database sizes, b) the frequent failures of commodity hardware, c) the strict availability requirements of modern, global applications and d) the fact that software upgrades and other maintenance tasks are managed by the Cloud platform, introducing unexpected failures for the users. This paper describes the design of our recovery algorithm and demonstrates how it allowed us to improve the availability of Azure SQL Database by guaranteeing consistent recovery times of under 3 minutes for 99.999% of recovery cases in production.

No abstract