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

What is photons how can it have 0 mass?, Light is quantized. Photons are li...

Light is quantized. Photons are light quanta. It has zero REST mass. Therefore, it always travels at maximum speed permitted by relativity.

What are the applications of electron microscopy in industry, What are the ...

What are the applications of electron microscopy in industry? Industrial applications of electron microscopy: a. High-resolution imaging and Forensics b. Particle detecti

What is physical quantity, A quantity that can be calculated by instrument,...

A quantity that can be calculated by instrument, clearly defined and has proper units is known as physical value. Physical quantities are described as fundamental and derived quant

Describe the operation of a transistor amplifier, Describe the operation of...

Describe the operation of a transistor amplifier in CE configuration. Ans:  Operation  of  a  Transistor  Amplifier  in  CE  configuration:    A  Common  Emitter  NPN transist

Static limit, Static limit: The distance through a rotating black hole...

Static limit: The distance through a rotating black hole where no observer can probably remain at rest (w.r.t. the distant stars) due to inertial frame dragging; this region i

Arago spot, Arago spot (D.F.J. Arago) A bright spot which appears in th...

Arago spot (D.F.J. Arago) A bright spot which appears in the shadow of a uniform disc being backlit through monochromatic light emanating from a point source.

Electronics 1, norton theorem and its application and uses in sciences

norton theorem and its application and uses in sciences

Superconductivity, Superconductivity The phenomena from which, at suff...

Superconductivity The phenomena from which, at sufficiently low temperatures, a conductor can conduct charge along with zero resistance. The current theory for describing supe

G m counter, describe the construction and working of geiger muller counter...

describe the construction and working of geiger muller counter. give its important application.

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