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Application that you have considered is pipe flow. Pipe flow can be assumes as isentropic flow. Isentropic equations are non-linear. (Non-linear i'm using here is algebraic non-linearity. Please note the governing equation of fluid mechanics is also non-linear PDE). So resulting gas equation will be non-linear in nature. We know ideal gas relation is ...


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An equivalent Ohms law can be applied to gas flow and pressure drop, but only for particular mechanical flow restrictions and limited to a range of flow. But more generally for orifices and tubes the relationship between pressure and flow is quadratic, explained predominantly by the energy equation for flow, also known as Bernoulli's equation. In the ...


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I once asked Putterman after a similar colloquium what he meant by this statement, and his answer was "long time tails". Long time tails are fractional powers that appear in the long time behavior of correlation functions, see, for example, here and here. These fractional powers are seen in molecular dynamics (they are more difficult to see experimentally), ...


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They are derivable from classical mechanics using either the continuum or molecular points of view. Starting with a continuum view, one applies conservation of mass, momentum, and energy to a control volume and the result is the Navier Stokes equations. The Navier Stokes equations, in the usual form, apply to Newtonian fluids, that is fluids whose stress ...


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None of the interesting equations in physics can be derived from simpler principles, because if they could they wouldn't give any new information. That is, those simpler principles would already fully describe the system. Any new equation, whether it's the Navier-Stokes equations, Einstein's equations, the Schrodinger equation, or whatever, must be ...



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