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

Electrical scientists-discover the atom research paper, how would you descr...

how would you describe the discoveries of Benjamin franklin, Robert millikan, cgarles-augastin de coulomb and Ernest ruthford?

Electromagnetic induction, what is construction,,, principle...and working ...

what is construction,,, principle...and working of AC generator

State hooke''s law, Hooke's law is valid for only little deformation. Hook...

Hooke's law is valid for only little deformation. Hooke's principle describes that the extension produced in the wire is directly proportional to the load applied within elastic l

Calculate the current through the circuit, Q. In the given circuit, calcula...

Q. In the given circuit, calculate the current through the circuit and mention its direction . Let the current be I. 5I + 10 I + 5 I = 10 + 20 that is 20 I = 30 Current I =

Explain corrosion, Explain corrosion This corrosion can happen either ...

Explain corrosion This corrosion can happen either when a conducting liquid is in contact with a metal or when two dissimilar metals /alloys are is partially immersed in a con

Evaluate the eigen frequencies and explain the normal modes, A mass M moves...

A mass M moves horizontally along a smooth rail. A pendulum is hung from M with a weightless rod and mass  m  at its end. Find the eigen frequencies and describe the normal modes

Explian the conditions of simple harmonic motion, For SHM to occur, three c...

For SHM to occur, three conditions must be satisfied. 1.There must be a position of stable equilibrium. At the equation in equilibrium potential energy is minimized.     That is,

Fraunhofer, EXplain fraunhofer diffraction due to a single slit and deduce ...

EXplain fraunhofer diffraction due to a single slit and deduce the position of maxima and minima and find their relative intensities

What fraction of the sample will be left over, Q. Tritium has a half life p...

Q. Tritium has a half life period of 12.5 years. What fraction of the sample will be left over after 25 years? HLP = 12.5 years Number of HLPs in 25 years = 25 / 12.5 =2

Determine the load power factor, Two wattmeters indicate 10 kW and 3 kW res...

Two wattmeters indicate 10 kW and 3 kW respectively when linked to measure the input power to a 3-phase balanced load, the reverse switch being operated on the meter showing the 3k

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