Harmonic analysis of large systems. I. Methodology

Methods have been developed for the determination of vibrational frequencies and normal modes of large systems in the full conformational space (including all degrees of freedom) and in a reduced conformational space (reducing the number of degrees of freedom). The computational method, which includes Hessian generation and storage, full and iterative diagonalization techniques, and the refinement of the results, is presented. A method is given for the quasiharmonic analysis and the reduced basis quasiharmonic analysis. The underlying principle is that from the atomic fluctuations, an effective harmonic force field can be determined relative to the dynamic average structure. Normal mode analysis tools can be used to characterize quasiharmonic modes of vibration. These correspond to conventional normal modes except that anharmonic effects are included. Numerous techniques for the analyses of vibrational frequencies and normal modes are described. Criteria for the analysis of the similarity of low-frequency normal modes is presented. The approach to determining the natural frequencies and normal modes of vibration described here is general and applicable to any large system. © 1995 John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

The Dunford-Pettis Property for some Function Algebras in Several Complex Variables

The Dunford-Pettis property is shown to hold for the uniformalgebra A() and its dual for some standard domains , includingstrongly pseudoconvex bounded domains in Cⁿ, pseudoconvex boundeddomains of finite type in C², and bounded domains in C. Previouslythe result was known for the unit ball and unit polydisc inCⁿ. Techniques used involve Bourgain algebras, Hankel operators,properties of the Bergman kernel, quasi-metrics on the boundary,and -theory.     

Convergence of diagonally stationary sequences in convex optimization

LetX be a real normed linear space,f, f ⁿ, n , be extended real-valued proper closed convex functions onX. A sequence {x _n} inX is called diagonally stationary for {f ⁿ} if for alln there existsx* _n f ⁿ (x _n) such that x* _{n *} 0. Such sequences arise in approximation methods for the problem of minimizingf. Some general convergence results based upon variational convergence theory and appropriate equi-well-posedness are presented.     

Aspects of nucleon Compton scattering

We consider the spin-averaged nucleon forward Compton scattering amplitude in heavy baryon chiral perturbation theory including all terms to order . The chiral prediction for the spin-averaged forward Compton scattering amplitude is in good agreement with the data for photon energies110 MeV. We also evaluate the nucleon electric and magnetic Compton polarizabilities to this order and discuss the uncertainties of the various counter terms entering the chiral expansion of these quantities.     

Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model

For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t ^–(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1.