Jones, Peter P. (2013) Determining cluster-cluster aggregation rate kernals using inverse methods. PhD thesis, University of Warwick.

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Abstract

We investigate the potential of inverse methods for retrieving adequate information about
the rate kernel functions of cluster-cluster aggregation processes from mass density distribution
data. Since many of the classical physical kernels have fractional order exponents the
ability of an inverse method to appropriately represent such functions is a key concern. In
early chapters, the properties of the Smoluchowski Coagulation Equation and its simulation
using Monte Carlo techniques are introduced. Two key discoveries made using the Monte
Carlo simulations are briefly reported. First, that for a range of nonlocal solutions of finite
mass spectrum aggregation systems with a source of mass injection, collective oscillations
of the solution can persist indefinitely despite the presence of significant noise. Second,
that for similar finite mass spectrum systems with (deterministic) stable, but sensitive, nonlocal
stationary solutions, the presence of noise in the system can give rise to behaviour
indicative of phase-remembering, noise-driven quasicycles. The main research material on
inverse methods is then presented in two subsequent chapters. The first of these chapters
investigates the capacity of an existing inverse method in respect of the concerns about
fractional order exponents in homogeneous kernels. The second chapter then introduces a
new more powerful nonlinear inverse method, based upon a novel factorisation of homogeneous
kernels, whose properties are assessed in respect of both stationary and scaling mass
distribution data inputs.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Monte Carlo method, Inversion (Geophysics), Kernel functions, Aggregation (Chemistry)
Official Date:	July 2013
Dates:	Date Event July 2013 Submitted
Institution:	University of Warwick
Theses Department:	Centre for Complexity Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Connaughton, Colm
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC)
Extent:	x, 114 leaves : illustrations.
Language:	eng

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