Forward scattering theory of electric-field-gradient-induced birefringence

We attempt to resolve the discrepancy between the Buckingham—Longuet-Higgins (BLH) and Imrie—Raab (IR) theories of linear birefringence induced in a gas of dipolar molecules by an electric field gradient. To this end we present a new calculation of the effect, based on forward scattering of a light beam incident on a thin lamina of gas molecules. We work to electric quadrupole—magnetic dipole order. The beam undergoes a time delay which is proportional to the thickness of the lamina and the electric field gradient, and can therefore be interpreted in terms of a contribution to the refractive index of the gas due to the field gradient. The birefringence is obtained by considering appropriate polarizations of the incident beam. To avoid the occurrence of a divergent quantity, such as appears in the BLH theory, it is essential to take account of the finite beam width. Calculations are performed using both primitive (traced) and traceless molecular quadrupole moments; as required on basic grounds, these results are equivalent. They are also identical to the BLH result. By contrast, the IR result is physically unacceptable because it is not invariant with respect to the use of traced and traceless moments. The source of error in the IR theory remains unclear.     

On the theory of the Buckingham effect

We apply general arguments (based on spatial transformation properties, intrinsic symmetry and dimensional analysis) to the theory of the Buckingham effect (electric-field–gradient-induced birefringence in a gas). These yield, in a simple manner, the temperature-dependent and temperature-independent terms in the birefringence (each to within a numerical factor), and also the expression, derived by Buckingham and Longuet-Higgins, for the effective quadrupole centre of a molecule. We show in addition how the calculation of the two numerical factors can be simplified in our approach.     

Hlder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

A Hilbert transform for Hlder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in R2n , has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hlder exponents, the diameter of Γ and a specific d-sum (d d) of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.     

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.     

MODELING HARVEST SCHEDULING IN MULTIFUNCTIONAL PLANNING OF FORESTS FOR LONGTERM WATER YIELD OPTIMIZATION

In this study, wood production and hydrologic functions of forests were accommodated within a planning procedure for separate working circles (areas dedicated to certain forest functions) that were delineated according to an Ecosystem‐Based Functional Planning approach. Mixed integer goal programming was used as the optimization technique. The timing and scheduling of a maintenance cutting (partial harvest) was the decision variable in the modeling effort, and an original formulation was developed as a multiobjective planning procedure. Four sample planning strategies were developed and model outputs were evaluated according to these strategies. Spatial characteristics of stands were considered, and used to prohibit the regeneration of adjacent stands during the same time period. Because of the positive relationship between qualified water production and standing timber volume in the forest, the model attempts to maximize qualified water production levels by increasing standing volume stocks in the forest through the delay of regeneration activities.     

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.     

Beyond Flory-Huggins theory: new classes of blend miscibility associated with monomer structural asymmetry

Flory-Huggins (FH) theory is restricted to polymer mixtures whose monomers are structurally identical, a situation limited to isotopic blends and computer simulations. We investigate the influence of monomer structure on blend miscibility and scattering properties using the lattice cluster theory generalization of the FH model. Monomer structural asymmetry is shown to profoundly affect blend miscibility (T(c),phi(c)), chain swelling (T(theta)), and the scale (xi) and intensity [S(0)] of composition fluctuations. Four distinct blend miscibility classes are identified and experimental evidence for these classes is discussed.     

Variable-frequency EPR study of Mn(2+)-doped NH(4)Cl(0.9)I(0.1) single crystal at 9.6, 36, and 249.9 GHz: structural phase transition

Multifrequency electron paramagnetic resonance studies on the Mn(2+) impurity ion in a mixed single crystal NH(4)Cl(0.9)I(0.1) were carried out at 9.62 (X-band) in the range 120-295 K, at 35.87 (Q-band) at 77 and 295 K, and at 249.9 GHz (far-infrared band) at 253 K. The high-field EPR spectra at 249.9 GHz are well into the high-field limit leading to a considerable simplification of the spectra and their interpretation. Three magnetically inequivalent, but physically equivalent, Mn(2+) ions with their respective magnetic Z-axes oriented along the crystallographic [100], [010], [001] axes were observed. Simultaneous fitting of EPR line positions observed at X-, Q-, and far infra-red bands was performed using a least-squares procedure and matrix diagonalization to estimate accurately the Mn(2+) spin-Hamiltonian parameters. The temperature variation of the linewidth and peak-to-peak intensities of the EPR lines indicate the presence of lambda-transitions in the mixed NH(4)Cl(0.9)I(0.1) crystal at 242 and 228 K consistent with those observed in the pure NH(4)Cl and NH(4)I crystals, respectively. A superposition-model analysis of the spin-Hamiltonian parameters reveals that the local environment of the Mn(2+) ion is considerably reorganized to produce axially symmetric crystal fields about the respective Z-axes of the three magnetically inequivalent ions as a consequence of the vacancy created due to charge-compensation when the divalent Mn(2+) ion substitutes for a monovalent NH(4)(+) ion in the NH(4)Cl(0.9)I(0.1) crystal. This reorganization is almost the same as that observed in NH(4)Cl and NH(4)I single crystals, although the latter two are characterized by different, simple cubic and face-centered cubic, structures.