A. C. Maggs

Dynamic concentration of motors in microtubule arrays.

We present experimental and theoretical studies of the dynamics of molecular motors in microtubule arrays and asters. By solving a convection-diffusion equation we find that the density profile of motors in a two-dimensional aster is characterized by continuously varying exponents. Simulations are used to verify the assumptions of the continuum model. We observe the concentration profiles of kinesin moving in quasi-two-dimensional artificial asters by fluorescent microscopy and compare with our theoretical results.

Local simulation algorithms for Coulomb interactions.

We consider a problem in dynamically constrained Monte Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simple implementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. There are analogies between our formulation of electrostatics and the bosonic Hubbard model in the phase approximation. Cluster methods developed for this model further improve the efficiency of the electrostatics algorithm.

Local Molecular Dynamics with Coulombic Interactions

We propose a local, O(N) molecular dynamics algorithm for the simulation of charged systems. The long ranged Coulomb potential is generated by a propagating electric field that obeys modified Maxwell equations. On coupling the electrodynamic equations to an external thermostat we show that the algorithm produces an effective Coulomb potential between particles. On annealing the electrodynamic degrees of freedom the field configuration converges to a solution of the Poisson equation much like the electronic degrees of freedom approach the ground state in ab initio molecular dynamics.

Phonons in two-dimensional soft colloidal crystals

The vibrational modes of pristine and polycrystalline monolayer colloidal crystals composed of thermosensitive microgel particles are measured using video microscopy and covariance matrix analysis. At low frequencies, the Debye relation for two-dimensional harmonic crystals is observed in both crystal types; at higher frequencies, evidence for van Hove singularities in the phonon density of states is significantly smeared out by experimental noise and measurement statistics. The effects of these errors are analyzed using numerical simulations. We introduce methods to correct for these limitations, which can be applied to disordered systems as well as crystalline ones, and we show that application of the error correction procedure to the experimental data leads to more pronounced van Hove singularities in the pristine crystal. Finally, quasilocalized low-frequency modes in polycrystalline two-dimensional colloidal crystals are identified and demonstrated to correlate with structural defects such as dislocations, suggesting that quasilocalized low-frequency phonon modes may be used to identify local regions vulnerable to rearrangements in crystalline as well as amorphous solids.

A minimizing principle for the Poisson-Boltzmann equation

The Poisson-Boltzmann equation is often presented via a variational formulation based on the electrostatic potential. However, the functional has the defect of being non-convex. It cannot be used as a local minimization principle while coupled to other dynamic degrees of freedom. We formulate a convex dual functional which is numerically equivalent at its minimum and which is more suited to local optimization.

Collective dispersion forces in the fluid state

Dispersion interactions lead to effective many-body interactions which go beyond the approximation of pair potentials widely used in modeling of materials, leading in the continuum limit to Lifshitz theory. We introduce quantum dispersion interactions in simulations of polarizable atoms, incorporating the fully summed, non-retarded Lifthitz theory in arbitrary fluctuating geometries. We sample the quantum degrees of freedom using a heat bath algorithm adapted to the polarization fluctuations of individual atoms. We demonstrate asymmetric screening of interactions in a binary fluid.

Local simulation algorithms for Coulombic interactions

We consider a problem in dynamically constrained Monte Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simple implementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. There are analogies between our formulation of electrostatics and the bosonic Hubbard model in the phase approximation. Cluster methods developed for this model further improve the efficiency of the electrostatics algorithm.

Structural interactions in ionic liquids linked to higher-order Poisson-Boltzmann equations

We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by Bazant et al. [Phys. Rev. Lett. 106, 046102 (2011)]PRLTAO0031-900710.1103/PhysRevLett.106.046102, whereby the structuring near the surface is determined by bulk coefficients.

Truncated correlations in video microscopy of colloidal solids

Studies by video microscopy on fluctuating colloids measure the real-space correlations in particle motion. This set of correlations is then treated as a matrix, in order to study the spectrum and mode structure. We show that in general the deduced modes are modified by the truncation of the full real-space correlations. We perform a theoretical analysis of the truncation, find the boundary conditions imposed by the truncation, and propose practical windowing strategies to eliminate artefacts. We study the problem from various perspectives, to compile a survey for experimentalists.

Elastic fluctuations as observed in a confocal slice

Recent confocal experiments on colloidal solids, as well as jammed and disordered materials, motivate a fuller study of the projection of three-dimensional fluctuations onto a two-dimensional confocal slice. We show that the effective theory of a projected crystal displays several exceptional features, and we give analytic expressions relating three-dimensional elastic constants to observed two-dimensional properties.Recent confocal experiments on colloidal solids motivate a fuller study of the projection of three-dimensional fluctuations onto a two-dimensional confocal slice. We show that the effective theory of a projected crystal displays several exceptional features, such as non-standard exponents in the dispersion relations. We provide analytic expressions for the effective two-dimensional elastic properties which allow one to work back from sliced experimental observations to three-dimensional elastic constants.