4,930 research outputs found
On the piecewise-concave approximations of functions
The piecewise-concave function may be used to approximate a wide range of
other functions to arbitrary precision over a bounded set. In this short paper,
this property is proven for three function classes: (a) the multivariate twice
continuously differentiable function, (b) the univariate Lipschitz-continuous
function, and (c) the multivariate separable Lipschitz-continuous function.Comment: 4 pages; written as a supplement to submitted journal pape
Coalescence Model for Crumpled Globules Formed in Polymer Collapse
The rapid collapse of a polymer, due to external forces or changes in
solvent, yields a long-lived `crumpled globule.' The conjectured fractal
structure shaped by hierarchical collapse dynamics has proved difficult to
establish, even with large simulations. To unravel this puzzle, we study a
coarse-grained model of in-falling spherical blobs that coalesce upon contact.
Distances between pairs of monomers are assigned upon their initial
coalescence, and do not `equilibrate' subsequently. Surprisingly, the model
reproduces quantitatively the dependence of distance on segment length,
suggesting that the slow approach to scaling is related to the wide
distribution of blob sizes
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