Causality principle for the klein- gordon equation, Physics

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 statesĀ  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.

Posted Date: 4/2/2013 3:26:32 AM | Location : United States







Related Discussions:- Causality principle for the klein- gordon equation, Assignment Help, Ask Question on Causality principle for the klein- gordon equation, Get Answer, Expert's Help, Causality principle for the klein- gordon equation Discussions

Write discussion on Causality principle for the klein- gordon equation
Your posts are moderated
Related Questions
Draw the graph showing the variation of binding energy per nucleon with mass number. Give the reason for the decline of binding energy per nucleon for nuclei with high mass numbers

What is the wavelength of electromagnetic waves of frequency 5 x 1019Hz in free space? Give its two applications.

STABLE EQUILIBRIUM If object is in stable equilibrium and if we displace object to a very little displacement dr then it will return back to starting position. UNSTABLE EQU

Is there any other proof that light is an electromagnetic wave other than its speed has the same value as the inverse square root of the permittivity and permeability constants of

Let's say I have a pinball (solid sphere) with a given mass and radius, and it is held back at a certain distance from equilibrium on a spring. The spring constant k is given, and

If Young' two slit interference experiment is done with white light what could be seen?

#question.knk

Portrayed is a ray from an object which heads toward and then into a lens. Suppose if the ray is a principal ray where does it go from there? Ans: This is the simple p

SPEED: The distance covered by a body in unit time is known as speed. It is represented by V.