Ginzburg–Landau Vortices Driven by the Landau–Lifshitz–Gilbert Equation

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg–Landau vortices for sphere-valued maps. In particular, we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization are ruled by the Landau–Lifshitz–Gilbert equation, which combines characteristic properties of a nonlinear Schrödinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation.     

Sensitivity Analysis for a Class of H 0 1 ${{H_{0}^{1}}}$ -Elliptic Variational Inequalities of the Second Kind

Set-Valued and Variational Analysis - We study the stability of solutions to ${H_{0}^{1}}$ -elliptic variational inequalities of the second kind that contain a non-differentiable Nemytskii...     

Analogues of Non-Gibbsianness in Joint Measures of Disordered Mean Field Models

It is known that the joint measures on the product of spin-space and disorder space are very often non-Gibbsian measures, for lattice systems with quenched disorder, at low temperature. Are there reflections of this non-Gibbsianness in the corresponding mean-field models? We study the continuity properties of the conditional probabilities in finite volume of the following mean field models: (a) joint measures of random field Ising, (b) joint measures of dilute Ising, (c) decimation of ferromagnetic Ising. The conditional probabilities are functions of the empirical mean of the conditionings; so we look at the large volume behavior of these functions to discover non-trivial limiting objects. For (a) we find (1) discontinuous dependence for almost any realization and (2) dependence of the conditional probabilities on the phase. In contrast to that we see continuous behavior for (b) and (c), for almost any realization. This is in complete analogy to the behavior of the corresponding lattice models in high dimensions. It shows that non-Gibbsian behavior which seems a genuine lattice phenomenon can be partially understood already on the level of mean-field models.     

A mathematical investigation of the Car-Parrinello method

The Car-Parrinello method for ab-initio molecular dynamics avoids the explicit minimization of energy functionals given by functional density theory in the context of the quantum adiabatic approximation (time-dependent Born-Oppenheimer approximation). Instead, it introduces a fictitious classical dynamics for the electronic orbitals. For many realistic systems this concept allowed first-principle computer simulations for the first time. In this paper we study the quantitative influence of the involved parameter , the fictitious electronic mass of the method. In particular, we prove by use of a carefully chosen two-time-scale asymptotics that the deviation of the Car-Parrinello method from the adiabatic model is of order – provided one starts in the ground state of the electronic system and the electronic excitation spectrum satisfies a certain non-degeneracy condition. Analyzing a two-level model problem we prove that our result cannot be improved in general. Received June 14, 1996     

About coupling constant singularities in quantum electrodynamics

The contribution of the multibubble insertions in the photon propagator to the anomalous magnetic moment of the electron is reexamined. Using the asymptotic form of the photon propagator one finds a softer singularity than that found in a recent analysis.     

The accuracy of ab initio molecular geometries for systems containing second-row atoms

The performance of the standard hierarchy of ab initio models--that is, Hartree-Fock theory, second-order Moller-Plesset theory, coupled-cluster singles-and-doubles theory, and coupled-cluster singles-doubles-approximate-triples theory--in combination with correlation-consistent basis sets is investigated for equilibrium geometries of molecules containing second-row elements. From an analysis on a collection of 31 molecules (yielding statistical samples of 41 bond distances and 13 bond angles), the statistical errors (mean deviation, mean absolute deviation, standard deviation, and maximum absolute deviation) are established at each level of theory. The importance of core correlation is examined by comparing calculations in the frozen-core approximation with calculations where all electrons are correlated.     

Scattering spherical voids in nanocrystalline TiO2- enhancement of efficiency in dye-sensitized solar cells

Spherical voids as light scattering centers in nanocrystalline TiO2 films were realized with polystyrene particles of diameter 400 nm, thus enhancing the photovoltaic performance by 25% on large areas, as well as providing an indication that these films can be used with electrolytes of higher viscosity.