Organizing Committee
Abstract

This workshop will explore emergent phenomena in the context of small clusters, supramolecular self-assembly and the shape of self-assembled structures such as polymer vesicles. The emphasis will be on surprises which arise when common conditions are not satisfied, for instance when the number of components is small, or they are highly non-spherical, or there are several types of components. Interactions vary from hard sphere repulsion to competition between coarse-grained liquid-crystalline ordering competing with shape deformation.

Examples of this behavior are common in materials such as bulk homopolymers (rubber), copolymers, liquid crystals and colloidal aggregates. A basic mathematical setting would be to consider small clusters of hard spheres with isotropic short-range attractions and study the shape of the clusters as a function of the number of components. One known surprise is that highly symmetric structures are suppressed by rotational entropy.

This emphasizes the need to accurately count the number of particle configurations that lead to the same final state. Small clusters can also generate anisotropic building blocks which can in turn serve as nano- or meso-scale building blocks for supermolecules and bulk materials (supramolecular chemistry) freed from the limited scope of atoms and quantum-mechanical bonding. These structures frequently possess topological defects in their ground states because they lower the energy. The challenge is to determine the shape and equilibrium defect structure of such superatoms and the number and geometry of their arrangement.

The number of defects determines the effective valence of the super atoms and the global geometry of their arrangement determines the types of directional bonding possible when defects are linked together. The phenomenon of the appearance of singularities/defects because they are minimizers not necessarily required by topology or boundary conditions is also encountered in the study of harmonic maps. Moving up to self-assembly of large numbers of units, block copolymers self-assemble into a wide variety of structures including vesicles, nano-fibers and tori.

Many of the structures formed are essentially two-dimensional surfaces embedded in R3. The mathematical challenge is to find both the shape and the order of the assembled object. This requires minimizing of a functional that depends on both the local and global order of the relevant matter fields and the shape of the surface.

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Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, March 16, 2015
TimeEventLocationMaterials
8:30 - 8:55am EDTICERM Workshop Registration: Small Clusters, Polymer Vesicles and Unusual Minima11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:10am EDTTheme of workshop - Mark Bowick, Syracuse University11th Floor Lecture Hall 
9:10 - 10:10am EDTClusters with Short-range Interactions- a Tutorial - Miranda Holmes-Cerfon, Courant Institute of Mathematical Sciences11th Floor Lecture Hall
10:10 - 10:40am EDTDiscussion period11th Floor Lecture Hall 
10:40 - 11:10am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:10 - 12:10pm EDTShape selection in frustrated elastic sheets - Eran Sharon, Hebrew University of Jerusalem11th Floor Lecture Hall
12:10 - 12:40pm EDTDiscussion period11th Floor Lecture Hall 
12:40 - 2:20pm EDTBreak for Lunch  
2:20 - 2:50pm EDTFrom smooth manifolds to faceted polyhedra, and back - L. Mahadevan, Harvard University11th Floor Lecture Hall 
3:00 - 3:30pm EDTThe physics and geometry of colloidal sphere clusters - Vinothan Manoharan, Harvard University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Lecture Hall 
4:00 - 5:00pm EDTSelf-assembly with shaped particles - Sharon Glotzer, University of Michigan11th Floor Lecture Hall 
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, March 17, 2015
TimeEventLocationMaterials
9:00 - 10:00am EDTSingularities in Maps - Robert Hardt, Rice University11th Floor Lecture Hall 
10:00 - 10:30am EDTDiscussion period11th Floor Lecture Hall 
10:25 - 10:30am EDTWorkshop Group Photo11th Floor Lecture Hall 
10:25 - 10:30am EDTWorkshop Group Photo11th Floor Lecture Hall 
10:30 - 11:50am EDTStatistical Mechanics and Combinatorics (ongoing semester course) - Richard Kenyon, Brown University10th Floor Classroom 
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTTopology of Broken Translational Symmetry - Randy Kamien, University of Pennsylvania11th Floor Lecture Hall 
12:00 - 12:30pm EDTDiscussion period11th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch  
2:30 - 3:00pm EDTOn vector-valued singular perturbation problems involving potentials vanishing on curves. - Itai Shafrir, Technion-Israel Institute of Technology11th Floor Lecture Hall
3:10 - 3:40pm EDTNonspherical Bubble Clusters - John Sullivan, TU Berlin11th Floor Lecture Hall
3:40 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:30pm EDTDr. Wrinkle and Mr. Hyde- directing pattern formation in anisotropic elastic films - Elisabetta Matsumoto, Princeton University11th Floor Lecture Hall
Wednesday, March 18, 2015
TimeEventLocationMaterials
9:00 - 10:00am EDTExploring the Energy Landscapes of Clusters and Unusual Minima - David Wales, Cambridge University11th Floor Lecture Hall
10:00 - 10:30am EDTDiscussion period11th Floor Lecture Hall 
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:30pm EDTPoster Session11th Floor Lecture Hall and Collaborative Space 
12:30 - 2:15pm EDTBreak for Lunch  
2:15 - 2:45pm EDTMetastability, Spectra, and Eigencurrents of Lennard-Jones Clusters - Maria Cameron, University of Maryland11th Floor Lecture Hall
3:00 - 3:30pm EDTNumerical Methods and Uniqueness for the Canham-Helfrich Model of Biomembranes - Thomas Yu, Drexel University11th Floor Lecture Hall
3:30 - 3:50pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:50 - 4:20pm EDTGeometric frustration in twisted filament assemblies- Non-euclidean packing and morphology of self-limiting bundles - Greg Grason, University of Massachusetts11th Floor Lecture Hall
4:30 - 5:00pm EDTRandom Organization, Hyperuniformity and Photonic Bandgap - Paul Chaikin, New York University11th Floor Lecture Hall
Thursday, March 19, 2015
TimeEventLocationMaterials
9:00 - 10:00am EDTFlavors of Rigidity for Sticky Spheres - Robert Connelly, Cornell University11th Floor Lecture Hall
10:00 - 10:30am EDTDiscussion period11th Floor Lecture Hall 
10:30 - 11:50am EDTStatistical Mechanics and Combinatorics (ongoing semester course) - Richard Kenyon, Brown University10th Floor Classroom 
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTThe Duality between Floppy and Rigid Modes in the Jamming-Unjamming Transitions - Gustavo During, Instituto de Fisica, Universidad Catolica de Chile11th Floor Lecture Hall
12:00 - 12:30pm EDTDiscussion period11th Floor Lecture Hall 
12:30 - 2:15pm EDTBreak for Lunch  
2:15 - 2:45pm EDTEASAL- efficient atlasing, search and analysis of assembly landscapes under short-ranged potentials using geometrization, stratification and Cayley convexification. - Meera Sitharam, University of Florida11th Floor Lecture Hall
2:55 - 3:25pm EDTCounting degrees of freedom in periodic frameworks - Louis Theran, Aalto University11th Floor Lecture Hall
3:25 - 3:50pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:50 - 4:20pm EDTTopological soft matter- from linkages to kinks - Bryan Chen, Instituut-Lorentz for Theoretical Physics, Leiden University11th Floor Lecture Hall
4:30 - 5:00pm EDTDislocation modes and buckling in topological metamaterials - Jayson Paulose, Rijksuniversiteit te Leiden 
Friday, March 20, 2015
TimeEventLocationMaterials
9:00 - 10:00am EDTInverse problems / packing&information theory - Henry Cohn, Microsoft Research11th Floor Lecture Hall 
10:00 - 10:30am EDTDiscussion period11th Floor Lecture Hall 
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:30pm EDTHaving a ball with sphere parking. - Beth Chen, Harvard University11th Floor Lecture Hall
12:30 - 2:00pm EDTBreak for Lunch  
2:00 - 2:30pm EDTTangent Unit-Vector Fields for Liquid Crystals and Nanoparticles - Dr Apala Majumdar, University of Bath, United Kingdom11th Floor Lecture Hall
2:30 - 3:00pm EDTUnusual Minima on Curved Surfaces - Mark Bowick, Syracuse University11th Floor Lecture Hall 
3:00 - 3:30pm EDTDiscussion period11th Floor Lecture Hall 
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 

Associated Semester Workshops

Phase Transitions and Emergent Properties
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Statistical Mechanics and Combinatorics (ongoing semester course)
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Crystals, Quasicrystals and Random Networks
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Limit Shapes
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Lecture Videos