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Suppose Fluid (say, water) occupies a domain D 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 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.
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 .
Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion- transport equation:
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.
Explain the presence of unmodified radiation in Compton scattering.
purpose of using Maxwell''s corkscrew rule
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Define about the Modified Joule-Thomson? Container A of variable volume V controlled by a frictionless piston immersed in a bath at temperature T. This container is connected
Dielectric constant of vacuum is (A) Infinity. (B) 100. (C) One. (D) Zero. Ans: Dielectric constant of vacuum is one.
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