## Saturday, March 10, 2007

### Relativistic Fluid Dynamics

The Navier-Stokes equations

A bubble is a minimal-energy surface
The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances such as liquids and gases. These equations establish that changes in momentum in infinitesimal volumes of fluid are simply the product of changes in pressure and dissipative viscous forces (similar to friction) acting inside the fluid. These viscous forces originate in molecular interactions and dictate how viscous a fluid is. Thus, the Navier-Stokes equations are a dynamical statement of the balance of forces acting at any given region of the fluid.

In educating myself I learnt to trust my intuition when it comes to defining the basis of "new physics" that was to emerge. As well as, the new particle manifestation that would arise from "specific points" on interaction. What was suppose to be our starting point. This is really difficult for me to put into words, yet, if you knew that there was a "change over/cross over point" and how was this defined? It seemed to me, we had to have a place that would do this.

A more fundamental property than the disappearance of viscosity becomes visible if superfluid is placed in a rotating container. Instead of rotating uniformly with the container, the rotating state consists of quantized vortices. That is, when the container is rotated at speed below the first critical velocity (related to the quantum numbers for the element in question) the liquid remains perfectly stationary. Once the first critical velocity is reached, the superfluid will very quickly begin spinning at the critical speed. The speed is quantized - i.e. it can only spin at certain speeds.

"Nothing" is difficult to talk about, and "empty space" is not really empty. So to think "nothing" is a very hard one for me to grasp. If one thinks about what "sprang into being" I of course had to find this "place of traversing" from "one state of being" to another. What things help us to define the nature of that point?

Example of the viscosity of milk and water. Liquids with higher viscosities will not make such a splash.

Viscosity is a measure of the resistance of a fluid to deform under shear stress. It is commonly perceived as "thickness", or resistance to flow. Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of fluid friction. Thus, water is "thin", having a lower viscosity, while vegetable oil is "thick" having a higher viscosity. All real fluids (except superfluids) have some resistance to shear stress, but a fluid which has no resistance to shear stress is known as an ideal fluid or inviscid fluid (Symon 1971).

I used the question mark not to befuddle those that read here or sanction any post to some idea about what the title following with a question mark, is worth so many points on the "flowery scale."

On the other hand, gravity in the form of curved space would permeate the whole bulk of the higher dimensional spacetime …. Stephen Hawking1

I shall have to define "flowery scale" sometime, but I would rather not give any credit to those who hold a position in science who have categorize people according to that same point system. Oh and please, do not consider the flowers less then what I hold as of high value in these "maturations" to be thought less then either.

While we had been witness to the collider experiments we were also quite aware that that such events had to be taking place with earth, from event sources released in space.

Relativistic Fluid Dynamics: Physics for Many Different Scales-Nils Andersson

In writing this review, we have tried to discuss the different building blocks that are needed if one wants to construct a relativistic theory for fluids. Although there are numerous alternatives, we opted to base our discussion of the fluid equations of motion on the variational approach pioneered by Taub [108] and in recent years developed considerably by Carter [17, 19, 21]. This is an appealing strategy because it leads to a natural formulation for multi-fluid problems. Having developed the variational framework, we discussed applications. Here we had to decide what to include and what to leave out. Our decisions were not based on any particular logic, we simply included topics that were either familiar to us, or interested us at the time. That may seem a little peculiar, but one should keep in mind that this is a “living” review. Our intention is to add further applications when the article is updated. On the formal side, we could consider how one accounts for elastic media and magnetic fields, as well as technical issues concerning relativistic vortices (and cosmic strings). On the application side, we may discuss many issues for astrophysical fluid flows (like supernova core collapse, jets, gamma-ray bursts, and cosmology).

In updating this review we will obviously also correct the mistakes that are sure to be found by helpful colleagues. We look forward to receiving any comments on this review. After all, fluids describe physics at many different scales and we clearly have a lot of physics to learn. The only thing that is certain is that we will enjoy the learning process!

Spacetime Curvatures

Flat space time? The thought there are strong gravitational forces at work and where are these located? Can there "be" amidst this strong curvature, the idea that a super fluid born, would have a place where a state of inertia could exist? I thought quickly of what happens when the blackhole collapses and what could come of it?

Of course this concept of inertia is strong in my mind but would need better clarifications as I am relaying it here in this circumstance.

But looking for these locations in Lagrangian views of the Sun Earth relation, it seemed viable to me that such a state could have gone from a very strong gravitational inclination( our suns, increase temperatures of the collapsing blackhole) to one that is "very free" and "not flat" but would allow information both ways(from before to now) to be traversed, as if in a jet or cylinder. So that the space around it would be expression not only the earlier constituents of the universe before this translation but manifest into the new physics with which would motive this universe, new particle manifestation, from what did not exist before.

1The Universe in a Nutshell, by Stephen Hawking. Bantam Books, ISBN 0-553-80202-X-Chapter 7, Page 181