### Abstract

The stability of boiling water reactors (BWRs) is revisited in terms of catastrophe theory. The hypothesis is proposed that the stability parameter (decay ratio) of a complex, many-variable non-linear system might obey a cusp catastrophe. The incentive for this surmise comes from indications in real measurements that in certain cases the decay ratio appears to behave discontinuously and might show a hysteresis as a function of the control parameters reactor power and coolant flow. Such observations can be explained by a phenomenological catastrophe model suggested in this article. Since a cusp-type behaviour implies that the decay ratio is many-valued in a certain region of the power-flow map, a mechanism is suggested how a Hopf bifurcation with multiplicative noise can lead to such a behaviour.

Original language | English (US) |
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Title of host publication | Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 |

Publisher | American Nuclear Society |

Pages | 763-774 |

Number of pages | 12 |

ISBN (Electronic) | 9781510808041 |

State | Published - Jan 1 2015 |

Event | Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 - Nashville, United States Duration: Apr 19 2015 → Apr 23 2015 |

### Publication series

Name | Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 |
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Volume | 1 |

### Other

Other | Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 |
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Country | United States |

City | Nashville |

Period | 4/19/15 → 4/23/15 |

### Fingerprint

### Keywords

- BWR
- Catastrophe theory
- Stability

### ASJC Scopus subject areas

- Mathematics(all)
- Nuclear and High Energy Physics

### Cite this

**The stability of boiling water reactors as a catastrophe phenomenon.** / Pázsit, I.; Dykin, V.; Konno, H.; Kozlowski, Tomasz.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015.*Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015, vol. 1, American Nuclear Society, pp. 763-774, Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015, Nashville, United States, 4/19/15.

}

TY - GEN

T1 - The stability of boiling water reactors as a catastrophe phenomenon

AU - Pázsit, I.

AU - Dykin, V.

AU - Konno, H.

AU - Kozlowski, Tomasz

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The stability of boiling water reactors (BWRs) is revisited in terms of catastrophe theory. The hypothesis is proposed that the stability parameter (decay ratio) of a complex, many-variable non-linear system might obey a cusp catastrophe. The incentive for this surmise comes from indications in real measurements that in certain cases the decay ratio appears to behave discontinuously and might show a hysteresis as a function of the control parameters reactor power and coolant flow. Such observations can be explained by a phenomenological catastrophe model suggested in this article. Since a cusp-type behaviour implies that the decay ratio is many-valued in a certain region of the power-flow map, a mechanism is suggested how a Hopf bifurcation with multiplicative noise can lead to such a behaviour.

AB - The stability of boiling water reactors (BWRs) is revisited in terms of catastrophe theory. The hypothesis is proposed that the stability parameter (decay ratio) of a complex, many-variable non-linear system might obey a cusp catastrophe. The incentive for this surmise comes from indications in real measurements that in certain cases the decay ratio appears to behave discontinuously and might show a hysteresis as a function of the control parameters reactor power and coolant flow. Such observations can be explained by a phenomenological catastrophe model suggested in this article. Since a cusp-type behaviour implies that the decay ratio is many-valued in a certain region of the power-flow map, a mechanism is suggested how a Hopf bifurcation with multiplicative noise can lead to such a behaviour.

KW - BWR

KW - Catastrophe theory

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=84949507606&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949507606&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84949507606

T3 - Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015

SP - 763

EP - 774

BT - Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015

PB - American Nuclear Society

ER -