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.     

Analysis of the CH3D Nonad from 2000 to 3300 cm

As part of the simultaneous analysis of line positions and intensities of the first two polyads of monodeuterated methane, the results achieved for the region 3-5 μm are reported. It involves the three highest fundamentals, (ν₁, ν₂, ν₄), overlapped by overtone (2ν₃, 2ν₅, 2ν₆) and combination (ν₃+ν₆, ν₃+ν₅, ν₅+ν₆) bands. The theoretical model was based on the global tensorial model implemented in the MIRS package. Some 10 000 line positions and 2400 line intensities have been modeled to ±0.000 88 cm⁻¹ and ±3.6% respectively, using measurements obtained at 0.0056 and 0.011 cm⁻¹ resolution with the Fourier transform spectrometer at National Solar Observatory located at Kitt Peak. The strongest band in this polyad is ν₄(E) at 3016.7 cm⁻¹ with a strength of 6.3×10⁻¹⁸ cm⁻¹/(molecule cm⁻²) at 296 K; the weakest band is 2ν₃(E) at 2597.7 cm⁻¹ with a strength of 1.9×10⁻²⁰ cm⁻¹/(molecule cm⁻²) at 296 K. The total calculated absorption arising from the CH₃D nonad is 8.95×10⁻¹⁸ cm⁻¹/(molecule cm⁻²) at 296 K.     

Dynamical versus variational symmetries: understanding Noether's first theorem

It is argued that awareness of the distinction between dynamical and variational symmetries is crucial to understanding the significance of Noether's 1918 work. Special attention is paid, by way of a number of striking examples, to Noether's first theorem, which establishes a correlation between dynamical symmetries and conservation principles.     

A determination of zeeman parameters for NO2 in its ground state

Extensive measurements of magnetic dipole transitions in the gas phase E.P.R. spectrum of NO₂ in its [Xtilde] ² A ₁ state are reported. This type of transition was first identified by Burch, Tanttila and Mizushima. The data have been fitted simultaneously with measurements from the far infra-red laser magnetic resonance spectrum of NO₂ to determine the principal components of the electron spin g-tensor. The results are consistent with Curl's relationship between the components of the electron spin and spin-rotation tensors. It is necessary to include the effects of centrifugal distortion of the spin-rotation interaction and two parameters describing this interaction are determined in the course of the analysis. Some discussion of the origins of these parameters is included.     

Anharmonic corrections for linear triatomic molecules subject to the Rennet-Teller effect

The effects of vibrational anharmonic terms and of the g_K -correction on the energy levels of a triatomic molecule in a degenerate electronic state are considered. The electronic wavefunctions are described using the approach first suggested in the original paper of Renner. Formulae for the anharmonic corrections in a number of different situations are derived. For an electronic Π state the corrections are given in the form where i runs over the various contributions and x ₁, x ₂, … depend on the anharmonic force constants. The functions F_i can be determined numerically (see equations (4.3) and 4.7)). For the case without spin-orbit interaction the F_i s are given explicitly to first order in ∈ in table 1. Further-more, the same results apply for levels with |K|=v ₂+1 even if the spinorbit interaction is not negligible. Explicit results for levels with |K|<v ₂ including spin-orbit interaction are given in tables 2 and 3. The cases with larger values for Λ (2, 3, …) are also considered. The energy level formulae for a Δ state differ from those derived earlier by Merer and Travis. In particular, the small separation between the vibronic Φ and Π levels with v ₂=1 is now found to be 4g_K . The additional terms that arise from end-over-end rotation of the molecule are discussed in § 6.     

Texture development and deformation mechanisms during uniaxial straining of U–Nb shape-memory alloys

The shape–memory effect is well documented in uranium–niobium alloys near the α″–γ^o metastable phase boundary. In situ neutron diffraction measurements during uniaxial loading indicate that U–14?at.%?Nb (in the α″ monoclinic phase field) deforms by stress–induced twin reorientation. Alternatively, U–16?at.%?Nb (initially γ^o tetragonal) undergoes a stress–induced phase transformation to the α″ monoclinic phase. The crystallographic texture of the monoclinic phase of both compositions has been measured and qualitatively interpreted by considering the orientation relationship between the most favoured α′′ variant and the parent phase. In addition, previously published observations of deformation structures within the shape–memory regime of a U–13?at.%?Nb alloy are discussed within the context of the same model.     

Opportunities with Synchrotron Radiation at the Mesoscale

What is mesoscale science? The modifier “meso” can mean different things to different communities. In many areas of science, “mesoscale” generally refers to a middle-ground domain of length, energy, or time where theories accurate at both lower and higher scales fail. In materials science, for example, mesoscale behavior often rises when quantum behavior begins to fade, collective effects become important, or statistical variation and defects appear, often at length scales larger than a few nm. However, for atmospheric scientists and ecologists, mesoscale means miles. For meterologists, mesoscale means hundreds to thousands of miles. The mesoscale arena for cosmologists is many light-years across.     

High-sensitivity,fiber-optic,flexural disk hydrophone with reduced acceleration response

Abstract

A hydrophone consisting of a hollow cylinder whose flexible, circular end plates are bonded to pairs of pat, spiral wound coils of optical fiber is described. When the end plate/disk is deformed due to a pressure difference, the outer and inner fiber coils experience opposite strains resulting in a “push—pull” optical path length difference which is detected in an all-fiber Michelson interferometer. The close proximity of the interferometric fiber coils, separated by the thin thermally conducting end plate, rejects thermal gradient-induced signals. The addition of a second identical end plate and fiber coil pair at the opposite end of the cylinder will double the acoustic sensitivity while canceling acceleration induced signals. The calculated and measured optical strain of a single simply supported plate, single-coil sensor (8.0 cm diameter, 3.0 mm thickness) using static pressure, acoustic pressure, and acceleration are in good agreement and yield a sensitivity of 0.21 rad/Pa (ΔΦ/ΦΔP = -301 dB re I μPa-1) below its resonance frequency of 3 kHz. The calculated and measured strain for a dual clamped disk (4.5 cm diameter, 1.0 mm thickness) acceleration-canceling sensor with four 8-m coils are in good agreement also and yield a sensitivity of 1.0 rad/Pa (ΔΦ/ΦpΔP = -291 dB re 1 μPa^?1) below the disk resonance frequency of 4.5 kHz. These are the highest fiber-optic, omnidirectional hydrophone sensitivities reported to date.     

A critique of the disturbance theory of indeterminacy in quantum mechanics

Heisenberg'sgendanken experiments in quantum mechanics have given rise to a widespread belief that the indeterminacy relations holding for the variables of a quantal system can be explained quasiclassically in terms of a disturbance suffered by the system in interaction with a quantal measurement, or state preparation, agent. There are a number of criticisms of this doctrine in the literature, which are critically examined in this article and found to be ininconclusive, the chief error being the conflation of this disturbance with the projection postulate. We present a critique of the disturbance theory based on the fact that the required disturbance will in general depend on the interaction time of the system and state-preparer. This point is exploited in the construction of a spin-interaction model which acts as a counterexample to the disturbance doctrine, while remaining faithful to the spirit of Heisenberg'sgedanken experiments. Several consequences of this result are discussed.This work formed part of a thesis submitted by one of us (HRB) in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the University of London.