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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.
THE SEMICONDUCTOR in which number of electrons or holes is smaller than N c and N v density of state in CB or VB are called non-degenerate semiconductor. The general exponential
How is temporal coherence key of characteristics of laser? Temporal coherence: This coherence is a measure of the correlation among the phases of a light wave at various poi
State Triangle Law & Derive
The energy possessed by a object by virtue of its position or its configuration is called its potential energy. Concept of potential energy is valid only in conservative field.
The phenomenon of diffraction was first discovered by Girmaldi. Its experimental study was completed by Newton's and young. The theoretical explanation was first provided by Fresne
An atom has 26 electrons and its atomic weight is 56. The number of neutrons in the nucleus of the atom will be : (1) 26 (2) 30 (3) 36 (
NEWTON ? "The force which forms an acceleration of 1 ms-2 in a mass of 1 kg". It is represented by N.
The molecules of diatomic and linear polyatomic gases are made up of two atoms joined rigidly to one another by a bond. Such a particle cannot only move as a entire but can also ro
michelson interferometer principle
The radioisotope 222 84 Po undergoes alpha decay to form an isotope of lead (lead has atomic number 82). Verify what the mass number of that isotope must be by writing a nuc
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