l*********r
发帖数: 1 | 1 what are the basic assumptions and results of the zipper model for helix
formation?
statistical(Boltzmann) definition of entropy?
methods for determining molecular siza and shape?
i appreciate ur help very much | c*w
发帖数: 4736 | 2 only answer to the second question, :P
classical defination of entropy:
1/T = (partial(S)/partial(U))|N(partial quantity)=const
statistical defination of entropy:
S = k * xigma
xigma = ln(g(N,U))
g(N,U) is the total number of states of system with N particles
and total energy U. | B***y
发帖数: 83 | 3
这题目应该用角变量来做：
令 y = dx/dt, 则， 原方程变为
dx/dt = y
dy/dt = -P(t) x
令 k = tan theta = y/x, (tan 既 sin/cos) 则k 变量满足Ricatti方程
dk/dt = -P(t) - k^2
theta 满足方程：
d(theta)/dt = -P cos^2 (theta) - sin^2 (theta), theta \in R. (*)
原方程有2pi 周期解当且仅当 theta(2pi) - theta(0) = 2pi Z, Z 为一整数。
现在考虑 替换 P(t) by n^2 和 (n+1)^2, 也即考虑下面两方程：
d(theta_1)/dt = -n^2 cos^2 (theta_1) - sin^2 (theta_1), (**)
d(theta_2)/dt = -(n+1)^2 cos^2 (theta_2) - sin^2 (theta_2), (***)
因为 n^2 < P < (n+1)^ |
|
