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 Physical model of (infinite) tetration=(NON-isotropic) turbulence Ivars Long Time Fellow    Posts: 366 Threads: 26 Joined: Oct 2007 03/17/2009, 08:52 PM (This post was last modified: 03/18/2009, 06:49 PM by Ivars.) I will give it a try: Let us take first order homogenous delay differential equation without dependence of derivative of solution on at the same moment of time : Here T is delay, which shows how values of solution T moments in past ( or future if T<0) impact derivative of solution at current moment . Let us introduce new function such that : then As is known from literature, solution of such delay equation is given by : So Where is a k-th branch of Lambert W function. To reach the solution I am looking for, of form: Coefficients have to be: so This can be expressed as infinite product, with each term of sum as exponent of one multiplier in this infinite product. From here, obviously: so Now if we look back to original delay equation, this means that solution of a form: is one of particular solutions corresponding to particular branch of W function of a homogenous logarithmic first order differential equation with IMAGINARY DELAY . corresponds to Imaginary delay . We can generalize this to imaginary delay . (Not sure if + sign is OK). Then we have particular solutions of : In form: Where I hope there are not too many mistakes I think I could not choose coefficients so arbitrary, it must have an impact on initial conditions or so called preshape function for times which I do not know how to calculate. Next question is how these logarithmic differential delay equations (and thus processes they represent) with imaginary delay have to be nested to produce tetration and , perhaps, turbulence. In case of turbulence, the statistical character of processes will have to be added, somewhere, so that we deal with mean values , distributions and structure functions. (probably, In projective space as that is the space of turbulent time). Ivars « Next Oldest | Next Newest »

 Messages In This Thread Physical model of (infinite) tetration=(NON-isotropic) turbulence - by Ivars - 02/13/2009, 07:27 AM RE: Physical model of (infinite) tetration=(NON-isotropic) turbulence - by Ivars - 02/18/2009, 07:29 PM RE: Physical model of (infinite) tetration=(NON-isotropic) turbulence - by Ivars - 02/20/2009, 10:31 PM RE: Physical model of (infinite) tetration=(NON-isotropic) turbulence - by Ivars - 02/25/2009, 10:27 PM RE: Physical model of (infinite) tetration=(NON-isotropic) turbulence - by bo198214 - 02/26/2009, 12:01 AM RE: Physical model of (infinite) tetration=(NON-isotropic) turbulence - by Ivars - 02/26/2009, 06:53 PM RE: Physical model of (infinite) tetration=(NON-isotropic) turbulence - by Ivars - 03/17/2009, 08:51 AM RE: Physical model of (infinite) tetration=(NON-isotropic) turbulence - by Ivars - 03/17/2009, 08:52 PM

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