From fork-admin@xent.com Tue Sep 17 23:29:46 2002 Return-Path: Delivered-To: yyyy@localhost.example.com Received: from localhost (jalapeno [127.0.0.1]) by jmason.org (Postfix) with ESMTP id 3F52416F03 for ; Tue, 17 Sep 2002 23:29:46 +0100 (IST) Received: from jalapeno [127.0.0.1] by localhost with IMAP (fetchmail-5.9.0) for jm@localhost (single-drop); Tue, 17 Sep 2002 23:29:46 +0100 (IST) Received: from xent.com ([64.161.22.236]) by dogma.slashnull.org (8.11.6/8.11.6) with ESMTP id g8HJXcC23989 for ; Tue, 17 Sep 2002 20:33:38 +0100 Received: from lair.xent.com (localhost [127.0.0.1]) by xent.com (Postfix) with ESMTP id 454BD2940A6; Tue, 17 Sep 2002 12:30:06 -0700 (PDT) Delivered-To: fork@example.com Received: from localhost.localdomain (pm1-28.sba1.netlojix.net [207.71.218.76]) by xent.com (Postfix) with ESMTP id 1DD2429409F for ; Tue, 17 Sep 2002 12:29:01 -0700 (PDT) Received: (from dave@localhost) by maltesecat (8.8.7/8.8.7a) id MAA26187; Tue, 17 Sep 2002 12:40:05 -0700 Message-Id: <200209171940.MAA26187@maltesecat> To: fork@example.com Subject: Re: The Big Jump In-Reply-To: Message from fork-request@xent.com of "Mon, 09 Sep 2002 19:25:02 PDT." <20020910022502.8777.4915.Mailman@lair.xent.com> From: Dave Long Sender: fork-admin@xent.com Errors-To: fork-admin@xent.com X-Beenthere: fork@example.com X-Mailman-Version: 2.0.11 Precedence: bulk List-Help: List-Post: List-Subscribe: , List-Id: Friends of Rohit Khare List-Unsubscribe: , List-Archive: Date: Tue, 17 Sep 2002 12:40:05 -0700 X-Spam-Status: No, hits=-7.3 required=7.0 tests=AWL,IN_REP_TO,KNOWN_MAILING_LIST,QUOTED_EMAIL_TEXT version=2.50-cvs X-Spam-Level: > All else being equal, the terminal velocity is inversely proportional to the > square root of air density. Air density drops off pretty quickly, and I > really should be doing something other than digging up the math for that. I > think it involves calculus to integrate the amount of mass as the column of > the atmosphere trails off. Chemistry types have a method for dealing with this question without dragging in the calculus: Suppose an atmosphere to be mainly affected by gravity, resulting in the potential energy for a mass M to be linear in height h: Mgh. What relative concentrations will we have when two different packets of air are in equilibrium? If they are at the same height, we will have half the mass in one, and half the mass in the other, and the amount flowing from one to the other balances the amount flowing in the opposite direction.[0] If they are at differing heights, then a greater percentage of the higher air tends to descend than that percentage of the lower air which ascends. In order for the two flows to balance, the higher packet must contain less air than the lower, and the mass balance of the flows corresponds thusly: high percentage of thin air --------------------------- low percentage of dense air Now, rates are exponential in energy differences[1], so that theoretically we should expect an exponential decay in height, to compensate. How does it go in practice? -Dave [0] How well does it balance? Chemical equilibria seem stable, as they deal with very large numbers over a very long time. Economic equilibria are viewed from the mayfly standpoint of individual people, and so, at best, the shot noise is very visible. [1] That is to say, rates will be exponential in the free energy differences between endpoints and a transition state. We can ignore that complication in this model.