Unstructured Adaptive Grid Flow Simulations of Inert and Reactive Gas Mixtures

Unstructured adaptive grid flow simulation is applied to the calculation of high-speed compressible flows of inert and reactive gas mixtures. In the present case, the flowfield is simulated using the 2-D Euler equations, which are discretized in a cell-centered finite volume procedure on unstructured triangular meshes. Interface fluxes are calculated by a Liou flux vector splitting scheme which has been adapted to an unstructured grid context by the authors. Physicochemical properties are functions of the local mixture composition, temperature, and pressure, which are computed using the CHEMKIN-II subroutines. Computational results are presented for the case of premixed hydrogen–air supersonic flow over a 2-D wedge. In such a configuration, combustion may be triggered behind the oblique shock wave and transition to an oblique detonation wave is eventually obtained. It is shown that the solution adaptive procedure implemented is able to correctly define the important wave fronts. A parametric analysis of the influence of the adaptation parameters on the computed solution is performed.     

Divergence- and Curl-Preserving Prolongation and Restriction Formulas

We present new second-order prolongation and restriction formulas which preserve the divergence and, in some cases, the curl of a discretized vector field. The formulas are suitable for adaptive and hierarchical mesh algorithms with a factor-of-2 linear resolution change. We examine both staggered and collocated discretizations for the vector field on two- and three-dimensional Cartesian grids. The new formulas can be used in combination with numerical schemes that require a divergence-free solution in some discrete sense, such as the constrained transport schemes of computational magnetohydrodynamics. We also obtain divergence-preserving interpolation functions which may be used for streamline or field line tracing.     

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.     

Transparent Boundary Conditions for Split-Step Padé Approximations of the One-Way Helmholtz Equation

In this paper, we generalize the nonlocal discrete transparent boundary condition introduced by F. Schmidt and P. Deuflhard (1995, Comput. Math. Appl.29, 53–76) and by F. Schmidt and D. Yevick (1997, J. Comput. Phys.134, 96–107) to propagation methods based on arbitrary Padé approximations of the two-dimensional one-way Helmholtz equation. Our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition, which then yields an unconditionally stable propagation method.     

Particle Transport through Scattering Regions with Clear Layers and Inclusions

This paper introduces generalized diffusion models for the transport of particles in scattering media with nonscattering inclusions. Classical diffusion is known as a good approximation of transport only in scattering media. Based on asymptotic expansions and the coupling of transport and diffusion models, generalized diffusion equations with nonlocal interface conditions are proposed which offer a computationally cheap, yet accurate, alternative to solving the full phase-space transport equations. The paper shows which computational model should be used depending on the size and shape of the nonscattering inclusions in the simplified setting of two space dimensions. An important application is the treatment of clear layers in near-infrared (NIR) spectroscopy, an imaging technique based on the propagation of NIR photons in human tissues.     

Tagging of the Magnetization with the Transition Zones of 360° Rotations Generated by a Tandem of Two Adiabatic DANTE Inversion Sequences

A new technique is presented for generating myocardial tagging using the signal intensity minima of the transition zones between the bands of 0° and 360° rotations, induced by a tandem of two adiabatic delays alternating with nutations for tailored excitation (DANTE) inversion sequences. With this approach, the underlying matrix corresponds to magnetization that has experienced 0° or 360° rotations. The DANTE sequences were implemented from adiabatic parent pulses for insensitivity of the underlying matrix to B₁ inhomogeneity. The performance of the proposed tagging technique is demonstrated theoretically with computer simulations and experimentally on phantom and on the canine heart, using a surface coil for both RF transmission and signal reception. The simulations and the experimental data demonstrated uniform grid contrast and sharp tagging profiles over a twofold variation of the B₁ field magnitude.     

A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes

A new finite volume method is presented for discretizing general linear or nonlinear elliptic second-order partial-differential equations with mixed boundary conditions. The advantage of this method is that arbitrary distorted meshes can be used without the numerical results being altered. The resulting algorithm has more unknowns than standard methods like finite difference or finite element methods. However, the matrices that need to be inverted are positive definite, so the most powerful linear solvers can be applied. The method has been tested on a few elliptic and parabolic equations, either linear, as in the case of the standard heat diffusion equation, or nonlinear, as in the case of the radiation diffusion equation and the resistive diffusion equation with Hall term.     

The Three Dimensional Non-conforming Finite Element Solution of the Chapman–Ferraro Problem

We demonstrate the feasibility of using a non-conforming, piecewise harmonic finite element method on an unstructured grid in solving a magnetospheric physics problem. We use this approach to construct a global discrete model of the magnetic field of the magnetosphere that includes the effects of shielding currents at the outer boundary (the magnetopause). As in the approach of F. R. Toffolettoet al.(1994,Geophys. Res. Lett.21, 7) the internal magnetospheric field model is that of R. V. Hilmer and G.-H. Voigt (1995,J. Geophys. Res.) while the magnetopause shape is based on an empirically determined approximation (1997, J. Shueet al.,J. Geophys. Res.102, 9497). The results is a magnetic field model whose field lines are completely confined within the magnetosphere. The presented numerical results indicate that the discrete non-conforming finite element model is well-suited for magnetospheric field modeling.     

Multiscale Lattice Boltzmann Schemes with Turbulence Modeling

The viability of multiscale lattice Boltzmann schemes for the numerical simulation of turbulent flows is discussed and numerically demonstrated for turboaxial machine applications. The extension of boundary-fitting formulas based on wall functions is proposed, which enables the efficient computation of turbulent flows in complex curvilinear geometry using a simple Cartesian grid. Examples of two-dimensional turbulent flows in an axial compressor cascade are presented.     

Probing Proteins in Solution by Xe NMR Spectroscopy

The interaction of xenon with different proteins in aqueous solution is investigated by ¹²⁹Xe NMR spectroscopy. Chemical shifts are measured in horse metmyoglobin, hen egg white lysozyme, and horse cytochrome c solutions as a function of xenon concentration. In these systems, xenon is in fast exchange between all possible environments. The results suggest that nonspecific interactions exist between xenon and the protein exteriors and the data are analyzed in term of parameters which characterize the protein surfaces. The experimental data for horse metmyoglobin are interpreted using a model in which xenon forms a 1:1 complex with the protein and the chemical shift of the complexed xenon is reported (Locci et al., Keystone Symposia “Frontiers of NMR in Molecular Biology VI”, Jan. 9–15, 1999, Breckenridge, CO, Abstract E216, p. 53; Locci et al., XeMAT 2000 “Optical Polarization and Xenon NMR of Materials”, June 28–30, 2000, Sestri Levante, Italy, p. 46).     

Convection-Diffusion Lattice Boltzmann Scheme for Irregular Lattices

In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the Maxwell–Boltzmann distribution. The axioma holds for both Bravais and irregular lattices, implying a single framework for LB schemes for all lattice types. By solving benchmark problems we have shown that the scheme is indeed consistent with convection diffusion. Furthermore, we have compared the performance of the LB schemes with that of finite difference and finite element schemes. The comparison shows that the LB scheme has a similar performance as the one-step second-order Lax–Wendroff scheme: it has little numerical diffusion, but has a slight dispersion error. By changing the relaxation parameter ω the dispersion error can be balanced by a small increase of the numerical diffusion.     

Determination of membrane Peptide orientation by 1H-detected 2H NMR spectroscopy

We demonstrate the application of the proton inverse detected deuteron (PRIDE) NMR technique to the measurement of the orientation of membrane-bound peptides with enhanced sensitivity. Gramicidin D, a transmembrane peptide, and ovispirin, a surface-bound peptide, were used as model systems. The peptides were 2H-labeled by 1H/2H exchange and oriented uniaxially on glass plates. The directly detected 2H spectra of both peptides showed only a strong D(2)O signal and no large quadrupolar splittings. In contrast, the PRIDE spectrum of gramicidin exhibited quadrupolar splittings as large as 281 kHz, consistent with its transmembrane orientation. Moreover, the large D(2)O signal in the directly detected 2H spectra was cleanly suppressed in the PRIDE spectrum. For ovispirin, the 1H indirectly detected 2H spectrum revealed a 104 kHz splitting and a zero-frequency peak. The former reflects the in-plane orientation of most of the helix axis, while the latter results from residues with a magic-angle orientation of the N-D bonds. These are consistent with previous 15N NMR results on ovispirin. The combination of PRIDE and exchange labeling provides an economical and sensitive method of studying membrane peptide orientations in lipid bilayers without the influence of D(2)O and with the ability to detect N-D bonds at the magic angle from the bilayer normal.     

Analysis of protein/ligand interactions with NMR diffusion measurements: the importance of eliminating the protein background

Pulsed-field gradient nuclear magnetic resonance (PFG-NMR) is a well-established method for the determination of translational diffusion coefficients. Recently, this method has found applicability in the combinatorial arena with the introduction of affinity NMR for characterizing protein/ligand interactions. Although affinity NMR has been reported to be an effective method for the identification of active compounds in a complex mixture, there are limitations of this method. We have developed a simple mathematical model to predict optimum concentration ratios of the ligand and protein in order to observe maximum changes in the ligand diffusion coefficient upon protein binding. The ligand/protein systems of L-tryptophan and ibuprofen binding to human serum albumin were chosen to demonstrate the usefulness of this model. However, even when the conditions of the mathematical model are satisfied, the spectral background arising from the protein in proton-detected experiments can be problematic. To this end, we have employed spectral subtraction of the protein spectrum to yield ligand diffusion coefficients that are in agreement with those predicted by simulation.     

High-Order Nonreflecting Boundary Conditions without High-Order Derivatives

A wave problem in an unbounded domain is often treated numerically by truncating the infinite domain via an artificial boundary , imposing a so-called nonreflecting boundary condition (NRBC) on , and then solving the problem numerically in the finite domain bounded by . A general approach is devised here to construct high-order local NRBCs with a symmetric structure and with only low (first- or second-) order spatial and/or temporal derivatives. This enables the practical use of NRBCs of arbitrarily high order. In the case of time-harmonic waves with finite element discretization, the approach yields a symmetric C⁰ finite element formulation in which standard elements can be employed. The general methodology is presented for both the time-harmonic case (Helmholtz equation) and the time-dependent case (the wave equation) and is demonstrated numerically in the former case.     

NMR spectral quantitation by principal component analysis. III. A generalized procedure for determination of lineshape variations

We present a general procedure for automatic quantitation of a series of spectral peaks based on principal component analysis (PCA). PCA has been previously used for spectral quantitation of a single resonant peak of constant shape but variable amplitude. Here we extend this procedure to estimate all of the peak parameters: amplitude, position (frequency), phase and linewidth. The procedure consists of a series of iterative steps in which the estimates of position and phase from one stage of iteration are used to correct the spectra prior to the next stage. The process is convergent to a stable result, typically in less than 5 iterations. If desired, remaining linewidth variations can then be corrected. Correction of (typically) unwanted variations of these types is important not only for direct peak quantitation, but also as a preprocessing step for spectral data prior to application of pattern recognition/classification techniques. The procedure is demonstrated on simulated data and on a set of 992 (31)P NMR in vivo spectra taken from a kinetic study of rat muscle energetics. The proposed procedure is robust, makes very limited assumptions about the lineshape, and performs well with data of low signal-to-noise ratio.     

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.     

Sensitivity enhancement in structural measurements by solid state NMR through pulsed spin locking

Free induction decay (FID) signals in solid state NMR measurements performed with magic angle spinning can often be extended in time by factors on the order of 10 by a simple pulsed spin locking technique. The sensitivity of a structural measurement in which the structural information is contained in the dependence of the integrated FID amplitude on a preceding evolution period can therefore be enhanced substantially by pulsed spin locking in the signal detection period. We demonstrate sensitivity enhancements in a variety of solid state NMR techniques that are applicable to selectively isotopically labeled samples, including 13C-15N rotational echo double resonance (REDOR), 13C-13C dipolar recoupling measurements using the constant-time finite-pulse radio-frequency-driven recoupling (fpRFDR-CT) and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) techniques, and torsion angle measurements using the double quantum chemical shift anisotropy (DQCSA) technique. Further, we demonstrate that the structural information in the solid state NMR data is not distorted by pulsed spin locking in the detection period.     

2D(13)C-(13)C MAS NMR correlation spectroscopy with mixing by true (1)H spin diffusion reveals long-range intermolecular distance restraints in ultra high magnetic field

An improved 2D (13)C-(13)C CP(3) MAS NMR correlation experiment with mixing by true (1)H spin diffusion is presented. With CP(3), correlations can be detected over a much longer range than with direct (1)H-(13)C or (13)C-(13)C dipolar recoupling. The experiment employs a (1)H spin diffusion mixing period tau(m) sandwiched between two cross-polarization periods. An optimized CP(3) sequence for measuring polarization transfer on a length scale between 0.3 and 1.0 nm using short mixing times of 0.1 ms < tau(m) < 1 ms is presented. For such a short tau(m), cross talk from residual transverse magnetization of the donating nuclear species after a CP can be suppressed by extended phase cycling. The utility of the experiment for genuine structure determination is demonstrated using a self-aggregated Chl a/H(2)O sample. The number of intramolecular cross-peaks increases for longer mixing times and this obscures the intermolecular transfer events. Hence, the experiment will be useful for short mixing times only. For a short tau(m) = 0.1 ms, intermolecular correlations are detected between the ends of phytyl tails and ring carbons of neighboring Chl a molecules in the aggregate. In this way the model for the structure, with stacks of Chl a that are arranged back to back with interdigitating phytyl chains stretched between two bilayers, is validated.     

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.     

Moving Mesh Methods in Multiple Dimensions Based on Harmonic Maps

In practice, there are three types of adaptive methods using the finite element approach, namely the h-method, p-method, and r-method. In the h-method, the overall method contains two parts, a solution algorithm and a mesh selection algorithm. These two parts are independent of each other in the sense that the change of the PDEs will affect the first part only. However, in some of the existing versions of the r-method (also known as the moving mesh method), these two parts are strongly associated with each other and as a result any change of the PDEs will result in the rewriting of the whole code. In this work, we will propose a moving mesh method which also contains two parts, a solution algorithm and a mesh-redistribution algorithm. Our efforts are to keep the advantages of the r-method (e.g., keep the number of nodes unchanged) and of the h-method (e.g., the two parts in the code are independent). A framework for adaptive meshes based on the Hamilton–Schoen–Yau theory was proposed by Dvinsky. In this work, we will extend Dvinsky's method to provide an efficient solver for the mesh-redistribution algorithm. The key idea is to construct the harmonic map between the physical space and a parameter space by an iteration procedure. Each iteration step is to move the mesh closer to the harmonic map. This procedure is simple and easy to program and also enables us to keep the map harmonic even after long times of numerical integration. The numerical schemes are applied to a number of test problems in two dimensions. It is observed that the mesh-redistribution strategy based on the harmonic maps adapts the mesh extremely well to the solution without producing skew elements for multi-dimensional computations.