The principal emphasis of Prof. Ashby's research is on theoretical general relativity with practical applications. For example, studies of relativistic effects within navigational satellite systems such as the Global Positioning System (a set of 24 satellites carrying atomic clocks) show that several relativistic effects must be accounted for in order for the system work properly.
Another application is to the study of relativistic perturbations of the motion of earth-orbiting satellites, and to the interpretation of the results of accurate laser ranging experiments from the earth to such satellites as LAGEOS. Accounting for relativistic effects due to motion of the earth around the sun, such as the effects of Lorentz contraction and breakdown of simulataneity, on the higher order multipole gravitational potentials of the earth, is important in the determination of the earth's mass. Simulation of accurate ranging between the Earth and an orbiter or lander on the planet Mercury show that ranging experiments are among the best available techniques to test alternative theories of gravitation. Another area of current active interest is the generation of gravitation waves by compact objects such as neutron stars, spiraling into, and being captured by, very massive black holes.
A secondary area of interest is statistical mechnics. In particular,
solutions of the Uehling-Uhlenbeck equations are being studied with the
aid of a set of orthogoanl polynomials, analagous to Sonine polynomials,
but constructed to provide convenient solutions to the problem of transport
in situations where quantum effects are important. Applications being looked
at included transport in mixtures of liquid Helium II, liquid helium IV,
and dilute gases at low temperatures.
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