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math.columbia.edu

Resources For Current Students Your Academic Advisor is the Program Director: Jaehyuk Choi E: jc6569@columbia.eduT: 212-854-2643426 Mathematics Building (Office Hours) The Career Development Advisor:

projecteuclid.org

In 1691, James (Jacob) Bernoulli proposed a problem called elastica problem: What shape of elastica, an ideal thin elastic rod on a plane, is allowed? Daniel Bernoulli discovered its energy functional, Euler-Bernoulli energy function, and the minimal principle of the elastica. Using it, Euler essentially solved the problem in 1744 by developing the variational method, elliptic integral theory and so on. This article starts with a review of its mathematical meaning and historical background. After that we present one of its extensions, statistical mechanics of elastica as a model of the DNA and the large polymers. We will call it a quantized elastica, and show that it is connected with the modified Korteweg-de Vries hierarchy, loop space, submanifold Dirac operators, moduli spaces of the real hyperelliptic curves and so on. By reviewing the other extensions of the elastica problem, we will see that elastica is in the center of mathematics even now.

jmp.aip.org

journal of mathematical physics, since 1960, publishes some of the best papers from outstanding mathematicians and physicists. it was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods suitable for such applications and for the formulation of physical theories.