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78 lines
2 KiB
Text
78 lines
2 KiB
Text
/-
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HyperFlow.lean - Fixed-Point Hyperbolic Flow Dynamics
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-/
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import Mathlib.Data.Nat.Basic
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import Mathlib.Data.Int.Basic
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import Semantics.DynamicCanal
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import Semantics.LocalDerivative
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import Semantics.MetricCore
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import Semantics.FixedPoint
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namespace Semantics.HyperFlow
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open DynamicCanal
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open Semantics.LocalDerivative (Scalar StabilityClass LocalDerivative matrixFrobeniusNorm matrixL1Norm divergence antisymmetricPart)
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open Semantics.MetricCore (Metric)
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structure HyperFlowSignature where
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divergence : Q16_16
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shearMagnitude : Q16_16
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stressMagnitude : Q16_16
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transportMagnitude : Q16_16
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anisotropy : Q16_16
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spectralSpread : Q16_16
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couplingDensity : Q16_16
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compressibilityIndex : Q16_16
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curvatureEnergy : Q16_16
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deriving Repr, DecidableEq, BEq
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inductive HyperFlowRegime
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| coherent
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| shearLayer
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| compressive
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| dispersive
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| turbulentLike
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| collapse
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deriving Repr, DecidableEq, BEq
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inductive MediumRegime
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| incompressibleFluid
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| compressibleFluid
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| gasLike
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| rarefiedGas
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| plasmaLike
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| magnetizedPlasma
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| rarefiedPlasma
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| collapse
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deriving Repr, DecidableEq, BEq
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inductive PlasmaManifoldRegime
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| diffuse
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| sheet
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| filament
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| reconnectionLike
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| coherentTorus
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| collapsed
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deriving Repr, DecidableEq, BEq
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def hyperFlowSignature (ld : LocalDerivative) (metric : Metric) : HyperFlowSignature :=
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{ divergence := divergence ld
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, shearMagnitude := matrixFrobeniusNorm (antisymmetricPart ld)
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, stressMagnitude := metric.coupling * (matrixFrobeniusNorm ld.jacobian)
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, transportMagnitude := matrixL1Norm ld.jacobian
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, anisotropy := Q16_16.zero
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, spectralSpread := matrixL1Norm ld.jacobian
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, couplingDensity := Q16_16.zero
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, compressibilityIndex := Q16_16.zero
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, curvatureEnergy := matrixFrobeniusNorm ld.hessian }
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def classifyHyperFlow (_signature : HyperFlowSignature) (stability : StabilityClass) : HyperFlowRegime :=
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match stability with
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| .collapsed => .collapse
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| .singular => .compressive
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| .throat => .compressive
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| .unstable => .turbulentLike
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| .stable => .coherent
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end Semantics.HyperFlow
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