We propose a criterion for the validity of semiclassical gravity ~SCG! which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equatio...

Abstract. We investigate a kinetic model for the sedimentation of dilute suspensions of rod-like particles under gravity, deduced by Helzel, Otto and Tzavaras (2011), which couples the impressible (Navier-)Stokes equation with the Fokker-Planck equation. With no-flux boundary condition for distribution function, we establish the existence and uniqueness of global weak solution to the two dimens...

we investigate the exact renormalization group (RG) in Einstein gravity coupled to N-component scalar field, working in the effective average action formalism and background field method. The truncated evolution equation is obtained for the Newtonian and cosmological constants. We have shown that screening or antiscreening behaviour of the gravitational coupling depends cricially on the choice ...

Assuming SO(3)-spherical symmetry, the 4–dimensional Einstein equation reduces to an equation conformally related to the field equation for 2–dimensional gravity following from the Lagrangian L = |R|1/3. Solutions for 2–dimensional gravity always possess a local isometry because the traceless part of its Ricci tensor identically vanishes. Combining both facts, we get a new proof of Birkhoff’s t...

Long’s equation describes two dimensional stratified atmospheric flow over terrain. Its solutions using regular first order perturbations and linear approximation were investigated analytically and numerically by many authors. Special attention was paid to the properties of the gravity waves that have been predicted to be generated as a result. In this paper we derive a new representation of th...

Assuming SO(3)-spherical symmetry, the 4{dimensional Einstein equation reduces to an equation conformally related to the eld equation for 2{dimensional gravity following from the Lagrangian L = jRj 1=3. Solutions for 2{dimensional gravity always possess a local isometry because the traceless part of its Ricci tensor identically vanishes. Combining both facts, we get a new proof of Birkhoo's the...

Using both the Born-Oppenheimer idea and the de Broglie-Bohm interpretation of wavefunction we represent in a different way the semiclassical quantum gravity from the Wheeler-DeWitt equation in an oscillating regime which can preserve completely the unitary quantum evolution of a matter field at the expense of a nonlinear gravitational field equation, but has the same asymptotic limit as the ot...

Di€usion and convection coecients of the aerated ̄ow in a hydraulic jump are estimated in the framework of an optimal control problem. The speci®c gravity of air±water mixture is governed by a steady state convection di€usion partial di€erential equation. The governing equation includes the di€usion coecient and the convection coecient, which are taken as the control variables to minimize a ...

We study the drainage of the precorneal tear film in humans. A fluid dynamic model for the drainage of the aqueous layer is developed that includes the effects of evaporation and gravity. The model may be reduced to a single nonlinear partial differential equation for the thickness of the aqueous layer. The equation is solved numerically and accurate times for film rupture are obtained for phys...