Causality principle for the klein- gordon equation, Physics

Assignment Help:

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.


Related Discussions:- Causality principle for the klein- gordon equation

A cubical block of wood weighing, A cubical block of wood weighing 200g has...

A cubical block of wood weighing 200g has a lead piece fastened underneath. Find the mass of the lead piece which will just allow the block to float in water. Exact gravity of wood

Capacitors in series, Capacitors in series: When three capacitors are c...

Capacitors in series: When three capacitors are connected in series.  If one electron moves from the negative terminal of the cell to the right hand plate of C 3 , and one elec

Ohm’s law verification, Ohm's law : The electric current (i) in a conductor...

Ohm's law : The electric current (i) in a conductor is proportional to the potential difference (V) between its ends of a constant temperature (T).   Verification: To v

National ambient air quality standards, The town of Smog, Idaho is located ...

The town of Smog, Idaho is located in a river valley and has a footprint of 6 km x 2 km.  It has an average daily emission rate of 1000 kg/day of PM 2.5  into the atmosphere from

Kinametic, whatis meant by kinametic?

whatis meant by kinametic?

Explain the rate of energy, By what factor would the I 2 R loss in transmis...

By what factor would the I 2 R loss in transmission wires be reduced if the transmission voltage were boosted from 220 V to 22 kV? Suppose that the rate of energy delivered is

What do you mean by a shunt, What do you mean by a shunt? Reduce expression...

What do you mean by a shunt? Reduce expressions for the current flowing through the shunt resistance and galvanometer. Describe the principle on which a transformer works. Defin

Determine the voltage drop across each impedance, The following three imped...

The following three impedances are connected in series across a 40V, 20kHz supply: (i) a resistance of 8, (ii) a coil of inductance 130µHand5 resistance, and (iii) a 10 r

Carrier concentration of metals, derive an expression for density of states...

derive an expression for density of states and hence deduce an expression for carrier concentration of metals

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd