Get Theoretical Biology and Complexity. Three Essays on the PDF

By Robert J. Rosen

ISBN-10: 0125972806

ISBN-13: 9780125972802

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Extra info for Theoretical Biology and Complexity. Three Essays on the Natural Philosophy of Complex Systems

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With slippage, there is a drag force, that is, a viscous force. The faster volume element with velocity v^iy) transfers some of its momentum to the slower volume element with velocity v^{y -h Ay). In other words, some x-component of momentum is transferred in the >'-direction. The amount transferred (per unit time and unit area) is denoted Ty^. In general, when Vy and are not constant, there are momentum transfers associated with all other directions, that is, with all 38 I. W. R I C H A R D S O N v^(y + Ay) FIG.

C , the informational potential μ, also has gauge. H . Perpetual Motion The universal dictum against perpetual motion of the first kind was used in Section I V to establish that the driving force Fj^(w) must necessarily be the gradient of a scalar function, namely, the scalar potential energy u^. Since Fk(") = — is a necessary and sufficient condition for the work integral to be zero over any arbitrary closed path in space, the converse holds. That is, if one bases dynamics upon gradient forces, then perpetual motion is prohibited.

R I C H A R D S O N Ai Μ, = ΑΙΦ· Φ' Du /Ii FIG. 4. The second term on the left-hand side of (128) is a dyadic, which can be written as V . ε,Α[Φ\ = Q ^ i v , . νΦ' + Φ ' V . QA'v,. (130) The substantial derivative on the right-hand side of (118) can be expanded to CkA[ [οΦ'/θί + (Vk · ν ) Φ ' ] = a' δΦ'/δί + ε„Α{ν^ \Φ' (131) using (29). This term-by-term examination of the growth equation (128) results in a significant reduction. Equation (127) can now be written Φ'θα'/θί = - Φ ' ν . ^ ^ ί ν ^ .

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Theoretical Biology and Complexity. Three Essays on the Natural Philosophy of Complex Systems by Robert J. Rosen


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