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 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.

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
A plane e-m wave goes along vertical downward direction. At a provided instant, the direction of E at a point is towards east. Find the direction of B?

Before manufacturing of transformers we must know the important parts of transformer which need to be manufactured. Following are the main parts of transformers. (a)          Fo

The copper clad laminate manufacturing process is formed in heated press which has highly polished stainless steel press plates. The manufacturing process starts by placing a sheet

Demerits of Vacuum Diode over Semiconductor Diode (i)  Bigger in size (ii)  Less efficiency (iii)  Expensive

The vapour pressure of a substance at  20.0 o C is 38.1  kPa and its enthalpy of vaporisation is 49.6  kJ mol -1 . Estimate the temperature at which its vapour pressure is 80.0 k

Uses of Ultrasonics: 1. Ultrasonic are used in diagnosis of disease, physical therapy as surgical tool & industry. 2. They are used in sounding devices to calculate the dept

how to solve problems on constrained relations

Hookes Law Hooke's equation actually holds (to some extent) in several other situations whereas an elastic body is deformed, like as wind blowing on a tall building, a musician


Davisson and Germer scattered electrons from a crystal of nickel. The scattered electrons formed a strong diffraction pattern. What significant conclusion was drawn from thi