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

Inertia in an automobile, Inertia in an automobile  You can view the sa...

Inertia in an automobile  You can view the same effect as in experiment 8 when you are riding in a car that is rapidly stopped. You have to brace yourself to keep from sliding

A simple wheel and axle, A simple wheel and axle Remove the cover from ...

A simple wheel and axle Remove the cover from a pencil sharpener and bind a string tightly around the end of the shaft. Bind a weight of various kilograms to the end of the str

What is the initial velocity of an emitted photoelectron, The stopping pote...

The stopping potential of a photocell is 2.3 V. What is the initial velocity of an emitted photoelectron that is brought to a stop by the photocell?

An example of measured wavelength by astronomers on earth, A galaxy in the ...

A galaxy in the constellation UrsaMajor is receding from the earth at 15,000 km/s. If one of the characteristic wavelengths of the light the galaxy emits is 550 nm, what is the cor

What are the applications of heterojunction laser, What are the application...

What are the applications of Heterojunction Laser? Applications of Heterojunction laser: a. Into consumer electronics, semiconductor lasers are utilized in VCD/CD /DVD playe

Inelastic collision, Inelastic Collision Collisions among objects are g...

Inelastic Collision Collisions among objects are governed through laws of momentum and energy. While a collision occurs within an isolated system, the total momentum of the sys

What is a frame of reference, Q. What is a frame of reference? A syste...

Q. What is a frame of reference? A system of co-ordinate axes which describe the position of a particle in two or three dimensional space is called a frame of reference.

A body has a weight w kg on the surface of earth, A body has a weight W kg ...

A body has a weight W kg on the surface of earth. What will be its weight on the surface of moon in gravitational units of force and SI units? Ans) mass of body=W/g At moon w

Potential barrier, The potential difference created across the P-N junction...

The potential difference created across the P-N junction due to the diffusion of electron and holes is called potential barrier. For and for silicon    On the average the

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