results_S0=0.125.mws

# This plot shows that there exist a values of R3 for which sigma=0 when l approches to infinity. Now I need your help to find that R3.

 Well my calculated guess is that value of R3 for which sigma=0 is -0.6. But i need to confrom.

your above animation shows that that phase change front S0=0.0275 is stable for shortwave number (l approches to infinity) 

@Axel Vogt 

outwith information about  R3 for l approches infinity and sigma tends to zero my results are incomplete. So, still i need to find R3 for l approches infinity and sigma tends to zero.

@Axel Vogt 

outwith information about  R3 for l approches infinity and sigma tends to zero my results are incomplete. So, still i need to find R3 for l approches infinity and sigma tends to zero.

@Axel Vogt 

sorry my previous maple sheet has a typo. The new one is attached. Still I nee to find R3 when l approches to infinity.

results.mws

@Axel Vogt 

sorry my previous maple sheet has a typo. The new one is attached. Still I nee to find R3 when l approches to infinity.

results.mws

@Axel Vogt 

I have solved the problem which i sent to you in the pdf file. is there any way to check the results numerical and also i am feeling a little hard to follow ur sheet.

results.mws

@Axel Vogt 

I have solved the problem which i sent to you in the pdf file. is there any way to check the results numerical and also i am feeling a little hard to follow ur sheet.

results.mws

it seems to me okay but i have to make some other test on it to get to some conclusion. could you send me the maple sheet. By the way in the plot you use "R". bcoz R is in my equation so may be u use R for R3 which mix with the other R or i am thinking to much.

This one  is just an example the vertical line is sigma. 

somecommon test on in this maple sheet.

20110205_dispersiond.mws

Thx

it seems to me okay but i have to make some other test on it to get to some conclusion. could you send me the maple sheet. By the way in the plot you use "R". bcoz R is in my equation so may be u use R for R3 which mix with the other R or i am thinking to much.

This one  is just an example the vertical line is sigma. 

somecommon test on in this maple sheet.

20110205_dispersiond.mws

Thx

@Axel Vogt

 Plz see the attached file.

Thx

section3.PDF

@Axel Vogt

 Plz see the attached file.

Thx

section3.PDF

@Axel Vogt 

This huge equation is commonly known as dispersion equation, in which sigma is the growth rate and l is the wave number. This equation represents the stability behaviour of a phase change front in a configration in which liquid overlies vapour. R3 is known as The Rayleigh number. So, I am trying to find the critical R3, above  which the system maybe stable or unstable in the following two ways

1). first I try to find R3 when sigma and l both approches zero. if sigma=0, for any wave number for this critical R3 then the front is marginally stable. If sigma<0 then stable for zero wave number, if sigma>0, then untsable.

2). second I try to find R3 when sigma approches zero and l approches in  infinity. the same understand as above.

Hope it make some sense

@Axel Vogt 

This huge equation is commonly known as dispersion equation, in which sigma is the growth rate and l is the wave number. This equation represents the stability behaviour of a phase change front in a configration in which liquid overlies vapour. R3 is known as The Rayleigh number. So, I am trying to find the critical R3, above  which the system maybe stable or unstable in the following two ways

1). first I try to find R3 when sigma and l both approches zero. if sigma=0, for any wave number for this critical R3 then the front is marginally stable. If sigma<0 then stable for zero wave number, if sigma>0, then untsable.

2). second I try to find R3 when sigma approches zero and l approches in  infinity. the same understand as above.

Hope it make some sense

@Axel Vogt 

Thx for your time. I am sorry I didnt menstion that R3<0. How much it will effect the output? 

@Axel Vogt 

Thx for your time. I am sorry I didnt menstion that R3<0. How much it will effect the output?