Step fluctuations and random walks

The probability distribution p(l) of an atom to return to a step at distance l from the detachment site, with a random walk in between, is exactly enumerated. In particular, we study the dependence of p(l) on step roughness, presence of other reflecting or absorbing steps, interaction between steps and diffusing atom, as well as concentration of defects on the terrace neighbouring the step. Applying Monte Carlo techniques, the time evolution of equilibrium step fluctuations is computed for specific forms of return probabilities. Results are compared to previous theoretical and experimental findings.Comment: 16 pages, 6 figure

Ricci flows with unbounded curvature

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference

Dynamics of surface steps

In the framework of SOS models, the dynamics of isolated and pairs of surface steps of monoatomic height is studied, for step--edge diffusion and for evaporation kinetics, using Monte Carlo techniques. In particular, various interesting crossover phenomena are identified. Simulational results are compared, especially, to those of continuum theories and random walk descriptions.Comment: 13 pages in elsart style, 4 eps figures, submitted to Physica

Fluctuations of steps on crystal surfaces

Fluctuations of isolated and pairs of ascending steps of monoatomic height are studied in the framework of SOS models, using mainly Monte Carlo techniques. Below the roughening transistion of the surface, the profiles of long steps show the same scaling features for terrace and surface diffusion. For a pair of short steps, their separation distance is found to grow as $t^{1/3}$ at late stages. Above roughening, simulational data on surface diffusion agree well with the classical continuum theory of Mullins.Comment: 4 pages, 2 eps figure

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

Rotational spectroscopy of rare iron monoxide isotopologues: A mass-independent analysis

We present pure rotational transitions of the rare iron monoxide isotopologues.,andin their lowest spin states. For, the rotational spectrum reveals hyperfine splitting due to the nuclear spin of. We use Dunham-like parameters to analyse the new laboratory data together with data from the literature. In particular, we are able to derive the Born-Oppenheimer breakdown parametersandand the corresponding equilibrium bond length of. With these new accurate molecular parameters line positions on a sub-MHz accuracy level can be calculated, including those of the radioactive isotopologue. The new data allow for an astronomical search for the rareisotopologues using sensitive radio telescopes, like the Atacama Large Millimetre/submillimetre Array

Using the Wigner-Ibach Surmise to Analyze Terrace-Width Distributions: History, User's Guide, and Advances

A history is given of the applications of the simple expression generalized from the surmise by Wigner and also by Ibach to extract the strength of the interaction between steps on a vicinal surface, via the terrace width distribution (TWD). A concise guide for use with experiments and a summary of some recent extensions are provided.Comment: 11 pages, 4 figures, reformatted (with revtex) version of refereed paper for special issue of Applied Physics A entitled "From Surface Science to Device Physics", in honor of the retirements of Prof. H. Ibach and Prof. H. L\"ut

A contiuum model for low temperature relaxation of crystal steps

High and low temperature relaxation of crystal steps are described in a unified picture, using a continuum model based on a modified expression of the step free energy. Results are in agreement with experiments and Monte Carlo simulations of step fluctuations and monolayer cluster diffusion and relaxation. In an extended model where mass exchange with neighboring terraces is allowed, step transparency and a low temperature regime for unstable step meandering are found.Comment: Submitted to Phys.Rev.Let