E.S.R. and D.S.C. investigations of phase transitions in polymorphic 4-n-alkoxybenzylidene-4′-n-alkylanilines

Abstract

It is shown that the McMillan parameter M = T _SAN/T _N1 (where T _SAN and T _NI are respectively the temperatures of the smectic A to nematic (SAN) and the nematic to isotropic (NI) phase transitions) is useful in analysing the crossover between second and first order behaviour of the S_NN transition in the nO.m homologous liquid crystal series (the 4-n-alkoxybenzylidene-4′-n-alkylanilines). Using a phase diagram of orientational ordering versus M for this series, as obtained in this work (from E.S.R. and D.S.C), a symmetric tricritical point with mean field exponent β₂ = 1 is demonstrated. In a preliminary study of E.S.R. linewidth parameters B and C of nitroxide spin probes dissolved in members of the nO.m series exhibiting a first order S_AN transition, critical-type divergences are observed near this transition. In the case where M is closer to 0.959 (the value at the tricritical point), these divergences appear similar to those previously observed in related nO.m members with a second order S_AN transition; however, they are considerably enhanced for an M value closer to unity (i.e. more removed from the tricritical point). This indicates the importance of coupling between orientational and positional order parameters in the observed critical-type divergences.     

Calculation of Double-Quantum-Coherence Two-dimensional Spectra: Distance Measurements and Orientational Correlations

The double-quantum-coherence (DQC) echo signal for two coupled nitroxides separated by distances ?10 Å, is calculated rigorously for the six-pulse sequence. Successive application of six pulses on the initial density matrix, with appropriate inter-pulse time evolution and coherence pathway selection leaves only the coherent pathways of interest. The amplitude of the echo signal following the last π pulse can be used to obtain a one-dimensional (1D) dipolar spectrum (Pake doublet), and the echo envelope can be used to construct the 2D DQC spectrum. The calculations are carried out using the product space spanned by the two electron-spin magnetic quantum numbers m ₁, m ₂ and the two nuclear-spin magnetic quantum numbers M ₁, M ₂, describing, e.g. two coupled nitroxides in bilabeled proteins. The density matrix is subjected to a cascade of unitary transformations taking into account dipolar and electron exchange interactions during each pulse and during the evolution in the absence of a pulse. The unitary transformations use the eigensystem of the effective spin Hamiltonians obtained by numerical matrix diagonalization. Simulations are carried out for a range of dipolar interactions, D, and microwave magnetic field strength B ₁ for both fixed and random orientations of the two ¹⁴N (and ¹⁵N) nitroxides. Relaxation effects were not included. Several examples of 1D and 2D Fourier transforms of the time-domain signals versus dipolar evolution and spin-echo envelope time variables are shown for illustration. Comparisons are made between 1D rigorous simulations and analytical approximations. The rigorous simulations presented here provide insights into DQC electron spin resonance spectroscopy, they serve as a standard to evaluate the results of approximate theories, and they can be employed to plan future DQC experiments.     

Auditory correlates of perceived mallet hardness for a set of recorded percussive sound events

A psychophysical investigation of timbre was undertaken with the intent of deriving quantitative results that could be useful in musical applications. Recordings of metal objects being struck with percussion mallets were rated by subjects on a unidimensional perceptual scale of perceived mallet hardness. Four acoustical parameters of the attack portion (first 325 ms) were defined and evaluated as predictors of perceived mallet hardness rating. To measure these parameters, a critical-band filter bank was employed. Two curves were extracted from the filter-bank output: (1) spectral level (log of area under spectrum) over time, and (2) spectral centroid over time. For each curve, two parameters were measured: the mean and the slope of the spectral level curve, and the mean and the time-weighted average of the spectral centroid curve. Multiple regression analysis was used to relate the perceptual ratings to these four acoustical parameters, and a good fit was achieved (multiple R-squared = 0.725, F = 1135.8, p less than 0.01). The resulting function is suitable for quantitatively predicting the perceptual dimension of perceived mallet hardness.     

CGC using a programmable electronic pressure controller

Capillary gas chromatographic separations were performed with an electronic pressure control system developed to provide precise closed-loop control of inlet pressure through the use of a solid state micro-machined pressure sensor and electronically controlled proportional valve. The closed-loop control of the electronic system provided better precision than the open-loop control achieved by manual pressure regulation. Closed-loop control can perform pressure programming, which can be combined with temperature programming to optimize separations. The pressure sensor monitors the integrity of the flow system and singals the controller to reduce flow in the presence of a sudden loss of system pressure.     

Twisted equivariant K-theory with complex coefficients

Using a global version of the equivariant Chern character, wedescribe the complexified twisted equivariant K-theory of aspace with a compact Lie group action in terms of fixed-pointdata. We apply this to the case of a compact group acting onitself by conjugation and relate the result to the Verlindealgebra and to the Kac numerator at q=1. Verlinde's formulais also discussed in this context. Received February 28, 2007.     

The plastic compressibility of 7075-T651 aluminum-alloy plate

The change in volume, and therefore the change in mass density, of an aluminum alloy was measured in uniaxial tension using clip-on extensometers. The experimental data do not agree with the assumption of plastic incompressibility found in the classical theories of plasticity. In fact, the elastic and plastic volume changes are of the same order of magnitude. Plastic anisotropy is thought to be the prime cause of this plastic compressibility.     

Dispersion of T1 and T2 Nuclear Magnetic Resonance Relaxation in Crude Oils

Crude oils, which are complex mixtures of hydrocarbons, can be characterized by nuclear magnetic resonace diffusion and relaxation methods to yield physical properties and chemical compositions. In particular, the field dependence, or dispersion, of T₁ relaxation can be used to investigate the presence and dynamics of asphaltenes, the large molecules primarily responsible for the high viscosity in heavy crudes. However, the T₂ relaxation dispersion of crude oils, which provides additional insight when measured alongside T₁, has yet to be investigated systematically. Here we present the field dependence of T₁‐T₂ correlations of several crude oils with disparate densities. While asphaltene and resin‐containing crude oils exhibit significant T₁ dispersion, minimal T₂ dispersion is seen in all oils. This contrasting behavior between T₁ and T₂ cannot result from random molecular motions, and thus, we attribute our dispersion results to highly correlated molecular dynamics in asphaltene‐containing crude oils.     

The analysis of elliptic families

In this paper we specialize the results obtained in [BF1] to the case of a family of Dirac operators. We first calculate the curvature of the unitary connection on the determinant bundle which we introduced in [BF1].We also calculate the odd Chern forms of Quillen for a family of self-adjoint Dirac operators and give a simple proof of certain results of Atiyah-Patodi-Singer on êta invariants.We finally give a heat equation proof of the holonomy theorem, in the form suggested by Witten [W 1, 2].     

A variable temperature EPR study of Mn-doped NH4Cl0.9I0.1 single crystal at 170 GHz: Zero-field splitting parameter and its absolute sign

EPR measurements have been carried out on a single crystal of Mn(2+)-doped NH(4)Cl(0.9)I(0.1) at 170-GHz in the temperature range of 312-4.2K. The spectra have been analyzed (i) to estimate the spin-Hamiltonian parameters; (ii) to study the temperature variation of the zero-field splitting (ZFS) parameter; (iii) to confirm the negative absolute sign of the ZFS parameter unequivocally from the temperature-dependent relative intensities of hyperfine sextets at temperatures below 10K; and (iv) to detect the occurrence of a structural phase transition at 4.35K from the change in the structure of the EPR lines with temperature below 10K.     

A derivation of the exact pi-electron hamiltonian

The exact pi-electron hamiltonian is derived from the full many-electron Schrödinger equation. The derivation employs techniques which also enable the development of open shell generalized perturbation theory. The parameters occurring in the pi-hamiltonian are therefore amenable to calculation using the approximate theories and methods of Sinano?lu, Nesbet, Kelly, etc. To a good approximation, the pi-hamiltonian is found to be generally consistent with its customarily assumed form.