Table of contents

A novel multigrid method for the accurate and efficient simulation of turbulent flows is described and demonstrated. The method's efficiency relative to direct simulations is of the order of the ratio of required integration time to the smallest-eddy turnover time, potentially resulting in orders-of-magnitude improvement for a large class of turbulence problems.

We consider the growth of rigid, non-branching polymers nucleated from a planar surface. In contrast to DLA models, the present theory includes effects of both a finite concentration of monomers and reversibility of the growth. In addition, we consider an assembly/disassembly process that is accompanied by reduction of the monomers' ability to repolymerize, which we call monomer degradation. The analysis of mean-field equations and numerical simulations both lead to scaling solutions for reversible as well as irreversible growth. For instance, we find that (in the absence of monomer degradation) a diffusive scaling regime, typical for DLA-like problems, can be defined that crosses over to a linear scaling regime at a time-dependent length scale. In the presence of monomer degradation, however, the diffusive regime disappears and an array with constant polymer density grows linearly in time. This unusual behavior is due to a depletion of monomers that allows only a finite subpopulation of polymers to "escape", leaving all other polymers growing and shrinking in the vicinity of the nucleating surface.

A lattice model for the ordering of melts of "living polymers", incorporating semi-flexibility, vacancies and open ends, is studied in two dimensions by Monte Carlo simulations and the analysis of exactly solvable limits. We present evidence for high-temperature disordered, and low-temperature ordered phases separated by a continuous transition. If the density of open ends is small, strong crossover effects, arising because of the proximity of the power law phase in the F-model limit of our model, dominate our simulations. The distribution of polymer lengths always has an exponential tail; however, in the crossover regime, it decays with a power law for small and intermediate lengths. The relevance of our study to other lattice models for melts of semi-flexible polymers is discussed.

A semi-classical method derived from the Robert and Bonamy formalism based on electrostatic and atom-atom potentials has been used to calculate rotational relaxation rates in ozone with different collision partners (O₂, N₂, O₃) in the 200-300 K temperature range. The theoretical cross-sections agree reasonably well with the available experimental data.

We discuss theoretically the influence of the distribution of the charged monomers on the conformational properties of polyampholyte chains using the random phase approximation. If the distribution is quenched with random positions of the positive and negative charges, the polyampholyte collapses and locally has the same structure as a salt solution. It can be described by the Debye-Hückel theory. If the charges are alternating, the collapsed chain is a dielectric medium that can be characterized by a finite negative virial coefficient. Alternating polyampholytes are more soluble than random polyampholytes. We also study intermediate distributions and the annealed problem where the charges are due to the dissociation of acidic and basic monomers.

Semi-ballistic transport occurs when cavities have a moderate amount of elastic scattering, so that transport in the long direction(s) become diffusive. Transmission patterns are studied in this regime for disordered waveguides and for Fabry-Pérot interferometers with "dirty" mirrors. The results have implications for mesoscopic conductors at zero temperature. It is shown that the average "Ohmic" conductivity of disordered quantum wires in the semi-ballistic regime decreases significantly when a new transmission channel is opened; for films this occurs in a universal way. The transmission current of certain GaAs-AlGaAs double-barrier quantum wells is shown to have a broad resonance linewidth, induced by intrinsic irregularities in the barrier interfaces.

In this letter we report further experimental evidence of extended self-similarity in the structure functions of the velocity field of fully developed turbulence. We study the behaviour of high-order structure functions close to the Kolmogorov scale η where extended self-similarity is observed.

Perovskite (CaTiO₃) is a model compound for the Earth's most abundant mineral, the perovskite (Mg, Fe)SiO₃. High-temperature structural investigations using neutron powder diffraction reveal a phase transition to a highly disordered cubic phase. As one approaches this transition, the TiO₆ octahedra become less distorted and their rotational disorder is reflected by the large atomic-displacement parameters of the oxygens in the (a, b)-plane, suggesting that the high-temperature transition to the cubic phase could be triggered by the onset of mobility in the oxygen sublattice. This would account for the fact that no intermediate tetragonal phase is observed.

The influence of local disorder on the thermodynamics of interacting electrons is studied within the infinite-dimensional disordered Hubbard model. Using a finite-temperature quantum Monte Carlo method, the averaged local moment and staggered susceptibility are calculated and the magnetic phase diagram at half-filling is constructed. From the averaged compressibility in the paramagnetic and antiferromagnetic phase we determine the metal-insulator transitions of the system. A rich transition scenario is revealed. Quite unexpectedly the disorder is found to stabilize the magnetic order in the strong-coupling limit.

We have found the exact ground state for a large class of antiferromagnetic spin-1 models with nearest-neighbour interactions on a linear chain. All ground-state properties can be calculated. The ground state is determined as a matrix product of individual site states and has the properties of the Haldane scenario.

Using perturbed γ-ray distribution techniques and in-beam Mössbauer spectroscopy, the magnetism, electronic structure, and lattice sites of Fe ions implanted into Y have been investigated. About 65% of the Fe atoms occupy interstitial sites, which come out to be non-magnetic. The remaining fractions is found on substitutional sites, and exhibits a nearly Curie-type susceptibility and Korringa-type spin dynamics. Local spin density calculations predict the magnetic moment, the hyperfine field and the isomer shift in agreement with the experimental results.

A theoretical study of the nuclear fusion in condensed matter is reported. We present a simple model for the fusion with two effects, impacting and screening, characterized by impacting factor Q and screening length λ, respectively. Explicit expressions and results are given for the fusion rate R(E₀/Q, λ), where E₀ is the incident energy. R is enhanced by the cooperation of the two effects. Calculated fusion yields and/or rates are, respectively, in reasonable agreement with the experimental data obtained in cluster-impact fusion and deuterium-implanted titanium fusion. Predicted cold-fusion rates are still lower than the one observed experimentally, except on extremely high density of deuteron atoms and strongly coherent collisions in solids.

We present a mechanism of cell or organelle motility based on alternating contractions and dilations of a gel, with slightly different permeabilities in the contracted/expanded states. Some cells move by flagellal or cilial "swimming". Others move by using reversible adhesion to a substrate and are thus able to crawl. In this work we are interested in an even more primitive method of propulsion, that of non-linear osmotic swimming. Such a method can be used by cells which have no access to a substrate or possibly by organelles within cells.