Bootstrapped Newtonian gravity was developed with the purpose of estimating the impact of quantum physics in the nonlinear regime of the gravitational interaction, akin to corpuscular models of black holes and inflation. In this work, we set the ground for extending the bootstrapped Newtonian picture to cosmological spaces. We further discuss how such models of quantum cosmology can lead to a natural solution to the cosmological constant problem.
Abstract
When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.
Abstract
The aim of this paper is to study a quasistatic contact problem between an
electro-elastic viscoplastic body with damage and an electrically conductive
foundation. The contact is modelled with an electrical condition, normal
compliance and the associated version of Coulomb’s law of dry friction in
which slip dependent friction is included. We derive a variational
formulation for the model and, under a smallness assumption, we prove the
existence and uniqueness of a weak solution.
The method to be described provides an alternative means of dealing with certain non-standard linear boundary-value problems. It is developed in several applications to the theory of gravity-capillary waves. The analysis is based on a variational formulation of the hydrodynamic problem, being motivated by and extending the original study by Benjamin and Scott [3].
Variational formulation of the problems of mechanics and its matrix analogy
