@article{b,
title = {Stationary Growth and Unique Invariant Harmonic Measure of Cylindrical Diffusion Limited Aggregation},
author = {Riccardo Marchetti and Alessandro Taloni and Emanuele Caglioti and Vittorio Loreto and Luciano Pietronero},
url = {http://prl.aps.org/},
year = {2012},
date = {2012-01-01},
journal = {PHYSICAL REVIEW LETTERS},
volume = {109},
publisher = {AMER PHYSICAL SOC},
abstract = {We prove that the harmonic measure is stationary, unique, and invariant on the interface of diffusion limited aggregation (DLA) growing on a cylinder surface. We provide a detailed theoretical analysis puzzling together multiscaling, multifractality, and conformal invariance, supported by extensive numerical simulations of clusters built using conformal mappings and on a lattice. The growth properties of the active and frozen zones are clearly elucidated. We show that the unique scaling exponent characterizing the stationary growth is the DLA fractal dimension.},
keywords = {caglioti, complex_systems, loreto, marchetti, pietronero, taloni},
pubstate = {published},
tppubtype = {article}
}
We prove that the harmonic measure is stationary, unique, and invariant on the interface of diffusion limited aggregation (DLA) growing on a cylinder surface. We provide a detailed theoretical analysis puzzling together multiscaling, multifractality, and conformal invariance, supported by extensive numerical simulations of clusters built using conformal mappings and on a lattice. The growth properties of the active and frozen zones are clearly elucidated. We show that the unique scaling exponent characterizing the stationary growth is the DLA fractal dimension.
@article{b,
title = {Conformal approach to cylindrical DLA},
author = {Alessandro Taloni and Emanuele Cagliori and Vittorio Loreto and Luciano Pietronero},
url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-37649026579&partnerID=65&md5=18e07a1e17966902ff4a2c6e9b9dadfc
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=000241413300004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=0c7ff228ccbaaa74236f48834a34396a},
year = {2006},
date = {2006-01-01},
journal = {JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT},
volume = {Art. n. P09004},
abstract = {We extend the conformal mapping approach elaborated for the radial diffusion limited aggregation model (DLA) to cylindrical geometry. We introduce in particular a complex function which allows a cylindrical cluster to be grown using as an intermediate step a radial aggregate. The aggregate grown exhibits the same self-affine features as the original cylindrical DLA. The specific choice of the transformation allows us to study the relationship between the radial and the cylindrical geometry. In particular the cylindrical aggregate can be seen as a radial aggregate with particles of size increasing with the radius. On the other hand, the radial aggregate can be seen as a cylindrical aggregate with particles of size decreasing with the height. This framework, which shifts the point of view from the geometry to the size of the particles, can open the way to more quantitative studies on the relationship between radial and cylindrical DLA.},
keywords = {caglioti, DLA, fractals, loreto, pietronero, self_organization, statistical_physics, taloni},
pubstate = {published},
tppubtype = {article}
}
We extend the conformal mapping approach elaborated for the radial diffusion limited aggregation model (DLA) to cylindrical geometry. We introduce in particular a complex function which allows a cylindrical cluster to be grown using as an intermediate step a radial aggregate. The aggregate grown exhibits the same self-affine features as the original cylindrical DLA. The specific choice of the transformation allows us to study the relationship between the radial and the cylindrical geometry. In particular the cylindrical aggregate can be seen as a radial aggregate with particles of size increasing with the radius. On the other hand, the radial aggregate can be seen as a cylindrical aggregate with particles of size decreasing with the height. This framework, which shifts the point of view from the geometry to the size of the particles, can open the way to more quantitative studies on the relationship between radial and cylindrical DLA.
