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

Determine grating element in specturm, A beam of light of wavelength λ = ...

A beam of light of wavelength λ = 5000Å falling normally on a plane diffraction grating. The 1 st order spectrum is derived in a direction making an angle θ 1 with the norma

Give the example for electrophilic substitution reaction, The species, whic...

The species, which accepts the electrons, are known as Electrophiles (or) Electrophilic reagents. When the atom (or) group of atoms there in the organic compound is replaced by

Electric dipole, what are the subtopics of electric dipole with detail expl...

what are the subtopics of electric dipole with detail explain

Dynamics, Piles of snow on slippery roofs can become dangerous projectiles ...

Piles of snow on slippery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch of 27. As the snow begins to melt, the c

What is electrostatic shielding, Q. What is electrostatic shielding? i...

Q. What is electrostatic shielding? i) It is the method of isolating a certain region of space from external field. ii) It is basis on the fact that electric field inside a

What is the magnitude of the acceleration, A toy train moves in a circle of...

A toy train moves in a circle of 8 meters radius with a speed of 4 meters per second.  What is the magnitude of the acceleration of the train? Ans: The magnitude of the acce

Ionisation, Ionisation: If the amount of external energy is large enoug...

Ionisation: If the amount of external energy is large enough the valence electron can gain sufficient kinetic energy (energy of movement) to be removed completely from its atom

Determine the north pole of a compass needle, The magnetic field of Earth r...

The magnetic field of Earth resembles the field of a bar magnet. The north pole of a compass needle, used for navigation, generally points toward the geographic north pole.

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