  In this paper it is shown that every non-periodic ergodic system has two
topologically weakly mixing, fully supported models: one is non-minimal but has
a dense set of minimal points; and the other one is proximal. Also for
independent interests, for a given Kakutani-Rokhlin tower with relatively prime
column heights, it is demonstrated how to get a new taller Kakutani-Rokhlin
tower with same property, which can be used in Weiss's proof of the
Jewett-Krieger's theorem and the proofs of our theorems. Applications of the
results are given.
