563,744 research outputs found

    How Peclet number affects microstructure and transient cluster aggregation in sedimenting colloidal suspensions

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    We study how varying the P \'eclet number (Pe) affects the steady state sedimentation of colloidal particles that interact through short-ranged attractions. By employing a hybrid molecular dynamics simulation method we demonstrate that the average sedimentation velocity changes from a non- monotonic dependence on packing fraction {\phi} at low Pe numbers, to a monotonic decrease with {\phi} at higher Pe numbers. At low Pe number the pair correlation functions are close to their equilibrium values, but as the Pe number increases, important deviations from equilibrium forms are observed. Although the attractive forces we employ are not strong enough to form permanent clusters, they do induce transient clusters whose behaviour is also affected by Pe number. In particular, clusters are more likely to fragment and less likely to aggregate at larger Pe numbers, and the probability of finding larger clusters decreases with increasing Pe number. Interestingly, the life-time of the clusters is more or less independent of Pe number in the range we study. Instead, the change in cluster distribution occurs because larger clusters are less likely to form with increasing Pe number. These results illustrate some of the subtleties that occur in the crossover from equilibrium like to purely non-equilibrium behaviour as the balance between convective and thermal forces changes.Comment: 8 page

    Clustering Partially Observed Graphs via Convex Optimization

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    This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know whether or not there is an edge. We want to organize the nodes into disjoint clusters so that there is relatively dense (observed) connectivity within clusters, and sparse across clusters. We take a novel yet natural approach to this problem, by focusing on finding the clustering that minimizes the number of "disagreements"---i.e., the sum of the number of (observed) missing edges within clusters, and (observed) present edges across clusters. Our algorithm uses convex optimization; its basis is a reduction of disagreement minimization to the problem of recovering an (unknown) low-rank matrix and an (unknown) sparse matrix from their partially observed sum. We evaluate the performance of our algorithm on the classical Planted Partition/Stochastic Block Model. Our main theorem provides sufficient conditions for the success of our algorithm as a function of the minimum cluster size, edge density and observation probability; in particular, the results characterize the tradeoff between the observation probability and the edge density gap. When there are a constant number of clusters of equal size, our results are optimal up to logarithmic factors.Comment: This is the final version published in Journal of Machine Learning Research (JMLR). Partial results appeared in International Conference on Machine Learning (ICML) 201

    The same, but different: Stochasticity in binary destruction

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    Observations of binaries in clusters tend to be of visual binaries with separations of 10s - 100s au. Such binaries are 'intermediates' and their destruction or survival depends on the exact details of their individual dynamical history. We investigate the stochasticity of the destruction of such binaries and the differences between the initial and processed populations using N-body simulations. We concentrate on Orion Nebula Cluster-like clusters, where the observed binary separation distribution ranges from 62 - 620 au. We find that, starting from the same initial binary population in statistically identical clusters, the number of intermediate binaries that are destroyed after 1 Myr can vary by a factor of >2, and that the resulting separation distributions can be statistically completely different in initially substructured clusters. We also find that the mass ratio distributions are altered (destroying more low mass ratio systems), but not as significantly as the binary fractions or separation distributions. We conclude that finding very different intermediate (visual) binary populations in different clusters does not provide conclusive evidence that the initial populations were different.Comment: 11 pages, 7 figures, accepted for publication in MNRA

    Dwarf galaxy populations in present-day galaxy clusters: I. Abundances and red fractions

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    We compare the galaxy population in the Virgo, Fornax, Coma and Perseus cluster to a state-of-the-art semi-analytic model, focusing on the regime of dwarf galaxies with luminosities from approximately 10^8 L_sun to 10^9 L_sun. We find that the number density profiles of dwarfs in observed clusters are reproduced reasonably well, and that the red fractions of model clusters provide a good match to Coma and Perseus. On the other hand, the red fraction among dwarf galaxies in Virgo is clearly lower than in model clusters. We argue that this is mainly caused by the treatment of environmental effects in the model. This explanation is supported by our finding that the colours of central ("field") dwarf galaxies are reproduced well, in contrast to previous claims. Finally, we find that the dwarf-to-giant ratio in model clusters is too high. This may indicate that the current model prescription for tidal disruption of faint galaxies is still not efficient enough.Comment: 20 pages, 10 figures. Accepted by MNRAS. Includes the modifications after referee report. Main results unchanged, interpretation slightly change
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