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Anisotropic Coverings of Fractal sets

Anisotropic Coverings of Fractal sets. Harry Kennard h.r.kennard@open.ac.uk PhD Candidate Department of Applied Mathematics The Open University Supervisor: Professor Michael Wilkinson. Outline of the paper. Outline of the Talk.

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Anisotropic Coverings of Fractal sets

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  1. Anisotropic Coverings of Fractal sets Harry Kennard h.r.kennard@open.ac.uk PhD Candidate Department of Applied Mathematics The Open University Supervisor: Professor Michael Wilkinson

  2. Outline of the paper Outline of the Talk 1 Motivation2 Method3 Generalised Sierpinski Model4 Inertial particles in a random flow

  3. MotivationMethod Sierpinski Inertial

  4. MotivationMethod Sierpinski Inertial Locally Cartesian product structure

  5. k k’ MotivationMethod Sierpinski Inertial Isotropicscattering Coherent scattering Require a function to characterise fractal anisotropy

  6. δ ε vs. get straight lines plot MotivationMethod Sierpinski Inertial

  7. MotivationMethod Sierpinski Inertial

  8. MotivationMethod Sierpinski Inertial

  9. MotivationMethod Sierpinski Inertial

  10. MotivationMethod Sierpinski Inertial Just circles!

  11. MotivationMethod Sierpinski Inertial Upper bound N is independent of ellipse orientation in the disk of this lie in the ellipse

  12. MotivationMethod Sierpinski Inertial explain sier generalizations

  13. MotivationMethod Sierpinski Inertial

  14. MotivationMethod Sierpinski Inertial Inertial particles move in an incompressible fluid (velocity field u) under a synthetic turbulent velocity field Particles, and hence the flow and distribution of them, is characterised by η [0:1]

  15. MotivationMethod Sierpinski Inertial η=0.9

  16. η M. Wilkinson, B. Mehlig and K. Gustavsson,Eurohysics Lett., 89, 50002, (2010). MotivationMethod Sierpinski Inertial η=0.1

  17. η M. Wilkinson, B. Mehlig and K. Gustavsson,Eurohysics Lett., 89, 50002, (2010). MotivationMethod Sierpinski Inertial η=0.4 η

  18. η M. Wilkinson, B. Mehlig and K. Gustavsson,Eurohysics Lett., 89, 50002, (2010). MotivationMethod Sierpinski Inertial

  19. Thank You – Any Questions? Harry Kennard h.r.kennard@open.ac.uk PhD Candidate Department of Applied Mathematics The Open University Supervisor: Professor Michael Wilkinson

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