Topology and Liquid Crystals

Liquid crystal molecules can be molded into shapes which resemble a Hopf fibration, a complex shape from topology resembling a series of linked rings wrapped into a torus. This fascinating shape has applications in mathematics, quantum physics, and computer graphics.

From the lab of Bryan Gin-Ge Chen, former grad student of Prof. Randy Kamien.

Kirigami Topology

Professor Randall Kamien studies the physics and mathematics of kirigami — an extension of origami that allows cutting holes into the paper.  By treating the sheet of paper as a two-dimensional crystalline lattice, the folds, cuts, and pleats, can be understood in terms of topological defects in the underlying structure.

Microfluidics

 

Microfluidic channel in place for video microscopy.

Right: Schematic of microchannel, and example velocity profiles superposed on an actual image of the colloidal NIPA suspension.

From the labs of Profs. Doug Durian and Jerry Golub

 

Jammed States of Matter

Almost any system composed of discrete pieces large enough that thermal fluctuations can be ignored can have a jamming transition: a point at which fluid flow is impeded by a change of state into a stable amorphous solid.  The behavior is general enough to explain a pile of sand, a jar of candies, or cars in a traffic jam.  Professor Andrea Liu was involved in recent theoretical breakthroughs in the study of this phenomenon.

 

Quintic Calabi-Yau manifold

In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. In order to solve certain classic problems of unified gauge theories, the 4-dimensional effective theory should be in a space which is a Calabi-Yau manifold of complex dimension 3.

 

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