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.

Confirmed Speakers & Participants

Workshop Schedule

Monday, March 16, 2015
TimeEventLocationMaterials
8:30 - 8:55ICERM Workshop Registration: Small Clusters, Polymer Vesicles and Unusual Minima11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:10Theme of workshop - Mark Bowick, Syracuse University11th Floor Lecture Hall 
9:10 - 10:10Clusters with Short-range Interactions- a Tutorial - Miranda Holmes-Cerfon, Courant Institute of Mathematical Sciences11th Floor Lecture Hall
10:10 - 10:40Discussion period11th Floor Lecture Hall 
10:40 - 11:10Coffee/Tea Break11th Floor Collaborative Space 
11:10 - 12:10Shape selection in frustrated elastic sheets - Eran Sharon, Hebrew University of Jerusalem11th Floor Lecture Hall
12:10 - 12:40Discussion period11th Floor Lecture Hall 
12:40 - 2:20Break for Lunch  
2:20 - 2:50From smooth manifolds to faceted polyhedra, and back - L. Mahadevan, Harvard University11th Floor Lecture Hall 
3:00 - 3:30The physics and geometry of colloidal sphere clusters - Vinothan Manoharan, Harvard University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Lecture Hall 
4:00 - 5:00Self-assembly with shaped particles - Sharon Glotzer, University of Michigan11th Floor Lecture Hall 
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, March 17, 2015
TimeEventLocationMaterials
9:00 - 10:00Topology and Singularities - Robert Hardt, Rice University11th Floor Lecture Hall
10:00 - 10:30Discussion period11th Floor Lecture Hall 
10:25 - 10:30Workshop Group Photo11th Floor Lecture Hall 
10:25 - 10:30Workshop Group Photo11th Floor Lecture Hall 
10:30 - 11:50Statistical Mechanics and Combinatorics (ongoing semester course) - Richard Kenyon, Brown University10th Floor Classroom 
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00Topology of Broken Translational Symmetry - Randy Kamien, University of Pennsylvania11th Floor Lecture Hall 
12:00 - 12:30Discussion period11th Floor Lecture Hall 
12:30 - 2:30Break for Lunch  
2:30 - 3:00On vector-valued singular perturbation problems involving potentials vanishing on curves. - Itai Shafrir, Technion-Israel Institute of Technology11th Floor Lecture Hall
3:10 - 3:40Nonspherical Bubble Clusters - John Sullivan, TU Berlin11th Floor Lecture Hall
3:40 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:30Dr. 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 - 10:00Exploring the Energy Landscapes of Clusters and Unusual Minima - David Wales, Cambridge University11th Floor Lecture Hall
10:00 - 10:30Discussion period11th Floor Lecture Hall 
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:30Poster Session11th Floor Lecture Hall and Collaborative Space 
12:30 - 2:15Break for Lunch  
2:15 - 2:45Metastability, Spectra, and Eigencurrents of Lennard-Jones Clusters - Maria Cameron, University of Maryland11th Floor Lecture Hall
3:00 - 3:30Numerical Methods and Uniqueness for the Canham-Helfrich Model of Biomembranes - Thomas Yu, Drexel University11th Floor Lecture Hall
3:30 - 3:50Coffee/Tea Break11th Floor Collaborative Space 
3:50 - 4:20Geometric frustration in twisted filament assemblies- Non-euclidean packing and morphology of self-limiting bundles - Greg Grason, University of Massachusetts11th Floor Lecture Hall
4:30 - 5:00Random Organization, Hyperuniformity and Photonic Bandgap - Paul Chaikin, New York University11th Floor Lecture Hall
Thursday, March 19, 2015
TimeEventLocationMaterials
9:00 - 10:00Flavors of Rigidity for Sticky Spheres - Robert Connelly, Cornell University11th Floor Lecture Hall
10:00 - 10:30Discussion period11th Floor Lecture Hall 
10:30 - 11:50Statistical Mechanics and Combinatorics (ongoing semester course) - Richard Kenyon, Brown University10th Floor Classroom 
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00The 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 - 12:30Discussion period11th Floor Lecture Hall 
12:30 - 2:15Break for Lunch  
2:15 - 2:45EASAL- 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 - 3:25Counting degrees of freedom in periodic frameworks - Louis Theran, Aalto University11th Floor Lecture Hall
3:25 - 3:50Coffee/Tea Break11th Floor Collaborative Space 
3:50 - 4:20Topological soft matter- from linkages to kinks - Bryan Chen, Instituut-Lorentz for Theoretical Physics, Leiden University11th Floor Lecture Hall
4:30 - 5:00Dislocation modes and buckling in topological metamaterials - Jayson Paulose, Rijksuniversiteit te Leiden 
Friday, March 20, 2015
TimeEventLocationMaterials
9:00 - 10:00Inverse problems / packing&information theory - Henry Cohn, Microsoft Research11th Floor Lecture Hall 
10:00 - 10:30Discussion period11th Floor Lecture Hall 
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:30Having a ball with sphere parking. - Beth Chen, Harvard University11th Floor Lecture Hall
12:30 - 2:00Break for Lunch  
2:00 - 2:30Tangent Unit-Vector Fields for Liquid Crystals and Nanoparticles - Dr Apala Majumdar, University of Bath, United Kingdom11th Floor Lecture Hall
2:30 - 3:00Unusual Minima on Curved Surfaces - Mark Bowick, Syracuse University11th Floor Lecture Hall 
3:00 - 3:30Discussion period11th Floor Lecture Hall 
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 

Associated Semester Workshops

Phase Transitions and Emergent Properties
Crystals, Quasicrystals and Random Networks
Limit Shapes

Lecture Videos

Topological soft matter- from linkages to kinks

Bryan Chen
Instituut-Lorentz for Theoretical Physics, Leiden University
March 19, 2015

Clusters with Short-range Interactions- a Tutorial

Miranda Holmes-Cerfon
Courant Institute of Mathematical Sciences
March 16, 2015