Search results for "FUNCTIONALS"
showing 5 items of 45 documents
The Radó–Kneser–Choquet theorem for $p$-harmonic mappings between Riemannian surfaces
2020
In the planar setting the Rad\'o-Kneser-Choquet theorem states that a harmonic map from the unit disk onto a Jordan domain bounded by a convex curve is a diffeomorphism provided that the boundary mapping is a homeomorphism. We prove the injectivity criterion of Rad\'o-Kneser-Choquet for $p$-harmonic mappings between Riemannian surfaces. In our proof of the injecticity criterion we approximate the $p$-harmonic map with auxiliary mappings that solve uniformly elliptic systems. We prove that each auxiliary mapping has a positive Jacobian by a homotopy argument. We keep the maps injective all the way through the homotopy with the help of the minimum principle for a certain subharmonic expressio…
Uncertainty analysis and symmetry restoration in nuclear self-consistent methods
2015
This thesis contains two articles, in the following denoted by I and II, and an introduction to them. In Chapter 1, I present the theoretical models of nuclear structure. In Chapter 2, I introduce the basic ideas about the density functional theory (DFT) and self-consistent mean-field (SCMF) calculations. In Chapter 3, I give the formulae for the uncertainty propagation, which is the error analysis method used in article I. As a proper tool to survey the predictive power of theoretical models, the error analysis now has become more and more widely used. By analyzing the propagation of uncertainties, one tries to find out the e ectiveness of the calculation with a given parameter set obtaine…
Structure and dynamics in liquid bismuth and Bin clusters: A density functional study
2014
Density functional/molecular dynamics simulations with more than 500 atoms have been performed on liquid bismuth at 573, 773, 923, and 1023 K and on neutral Bi clusters with up to 14 atoms. There are similar structural patterns (coordination numbers, bond angles, and ring patterns) in the liquid and the clusters, with significant differences from the rhombohedral crystalline form. We study the details of the structure (structure factor, pair, and cavity distribution functions) and dynamical properties (vibration frequencies, diffusion constants, power spectra), and compare with experimental results where available. While the three short covalent bonds typical to pnictogens are characteristi…
Relationship between volume and energy of vector fields
2001
Abstract A unified study of energy and volume functionals is presented here by determining the critical points of a functional that extends simultaneously energy and volume and that is defined on the product of the manifold of smooth maps C∞(M,N) times the manifold M of riemannian metrics on M. The restriction of this functional to different submanifolds of the space of vector fields X (M)× M is also considered, and used to study several functionals generalizing volume and energy or total bending of vector fields
Conformational investigation of alpha,beta-dehydropeptides. IX. N-Acetyl-(E)-alpha,beta-methylamide: stereoelectronic properties from infrared and th…
1998
The Fourier transform infrared spectra of Ac-(E)-deltaAbu-NHMe were analyzed to determine the predominant solution conformation(s) of this (E)-alpha,beta-dehydropeptide-related compound and the electron density perturbation in its amide groups. The measurements were performed in dichloromethane and acetonitrile in the region of mode vs (N-H), amide I, amide II and vs (C(alpha)=Cbeta). The equilibrium geometrical parameters, calculated by a method based on the density functional theory with the B3LYP functional and the 6-31G* basis set, were used to support spectroscopic interpretation and gain some deeper insight into the molecule. The experimental and theoretical data were compared with th…