Effects of dust absorption on spectroscopic studies of turbulence

We study the effect of dust absorption on the recovery velocity and density spectra as well as on the anisotropies of magnetohydrodynamic turbulence using the Velocity Channel Analysis (VCA), Velocity Coordinate Spectrum (VCS) and Velocity Centroids. The dust limits volume up to an optical depth of unity. We show that in the case of the emissivity proportional to the density of emitters, the effects of random density get suppressed for strong dust absorption intensity variations arise from the velocity fluctuations only. However, for the emissivity proportional to squared density, both density and velocity fluctuations affect the observed intensities. We predict a new asymptotic regime for the spectrum of fluctuations for large scales exceeding the physical depths to unit optical depth. The spectrum gets shallower by unity in this regime. In addition, the dust absorption removes the degeneracy resulted in the universal $K^{-3}$ spectrum of intensity fluctuations of self-absorbing medium reported by Lazarian \& Pogosyan. We show that the predicted result is consistent with the available HII region emission data. We find that for sub-Alfv\'enic and trans-Alfv\'enic turbulence one can get the information about both the magnetic field direction and the fundamental Alfv\'en, fast and slow modes that constitute MHD turbulence.Comment: Published in MNRAS, minor changes to match the published versio

Current-Induced Step Bending Instability on Vicinal Surfaces

We model an apparent instability seen in recent experiments on current induced step bunching on Si(111) surfaces using a generalized 2D BCF model, where adatoms have a diffusion bias parallel to the step edges and there is an attachment barrier at the step edge. We find a new linear instability with novel step patterns. Monte Carlo simulations on a solid-on-solid model are used to study the instability beyond the linear regime.Comment: 4 pages, 4 figure

On generalized cluster algorithms for frustrated spin models

Standard Monte Carlo cluster algorithms have proven to be very effective for many different spin models, however they fail for frustrated spin systems. Recently a generalized cluster algorithm was introduced that works extremely well for the fully frustrated Ising model on a square lattice, by placing bonds between sites based on information from plaquettes rather than links of the lattice. Here we study some properties of this algorithm and some variants of it. We introduce a practical methodology for constructing a generalized cluster algorithm for a given spin model, and investigate apply this method to some other frustrated Ising models. We find that such algorithms work well for simple fully frustrated Ising models in two dimensions, but appear to work poorly or not at all for more complex models such as spin glasses.Comment: 34 pages in RevTeX. No figures included. A compressed postscript file for the paper with figures can be obtained via anonymous ftp to minerva.npac.syr.edu in users/paulc/papers/SCCS-527.ps.Z. Syracuse University NPAC technical report SCCS-52

Cluster update and recognition

We present a fast and robust cluster update algorithm that is especially efficient in implementing the task of image segmentation using the method of superparamagnetic clustering. We apply it to a Potts model with spin interactions that are are defined by gray-scale differences within the image. Motivated by biological systems, we introduce the concept of neural inhibition to the Potts model realization of the segmentation problem. Including the inhibition term in the Hamiltonian results in enhanced contrast and thereby significantly improves segmentation quality. As a second benefit we can - after equilibration - directly identify the image segments as the clusters formed by the clustering algorithm. To construct a new spin configuration the algorithm performs the standard steps of (1) forming clusters and of (2) updating the spins in a cluster simultaneously. As opposed to standard algorithms, however, we share the interaction energy between the two steps. Thus the update probabilities are not independent of the interaction energies. As a consequence, we observe an acceleration of the relaxation by a factor of 10 compared to the Swendson and Wang procedure.Comment: 4 pages, 2 figure

Dual Monte Carlo and Cluster Algorithms

We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm, make explicit the assumptions embodied in all clusters of which we are aware, and define the construction of free cluster algorithms. We also illustrate these procedures by rederiving the Swendsen-Wang algorithm, presenting the details of the loop algorithm for a worldline simulation of a quantum $S=$ 1/2 model, and proposing a free cluster version of the Swendsen-Wang replica method for the random Ising model. How the principle of maximum entropy might be used to aid the construction of cluster algorithms is also discussed.Comment: 25 pages, 4 figures, to appear in Phys.Rev.

From Discrete Hopping to Continuum Modeling on Vicinal Surfaces with Applications to Si(001) Electromigration

Coarse-grained modeling of dynamics on vicinal surfaces concentrates on the diffusion of adatoms on terraces with boundary conditions at sharp steps, as first studied by Burton, Cabrera and Frank (BCF). Recent electromigration experiments on vicinal Si surfaces suggest the need for more general boundary conditions in a BCF approach. We study a discrete 1D hopping model that takes into account asymmetry in the hopping rates in the region around a step and the finite probability of incorporation into the solid at the step site. By expanding the continuous concentration field in a Taylor series evaluated at discrete sites near the step, we relate the kinetic coefficients and permeability rate in general sharp step models to the physically suggestive parameters of the hopping models. In particular we find that both the kinetic coefficients and permeability rate can be negative when diffusion is faster near the step than on terraces. These ideas are used to provide an understanding of recent electromigration experiment on Si(001) surfaces where step bunching is induced by an electric field directed at various angles to the steps.Comment: 10 pages, 4 figure