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Spatiotemporal Modeling & Simulation of the Second Order Moments of the Transport Equation

Ayyoubzadeh, Mohsen | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47218 (46)
  4. University: Sharif University of Technology
  5. Department: Energy Engineering
  6. Advisor(s): Vosoughi, Naser
  7. Abstract:
  8. Precise knowledge of the laws which govern a system is of interest for two reasons. First, it paves the way to understand the subtle behaviors of the system, which are not understandable from simpler models of the system. Second, it helps in the design of experimental requirements needed to observe these behaviors. The behavior of neutrons in a system, which could be a reactor or a detector, is stochastic from two perspectives. First of all, since the place of the atoms of a medium are randomly sited, at least from a neutrons point of view, the collision sites are random places, which contributes to the stochasticity of the transport phenomena. This type of randomness is somewhat similar to the random behavior of the molecules of a gas, which are examined in the kinetic theory of gases. Second, because of the quantum physical aspect of the neutron-nuclei interactions, one could only calculate the probability of the different type of interactions, which results in a non-deterministic behavior. The random number of neutrons released after a fission is also related to this later aspect. These two reasons seem sufficient for one to pursue a probabilistic description for the neutron transport phenomenon in a system.
    In many nuclear engineering applications, the determination of the mean behavior of the observable quantities is considered sufficient. That is mainly due to the large neutron populations and ergodic systems, which are mostly encountered. However, these two conditions are not always present. As a violation of the first condition, one could think of the behavior of a zero-power reactor, or a reactor at start-up. A violation to the second occurs frequently for non-Boltzmanian quantities, such as the pulse height, coincidence counts, and the length of a chain. One is obligated to resort to a probabilistic description to be able to model such behaviors.
    The aim of the current dissertation is the derivation of the equations which govern the stochastic behavior of nuclear systems, specifically the behavior of the variance and correlations in such systems. The generalization of a particles presence probability density function, which describe the population density in phase space, the derivation of its moments, finding suitable approximations for these equations and finally the development of software solver for obtaining numerical results to these quantities are included in this dissertation. Moreover, exploiting the techniques of stochastic differential equation modeling in describing the randomness in these systems is sought after
  9. Keywords:
  10. Monte Carlo Simulation ; Mathematical Model ; Noise Analysis ; Stochastic Transport Equation ; Stochastic Differential Equation ; Covariance Numerical Solver ; Nuclear System Random Behavior

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