The Geometry of Soft Materials: A Primer

By Randall D. Kamien. 2002

354 citations recorded by the source corpus.

We present an overview of the dieren tial geometry of curves and surfaces using examples from soft matter as illustrations. The presentation requires a background only in vector calculus and is otherwise self-contained.

Subfields: Fluid Flow and Transfer Processes, Geometry and Topology, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/e85f64f2e7a65e36589922e6b03b741cbcd80ade

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In Fluid Flow and Transfer Processes

In Geometry and Topology

In Mechanical Engineering

Citations in the corpus

Linked and knotted beams of light (2008, background): “Two closed field lines c 1 ( τ ) , c 2 ( τ ) are linked if they have non-vanishing Gauss linking integra”
Drops and shells of liquid crystal (2011, methodology): “Similarly to the Euler theorem, there is a theorem due to Poincare and Hopf, which states that the total topological charge for nematic or vector order on the sphere has to be +2 [2, 5 , 20].”
Dynamics of filaments and membranes in a viscous fluid (2009, methodology): “Like the review (Kamien, 2002), we give a unified treatment of curves and surfaces from the “extrinsic” point of view, in which distances along curves and surfaces sitting in three-dimensional space are measured using the notion of distance in that three-dimensional space.”
Colloquium: Disclination loops, point defects, and all that in nematic liquid crystals (2012, neutral): “absolute value of the Jacobian, we measure positive and negative area and thus will properly count the analog of increasing and decreasing as needed in (5) for the winding number. See, for instance, (Kamien, 2002) for the derivation of this Jacobian and its connection to Gaussian curvature. Therefor”
Anisotropy of building blocks and their assembly into complex structures. (2007, background): “Attempts to rationalize principles of self-organization in copolymers and surfactants through the use of geometric concepts have provided insight into the universality of certain structure”