Consensus using Asynchronous Failure Detectors

The FLP result shows that crash-tolerant consensus is impossible to solve in asynchronous systems, and several solutions have been proposed for crash-tolerant consensus under alternative (stronger) models. One popular approach is to augment the asynchronous system with appropriate failure detectors, which provide (potentially unreliable) information about process crashes in the system, to circumvent the FLP impossibility. In this paper, we demonstrate the exact mechanism by which (sufficiently powerful) asynchronous failure detectors enable solving crash-tolerant consensus. Our approach, which borrows arguments from the FLP impossibility proof and the famous result from CHT, which shows that $\Omega$ is a weakest failure detector to solve consensus, also yields a natural proof to $\Omega$ as a weakest asynchronous failure detector to solve consensus. The use of I/O automata theory in our approach enables us to model execution in a more detailed fashion than CHT and also addresses the latent assumptions and assertions in the original result in CHT

Onset Temperature of Slow Dynamics in Glass Forming Liquids

The behaviour of a model glass forming liquid is analyzed for a range of densities, with a focus on the temperature interval where the liquid begins to display non-Arrhenius temperature dependence of relaxation times. Analyzing the dynamics along with properties of local potential energy minima sampled by the liquid, a crossover or onset temperature $T_s$ is identified below which the liquid manifests {\it slow dynamics}, and a change in the character of typical local potential energy minima.Comment: 16 pages, 5 figures, to appear in PhysChemCom

SMARANDACHE NUMBER RELATED TRIANGLES

Given a triangle in Euclidean geometry it is well known that there exist an infinity of triangles each of which is similar to the given one. In Section I we make certain observations on Smarandache numbers