Mathematical Biofluiddynamics (CBMS-NSF Regional Conference by Sir James Lighthill

By Sir James Lighthill

Addresses exterior biofluiddynamics pertaining to animal locomotion via surrounding fluid media - and inner biofluiddynamics bearing on warmth and mass shipping by means of fluid movement structures inside of an animal.

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R&. "O'~ qv& '--,.. t~t Fig. 3. 17) Neutrons, in view of their large mass, are scattered mainly by nuclei, so information about correlations of nuclei can be obtained in a more natural way by means of neutron scattering, for which proportionality of the scattering intensity to the structure factor J(k) '" S(k) also holds. Thus, by measuring the scattering intensity one can experimentally find h(r) by taking the inverse Fourier transform of S(k). The structure factor therefore represents a direct link between theory and experiment.

We obtained this erroneous result because the atmosphere was considered to be in thermal equilibrium, which is not true. However, this result shows that the gravitational field is not able to keep the gas in thermal equilibrium, and the atmosphere should ultimately diffuse into space. For Earth this process is extremely slow, and during its lifetime Earth has not lost an appreciable amount of its atmosphere. For the Moon the process is significantly faster because its gravitational field is many times weaker, so the Moon now has no atmosphere.

3) is equal to N(N - 1) = N2 - N. 13) Note that this result is independent of any special assumptions about the interaction energy UN, such as pairwise additivity; recall that derivation of the pressure equation and the energy equation was based on the assumption of pairwise additivity. 4 Thermodynamic consistency At the beginning of this chapter we briefly mentioned a problem of thermodynamic consistency. Let us demonstrate it in an explicit way by calculating the pressure from the compressibility equation and comparing with the virial equation.

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