Mass Flux Schemes and Connection to Shock Instability

We analyze numerical mass fluxes with an emphasis on their capability for accurately capturing shock and contact discontinuities. The study of mass flux is useful because it is the term common to all conservation equations and the numerical diffusivity introduced in it bears a direct consequence to the prediction of contact (stationary and moving) discontinuities, which are considered to be the limiting case of the boundary layer. We examine several prominent numerical flux schemes and analyze the structure of numerical diffusivity. This leads to a detailed investigation into the cause of certain catastrophic breakdowns by some numerical flux schemes. In particular, we identify the dissipative terms that are responsible for shock instabilities, such as the odd–even decoupling and the so-called “carbuncle phenomenon”. As a result, we propose a conjecture stating the connection of the pressure difference term to these multidimensional shock instabilities and hence a cure to those difficulties. The validity of this conjecture has been confirmed by examining a wide class of upwind schemes. The conjecture is useful to the flux function development, for it indicates whether the flux scheme under consideration will be afflicted with these kinds of failings. Thus, a class of shock-stable schemes can be identified. Interestingly, a shock-stable scheme's self-correcting capability is demonstrated with respect to carbuncle-contaminated profiles for flows at both low supersonic and high Mach numbers.     

Dynamics of Spin I=3/2 under Spin-Locking Conditions in an Ordered Environment

We have derived approximate analytic solutions to the master equation describing the evolution of the spin I=3/2 density operator in the presence of a radio-frequency (RF) field and both static and fluctuating quadrupolar interactions. Spectra resulting from Fourier transformation of the evolutions of the on-resonance spin-locked magnetization into the various coherences display two satellite pairs and, in some cases, a central line. The central line is generally trimodal, consisting of a narrow component related to a slowly relaxing mode and two broad components pertaining to two faster relaxing modes. The rates of the fast modes are sensitive to slow molecular motion. Neither the amplitude nor the width of the narrow component is affected by the magnitude of the static coupling, whereas the corresponding features of the broad components depend in a rather complicated manner on the spin-lock field strength and static quadrupolar interaction. Under certain experimental conditions, the dependencies of the amplitudes on the dynamics are seen to vanish and the relaxation rates reduce to relatively simple expressions. One of the promising emerging features is the fact that the evolutions into the selectively detected quadrupolar spin polarization order and the rank-two double-quantum coherence do not exhibit a slowly relaxing mode and are particularly sensitive to slow molecular motion. Furthermore, these coherences can only be excited in the presence of a static coupling and this makes it possible to discern nuclei in anisotropic from those in isotropic environment. The feasibility of the spin-lock pulse sequences with limited RF power and a nonvanishing average electric field gradient has been demonstrated through experiments on sodium in a dense lyotropic DNA liquid crystal.     

Linewidth-Resolved N HSQC, a Simple 3D Method to Measure N Relaxation Times from T1 and T2 Linewidths

A three-dimensional approach for measuring ¹⁵N relaxation times is described. Instead of selecting particular values for the relaxation period, in the proposed method the relaxation period is incremented periodically in order to create a 3D spectrum. This additional frequency domain of the transformed spectrum contains the relaxation time information in the T₁ and T₂ linewidths, and thus the longitudinal and transverse ¹⁵N relaxation times can be measured without determination of 2D cross peak volumes/intensities and subsequent curve fitting procedures.     

Implementation Aspects of 3D Lattice-BGK: Boundaries, Accuracy, and a New Fast Relaxation Method

In many realistic fluid-dynamical simulations the specification of the boundary conditions, the error sources, and the number of time steps to reach a steady state are important practical considerations. In this paper we study these issues in the case of the lattice-BGK model. The objective is to present a comprehensive overview of some pitfalls and shortcomings of the lattice-BGK method and to introduce some new ideas useful in practical simulations. We begin with an evaluation of the widely used bounce-back boundary condition in staircase geometries by simulating flow in an inclined tube. It is shown that the bounce-back scheme is first-order accurate in space when the location of the non-slip wall is assumed to be at the boundary nodes. Moreover, for a specific inclination angle of 45 degrees, the scheme is found to be second-order accurate when the location of the non-slip velocity is fitted halfway between the last fluid nodes and the first solid nodes. The error as a function of the relaxation parameter is in that case qualitatively similar to that of flat walls. Next, a comparison of simulations of fluid flow by means of pressure boundaries and by means of body force is presented. A good agreement between these two boundary conditions has been found in the creeping-flow regime. For higher Reynolds numbers differences have been found that are probably caused by problems associated with the pressure boundaries. Furthermore, two widely used 3D models, namelyD₃Q₁₅andD₃Q₁₉, are analysed. It is shown that theD₃Q₁₅model may induce artificial checkerboard invariants due to the connectivity of the lattice. Finally, a new iterative method, which significantly reduces the saturation time, is presented and validated on different benchmark problems.     

Angular Flow in Toroid Cavity Probes

NMR signals from samples that rotate uniformly about the central conductor of a TCD (toroid cavity detector) exhibit frequency shifts that are directly proportional to the sample's angular velocity. This newly observed effect is based on the unique radiofrequency field inside TCDs, which is variable in direction. If a liquid sample is pumped through a capillary tube wound about the central conductor, the frequency shift is proportional to the flow rate. A mathematical relationship between a volumetric flow rate and the frequency shift is established and experimentally verified to high precision. Additionally, two-dimensional flow-resolved NMR spectroscopy for discrimination between components with different flow velocities yet retaining chemical shift information for structural analysis is presented. The application of the two-dimensional method in chromatographic NMR is suggested. Furthermore, utilization of the frequency-shift effect for rheologic studies if combined with toroid-cavity rotating-frame imaging is proposed.     

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.     

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.     

H NMR Characterization of the Product from Single Solid-Phase Resin Beads Using Capillary NMR Flow Probes

A capillary NMR flow probe was designed to generate high-resolution ¹H NMR spectra at 600 MHz from the cleaved product of individual 160-μm Tentagel combinatorial chemistry beads. By injecting a dissolved sample sandwiched between an immiscible, perfluorinated organic liquid directly into the probe, NMR spectra of the product cleaved from single beads were acquired in just 1 h of spectrometer time without diffusional dilution. Sample handling efficiency on the single bead scale was comparable to that obtained with a bulk sample. Using the relative intensity of the DMSO-d₅H versus the analyte signals in a fully relaxed CPMG spectrum, the amount of product cleaved from a single bead was determined to be 540±170 pmol in one of the samples. Following the NMR data collection, the samples were examined with electrospray ionization mass spectrometry to provide additional structural information. By coupling with microliter-volume fluidic capabilities, the capillary flow probe described here will enable multidimensional characterization of single solid-phase resin products in an online manner.     

Separating Structure and Dynamics in CSA/DD Cross-Correlated Relaxation: A Case Study on Trehalose and Ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of ¹³C CSA and ¹³C–¹H dipolar coupling in a disaccharide, α,α- -trehalose, at natural abundance of ¹³C as well as interference of amide ¹⁵N CSA and ¹⁵N–¹H dipolar coupling in uniformly ¹⁵N-labeled ubiquitin. We demonstrate that the standard heteronuclear T₁, T₂, and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

Multigrid Solution of the Incompressible Navier–Stokes Equations for Density-Stratified Flow past Three-Dimensional Obstacles

The steady incompressible Navier–Stokes equations in three dimensions are solved for neutral and stably stratified flow past three-dimensional obstacles of increasing spanwise width. The continuous equations are approximated using a finite volume discretisation on staggered grids with a flux-limited monotonic scheme for the advective terms. The discrete equations which arise are solved using a nonlinear multigrid algorithm with up to four grid levels using the SIMPLE pressure correction method as smoother. When at its most effective the multigrid algorithm is demonstrated to yield convergence rates which are independent of the grid density. However, it is found that the asymptotic convergence rate depends on the choice of the limiter used for the advective terms of the density equation, and some commonly used schemes are investigated. The variation with obstacle width of the influence of the stratification on the flow field is described and the results of the three-dimensional computations are compared with those of the corresponding computation of flow over a two-dimensional obstacle (of effectively infinite width). Also given are the results of time-dependent computations for three-dimensional flows under conditions of strong static stability when lee-wave propagation is present and the multigrid algorithm is used to compute the flow at each time step.     

IR Spectrum of C8H2: Integrated Band Intensities and Some Observational Implications

Polyynes are of astrophysical interest since they appear to be involved in organic chemistry in very different mediums. In Titan's atmosphere, the lightest polyyne, C₄H₂, was detected by Voyager. Recently C₄H₂ and C₆H₂ have been discovered in a protoplanetary nebula, suggesting polyynes as a possible chemical pathway to PAH (polycyclic aromatic hydrocarbons). Moreover, several experimental simulations and modeling imply their production from the photochemistry of methane and their involvement in the formation of organic aerosols. After the study of C₄H₂ and C₆H₂ spectra in the UV and IR wavelength range, we report here the first spectrum of gaseous C₈H₂ in the range 400–4000 cm⁻¹ at room temperature and low resolution. The task was hardly achieved because of the high instability of this molecule with temperature and pressure. To avoid exothermic polymerization, the compound as mixed with a solvent. We have performed a separate spectroscopic study of the solvent to determine C₈H₂ partial pressure within the mixture. This allowed us to calculate C₈H₂ integrated band intensities. In the studied wavelength range, C₈H₂ presents three main bands similar to those of C₆H₂ in terms of vibrational type, position, and relative intensity. To study the possible identification of these polyynes by spatial observatories (Cassini–Huygens, ISO), we have also measured the C₆H₂ and C₈H₂ infrared spectra in the range 400–1500 cm⁻¹ at 0.35 cm⁻¹ resolution.     

Signal enhancement in 5QMAS spectra of spin-5/2 quadrupolar nuclei

5QMAS experiments on spin-5/2 systems display a low sensitivity compared with their 3QMAS counterparts. Nevertheless, the superior resolution of 5QMAS over 3QMAS makes these experiments a favorable choice for many materials. We report an enhancement scheme for the 5QMAS experiment, using an improved five-quantum excitation pulse scheme combined with a FAM-II conversion pulse. The results are verified experimentally on a polycrystalline sample of gamma-(27)Al(2)O(3), showing an enhancement factor of 2.4 over the simple two-pulse (CW) 5QMAS scheme. Numerical computations of the efficiency parameter epsilon support these results.     

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.     

Phase-Accuracy Comparisons and Improved Far-Field Estimates for 3-D Edge Elements on Tetrahedral Meshes

Edge-element methods have proved very effective for 3-D electromagnetic computations and are widely used on unstructured meshes. However, the accuracy of standard edge elements can be criticised because of their low order. This paper analyses discrete dispersion relations together with numerical propagation accuracy to determine the effect of tetrahedral shape on the phase accuracy of standard 3-D edge-element approximations in comparison to other methods. Scattering computations for the sphere obtained with edge elements are compared with results obtained with vertex elements, and a new formulation of the far-field integral approximations for use with edge elements is shown to give improved cross sections over conventional formulations.     

Relaxation Behavior of Laser-Polarized Xe Gas: Size Dependency and Wall Effect of the T1 Relaxation Time in Glass and Gelatin Bulbs

Size dependency of the relaxation time T₁ was measured for laser-polarized ¹²⁹Xe gas encapsulated in different sized cavities made by glass bulbs or gelatin capsules. The use of laser-polarized gas enhances the sensitivity a great deal, making it possible to measure the longer ¹²⁹Xe relaxation time in quite a short time. The size dependency is analyzed on the basis of the kinetic theory of gases and a relationship is derived in which the relaxation rate is connected with the square inverse of the diameter of the cavity. Such an analysis provides a novel parameter which denotes the wall effect on the relaxation rate when a gas molecule collides with the surface once in a second. The relaxation time of ¹²⁹Xe gas is also dependent on the material which forms the cavity. This dependency is large and the relaxation study using polarized ¹²⁹Xe gas is expected to offer important information about the state of the matter of the cavity wall.     

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.     

Millimeter-Wave Spectroscopy, High-Resolution Infrared Spectrum, ab Initio Calculations, and Molecular Geometry of FPS

The transient thiophosphenous fluoride FPS was produced by pyrolysis of 2.5% F₂PSPF₂ in Ar at 1300–1800°C. High-resolution (≥0.004 cm⁻¹) Fourier transform infrared spectra of the a-type ν₁ and b-type ν₂ bands, centered respectively at 803.249 and 726.268 cm⁻¹, were measured and fitted to rotational and quartic centrifugal distortion parameters. The millimeter-wave spectrum, essentially b-type, was measured between 300 and 370 GHz in the ground state and in the ν₃ excited state for FP³²S and in the ground state for FP³⁴S. The frequencies were fitted to a Watson-type A-reduced Hamiltonian up to sextic distortion terms. High level ab initio calculations with large basis sets were performed on FPS and supported the first identification of its infrared and millimeter wave spectra. The calculated anharmonic force field provided precise ab initio rovibrational α constants which were combined with the experimental molecular parameters to determine an accurate equilibrium structure of the molecule: r_e(PS)=188.86 pm, r_e(PF)=158.70 pm, θ(FPS)=109.28°. The collision-controlled 1/e lifetime measured in a 10-Pa (1 : 20) F₂PSPF₂/Ar mixture was 2 s, more than two orders of magnitude larger than that of FPO under the same experimental conditions.     

Measurement of Small One-Bond Proton–Carbon Residual Dipolar Coupling Constants in Partially Oriented C Natural Abundance Oligosaccharide Samples: Analysis of Heteronuclear JCH-Modulated Spectra with the BIRD Inversion Pulse

Two 2D J-modulated HSQC-based experiments were designed for precise determination of small residual dipolar one-bond carbon–proton coupling constants in ¹³C natural abundance carbohydrates. Crucial to the precision of a few hundredths of Hz achieved by these methods was the use of long modulation intervals and BIRD pulses, which acted as semiselective inversion pulses. The BIRD pulses eliminated effective evolution of all but ¹J_CH couplings, resulting in signal modulation that can be described by simple modulation functions. A thorough analysis of such modulation functions for a typical four-spin carbohydrate spin system was performed for both experiments. The results showed that the evolution of the ¹H–¹H and long-range ¹H–¹³C couplings during the BIRD pulses did not necessitate the introduction of more complicated modulation functions. The effects of pulse imperfections were also inspected. While weakly coupled spin systems can be analyzed by simple fitting of cross peak intensities, in strongly coupled spin systems the evolution of the density matrix needs to be considered in order to analyse data accurately. However, if strong coupling effects are modest the errors in coupling constants determined by the “weak coupling” analysis are of similar magnitudes in oriented and isotropic samples and are partially cancelled during dipolar coupling calculation. Simple criteria have been established as to when the strong coupling treatment needs to be invoked.     

Simultaneous selective detection of multiple quantum spectra

A three-dimensional multiple-quantum NMR experiment that produces individual spectra of all quantum orders is described. The separation of different quantum orders is accomplished via Fourier transformation with respect to the phase of the first two pulses of a generic three-pulse multiple-quantum sequence. This dramatically reduces the time required to obtain several selectively detected spectra and enhances the sensitivity and digital resolution from that obtained using the original two-dimensional technique. The experiment is demonstrated on the protons of para-chlorotoluene dissolved in the nematic liquid crystal Merck ZLI-1132.     

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.