Two-sided Mullins-Sekerka flow does not preserve convexity

Proceedings of the Third Mississippi State Conference on Difference Equations and Computational Simulations. Mississippi State, MS. 1997
Two-sided Mullins-Sekerka flow does not preserve convexity
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Abstract

The (two-sided) Mullins-Sekerka model is a nonlocal evolution model for closed hypersurfaces, which was originally proposed as a model for phase transitions of materials of negligible specific heat. Under this evolution the propagating interfaces maintain the enclosed volume while the area of the interfaces decreases.

We will show by means of an example that the Mullins-Sekerka flow does not preserve convexity in two space dimensions, where we consider both the Mullins-Sekerka model on a bounded domain, and the Mullins-Sekerka model defined on the whole plane.

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

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

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.

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