Local simulation algorithms for Coulomb gases with dynamical dielectric effects.

We discuss the application of the local lattice technique of Maggs and Rossetto [Phys. Rev. Lett. 88, 196402 (2002)] to problems that involve the motion of objects with different dielectric constants than the background. In these systems, the simulation method produces a spurious interaction force which causes the particles to move in an unphysical manner. We show that this term can be removed using a variant of a method known from high-energy physics simulations, the multiboson method, and demonstrate the effectiveness of this corrective method on a system of neutral particles. We then apply our method to a one-component plasma to show the effect of the spurious interaction term on a charged system.

Improved local lattice approach for Coulombic simulations.

An improved approach to the simulation of strongly fluctuating Coulomb gases, based on a local lattice technique introduced by Maggs and Rossetto [A.C. Maggs and V. Rossetto, Phys. Rev. Lett. 88, 196402 (2002)], is described and then tested in a problem of biophysical interest. The low acceptance rates for charged particle moves in regimes of physical interest are increased to a serviceable level by use of a coupled particle-field update procedure in the new method. Sensitivity of the results to lattice discretization effects is also studied using asymmetric lattices.

Three-dimensional Poisson-Nernst-Planck theory studies: influence of membrane electrostatics on gramicidin A channel conductance.

A recently introduced real-space lattice methodology for solving the three-dimensional Poisson-Nernst-Planck equations is used to compute current-voltage relations for ion permeation through the gramicidin A ion channel embedded in membranes characterized by surface dipoles and/or surface charge. Comparisons to a variety of experimental results, presented herein, have proven largely successful. Strengths and weaknesses of the method are discussed.

A theoretical description of microdialysis with mass transport coupled to chemical events.

A random-walk simulation of microdialysis is used to examine how a reaction that consumes analyte in the medium external to the probe affects the extraction and recovery processes. The simulations suggest that such a reaction can promote the extraction process while simultaneously inhibiting the recovery process, which appears to be consistent with recent experimental evidence of asymmetry in the extraction and recovery of the neurotransmitter, dopamine, during brain microdialysis. This suggests that quantitative microdialysis strategies that rely on the extraction fraction as a measure of the probe recovery value, such as the no-net-flux method, will produce an underestimate of the analyte concentration in the external medium when that analyte is consumed by a reaction in the external medium. Furthermore, if experimental conditions arise under which the kinetics of the reaction are changed, then changes in the extraction and recovery processes are likely to occur as well. The implications of these theoretical findings for the quantitative interpretation of in vivo microdialysis results obtained for the neurotransmitter dopamine are examined.

A lattice relaxation algorithm for three-dimensional Poisson-Nernst-Planck theory with application to ion transport through the gramicidin A channel.

A lattice relaxation algorithm is developed to solve the Poisson-Nernst-Planck (PNP) equations for ion transport through arbitrary three-dimensional volumes. Calculations of systems characterized by simple parallel plate and cylindrical pore geometries are presented in order to calibrate the accuracy of the method. A study of ion transport through gramicidin A dimer is carried out within this PNP framework. Good agreement with experimental measurements is obtained. Strengths and weaknesses of the PNP approach are discussed.

Statistical mechanics of charged polymers in electrolyte solutions: a lattice field theory approach.

The lattice field theory approach to the statistical mechanics of a classical Coulomb gas [R.D. Coalson and A. Duncan, J. Chem. Phys. 97, 5653 (1992)] is generalized to include charged polymer chains. Saddle-point analysis is done on the functional integral representing the partition function of the full system. Mean-field level analysis requires extremization of a real-valued functional which possesses a single minimum, thus guaranteeing a unique solution. The full mean-field equations for such a coupled system are derived, as well as the leading (one-loop) fluctuation corrections. Two different numerical real-space lattice procedures are developed to implement the generalized theory; these are applied to the problem of a charged polymer confined to a spherical cavity in an electrolyte solution. The results provide insight into the physics of confined polyelectrolytes.

Optimal control theory for optical waveguide design: application to Y-branch structures.

A recently introduced optimal control theory method for optical waveguide design is applied to Y-branch waveguides and Mach-Zehnder modulators. The method simultaneously optimizes many parameters in a chosen design scheme; computational effort scales mildly with the number of parameters considered. Significant improvement in guiding efficiency relative to intuitively reasonable initial parameter choices is obtained in all cases.