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

Electrostatics, Can the whole charge of a body is transfer to another body

Can the whole charge of a body is transfer to another body

Speed of light in vacuo, Speed of light (in vacuo); c The speed on whic...

Speed of light (in vacuo); c The speed on which electromagnetic radiation propagates within a vacuum; it is described as 299 792 458 m/s.

Potentiometer, The emf of the driver cell of a potentiometer is 2V & its in...

The emf of the driver cell of a potentiometer is 2V & its internal resistance is negligible . The length of the potentiometer wire is 100cm & resistance is 5 ohm.How much resistanc

Penetration and ionization, #question.on which factor ionization and penetr...

#question.on which factor ionization and penetration depend ? how william cloud methode work to decet charge ?.

silver, Silver   Symbol     Ag ...

Silver   Symbol     Ag Atomic weight 107.868  Atomic number   47 discovery

Calculate the refractive index of liquid, Focal length of convex lens is 0....

Focal length of convex lens is 0.1 m. A liquid lens is formed between a plane surface and one face of this lens of radius of curvature 0.12m. The converging combination formed is f

Scintillation counter construction and working, Describe the principle cons...

Describe the principle construction and working of a scintillation counter.  With suitable diagram explain various components of a scintillation counting system. Principle Sci

List various problem solving techniques, P r oblem Solving Technique ...

P r oblem Solving Technique There are two approaches to solve a problem. They are:- 1.   Top down -A top down design approach starts by identifying the major components

Determine the vertical support reactions, The I beam weighs 0.6kN/m and sup...

The I beam weighs 0.6kN/m and supports the load which is P33 kN as shown. The distance from the load to point B is P34 m.  Determine the vertical support reactions at A and B.  (A

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