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

Triode as an amplifiers, Amplifier is a functioning by which the amplitude ...

Amplifier is a functioning by which the amplitude of variation of ac signal voltage / current/ power can be enhanced (i) Principle and circuit diagram: The amplifying action of

BIOPHYSICS, 1. Cell growth. if V is the volume of a spherical cell, the...

1. Cell growth. if V is the volume of a spherical cell, then, in certain cell growth or for some fetal growth models, the rate of change of V is given by dV/dt =kV2/3, where k

Hawking radiation, Hawking radiation (S.W. Hawking; 1973): Black holes...

Hawking radiation (S.W. Hawking; 1973): Black holes emit radiation such as any other hot body. Virtual particle-antiparticle pairs are being formed in supposedly empty space c

Inertia on a bicycle, Inertia on a bicycle Get your bicycle going and t...

Inertia on a bicycle Get your bicycle going and then apply the brakes rapidly. View the tendency of your body to stay in motion and pitch you over the handlebars. This is the r

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

Describe stoke''s formula, Stokes' Formula: When a spherical object falls ...

Stokes' Formula: When a spherical object falls by the fluid, layer in immediate touch with it, sticks to it and goes along with the object with the same speed. The layer next to i

Currents, explain and give examples of the two types of current

explain and give examples of the two types of current

What sources electromagnetic radiation, Question: What sources electrom...

Question: What sources electromagnetic radiation (a.k.a. light a.k.a. electromagnetic waves)? select the one BEST answer. Answer: Note the significant distinction betwe

Electricitye.., what is the use of muslin bag in a dry cell

what is the use of muslin bag in a dry cell

Relation between velocity wavelength and frequency, Relation among velocity...

Relation among velocity wavelength and Frequency: Consider a wave of wavelength , frequency f and travelling with velocity v. The distance travel by the sound wave during th

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