Oscillatory thermal instability and the Bhopal disaster

A stability analysis is presented of the hydrolysis of methyl isocyanate (MIC) using a homogeneous flow reactor paradigm. The results simulate the thermal runaway that occurred inside the storage tank of MIC at the Bhopal Union Carbide plant in December 1984. The stability properties of the model indicate that the thermal runaway may have been due to a large amplitude, hard thermal oscillation initiated at a subcritical Hopf bifurcation. This type of thermal misbehavior cannot be predicted using conventional thermal diagrams, and may be typical of liquid thermoreactive systems.Comment: 12 pages, 5 figures. Submitted to Process Safety and Environmental Protection 08 July 2010. A belated submission from work that should have been written up and published years ag

The case of the trapped singularities

A case study in bifurcation and stability analysis is presented, in which reduced dynamical system modelling yields substantial new global and predictive information about the behaviour of a complex system. The first smooth pathway, free of pathological and persistent degenerate singularities, is surveyed through the parameter space of a nonlinear dynamical model for a gradient-driven, turbulence-shear flow energetics in magnetized fusion plasmas. Along the route various obstacles and features are identified and treated appropriately. An organizing centre of low codimension is shown to be robust, several trapped singularities are found and released, and domains of hysteresis, threefold stable equilibria, and limit cycles are mapped. Characterization of this rich dynamical landscape achieves unification of previous disparate models for plasma confinement transitions, supplies valuable intelligence on the big issue of shear flow suppression of turbulence, and suggests targeted experimental design, control and optimization strategies.Comment: 21 pages, 12 figures, 34 postscript figure file

Geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution

Computer program on axisymmetric response of shells with other meridional geometries and response of shells subjected to asymmetric loads is described. Description of theory, method of solution, instructions for preparing input data, and two sample problems to illustrate data preparation and output format are included

Phenol Deoxygenation over Hydrotreating Catalysts

Phenol deoxygenation has been investigated as a model reaction for the deoxygenation of fatty acid methyl esters in biodiesel. Hydrodeoxygenated biodiesel is a drop-in fuel for petroleum diesel, and is a premium diesel with a high cetane number. As the first step in this research, two molybdenum catalysts were prepared, characterized and tested in a small-scale reactor. These catalysts were found to produce small amounts of benzene and cyclohexanol in the product stream, and confirmed the activity of the catalyst. A commercial cobalt molybdenum catalyst (Harshaw HT-400) was also tested and benzene, cyclohexanol, and cyclohexane were identified as products. Future work aims to synthesize catalysts to produce a high yield of cyclohexane. Once the conditions are optimized, we will do tests with biodiesel

Dynamical Systems, Stability, and Chaos

In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics and control theory, and focussing on qualitative theory. From this perspective we show how concepts of stability enable us to classify dynamical equations and their solutions and connect the key issues of nonlinearity, bifurcation, control, and uncertainty that are common to time-dependent problems in natural and engineered systems. We discuss stability and bifurcations in three simple model problems, and conclude with a survey of recent extensions of stability theory to complex networks.Comment: 28 pages, 10 figures. 26/04/2007: The book title was changed at the last minute. No other changes have been made. Chapter 1 in: J.P. Denier and J.S. Frederiksen (editors), Frontiers in Turbulence and Coherent Structures. World Scientific Singapore 2007 (in press

Concentration of the distance between points in the unit ball

We prove that in every finite dimensional normed space, for “most” pairs (x, y) of points in the unit ball, ║x − y║ is more than √2(1 − ε). As a consequence, we obtain a result proved by Bourgain, using QS-decomposition, that guarantees an exponentially large number of points in the unit ball any two of which are separated by more than √2(1 − ε)

Heavy Quark Production at High Energy

We report on QCD radiative corrections to heavy quark production valid at high energy. The formulae presented will allow a matched calculation of the total cross section which is correct at O(\as^3) and includes resummation of all terms of order \as^3 [\as \ln (s/m^2)]^n. We also include asymptotic estimates of the effect of the high energy resummation. A complete description of the calculation of the heavy quark impact factor is included in an appendix.Comment: 32 pages (LaTeX) with three figures. Resubmission to agree with published version, which contains a new note added in proof and modifications of text of appendix

Nonlinear Simulation of Drift Wave Turbulence

In a two-dimensional version of the modified Hasegawa-Wakatani (HW) model, which describes electrostatic resistive drift wave turbulence, the resistive coupling between vorticity and density does not act on the zonal components ($k_{y}=0$). It is therefore necessary to modify the HW model to treat the zonal components properly. The modified equations are solved numerically, and visualization and analysis of the solutions show generation of stable zonal flows, through conversion of turbulent kinetic energy, and the consequent turbulence and transport suppression. It is demonstrated by comparison that the modification is essential for generation of zonal flows.Comment: Accepted for publication in the Proceedings of the CSIRO/COSNet Workshop on Turbulence and Coherent Structures, Canberra, Australia, 10-13 January 2006 (World Scientific, in press, eds. J.P. Denier and J.S. Frederiksen): 12 pages, 6 figure