449 research outputs found
Geometrical frustration yields fiber formation in self-assembly
Controlling the self-assembly of supramolecular structures is vital for
living cells, and a central challenge for engineering at the nano- and
microscales. Nevertheless, even particles without optimized shapes can robustly
form well-defined morphologies. This is the case in numerous medical conditions
where normally soluble proteins aggregate into fibers. Beyond the diversity of
molecular mechanisms involved, we propose that fibers generically arise from
the aggregation of irregular particles with short-range interactions. Using a
minimal model of ill-fitting, sticky particles, we demonstrate robust fiber
formation for a variety of particle shapes and aggregation conditions.
Geometrical frustration plays a crucial role in this process, and accounts for
the range of parameters in which fibers form as well as for their metastable
character.Comment: 6 pages, 5 figures, 1 ancillary movie; to appear in Nature Physic
Characteristic Angles in the Wetting of an Angular Region: Surface Shape
The shape of a liquid surface bounded by an acute or obtuse planar angular
sector is considered by using classical analysis methods. For acute angular
sectors the two principal curvatures are of the order of the (fixed) mean
curvature. But for obtuse sectors, the principal curvatures both diverge as the
vertex is approached. The power-law divergence becomes stronger with increasing
opening angle. Possible implications of this contrasting behavior are
suggested.Comment: 19 pages, 9 figures, LaTeX; submitted to The European Physics Journal
E; v2: Introduction was revised (a number of references added), minor changes
to the main part (mostly typos), former Implications subsection was almost
entirely rewritten and is now called Experimental Realizations (experimental
results and two figures added); v3: Introduction was slightly modified, four
references added; v4: Title was modified, section Calculation was
significantly modified (subsections Bounary Problem and Horizontal Solution
almost entirely rewritten, minor changes to the other subsections),
subsection Curvature in section Discussion was revised, one reference adde
Conserved Linking in Single- and Double-Stranded Polymers
We demonstrate a variant of the Bond Fluctuation lattice Monte Carlo model in
which moves through cis conformations are forbidden. Ring polymers in this
model have a conserved quantity that amounts to a topological linking number.
Increased linking number reduces the radius of gyration mildly. A linking
number of order 0.2 per bond leads to an eight-percent reduction of the radius
for 128-bond chains. This percentage appears to rise with increasing chain
length, contrary to expectation. For ring chains evolving without the
conservation of linking number, we demonstrate a substantial anti-correlation
between the twist and writhe variables whose sum yields the linking number. We
raise the possibility that our observed anti-correlations may have counterparts
in the most important practical polymer that conserves linking number, DNA.Comment: Revised title, minor changes, updated references. 36 pages, including
14 figures. More formats available at
http://rainbow.uchicago.edu/~plewa/webpaper
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