What is the approximate density of a fish, compared with the density of the water in which it swims?
Professor of Physics Paul Goldbart, in collaboration with Xiangjun Xing (Syracuse) and Leo Radzihovsky (Colorado), has solved a theory problem that has puzzled physicists since the 1940s (Phys. Rev. Lett. 98, 075502 ).
Measuring the force produced by stretching a rubber band to its limits is easy, but the standard theory of rubbery materials cannot predict this force.
When they are not stretched too much, rubbery materials act as simple springs, obeying Hooke's law. Thus, a 10-percent increase in stretching force will extend a typical rubber band 10 percent farther. But at greater stretching forces, that simple linear relation fails. The existence of the nonlinearity has long been known, but understanding its origins and developing a theory that correctly captures it "has been a challenge to the physics community for 60 years," said Goldbart.
By including the extra entropy associated with long length-scale motion while simultaneously coping with the essentially incompressible nature of rubbery materials, the researchers are now able to construct a theory that agrees with experiment, not only in the Hookean regime but also beyond—deep into the nonlinear regime. Read more...
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