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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.
Production of audio and video signals Iconoscope is a type of camera consisting of a cathode ray beam and a photoelectric cell. The picture is scanned with the help of iconosco
Bell's inequality (J.S. Bell; 1964) A quantum mechanical theorem shows that if quantum mechanics were to rely on hidden variables, it ought to have nonlocal properties.
What do you mean by normal shift? Derive the mathematical expression for normal shift produced when an object in a denser medium is viewed normally through air.
Time Dilation A description in which the phenomenon of time dilation from the special theory of associtively necessarily follows from the idea in which the speed of light is th
What are semiconductors? Give an example for n-type semiconductors. Semiconductors are materials having electrical conductivity among that of insulators and conductors. This i
Q State Kirchoff's first law in electricity? Kirchoff's first law (current law) the algebraic total of the currents meeting at any junction in a circuit is zero. This law
He chemical effects of electricity
Weiss constant: A characteristic constant based on the material, utilized in calculating the susceptibility of paramagnetic materials.
Why hot air rises up ?
Write the relation for the force acting on a charge carrier q moving with a velocity by a magnetic field in vector notation. Using this relation, reduce the conditions under which
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