Title: how do you begin in fluid-dinamycs Post by: kujonai on December 09, 2009, 04:29:13 AM hello, what themes do you recommend to learn about fluid-dinamycs? , where can i begin for ?, and how is related fluid-dynamics and the fractasl?
regards Title: Re: how do you begin in fluid-dinamycs Post by: jehovajah on December 09, 2009, 06:31:30 AM Briefly. The expansions used to describe the motions of fluids in a flow require repeated derivatives and that in itself is iterative. Then on top of that these equations do not admit to simplistic so called elegant solutions and have to be solved by iterative computational means after some simplification condition or assumption. So in my definition of fractal as the product of any iterative process/ procedure, the results from these efforts are fractal. By inspection by eye the results look fractal and develop fractal structures as each iteration is applied. It is assumed that the iterations represent the steps in time, but that is a whole other topic.
With regard to scale and self similarity work is being done to uphold the scale relationships between similar results in larger and larger systems. My advice to any one thinking about the mathematics is to get ahead of the curve and realise that mathematical descriptions are all fractal, that is the result of iterations. If you can approach it that way then you will see something that older mathematicians have forgotten or pushed to one side. I would start by researching the navier stokes equations and refreshing your vector math and calculus all of which are iterative in nature. Title: Re: how do you begin in fluid-dinamycs Post by: lkmitch on December 09, 2009, 04:49:30 PM hello, what themes do you recommend to learn about fluid-dinamycs? , where can i begin for ?, and how is related fluid-dynamics and the fractasl? regards Mathematically, fluid dynamics is typically expressed as an application of Newton's Laws of Motion (conservation of mass, momentum, and energy) to a fluid. This generally results in the Navier-Stokes equations, which are nonlinear, unsteady, partial differential vector equations. In other words, quite nasty. General solutions often involve iterative procedures of nonlinear and/or matrix equations, and we've seen how that can generate fractals. Physically, those fractals are often related to transfer of energy between scales of fluid motion. So, study all of those things, and you'll have an understand of fluid dynamics and fractals. :) And study turbulence. A lot. Title: Re: how do you begin in fluid-dinamycs Post by: kujonai on December 09, 2009, 05:56:38 PM thanks, in other words, the equations of motion and turbulence is resolved through numeric aproxs and iterating, fractals, turbulence and motion laws. : ::) ::)
regards Title: Re: how do you begin in fluid-dinamycs Post by: kram1032 on December 09, 2009, 07:17:23 PM Is there a quantum-equivalent to the navier-strokes formulae?
(eg using quantum mechanics stuff, rather than newtonean) Just wonder in which way the results would differ :) Title: Re: how do you begin in fluid-dinamycs Post by: lkmitch on December 11, 2009, 05:49:57 PM Is there a quantum-equivalent to the navier-strokes formulae? (eg using quantum mechanics stuff, rather than newtonean) Just wonder in which way the results would differ :) Not to my knowledge--the domains are completely different. At the quantum scale, there aren't even atoms, let alone molecules or fluids. Title: Re: how do you begin in fluid-dinamycs Post by: kram1032 on December 13, 2009, 05:59:51 PM afaik, there is something like quark plasma or something at very high temperatures, where even protones and neutrones aren't stable anymore.... (and even something beyond...) Once found that on Wikipedia^^ |