Distinguishing step relaxation mechanisms via pair correlation functions

Theoretical predictions of coupled step motion are tested by direct STM measurement of the fluctuations of near-neighbor pairs of steps on Si(111)-root3 x root3 R30 - Al at 970K. The average magnitude of the pair-correlation function is within one standard deviation of zero, consistent with uncorrelated near-neighbor step fluctuations. The time dependence of the pair-correlation function shows no statistically significant agreement with the predicted t^1/2 growth of pair correlations via rate-limiting atomic diffusion between adjacent steps. The physical considerations governing uncorrelated step fluctuations occurring via random attachment/detachment events at the step edge are discussed.Comment: 17 pages, 4 figure

Central limit theorem for multiplicative class functions on the symmetric group

Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance.Comment: 23 pages; the mathematics is the same as in the previous version, but there are several improvments in the presentation, including a more intuitve name for the considered function

Words with the Maximum Number of Abelian Squares

An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain $\Theta(n^2)$ distinct factors that are abelian squares. We study infinite words such that the number of abelian square factors of length $n$ grows quadratically with $n$.Comment: To appear in the proceedings of WORDS 201

Fluctuations, line tensions, and correlation times of nanoscale islands on surfaces

We analyze in detail the fluctuations and correlations of the (spatial) Fourier modes of nano-scale single-layer islands on (111) fcc crystal surfaces. We analytically show that the Fourier modes of the fluctuations couple due to the anisotropy of the crystal, changing the power spectrum of the fluctuations, and that the actual eigenmodes of the fluctuations are the appropriate linear combinations of the Fourier modes. Using kinetic Monte Carlo simulations with bond-counting parameters that best match realistic energy barriers for hopping rates, we deduce absolute line tensions as a function of azimuthal orientation from the analyses of the fluctuation of each individual mode. The autocorrelation functions of these modes give the scaling of the correlation times with wavelength, providing us with the rate-limiting kinetics driving the fluctuations, here step-edge diffusion. The results for the energetic parameters are in reasonable agreement with available experimental data for Pb(111) surfaces, and we compare the correlation times of island-edge fluctuations to relaxation times of quenched Pb crystallites.Comment: 11 pages, 8 figures; to appear in PRB 70, xxx (15 Dec 2004), changes in MC and its implication

Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2

The spectral correlation of a chaotic system with spin 1/2 is universally described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the semiclassical limit. In semiclassical theory, the spectral form factor is expressed in terms of the periodic orbits and the spin state is simulated by the uniform distribution on a sphere. In this paper, instead of the uniform distribution, we introduce Brownian motion on a sphere to yield the parametric motion of the energy levels. As a result, the small time expansion of the form factor is obtained and found to be in agreement with the prediction of parametric random matrices in the transition within the GSE universality class. Moreover, by starting the Brownian motion from a point distribution on the sphere, we gradually increase the effect of the spin and calculate the form factor describing the transition from the GOE (Gaussian Orthogonal Ensemble) class to the GSE class.Comment: 25 pages, 2 figure

Projector 2: contig mapping for efficient gap-closure of prokaryotic genome sequence assemblies

With genome sequencing efforts increasing exponentially, valuable information accumulates on genomic content of the various organisms sequenced. Projector 2 uses (un)finished genomic sequences of an organism as a template to infer linkage information for a genome sequence assembly of a related organism being sequenced. The remaining gaps between contigs for which no linkage information is present can subsequently be closed with direct PCR strategies. Compared with other implementations, Projector 2 has several distinctive features: a user-friendly web interface, automatic removal of repetitive elements (repeat-masking) and automated primer design for gap-closure purposes. Moreover, when using multiple fragments of a template genome, primers for multiplex PCR strategies can also be designed. Primer design takes into account that, in many cases, contig ends contain unreliable DNA sequences and repetitive sequences. Closing the remaining gaps in prokaryotic genome sequence assemblies is thereby made very efficient and virtually effortless. We demonstrate that the use of single or multiple fragments of a template genome (i.e. unfinished genome sequences) in combination with repeat-masking results in mapping success rates close to 100%. The web interface is freely accessible at

Ultrafast rerouting of light via slow modes in a nanophotonic directional coupler

We demonstrate that two coupled photonic-crystal waveguides can route two subsequently arriving light pulses to different output ports even though the pulses are only 3 ps apart. This rerouting of light is due to an ultrafast shift in the transmittance spectrum triggered by the generation of electrons and holes in the Si base material by a femtosecond laser pulse. The use of slow-light modes allows for a coupler length of only 5.2 μm. Since these modes are not directly involved, the 3 ps dead time is solely determined by the duration of the input pulse rather than its transit time through the device.We acknowledge funding through the EU FP6-FET “SPLASH” project. This work is also part of the research program of FOM, which is financially supported by the NWO