Condensed Matter Theory

Abstract:

We summarize results for two exactly soluble classes of bond-diluted models for rigidity percolation, which can serve as a benchmark for numerical and approximate methods. For bond dilution problems involving rigidity, the number of floppy modes F plays the role of a free energy. Both models involve pathological lattices with two-dimensional vector displacements. The first model involves hierarchical lattices where renormalization group calculations can be used to give exact solutions. Algebraic scaling transformations produce a transition of the second order, with an unstable critical point and associated scaling laws at a mean coordination =4.41, which is above the 'mean field' value =4 predicted by Maxwell constraint counting. The order parameter exponent associated with the spanning rigid cluster geometry is β=0.0775 and that associated with the divergence of the correlation length and the anomalous lattice dimension d is dν=3.533. The second model involves Bethe lattices where the rigidity transition is massively first order by a mean coordination =3.94 slightly below that predicted by Maxwell constraint counting. We show how a Maxwell equal area construction can be used to locate the first-order transition and how this result agrees with simulation results on larger random-bond lattices using the pebble game algorithm.

Abstract:

We propose a simple system of optically driven colloids that convert light into heat and move in response to self-generated and collectively generated thermal gradients. We show that the system exhibits self-organization into a moving cometlike swarm and characterize the structure and response of the swarm to a light-intensity-dependent external tuning parameter. We observe many interesting features in this nonequilibrium system including circulation and evaporation, intensity-dependent shape, density and temperature fluctuations, and ejection of hot colloids from the swarm tip. © 2014 American Physical Society.

Abstract:

A heterogeneous and dilute suspension of catalytically active colloids is studied as a nonequilibrium analogue of ionic systems, which has the remarkable feature of action-reaction symmetry breaking. Symmetrically coated colloids are found to join up to form self-assembled molecules that could be inert or have spontaneous activity in the form of net translational velocity and spin depending on their symmetry properties and their constituents. The type of activity can be adjusted by changing the surface chemistry and ambient variables that control the surface reactions and the phoretic drift. © 2014 American Physical Society.