On continuum modeling of sputter erosion under normal incidence: interplay between nonlocality and nonlinearity

Under specific experimental circumstances, sputter erosion on semiconductor materials exhibits highly ordered hexagonal dot-like nanostructures. In a recent attempt to theoretically understand this pattern forming process, Facsko et al. [Phys. Rev. B 69, 153412 (2004)] suggested a nonlocal, damped Kuramoto-Sivashinsky equation as a potential candidate for an adequate continuum model of this self-organizing process. In this study we theoretically investigate this proposal by (i) formally deriving such a nonlocal equation as minimal model from balance considerations, (ii) showing that it can be exactly mapped to a local, damped Kuramoto-Sivashinsky equation, and (iii) inspecting the consequences of the resulting non-stationary erosion dynamics.Comment: 7 pages, 2 Postscript figures, accepted by Phys. Rev. B corrected typos, few minor change

How ripples turn into dots: modeling ion-beam erosion under oblique incidence

Pattern formation on semiconductor surfaces induced by low energetic ion-beam erosion under normal and oblique incidence is theoretically investigated using a continuum model in form of a stochastic, nonlocal, anisotropic Kuramoto-Sivashinsky equation. Depending on the size of the parameters this model exhibits hexagonally ordered dot, ripple, less regular and even rather smooth patterns. We investigate the transitional behavior between such states and suggest how transitions can be experimentally detected.Comment: 11 pages, 4 figures, submitted for publication, revised versio

Kinematic and Thermal Structure at the onset of high-mass star formation

We want to understand the kinematic and thermal properties of young massive gas clumps prior to and at the earliest evolutionary stages of high-mass star formation. Do we find signatures of gravitational collapse? Do we find temperature gradients in the vicinity or absence of infrared emission sources? Do we find coherent velocity structures toward the center of the dense and cold gas clumps? To determine kinematics and gas temperatures, we used ammonia, because it is known to be a good tracer and thermometer of dense gas. We observed the NH$_3$(1,1) and (2,2) lines within seven very young high-mass star-forming regions with the VLA and the Effelsberg 100m telescope. This allows us to study velocity structures, linewidths, and gas temperatures at high spatial resolution of 3-5$"$, corresponding to $\sim$0.05 pc. We find on average cold gas clumps with temperatures in the range between 10 K and 30 K. The observations do not reveal a clear correlation between infrared emission peaks and ammonia temperature peaks. We report an upper limit for the linewidth of $\sim$1.3 km s$^{-1}$, at the spectral resolution limit of our VLA observation. This indicates a relatively low level of turbulence on the scale of the observations. Velocity gradients are present in almost all regions with typical velocity differences of 1 to 2 km s$^{-1}$ and gradients of 5 to 10 km s$^{-1}$ pc$^{-1}$. These velocity gradients are smooth in most cases, but there is one exceptional source (ISOSS23053), for which we find several velocity components with a steep velocity gradient toward the clump centers that is larger than 30 km s$^{-1}$ pc$^{-1}$. This steep velocity gradient is consistent with recent models of cloud collapse. Furthermore, we report a spatial correlation of ammonia and cold dust, but we also find decreasing ammonia emission close to infrared emission sources.Comment: 20 pages, 10 figure

Hierarchical fragmentation and collapse signatures in a high-mass starless region

Aims: Understanding the fragmentation and collapse properties of the dense gas during the onset of high-mass star formation. Methods: We observed the massive (~800M_sun) starless gas clump IRDC18310-4 with the Plateau de Bure Interferometer (PdBI) at sub-arcsecond resolution in the 1.07mm continuum andN2H+(3-2) line emission. Results: Zooming from a single-dish low-resolution map to previous 3mm PdBI data, and now the new 1.07mm continuum observations, the sub-structures hierarchically fragment on the increasingly smaller spatial scales. While the fragment separations may still be roughly consistent with pure thermal Jeans fragmentation, the derived core masses are almost two orders of magnitude larger than the typical Jeans mass at the given densities and temperatures. However, the data can be reconciled with models using non-homogeneous initial density structures, turbulence and/or magnetic fields. While most sub-cores remain (far-)infrared dark even at 70mum, we identify weak 70mum emission toward one core with a comparably low luminosity of ~16L_sun, re-enforcing the general youth of the region. The spectral line data always exhibit multiple spectral components toward each core with comparably small line widths for the individual components (in the 0.3 to 1.0km/s regime). Based on single-dish C18O(2-1) data we estimate a low virial-to-gas-mass ratio <=0.25. We discuss that the likely origin of these spectral properties may be the global collapse of the original gas clump that results in multiple spectral components along each line of sight. Even within this dynamic picture the individual collapsing gas cores appear to have very low levels of internal turbulence.Comment: 8 pages, 4 figures, A&A in pres

A QUBO formulation for the Tree Containment problem

Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze phylogenetic networks, the problem of deciding whether or not a given rooted phylogenetic network embeds a given rooted phylogenetic tree is of recurring interest. This problem, formally know as Tree Containment, is NP-complete in general and polynomial-time solvable for certain classes of phylogenetic networks. In this paper, we connect ideas from quantum computing and phylogenetics to present an efficient Quadratic Unconstrained Binary Optimization formulation for Tree Containment in the general setting. For an instance (N,T) of Tree Containment, where N is a phylogenetic network with n_N vertices and T is a phylogenetic tree with n_T vertices, the number of logical qubits that are required for our formulation is O(n_N n_T).Comment: final version accepted for publication in Theoretical Computer Scienc

Influence of the Dufour effect on convection in binary gas mixtures

Linear and nonlinear properties of convection in binary fluid layers heated from below are investigated, in particular for gas parameters. A Galerkin approximation for realistic boundary conditions that describes stationary and oscillatory convection in the form of straight parallel rolls is used to determine the influence of the Dufour effect on the bifurcation behaviour of convective flow intensity, vertical heat current, and concentration mixing. The Dufour--induced changes in the bifurcation topology and the existence regimes of stationary and traveling wave convection are elucidated. To check the validity of the Galerkin results we compare with finite--difference numerical simulations of the full hydrodynamical field equations. Furthermore, we report on the scaling behaviour of linear properties of the stationary instability.Comment: 14 pages and 10 figures as uuencoded Postscript file (using uufiles

Carbon in different phases ([CII], [CI], and CO) in infrared dark clouds: Cloud formation signatures and carbon gas fractions

Context: How do molecular clouds form out of the atomic phase? And what are the relative fractions of carbon in the ionized, atomic and molecular phase? These are questions at the heart of cloud and star formation. Methods: Using multiple observatories from Herschel and SOFIA to APEX and the IRAM 30m telescope, we mapped the ionized, atomic and molecular carbon ([CII]@1900GHz, [CI]@492GHz and C18O(2-1)@220GHz) at high spatial resolution (12"-25") in four young massive infrared dark clouds (IRDCs). Results: The three carbon phases were successfully mapped in all four regions, only in one source the [CII] line remained a non-detection. Both the molecular and atomic phases trace the dense structures well, with [CI] also tracing material at lower column densities. [CII] exhibits diverse morphologies in our sample, from compact to diffuse structures probing the cloud environment. In at least two out of the four regions, we find kinematic signatures strongly indicating that the dense gas filaments have formed out of a dynamically active and turbulent atomic/molecular cloud, potentially from converging gas flows. The atomic-to-molecular carbon gas mass ratios are low between 7% and 12% with the lowest values found toward the most quiescent region. In the three regions where [CII] is detected, its mass is always higher by a factor of a few than that of the atomic carbon. The ionized carbon emission depends as well on the radiation field, however, we also find strong [CII] emission in a region without significant external sources, indicating that other processes, e.g., energetic gas flows can contribute to the [CII] excitation as well.Comment: 15 pages, 18 figures, accepted by Astronomy & Astrophysics, a higher resolution version can be found at http://www.mpia.de/homes/beuther/papers.htm

Kinematic structure of massive star-forming regions - I. Accretion along filaments

The mid- and far-infrared view on high-mass star formation, in particular with the results from the Herschel space observatory, has shed light on many aspects of massive star formation. However, these continuum studies lack kinematic information. We study the kinematics of the molecular gas in high-mass star-forming regions. We complemented the PACS and SPIRE far-infrared data of 16 high-mass star-forming regions from the Herschel key project EPoS with N2H+ molecular line data from the MOPRA and Nobeyama 45m telescope. Using the full N2H+ hyperfine structure, we produced column density, velocity, and linewidth maps. These were correlated with PACS 70micron images and PACS point sources. In addition, we searched for velocity gradients. For several regions, the data suggest that the linewidth on the scale of clumps is dominated by outflows or unresolved velocity gradients. IRDC18454 and G11.11 show two velocity components along several lines of sight. We find that all regions with a diameter larger than 1pc show either velocity gradients or fragment into independent structures with distinct velocities. The velocity profiles of three regions with a smooth gradient are consistent with gas flows along the filament, suggesting accretion flows onto the densest regions. We show that the kinematics of several regions have a significant and complex velocity structure. For three filaments, we suggest that gas flows toward the more massive clumps are present.Comment: accepted by A&

Fragmentation and dynamical collapse of the starless high-mass star-forming region IRDC18310-4

Aims: We study the fragmentation and dynamical properties of a massive starless gas clump at the onset of high-mass star formation. Methods: Based on Herschel continuum data we identify a massive gas clump that remains far-infrared dark up to 100mum wavelengths. The fragmentation and dynamical properties are investigated by means of Plateau de Bure Interferometer and Nobeyama 45m single-dish spectral line and continuum observations. Results: The massive gas reservoir fragments at spatial scales of ~18000AU in four cores. Comparing the spatial extent of this high-mass region with intermediate- to low-mass starless cores from the literature, we find that linear sizes do not vary significantly over the whole mass regime. However, the high-mass regions squeeze much more gas into these similar volumes and hence have orders of magnitude larger densities. The fragmentation properties of the presented low-to high-mass regions are consistent with gravitational instable Jeans fragmentation. Furthermore, we find multiple velocity components associated with the resolved cores. Recent radiative transfer hydrodynamic simulations of the dynamic collapse of massive gas clumps also result in multiple velocity components along the line of sight because of the clumpy structure of the regions. This result is supported by a ratio between viral and total gas mass for the whole region <1. Conclusions: This apparently still starless high-mass gas clump exhibits clear signatures of early fragmentation and dynamic collapse prior to the formation of an embedded heating source. A comparison with regions of lower mass reveals that the linear size of star-forming regions does not necessarily have to vary much for different masses, however, the mass reservoirs and gas densities are orders of magnitude enhanced for high-mass regions compared to their lower-mass siblings.Comment: 11 pages, 10 figures, accepted to Astronomy and Astrophysics, high-resolution version with all figures included can be found at http://www.mpia.de/homes/beuther/papers.htm