Generating Equidistributed Meshes in 2D via Domain Decomposition

In this paper we consider Schwarz domain decomposition applied to the generation of 2D spatial meshes by a local equidistribution principle. We briefly review the derivation of the local equidistribution principle and the appropriate choice of boundary conditions. We then introduce classical and optimized Schwarz domain decomposition methods to solve the resulting system of nonlinear equations. The implementation of these iterations are discussed, and we conclude with numerical examples to illustrate the performance of the approach

Phase separation and rotor self-assembly in active particle suspensions

Adding a non-adsorbing polymer to passive colloids induces an attraction between the particles via the `depletion' mechanism. High enough polymer concentrations lead to phase separation. We combine experiments, theory and simulations to demonstrate that using active colloids (such as motile bacteria) dramatically changes the physics of such mixtures. First, significantly stronger inter-particle attraction is needed to cause phase separation. Secondly, the finite size aggregates formed at lower inter-particle attraction show unidirectional rotation. These micro-rotors demonstrate the self assembly of functional structures using active particles. The angular speed of the rotating clusters scales approximately as the inverse of their size, which may be understood theoretically by assuming that the torques exerted by the outermost bacteria in a cluster add up randomly. Our simulations suggest that both the suppression of phase separation and the self assembly of rotors are generic features of aggregating swimmers, and should therefore occur in a variety of biological and synthetic active particle systems.Comment: Main text: 6 pages, 5 figures. Supplementary information: 5 pages, 4 figures. Supplementary movies available from httP://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1116334109/-/DCSupplementa

Activities of the Gulf Coast Research Laboratory During Fiscal Year 1977-78: A Summary Report

Annual report of the Gulf Coast Research Laboratory for fiscal year 1977-1978

Activities of the Gulf Coast Research Laboratory During Fiscal Year 1976-77: A Summary Report

Annual report of the Gulf Coast Research Laboratory for fiscal year 1976-1977

Activities of the Gulf Coast Research Laboratory During Fiscal Year 1975-76: A Summary Report

Annual report of the Gulf Coast Research Laboratory for fiscal year 1975-1976

Activities of the Gulf Coast Research Laboratory During Fiscal Year 1979-80: A Summary Report

Annual report of the Gulf Coast Research Laboratory from fiscal year 1979-1980

Activities of the Gulf Coast Research Laboratory During Fiscal Year 1978-79: A Summary Report

Annual report of the Gulf Coast Research Laboratory for fiscal year 1978-1979

Activities of the Gulf Coast Research Laboratory During Fiscal Year 1979-80: A Summary Report

Annual report of the Gulf Coast Research Laboratory from fiscal year 1979-1980

Active and driven hydrodynamic crystals

Motivated by the experimental ability to produce monodisperse particles in microfluidic devices, we study theoretically the hydrodynamic stability of driven and active crystals. We first recall the theoretical tools allowing to quantify the dynamics of elongated particles in a confined fluid. In this regime hydrodynamic interactions between particles arise from a superposition of potential dipolar singularities. We exploit this feature to derive the equations of motion for the particle positions and orientations. After showing that all five planar Bravais lattices are stationary solutions of the equations of motion, we consider separately the case where the particles are passively driven by an external force, and the situation where they are self-propelling. We first demonstrate that phonon modes propagate in driven crystals, which are always marginally stable. The spatial structure of the eigenmodes depend solely on the symmetries of the lattices, and on the orientation of the driving force. For active crystals, the stability of the particle positions and orientations depends not only on the symmetry of the crystals but also on the perturbation wavelengths and on the crystal density. Unlike unconfined fluids, the stability of active crystals is independent of the nature of the propulsion mechanism at the single particle level. The square and rectangular lattices are found to be linearly unstable at short wavelengths provided the volume fraction of the crystals is high enough. Differently, hexagonal, oblique, and face-centered crystals are always unstable. Our work provides a theoretical basis for future experimental work on flowing microfluidic crystals.Comment: 10 pages, 10 figure