Spectral Order Research Articles

Aqueous dispersions of cholesteric liquid crystals and their optical properties

This paper reports on a theoretical and experimental investigation of light transmission by a layer of aqueous suspension of polymer dispersed cholesteric liquid crystals (CLC) with a helical molecular structure. The transmission spectra and the spectral order parameter of the supramolecular texture of CLC confirm the high degree of ordering of CLC molecules in the spherical cells. Cell morphology and the spectral dependences of light transmission by the plane-parallel layer of CLC aqueous dispersion are considered.

NMR and molecular structure of partially oriented mono and <i>para</i> methyl- and chlorobenzenes dissolved in nematic liquid crystals

Spectral parameters, order parameters, and structural parameters, including the vibrationally corrected ralpha structure of the partially oriented solutes p-xylene, p-chlorotoluene, p-dichlorobenzene, toluene, and chlorobenzene dissolved in three liquid crystal mixtures, are reported. For samples containing the three solutes p-xylene, p-dichlorobenzene, and 1,3,5-trichlorobenzene, multiple quantum (MQ) nuclear magnetic resonance was used to aid in the analysis of the complex high-resolution spectra of the p-xylene. The high-resolution spectra of 1,3,5-trichlorobenzene and p-dichlorobenzene were easily identified and analyzed once the calculated p-xylene spectrum was subtracted from the experimental one. The methyl groups of p-xylene, p-chlorotoluene, and toluene have similar geometries when the structure is determined from dipolar couplings corrected for harmonic vibrations.Key words: nematic liquid crystal, NMR, molecular structure, order parameter.

MIXED hp-FEM ON ANISOTROPIC MESHES

Mixed hp-FEM for incompressible fluid flow on anisotropic meshes are analyzed. A discrete inf–sup condition is proved with a constant independent of the meshwidth and the aspect ratio. For each polynomial degree k≥2 we present velocity-pressure subspace pairs which are stable on quadrilateral mesh-patches independently of the element aspect ratio, implying in particular divergence stability on the so-called Shishkin-meshes. Moreover, the inf–sup constant is shown to depend on the spectral order k like k-1/2 for quadrilateral meshes and like k-3 for meshes containing triangles. New consistency results for spectral elements on anisotropic meshes are also proved.

Book Review: Proceedings of the Third International Conference on Spectral and High Order Methods

Book Review: Proceedings of the Third International Conference on Spectral and High Order Methods

Simulating the Performance of Michelson- and Sagnac-based Laser Interferometric Gravitational Wave Detectors in the Presence of Mirror Tilt and Curvature Errors

We model the behaviour of single-bounce delay-line dual recycled Sagnac-based interferometer and compare its performance with that of single-bounce Michelson-based system. Geometric imperfections such as mirror tilt and curvature mismatch can strongly influence the performance of the Sagnac device due to the inherently smaller free spectral range (FSR) and higher order mode spacing. This leads to a greater number of higher order modes near, or within the signal band in the signal recycling cavity of the instrument. The important consequence of that is, in general, a greater sensitivity of a Sagnac system to nonideal parameters and imperfections of various kind affecting the performance of a real interferometer. A number of optical configurations have also been examined numerically to determine the best possible optical arrangement, in the presence of such geometric imperfections. We show that there is an optimum choice for the nominal radius of curvature of the end mirrors which results from balancing the loss due to mirror tilt against that due to curvature mismatch.

Parallel Domain Decomposition Solver for Adaptive hp Finite Element Methods

In this paper, the development and implementation of highly parallelizable domain decomposition solvers for adaptive hp finite element methods is discussed. Two-level orthogonalization is used to obtain a reduced system which is preconditioned by a coarse grid operator. The condition number of the preconditioned system, for Poisson problems in two space dimensions, is proved to be bounded by C(1 + Hp/h)2(1 + log p)2 and Cp(1 + Hp/h)2(1 + log p)2 for different choices of coarse grid operators, where H is the subdomain size, p is the maximum spectral order, h is the size of the smallest element in the subdomain, and C is a constant independent of the mesh parameters. The work here extends the work of Bramble et al. [Math Comp., 47 (1986), pp. 103--134] on the h-version and Babuska et al. [SIAM J. Numer. Anal., 29 (1991), pp. 624--661] on the p-version of the finite element method. A preliminary version of this solver was first announced by Oden, Patra, and Feng in [Domain Decomposition Solver for Adaptive hp Finite Elements, VII Conference on Domain Decomposition, State College, PA, October 1993]. Numerical experiments show fast convergence of the solver and good control of the condition number on a variety of discretizations.

On the Optimal Number of Subdomains for Hyperbolic Problems on Parallel Computers

The computational complexity for parallel implementation of multidomain spectral methods is studied to derive the optimal number of subdomains, q, and spectral order, n, for the numerical solution of hyperbolic problems. The complexity analysis is based on theoretical results that predict error as a function of (q,n) for problems having wavelike solutions. These are combined with a linear com munication cost model to study the impact of communica tion overhead and imposed granularity on the optimal choice of ( q,n) as a function of the number of processors. It is shown that, for present-day multicomputers, the im pact of communication overhead does not significantly shift ( q,n) from the optimal uniprocessor values and that the effects of granularity are more important.

Higher order moment processing of laser Doppler perfusion signals

The laser Doppler technique is used to assess tissue perfusion. Traditionally an integrated, v-weighted (firstorder filter) power spectrum is used to estimate perfusion. In order to be able to obtain selective information about the flow in vessels with different blood cell velocities, higher order filters have been implemented, investigated, and evaluated. Theoretical considerations show that the output of the signal processor will depend on the flow speed, for a given concentration of blood cells, according to Sout}vn where v is the average blood cell speed and n is the spectral filter order. An implementation of filters using zero-, first-, second-, and third-order spectral moments was utilized to experimentally verify the theory by using a laser Doppler perfusion imager. Two different flow models were utilized: A Plexiglas model was used to demonstrate the various signatures of the power spectrum for different flow speeds and filter orders, whereas a Delrin model was used to study the relationship between the flow velocity and the output of the signal processor for the different filters. The results show good agreement with theory and also good reproducibility. Recordings made on the skin of the wrist area demonstrated that the flow in small veins can be visualized by the use of higher spectral orders.

Higher order moment processing of laser Doppler perfusion signals

The laser Doppler technique is used to assess tissue perfusion. Traditionally an integrated, v-weighted (firstorder filter) power spectrum is used to estimate perfusion. In order to be able to obtain selective information about the flow in vessels with different blood cell velocities, higher order filters have been implemented, investigated, and evaluated. Theoretical considerations show that the output of the signal processor will depend on the flow speed, for a given concentration of blood cells, according to Sout}vn where v is the average blood cell speed and n is the spectral filter order. An implementation of filters using zero-, first-, second-, and third-order spectral moments was utilized to experimentally verify the theory by using a laser Doppler perfusion imager. Two different flow models were utilized: A Plexiglas model was used to demonstrate the various signatures of the power spectrum for different flow speeds and filter orders, whereas a Delrin model was used to study the relationship between the flow velocity and the output of the signal processor for the different filters. The results show good agreement with theory and also good reproducibility. Recordings made on the skin of the wrist area demonstrated that the flow in small veins can be visualized by the use of higher spectral orders.

Liquid-crystal projection image depixelization by spatial phase scrambling

A technique that removes the pixel structure by scrambling the relative phases among multiple spatial spectra is described. Because of the pixel structure of the liquid-crystal-display (LCD) panel, multiple spectra are generated at the Fourier-spectrum plane (usually at the back focal plane of the imaging lens). A transparent phase mask is placed at the Fourier-spectrum plane such that each spectral order is modulated by one of the subareas of the phase mask, and the phase delay resulting from each pair of subareas is longer than the coherent length of the light source, which is approximately 1 μm for the wideband white light sources used in most of LCD's. Such a phase-scrambling technique eliminates the coherence between different spectral orders; therefore, the reconstructed images from the multiple spectra will superimpose incoherently, and the pixel structure will not be observed in the projection image.

Identification of Isomeric Naphthyl-Anthracenes Generated from the Pyrolysis of an Anthracene/Naphthalene Mixture

Abstract A 1:1 mole-ratio mixture of anthracene and naphthalene was pyrolyzed in a drop-tube furnace. the product mixture was analyzed by high performance liquid chromatography with diode-array, UV-absorption spectrometric detection (HPLC/DAD) and by gas chromatography/mass spectrometry (GCMS). In addition to previously characterized bianthracene and binaphthalene isomers, 6 isomeric naphthyl-anthracenes were identified. Because of the unavailability of standard reference compounds, structural elucidation was achieved by comparing UV spectral features, mass spectral fragmentation patterns, and GCMS and HPLC elution order with those for bianthracenes, binaphthalenes and other structurally similar molecules. In addition, steric hindrance to rotation at the naphthalene-anthracene bond, a factor that governs the degree of non-planarity of the isomers and thus influences HPLC elution order and MS fragmentation patterns, was estimated using a semi-empirical molecular orbital model.

Application of Diode Array Detection with a C-30 Reversed Phase Column for the Separation and Identification of Saponified Orange Juice Carotenoids

Thirty-nine carotenoid pigments in saponified orange (Citrus sinensis) juice were separated using a water, methanol, methyl-tert-butyl ether gradient on a non-endcapped C-30 reversed phase column. Pigments were extracted using the International Fruit Juice Union method for orange juice carotenoids, which employs precipitation with Carrez reagent and resolubilizing with acetone. Chromatographic resolution, Rs, between lutein and zeaxanthin was 2.9. Pigments were identified on the basis of diode array spectral characteristics, retention times, and relative elution order compared to authentic standards and literature values. An examination of the diode array data from the chromatographically resolved peaks indicated that the most useful information could be obtained from monitoring the chromatographic effluent at 350, 430, and 486 nm. More carotenoid peaks were detected at 430 nm, but greater selectivity for several carotenoids was obtained at 350 and 486 nm. At 430 nm the six largest carotenoid peaks observ...

Minimal upper bounds of commuting operators

Let ( x i ) (x_{i}) be a finite collection of commuting self-adjoint elements of a von Neumann algebra M \mathcal {M} . Then within the (abelian) C*-algebra they generate, these elements have a least upper bound x x . We show that within M \mathcal {M} , x x is a minimal upper bound in the sense that if y y is any self-adjoint element such that x i ≤ y ≤ x x_{i} \leq y \leq x for all i i , then y = x y = x . The corresponding assertion for infinite collections ( x i ) (x_{i}) is shown to be false in general, although it does hold in any finite von Neumann algebra. We use this sort of result to show that if N ⊂ M \mathcal {N} \subset \mathcal {M} are von Neumann algebras, Φ : M → N \Phi : \mathcal {M} \to \mathcal {N} is a faithful conditional expectation, and x ∈ M x \in \mathcal {M} is positive, then Φ ( x n ) 1 / n \Phi (x^{n})^{1/n} converges in the strong operator topology to the “spectral order majorant” of x x in N \mathcal {N} .

High-precision wavelength measurements of the 1s2 1S-1snp 1P resonance lines in He-like nitrogen and oxygen

Spectra of C, N and O have been generated simultaneously by focusing 1 GW laser pulses on targets made of either ammonium hydrogen carbonate or ammonium oxalate. These materials, in the form of compressed powders, were found to give significantly smaller linewidths than more conventional targets such as boron nitride or aluminium oxide. The wavelengths of the 1s2 1S-1snp 1P (n=2-4) resonance lines in N VI and O VII (17-30 AA) have been determined with uncertainties ranging from 0.2 to 0.7 mAA, by measurements in up to the 8th spectral order. Previous experimental results are confirmed, but the substantially increased accuracy of the present values reveals small but significant and systematic discrepancies with theoretical predictions for the 1s2 1S-1s2p 1P transition in N VI and O VII.

A comparison of autoregressive spectral estimation algorithms and order determination methods in ultrasonic tissue characterization

Several autoregressive (AR) methods for spectral estimation were applied toward the task of estimating ultrasonic backscatter coefficients from small volumes of tissue. Data were acquired from a homogeneous tissue-mimicking phantom and from a normal human liver in vivo. AR methods performed better at short record lengths than the traditional DFT (discrete Fourier Transform) approach. The DFT method consistently underestimated backscatter coefficients at small gate lengths. Burg's algorithm, the Modified Covariance algorithm, and the Recursive Maximum Likelihood Estimation algorithm performed comparably. The Yule-Walker algorithm did not perform as well as these but offered a slight improvement over the DFT. Several order determination methods were tested. These included residual variance (RV), final prediction error (FPE), Akaike information criterion (AIC), and Minimum Description Length (MDL). The AIC and MDL produced misleading results at higher orders. The RV and FPE yielded better results. The autoregressive method offers promise for enhanced spatial resolution and accuracy in ultrasonic tissue characterization and nondestructive evaluation of materials.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spectral and rank order approaches to texture analysis

AbstractThere are two major approaches to texture analysis, both supported by physiological evidence: those based on the spatial statistics, and those based on its spectral properties. One of the most sophisticated spectral approaches to texture is that based on the Wigner distribution where the attributes computed for each pixel encapsulate both the local spectral and phase properties of the local Fourier transform in a unique real spectrum. On the other hand, some of the most efficient methods which operate in the spatial domain alone, are those based on rank order functions. Before one embarks on the use of the sophisticated methods, it is worth exploring the efficient ones to the limit of their performance. In this paper we investigate these two major approaches and compare their performance both in terms of quality of results and efficiency. The problem we consider is that of detecting defective blobs and cracks on complex textural backgrounds. We show that in most cases rank order approaches can perform well, although no unique method can be employed for both types of defects. On the other hand, the Wigner approach with a very small modification can cope with both types of defects and handle even the identification of very subtle cracks. Thus, it seems that for any real time performance inspection system, the rank order approaches should form the front end with the more sophisticated methods coming in play when necessary.

Complex wavenumber Fourier analysis of the p-version finite element method

High-order finite element discretizations of the reduced wave equation have frequency bands where the solutions are harmonic decaying waves. In these so called “stopping” bands, the solutions are not purely propagating (real wavenumbers) but are attenuated (complex wavenumbers). In this paper we extend the standard dispersion analysis technique to include complex wavenumbers. We then use this complex Fourier analysis technique to examine the dispersion and attenuation characteristics of the p-version finite element method. Practical guidelines are reported for phase and amplitude accuracy in terms of the spectral order and the number of elements per wavelength.

Bilayer packing characteristics of mixed chain phospholipid derivatives: Raman spectroscopic and differential scanning calorimetric studies of 1-stearoyl-2-capryl- sn-glycero-3-phosphocholine (C(18) : C(10)PC) and 1-stearoyl-2-capryl- sn-glycero-3-phospho- N-trimethylpropanolamine (C(18) : C(10)TMPC)

Raman spectroscopy and high-sensitivity differential scanning calorimetry (DSC) were used to compare the effects of headgroup conformation on the acyl chain packing arrangements in two highly asymmetric phosphatidylcholine (PC) analogues 1-stearoyl-2-capryl- sn-glycero-3-phosphocholine (C(18) : C(10)PC) and a polar headgroup derivative of C(18): C(10)PC, 1-stearoyl-2-capryl- sn-glycero-3-phospho- N-trimethylpropanolamine (C(18):C(10)TMPC), which contains an additional methylene group within the choline moiety; namely, PO(CH 2) 3N(CH 3) 3. The C(18): C(10)TMPC headgroup exhibits an extended trans conformation which is independent of bilayer phase. A comparison of gel phase spectral order parameters of the two lipid species indicates a mixed interdigitated state characteristic of three chains per headgroup for C(18):C(10)TMPC. A more intermolecularly ordered liquid crystalline phase is observed, however, for the C(18):C(10)TMPC bilayers. The phase transition cooperative unit size estimated for the C(18):C(10)PC bilayers (≈ 140 molecules per unit) is about 7-fold greater than that for the C(18):C(10)TMPC dispersions (≈ 20 molecules per unit). We suggest that the extended headgroup for C(18):C(10)TMPC induces a slight tilt in the gel phase packing arrangements for the acyl chains, which may persist in the partially interdigitated liquid crystalline phase bilayer. Macroscopically, tighter packed multilamellar dispersions of C(18):C(10)TMPC occur for systems prepared first in the presence of a higher ionic strength medium. The stacked bilayers may then be transferred to a lower ionic strength environment without loss of their more closely packed adjacent lamellae.

TESTS OF LIQUID-CRYSTAL SCREENS FOR USE IN MULTI-OBJECT SLIT SPECTROSCOPY

ABSTRACT We examined the use of liquid-crystal (LC) technology to build an easily reconfigurable focal-plane slit system for multi-object spectroscopy (MOS). Several kinds of LC screens were analyzed in a spectrophotometer and at the focus of the spectrograph on the 24-inch telescope at Sommers-Bausch Observatory (SBO) on the CU Boulder campus. Depending on the crystal material used, transmission can be as high as > 80% in the clear state across the visible spectrum, and constrast ratios (ratio of clear- to opaque-state transmission) of >100:1 can be attained, but high contrast and high transmission are not both present in the same LCs. While significant difficulties exist in fabricating LCs as competitive MOS focal plane slits, there exist no fundamental obstacles to implementing this technology in an astronomical setting. The major problems for currently avaiable LCs include: 1. In order to obtain clear-state transmission of > 80% across one free spectral order, even the best contrast ratios currently available for a single screen ( 100:1) are not good enough for faint-object spectroscopy. 2. To use the LC types which yield high clear-state transmission, thin-film transistors (TFTs) must be used to address individual pixels. Currently, development costs for such devices are quite high, though remanufacture costs are low. Based on our tests, by stacking two screens of the best LCs currently available, an LC MOS slit assembly could be configured to give a clear-state transmission of 50-70% across the optical band with off-state opacities approaching 10 magnitudes in that same range. While these specifications are already competitive with other MOS schemes currently in use, the major drawback of an LC MOS at this time appears to be obtaining sufficient opacity between slits to obtain accurate sky subtraction.

A broadband dual slant strip grating for elimination of specular reflection of em waves

Conventional corrugated surfaces and strip gratings are used for eliminating specular reflections from a conducting surface for TE or TM polarization waves. This article presents the development of a dual slant strip grating for the elimination of specular reflections from conducting surfaces for both TE and TM polarizations, with an enhancement in bandwidth. Perfect blazing for n= -1 spectral order is also provided by the system.