A real number alpha is said to be b-normal if every m-long string of digits appears in the base-b expansion of alpha with limiting frequency b-m. We prove that alpha is b-normal if and only if it possesses no base-b ''hot spot''. In other words, alpha is b-normal if and only if there is no real number y such that smaller and smaller neighborhoods of y are visited by the successive shifts of the base-b expansion of alpha with larger and larger frequencies, relative to the lengths of these neighborhoods

Simulation of ductile fracture at the atomic scale reveals many aspects of the fracture process including specific mechanisms associated with void nucleation and growth as a precursor to fracture and the plastic deformation of the material surrounding the voids and cracks. Recently we have studied void coalescence in ductile metals using large-scale atomistic and continuum simulations. Here we review that work and present some related investigations. The atomistic simulations involve three-dimensional strain-controlled multi-million atom molecular dynamics simulations of copper. The correlated growth of two voids during the coalescence process leading to fracture is investigated, both in terms of its onset and the ensuing dynamical interactions. Void interactions are quantified through the rate of reduction of the distance between the voids, through the correlated directional growth of the voids, and through correlated shape evolution of the voids. The critical inter-void ligament distance marking the onset of coalescence is shown to be approximately one void radius based on the quantification measurements used, independent of the initial separation distance between the voids and the strain-rate of the expansion of the system. No pronounced shear flow is found in the coalescence process.

Rapidly growing electricity demand brings into question theability of traditional grids to expand correspondingly while providingreliable service. An alternative path is the wider application ofdistributed energy resource (DER) that apply combined heat and power(CHP). It can potentially shave peak loads and satiate its growing thirstfor electricity demand, improve overall energy efficiency, and lowercarbon and other pollutant emissions. This research investigates a methodof choosing economically optimal DER, expanding on prior studies at theBerkeley Lab using the DER design optimization program, the DistributedEnergy Resources Customer Adoption Model (DER-CAM). DER-CAM finds theoptimal combination of installed equipment from available DERtechnologies, given prevailing utility tariffs, site electrical andthermal loads, and a menu of available equipment. It provides a globaloptimization, albeit idealized, that shows how the site energy loads canbe served at minimum cost by selection and operation of on-sitegeneration, heat recovery, and cooling. Utility electricity and gastariffs are key factors determining the economic benefit of a CHPinstallation, however often be neglected. This paper describespreliminary analysis on CHP investment climate in the U.S. and Japan. DERtechnologies, energy prices, and incentive measures has beeninvestigated.

This article discusses low-coordinate iron dinitrogen complexes. Understanding the interaction of N₂ with iron is relevant to the iron catalyst used in the Haber process and to possible roles of the FeMoco active site of nitrogenase.