# Neutron diffusion : concepts and uncertainty analysis for engineers and scientists

PrefaceBasic Reactor PrinciplesAnatomic structureBinding EnergyCalculation of 1 uNuclear ReactionsNuclear FusionRadioactivityRate of Radioactive DecayRadioactive EquilibriumRadioactive Disintegration SeriesArtificial RadioactivityNuclear FissionBasic Reactor PrinciplesPrinciples, Production, and Interaction of Neutrons with MatterProduction of NeutronsNeutron Reactions and RadiationProperties of a RayProperties of в RayProperties of y RayInelastic and Elastic Scattering of NeutronsElastic ScatteringMaxwell-Boltzmann DistributionBibliographyNeutron Diffusion TheoryCross Section of Neutron ReactionsTransport Cross SectionRates of Neutron ReactionsNeutron Diffusion EquationHelmholtz EquationBibliographyFundamentals of UncertaintyProbabilistic UncertaintyElementary Properties of ProbabilityConditional ProbabilityRandom VariablesDistributionsBinomial DistributionPoisson DistributionNormal or Gaussian DistributionStochastic Differential EquationsEuler-Maruyama and Milstein MethodsEuler-Maruyama MethodMilstein MethodInterval UncertaintyDegenerate IntervalsIntersection, Union and Interval HullWidth, Absolute Value and MidpointInterval ArithmeticFuzzy UncertaintyDefinitionsFuzzy SetSupport of a Fuzzy Seta-Level Set of a Fuzzy SetConvexity of a Fuzzy SetHeight of a Fuzzy SetFuzzy NumbersTriangular Fuzzy NumberTrapezoidal Fuzzy NumberFuzzy ArithmeticInterval and Fuzzy Systems of EquationsLinear System of Equations with Triangular Fuzzy NumbersLinear System of Equations with Trapezoidal Fuzzy NumbersFuzzy Eigenvalue ProblemsBibliographyUncertain Neutron DiffusionUncertain Factors Involved in Neutron Diffusion TheoryDiffusion Coefficient and Absorption CoefficientFuzzy Finite Element MethodUncertainty Caused by the Stochastic ProcessHybrid UncertaintiesModelling of the Uncertain Neutron Diffusion EquationBibliographyOne-Group ModelAnalytical MethodSeparation of Variable MethodOne-Dimensional Wave EquationBoundary ConditionsNumerical MethodsFinite Difference MethodTaylor Series ExpansionFinite Difference by PolynomialsFinite Difference EquationsFinite Element MethodFinite Elements for Ordinary Differential EquationsBibliographyUncertain One-Group ModelBackgroundFormulation of the ProblemCase Study 1DiscussionCase Study 2DiscussionBibliographyMultigroup ModelBackgroundGroup Diffusion EquationFormulationMultigroup Neutron Diffusion EquationBibliographyUncertain Multigroup ModelFuzzy Finite Element for Coupled Differential EquationsFuzzy Multigroup Neutron Diffusion EquationCase StudyResults and DiscussionThermal-Group Neutron FluxesFast-Group Neutron FluxesBibliographyPoint Kinetic DiffusionReactivityPrompt and Delayed NeutronsDelayed Neutron ParametersPoint Reactor Kinetic Equations for a Non-Stationary One-Group Bare Reactor with Delayed NeutronsBibliographyStochastic Point Kinetic DiffusionBirth-Death ProcessesPure Death ProcessPure Birth ProcessStochastic Point Kinetic ModelBibliographyHybridized Uncertainty in Point Kinetic DiffusionBlack-Scholes Stochastic Differential EquationPreliminaryAnalytical Solution of Stochastic Differential EquationsSolution of Fuzzy Stochastic Differential EquationsExample ProblemsLangevin Stochastic Differential EquationSolution of Fuzzy Stochastic Differential EquationsExample ProblemPoint Kinetic Neutron Diffusion EquationStochastic Point Kinetic Model with Fuzzy ParametersCase StudyBibliography