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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.
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A satellite has a mass of 5900 kg and is in a circular orbit 3.0 x 10 5 m above the surface of a planet. The period of the orbit is two hours. The radius of the planet is 4.15 x 1
Describe Fresnel''s theory of optical rotation
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Which of the following colours of visible light has the longest wavelength? Is it: a) Violet b) Green c) Yellow d) Red Ans: Red colour of visible light h
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