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PhaseSpaceRepr

caustic

Trait PhaseSpaceRepr 

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pub trait PhaseSpaceRepr: Send + Sync {
    // Required methods
    fn compute_density(&self) -> DensityField;
    fn advect_x(&mut self, displacement: &DisplacementField, dt: f64);
    fn advect_v(&mut self, acceleration: &AccelerationField, dt: f64);
    fn moment(&self, position: &[f64; 3], order: usize) -> Tensor;
    fn total_mass(&self) -> f64;
    fn casimir_c2(&self) -> f64;
    fn entropy(&self) -> f64;
    fn stream_count(&self) -> StreamCountField;
    fn velocity_distribution(&self, position: &[f64; 3]) -> Vec<f64>;
    fn as_any(&self) -> &dyn Any;

    // Provided methods
    fn total_kinetic_energy(&self) -> f64 { ... }
    fn to_snapshot(&self, time: f64) -> PhaseSpaceSnapshot { ... }
}
Expand description

Central trait for all phase-space storage and manipulation strategies.

Implementations differ in memory layout and algorithmic complexity:

  • UniformGrid6D: O(N⁶) brute-force grid
  • TensorTrain: O(N³r³) low-rank decomposition
  • SheetTracker: O(N³) Lagrangian cold sheet

Required Methods§

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fn compute_density(&self) -> DensityField

Integrate f over all velocities: ρ(x) = ∫f dv³. This is the coupling moment to the Poisson equation.

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fn advect_x(&mut self, displacement: &DisplacementField, dt: f64)

Drift sub-step: advect f in spatial coordinates by displacement Δx = v·dt. Pure translation in x at constant v.

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fn advect_v(&mut self, acceleration: &AccelerationField, dt: f64)

Kick sub-step: advect f in velocity coordinates by Δv = g·dt. Pure translation in v at constant x.

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fn moment(&self, position: &[f64; 3], order: usize) -> Tensor

Compute velocity moment of order n at given spatial position. Order 0 = density, 1 = mean velocity, 2 = dispersion tensor.

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fn total_mass(&self) -> f64

Total mass M = ∫f dx³dv³. Should be conserved to machine precision.

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fn casimir_c2(&self) -> f64

Casimir invariant C₂ = ∫f² dx³dv³. Increase over time indicates numerical diffusion.

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fn entropy(&self) -> f64

Boltzmann entropy S = −∫f ln f dx³dv³. Should be exactly conserved; growth = numerical error.

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fn stream_count(&self) -> StreamCountField

Number of distinct velocity streams at each spatial point. Detects caustic surfaces (sheet folds).

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fn velocity_distribution(&self, position: &[f64; 3]) -> Vec<f64>

Extract the local velocity distribution f(v|x) at a given spatial position. Used for dark matter detection predictions.

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fn as_any(&self) -> &dyn Any

Downcast to concrete type for implementation-specific queries (e.g. HT rank data).

Provided Methods§

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fn total_kinetic_energy(&self) -> f64

Total kinetic energy T = ½∫fv² dx³dv³.

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fn to_snapshot(&self, time: f64) -> PhaseSpaceSnapshot

Extract a full 6D snapshot of the current state.

Implementors§