Processes which propagate faster than exponentially
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From: Robert on 15 Jan 2010 13:23 On 15 Jan, 18:08, "Androcles" <Headmas...(a)Hogwarts.physics_r> wrote: > "I.N. Galidakis" <morph...(a)olympus.mons> wrote in message > > news:1263572066.510809(a)athprx04...> Apologies for the crosspost, but this is related to many areas. Is anyone > > aware > > of any physical/chemical/nuclear processes which propagate at rates faster > > than > > exponential? > > > From my search so far, it appears that the fastest processes available, > > like > > cancer and viruses in biology, and nuclear explosions and supernova > > explosions > > in physics all propagate at most exponentially. > > > Many thanks, > > -- > > Ioannis > > ================================================= > If you mean faster than y = exp(-t) then yes, y = A.exp(-t) is faster for A > > 1. > Or to put it another way, the isotope carbon 14 has a shorter half life > ( 5,730 ± 40 years) than the isotope uranium 238, (4.46 billion years). > > The human population doubles every 33 years but it once doubled every > 100 years. This is due to more people not suffering infant mortality from > disease (countered by modern medicine) and living longer, yet still > reproducing at the same rate (not countered in the third world). > Obviously if you have more births than deaths then you have population > growth that is exponential . If you have less births than deaths then you > have population decline. By upsetting the balance with medicine you > change from exponential growth to super-exponential growth. > > The slope of the curve gets steeper for exponential growth (fixed birth > and death rates) and steeper yet for super-exponential growth. > > In computer models of locust swarms the exponential growth of > the population always results in them eating all there is and then > starving and dying. Human beings were headed that way naturally > but have hastened their own demise by their use of medicine to > prolong their lives. The land we live on is finite. faster than exponential means faster than exponential with *any* growth constant. but thanks for the malthusian spam
From: Robert on 15 Jan 2010 13:50 Well, for anyone that hasn't kill filed me, the "worthless caveat" is essential to the OP's question. Would as x->oo, for all t, f(x)/e^xt -> oo be an adequate definition for a function with faster than exponential growth?
From: Rod on 15 Jan 2010 14:00 "I.N. Galidakis" <morpheus(a)olympus.mons> wrote in message news:1263572066.510809(a)athprx04... > Apologies for the crosspost, but this is related to many areas. Is anyone > aware > of any physical/chemical/nuclear processes which propagate at rates faster > than > exponential? > > From my search so far, it appears that the fastest processes available, > like > cancer and viruses in biology, and nuclear explosions and supernova > explosions > in physics all propagate at most exponentially. > > Many thanks, > -- > Ioannis > There seems to be a few examples of double exponential i.e. exp(exp(x)) see http://en.wikipedia.org/wiki/Double_exponential_function#Physics factorials or gamma function are also faster then exp
From: I.N. Galidakis on 15 Jan 2010 14:09 Robert wrote: > Well, for anyone that hasn't kill filed me, the "worthless caveat" is > essential to the OP's question. > > Would > > as x->oo, for all t, f(x)/e^xt -> oo > > be an adequate definition for a function with faster than exponential > growth? Yes. Sorry for the (created) confusion. As far as I am concerned, I mean anything like: f(x) ~ a^x, with a > e. Thanks again to all the responders. -- Ioannis
From: I.N. Galidakis on 15 Jan 2010 14:13
Rod wrote: > "I.N. Galidakis" <morpheus(a)olympus.mons> wrote in message > news:1263572066.510809(a)athprx04... >> Apologies for the crosspost, but this is related to many areas. Is anyone >> aware >> of any physical/chemical/nuclear processes which propagate at rates faster >> than >> exponential? >> >> From my search so far, it appears that the fastest processes available, >> like >> cancer and viruses in biology, and nuclear explosions and supernova >> explosions >> in physics all propagate at most exponentially. >> >> Many thanks, >> -- >> Ioannis >> > > There seems to be a few examples of double exponential i.e. exp(exp(x)) > see > http://en.wikipedia.org/wiki/Double_exponential_function#Physics > > factorials or gamma function are also faster then exp Thanks. That's one example. So the bound now moves to exp(exp(x)). -- Ioannis |