Effects of H2O and D2O on polyproline II helical structure

The interaction of solvent with a polypeptide chain is one of the primary factors controlling protein folding and stability. In biologically relevant systems, this solvent is most often water. Experimental estimates of the role of water in peptide folding can be obtained from solvent perturbation experiments. The simplest perturbant for H2O water is its isotopic D2O form. The solvation of peptides known to form PII helices with D2O versus H2O increases their propensity to adopt the PII conformation.     

Light quarks and instantons

Instantons and anti-instantons can profoundly influence the structure of a non-Abelian gauge theory involving N flavors of massless quarks. Interactions of the quarks with these pseudoparticles can spontaneously generate a quark mass, break the theory's SU(N) × SU(N) chiral symmetry and bind quark-antiquark pairs to form N² ? 1 Goldstone bosons. If the spontaneously generated quark mass is small, multipseudoparticle configurations can be treated in a dilute gas approximation.     

X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

A study of correlation functions for the delta-function Bose gas

The Gel'fand-Levitan equation for the quantum nonlinear Schrödinger field theory is used to investigate the correlation functions of the delta-function Bose gas. Operator expressions are derived for the field and for nonlocal products of fields in terms of the quantized reflection operators which create and annihilate eigenstates of the Hamiltonian. For the two-point function, an explicit series expression is obtained in which the nth term is determined by well-defined n-body combinatorics in an infinite volume. The inductive properties of this series are discussed and used to express the temperature and chemical potential dependence of the correlation functions entirely in terms of previously known thermodynamic functions. The zero separation limit of the series for the two-point function reproduces the thermodynamics derived by Yang and Yang, while the infinite coupling limit gives the Fredholm determinant result of Schultz and Lenard. The latter is related to the Painlevé V equation by the monodromy arguments of Jimbo, Miwa, Mori, and Sato. The (1/c) correction to the large coupling limit is calculated from the Gel'fand-Levitan series and expressed in terms of solutions to Painlevé V. The asymptotic behavior of the relevant Painlevé function is discussed and related to the long range behavior of the correlation function.     

On using polynomial chaos for modeling uncertainty in acoustic propagation

The use of polynomial chaos for incorporating environmental variability into propagation models is investigated in the context of a simplified one-dimensional model, which is relevant for acoustic propagation when the random sound speed is independent of depth. Environmental variability is described by a spectral representation of a stochastic process and the chaotic representation of the wave field then consists of an expansion in terms of orthogonal random polynomials. Issues concerning implementation of the relevant equations, the accuracy of the approximation, uniformity of the expansion over the propagation range, and the computational burden necessary to evaluate different field statistics are addressed. When the correlation length of the environmental fluctuations is small, low-order expansions work well, while for large correlation lengths the convergence of the expansion is highly range dependent and requires high-order approximants. These conclusions also apply in higher-dimensional propagation problems.     

Analysis of coefficient identification problems associated to the inverse Euler-Bernoulli beam theory

A rigorous investigation of the identification of a heterogeneousflexural rigidity coefficient in the Euler-Bernoulli steady-statebeam theory in the presence of a prescribed load is presented.Mathematically, this study is an extension to higher-order differentialequations of the coefficient identification problem analysedby Marcellini (1982) for the one-dimensional Poisson equation.In addition, various types of boundary conditions are discussed.Conditions for the well-posedness of these inverse problemsare established and, furthermore, numerical results obtainedusing a regularization algorithm are presented.