APPLICATIONS OF GEOMETRIC THEORY TO NONLINEAR REACTOR DYNAMICS

Journal Article · Sat Jul 01 04:00:00 EDT 1961 · Nuclear Sci. and Eng.

OSTI ID:4026553

Gyftopoulos, E P

Some basic theorems of the geometric theory of differential equations are reviewed, without proofs, in an attempt to clarify: (a) what relationship exists between the general solution of a set of nonlinenr differential equations and the solution of its linear approximation and under what conditions thin relationship can be used; (b) how the geometric theory can be used to find propenties of boundedness, stability, and periodicity of the solutions of nonlinenr differentinl systems. These theroms are illustuated by means of twothird order examples. The first is the xenon controlled reactor and the second a two-reginn reactor with two temperature coefficients of reactivity. It is shown without involved computatinns or any approximnations that: (a) Xenon controlled reactor--- when the reactivity controlled by xenon is smaller than the prompt xenon yield, the reactor power is always bounded but periodic oscillations may arise. When the reactivity controlled by xenon is greater than the prompt xenon yield the reactor power is unbounded; (b) Twn-region reactor--- this reactor does not admit periodic solutions. When the temperatare coefficients are of opposite sign, conditions are derived for the reactor power to be bounded. (auth)

• Research Organization: Massachusetts Inst. of Tech., Cambridge
• NSA Number: NSA-15-024548
• OSTI ID: 4026553
• Journal Information: Nuclear Sci. and Eng., Journal Name: Nuclear Sci. and Eng. Vol. Vol: 10
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

CONTROL
DIFFERENTIAL EQUATIONS
MATHEMATICS
NONLINEAR PROBLEMS
OSCILLATIONS
POISONING
REACTIVITY
REACTOR CORE
REACTOR TECHNOLOGY
REACTORS
STABILITY
TEMPERATURE
XENON
ZONES