Patterns around us Sat STEM program, Umass Amherst March

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

Types of patterns Spontaneous EngineeredHybrid

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

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

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

The taxpayer perspective NSF-MRSEC Surface instabilities In polymers W.M. Keck Foundation Unfurling of ultrathin sheets 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

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

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

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

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

Buckling Instability governed by weak bending resistance of thin objects

Wrinkling on a liquid bath

Wavelength governed by competition of forces: bending resistance (sheet) versus gravity (liquid)

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

Wrinkling on flesh Wavelength governed 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)

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

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

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

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

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

What do you see ? Chocolate ??

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

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

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

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

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

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

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

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

Summary Spontaneous pattern formation is cool ! Thanks you for listening !

Doing it with surface tension Courtesy of M. Pineirua, ESPCI high tension low tension

Patterns around us 1. Introduction I: spontaneous patterns show many examples: spontaneous, engineered, intermediate what is a “pattern”? some recognized structure (simply periodic, partly periodic – e.g. spirals, “ordered chaos”) repeated appearance / dominance of a few length scales Classification into: “engineered” patterns – metro lines, manhattan “spontaneous” - sand dunes, ocean waves, dendritic growth, ion sputtering, plant leaves, zebra stripes “intermediate” – venation networks, pinecorns, bacterial colonies, spider web 2. Introduction II: Why to study patterns? Funding: Origami grant, Career grant, Keck grant …, MRSEC IREG II Tax-payer perspective (show me the money) Useful applications: material science - cheap nano-patterning, Bio-applications – treating wrinkles and scars. Physical insight: Recognizing universality in phenomena - across different length scales, across distinct physical systems Education (why should kids be interested in this) Eye opening experience. Bridging bio-physics-chemistry Zest for Math A graph with circles: Spontaneous patterns > usefulness, physics, stimulate math skills

3. Principles of pattern formation Euler buckling – instability Wrinkling on water (Huang) and on flesh (Cerda 03) –force balance (competing forces), show data from PRL 2010, demo skin Viscous fingering (later here). competition of rates – driving versus viscous diffusion of pressure. Faraday wave Zebra stripes / ZB (competing rate of diffusion and reaction) Learning: Universal principle (see pattern - look for competing mechanisms) Usefulness (one application – metrology) Math skills (plot data - > fit to functions -> discover simple physical laws 4. What do we do here Wrinkling and crumpling (start by chocolate picture, go to blisters and to drop on sheet – from Oxford) Keck paragraph and picture – shrink-wrap, nanometric wall paper,.. Suppressing delamination (contrast wrinkles and blisters picture) New metrology (measure wrinkle pattern to determine properties of ultrathin films) patterning surfaces (Crosby) Medical applications (find tension direction) Sharp folds (Menon and Dominic), and creases (Hayward, Evan) – from here to brain (show picture) Origami-inspired design