An Efficient Algorithm for Truncating Spatial Domain in Modeling Light Scattering by Finite-Difference Technique

The finite-difference time domain technique is one of the most robust and accurate numerical methods for the solution of light scattering by small particles with arbitrary composition and geometry. In practice, this method requires that the spatial domain for the computation of near-field be truncated. An absorbing boundary condition must be imposed in conjunction with this truncation. The performance of this boundary condition is essential to the stability of numerical computations and the reliability of results. In the present study, a new boundary condition, referred to as the mixed T algorithm, has been developed, which is a generalization of the transmitting boundary condition originally developed by Liao and co-workers. The present algorithm does not require spatial interpolation for wave values at interior grid points. In addition, it produces two minima of spurious reflections at small and large incident angles, allowing efficient absorption of the scattered waves at the boundary for large incident angles. When the third-order mixed T algorithm is used, the reflection coefficient of the boundary is less than 1% for incident angles from 0° to about 70°. We find that the numerical instability associated with the transmitting boundary condition is caused by the location-dependent amplitude of outgoing waves in the vicinity of the boundary. For this reason, the mixed T algorithm is stabilized by consistently introducing diffusive coefficients into the boundary equation. When the stabilized algorithm is applied, the near-field within the truncated domain can be computed by using single-precision arithmetic without overflows for more than 10⁵steps in the time-marching iteration. Finally, the new absorbing boundary condition is validated by carrying out numerical experiments involving the propagation of a TM wave excited by a sinusoidal point source, simultaneous simulation of the wave propagation in small and large domains, and the scattering of a TM wave by an infinite circular cylinder.     

An Efficient NMR Experiment for Analyzing Sugar-Puckering in Unlabeled DNA: Application to the 26-kDa Dead Ringer–DNA Complex

We present a new NMR experiment for estimating the type and degree of sugar-puckering in high-molecular-weight unlabeled DNA molecules. The experiment consists of a NOESY sequence preceded by a constant-time scalar coupling period. Two subexperiments are compared, each differing in the amount of time the (3)J(H3'H2') and (3)J(H3'H2") couplings are active on the H3' magnetization. The resultant data are easy to analyze, since a comparison of the signal intensities of any resolved NOE cross peak originating from H3' atoms of the duplex can be used to estimate the sum of the (3)J(H3'H2') and (3)J(H3'H2") couplings and thus the puckering type of the deoxyribose ring. Isotope filters to eliminate signals of the (13)C-labeled component in the F1-dimension are implemented, facilitating analyses of high-molecular-weight protein-DNA complexes containing (13)C-labeled protein and unlabeled DNA. The utility of the experiment is demonstrated on the 26-kDa Dead Ringer protein-DNA complex and reveals that the DNA uniformly adopts the S-type configuration when bound to protein.     

An Efficient Finite Element Method for Computing Spectra of Photonic and Acoustic Band-Gap Materials: I. Scalar Case

The paper describes an efficient finite element method for computing spectra of photonic and acoustic band-gap materials. In the photonic case only the scalar models are treated. The full vector model will be considered in the next publication.     

A New Unconditionally Stable Algorithm for Steady-State Fluid Simulation of High Density Plasma Discharge

A new unconditionally stable algorithm for steady-state fluid simulation of high density plasma discharge is suggested. The physical origin of restriction on simulation time step is discussed and a new method to overcome it is explained. To compare the new method with previous other methods, a one-dimensional fluid simulation of inductively coupled plasma discharge is performed.     

Design and implementation of a protection system for NMR spectrometers

We have implemented a scheme, SPECMON, for monitoring various parameters of a spectrometer, such as nitrogen pressure and sample temperature, and taking corrective action. The scheme is based on considerations of protection management which are of general application. Evaluation of the spectrometer state is incorporated in macros of the application software (VNMR) and is therefore very flexible. In contrast, corrective action is limited to the single one which is deemed fully safe: complete shutdown of the spectrometer and logging. Shutdown is implemented by a minor hardware modification of the spectrometer: the introduction of a second input to a relay already present for protection of the spectrometer power supply. Monitoring is handled by the host computer, and the shutdown command is transmitted via control lines of its series port, independent of the standard connection between the host computer and the NMR system console. The monitoring system (software and hardware) is unobtrusive in normal conditions, and it can be tested without affecting the operation of the spectrometer.     

An Extension of Alias Sampling Method for Parametrized Probability Distributions

An extension of the alias sampling technique for distribution functions depending on a number of parameters was developed. It takes advantage of modern computer architectures with large amounts of cheap memory, by using discrete representations of probability distribution functions. The sampling is done by fast interpolation techniques involving only elementary logical and arithmetical operations, allowing one to keep a higher degree of accuracy as the grids spacing is controlled by the user. By this method it is possible to obtain the value of interest by direct interpolation between the sampled values obtained with the same set of random numbers for the grid values of the parameters adjacent to the values of interest. Sampling tests carried for the case of Molière electron multi-scatter angle distribution show that this method can be successfully used in Monte Carlo codes for sampling complex probability distributions.     

Accurate Measurement of Small Spin–Spin Couplings in Partially Aligned Molecules Using a Novel J-Mismatch Compensated Spin-State-Selection Filter

The accurate measurement of small spin–spin coupling constants in macromolecules dissolved in a liquid crystalline phase is important in the context of molecular structure investigation by modern liquid state NMR. A new spin-state-selection filter, DIPSAP, is presented with significantly reduced sensitivity to J-mismatch of the filter delays compared to previously proposed pulse sequences. DIPSAP presents an attractive new approach for the accurate measurement of small spin–spin coupling constants in molecules dissolved in anisotropic solution. Application to the measurement of ¹⁵N–¹³C′ and ¹H^N–¹³C′ coupling constants in the peptide planes of ¹³C, ¹⁵N labeled proteins demonstrates the high accuracy obtained by a DIPSAP-based experiment.     

An open magnet utilizing ferro-refraction current magnification

Ferro-refraction is the field magnification that is obtained when a current segment is near a high magnetic permeable boundary. It is shown that ferro-refraction may be used in the design of magnets for NMR or MRI to increase the efficiency of these magnets. The field may be modeled analytically with the Biot--Savart law and the inclusion of mirror image currents. Ferro-refraction is particularly useful in the design of monohedral magnets, magnets producing a remote homogeneous region which have the magnetic sources arranged to one side. These magnets have also been called planar magnets. Two designs for a monohedral magnet which produce good agreement between experimental and analytic results are presented.     

A General Deterministic Treatment of Derivatives in Particle Methods

A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection–diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing derivatives near the edge of particle coverage is introduced, using “one-sided” integrals that only look for information where it is available. The use of these integral approximations in wave propagation applications is considered and their error is analyzed in this context using Fourier methods. Finally, simple tests are performed to demonstrate the characteristics of the treatment, including an assessment of the effects of particle dispersion, and their results are discussed.     

An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows

A three-dimensional, incompressible, multiphase particle-in-cell method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to an Eulerian grid and then mapping back computed stress tensors to particle positions. A subgrid particle, normal stress model for discrete particles which is robust and eliminates the need for an implicit calculation of the particle normal stress on the grid is presented. Interpolation operators and their properties are defined which provide compact support, are conservative, and provide fast solution for a large particle population. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. Particles are implicitly coupled to the fluid phase, and the fluid momentum and pressure equations are implicitly solved, which gives a robust solution.     

High-Order Scheme for a Nonlinear Maxwell System Modelling Kerr Effect

This paper is devoted to the derivation of an efficient numerical scheme for the Kerr–Maxwell system. We begin by studying the 1-D Riemann problem. We obtain a result of existence and uniqueness for large data. Then we develop a high-order Roe solver and exhibit solutions in 1-D and 2-D simulations.     

Accurate ω-ψ Spectral Solution of the Singular Driven Cavity Problem

This article provides accurate spectral solutions of the driven cavity problem, calculated in the vorticity–stream function representation without smoothing the corner singularities—a prima facie impossible task. As in a recent benchmark spectral calculation by primitive variables of Botella and Peyret, closed-form contributions of the singular solution for both zero and finite Reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form. The method employed is based on a split approach to the vorticity and stream function equations, a Galerkin–Legendre approximation of the problem for the perturbation, and an evaluation of the nonlinear terms by Gauss–Legendre numerical integration. Results computed for Re=0, 100, and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation–Chebyshev projection method. The validity of the proposed singularity subtraction scheme for computing time-dependent solutions is also established.     

An Error Indicator Monitor Function for an r-Adaptive Finite-Element Method

An r-adaptive finite-element method based on moving-mesh partial differential equations (PDEs) and an error indicator is presented. The error indicator is obtained by applying a technique developed by Bank and Weiser to elliptic equations which result in this case from temporal discretization of the underlying physical PDEs on moving meshes. The construction of the monitor function based on the error indicator is discussed. Numerical results obtained with the current method and the commonly used method based on solution gradients are presented and analyzed for several examples.     

Modeling Three-Dimensional Multiphase Flow Using a Level Contour Reconstruction Method for Front Tracking without Connectivity

Three-dimensional multiphase flow and flow with phase change are simulated using a simplified method of tracking and reconstructing the phase interface. The new level contour reconstruction technique presented here enables front tracking methods to naturally, automatically, and robustly model the merging and breakup of interfaces in three-dimensional flows. The method is designed so that the phase surface is treated as a collection of physically linked but not logically connected surface elements. Eliminating the need to bookkeep logical connections between neighboring surface elements greatly simplifies the Lagrangian tracking of interfaces, particularly for 3D flows exhibiting topology change. The motivation for this new method is the modeling of complex three-dimensional boiling flows where repeated merging and breakup are inherent features of the interface dynamics. Results of 3D film boiling simulations with multiple interacting bubbles are presented. The capabilities of the new interface reconstruction method are also tested in a variety of two-phase flows without phase change. Three-dimensional simulations of bubble merging and droplet collision, coalescence, and breakup demonstrate the new method's ability to easily handle topology change by film rupture or filamentary breakup. Validation tests are conducted for drop oscillation and bubble rise. The susceptibility of the numerical method to parasitic currents is also thoroughly assessed.     

Tailored HCCH-TOCSY experiment for resonance assignment in the proximity of a paramagnetic center

The presence of a paramagnetic center may disturb both coherent and incoherent communication between nuclear spins that are affected, to some extent, by the hyperfine interaction. This is a limiting factor to an extensive use of paramagnetic probes in NMR spectroscopy to enhance partial alignment and to exploit cross correlation effects and pseudocontact shifts. We propose here an HCCH-TOCSY experiment tailored to identify spin systems involving resonances that are partly or completely affected by hyperfine interaction. The efficiency of polarization transfer steps when fast relaxing nuclei are involved is discussed. The sequence is tested for the protein Calbindin D(9k), in which one of the two native Ca2+ ions is replaced by the paramagnetic Ce3+ ion as well as for the oxidized form of cytochrome b(562).     

On Backtracking Failure in Newton–GMRES Methods with a Demonstration for the Navier–Stokes Equations

In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the Navier–Stokes equations with heat and mass transport. Specifically, it was observed that a Newton–GMRES method globalized by backtracking (linesearch, damping) may be less robust when high accuracy is required of each linear solve in the Newton sequence than when less accuracy is required. In this brief discussion, we offer a possible explanation for this phenomenon, together with an illustrative numerical experiment involving the Navier–Stokes equations.     

Determination of the chemical shielding tensor orientation from two or one of the three conventional rotations of a single crystal

Chemical shift anisotropy (CSA) is an immensely useful interaction to study the structure, dynamics, and function of a wide variety of chemical and biological molecules. Traditionally the only unambiguous way to determine both the principal values and the orientation of the principal axes of the CSA tensor has been to follow the chemical shift frequency changes as a crystal of known structure is rotated relative to the direction of the external magnetic field. This classic method employs rotations about three mutually orthogonal axes of a single crystal. It is shown here that just two, or one, of the above rotations suffice to determine the CSA tensor orientation by borrowing, the easy to obtain, principal values of CSA from an independent source. Methods for using two rotation patterns or even a single rotation pattern are described and illustrated with known chemical shielding tensors.     

Multifrequency Probe for Pulsed EPR and ENDOR Spectroscopy

The design, construction, and performance of a multifrequency pulsed EPR and ENDOR probe for use at cryogenic temperatures are described. Interchangeable resonators based on a folded strip line design allow variation of the resonance frequency over a range of 5-11 GHz. Variable coupling to the resonator is achieved capacitively via a simple mechanical adjustment which is thermally and mechanically stable. The entire assembly is robust and easily fabricated. Common methods of analyzing the resonator parameters such as the Q-factor and coupling coefficient are discussed quantitatively. Probe performance data and multifrequency pulsed ENDOR spectra are presented.