Things only move when they are forced to move! A bicycle only moves when a force is applied
in the form of pedaling. A cloud on the sky only moves when a force is applied in the form of a
storm or a wind. A soccer ball only flies into the goal net when a force in the form of a beautiful
and precise shot from Peter Møller or another great soccer player is applied. Thus all sorts of
transport only take place when a force, called a driving force, is applied. This is also the case
when we are talking about transport of other...
During development, cells and tissues undergo dynamic changes in pattern
and form that employ a wider range of physical mechanisms than at any other
time during an organism’s life. Biological Physics of the Developing Embryo presents
a framework within which physics can be used to analyze these biological
Written to be accessible to both biologists and physicists, major stages
and components of biological development are introduced and then analyzed
from the viewpoint of physics. The presentation of physical models requires no
mathematics beyond basic calculus.
The stochastic 2D Navier-Stokes equations on the torus driven by degenerate noise are studied. We characterize the smallest closed invariant subspace for this model and show that the dynamics restricted to that subspace is ergodic. In particular, our results yield a purely geometric characterization of a class of noises for which the equation is ergodic in L2 (T2 ). Unlike previous 0 works, this class is independent of the viscosity and the strength of the noise.