Concentration fluctuations in atmospheric dispersion

This report summarizes work done at Brunel University under Agreement No.2066/62 from 15 July 1986 to 14 July 1989. The title of the project was Concentration Fluctuations in Atmospheric Dispersion. The report has three principal components. These are: (i) theoretical work on the electrostatic effects associated with dispersing charged tracers. (ii) extensive analysis of several datasets taken with the CDE sensor system, particularly one obtained at RAF Cardington on 10 May 1988; (iii) interpretation of the results of the analysis. The conclusions of the report include recommendations for further work to exploit the advantages that the system has over many others

Design, implementation and testing of an integrated branch and bound algorithm for piecewise linear and discrete programming problems within an LP framework

A number of discrete variable representations are well accepted and find regular use within LP systems. These are Binary variables, General Integer variables, Variable Upper Bounds or Semi Continuous variables, Special Ordered Sets of type One and type Two. The FortLP system has been extended to include these representations. A Branch and Bound algorithm is designed in which the choice of sub-problems and branching variables are kept general. This provides considerable scope of experimentation with tree development heuristics and the tree search can then be guided by search parameters specified by user subroutines. The data structures for representing the variables and the definition of the branch and bound tree are described. The results of experimental investigation for a few test problems are reported

Quantum Jump from Singularity to Outside of Black Hole

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitariness in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.Comment: 7 figures, v2 more comprehensive, v3 matches the published versio