Mixtures of lattice polymers with structured monomers

The influence of monomer structure on the thermodynamic properties of lattice model polymer blends is investigated through Monte Carlo computations. The model of lattice polymers with monomer structure has been used extensively in the context of the lattice cluster theory (LCT), a thermodynamic theory for polymer mixtures in the liquid state. The Monte Carlo computations provide the first unequivocal test of the accuracy of the LCT predictions for binary mixtures of polymers with structured monomers. Four types of monomer structures are analyzed, corresponding to to the monomers of polyethylene, polypropylene, polyethylethylene, and polyisobutylene (PIB). Most computations use chains with M=12 and 24 beads and the total volume fraction of the beads is phi=0.6. Both structurally symmetric and asymmetric blends are investigated. For the symmetric case, the predictions of the LCT for the energies of mixing and the liquid-liquid coexistence curves are in qualitative agreement with the Monte Carlo computations, except for the PIB/PIB symmetric blend. For structurally asymmetric blends, the LCT does not capture contributions to the energy of mixing arising solely from structural differences between the components. Computational estimates of the nonideal entropy of mixing indicate that the LCT also underestimates the entropic cost of mixing chains with different structures, thus explaining some discrepancies between the theoretical and the Monte Carlo liquid--liquid coexistence curves.     

Protein structure determination using long-distance constraints from double-quantum coherence ESR: study of T4 lysozyme

We report the use of a novel pulsed ESR technique for distance measurement, based on the detection of double quantum coherence (DQC), which yields high quality dipolar spectra, to significantly extend the range of measurable distances in proteins using nitroxide spin-labels. Eight T4 lysozyme (T4L) mutants, doubly labeled with methanethiosulfonate spin-label (MTSSL), have been studied using DQC-ESR at 9 and 17 GHz. The distances span the range from 20 A for the 65/76 mutant to 47 A for the 61/135 mutant. The high quality of the dipolar spectra also allows the determination of the distance distributions, the width of which can be used to set upper and lower bounds in future computational strategy. It is also demonstrated that the shape of these distributions can reveal the presence of multiple conformations of the spin-label, an issue of critical relevance to the structural interpretation of the distances. The distances and distributions found in this study are readily rationalized in terms of the known crystal structure, the characteristic conformers of the nitroxide side chains, and molecular modeling. This study sets the stage for the use of DQC-ESR for determining the tertiary structure of large proteins with just a small number of long-distance constraints.     

Comparison of low-order multireference many-body perturbation theories

Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.     

Oxygen effects on the EPR signals from wood charcoals: experimental results and the development of a model

Charcoals prepared from certain tropical woods contain stable paramagnetic centers, and these have been characterized by EPR spectroscopy in the absence and presence of oxygen. The EPR-detectable spin density has been determined, as has been the temperature- and frequency-dependence of the oxygen broadening of the EPR signal, which is orders of magnitude larger than that observed with other materials, such as lithium phthalocyanine. Three Lorentzian components are required to fit the char EPR spectrum in the presence of oxygen, and the oxygen-dependence of the line width, intensity, and resonance position of the three components have been quantified. These results and the properties of porous carbonaceous materials are used to develop a model to explain the effect of oxygen on the char EPR spectral properties. The model is based on oxygen adsorption on the char surface according to a Langmuir isotherm and a dipolar interaction between the paramagnetic adsorbed gas and the charcoal spins. The three EPR components are correlated with the three known classes (sizes) of pores in charcoal, with the largest line broadening attributed to dipolar relaxation of spins in micropores, which have a larger specific surface area and a higher concentration of adsorbed oxygen. An attenuated, but similar, EPR response to oxygen by chars when they are immersed in aqueous solution is attributed to water competition with oxygen for adsorption on the char surface.     

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.     

Invariants de Maslov équivariants

We construct two cohomological invariants associated to pairs of Lagrangian sub-bundles of a symplectic bundle on a compact manifold upon which a compact Lie group is acting. The first invariant, which we call the classical equivariant Maslov H-invariant, provides an obstruction to Lagrangian transversality and lives in the Borel cohomology. The second invariant, which we call the equivariant Maslov U-invariant, generalises the author's results in K-Theory 13 (1998), 347–361 to the equivariant context and provides a necessary and sufficient condition for equivariant Lagrangian transversality, up to homotopic stability, and lives in the U-theory (intermediate between the real complex K-theories). As an application, we show that two Lagrangian sub-bundles of a symplectic bundle on a homogeneous space are always stably transverse.     

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.     

A 236 GHz Fe3+ EPR Study of Nanoparticles of the Ferromagnetic Room-Temperature Semiconductor Sn1−x Fe x O2 (x = 0.005)

High-frequency (236 GHz) electron paramagnetic resonance (EPR) studies of Fe³⁺ ions at 255 K are reported in a Sn_1?x Fe _x O₂ powder with x = 0.005, which is a ferromagnetic semiconductor at room temperature. The observed EPR spectrum can be simulated reasonably well as the overlap of spectra due to four magnetically inequivalent high-spin (HS) Fe³⁺ ions (S = 5/2). The spectrum intensity is calculated, using the overlap I(BL) + (I(HS1) + I(HS2) + I(HS3) + I(HS4)) × exp(?0.00001B), where B is the magnetic field intensity in Gauss, I represents the intensity of an EPR line (HS1, HS2, HS3, HS4), and BL stands for the baseline (the exponential factor, as found by fitting to the experimental spectrum, is related to the Boltzmann population distribution of energy levels at 255 K, which is the temperature of the sample in the spectrometer). These high-frequency EPR results are significantly different from those at X-band. The large values of the zero-field splitting parameter (D) observed here for the four centers at the high frequency of 236 GHz are beyond the capability of X-band, which can only record spectra of ions with much smaller D values than those reported here.     

Simulating electron spin resonance spectra of nitroxide spin labels from molecular dynamics and stochastic trajectories

Simulating electron spin resonance spectra of nitroxide spin labels from motional models is necessary for the quantitative analysis of experimental spectra. We present a framework for modeling the spin label dynamics by using trajectories such as those from molecular dynamics (MD) simulations combined with stochastic treatment of the global protein tumbling. This is achieved in the time domain after two efficient numerical integrators are developed: One for the quantal dynamics of the spins and the other for the classical rotational diffusion. For the quantal dynamics, we propagate the relevant part of the spin density matrix in Hilbert space. For the diffusional tumbling, we work with quaternions, which enables the treatment of anisotropic diffusion in a potential expanded as a sum of spherical harmonics. Time-averaging arguments are invoked to bridge the gap between the smaller time step of the MD trajectories and the larger time steps appropriate for the rotational diffusion and/or quantal spin dynamics.     

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].