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In earlier DFT studies of ferroelectric materials, GGAs such as PBE were avoided as they tended to exaggerate the ferroelectric distortion. Instead, LDA calculations were performed and an artificial (offset) pressure was applied to compensate for LDA otherwise overestimating lattice constants Philippe Ghosez, Javier Junquera: cond-mat/0605299 "First-...


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At least to address the computational aspects of the turbulent, compressible flow solver parts, I will quote Kyle Kanos: On a more programmatical aspect, Toro's Riemann Solvers and Numerical Methods and LeVeque's Finite Volume Methods for Hyperbolic Problems are pretty much the bible for how to write code that will accurately model fluid flows. In both ...


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It is instructive to come back first to NRG (Numerical Renormalization Group) proposed by Ken Wilson (Nobel prize laureate for his work on Renormalization Group in the context of critical phenomena). Consider a translation-invariant 1D quantum Hamiltonian (for example a quantum spin chain). Start with a sufficiently small system of size $\ell$ so that the ...


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$T=1.94$ sec is certainly compatible with the big, but noisy peak at .5Hz. Why are you worrying about the tiny peak at about 2.6Hz? Your data looks very noisy so random but meaningless peaks are to be expected. I still don't understand why your FFT is so noisy given the smooth data of black points in the first plot. You say that you interpolate? Why do ...


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The answer by tpg2114 does a good job of explaining why the loss of energy in the flow due to viscous effects should result in a reduction in lift. I would like to add a few comments about the effective modification of the airfoil shape due to the boundary layer (since the question specifically asked about that). At sufficiently high Reynolds numbers, flows ...


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The general trick is to convert the one second-order differential into two first-order ones. This is done by introducing an extra variable to carry around: \begin{align} \frac{\mathrm dv}{\mathrm dt}&=f(x,\,t)\\ \frac{\mathrm dx}{\mathrm dt}&=v \end{align} for whatever function $f(\cdot)$ you need. This can easily be applied to numerical integration ...


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The easiest way to approach these kinds of questions for me is to forget the equations for a moment and think just in terms of energy and work. In the inviscid case, there is no drag on the airfoil. This means all of the changes in pressure can be used to do something, like create lift. Note: since there isn't anything other than pressure and velocity ...


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There is a free book online titled Computational Physics and the author is Konstantinos Anagnostopoulos. The book is available for download in PDF format. There are 2 versions of the book. One where the computer codes in the book are in Fortran and another copy for C++. I've only used the Fortran version but I assume the only differences are in the codes. ...


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'Critique of the replica trick' written in 1985 by Verbaarschot and Zirnbauer seems to be a good starting point to answer the last part of your question Perhaps more importantly for me, is there a nice characterization of physical situations when it is clear that this trick should fail? In their introduction, they explain that soon after its introduction ...


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