Topological correlations in soap froths

Correlation in two-dimensional soap froth is analysed with an effective potential for the first time. Cells with equal number of sides repel (with linear correlation) while cells with different number of sides attract (with NON-bilinear) for nearest neighbours, which cannot be explained by the maximum entropy argument. Also, the analysis indicates that froth is correlated up to the third shell neighbours at least, contradicting the conventional ideas that froth is not strongly correlated.Comment: 10 Pages LaTeX, 6 Postscript figure

Topological correlations and asymptotic freedom in cellular aggregates

In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two cells of the pair. Assuming this form for the pair correlations, we make explicit the conditions of statistical independence at large distance. When, on average, the defects do not contribute, the layer population and the enclosed topological charge both increase polynomially with distance. In dimension 2, the exponent of the leading terms depend on sum rules satisfied, or not, by the maximum entropy coefficients.Comment: Available online at http://www.sciencedirect.co

Abel Symposia

Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics

The plasma structure of coronal hole solar wind: Origins and evolution

Whereas slow solar wind is known to be highly structured, the fast (coronal hole origin) wind is usually considered to be homogeneous. Using measurements from Helios 1 + 2, ACE, Wind, and Ulysses, structure in the coronal hole origin solar wind is examined from 0.3 AU to 2.3 AU. Care is taken to collect and analyze intervals of “unperturbed coronal hole plasma.” In these intervals, solar wind structure is seen in the proton number density, proton temperature, proton specific entropy, magnetic field strength, magnetic field to density ratio, electron heat flux, helium abundance, heavy‐ion charge‐state ratios, and Alfvenicity. Typical structure amplitudes are factors of 2, far from homogeneous. Variations are also seen in the solar wind radial velocity. Using estimates of the motion of the solar wind origin footpoint on the Sun for the various spacecraft, the satellite time series measurements are converted to distance along the photosphere. Typical variation scale lengths for the solar wind structure are several variations per supergranule. The structure amplitude and structure scale sizes do not evolve with distance from the Sun from 0.3 to 2.3 AU. An argument is quantified that these variations are the scale expected for solar wind production in open magnetic flux funnels in coronal holes. Additionally, a population of magnetic field foldings (switchbacks, reversals) in the coronal hole plasma is examined: this population evolves with distance from the Sun such that the magnetic field is mostly Parker spiral aligned at 0.3 AU and becomes more misaligned with distance outward.Key PointsCoronal hole origin solar wind is structured as seen by density, field strength, helium abundance, entropy, strahl, Alfvenicity, and so onThe structure exhibits several variations per supergranule; the structure does not evolve with distance from the Sun from 0.3 AU to 2.3 AUThe structure scale sizes might be consistent with scale sizes of the open flux funnels emanating from coronal holesPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/133555/1/jgra52697.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/133555/2/jgra52697_am.pd

Numerical simulation of a coarsening two-dimensional network

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