The Density Matrix Renormalization Group and the Nuclear Shell Model

We summarize recent efforts to develop an angular-momentum-conserving variant of the Density Matrix Renormalization Group method into a practical truncation strategy for large-scale shell model calculations of atomic nuclei. Following a brief description of the key elements of the method, we report the results of test calculations for $^{48}$Cr and $^{56}$Ni. In both cases we consider nucleons limited to the 2p-1f shell and interacting via the KB3 interaction. Both calculations produce a high level of agreement with the exact shell-model results. Furthermore, and most importantly, the fraction of the complete space required to achieve this high level of agreement goes down rapidly as the size of the full space grows

Capture of manufacturing uncertainty in turbine blades through probabilistic techniques

Efficient designing of the turbine blades is critical to the performance of an aircraft engine. An area of significant research interest is the capture of manufacturing uncertainty in the shapes of these turbine blades. The available data used for estimation of this manufacturing uncertainty inevitably contains the effects of measurement error/noise. In the present work, we propose the application of Principal Component Analysis (PCA) for de-noising the measurement data and quantifying the underlying manufacturing uncertainty. Once the PCA is performed, a method for dimensionality reduction has been proposed which utilizes prior information available on the variance of measurement error for different measurement types. Numerical studies indicate that approximately 82% of the variation in the measurements from their design values is accounted for by the manufacturing uncertainty, while the remaining 18% variation is filtered out as measurement error

Density Matrix Renormalization Group study of 48^{48}Cr and 56^{56}Ni

We discuss the development of an angular-momentum-conserving variant of the Density Matrix Renormalization Group (DMRG) method for use in large-scale shell-model calculations of atomic nuclei and report a first application of the method to the ground state of $^{56}$Ni and improved results for $^{48}$Cr. In both cases, we see a high level of agreement with the exact results. A comparison of the two shows a dramatic reduction in the fraction of the space required to achieve accuracy as the size of the problem grows.Comment: 4 pages. Published in PRC Rapi

Aquacrops of Darbhanga District in north Bihar and their commercial significance

Darbhanga district in North Bihar is characterised by thick alluvial soil, moderately good rainfall, high humidity, ample sunshine and numerous water resources in the form of perennial rivers, tributaries, streams, lakes, ponds, pools and puddles. The aquacrops of this district include several species of commercially important fishes, aquatic cash crops such as makhana (Euryale ferox), singhara (Trapa spp.), lotus, lilly, Khubi etc. and molluscs. This paper highlights the commercial significance of these aquacrops and offers suggestions for their sustained development