The flow of blood through the cardiovascular system depends on basic principles of liquid flow in tubes elucidated by Bernoulli and Poiseuille. The elementary equations are described involving pressures related to velocity, acceleration/deceleration, gravity, and viscous resistance to flow (Bernoulli-Poiseuille equation). The roles of vascular diameter and number of branches are emphasized. In ...

Considering the non-Newtonian gravity proposed in grand unification theories, we show that the stability and observed global properties of neutron stars cannot rule out the supersoft nuclear symmetry energies at suprasaturation densities. The degree of possible violation of the inverse-square law of gravity in neutron stars is estimated using an equation of state of neutron-rich nuclear matter ...

Previous research regarding the solutions of Long’s equation always presumed that the flow far upstream is without shear. In this paper we derive the proper form of this equation when shear is present. We then apply a sequence of transformations to this equation which make it possible to linearize it while preserving its physical contents. We then derive conditions under which the solutions of ...

We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from two. We determine the scaling properties of the quantum gravity averaged diffusion kernel. email [email protected] email [email protected] email [email protected]....

Non-critical string field theory for 2d quantum gravity coupled to (p,q)–conformal fields Abstract We propose a non-critical string field theory for 2d quantum gravity coupled to (p,q) conformal fields. The Hamiltonian is described by the generators of the W p algebra, and the Schwinger-Dyson equation is equivalent to a vacuum condition imposed on the generators of W p algebra.

In a teleparallel theory of (2+1)-dimensional gravity developed in a previous paper, we examine generators of internal Lorentz transformations and of general affine coordinate transformations for static circularly symmetric exact solutions of gravitational field equation. The “spin” angular momentum, the energy-momentum and the “extended orbital angular momentum” are explicitly given for each s...

The main cosmological models on the brane are presented. A generic equation is given, from which the Friedmann equations of the Randall-Sundrum, induced gravity, Gauss-Bonnet and the combined induced gravity and Gauss-Bonnet cosmological models are obtained. We discuss the modifications they bring to the standard cosmology and the main features of their inflationary dynamics. Talk given at Pasc...

Long’s equation describes two dimensional stratified atmospheric flow over terrain which is represented by the geometry of the domain. The solutions of this equation over simple topography were investigated analytically and numerically by many authors. In this paper we derive a new terrain following formulation of this equation which incorporates the terrain as part of the differential equation...

Loop quantum gravity is one of the leading candidate theory to non-perturbatively quantize gravity. In this framework, holonomy corrections to the equation of propagation of gravitons in a FLRW background have been derived. We investigate the consequences of those corrections on the tensor power spectrum in de-Sitter and slow-roll inflations, for n=-1/2. Depending on the value of the Barbero-Im...

Using the differential equation approach to W-algebras, we discuss the inclusion of punctures in W-string theory. The key result is the existence of different kinds of punctures in W-strings. We obtain the moduli associated with these punctures and present evidence in existing W-string theories for these punctures. The W3 case is worked out in detail. It is conjectured that the (1, 3) minimal m...