Noise and Nonlinear Phenomena in Nuclear Systems

The main goal of the meeting was to facilitate and encourage the application of recent developments in the physical and mathematical sciences to the analysis of deterministic and stochastic processes in nuclear engineering. In contrast with the rapid growth (triggered by computer developments) of nonlinear analysis in other branches of the physical sciences, the theoretical analysis of nuclear reactors is still based on linearized models of the neutronics and thermal-hydraulic feedback loop, an approach that ignores some intrinsic nonlinearities of the real system. The subject of noise was added because of the importance of the noise technique in detecting abnormalities associated with perturbations of sufficient amplitude to generate nonlinear processes. Consequently the organizers of the meeting invited a group of leading researchers in the field of noise and nonlinear phenomena in nuclear systems to report on recent advances in their area of research. A selected subgroup of researchers in areas outside the reactor field provided enlightenment on new theoretical developments of immediate relevance to nuclear dynamics theory.

Table of Contents:
I. Introduction: Basic Concepts.- A Glimpse into the World of Random Walks.- Stochastic Bifurcations in a Generic Dynamical System: A Qualitative Analysis.- Unified Theory of Fluctuations and Parametric Noise.- An Influence Functional Approach for the Elimination of Variables in Stochastic Processes.- Mixing Properties and Resonances in Chaotic Dynamical Systems.- II. Stochastic Processes in Linear Nuclear Systems: Theory.- Application of Stochastic Transport Theory to the Determination of the Statistical Descriptors Used in Noise Analysis.- Determination of Kinetics Parameters Using Stochastic Methods in a 252Cf Driven System.- Solving Low Power Stochastic Equations: Nonlinear Studies.- Contribution to the Discussion.- Exact and Inexact, Explicit and Implicit Solution Techniques for the Forward and Backward Kolgomorow Equations.- III: Stochastic Processes in Linear Nuclear Systems: Applications.- Some Applications of Stochastic Processes in Neutron Coincidence: Measurements Used in Nuclear Safeguards.- Application of Statistical Correlation Techniques for Measurement of the Keff of Highly Subcritical Systems.- Stochastic Aspects of Neutron Multiplication in Fusion Blanket Materials and Spallation Targets.- Stochastic Calculations of the Effective Density Factor.- Statistical Correlation Calculation of the Time Constant Alpha in Monte Carlo Simulation of Subcritical Assemblies.- IV. Stochastic Processes in Nonlinear Nuclear System: Theory.- Nonlinear Stochastic Theory and Identification of Nonlinearity in Nuclear Reactors.- Stochastic Nonlinear Dynamics of Nuclear Power Plants: Noise Effects on Nonlinear Stability.- The Role of Fluctuations in Nuclear Reactor Transients.- The Effect of Fuel Depletion on Stochastic Behaviour in Supercritical Systems.- Contribution to theDiscussion: Backward Kolgomorov Equations with Feedback.- Steady State Dynamics of Nonlinear Nuclear Reactor Systems.- Nonlinear Effects in Structural Vibration Induced Fluctuations.- V. Stochastic Processes in Nonlinear Nuclear Systems: Applications.- Bispectrum Estimation Using Overlapped Segments.- Nonlinear AR-Noise Investigated Via a Kalman Filter.- Characteristics of Adaptiveness and Self-Organizing as Applied to the Nonlinear Nuclear Systems.- The Monte Carlo Simulation of Thermal Noise in Fast Reactors.- Pump Induced Linear and Nonlinear Vibrations at PWR.- VI. Nonlinear Dynamics and Transition to Chaos in Nuclear Systems. Part I.- Variational Methods for Analyzing Limit Cicles in BWR.- Nonlinear Dynamics and Chaos in Boiling Water Reactors.- Nonlinear Dynamics of Three-Dimensional Point Fission Reactors.- Phase Plane Analysis of Nuclear-Coupled Density-Wave Oscillations.- VII. Nonlinear Dynamics and Transition to Chaos in Nuclear Systems. Part II.- Nonlinear Dynamics of the Nuclear Breeding Process.- Nonlinear Xenon Oscillations.- Nonlinear Reactor Stability Analysis with Arbitrary Feedback.- A Stochastic Method for Nuclear Power Plant Diagnosis.- Stochastic Nuclear Reactor Theory: Breit-Wigner Nuclear Noise.