ON GILL'S STABILITY PROBLEM WITH INTERNAL HEATING

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

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Some Structural Properties of Systolic Tree Automata

Fundamenta Informaticae ◽

10.3233/fi-1989-12409 ◽

1989 ◽

Vol 12 (4) ◽

pp. 571-585

Author(s):

E. Fachini ◽

A. Maggiolo Schettini ◽

G. Resta ◽

D. Sangiorgi

Keyword(s):

Structural Properties ◽

Stability Problem ◽

Sufficient Condition ◽

Tree Automata ◽

Necessary And Sufficient Condition ◽

The Stability ◽

Necessary And Sufficient

We prove that the classes of languages accepted by systolic automata over t-ary trees (t-STA) are always either equal or incomparable if one varies t. We introduce systolic tree automata with base (T(b)-STA), a subclass of STA with interesting properties of modularity, and we give a necessary and sufficient condition for the equivalence between a T(b)-STA and a t-STA, for a given base b. Finally, we show that the stability problem for T(b)-ST A is decidible.

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Can D-D fusion contribute to Jupiter's excess heat?

Symposium - International Astronomical Union ◽

10.1017/s0074180900218068 ◽

2004 ◽

Vol 202 ◽

pp. 280-282

Author(s):

Rachid Ouyed

Keyword(s):

Planet Formation ◽

Internal Heating ◽

Excess Heat ◽

Heating Source ◽

General Aspects

We explore the highly speculative idea of Deuterium - Deuterium (D-D) fusion inside Jupiter as an internal heating source. We suggest that D could have been brought deep inside the planet by planetesimals (during the process of planet formation) and deposited through planetesimal/ices vaporization. Here, the general aspects of the model are presented.

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