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Another form of the
Langevin used in Statistical mechanics ignores inertial accelerations like ma, and instead approximate the velocity of the suspended particles as having a velocity that is linearly related to the forces acting upon the particle. This is in the small particle limit, so
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I'm having difficulty understanding the meaning of these equations because theres no mention here (or anywhere that i can find so far on the internet) as to what the index is referring to within the equations. Is it as simple as coordinates? or a more complicated set of operators?
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To do: -Add a section (or a new page? or both with one a summary of the other?) on noise terms, explaining what is meant by a 'continuous random function', what is needed to specify it (correlation functions) (i.e. the systems described on the page are not completely specified).
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Can we add a clarification to what the variables mean? I know what m, ma, d, dv and F are, but the majority of people looking this up on
Knowledge are probably doing so because they are unfamiliar with Physics. I am still working on figuring out B and n(t)
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Citation: For development of new methods for the solution of the nonlinear
Langevin equation without the use of the Fokker-Planck equation, allowing the exact calculation of correlation times and mean first passage times." 15:07, 16 June 2010
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is known as the "mobility" of the particle in a viscous fluid. Whilst this would be a minor edit to the page, I think it is a valid one to mention this small particle limit. --
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is more specific than just an SDE in physics, although it is sometimes used in that way. Thus I've moved some of the more general info I added a while back to a new article
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Is the following information relevant to the part on solving (non-linear) Langevin
Equations & can appropriate text be put in by someone qualified to do so?
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It is from a citation for Prof W.T.Coffey (author of cited books on The
Langevin Equation) when he became a Fellow of the American Physical Society in 1999:
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is negligible in comparision to the other terms. Consequently, the form of "the" Langevin equation I am used to using is
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439:{\displaystyle \zeta {\frac {d\mathbf {x} }{dt}}={\frac {\partial \mathbf {V} }{\partial x}}+\mathbf {f} \left(t\right)}
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I added a link to the Wiener process page for the noise term. Also, this article really should be combined with the
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271:-More examples of Langevin equations (e.g.from lasers, chemical kinetics, population dynamics etc.)
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Knowledge. If you would like to participate, please visit the project page, where you can join
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for the fluctating force. After all it should be article and not a collection of sections.
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There is a very short merge discussion on the talk page there. At
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This section should use the same conventions as other sections:
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It appears that this was fixed, at some point in the past.
274:-Tidy up inline maths (...help on this would be good...)
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