Searching with iterated maps.

In many problems that require extensive searching, the solution can be described as satisfying two competing constraints, where satisfying each independently does not pose a challenge. As an alternative to tree-based and stochastic searching, for these problems we propose using an iterated map built from the projections to the two constraint sets. Algorithms of this kind have been the method of choice in a large variety of signal-processing applications; we show here that the scope of these algorithms is surprisingly broad, with applications as diverse as protein folding and Sudoku.

Deconstructing the energy landscape: constraint-based algorithms for folding heteropolymers.

We apply the computational methodology of phase retrieval to the problem of folding heteropolymers. The ground state fold of the polymer is defined by the intersection of two sets in the configuration space of its constituent monomers: a geometrical chain constraint and a threshold constraint on the contact energy. A dynamical system is then defined in terms of the projections to these constraint sets, such that its fixed points solve the set intersection problem.

Influence of shape on ordering of granular systems in two dimensions.

We investigate ordering properties of two-dimensional granular materials using several shapes created by welding ball bearings together. Ordered domains form much more easily in two than in three dimensions, even when configurations lack long-range order. The onset of ordered domains occurs near a packing density of 0.