26 October 2004 Higher harmonic nonlocal polymerization driven diffusion model: generalized nonlinearities and nonlocal responses
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Abstract
Non-local and non-linear models of photopolymer materials, which include diffusion effects, have recently received much attention in the literature. The material response is non-local as it is assumed that monomers are polymerised to form polymer chains and that these chains grow away from a point of initiation. The non-locality is defined in terms of a spatial non-local material response function. The numerical method of solution typically involves retaining either two or four harmonics of the Fourier series of monomer concentration in the calculation. In this paper a general set of equations is derived which allows inclusion of higher number of harmonics for any response function. The numerical convergence for varying number of harmonics retained is investigated with special care being taken to note the effect of the; non-local material variance σ, the power law degree k, and the rates of diffusion, D, and polymerisation F0. General non-linear material responses are also included.
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John V. Kelly, John V. Kelly, Jeff O'Brien, Jeff O'Brien, Feidhlim T. O'Neill, Feidhlim T. O'Neill, Michael R. Gleeson, Michael R. Gleeson, John T. Sheridan, John T. Sheridan, } "Higher harmonic nonlocal polymerization driven diffusion model: generalized nonlinearities and nonlocal responses", Proc. SPIE 5521, Organic Holographic Materials and Applications II, (26 October 2004); doi: 10.1117/12.560492; https://doi.org/10.1117/12.560492
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