Abstract:
We report recent progress on the test of mode coupling theory for molecular liquids (MMCT) for molecules of arbitrary shape. The MMCT equations in the long time limit are solved for supercooled water including all molecular degrees of freedom. In contrast to our earlier treatment of water as a linear molecule, we find that the glass transition temperature $T_c$ is overestimated by the theory as was found in the case of simple liquids. The nonergodicity parameters are calculated from the "full" set of MMCT-equations truncated at $l_{co}=2$. These results are compared $(i)$ with the nonergodicity parameters from MMCT with $l_{co}=2$ in the "dipole" approximation $n=n'=0$ and the diagonalization approximation $n=n'=0$,$l=l'$ and $(ii)$ with the corresponding results from a MD-simulation. This work supports the possibility that a reduction to the most prominent correlators may constitute a valid approximation for solving the MMCT equations for rigid molecules.

Abstract:
It has been shown that the extension of the elasticity theory in more than three dimensions allows a description of space-time as a properly stressed medium, even recovering the Minkowski metric in the case of uniaxial stress. The fundamental equation for the metric in the theory is shown to be the equilibrium equation for the medium. Examples of spherical and cylindrical symmetries in four dimensions are considered, evidencing convergencies and divergencies with the classical general relativity theory. Finally the possible meaning of the dynamics of the four dimensional elastic medium is discussed.

Abstract:
The chapter expounds a theory based on the interpretation of the dark energy as a strain energy of a physical continuum. The theory is based on the analogy that exists between the properties of space-time and the properties of elastic materials, when extended to four dimensions and the Lorentzian signature. In practice the starting point is an action integral that contains an additional term built as elastic potential energy of strained materials is. Besides this vacuum energy term matter/energy fields appear as usual. The strain energy term is based on the strain tensor of empty space-time which in turn is obtained from the non trivial part of the metric tensor. The Strained State Cosmology (SSC) is deduced from this approach when a Robertson-Walker symmetry is assumed: The result accounts for the accelerated expansion of the universe and agrees with observation passing four typical cosmological tests

Abstract:
Space time is described as a continuum four-dimensional medium similar to ordinary elastic continua. Exploiting the analogy internal stress states are considered. The internal ''stress'' is originated by the presence of defects. The defects are described according to the typical Volterra process. The case of a point defect in an otherwise isotropic four-dimensional medium is discussed showing that the resulting metric tensor corresponds to an expanding (or contracting) universe filled up with a non-zero energy-momentum density.

Abstract:
Considering the spacetime around a rotating massif body it is seen that the time of flight of a light ray is different whether it travels on one side of the source or on the other. The difference is proportional to the angular momentum of the body. In the case that a compact rapidly rotating object is the source of a gravitational lensing effect, the contribution coming from the above mentioned gravitational Aharonov-Bohm effect should be added to the other causes of phase difference between light rays coming from different images of the same object.

Abstract:
The presence of defects in material continua is known to produce internal permanent strained states. Extending the theory of defects to four dimensions and allowing for the appropriate signature, it is possible to apply these concepts to space-time. In this case a defect would induce a non-trivial metric tensor, which can be interpreted as a gravitational field. The image of a defect in space-time can be applied to the description of the Big Bang. A review of the four-dimensional generalisation of defects and an application to the expansion of the universe will be presented.

Abstract:
It is shown that, contrary to what is normally expected, it is possible to have angular momentum effects on the geometry of space time at the laboratory scale, much bigger than the purely Newtonian effects. This is due to the fact that the ratio between the angular momentum of a body and its mass, expressed as a length, is easily greater than the mass itself, again expressed as a length.

Abstract:
The paper considers the problem of finding the metric of space time around a rotating, weakly gravitating body. Both external and internal metric tensors are consistently found, together with an appropriate source tensor. All tensors are calculated at the lowest meaningful approximation in a power series. The two physical parameters entering the equations (the mass and the angular momentum per unit mass) are assumed to be such that the mass effects are negligible with respect to the rotation effects. A non zero Riemann tensor is obtained. The order of magnitude of the effects at the laboratory scale is such as to allow for experimental verification of the theory.

Abstract:
The paper treats the issue of the length of a rotating circumference as seen from on board the moving disk and from an inertial reference frame. It is shown that, properly defining a measuring process, the result is in both cases 2piR thus dissolving the Ehrenfest paradox. The same holds good when considering that, for the rotating observer, the perceived radius coincides with the curvature radius of a space-time helix and a complete round trip corresponds to an angle which differs from the one seen by the inertial observer. The apparent contradiction with the Lorentz contraction is discussed.

Abstract:
The essence of the gravitomagnetic clock effect is properly defined showing that its origin is in the topology of world lines with closed space projections. It is shown that, in weak field approximation and for a spherically symmetric central body, the loss of synchrony between two clocks counter-rotating along a circular geodesic is proportional to the angular momentum of the source of the gravitational field. Numerical estimates are presented for objects within the solar system. The less unfavorable situation is found around Jupiter.