Introduction Diffusion and chaos Deterministic diffusion Fractals Towards experiments Summary Deterministic chaos, fractals and diffusion: From simple models towards experiments Rainer Klages Queen Mary University of London, School of Mathematical Sciences Université Pierre et Marie Curie Paris, 16 September 2010 Deterministic chaos, fractals and diffusion Rainer Klages (QMUL) 1
25
Embed
Deterministic chaos, fractals and diffusion: From …klages/talks/paris_michel.pdfDeterministic chaos, fractals and diffusion: From simple models towards experiments Rainer Klages
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Introduction Diffusion and chaos Deterministic diffusion Fractals Towards experiments Summary
Deterministic chaos, fractals and diffusion:From simple models towards experiments
Rainer Klages
Queen Mary University of London, School of Mathematical Sciences
Université Pierre et Marie CurieParis, 16 September 2010
Deterministic chaos, fractals and diffusion Rainer Klages (QMUL) 1
Introduction Diffusion and chaos Deterministic diffusion Fractals Towards experiments Summary
Outline
1 Motivation: random walks, diffusion and deterministicchaos
2 A simple model for deterministic diffusion with a fractaldiffusion coefficient
3 From simple models towards experiments: particlebilliards and nanopores
Deterministic chaos, fractals and diffusion Rainer Klages (QMUL) 2
Introduction Diffusion and chaos Deterministic diffusion Fractals Towards experiments Summary
Introduction Diffusion and chaos Deterministic diffusion Fractals Towards experiments Summary
Molecular diffusion in zeolites
zeolites: nanoporous crystalline solids serving as molecularsieves, adsorbants; used in detergents and as catalysts for oilcracking
example: unit cell of Lindetype A zeolite; strictlyperiodic structure built by a“cage” of silica and oxygen
Schüring et al. (2002): MDsimulations with ethane yieldnon-monotonic temperaturedependence of diffusion coefficient
D(T ) = limt→∞
< [x(t) − x(0)]2 >
6tdue to dynamical correlations
Deterministic chaos, fractals and diffusion Rainer Klages (QMUL) 22
Introduction Diffusion and chaos Deterministic diffusion Fractals Towards experiments Summary
Summary
central theme:
relevance of deterministic chaosfor diffusion in periodic lattices
main theoretical finding:existence of diffusion coefficients that are irregular (fractal)functions under parameter variation, due to memory effects
expected to be typical for classical transport inlow-dimensional, spatially periodic systems
Deterministic chaos, fractals and diffusion Rainer Klages (QMUL) 23
Introduction Diffusion and chaos Deterministic diffusion Fractals Towards experiments Summary
some generalizations:
analogous theoretical results for other transport coefficientslike conductivities and chemical reaction-diffusionsame phenomena in anomalous diffusionirregularities are quite robust against random perturbations
clearcut verification in experiments? good candidates arenanoporesvibratory conveyorsantidot latticesJosephson junctions
approach should be particularly interesting for small systems
Deterministic chaos, fractals and diffusion Rainer Klages (QMUL) 24
Introduction Diffusion and chaos Deterministic diffusion Fractals Towards experiments Summary
Acknowledgements and literature
work performed with:
J.R.Dorfman (College Park, USA), P.Gaspard (Brussels),T.Harayama (Kyoto)
literature:
details and taster sections on www.maths.qmul.ac.uk/˜klages
Deterministic chaos, fractals and diffusion Rainer Klages (QMUL) 25