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

Executing simple harmonic motion, The total energy of a particle, executing...

The total energy of a particle, executing simple harmonic motion is Ans) In simple harmonic motion when  a particle is displaced to a position from its mean position, then its kin

Force and Force Diagrams, Explanation on forces and how to create force dia...

Explanation on forces and how to create force diagrams

All about bernoulli, write bernoulli,s equation using pressure,energy,and h...

write bernoulli,s equation using pressure,energy,and heads.

Evaluate the vibration frequency, A guitar string produces 4 beats/second w...

A guitar string produces 4 beats/second when sounded with a250Hz tuning fork and 9 beats/second when sounded with a 255 Hz tuning fork. What is the vibration frequency?

What is fraunhofer diffraction, Q. What is Fraunhofer diffraction? a) ...

Q. What is Fraunhofer diffraction? a) The source as well as the screen are at infinite distances from the obstacle producing diffraction. b) The wave front suffer diffracti

Physical interpretation of wave function, Physical interpretation of wave f...

Physical interpretation of wave function : Einstein proposed a historic relationship between energy and mass using postulates of STR. The variation of mass with velocity has modif

W is atomic weight and n is the atomic number of an element, If W is atomic...

If W is atomic weight and N is the atomic number of an element, then: (1) Number of e -1 = W- N (2) Number of 0 n 1 = W- N (3) Number of 1 H 1 = W-N (4) Number of 0

Determine the torque acting on the coil, A coil of area 100 cm 2 having 50...

A coil of area 100 cm 2 having 500 turns carries a current of 1mA. It is suspended in a uniform magnetic field of induction 10 -3 Wbm -2 . Its plane makes an angle of 600 with t

What are major fiber sensors, What are major fiber sensors? Major Fiber...

What are major fiber sensors? Major Fiber Sensors: a. Point sensors: Bragg gratings extended period gratings, Fabry-Perot interferometers. Maximum temperature can be as high

Plane and the package, Plane and The Package Suppose a plane moving alo...

Plane and The Package Suppose a plane moving along with a constant speed at an elevated height above the Earth's surface. Within the course of its flight, the plane drops a pac

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