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

Explain earth’s magnetic field , As per the most established theory it is b...

As per the most established theory it is because of the rotation of the earth where by the several charged ions there in the molten state in the core of the earth rotate and consti

Two long wires, a) Two long wires, carrying currents i 1 and i 2 , are pla...

a) Two long wires, carrying currents i 1 and i 2 , are placed perpendicular to each other in such a way that they just avoid to contact. Determine the magnetic force on a small le

Is cph a quantum energy unchangeable, Is CPH a quantum energy unchangeable?...

Is CPH a quantum energy unchangeable? Answer- Yes, the quantum energy (photon) is made of lots CPH, different between photons depend to the number of CPH that they are made of.

Explain snell''s law, Snell's Law: The ratio of sine of angle of incide...

Snell's Law: The ratio of sine of angle of incidence to the sine of angle of refraction is constant for all rays passing from one medium to another medium. That is Sini/Sinr

Define the merits of ultrasonic magnetostriction method, Define the merits ...

Define the merits of ultrasonic magnetostriction method. Merits of ultrasonic magnetostriction method: a.     Magnetostrictive materials are simply accessible and inexpensiv

Can you explain ohms law, Can you explain Ohms Law? Ans. If Temperature...

Can you explain Ohms Law? Ans. If Temperature remains constant then current flow is directly proportional to applied Voltage. I ∝ V, I = V/R (resistance of the conductor)

Compute the de broglie wavelength of electron, Q. The kinetic energy of an ...

Q. The kinetic energy of an electron 120 eV. Compute the de Broglie wavelength of electron. λ = h / √2mE λ = 6.626 X 10 -34 / √ 2 X 9.1 X 10 -31 X 120 X 1.6 X 10 -19

Assignment topic.., How we can increase the data input from 4 to 8 of multi...

How we can increase the data input from 4 to 8 of multipluxer and data outputs from 4to 8 of demultipluxer? Properly draw circuit diagram

Get interference pattern in youngs double slit experiment, What are the con...

What are the conditions to get interference pattern having good contrast in young's double slit experiment

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