For many years, the most active area of quantum cosmology has been the issue of choosing boundary conditions for the wave function of a universe. Recently, loop quantum cosmology, which is obtained from loop quantum gravity, has shed new light on this question. In this case, boundary conditions are not chosen by hand with some particular physical intuition in mind, but they are part of the dyna...

In this article it is shown that for specific initial conditions an input beam injected in a Multimode Periodic Segmented Waveguides (MPSW) does not diffract and remains collimated all along the waveguide whereas a speckle like pattern is expected at the output of a multimode structure. This nonintuitive behavior can be explained with the help of ray and wave chaos properties. A modal analysis ...

A motion of point vortices with periodic boundary conditions is studied by using Weierstrass zeta functions. Scattering and recoupling of a vortex pair by a third vortex becomes remarkable when the vortex density is large. Clustering of vortices with various initial conditions is quantitated by the L function used in point process theory in spatial ecology. It is shown that clustering persists ...

A spatially two-dimensional sixth order PDE describing the evolution of a growing crystalline surface h(x, y, t) that undergoes faceting is considered with periodic boundary conditions, such as its reduced onedimensional version. These equation are expressed in terms of the slopes u1 = hx and u2 = hy to establish the existence of global, connected attractors for both of the equations. Since uni...