Causality principle for the klein- gordon equation, Physics

Suppose Fluid (say, water) occupies a domain D 230_causality principle for the Klein- Gordon equation.png and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and will be transported by the fluid as well as diffused within it; let u= u(x,t) be the concentration of the substance( mass per unit volume). Let 826_causality principle for the Klein- Gordon equation1.png be the concentration flux (mass per unit area per unit time, analogous to heat flux). Let B(x) be a ball of radius r > 0 contained in D. Derive the conservation law.

995_causality principle for the Klein- Gordon equation2.png

Fick's law for diffusion states  that the concentration flux due to diffusion is proportional to the gradient of the concentration flux due to diffusion is proportional to the gradient of the concentration. Deduce that 1363_causality principle for the Klein- Gordon equation3.png.

Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion- transport equation:

783_causality principle for the Klein- Gordon equation4.png

this is the higher- dimensional transport equation. If the fluid is motionless, it is called the diffusion equation.

Determine the causality principle for the Klein- Gordon equation in one dimension. Deduce that the speed of propagation is at most c.

Posted Date: 4/2/2013 3:26:32 AM | Location : United States







Related Discussions:- Causality principle for the klein- gordon equation, Assignment Help, Ask Question on Causality principle for the klein- gordon equation, Get Answer, Expert's Help, Causality principle for the klein- gordon equation Discussions

Write discussion on Causality principle for the klein- gordon equation
Your posts are moderated
Related Questions
what is an atom

An explorer is riding his camel in the desert. Up ahead he sees what appears to be a pool of water.  He can tell if it is a real pool of water or a mirage by putting on his pol

The time needed for a net force of 10 newtons to change the velocity of a 5 kilograms mass by 3 meters/second is: a) 1.5 seconds b) 6 seconds c) 16.7 seconds d

Mention two salient features of immunity theory of ageing. Write the full form of ESR. What does the increase in ESR indicate?

Suppose a fluid (say, water) occupies a domain D ⊂ R 3 and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and will be transported by the fluid

A bar magnet having of two equal and opposite magnetic pole separated by a small distance. Poles are not precisely at the last. The smallest distance among two poles is known as ef

what condition is necessary for heat transfer occur

If the particles of a medium vibrate in the direction of wave motion the wave is known as longitudinal. a)      It goes in the form of compression and rarefaction. b)      A

Review guide: gases: heat, temperature, volume

Does destructive interference violate the principle of conservation of energy? Briefly explain.