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.
ICERM Workshop Registration: Small Clusters, Polymer Vesicles and Unusual Minima
11th Floor Collaborative Space
8:55 - 9:00
Welcome
ICERM Director
11th Floor Lecture Hall
9:00 - 9:10
Theme of workshop
Mark Bowick, Syracuse University
11th Floor Lecture Hall
9:10 - 10:10
Clusters with Short-range Interactions- a Tutorial
Miranda Holmes-Cerfon, Courant Institute of Mathematical Sciences
11th Floor Lecture Hall
10:10 - 10:40
Discussion period
11th Floor Lecture Hall
10:40 - 11:10
Coffee/Tea Break
11th Floor Collaborative Space
11:10 - 12:10
Shape selection in frustrated elastic sheets
Eran Sharon, Hebrew University of Jerusalem
11th Floor Lecture Hall
12:10 - 12:40
Discussion period
11th Floor Lecture Hall
12:40 - 2:20
Break for Lunch
2:20 - 2:50
From smooth manifolds to faceted polyhedra, and back
L. Mahadevan, Harvard University
11th Floor Lecture Hall
3:00 - 3:30
The physics and geometry of colloidal sphere clusters
Vinothan Manoharan, Harvard University
11th Floor Lecture Hall
3:30 - 4:00
Coffee/Tea Break
11th Floor Lecture Hall
4:00 - 5:00
Self-assembly with shaped particles
Sharon Glotzer, University of Michigan
11th Floor Lecture Hall
5:00 - 6:30
Welcome Reception
11th Floor Collaborative Space
Tuesday
March 17, 2015
Time
Description
Speaker
Location
Abstracts
Slides
9:00 - 10:00
Topology and Singularities
Robert Hardt, Rice University
11th Floor Lecture Hall
10:00 - 10:30
Discussion period
11th Floor Lecture Hall
10:25 - 10:30
Workshop Group Photo
11th Floor Lecture Hall
10:30 - 11:50
Statistical Mechanics and Combinatorics (ongoing semester course)
Richard Kenyon, Brown University
10th Floor Classroom
10:30 - 11:00
Coffee/Tea Break
11th Floor Collaborative Space
11:00 - 12:00
Topology of Broken Translational Symmetry
Randy Kamien, University of Pennsylvania
11th Floor Lecture Hall
12:00 - 12:30
Discussion period
11th Floor Lecture Hall
12:30 - 2:30
Break for Lunch
2:30 - 3:00
On vector-valued singular perturbation problems involving potentials vanishing on curves.
Itai Shafrir, Technion-Israel Institute of Technology
11th Floor Lecture Hall
3:10 - 3:40
Nonspherical Bubble Clusters
John Sullivan, TU Berlin
11th Floor Lecture Hall
3:40 - 4:00
Coffee/Tea Break
11th Floor Collaborative Space
4:00 - 4:30
Dr. Wrinkle and Mr. Hyde- directing pattern formation in anisotropic elastic films
Elisabetta Matsumoto, Princeton University
11th Floor Lecture Hall
Wednesday
March 18, 2015
Time
Description
Speaker
Location
Abstracts
Slides
9:00 - 10:00
Exploring the Energy Landscapes of Clusters and Unusual Minima
David Wales, Cambridge University
11th Floor Lecture Hall
10:00 - 10:30
Discussion period
11th Floor Lecture Hall
10:30 - 11:00
Coffee/Tea Break
11th Floor Collaborative Space
11:00 - 12:30
Poster Session
11th Floor Lecture Hall and Collaborative Space
12:30 - 2:15
Break for Lunch
2:15 - 2:45
Metastability, Spectra, and Eigencurrents of Lennard-Jones Clusters
Maria Cameron, University of Maryland
11th Floor Lecture Hall
3:00 - 3:30
Numerical Methods and Uniqueness for the Canham-Helfrich Model of Biomembranes
Thomas Yu, Drexel University
11th Floor Lecture Hall
3:30 - 3:50
Coffee/Tea Break
11th Floor Collaborative Space
3:50 - 4:20
Geometric frustration in twisted filament assemblies- Non-euclidean packing and morphology of self-limiting bundles
Greg Grason, University of Massachusetts
11th Floor Lecture Hall
4:30 - 5:00
Random Organization, Hyperuniformity and Photonic Bandgap
Paul Chaikin, New York University
11th Floor Lecture Hall
Thursday
March 19, 2015
Time
Description
Speaker
Location
Abstracts
Slides
9:00 - 10:00
Flavors of Rigidity for Sticky Spheres
Robert Connelly, Cornell University
11th Floor Lecture Hall
10:00 - 10:30
Discussion period
11th Floor Lecture Hall
10:30 - 11:50
Statistical Mechanics and Combinatorics (ongoing semester course)
Richard Kenyon, Brown University
10th Floor Classroom
10:30 - 11:00
Coffee/Tea Break
11th Floor Collaborative Space
11:00 - 12:00
The Duality between Floppy and Rigid Modes in the Jamming-Unjamming Transitions
Gustavo During, Instituto de Fisica, Universidad Catolica de Chile
11th Floor Lecture Hall
12:00 - 12:30
Discussion period
11th Floor Lecture Hall
12:30 - 2:15
Break for Lunch
2:15 - 2:45
EASAL- efficient atlasing, search and analysis of assembly landscapes under short-ranged potentials using geometrization, stratification and Cayley convexification.
Meera Sitharam, University of Florida
11th Floor Lecture Hall
2:55 - 3:25
Counting degrees of freedom in periodic frameworks
Louis Theran, Aalto University
11th Floor Lecture Hall
3:25 - 3:50
Coffee/Tea Break
11th Floor Collaborative Space
3:50 - 4:20
Topological soft matter- from linkages to kinks
Bryan Chen, Instituut-Lorentz for Theoretical Physics, Leiden University
11th Floor Lecture Hall
4:30 - 5:00
Dislocation modes and buckling in topological metamaterials
Jayson Paulose, Rijksuniversiteit te Leiden
Friday
March 20, 2015
Time
Description
Speaker
Location
Abstracts
Slides
9:00 - 10:00
Inverse problems / packing&information theory
Henry Cohn, Microsoft Research
11th Floor Lecture Hall
10:00 - 10:30
Discussion period
11th Floor Lecture Hall
10:30 - 11:00
Coffee/Tea Break
11th Floor Collaborative Space
11:00 - 12:30
Having a ball with sphere parking.
Beth Chen, Harvard University
11th Floor Lecture Hall
12:30 - 2:00
Break for Lunch
2:00 - 2:30
Tangent Unit-Vector Fields for Liquid Crystals and Nanoparticles
Dr Apala Majumdar, University of Bath, United Kingdom