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Start by defining an x (or y) axis which wraps over the pulley in the direction of the heavier mass. Then the mass of rope on each side can be expressed in terms of x (the distance that some point in the system moves from a reference position). The rope on the pulley is not a concern as a force since its weight is the same on each side. It does need to be ...


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The rope is simply another mass. It happens to be bendy. So you'd need to figure out, at any given configuration, what the forces on the various parts of the rope are. Say, gravity down on the part on each side of the pulley, pressure on the pulley, etc. Friction with the rope is going to be a coefficient, and it will be resisting motion. Depending on the ...


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It's basically a misnomer that has nothing to do with the "real" renormalization group. (I've heard this confirmed directly from professional practitioners.) You can come up with some vague similarities if you really stretch for it, but I don't think there's any conceptual insight to be gained from doing so.


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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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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 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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As a second idea, you could do a absolute value quiver plot on top of a phase angle quiver plot with $\arg E_x$ on $x$ axis and $\arg E_y$ on $y$ axis, just like the real part in blue, imaginary part in red plot in the above suggestions. But I guess this plot will be more informative in that phase and magnitude are more physical than real or imaginary parts. ...


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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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The field configuration is provided by your complex data. The way you plot them does not change di field configuration but it may provide a more or less faithful visual representation of your data. I assume that you really need the information contained in the complex field (are you sure that the physical quantity you are interested is not separately the ...


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I can answer the question of how looks like a viscous, heat-conducting compressible gas flows in a 2D pipe with a heater and a turbine. I use my code tested on several problems. First, consider the case without bypass. Figure 1 shows the distribution of velocity (left), pressure (center) and temperature (right). From these data it can be seen that the heated ...


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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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'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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You can solved this problem with the standard formulas that apply to projectile motion. Knowing that the vertical velocity is zero at the top, you can use the vertical distance to find the time up and the initial vertical velocity. Similarly, the distance back down determines the time down. The total time with the horizontal distance gives the horizontal ...


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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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There is a free computational physics book that also has free source code for the many simulations done. The codes are written in Fortran and C++. I can't read C++ but Fortran is easy. There is also a f2py converter for Fortran to python conversion. Most of the simple simulations can be converted without anything. There are also other f2XX conversion codes ...


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I have done many simulations on Excel spreadsheets. All the basic functions are available, variables are easily incremented, formulas can be propagated down or across the page (drag dot on lower right), and the results can be graphed. With the thoughtful use of iteration they can even be animated. If you can't afford Excel, the spreadsheet that comes ...


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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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You don't provide enough information, so the following is just some speculation. It is possible that the amplitude of the pendulum is large enough (as you know, the period is the same only for small amplitudes, and motion is not sinusoidal for large amplitudes), or the amplitude changes significantly during one experiment due to dissipation? In that case, ...


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