A numerical scheme for axisymmetric solutions of curvature driven free boundary problems, with applications to the Willmore Flow

Interfaces and Free Boundaries. 4, no. 1, pp. 89-109. 2002
A numerical scheme for axisymmetric solutions of curvature driven free boundary problems, with applications to the Willmore Flow
Uwe Mayer, Gieri Simonett
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Abstract

We present a numerical scheme for radially symmetric solutions to curvature driven moving boundary problems governed by a local law of motion, e.g. the mean curvature flow, the surface diffusion flow, and the Willmore flow. We then present several numerical experiments for the Willmore flow. In particular, we provide numerical evidence that the Willmore flow can develop singularities in finite time.

Another publication from the same author: Uwe Mayer

Proceedings of the Sixteenth ACM Conference on Economics and Computation (EC '15). ACM, New York, NY, USA (2015)

Canary in the e-Commerce Coal Mine: Detecting and Predicting Poor Experiences Using Buyer-to-Seller Messages

Dimitriy Masterov, Uwe Mayer, Steve Tadelis

Reputation and feedback systems in online marketplaces are often biased, making it difficult to ascertain the quality of sellers. We use post-transaction, buyer-to-seller message traffic to detect signals of unsatisfactory transactions on eBay. We posit that a message sent after the item was paid for serves as a reliable indicator that the buyer may be unhappy with that purchase, particularly when the message included words associated with a negative experience. The fraction of a seller's message traffic that was negative predicts whether a buyer who transacts with this seller will stop purchasing on eBay, implying that platforms can use these messages as an additional signal of seller quality.

Another publication from the same category: Mathematics

Archiv der Mathematik, 77, issue 5, pp. 434-448. 2001

Loss of convexity for a modified Mullins-Sekerka model arising in diblock copolymer melts

Joachim Escher, Uwe Mayer

This modified (two-sided) Mullins-Sekerka model is a nonlocal evolution model for closed hypersurfaces, which appears as a singular limit of a modified Cahn-Hilliard equation describing microphase separation of diblock copolymer.

Under this evolution the propagating interfaces maintain the enclosed volumes of the two phases. We will show by means of an example that this model does not preserve convexity in two space dimensions.

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