Effective cell-centred time-domain Maxwell's equations numerical solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed. © 2004 Elsevier Inc. All rights reserved.

Determination of chromophore charge states in the low pH color transition of the fluorescent protein Rtms5(H146S) via time-dependent DFT

The red fluorescent protein Rtms5H146S displays a transition from blue (absorbance λmax 590 nm) to yellow (absorbance λmax not, vert, similar453 nm) upon titration to low pH. The pKa of the reaction depends on the concentration of halide, offering promise for new expressible halide sensors. The protonation state involved in the low pH form of the chromophore remains, however, ambiguous. We report calculated excitation energies of different protonation states of an RFP chromophore model. These suggest that the relevant titration site is the phenoxy moiety of the chromophore, and the relevant base and conjugate acid are anionic and neutral chromophore species, respectively.

Transparent boundary conditions for wave propagation on unbounded domains

The numerical solution of the time dependent wave equation in an unbounded domain generally leads to a truncation of this domain, which requires the introduction of an artificial boundary with associated boundary conditions. Such nonreflecting conditions ensure the equivalence between the solution of the original problem in the unbounded region and the solution inside the artificial boundary. We consider the acoustic wave equation and derive exact transparent boundary conditions that are local in time and can be directly used in explicit methods. These conditions annihilate wave harmonics up to a given order on a spherical artificial boundary, and we show how to combine the derived boundary condition with a finite difference method. The analysis is complemented by a numerical example in two spatial dimensions that illustrates the usefulness and accuracy of transparent boundary conditions.

Fluctuations and single molecules

The fluorescence of single molecules coupled to a thermal bath is studied both experimentally and theoretically. The effect of different fluctuations on the coherence properties of resonance fluorescence is considered first. Coherence is measured in an interference experiment where a single molecule is used as a light source. A standard approach based on the optical Bloch equations apparently provides quite an accurate description of the interference experiment. Systems with long correlation times (where spectra are time dependent on any timescale) are considered next. It is shown that intensity-time-frequency correlation spectroscopy, which provides both high signal-to-noise ratio and high time resolution, is very suitable for such a case. The Bloch equations are further tested in an experiment where the shape of an excitation spectral line of a single molecule is accurately measured over six orders of magnitude of the exciting laser power. Significant deviations from the predictions of the Bloch equations are found. The role of critical parameters-the correlation time of the bath, the Rabi oscillation period, and the coupling constant between the bath and the molecule-is discussed. The paper also includes a short general introduction to the methodology of single-molecule studies.

A time-harmonic target-field method for designing unshielded RF coils in MRI

Time-harmonic methods are required in the accurate design of RF coils as operating frequency increases. This paper presents such a method to find a current density solution on the coil that will induce some desired magnetic field upon an asymmetrically located target region within. This inverse method appropriately considers the geometry of the coil via a Fourier series expansion, and incorporates some new regularization penalty functions in the solution process. A new technique is introduced by which the complex, time-dependent current density solution is approximated by a static coil winding pattern. Several winding pattern solutions are given, with more complex winding patterns corresponding to more desirable induced magnetic fields.

DOSY NMR studies of chemical exchange behavior of poly(2-hydroxyethyl methacrylate)

PFG-NMR was used to study the chemical exchange of linear PHEMA having a range of molecular weights with water in DMSO containing varying quantities of water. The aim was to investigate the use of PFG-NMR to study chemical exchange between a polymer with exchangeable protons and a small fast diffusing molecule to provide insight into the conformation adopted by a polymer in solution. The experimental data were simulated closely for the two-site exchange case using the Bloch equations modified for chemical exchange and diffusion. The exchange rate could be used to detect changes in polymer conformation resulting from changes in the solvent. PHEMA of MW 10 000 showed significant time-dependent changes in exchange rate, resulting from preferential solvation of the OH sites by water, and subsequent conformational changes which altered accessibility of the OH sites to water. This behavior was not observed for larger MW PHEMA, which adopted a stable conformation immediately. Large changes in the exchange rate were not reflected in changes to the hydrodynamic radius, suggesting that a minimal overall change in the chain dimensions occurred. DMSO was found to be a poor solvent for PHEMA, which adopts a compact conformation in DMSO. This work has demonstrated that PFG-NMR is a sensitive method for detecting subtle changes in polymer conformation in polymers with exchangeable protons.