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Turbulence in a pipe is derived directly from the Navier-Stokes equation. Analysis of numerical simulations revealed that small disturbances called 'mothers' induce other much stronger distur bances called 'daughters'. Daughters determine the look of turbulence, while mothers control the transfer of energy from the basic flow to the turbulent motion. From a practical point of view, ruling mothers means ruling turbulence. For theory, the mother-daughter process represents a mechanism permitting chaotic motion in a linearly stable system. The mechanism relies on a property of the linearized problem according to which the eigenfunctions become more and more collinear as the Reynolds number increases. The mathematical methods are described, comparisons with experi ments are made, mothers and daughters are analyzed, also graphically, with full particulars, and the systematic construction of small systems of differential equations to mimic the non-linear process by means as simple as possible is explained. We suggest that more then 20 but less than 180 essential degrees of freedom take part in the onset of turbulence.PACS number: 47.25. Ae O n s e t o f T u rb u le n c e in a P ip e

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The final period of nuclear fission is discussed. We propose the following picture: Nuclear scission happens because of an hydrodynamic instability triggered by random surface vibrations. Thus the scissioning complex ruptures at random positions. Measured total kinetic energies point to the very relevance of the instability, while the randomness of rupture shows up in neutron emission data. A Principal Difficulty with Present Fission TheoriesThere are presently two models for the description of nuclear fission [1,2]. They have been impressively modified and refined. For surveys see Wilets' booklet [3] and the references in an article by Wilkins et al. [4]. Despite their partial successes, both models run into specific disagreement with measurements, and this raises suspicion that both still miss an important aspect of the fission process. The statistical model [1,4] emphasizes the scission point. The two nascent fragments are imagined as two more or less dented pots in some contact. The pots are filled with nucleons which individually feel free to jump to and fro, but adhere statistical laws controlled by the level density. Crudely spoken, we havefor the probability P that one of the fragments incorporates A nucleons. The level density parameter a is approximately A~n/8 [5], A~, being the mass number of the compound nucleus and E~, its excitation energy. The dependence on A enters the righthand side of (1) . However, when the descent from saddle to scission point was treated in a somewhat more realistic fashion [7], the calculated mass distributions shrunk to dis-

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Strutinsky-type calculations indicate that the potential energy favors four channels in the nuclear fission o f 252Cf. The connection o f this finding with experimental results on the dis tribution of fragment mass, total kinetic energy, neutron multiplicities, and relative abundances is discussed. Similar calculations for 227Ac, 236U, and 258Fm show that the changing preponder ance of the four channels seems to describe striking trends in the fission o f the actinides, in particular the dip in the total kinetic energy at symmetrical fission of 236U and the enormously high average kinetic energy of the 258Fm fragments.

Fissioning nuclei produce with increasing excitation varying yields of fragments. For compound nuclei ranging from 232 Th to 242 Pu endowed with excitation energies typically between 0 and 10 MeV, we analyze these variations in terms of a fission-channel model. Most of the variations can be attributed to changing channel probabilities. We present a systematics of channel probabilities with respect to compound nuclei and their excitation energies, and we relate the systematics to potential energy which the nuclei experience when they float to scission. The trend, which is most difficult to explain, is a shift in the energy sensitivity of the standard channels, as one compares light with heavy compound nuclei. According to their behavior, we divide nuclei into standard I increasers and decreasers and attribute the difference to the standard secondary barriers. As a basic concept, bifurcation ratios are introduced, and a novel expression for transmission coefficients is proposed.