6 research outputs found

    Linear and nonlinear stability in nuclear reactors with delayed effects

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    The research of a nuclear reactor model has been observed, where the system consists of two differential equations with one delay. A linear analysis has been performed, the asymptotic stability model of the area D0 and D2 has been defined, in which a stable periodic solution of one frequency appears. In the nonlinear analysis the analytical expression of the solution is presented with the help of bifurcation theories. In the numerical experiment using the scientific simulation program “Model Maker” numerical Runge–Kutta IV series method asymptotically stable solution and a stable periodic solution has been received and compared to the stable periodic solution received in nonlinear analysis with the help of bifurcation theories

    Front propagation into unstable states

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    This paper is an introductory review of the problem of front propagation into unstable states. Our presentation is centered around the concept of the asymptotic linear spreading velocity v*, the asymptotic rate with which initially localized perturbations spread into an unstable state according to the linear dynamical equations obtained by linearizing the fully nonlinear equations about the unstable state. This allows us to give a precise definition of pulled fronts, nonlinear fronts whose asymptotic propagation speed equals v*, and pushed fronts, nonlinear fronts whose asymptotic speed v^dagger is larger than v*. In addition, this approach allows us to clarify many aspects of the front selection problem, the question whether for a given dynamical equation the front is pulled or pushed. It also is the basis for the universal expressions for the power law rate of approach of the transient velocity v(t) of a pulled front as it converges toward its asymptotic value v*. Almost half of the paper is devoted to reviewing many experimental and theoretical examples of front propagation into unstable states from this unified perspective. The paper also includes short sections on the derivation of the universal power law relaxation behavior of v(t), on the absence of a moving boundary approximation for pulled fronts, on the relation between so-called global modes and front propagation, and on stochastic fronts.Comment: final version with some added references; a single pdf file of the published version is available at http://www.lorentz.leidenuniv.nl/~saarloo

    Author Index Volume 231 (2009)

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