## Sunday, August 22, 2021

## Monday, December 14, 2020

## Saturday, December 05, 2020

### Perfect Fluid

# Perfect fluid

In physics, a **perfect fluid** is a fluid that can be completely characterized by its rest frame mass density $\rho _{m}$ and *isotropic* pressure *p*.

Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are neglected. Specifically, perfect fluids have no shear stresses, viscosity, or heat conduction.

In space-positive metric signature tensor notation, the stress–energy tensor of a perfect fluid can be written in the form

- $T^{\mu \nu }=\left(\rho _{m}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }+p\,\eta ^{\mu \nu }\,$

where *U* is the 4-velocity vector field of the fluid and where $\eta _{\mu \nu }=\operatorname {diag} (-1,1,1,1)$ is the metric tensor of Minkowski spacetime.

In time-positive metric signature tensor notation, the stress–energy tensor of a perfect fluid can be written in the form

- $T^{\mu \nu }=\left(\rho _{\text{m}}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }-p\,\eta ^{\mu \nu }\,$

where *U* is the 4-velocity of the fluid and where $\eta _{\mu \nu }=\operatorname {diag} (1,-1,-1,-1)$ is the metric tensor of Minkowski spacetime.

This takes on a particularly simple form in the rest frame

- $\left[{\begin{matrix}\rho _{e}&0&0&0\\0&p&0&0\\0&0&p&0\\0&0&0&p\end{matrix}}\right]$

where $\rho _{\text{e}}=\rho _{\text{m}}c^{2}$ is the *energy density* and $p$ is the *pressure* of the fluid.

Perfect fluids admit a Lagrangian formulation, which allows the techniques used in field theory, in particular, quantization,
to be applied to fluids. This formulation can be generalized, but
unfortunately, heat conduction and anisotropic stresses cannot be
treated in these generalized formulations.^{[why?]}

Perfect fluids are used in general relativity to model idealized distributions of matter, such as the interior of a star or an isotropic universe. In the latter case, the equation of state of the perfect fluid may be used in Friedmann–Lemaître–Robertson–Walker equations to describe the evolution of the universe.

In general relativity, the expression for the stress–energy tensor of a perfect fluid is written as

- $T^{\mu \nu }=\left(\rho _{m}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }+p\,g^{\mu \nu }\,$

where *U* is the 4-velocity vector field of the fluid and where $g_{\mu \nu }$ is the metric,
written with a space-positive signature.

## See also

## References

- The Large Scale Structure of Space-Time, by S.W.Hawking and G.F.R.Ellis, Cambridge University Press, 1973. ISBN 0-521-20016-4, ISBN 0-521-09906-4 (pbk.)

## External links

- Mark D. Roberts, [A Fluid Generalization of Membranes http://www.arXiv.org/abs/hep-th/0406164 hep-th/0406164].

## Tuesday, December 01, 2020

### Past String Conferences

Strings 2019, Brussels, Belgium

Strings 2018, Okinawa, Japan

Strings 2017, Israel

Strings 2016, Beijing, China

Strings 2015, Bengaluru, India

Strings 2014, Princeton, USA

Strings 2013, Seoul, Korea

Strings 2012, Munich, Germany

Strings 2011 Uppsala, Sweden

Strings 2010 Texas, USA

Strings 2009, Rome, Italy

Strings 2008, CERN, Switzerland

Strings 2007, Madrid, Spain

Strings 2006, Beijing, China

Strings 2005, Toronto, Canada

Strings 2004, Paris, France

Strings 2003, Kyoto, Japan

Strings 2002, Cambridge, United Kingdom

Strings 2001, Mumbai, India

Strings 2000, Ann Arbor, USA

Strings 1999, Potsdam, Germany

Strings 1998, Santa Barbara, USA

Strings 1997, Amsterdam, The Netherlands

Strings 1996, Santa Barbara, USA

Strings 1995, Los Angeles, USA

## Monday, November 23, 2020

### Solar Panel Revolution in the Wind?

I am encouraged by some research that is currently going on that is improving the efficiency of solar panels up and coming. This encouragement is based on designs I have seen in corollary manufacturing processes that could created a whole new industry.

It is a whole new research path that could greatly improve the energy retention otherwise seemingly at a standstill, although these manufacturing processes for solar panels are currently inexpensive.

I have been pondering these ideas for sometime now and since the move to electrics for transportation is now more important then ever as I open the door to the studious and bright innovators who wonder about these potentials.

## New solar panel design could increase efficiency by 125%

## Dr. Christian Schuster, researcher from the Department of Physics, told The Week news “We found a simple trick for boosting the absorption of slim solar cells. Our investigations show that our idea actually rivals the absorption enhancement of more sophisticated designs, while also absorbing more light deep in the plane and less light near the surface structure itself. Our design rule meets all relevant aspects of light trapping for solar cells, clearing the way for simple, practical, and yet outstanding diffractive structures, with a potential impact beyond photonic applications.” He added, “This design offers potential to further integrate solar cells into thinner, flexible materials and therefore create more opportunity to use solar power in more products.”

**See also**: Frogs, Foam and Fuel: UC Researchers Convert Solar Energy to Sugars

## Thursday, August 20, 2020

### Everyday Einstein: GPS & Relativity

See also: Everyday Einstein: GPS and Relativity @Perimeter Institute for Theoretical Physics