Preprint: Thermalization of rate-independent processes by entropic regularization

Somewhat belatedly, I’ve just uploaded to the arXiv a preprint of a joint paper with Marisol Koslowski, Florian Theil and Michael Ortiz entitled “Thermalization of rate-independent processes by entropic regularization”. The full paper is slated appear in Discrete and Continuous Dynamical Systems – Series S in early 2013.

The topic of the paper is a cute little extension of some of my PhD work, in which we show that the effect of coupling a rate-independent process (a decent model for plastic evolutions such as dry friction) to a heat bath (injecting a bit of statistically disordered energy) is equivalent to “softening” the dissipation potential by taking its Cramer transform (a smoothing and strict convexification procedure often used in large deviations theory).

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Varieties

Just a quick post to heartily recommend Terence Tao’s latest blog post, “A trivial remark about schemes”. My mathematical intuition has always been strongest in analysis; algebra and geometry have always seemed appealing in their exactness (cf. the old adage about algebra being the cult of the equal-to sign, and analysis the cult of the less-than-or-equal-to sign) but remote from my intuition. In particular, I never understood all this talk of varieties, nor the supposed equivalence between the algebraic geometry and commutative algebra points of view — whatever they were! Tao’s post does a wonderful job of clearing all that up within the first few paragraphs. Bravo!