Skip to main content Crate deep_causality_physics Copy item path Source pub use crate::quantities::condensed ::*;pub use crate::quantities::dynamics ::*;pub use crate::quantities::em ::*;pub use crate::quantities::fluids ::*;pub use crate::quantities::hypersonic ::*;pub use crate::quantities::materials ::*;pub use crate::quantities::mhd ::*;pub use crate::quantities::nuclear ::*;pub use crate::quantities::photonics ::*;pub use crate::quantities::relativity ::*;pub use crate::quantities::thermodynamics ::*;pub use crate::quantities ::*;pub use crate::theories ::*;beam diffraction finite_rate Finite-rate ionization network kernels: the two-way channel set that turns
the corridor’s electron density from a calibrated closure into a
prediction from published rate data. forward_clock Forward relativistic clock kernels — the complement of solve_gm_analytical_kernel grmhd ideal ionization Ionization kernels: the Saha equilibrium ionization fraction, the Tier-A
Park-2T ionization surrogate (the LER relaxation target), and the
electron-density reconstruction. moire phase plasma polarization qgt quantities All physics quantities, consolidated from kernel-local files and the former
units module. Every public type is re-exported flat from this module and
from the crate root so consumers always import via deep_causality_physics::TypeName
— imports remain stable regardless of where within quantities/ a type lives. quark_masses Light quark constituent masses for string fragmentation. ray resistive shock Shock and recovery-temperature kernels: the Rankine–Hugoniot normal-shock
temperature jump (mandatory — isentropic recovery alone is too cold to
ionize) and the Tier-A recovery-temperature reconstruction. solve_gm theories Gauge Theories: Particle Physics + Gravity Implementations thermochemistry Park two-temperature thermochemistry kernels: vibrational relaxation
(Landau–Teller with a Millikan–White relaxation time, integrated by the
closed-form LER exponential) and the Arrhenius reaction-rate coefficient. utils_tests Shared test fixtures for the physics test suite. wrapper EastCoastMetric A Lorentzian metric in East Coast (-+++) convention. KsPropagator An exact 3-D two-body (Kepler) propagator via KS regularisation, built from a single physical
state. Propagation is the constant-generator matrix exponential in the KS fictitious time; it is
exact to floating-point round-off for any dt, with no step-size error. MaxwellSolver A standard solver for Maxwell’s Equations in Geometric Algebra. ParticleData Particle data from the Particle Data Group. PhysicalVector PhysicsError TwoBodyPropagator An exact planar two-body (Kepler) propagator built from a single physical state. Propagation is the
constant-generator matrix exponential in eccentric anomaly (see the module docs); it is exact to
floating-point round-off for any dt, with no step-size error. WestCoastMetric A Lorentzian metric in West Coast (+—) convention. Metric Defines the metric signature of the Clifford Algebra Cl(p, q, r). MetricError Errors that can occur during metric operations. PhysicsErrorEnum Detailed classification of physics-related errors. AIR_N2_MOLE_FRACTION Mole fraction of N₂ in undissociated standard air (traces folded in). AIR_O2_MOLE_FRACTION Mole fraction of O₂ in undissociated standard air. ALPHA_EM Fine structure constant α = e²/(4π) ≈ 1/137 (low-energy limit) ALPHA_EM_MZ Running fine structure constant at Z pole: α(M_Z) ≈ 1/128 ATOMIC_MASS_CONSTANT AVOGADRO_CONSTANT BOHR_MAGNETON BOHR_RADIUS BOLTZMANN_CONSTANT CLASSICAL_ELECTRON_RADIUS COSMOLOGICAL_CONSTANT Cosmological constant upper bound (in m⁻²) EARTH_ANGULAR_MOMENTUM EARTH_GM Gravity Mass Constant EARTH_GRAVITY_ACCELERATION Gravitational acceleration EARTH_J2 Earth’s J2 Oblateness coefficient (JGM-3)
https://www.sciencedirect.com/topics/engineering/oblateness EARTH_MASS_KG EARTH_RADIUS EARTH_RADIUS_EQUATORIAL Earth’s Equatorial Radius (WGS-84) EARTH_ROTATION_RATE ELECTRON_CHARGE_TO_MASS_QUOTIENT ELECTRON_COMPTON_WAVELENGTH ELECTRON_MAGNETIC_MOMENT ELECTRON_MASS ELECTRON_MUON_MASS_RATIO ELECTRON_PROTON_MASS_RATIO ELEMENTARY_CHARGE EM_COUPLING Electromagnetic coupling constant e = √(4πα) ≈ 0.303 (low-energy) EM_COUPLING_MZ Running EM coupling at Z pole e(M_Z) = √(4π α(M_Z)) ≈ 0.313 FARADAY_CONSTANT FERMI_CONSTANT Fermi coupling constant G_F in GeV⁻² FINE_STRUCTURE_CONSTANT FIRST_RADIATION_CONSTANT G GEV2_TO_NB Unit conversion factor (ℏc)² to convert GeV⁻² to nanobarns (nb) GEV2_TO_PB Unit conversion factor (ℏc)² to convert GeV⁻² to picobarns (pb) GRAPHENE_LATTICE_CONST HARTREE_ENERGY HIGGS_MASS Higgs boson mass M_H in GeV HIGGS_VEV Higgs vacuum expectation value v = (√2 G_F)^(-1/2) ≈ 246 GeV JOSEPHSON_CONSTANT MAGNETIC_FLUX_QUANTUM MILLIKAN_WHITE_A_COEFFICIENT Millikan–White A_sr prefactor coefficient (natural-log form). Combined with
μ_sr^(1/2) · θ_v^(4/3) to give A_sr. Unit: amu⁻¹ᐟ² · K⁻⁴ᐟ³ (dimensional bookkeeping). MILLIKAN_WHITE_LOG_OFFSET Millikan–White additive log constant C (natural-log form, = 8.00·ln 10). MILLIKAN_WHITE_MU_OFFSET Millikan–White reduced-mass offset B in (T^(−1/3) − B·μ^(1/4)). Dimensionless-ish (amu⁻¹ᐟ⁴). MINKOWSKI_4D Default 4D Minkowski spacetime (East Coast convention). MOLAR_GAS_CONSTANT MUON_ELECTRON_MASS_RATIO MUON_MAGNETIC_MOMENT NEUTRON_MAGNETIC_MOMENT NEWTONIAN_CONSTANT_OF_GRAVITATION NO_IONIZATION_ENERGY_EV First ionization energy of NO (the dominant air ionization channel), used by
the Saha-equilibrium target. Unit: eV. (NO → NO⁺ + e⁻; ≈ 9.26 eV.) NUCLEAR_MAGNETON PARK_DISSOCIATION_Q Park’s classic controlling-temperature exponent for dissociation ,
T_q = T^q · T_v^(1−q) with q = 0.7 (Park 1990; the geometric mean
q = 0.5 is the alternative). The controlling-temperature choice is the
largest closure divergence among production codes (DPLR/LAURA/US3D); this
model adopts the Park lineage’s own published exponent for the Park rate
set. The ionization controller keeps the calibrated geometric mean. PARK_LIMITING_CROSS_SECTION Park limiting vibrational cross-section reference σ_ref. Unit: m². PARK_LIMITING_REFERENCE_TEMP Park limiting-cross-section reference temperature T_ref. Unit: K. PARK_NO_IONIZATION_ACTIVATION_TEMP Characteristic (activation) temperature θd for N + O ⇌ NO⁺ + e⁻. Unit: K. PARK_NO_IONIZATION_EXPONENT Temperature exponent η for N + O ⇌ NO⁺ + e⁻ (dimensionless). PARK_NO_IONIZATION_PREFACTOR Pre-exponential factor Cf for N + O ⇌ NO⁺ + e⁻. Unit: cm³·mol⁻¹·s⁻¹. PARTICLE_MINKOWSKI_4D Standard 4D Minkowski spacetime for Particle Physics. PDG_PARTICLES Common hadron database following PDG conventions. PLANCK_CONSTANT PLANCK_LENGTH Planck length in meters PLANCK_MASS Planck mass in kg PROTON_ELECTRON_MASS_RATIO PROTON_MAGNETIC_MOMENT PROTON_MASS REDUCED_PLANCK_CONSTANT RELATIVITY_MINKOWSKI_4D Standard 4D Minkowski spacetime for General Relativity. RP1232_EI_N_ACTIVATION_TEMP Activation temperature for N + e⁻ → N⁺ + 2e⁻. Unit: K. RP1232_EI_N_EXPONENT Temperature exponent for N + e⁻ → N⁺ + 2e⁻ (dimensionless). Table II
states −3.14; written as a quotient because the raw literal trips
clippy::approx_constant (it is a temperature exponent, not π). RP1232_EI_N_PREFACTOR Pre-exponential factor for N + e⁻ → N⁺ + 2e⁻. Unit: cm³·mol⁻¹·s⁻¹. RP1232_EI_O_ACTIVATION_TEMP Activation temperature for O + e⁻ → O⁺ + 2e⁻. Unit: K. RP1232_EI_O_EXPONENT Temperature exponent for O + e⁻ → O⁺ + 2e⁻ (dimensionless). RP1232_EI_O_PREFACTOR Pre-exponential factor for O + e⁻ → O⁺ + 2e⁻. Unit: cm³·mol⁻¹·s⁻¹. RP1232_N2_DISS_ACTIVATION_TEMP Activation temperature for N₂ + M → 2N + M. Unit: K. RP1232_N2_DISS_EXPONENT Temperature exponent for N₂ + M → 2N + M (dimensionless). RP1232_N2_DISS_PREFACTOR Pre-exponential factor for N₂ + M → 2N + M. Unit: cm³·mol⁻¹·s⁻¹. RP1232_N2_RECOMB_EXPONENT Temperature exponent for 2N + M → N₂ + M (dimensionless). RP1232_N2_RECOMB_PREFACTOR Pre-exponential factor for 2N + M → N₂ + M. Unit: cm⁶·mol⁻²·s⁻¹. RP1232_NO_DR_ACTIVATION_TEMP Activation temperature for NO⁺ + e⁻ → N + O (barrier-free). Unit: K. RP1232_NO_DR_EXPONENT Temperature exponent for NO⁺ + e⁻ → N + O (dimensionless). RP1232_NO_DR_PREFACTOR Pre-exponential factor for NO⁺ + e⁻ → N + O. Unit: cm³·mol⁻¹·s⁻¹. RP1232_O2_DISS_ACTIVATION_TEMP Activation temperature for O₂ + M → 2O + M. Unit: K. RP1232_O2_DISS_EXPONENT Temperature exponent for O₂ + M → 2O + M (dimensionless). RP1232_O2_DISS_PREFACTOR Pre-exponential factor for O₂ + M → 2O + M. Unit: cm³·mol⁻¹·s⁻¹. RP1232_O2_RECOMB_EXPONENT Temperature exponent for 2O + M → O₂ + M (dimensionless). RP1232_O2_RECOMB_PREFACTOR Pre-exponential factor for 2O + M → O₂ + M. Unit: cm⁶·mol⁻²·s⁻¹. RP1232_ZELDOVICH_ACTIVATION_TEMP Activation temperature for N₂ + O → NO + N. Unit: K. RP1232_ZELDOVICH_EXPONENT Temperature exponent for N₂ + O → NO + N (dimensionless). RP1232_ZELDOVICH_PREFACTOR Pre-exponential factor for N₂ + O → NO + N. Unit: cm³·mol⁻¹·s⁻¹. RYDBERG_CONSTANT SECOND_RADIATION_CONSTANT SIN2_THETA_W Weak mixing angle (sin²θ_W) SPEED_OF_LIGHT STEFAN_BOLTZMANN_CONSTANT THETA_VIB_N2 Characteristic vibrational temperature of N₂. Unit: K. THETA_VIB_NO Characteristic vibrational temperature of NO. Unit: K. THETA_VIB_O2 Characteristic vibrational temperature of O₂. Unit: K. THOMSON_CROSS_SECTION TOP_MASS Top quark mass m_t in GeV (heaviest Standard Model fermion) VACUUM_ELECTRIC_PERMITTIVITY VACUUM_MAGNETIC_PERMEABILITY VON_KLITZING_CONSTANT WIEN_DISPLACEMENT_LAW_CONSTANT W_MASS W boson mass in GeV Z_MASS Z boson mass in GeV Z_PARTIAL_WIDTH_EE Z boson partial width to electrons Γ_ee in GeV (PDG 2024) Z_PARTIAL_WIDTH_HAD Z boson hadronic partial width Γ_had in GeV (PDG 2024) Z_WIDTH Z boson total width Γ_Z in GeV (PDG 2024) LorentzianMetric Trait for convention-specific Lorentzian metric wrappers. QuantumGates Standard Quantum Gates interface. QuantumOps Core Quantum State Operations (Dirac Notation), parameterized over the
underlying real field $R$ so the operations can be carried out at f32,
f64, f128, or any other real-field precision. air_n2_mole_fraction Returns AIR_N2_MOLE_FRACTIONR. air_o2_mole_fraction Returns AIR_O2_MOLE_FRACTIONR. alfven_speed alfven_speed_kernel Calculates the characteristic speed of Alfven waves.
$$ v_A = \frac{B}{\sqrt{\mu_0 \rho}} $$ all_structure_constants Returns all non-zero structure constants as a list of (a, b, c, f^abc). angular_momentum Causal wrapper for kinematics::angular_momentum_kernel angular_momentum_kernel Calculates angular momentum as the outer product of radius and linear momentum: $L = r \wedge p$. apply_gate Causal wrapper for mechanics::apply_gate_kernel apply_gate_kernel Applies a quantum gate to a state: $|\psi’\rangle = U |\psi\rangle$. area_mach_ratio Causal wrapper for compressible::area_mach_ratio_kernel area_mach_ratio_kernel Area–Mach relation for quasi-one-dimensional isentropic duct flow:
A/A* = (1/M) · [ 2/(γ+1) · (1 + (γ−1)/2 · M²) ]^((γ+1)/(2(γ−1))),
where A* is the sonic-throat area. arrhenius_rate arrhenius_rate_kernel Arrhenius reaction-rate coefficient in the Park / Gupta form beam_spot_size beam_spot_size_kernel Extracts the beam spot size $w(z)$ from the complex beam parameter $q$. bernoulli_pressure Causal wrapper for mechanics::bernoulli_pressure_kernel bernoulli_pressure_kernel Calculates pressure $P_2$ using Bernoulli’s principle. bernoulli_total_head Causal wrapper for ideal_flow::bernoulli_total_head_kernel bernoulli_total_head_kernel Bernoulli total head H = p / (ρ · g) + u² / (2 · g) + h (m). binding_energy Causal wrapper for physics::binding_energy_kernel binding_energy_kernel Calculates nuclear binding energy (mass defect): $E = \Delta m c^2$. bistritzer_macdonald Wrapper for moire::bistritzer_macdonald_kernel bistritzer_macdonald_kernel Constructs the Bistritzer-MacDonald Continuum Hamiltonian for Twisted Bilayer Graphene (TBG). boltzmann_factor Causal wrapper for stats::boltzmann_factor_kernel boltzmann_factor_kernel Calculates the unnormalized Boltzmann factor: $e^{-E/k_BT}$. bond_number Causal wrapper for dimensionless::bond_number_kernel bond_number_kernel Bond (Eötvös) number Bo = ρ · g · L² / σ. Gravity to surface tension. born_probability Causal wrapper for mechanics::born_probability_kernel born_probability_kernel Calculates the Born probability: $P = |\langle \text{basis} | \text{state} \rangle|^2$. cahn_hilliard_flux Wrapper for phase::cahn_hilliard_flux_kernel cahn_hilliard_flux_kernel Calculates the Cahn-Hilliard Flux with degenerate mobility (Type B). capillary_number Causal wrapper for dimensionless::capillary_number_kernel capillary_number_kernel Capillary number Ca = μ · u / σ. Viscous to surface-tension forces. carnot_efficiency Causal wrapper for stats::carnot_efficiency_kernel carnot_efficiency_kernel Calculates Carnot Efficiency: $\eta = 1 - \frac{T_C}{T_H}$. chronometric_volume Causal wrapper for spacetime::chronometric_volume_kernel chronometric_volume_kernel Calculates Chronometric Volume (4-Volume) from 3 vectors? circulation Causal wrapper for ideal_flow::circulation_kernel circulation_kernel Circulation Γ = ∮ u · dl as a discrete line integral. commutator Causal wrapper for mechanics::commutator_kernel commutator_kernel Calculates commutator $[A, B] = AB - BA$. confinement_potential_kernel Computes the linear confining potential: $V(r) = \sigma r + V_0$. continuity_rhs Causal wrapper for governing::continuity_rhs_kernel continuity_rhs_kernel Continuity equation RHS: ∂ρ/∂t = −∇·(ρu) = −(u·∇ρ + ρ · ∇·u). convective_acceleration Causal wrapper for governing::convective_acceleration_kernel convective_acceleration_kernel Convective acceleration (u·∇)u. covariant_derivative_kernel Computes the gauge covariant derivative: $D_\mu \psi = \partial_\mu \psi + i g A_\mu \psi$. debye_length debye_length_kernel Calculates the Debye Length $\lambda_D$.
$$ \lambda_D = \sqrt{\frac{\epsilon_0 k_B T_e}{n_e e^2}} $$ degree_of_polarization degree_of_polarization_kernel Calculates the Degree of Polarization (DOP) from a Stokes vector. delta_criterion Causal wrapper for coherent_structures::delta_criterion_kernel delta_criterion_kernel Δ-criterion (Chong, Perry & Cantwell 1990; generalized form): the
discriminant of the depressed velocity-gradient characteristic polynomial
Δ = (p̃/3)³ + (q̃/2)² where
p̃ = Q − P²/3, q̃ = 2P³/27 − PQ/3 + R,
and (P, Q, R) are the velocity-gradient invariants in the CPC convention. dissipation_rate Causal wrapper for turbulence::dissipation_rate_kernel dissipation_rate_kernel Dissipation rate ε = 2 ν · S':S' = 2 ν · Σ_{i,j} S'_{ij}². dissociation_equilibrium_fraction dissociation_equilibrium_fraction_kernel Equilibrium dissociation fraction of a diatomic pool A₂ ⇌ 2A at fixed
nuclei density: solve [A]²/[A₂] = K with [A₂] = (n_nuclei − [A])/2 for
the atom share x = [A]/n_nuclei. Closed form:
[A] = (−K + √(K² + 8·K·n_nuclei))/4. k_eq and nuclei_density must be
in one consistent concentration basis. doppler_effect_approaching Monadic wrapper for general::doppler_effect_kernel doppler_effect_kernel Calculates the observed frequency due to the Doppler effect for longitudinal motion. dynamic_pressure Causal wrapper for ideal_flow::dynamic_pressure_kernel dynamic_pressure_kernel Dynamic pressure q = 0.5 · ρ · u² (Pa). eckert_number Causal wrapper for dimensionless::eckert_number_kernel eckert_number_kernel Eckert number Ec = u² / (c_p · ΔT). Kinetic energy to enthalpy difference. eddy_viscosity_boussinesq Causal wrapper for turbulence::eddy_viscosity_boussinesq_kernel eddy_viscosity_boussinesq_kernel Boussinesq-closure eddy viscosity ν_t. effective_band_drude_weight Wrapper for qgt::effective_band_drude_weight_kernel effective_band_drude_weight_kernel Approximates the Effective Band Drude Weight ($D$) using band curvature and quantum geometry. einstein_tensor Causal wrapper for gravity::einstein_tensor_kernel einstein_tensor_kernel Calculates the Einstein Tensor: $G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu}$. electron_density electron_density_kernel Electron density n_e = α · n_tot from an ionization fraction. electron_impact_ionization_n_rate electron_impact_ionization_n_rate_kernel Thresholded electron-impact ionization N + e⁻ → N⁺ + 2e⁻, rated at the
electron temperature (k_f = 1.1e32 · T_e⁻³·¹⁴ · exp(−1.69e5/T_e)
cm³·mol⁻¹·s⁻¹). Table II states a ±36 percent spread on the prefactor and
the source notes these expansion-flow rates tend to be lower than
compressive-flow data; the validation band absorbs both. electron_impact_ionization_o_rate electron_impact_ionization_o_rate_kernel Thresholded electron-impact ionization O + e⁻ → O⁺ + 2e⁻, rated at the
electron temperature (k_f = 3.6e31 · T_e⁻²·⁹¹ · exp(−1.58e5/T_e)
cm³·mol⁻¹·s⁻¹). Same data-quality caveats as the N channel. energy_density_kernel Calculates the Electromagnetic Energy Density: $u = \frac{1}{2}(E^2 + B^2)$. energy_momentum_tensor_em energy_momentum_tensor_em_kernel Calculates the electromagnetic stress-energy tensor $T^{\mu\nu}{EM}$.
$$ T^{\mu\nu} = F^{\mu\alpha}F^\nu \alpha - \frac{1}{4} g^{\mu\nu} F_{\alpha\beta}F^{\alpha\beta} $$ enstrophy_density Causal wrapper for kinematics::enstrophy_density_kernel enstrophy_density_kernel Enstrophy density ξ = 0.5 · ‖ω‖². entropy_production_rate Causal wrapper for compressible::entropy_production_rate_kernel entropy_production_rate_kernel Local entropy-production rate density (W/(m³·K)) for a Newtonian fluid:
σ = Φ/T + κ · ‖∇T‖² / T²
where Φ = τ : ∇u is viscous dissipation and κ is thermal conductivity. escape_velocity Causal wrapper for mechanics::escape_velocity_kernel escape_velocity_kernel Calculates escape velocity: $v_e = \sqrt{\frac{2GM}{r}}$. expectation_value Causal wrapper for mechanics::expectation_value_kernel expectation_value_kernel Calculates the expectation value: $\langle A \rangle = \langle \psi | A | \psi \rangle$. fidelity Causal wrapper for mechanics::fidelity_kernel fidelity_kernel Calculates Quantum Fidelity: $F = |\langle \psi_{\text{ideal}} | \psi_{\text{actual}} \rangle|^2$. finite_rate_ionization_fixed_point finite_rate_ionization_fixed_point_kernel The network’s closed-form fixed point: the electron concentration where
production balances loss, β·x² − k_lin·x − p = 0 with quadratic loss
through quasi-neutrality (n_NO⁺ ≈ n_e), solved as
x* = (k_lin + √(k_lin² + 4·β·p)) / (2β). foppl_von_karman_strain Wrapper for moire::foppl_von_karman_strain_kernel foppl_von_karman_strain_kernel Calculates the Föppl-von Kármán stress tensor using the complete theory (Field-based). foppl_von_karman_strain_simple Wrapper for moire::foppl_von_karman_strain_simple_kernel foppl_von_karman_strain_simple_kernel Calculates the Föppl-von Kármán stress tensor (Simplified / Local). friction_velocity Causal wrapper for boundary_layer::friction_velocity_kernel friction_velocity_kernel Friction velocity u_τ = √(τ_w / ρ) (m/s). froude_number Causal wrapper for dimensionless::froude_number_kernel froude_number_kernel Froude number Fr = u / √(g · L). Inertial to gravitational forces. gaussian_q_propagation gaussian_q_propagation_kernel Propagates a Gaussian beam’s complex $q$-parameter through an ABCD optical system. gell_mann_matrices The 8 Gell-Mann matrices λ^a (a = 1..8), generators of SU(3). generalized_master_equation Causal wrapper for estimation::generalized_master_equation_kernel generalized_master_equation_kernel Generalized Master Equation Kernel. generate_schwarzschild_metric Generates a Schwarzschild-like 4D metric tensor. geodesic_deviation Causal wrapper for gravity::geodesic_deviation_kernel geodesic_deviation_kernel Calculates Geodesic Deviation acceleration: $A^\mu = -R^\mu_{\nu\sigma\rho} V^\nu n^\sigma V^\rho$. geodesic_integrator_kernel Integrates the geodesic equation using 4th-order Runge-Kutta (RK4). ginzburg_landau_free_energy Wrapper for phase::ginzburg_landau_free_energy_kernel ginzburg_landau_free_energy_kernel Calculates the Ginzburg-Landau Free Energy density. graphene_lattice_const Returns GRAPHENE_LATTICE_CONSTR. grashof_number Causal wrapper for dimensionless::grashof_number_kernel grashof_number_kernel Grashof number Gr = g · β · ΔT · L³ / ν². Buoyancy to viscous forces. grating_equation grating_equation_kernel Calculates the diffraction angle for a Grating using the Grating Equation. haruna_cz_gate Causal wrapper for mechanics::haruna_cz_gate_kernel haruna_cz_gate_kernel Implements Haruna’s Logical CZ Gate. haruna_hadamard_gate Causal wrapper for mechanics::haruna_hadamard_gate_kernel haruna_hadamard_gate_kernel Implements Haruna’s Logical Hadamard Gate. haruna_s_gate Causal wrapper for mechanics::haruna_s_gate_kernel haruna_s_gate_kernel Implements Haruna’s Logical S-Gate. haruna_t_gate Causal wrapper for mechanics::haruna_t_gate_kernel haruna_t_gate_kernel Implements Haruna’s Logical T-Gate. haruna_x_gate Causal wrapper for mechanics::haruna_x_gate_kernel haruna_x_gate_kernel Implements Haruna’s Logical X-Gate. haruna_z_gate Causal wrapper for mechanics::haruna_z_gate_kernel haruna_z_gate_kernel Implements Haruna’s Logical Z-Gate. heat_capacity Causal wrapper for stats::heat_capacity_kernel heat_capacity_kernel Calculates Heat Capacity: $C = \frac{dE}{dT}$. heat_diffusion Causal wrapper for stats::heat_diffusion_kernel heat_diffusion_kernel Calculates the Heat Equation step: $\frac{\partial u}{\partial t} = \alpha \Delta u$. helicity_density Causal wrapper for kinematics::helicity_density_kernel helicity_density_kernel Helicity density h = u · ω. hookes_law Causal wrapper for mechanics::hookes_law_kernel hookes_law_kernel Calculates generalized Hooke’s Law: $\sigma_{ij} = C_{ijkl} \epsilon_{kl}$. hydrostatic_pressure Causal wrapper for mechanics::hydrostatic_pressure_kernel hydrostatic_pressure_kernel Calculates hydrostatic pressure: $P = P_0 + \rho g h$. ideal_gas_law Causal wrapper for stats::ideal_gas_law_kernelRatio (or scalar). ideal_gas_law_kernel Calculates the Ideal Gas Constant $R$ from state variables: $R = \frac{PV}{nT}$. ideal_induction ideal_induction_kernel Calculates the time evolution of the magnetic field (Frozen-in flux).
$$ \frac{\partial \mathbf{B}}{\partial t} = \nabla \times (\mathbf{v} \times \mathbf{B}) $$ integral_length_scale Causal wrapper for turbulence::integral_length_scale_kernel integral_length_scale_kernel Integral length scale L = k^(3/2) / ε (m). isentropic_density_ratio Causal wrapper for compressible::isentropic_density_ratio_kernel isentropic_density_ratio_kernel Isentropic stagnation-to-static density ratio
ρ₀/ρ = (1 + (γ−1)/2 · M²)^(1/(γ−1)). isentropic_pressure_ratio Causal wrapper for compressible::isentropic_pressure_ratio_kernel isentropic_pressure_ratio_kernel Isentropic stagnation-to-static pressure ratio
p₀/p = (1 + (γ−1)/2 · M²)^(γ/(γ−1)). isentropic_temperature_ratio Causal wrapper for compressible::isentropic_temperature_ratio_kernel isentropic_temperature_ratio_kernel Isentropic stagnation-to-static temperature ratio
T₀/T = 1 + (γ−1)/2 · M². jones_rotation jones_rotation_kernel Rotates a Jones Matrix (operator) by an angle $\phi$. kalman_filter_linear Causal wrapper for estimation::kalman_filter_linear_kernel kalman_filter_linear_kernel Standard Linear Kalman Filter Update Step. kinetic_energy Causal wrapper for kinematics::kinetic_energy_kernel kinetic_energy_density Causal wrapper for governing::kinetic_energy_density_kernel kinetic_energy_density_kernel Kinetic energy density ρ · 0.5 · ‖u‖² (J/m³). kinetic_energy_kernel Calculates translational kinetic energy: $K = \frac{1}{2} m v^2$. klein_gordon Causal wrapper for mechanics::klein_gordon_kernel klein_gordon_kernel Calculates the Klein-Gordon operator action: $(\Delta + m^2)\psi$. knudsen_number Causal wrapper for dimensionless::knudsen_number_kernel knudsen_number_kernel Knudsen number Kn = λ / L. Mean free path to characteristic length. kolmogorov_length Causal wrapper for turbulence::kolmogorov_length_kernel kolmogorov_length_kernel Kolmogorov length scale η = (ν³ / ε)^(1/4) (m). kolmogorov_time Causal wrapper for turbulence::kolmogorov_time_kernel kolmogorov_time_kernel Kolmogorov time scale τ_η = (ν / ε)^(1/2) (s). kolmogorov_velocity Causal wrapper for turbulence::kolmogorov_velocity_kernel kolmogorov_velocity_kernel Kolmogorov velocity scale u_η = (ν · ε)^(1/4) (m/s). ks_bilinear_residual The KS bilinear constraint residual b(u, w) = u₄w₁ − u₃w₂ + u₂w₃ − u₁w₄. Zero iff (u, w) maps to
a physical 3-D (r, v). ks_project_velocity Project the KS velocity w onto the constraint surface b(u, ·) = 0, returning the nearest
constraint-satisfying velocity under the fixed gauge that keeps u. The constraint is linear in w
with gradient g = (u₄, −u₃, u₂, −u₁) and |g|² = |u|², so the orthogonal projection removes the
violating component: w' = w − (b(u,w)/|u|²)·g. Idempotent. ks_strang_step One Strang-split perturbed step (the B1 between-step perturbation hook): half-kick the velocity
with the caller-supplied non-conformal Cartesian acceleration, drift exactly along the KS conformal
core for dt, then half-kick again. The perturbation is never expressed inside the KS algebra
(FS-2). 2nd-order accurate; the exact core is untouched when accel returns zero. kutta_joukowski_lift Causal wrapper for ideal_flow::kutta_joukowski_lift_kernel kutta_joukowski_lift_kernel Kutta–Joukowski lift per unit span L' = ρ · u_∞ · Γ (N/m). lagrangian_density_kernel Calculates the Electromagnetic Lagrangian Density: $\mathcal{L} = -\frac{1}{4} F_{\mu\nu} F^{\mu\nu}$. lambda2 Causal wrapper for coherent_structures::lambda2_kernel lambda2_kernel λ₂-criterion (Jeong & Hussain 1995): the second-largest (middle)
eigenvalue of the symmetric tensor M = S² + Ω² where S and Ω are
the symmetric and antisymmetric parts of ∇u. larmor_radius larmor_radius_kernel Calculates the Larmor Radius (Gyroradius).
$$ r_L = \frac{m v_\perp}{|q| B} $$ lens_maker lens_maker_kernel Calculates optical power and focal length using the Lens Maker’s Equation. lewis_number Causal wrapper for dimensionless::lewis_number_kernel lewis_number_kernel Lewis number Le = α / D. Thermal to mass diffusivity. log_law_velocity Causal wrapper for boundary_layer::log_law_velocity_kernel log_law_velocity_kernel Logarithmic law of the wall u⁺ = (1/κ) · ln(y⁺) + B. logical_cz Calculates the Logical CZ gate: $CZ(\gamma_1, \gamma_2) = \exp(i \pi a(\gamma_1) a(\gamma_2))$. logical_hadamard Calculates the Logical Hadamard gate. logical_s Calculates the Logical S gate: $S(\gamma) = \exp(i \frac{\pi}{2} a(\gamma)^2)$. logical_t Calculates the Logical T gate. logical_x Calculates the Logical X gate: $X(\tilde{\gamma}) = \exp(i \pi b(\tilde{\gamma}))$. logical_z Calculates the Logical Z gate: $Z(\gamma) = \exp(i \pi a(\gamma))$. lorentz_force Causal wrapper for forces::lorentz_force_kernel lorentz_force_kernel Calculates the magnetic force component of the Lorentz Force: $F = J \times B$. lorenz_gauge Causal wrapper for fields::lorenz_gauge_kernel lorenz_gauge_kernel Calculates the Lorenz gauge condition: $\nabla \cdot A = 0$. mach_number Causal wrapper for dimensionless::mach_number_kernel mach_number_kernel Mach number M = u / a. Flow speed in units of the local sound speed. magnetic_helicity_density Causal wrapper for fields::magnetic_helicity_density_kernel magnetic_helicity_density_kernel Calculates Magnetic Helicity Density: $h = A \cdot B$. magnetic_pressure magnetic_pressure_kernel Calculates magnetic pressure.
$$ P_B = \frac{B^2}{2\mu_0} $$ magnetic_reconnection_rate magnetic_reconnection_rate_kernel Estimates reconnection rate (Sweet-Parker model simplified).
$$ v_{in} = \frac{v_A}{\sqrt{S}} $$ maxwell_gradient Causal wrapper for fields::maxwell_gradient_kernel maxwell_gradient_kernel Calculates the Maxwell gradient (Electromagnetic Field Tensor). n2_dissociation_equilibrium n2_dissociation_equilibrium_kernel Concentration-basis equilibrium constant of N₂ dissociation
(N₂ + M ⇌ 2N + M) from the RP-1232 Table II pair: K = k_f / k_b, unit
mol·cm⁻³ (the backward rate is three-body). Detailed balance holds by
construction because both rates come from one table row. newtonian_viscous_stress Causal wrapper for constitutive::newtonian_viscous_stress_kernel newtonian_viscous_stress_kernel Newtonian viscous stress with Stokes hypothesis (bulk viscosity ζ = 0):
τ = 2μ S − (2/3) μ (∇·u) I. newtonian_viscous_stress_with_bulk Causal wrapper for constitutive::newtonian_viscous_stress_with_bulk_kernel newtonian_viscous_stress_with_bulk_kernel Newtonian viscous stress with bulk viscosity:
τ = 2μ S − (2/3) μ (∇·u) I + ζ (∇·u) I. no_associative_ionization_rate no_associative_ionization_rate_kernel Associative ionization N + O → NO⁺ + e⁻ forward rate, rated at the
heavy-particle controlling temperature
(k_f = 9.03e9 · T⁰·⁵ · exp(−3.24e4/T) cm³·mol⁻¹·s⁻¹): the convenience
form of the shipped Arrhenius evaluation over the shipped reaction-7
constants, paired with
no_dissociative_recombination_rate_kernel no_dissociative_recombination_rate no_dissociative_recombination_rate_kernel Dissociative recombination NO⁺ + e⁻ → N + O: the two-body backward rate
of the associative-ionization channel, rated at the electron
temperature (barrier-free; k_b = 1.80e19 · T_e⁻¹ cm³·mol⁻¹·s⁻¹). This
is the physical blackout-exit mechanism: in cold dense air it decays a
carried electron population toward the local (low) equilibrium. nusselt_number Causal wrapper for dimensionless::nusselt_number_kernel nusselt_number_kernel Nusselt number Nu = h · L / k. Convective to conductive heat transfer. o2_dissociation_equilibrium o2_dissociation_equilibrium_kernel Concentration-basis equilibrium constant of O₂ dissociation
(O₂ + M ⇌ 2O + M) from the RP-1232 Table II pair: K = k_f / k_b, unit
mol·cm⁻³. orbital_velocity Causal wrapper for mechanics::orbital_velocity_kernel orbital_velocity_kernel Calculates orbital velocity: $v = \sqrt{\frac{GM}{r}}$. parallel_transport_kernel Parallel transports a vector along a discrete path using Christoffel symbols. park2t_ionization_surrogate park2t_ionization_surrogate_kernel Tier-A Park-2T ionization surrogate: the relaxation target α_eq(T, n)
that the LER IonizationStage relaxes toward. It is the Saha equilibrium for
the dominant NO ionization channel (E_ion ≈ 9.26 eV); being the full
equilibrium it carries electron-impact electrons as well as NO⁺. The gap
between the carried α and this target is the nonequilibrium lag. park_controlling_temperature park_controlling_temperature_kernel Park’s controlling temperature T_q = T_tr^q · T_v^(1−q) for the given
exponent q (the dissociation closure uses PARK_DISSOCIATION_Q park_dissociation_q Returns PARK_DISSOCIATION_QR. park_no_ionization_activation_temp Returns PARK_NO_IONIZATION_ACTIVATION_TEMPR. park_no_ionization_exponent Returns PARK_NO_IONIZATION_EXPONENTR. park_no_ionization_prefactor Returns PARK_NO_IONIZATION_PREFACTORR. particle_stokes_number Causal wrapper for dimensionless::particle_stokes_number_kernel particle_stokes_number_kernel Particle Stokes number St = τ_p · u / L. partition_function Causal wrapper for stats::partition_function_kernel partition_function_kernel Calculates Partition Function: $Z = \sum e^{-E_i / k_B T}$. pdg_lookup Lookup particle data by PDG ID. pdg_mass Get particle mass by PDG ID (convenience function). peclet_number Causal wrapper for dimensionless::peclet_number_kernel peclet_number_kernel Peclet number (thermal) Pe = u · L / α. Convective to diffusive heat transport. plasma_frequency plasma_frequency_kernel Calculates the (angular) electron plasma frequency $\omega_p$.
$$ \omega_p = \sqrt{\frac{n_e e^2}{\epsilon_0 m_e}} $$ power_law_apparent_viscosity Causal wrapper for constitutive::power_law_apparent_viscosity_kernel power_law_apparent_viscosity_kernel Power-law (Ostwald–de Waele) apparent viscosity: μ_eff = K · γ̇^(n−1). poynting_vector Causal wrapper for fields::poynting_vector_kernel poynting_vector_kernel Calculates the Poynting Vector (Energy Flux): $S = E \times B$. prandtl_number Causal wrapper for dimensionless::prandtl_number_kernel prandtl_number_kernel Prandtl number Pr = ν / α. Momentum diffusivity to thermal diffusivity. pressure_gradient_force Causal wrapper for governing::pressure_gradient_force_kernel pressure_gradient_force_kernel Pressure gradient force per unit mass −(1/ρ) · ∇p. pressure_work Causal wrapper for governing::pressure_work_kernel pressure_work_kernel Reversible pressure work p · ∇·u (W/m³). proca_equation Causal wrapper for fields::proca_equation_kernel proca_equation_kernel Calculates the Proca Equation (Massive Electromagnetism): $\delta F + m^2 A = J$. proper_time_kernel Computes the proper time along a discrete worldline. q_criterion Causal wrapper for coherent_structures::q_criterion_kernel q_criterion_kernel Q-criterion: Q = 0.5 · (‖Ω‖² − ‖S‖²) = −0.5 · tr(∇u · ∇u). quantum_geometric_tensor Wrapper for qgt::quantum_geometric_tensor_kernel quantum_geometric_tensor_kernel Calculates the Quantum Geometric Tensor (QGT) component $Q_{ij}^n(\mathbf{k})$ for band $n$. quasi_qgt Wrapper for qgt::quasi_qgt_kernel quasi_qgt_kernel Calculates the Quasi-QGT $q_{ij}^n(\mathbf{k})$. radioactive_decay Causal wrapper for physics::radioactive_decay_kernel radioactive_decay_kernel Calculates the remaining amount of a radioactive substance: $N(t) = N_0 \cdot 2^{-t / t_{1/2}}$. rankine_hugoniot_temperature rankine_hugoniot_temperature_kernel Post-shock temperature from the Rankine–Hugoniot normal-shock relations ray_transfer ray_transfer_kernel Applies an ABCD matrix to a ray vector. rayleigh_number Causal wrapper for dimensionless::rayleigh_number_kernel rayleigh_number_kernel Rayleigh number Ra = g · β · ΔT · L³ / (ν · α). Drives free convection. real_from_f64 Casts an f64 physical constant to a target real-field precision R. recovery_temperature recovery_temperature_kernel Recovery-temperature reconstruction T_tr = T_post − ½|u|²/c_p — the Tier-A
stand-in for the post-shock translational temperature, built from the
post-shock stagnation temperature and the local speed off the incompressible
velocity field. Labeled a reconstruction, not a true thermodynamic path. reduced_planck_constant Returns REDUCED_PLANCK_CONSTANTR. relativistic_clock_drift_rate_kernel The fractional proper-time rate offset dτ/dt − 1 of a clock at radius r moving at speed v, to
first post-Newtonian (1PN) order in a monopole field: relativistic_clock_offset_kernel The fractional clock-rate offset of a moving clock relative to a reference clock — both in the same
monopole field — to 1PN order: [Φ_clock − Φ_ref]/c² − [v_clock² − v_ref²]/(2c²). The leading 1s
cancel, so this is the directly-measurable frequency difference (e.g. a GPS satellite clock vs a geoid
clock). Multiply by elapsed coordinate time to get the accumulated τ offset. relativistic_current Wrapper for relativistic current density calculation. relativistic_current_kernel Calculates relativistic current density J^μ via covariant divergence. resistive_diffusion resistive_diffusion_kernel Calculates the diffusion term of the induction equation.
$$ \frac{\partial \mathbf{B}}{\partial t}_{diff} = \eta \nabla^2 \mathbf{B} $$ reynolds_number Causal wrapper for dimensionless::reynolds_number_kernel reynolds_number_kernel Reynolds number Re = u · L / ν. Ratio of inertial to viscous forces. reynolds_stress Causal wrapper for turbulence::reynolds_stress_kernel reynolds_stress_kernel Reynolds-stress tensor R_ij = ⟨u'_i u'_j⟩ packaged as a ReynoldsStress<R> richardson_number Causal wrapper for dimensionless::richardson_number_kernel richardson_number_kernel Richardson number Ri = g · β · ΔT · L / u². Buoyancy to shear forces. rotation_rate_tensor Causal wrapper for kinematics::rotation_rate_tensor_kernel rotation_rate_tensor_kernel Rate-of-rotation (spin) tensor Ω = 0.5 · (∇u − ∇uᵀ). rotational_kinetic_energy Causal wrapper for kinematics::rotational_kinetic_energy_kernel rotational_kinetic_energy_kernel Calculates rotational kinetic energy: $K_{rot} = \frac{1}{2} I \omega^2$. rp1232_ei_n_activation_temp Returns RP1232_EI_N_ACTIVATION_TEMPR. rp1232_ei_n_exponent Returns RP1232_EI_N_EXPONENTR. rp1232_ei_n_prefactor Returns RP1232_EI_N_PREFACTORR. rp1232_ei_o_activation_temp Returns RP1232_EI_O_ACTIVATION_TEMPR. rp1232_ei_o_exponent Returns RP1232_EI_O_EXPONENTR. rp1232_ei_o_prefactor Returns RP1232_EI_O_PREFACTORR. rp1232_n2_diss_activation_temp Returns RP1232_N2_DISS_ACTIVATION_TEMPR. rp1232_n2_diss_exponent Returns RP1232_N2_DISS_EXPONENTR. rp1232_n2_diss_prefactor Returns RP1232_N2_DISS_PREFACTORR. rp1232_n2_recomb_exponent Returns RP1232_N2_RECOMB_EXPONENTR. rp1232_n2_recomb_prefactor Returns RP1232_N2_RECOMB_PREFACTORR. rp1232_no_dr_activation_temp Returns RP1232_NO_DR_ACTIVATION_TEMPR. rp1232_no_dr_exponent Returns RP1232_NO_DR_EXPONENTR. rp1232_no_dr_prefactor Returns RP1232_NO_DR_PREFACTORR. rp1232_o2_diss_activation_temp Returns RP1232_O2_DISS_ACTIVATION_TEMPR. rp1232_o2_diss_exponent Returns RP1232_O2_DISS_EXPONENTR. rp1232_o2_diss_prefactor Returns RP1232_O2_DISS_PREFACTORR. rp1232_o2_recomb_exponent Returns RP1232_O2_RECOMB_EXPONENTR. rp1232_o2_recomb_prefactor Returns RP1232_O2_RECOMB_PREFACTORR. rp1232_zeldovich_activation_temp Returns RP1232_ZELDOVICH_ACTIVATION_TEMPR. rp1232_zeldovich_exponent Returns RP1232_ZELDOVICH_EXPONENTR. rp1232_zeldovich_prefactor Returns RP1232_ZELDOVICH_PREFACTORR. running_coupling_kernel Computes the running QCD coupling constant $\alpha_s(Q^2)$ (asymptotic freedom). saha_ionization_fraction saha_ionization_fraction_kernel Saha-equilibrium ionization fraction α = n_e / n_tot for a singly-ionized
gas, from scalar_advection_diffusion Causal wrapper for governing::scalar_advection_diffusion_kernel scalar_advection_diffusion_kernel Generic scalar transport RHS: −u · ∇φ + D · ∇²φ + S. schmidt_number Causal wrapper for dimensionless::schmidt_number_kernel schmidt_number_kernel Schmidt number Sc = ν / D. Momentum diffusivity to mass diffusivity. schwarzschild_radius Causal wrapper for mechanics::schwarzschild_radius_kernel schwarzschild_radius_kernel Calculates Schwarzschild radius: $r_s = \frac{2GM}{c^2}$. shannon_entropy Causal wrapper for stats::shannon_entropy_kernel shannon_entropy_kernel Calculates Shannon Entropy: $H = -\sum p_i \ln(p_i)$. single_slit_irradiance single_slit_irradiance_kernel Calculates the Single Slit Diffraction Irradiance. skin_friction_coefficient Causal wrapper for boundary_layer::skin_friction_coefficient_kernel skin_friction_coefficient_kernel Skin-friction coefficient C_f = τ_w / (0.5 · ρ · u_∞²). snells_law snells_law_kernel Calculates refracted angle using Snell’s Law or returns a Critical Angle error. solve_gm_analytical Causal wrapper for solve_gm_analytical_kernel solve_gm_analytical_kernel Recovers GM within the weak-field 1PN limit from two space-time coordinates. spacetime_interval Causal wrapper for spacetime::spacetime_interval_kernel spacetime_interval_kernel Calculates the spacetime interval $s^2 = g_{\mu\nu} x^\mu x^\nu$ (squared magnitude in metric). specific_enthalpy Causal wrapper for compressible::specific_enthalpy_kernel specific_enthalpy_kernel Specific enthalpy h = c_p · T (J/kg) for an ideal gas with constant c_p. speed_of_light Returns SPEED_OF_LIGHTR. speed_of_sound_ideal_gas Causal wrapper for compressible::speed_of_sound_ideal_gas_kernel speed_of_sound_ideal_gas_kernel Ideal-gas speed of sound a = √(γ · R_s · T). stokes_from_jones stokes_from_jones_kernel Converts a pure state Jones vector to a Stokes vector. strain_rate_tensor Causal wrapper for kinematics::strain_rate_tensor_kernel strain_rate_tensor_kernel Strain-rate tensor S = 0.5 · (∇u + ∇uᵀ). stream_function_2d Causal wrapper for ideal_flow::stream_function_2d_kernel stream_function_2d_kernel 2D stream-function differential update dψ = u · dy − v · dx. strouhal_number Causal wrapper for dimensionless::strouhal_number_kernel strouhal_number_kernel Strouhal number Sr = f · L / u. Oscillation frequency to flow. structure_constant Returns the totally antisymmetric SU(3) structure constants f^{abc}. swirling_strength Causal wrapper for coherent_structures::swirling_strength_kernel swirling_strength_kernel Swirling strength λ_ci (Zhou et al. 1999): the imaginary part of the
complex eigenvalue pair of ∇u, or zero when all eigenvalues are real. taylor_microscale Causal wrapper for turbulence::taylor_microscale_kernel taylor_microscale_kernel Taylor microscale λ = √(15 · ν · k / ε) (m). thermal_expansion Causal wrapper for mechanics::thermal_expansion_kernel thermal_expansion_kernel Calculates thermal expansion strain: $\epsilon = \alpha \Delta T$. time_dilation_angle Causal wrapper for spacetime::time_dilation_angle_kernel time_dilation_angle_kernel Calculates Time Dilation Angle (Rapidity $\eta$). torque Causal wrapper for kinematics::torque_kernel torque_kernel Calculates torque as the outer product of radius and force: $\tau = r \wedge F$. total_enthalpy Causal wrapper for compressible::total_enthalpy_kernel total_enthalpy_kernel Total (stagnation) enthalpy h_0 = h + 0.5 · ‖u‖² (J/kg). total_pressure_isentropic Causal wrapper for compressible::total_pressure_isentropic_kernel total_pressure_isentropic_kernel Isentropic stagnation pressure
p_0 = p · (1 + (γ−1)/2 · M²)^(γ/(γ−1)). total_temperature_isentropic Causal wrapper for compressible::total_temperature_isentropic_kernel total_temperature_isentropic_kernel Isentropic stagnation temperature
T_0 = T · (1 + (γ−1)/2 · M²). turbulent_kinetic_energy Causal wrapper for turbulence::turbulent_kinetic_energy_kernel turbulent_kinetic_energy_kernel Turbulent kinetic energy k = 0.5 · ⟨u' · u'⟩. velocity_gradient_invariants Causal wrapper for kinematics::velocity_gradient_invariants_kernel velocity_gradient_invariants_kernel Invariants (P, Q, R) of the velocity gradient tensor A = ∇u,
following the Chong–Perry–Cantwell (1990) convention used in vortex
classification: velocity_potential_2d Causal wrapper for ideal_flow::velocity_potential_2d_kernel velocity_potential_2d_kernel 2D velocity-potential differential update dφ = u · dx + v · dy. vibrational_relaxation vibrational_relaxation_kernel Vibrational relaxation toward the translational temperature, integrated over
dt by the closed-form Lagging-Equilibrium Relaxation (LER) exponential viscous_diffusion Causal wrapper for governing::viscous_diffusion_kernel viscous_diffusion_kernel Viscous diffusion acceleration ν · ∇²u. viscous_dissipation_rate Causal wrapper for governing::viscous_dissipation_rate_kernel viscous_dissipation_rate_kernel Viscous dissipation rate Φ = τ : ∇u (W/m³). viscous_length_scale Causal wrapper for boundary_layer::viscous_length_scale_kernel viscous_length_scale_kernel Viscous length scale δ_ν = ν / u_τ (m). viscous_sublayer_velocity Causal wrapper for boundary_layer::viscous_sublayer_velocity_kernel viscous_sublayer_velocity_kernel Viscous sublayer velocity profile u⁺ = y⁺ (valid for y⁺ ≲ 5). von_mises_stress Causal wrapper for mechanics::von_mises_stress_kernel von_mises_stress_kernel Calculates Von Mises Stress from a 3x3 Stress Tensor. vorticity_from_gradient Causal wrapper for kinematics::vorticity_from_gradient_kernel vorticity_from_gradient_kernel Vorticity vector ω = ∇ × u, computed from the velocity gradient. vorticity_transport Causal wrapper for governing::vorticity_transport_kernel vorticity_transport_kernel Vorticity transport RHS: −(u·∇)ω + (ω·∇)u + ν · ∇²ω. wall_shear_stress_newtonian Causal wrapper for boundary_layer::wall_shear_stress_newtonian_kernel wall_shear_stress_newtonian_kernel Newtonian wall shear stress magnitude τ_w = μ · |∂u/∂y|_wall (Pa). wave_speed Monadic wrapper for general::wave_speed_kernel wave_speed_kernel Calculates the speed of a wave given its frequency and wavelength. weber_number Causal wrapper for dimensionless::weber_number_kernel weber_number_kernel Weber number We = ρ · u² · L / σ. Inertial to surface-tension forces. wilson_loop_kernel Computes a simplified Wilson loop trace for confinement analysis. y_plus Causal wrapper for boundary_layer::y_plus_kernel y_plus_kernel Dimensionless wall distance y⁺ = y · u_τ / ν. zeldovich_exchange_rate zeldovich_exchange_rate_kernel Zeldovich exchange N₂ + O → NO + N forward rate
(k = 6.75e13 · exp(−3.75e4/T) cm³·mol⁻¹·s⁻¹): the low-activation
N-atom production path (37,500 K barrier against direct dissociation’s
113,100 K) that feeds associative ionization while direct N₂
dissociation is still frozen. Rated at the heavy-particle controlling
temperature. Gate Operator ParticleMetric For Particle Physics modules: West Coast (+—) PhysicsMetric Default physics metric (configurable): East Coast. RelativityMetric For General Relativity modules: East Coast (-+++)