Causality principle for the klein- gordon equation, Physics

Assignment Help:

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.


Related Discussions:- Causality principle for the klein- gordon equation

What is photo-conductive cell, It is based on the principle that conductivi...

It is based on the principle that conductivity of a semiconductor enhances with increase in the intensity of incident light. In this, a thin layer of some semiconductor (as

Abortion, I need five pages about abortion

I need five pages about abortion

Hall effect, What is hall Effect? Derive an expression for it.

What is hall Effect? Derive an expression for it.

Resonence, give example phenomena of resonance?

give example phenomena of resonance?

What do you mean by lateral shift, Q. What do you mean by lateral shift? an...

Q. What do you mean by lateral shift? and What could be the angle of incidence to have maximum lateral shift? Q. For what angle, lateral shift is minimum?

Chemistry in action - detergents, chemistry in action - Detergents A re...

chemistry in action - Detergents A result of high dissolving power, the logically happening water all time consists of dissolved matters, majorly ionic substances. Hard water h

What fraction of the sample will be left over, Q. Tritium has a half life p...

Q. Tritium has a half life period of 12.5 years. What fraction of the sample will be left over after 25 years? HLP = 12.5 years Number of HLPs in 25 years = 25 / 12.5 =2

Determine the velocity of an object, An impulse of 10 kilogram-meters per s...

An impulse of 10 kilogram-meters per second acting on an object whose mass is 5 kilogram will cause a change in the objects velocity of: a) 0.5 meters per second b) 2 met

Is this wavelength in vacuum, Is this wavelength in vacuum? Answer; as ...

Is this wavelength in vacuum? Answer; as per mass of CPH is constant, and Vc is for an alone CPH, so wavelength should be in vacuum, that there is not any gravity effect. But i

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd