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Patterns around us Sat STEM program, Umass Amherst

March 9 2013 . Patterns around us Sat STEM program, Umass Amherst. What is a “pattern”? . Basic structure repeated many times One characteristic length (or a few, or many ..) . Spontaneous. Engineered . Hybrid . Types of patterns . Spontaneous.

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Patterns around us Sat STEM program, Umass Amherst

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  1. March 9 2013 Patterns around usSat STEM program, Umass Amherst

  2. What is a “pattern”? • Basic structure repeated many times • One characteristic length (or a few, or many ..)

  3. Spontaneous Engineered Hybrid Types of patterns

  4. Spontaneous Reflect competition of 2-3 elementary forces Described by simple models An indirect probe of various system parameters

  5. Outline • Why do we study patterns • Pattern formation theory in a nutshell • A glimpse at some work at UMass Amherst

  6. Outline • Why do we study patterns • Pattern formation theory in a nutshell • A glimpse at some work at UMass Amherst

  7. The taxpayer perspective W.M. Keck Foundation Unfurling of ultrathin sheets NSF-MRSEC Surface instabilities In polymers NSF-DMR Origami-inspired material design NSF-DMR Morphologies of tensed sheets Goal I: Creating ``good” patterns e.g. cheap patterning of surfaces at nano-scale Goal II: Eliminating ``bad” patterns e.g. wrinkles and scars on skin, cracks in materials

  8. The physicist’s perspective • Exploring universal mechanisms in nature: • across different scales • across distinct physical systems

  9. The student perspective • Eye opening experience • Bridging bio-physics-chemistry • Zest for Math wrinkle length thickness

  10. interdisciplinary basic physics applications Spontaneous patterns stimulus and practice of mathematical thinking

  11. Outline • Why do we study patterns • Pattern formation theory in a nutshell • A glimpse at some work at UMass Amherst

  12. Buckling Instability governed by weak bending resistance of thin objects

  13. Wrinkling on a liquid bath

  14. Wrinkling on a liquid bath Wavelengthgoverned by competition of forces: bending resistance (sheet) versus gravity (liquid)

  15. Wrinkling on a liquid bath wrinkle length film’s thickness Usage: Indirect measurement of thickness of ultrathin films

  16. Wrinkling on flesh Wavelengthgoverned by competition of forces: bending resistance of sheet (=skin) versus Stiffness of substrate (=flesh) • Usage: • Indirect measurement of elasticity of flesh • Probing the stress in a skin (e.g. for surgery)

  17. Viscous Fingering Wavelengthgoverned by competition of rates: Injection rate versus Viscous diffusion of liquid pressure Usage/relevance: Oil recovery from porous rocks

  18. Chemical reactions Alain Turing 1950’s Zhabotinsky-Belosov 1960’s-1970’s Wavelengthgoverned by competition of rates: reaction rate versus diffusion rate (??)

  19. Faraday waves Wavelength and pattern governed by competition of forces: Shaking rate (inertia) versus Gravity

  20. Summary (I) • Interdisciplinary experience: an overarching principle for pattern formation in distinct systems • Applicability e.g. metrology of ultrathin films • Math skills: plot data --> fit to elementary functions --> discover new physical laws

  21. Outline • Why do we study patterns • Pattern formation theory in a nutshell • A glimpse at some work at UMass Amherst

  22. What do you see ? Chocolate ??

  23. What do you see ? spontaneous pattern formation: Wrinkles, Crumples, Folds, Blisters, Creases, …

  24. Sheet on a curved surface Glue a flat sheet on sphere Frustration !! To delaminate (blister) ? or To stay attached (wrinkle) ?

  25. A sheet on a drop sheet R sheet drop drop Decreasing drop’s radius R … top view (experiment) side view (schematic)

  26. A sheet on a drop sheet R sheet drop drop Decreasing drop’s radius R further … top view (experiment) side view (schematic)

  27. A sheet on a drop sheet R sheet drop drop Decreasing drop’s radius R even further … top view (experiment) side view (schematic)

  28. A sheet on a drop sheet R sheet drop drop Finally … top view (experiment) side view (schematic)

  29. A sheet on a drop sheet R sheet drop drop From wrinkling to crumpling

  30. A sheet on curved surface: wrinkles, crumples, blisters blisters wrinkles crumples Questions: 1) How can we suppress/enhance blistering? 2) How fast does a sheet spread on liquid bath?

  31. Summary • Spontaneous pattern formation is cool ! • Thanks you for listening !

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