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

Evaluate the maximum order of spectrum, A monochromatic light of wavelength...

A monochromatic light of wavelength 6000Å is incident on a plane diffraction grating with grating element 6 X 10 -5 cm. Evaluate the maximum order of spectrum that will be observe

How to find out neutral point, How to find out neutral point ? What all thi...

How to find out neutral point ? What all things we require to equate or form a equation to find the neutral poind and how to do it?

Thermal Physics and Optics, Describe the construction and working of a rubb...

Describe the construction and working of a rubby LASER with related diagrams?.

Surface mount devices, Surface Mount Devices (SMDs) are new components desi...

Surface Mount Devices (SMDs) are new components designed with soldering pads or short leads. They are much smaller in size as compared to leaded components. The SMDs are directly a

Work and energy, A 0.15 kg glider is moving to the right on frictionless ho...

A 0.15 kg glider is moving to the right on frictionless horizontal air track with speed of 0.8 m\s. It has a head on collision with 0.3 kg glider that is moving to the left with a

Calculate the x-ray energy flux - tungsten anode target, Consider an x-ray ...

Consider an x-ray tube in which electrons are accelerated by a constant high voltage of 250 kV. If the electron beam current is 10 mA, calculate the x-ray energy flux (energy fluen

Determine the same mass that of an electron, Which of the following has the...

Which of the following has the same mass as that of an electron: (1) Photon (2) Neutron (3) Positron (4) Proton Ans: Positron

What is the magnitude of the current in the circuit, A circuit which employ...

A circuit which employs a DIRECT CURRENT source has a branch which has a capacitor.  After the circuit has reached a steady state, what is the magnitude of the current in the c

Inverse square law of magnetism, State 'Inverse square law of  magnetism'....

State 'Inverse square law of  magnetism'.  A. Coulomb's inverse law of magnetism states that, "The force of attraction or repulsion between two magnetic  poles is directly pro

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