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The traditional field of continuum mechanics, which contains both
elasticity and fluid mechanics is going through a
resurgance due to possible applications to biology. Biological systems
bring in two novel aspects : (a) biological samples
are complex -- often they cannot be clearly demarcated into solid and
fluid. They may be viscoelastic. (b) biological samples
are living. This second aspect is the most important one. The
fundamental aspect of a living systems is that they are out of
equilibrium -- they generate entropy. This poses the question : how
do the equations of elasticity and fluid mechanics must
change to take into account the fundamental non-equilibrium nature of
these systems.
Within this broad framework, I will present three problems. One, how
to estimate the entropy generation rate, which is a measure of
activity, of living systems. Two, how the buckling of shells, a
traditional non-linear problem in elasticity, change if the shells are
made active. Three, how tools from quanum field theory can be
harnessed to model elastic properties of active solids.
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