What is the curvature parameter?

The transverse curvature parameter is defined as the ratio of the boundary-layer thickness and cylinder radius. For a very small transverse curvature parameter, the problem can be solved in two dimensions, but for a thin cylinder, the radius order can be the same as the order of the boundary-layer thickness.

What did Alexander Friedmann discover?

Ninety years ago, Russian physicist Alexander Friedmann (1888–1925) demonstrated for the first time that Albert Einstein’s general theory of relativity (GR) admits nonstatic solutions. It can, he found, describe a cosmos that expands, contracts, collapses, and might even have been born in a singularity.

What curvature will the universe have if the matter and energy density of the universe is equal to the critical density?

zero curvature
If the universe has an average mass density equal to the critical density, it is a flat universe with zero curvature, infinite volume, and expands forever though slowing down to zero infinitely far in the future.

What is curvature formula?

The curvature(K) of a path is measured using the radius of the curvature of the path at the given point. If y = f(x) is a curve at a particular point, then the formula for curvature is given as K = 1/R.

What did Alexander Friedmann do?

Alexander Friedmann was a Russian physicist and mathematician best-known for his work on the theory of relativity and in particular for introducing the possibility of an expanding universe.

How is the Friedmann equation used to determine the age of the universe?

The Friedmann equation includes the Hubble constant to give a much more accurate age of the universe. In this equation, G is the gravitational constant = 6.67*10-11Nm2/kg2, ρr is the radiation density of the universe, ρm is the matter density of the universe, and ρd is the dark energy density of the universe.

Who proposed the oscillating theory?

Einstein first proposed this theory in the 1920’s in response to the model of the expanding universe.

Who is Alexander Fridman?

Alexander Fridman is a professor at Drexel University and the director of the Nyheim Plasma Institute. He is one of the top plasma physicists and plasma chemists in the world.

What are the Friedmann equations for negative spatial curvature?

The equations for negative spatial curvature were given by Friedmann in 1924. The Friedmann equations start with the simplifying assumption that the universe is spatially homogeneous and isotropic, i.e. the cosmological principle; empirically, this is justified on scales larger than ~100 Mpc.

What are the basic assumptions of the Friedmann equations?

The Friedmann equations start with the simplifying assumption that the universe is spatially homogeneous and isotropic, i.e. the cosmological principle; empirically, this is justified on scales larger than ~100 Mpc. The cosmological principle implies that the metric of the universe must be of the form

What is the Friedmann equation for a flat k = 0 universe?

For some purposes, this separation is unnecessary, since the Friedmann equation treats all contributions to the density parameter equally: Thus, a flat k = 0 universe requires i = 1 at all times, whatever the form of the contributions to the density, even if the equation of state cannot be decomposed in this simple way.

When were the Friedmann equations of gravitation derived?

They were first derived by Alexander Friedmann in 1922 from Einstein’s field equations of gravitation for the Friedmann–Lemaître–Robertson–Walker metric and a perfect fluid with a given mass density and pressure . The equations for negative spatial curvature were given by Friedmann in 1924.