Welcome to Collaborative Laboratory for Applied and Interdisciplinary Mathematics (CLAIM)
The Kuramoto-Sivashinsky equation
The Kuramoto-Sivashinsky equation models the growth of an interface (top). In each trial, the thickness of the interface grows in a chaotic and unpredictable manner. The average over many trials, in contrast, shows smooth, predictable growth. The average behaviour may be universal, i.e. the same for a class of different models for growing interfaces. This is the topic of ongoing research of Lennaert van Veen with Takumasa Takeuchi of the Tokyo Institute of Technology.
Dr. Fedor Naumkin explores new materials using parallel computers rather than Bunsen burners and fume hoods. Using a mixture of classical and quantum physics, the properties of novel combinations of molecules can be predicted.
Light metal atoms can mediate assembling organic molecules into stable junctions with charge-controlled shapes, with molecular-switch and novel-material applications. Hydrogen can be atomically encapsulated inside Be cluster-cage aggregates (extendable to a nanofoam material) with a high storage capacity and with release controlled electrically, thus facilitating hydrogen-based energy solutions. Molecules can be trapped between counterions, forming metastable systems with huge dipole moments, thus enabling efficient optical sensors and energy storage at molecular level. Small aluminum cluster is transformed into a symmetric shell around a molecular carbon core, thus allowing shape-design of building blocks for nanocomposites.