The Linearly Independent Non Orthogonal yet Energy Preserving (LINOEP) vectors

It is well known that, in any inner product space, a set of linearly independent (LI) vectors can be transformed to a set of orthogonal vectors, spanning the same space, by the Gram-Schmidt Orthogonalization Method (GSOM). In this paper, we propose a transformation from a set of LI vectors to a set of LI non orthogonal yet energy (square of the norm) preserving (LINOEP) vectors in an inner product space and we refer it as LINOEP method. We also show that there are various solutions to preserve the square of the norm.Comment: 6 pages, 2 figure

Study of large-scale mixing in developing wakes behind streamlined bodies

Heat-tagging and conditional sampling techniques were used to study the large scale mixing process in the developing wake behind a streamlined body. The results were used to understand the manner in which the large eddy length scale evolves from a value appropriate to a boundary layer to that appropriate to the asymptotic far-wake

Two-Proton Radioactivity with 2p halo in light mass nuclei A==18−-34

Two-proton radioactivity with 2p halo is reported theoretically in light mass nuclei A $=$ 18-34. We predict $^{19}$Mg, $^{22}$Si, $^{26}$S, $^{30}$Ar and $^{34}$Ca as promising candidates of ground state 2p-radioactivity with S$_{2p}$ $$ 0. Observation of extended tail of spatial charge density distribution, larger charge radius and study of proton single particle states, Fermi energy and the wave functions indicate 2p halo like structure which supports direct 2p emission. The Coulomb and centrifugal barriers in experimentally identified 2p unbound $^{22}$Si show a quasi-bound state that ensures enough life time for such experimental probes. Our predictions are in good accord with experimental and other theoretical data available so far.Comment: 5 Pages, 5 figure