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Clement et al-science

Clement et al-science - Observational and Model Evidence...

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DOI: 10.1126/science.1171255 , 460 (2009); 325 Science et al. Amy C. Clement, Low-Level Cloud Feedback Observational and Model Evidence for Positive This copy is for your personal, non-commercial use only. . clicking here colleagues, clients, or customers by , you can order high-quality copies for your If you wish to distribute this article to others . here following the guidelines can be obtained by Permission to republish or repurpose articles or portions of articles (this information is current as of October 1, 2010 ): The following resources related to this article are available online at www.sciencemag.org http://www.sciencemag.org/cgi/content/full/325/5939/460 version of this article at: including high-resolution figures, can be found in the online Updated information and services, http://www.sciencemag.org/cgi/content/full/325/5939/460/DC1 can be found at: Supporting Online Material found at: can be related to this article A list of selected additional articles on the Science Web sites http://www.sciencemag.org/cgi/content/full/325/5939/460#related-content 8 article(s) on the ISI Web of Science. cited by This article has been http://www.sciencemag.org/cgi/content/full/325/5939/460#otherarticles 2 articles hosted by HighWire Press; see: cited by This article has been http://www.sciencemag.org/cgi/collection/atmos Atmospheric Science : subject collections This article appears in the following registered trademark of AAAS. is a Science 2009 by the American Association for the Advancement of Science; all rights reserved. The title Copyright American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the Science on October 1, 2010 www.sciencemag.org Downloaded from
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deformation of opposite sign until square. The elastic energy f E ( s ´, s ´´) of the resulting lam- inate of half-layers in a given state of curvature was then calculated to quadratic order in the principal curvatures s ´a n d s ´´. The layer elastic energy per volume obtained is f E = K /2 ( s ´+ s ´´) 2 K ( s ´ s ´´) + G ( s ´´ s ´), where K is the Frank elastic constant for mean curvature ( s ´+ s ´´), K is the Frank constant for Gaussian curvature ( s ´ s ´´), and G º b drives curvature in response to the frustrated internal in-plane layer strain b ( 16 ). For a minimal surface ( s = s ´= s ´´), the free energy is particularly sim- ple: f m E = K s 2 2 G s , making R p K / G the preferred radius of curvature. The energy f = f E ( s ´, s ´´) + D u ,where D u is the Gibbs potential per volume of the in-plane freezing, can be used to predict the structure of a filament, viewed as a set of ribbon-like layers twisted with a half-pitch h p / q ( 16 ). The central layer is a minimal sur- face of curvature s = q along its centerline, so that for a very narrow ribbon ( w
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