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Hello! In this paper https://pdfs.semanticscholar.org/e8a2/02f25555cd8c4f947bbbdff5a61a0ea0efd2.pdf the authors use VASP to determine MgSiO3 viscosity using the Green-Kubo relation where (i and j = x, y, z) is the stress tensor, t is time and t0 is the time origin. But I've seen other papers use: , where is the off-diagonal component of the stress tensor ( α and β are Cartesian components).
OK, so clearly these are essentially exactly the same equation but the second uses only the xy component whereas the first seems to suggest a summation? So which is correct?
Also, VASP outputs the stress tensor components as XX YY ZZ XY YZ ZX. So which of these should I use to input into the Green-Kubo equation? And are there missing components? what about yx, zy, xz?
Thanks in advance. Polyamorph ( talk) 15:01, 19 June 2018 (UTC)
the stress tensor is symmetric, thus having only six independent stress components, instead of the original nine, see also Stress_(mechanics)#General_stress. For the first question, I am not sure; it could be that only one off-diagonal component is nonzero in the context (for instance in a shear flow where water flows in from (x=±Inf,y=0) and out from (x=0,y=±Inf), and the flow is uniform across z), as is the case in many viscosity-measurement experiments; or it could be the Einstein notation by taking x and y as free variables (but then a factor 1/2 is missing). Tigraan Click here to contact me 16:49, 19 June 2018 (UTC)
Apparently aerial refueling doesn't make much economic sense for commercial jets. [1] But suppose radar operators were scanning for MH370 on the day of its disappearance and after almost all hope (and fuel) is lost, a passenger had gotten on the radio and said the pilots are dead, but some of us woke up, where are we, all we see down there is water!... Is there any conceivable way that some fast military aircraft swoops up from a carrier and slows down, and we see a boom projecting forward from it or a hose dangling down from in front of the wing, with a hard-bitten soldier or a decently designed robot on the end that can unscrew a gas cap and start pouring gas into the plane's tank so that the passengers don't end their adventure in the Indian Ocean? Or is it completely hopeless? Wnt ( talk) 17:38, 19 June 2018 (UTC)
Science desk | ||
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< June 18 | << May | June | Jul >> | June 20 > |
Welcome to the Wikipedia Science Reference Desk Archives |
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The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Hello! In this paper https://pdfs.semanticscholar.org/e8a2/02f25555cd8c4f947bbbdff5a61a0ea0efd2.pdf the authors use VASP to determine MgSiO3 viscosity using the Green-Kubo relation where (i and j = x, y, z) is the stress tensor, t is time and t0 is the time origin. But I've seen other papers use: , where is the off-diagonal component of the stress tensor ( α and β are Cartesian components).
OK, so clearly these are essentially exactly the same equation but the second uses only the xy component whereas the first seems to suggest a summation? So which is correct?
Also, VASP outputs the stress tensor components as XX YY ZZ XY YZ ZX. So which of these should I use to input into the Green-Kubo equation? And are there missing components? what about yx, zy, xz?
Thanks in advance. Polyamorph ( talk) 15:01, 19 June 2018 (UTC)
the stress tensor is symmetric, thus having only six independent stress components, instead of the original nine, see also Stress_(mechanics)#General_stress. For the first question, I am not sure; it could be that only one off-diagonal component is nonzero in the context (for instance in a shear flow where water flows in from (x=±Inf,y=0) and out from (x=0,y=±Inf), and the flow is uniform across z), as is the case in many viscosity-measurement experiments; or it could be the Einstein notation by taking x and y as free variables (but then a factor 1/2 is missing). Tigraan Click here to contact me 16:49, 19 June 2018 (UTC)
Apparently aerial refueling doesn't make much economic sense for commercial jets. [1] But suppose radar operators were scanning for MH370 on the day of its disappearance and after almost all hope (and fuel) is lost, a passenger had gotten on the radio and said the pilots are dead, but some of us woke up, where are we, all we see down there is water!... Is there any conceivable way that some fast military aircraft swoops up from a carrier and slows down, and we see a boom projecting forward from it or a hose dangling down from in front of the wing, with a hard-bitten soldier or a decently designed robot on the end that can unscrew a gas cap and start pouring gas into the plane's tank so that the passengers don't end their adventure in the Indian Ocean? Or is it completely hopeless? Wnt ( talk) 17:38, 19 June 2018 (UTC)