Gravity without averaging

Vibrational control without averaging

The standard approach to vibrational control applies first-order averaging methods to find an openloop periodic input that stabilizes an unstable equilibrium point. While the capability of stabilization without feedback is appealing, this formulation has drawbacks from a design perspective. An alternative design framework based on stability maps for second-order linear periodic systems is not a...

Averaging Problem in Cosmology and Macroscopic Gravity

Quantum Gravity Without Ghosts

An outline is given of a recently discovered technique for building a quantum e ective action that is completely independent of gaugexing choices and ghost determinants. One makes maximum use of the geometry and brebundle structure of the space of eld histories and introduces a set of nonlocal composite elds: the geodesic normal elds based on Vilkovisky's connection on the space of histories. T...

The averaging of gravity currents in porous media

We explore the problem of a moving free surface in a water-saturated porous medium that has either a homogeneous or a periodically heterogeneous permeability field. We identify scaling relations and derive similarity solutions for the homogeneous, constant coefficient case in both a Cartesian and an axisymmetric, radial coordinate system. We utilize these similarity scalings to identify half-he...

The Averaging Problem in Cosmology and Macroscopic Gravity

The averaging problem in cosmology and the approach of macroscopic gravity to resolve the problem is discussed. The averaged Einstein equations of macroscopic gravity are modified on cosmological scales by the macroscopic gravitational correlation tensor terms as compared with the Einstein equations of general relativity. This correlation tensor satisfies a system of structure and field equatio...