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Zimm-Rouse model A stochastic math-
ematical model for the dynamics of an ideal-
ized polymer chain. The linear chain is modeled
Z as a collection of N beads connected by N − 1
springs. A system of stochastic differential equa-
tions for the N particles defines a multivariate
Gaussian process. The equations can be solved
Zeeman effect The splitting or shift of spec- using normal mode method. This model is a gen-
tral lines due to the presence of an external mag- eralization of the Ornstein-Uhlenbeck process.
netic field.
Zorn’s lemma If S is a partially ordered
zigzag phenomenon Successive directions set such that each totally ordered subset has an
are orthogonal, causing Cauchy’s steepest ascent upper bound in S, then S has a maximal ele-
to converge slowly. The successive orthogonal- ment. Partially ordered means that for some pairs
ity comes from optimizing the (scalar) step size x, y ∈ S there is an ordering relation x ≤ y;
with (exact) line search, but the issue runs deeper. totally ordered means for each pair x, y ∈ S one
In general, the zigzag phenomenon causes small either has x ≤ y or y ≤ x. The Zorn lemma is
steps around a ridge. equivalent to the axiom of choice.

c

© 2003 by CRC Press LLC
© 2003 by CRC Press LLC