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 the voltage being applied to the secondary coil, A step-down transf...

A step-down transformer has 9000 turns on the primary coil and 150 turns on the secondary coil. The EMF in the primary coil is 16 V. What is the voltage being applied to th

Astronaut catch- momentum and collisions, Astronaut Catch A question su...

Astronaut Catch A question such as this includes momentum principles. In any example in that two objects collide and can be considered isolated from all other net forces and th

Vertical circular motion, Vertical Circular Motion A mass is in circul...

Vertical Circular Motion A mass is in circular motion within the vertical plane. We show the weight and force exerted through the tension within the string.

Explain radius of gyration, Radius of gyration may be explained as the dist...

Radius of gyration may be explained as the distance from the axis at which, if the entire mass of the object were to be concentrated, the moment of inertia would be the same about

What is pair production and pair annihilation, Q. What is pair production a...

Q. What is pair production and pair annihilation? Pair production: The conversion of a photon in to an electron-positron pair on its interaction with the strong electric fie

Optics, A spider is hanging by means of its own silk thread directly above ...

A spider is hanging by means of its own silk thread directly above a transparent fixed sphere of r = 20cm .... the refractive index of material of sphere is root(2).... and height

Optical activiy, what is the fresnel''s exlanation of optical activity

what is the fresnel''s exlanation of optical activity

Is a sewing needle magnetic or non magnetic, Is a sewing needle magnetic or...

Is a sewing needle magnetic or non magnetic? Answer:- When you purchase it in the store it isn't magnetized but if you rub it with a magnet it becomes magnetic.

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