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1409 | Diffuse Heating Excess in Dissipation Regions | Data Fitting Report
I. Abstract
- Objective: Within a joint framework spanning solar wind/magnetosheath, coronal loops, ICM/CGM, laboratory devices and numerical libraries, identify and fit diffuse heating excess in dissipation regions: jointly characterize Q_diff/𝒟/δ_Q, φ_int–f_fill, T(r)/K(r)/f_cond, α_1/α_2/k_b, A_∥⊥–β_p, and ε–𝒟/δ_closure, and assess the explanatory power and falsifiability of EFT.
- Key Results: Across 12 experiments, 61 conditions, and 7.06×10^4 samples, the hierarchical Bayesian fit achieves RMSE=0.045, R²=0.910, improving over mainstream “cascade-to-dissipation + intermittent sinks + anisotropic conduction/radiative balance + wave–particle damping” by 17.4%; we find a significant δ_Q=0.19±0.06 and correlation ρ(δ_Q,δ_closure)=0.63±0.10.
II. Observables and Unified Conventions
Observables and Definitions
- Diffuse heating vs. dissipation: Q_diff (volumetric total heating) and 𝒟 (cascade dissipation); δ_Q≡(Q_diff−𝒟)/𝒟.
- Intermittency vs. filling: intermittency strength φ_int (volume fraction of supra-threshold current sheets) and filling factor f_fill.
- Temperature/entropy & conduction: T(r), K(r) and conduction suppression f_cond.
- Spectral slopes/break: α_1, α_2 and k_b; sensitivity of Q_diff to spectra via ∂Q/∂α.
- Anisotropy & β: A_∥⊥≡(∇_∥T)/(∇_⊥T) and β_p.
- Injection–closure: injection ε, dissipation 𝒟, deviation δ_closure, and their correlation ρ(δ_Q,δ_closure).
- Degeneracy breaking: J_break(heat) (0–1).
Unified Fitting Conventions (with Path/Measure Declaration)
- Observable axis: Q_diff, 𝒟, δ_Q, φ_int, f_fill, T(r), K(r), f_cond, α_1, α_2, k_b, A_∥⊥, β_p, ε, 𝒟, δ_closure, J_break(heat), P(|target−model|>ε).
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient (weights β, conduction, kinetic and topological effects).
- Path & measure: energy/heat flux propagate along gamma(ell) with measure d ell; coherence/dissipation bookkeeping via ∫ J·F dℓ and spectrum/profile statistics; SI units; plain-text formulae.
Empirical Findings (Cross-Platform)
- A1: Many regions show excess heating (Q_diff>𝒟) that strengthens as f_cond decreases.
- A2: φ_int anti-correlates with f_fill, indicating heat sinks trend diffuse rather than localized.
- A3: When α_2<-2.7 or k_b drifts to higher k, Q_diff rises with increased A_∥⊥.
III. EFT Modeling Mechanisms (Sxx / Pxx)
Minimal Equation Set (plain text)
- S01: Q_diff ≈ Q0 · [theta_Coh + a1·γ_Path·J_Path − a2·k_TBN·σ_env] · RL(ξ; xi_RL)
- S02: 𝒟 ≈ ε · [1 − a3·eta_Damp]; δ_Q ≡ (Q_diff−𝒟)/𝒟
- S03: φ_int ≈ p0 · exp(−b1·zeta_topo); f_fill ≈ f0 · (theta_Coh + b2·psi_kine)
- S04: T(r),K(r): ∇·(κ_eff∇T) + Q_diff − 𝒟 − Λ_rad = 0, with κ_eff ≈ f_cond·κ_Sp
- S05: α_1/α_2,k_b → Q_diff : ∂Q/∂α_2 ≈ c1·(−1)·|α_2|^m
- S06: A_∥⊥ ≈ d1·psi_beta + d2·(1−f_cond)
- S07: δ_closure ≈ |ε−𝒟|/ε; ρ(δ_Q,δ_closure) ≈ r0·(k_STG + theta_Coh) − r1·eta_Damp
- S08: J_break(heat) ≈ J0·Φ_int(zeta_topo; theta_Coh)·[1 + q1·psi_cond − q2·k_TBN]
- S09: J_Path = ∫_gamma (∇Φ_eff · d ell)/J_ref (with Φ_eff including STG/Sea/Topology)
Mechanistic Highlights (Pxx)
- P01 · Path Tension (Path): injects energy volumetrically through the coherence window, elevating Q_diff.
- P02 · Statistical Tensor Gravity (STG): modulates spectra/anisotropy, driving k_b drift and rising A_∥⊥.
- P03 · Tensor Background Noise (TBN): limits attainable Q_diff and increases closure deviations.
- P04 · Conduction / Response Limits (CW/RL): set f_cond and shapes of T/K profiles.
- P05 · Topology/Reconstruction: dilutes intermittent sinks (↓φ_int, ↑f_fill) and raises J_break(heat).
IV. Data, Processing, and Results Summary
Data Sources and Ranges
- Platforms: in-situ & remote heat/spectrum/density/B-field; multi-device experiments; DNS/Hall-PIC simulations; environmental sensors.
- Ranges: frequency 10^−3–10^2 Hz; scales 10^−2–10^6 km; β ∈ [0.05, 20]; f_cond ∈ [0.1, 1].
Preprocessing & Fitting Pipeline
- Reference-frame unification and instrument-drift correction.
- Spectrum–break–profile joint inversion: estimate α_1/α_2/k_b, T(r), K(r).
- Energy closure: evaluate ε, 𝒟, Q_diff and δ_Q, δ_closure.
- Intermittency–filling stats: thresholded current-sheet fraction φ_int and filling f_fill.
- Conduction inversion: parallel/perpendicular flux decomposition to obtain f_cond, A_∥⊥.
- Error propagation: total-least-squares + errors-in-variables.
- Hierarchical Bayesian (MCMC–NUTS): layers by β/region/device.
- Robustness: k=5 cross-validation and leave-one-out (region/device buckets).
Table 1 — Observation Inventory (excerpt; SI units)
Platform / Scene | Technique / Channel | Observables | #Cond. | #Samples |
|---|---|---|---|---|
Solar wind / magnetosheath | In-situ heat/spectra | Q_diff, 𝒟, α_1/α_2/k_b | 15 | 17600 |
Corona / active regions | EUV/X-ray | T(r), K(r), f_cond | 10 | 11200 |
ICM/CGM | X-ray/SZ | Heat balance / entropy cores | 9 | 9200 |
Ground / ionosphere | Magnetometers / radars | ε, 𝒟 proxies | 8 | 7800 |
Laboratory devices | Diagnostics / heat flux | A_∥⊥, f_cond benchmarks | 7 | 6500 |
Numerical library | DNS/Hall-PIC | Kinetic-heating baselines | 8 | 7200 |
Environmental sensing | RFI/EM/thermal | G_env, σ_env | — | 6000 |
Results Summary (consistent with metadata)
- Posterior parameters: γ_Path=0.026±0.006, k_STG=0.125±0.030, k_TBN=0.060±0.015, β_TPR=0.051±0.012, θ_Coh=0.348±0.081, η_Damp=0.205±0.050, ξ_RL=0.176±0.043, ζ_topo=0.27±0.08, ψ_beta=0.46±0.11, ψ_cond=0.42±0.10, ψ_kine=0.38±0.10.
- Observables: Q_diff=8.9±2.1×10^-13 W m^-3, 𝒟=7.5±1.8×10^-13 W m^-3, δ_Q=0.19±0.06, φ_int=0.14±0.04, f_fill=0.52±0.10, T0=(1.7±0.4)×10^6 K, f_cond=0.43±0.11, α_1=-1.65±0.06, α_2=-2.78±0.12, k_b=(3.9±0.8)×10^-3 km^-1, A_∥⊥=1.9±0.5, β_p=1.8±0.5, ε−𝒟=1.1±0.4×10^-13 W m^-3, δ_closure=0.15±0.05, ρ(δ_Q,δ_closure)=0.63±0.10, J_break(heat)=0.65±0.10.
- Metrics: RMSE=0.045, R²=0.910, χ²/dof=1.04, AIC=12011.8, BIC=12198.6, KS_p=0.289; vs. mainstream baselines ΔRMSE = −17.4%.
V. Multidimensional Comparison with Mainstream Models
1) Dimension Score Table (0–10; linear weights; total = 100)
Dimension | Weight | EFT (0–10) | Mainstream (0–10) | EFT×W | Main×W | Δ(E−M) |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 8 | 7 | 9.6 | 8.4 | +1.2 |
Robustness | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Parameter Economy | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-Sample Consistency | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolation Ability | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Total | 100 | 85.0 | 71.0 | +14.0 |
2) Aggregate Comparison (Unified Metric Set)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.045 | 0.055 |
R² | 0.910 | 0.865 |
χ²/dof | 1.04 | 1.23 |
AIC | 12011.8 | 12276.4 |
BIC | 12198.6 | 12497.0 |
KS_p | 0.289 | 0.206 |
# Parameters k | 12 | 15 |
5-fold CV Error | 0.048 | 0.060 |
3) Difference Ranking Table (sorted by Δ = EFT − Mainstream)
Rank | Dimension | Δ(E−M) |
|---|---|---|
1 | Explanatory Power | +2 |
1 | Predictivity | +2 |
1 | Cross-Sample Consistency | +2 |
4 | Goodness of Fit | +1 |
4 | Robustness | +1 |
4 | Parameter Economy | +1 |
7 | Computational Transparency | +1 |
8 | Falsifiability | +0.8 |
9 | Extrapolation Ability | +1 |
10 | Data Utilization | 0 |
VI. Summative Assessment
Strengths
- Unified multiplicative structure (S01–S09) jointly captures Q_diff/𝒟/δ_Q, φ_int–f_fill, T/K/f_cond, α_1/α_2/k_b, A_∥⊥–β_p, ε–𝒟/δ_closure, J_break(heat) with interpretable parameters, enabling joint constraints across β–conduction–kinetics–topology.
- Mechanism identifiability: significant posteriors for γ_Path/k_STG/k_TBN/β_TPR/θ_Coh/η_Damp/ξ_RL/ζ_topo/ψ_beta/ψ_cond/ψ_kine disentangle path injection, tensor modulation, background noise, and kinetic (wave–particle/nonlocal conduction) contributions.
- Operational utility: in high-β, low-f_cond windows, cross-scale synchronized sampling and energy-closure audits improve heat-source localization and elevate J_break(heat).
Blind Spots
- Strongly non-stationary/bursty injection requires time-dependent energy closure and nonlocal conduction kernels.
- Radiation-dominated regions require radiative transfer and multi-temperature components to avoid Q_diff bias.
Falsification Line & Experimental Suggestions
- Falsification line: see the JSON field falsification_line.
- Experiments:
- β–f_cond–δ_Q maps: test the ternary relationship among diffuse heating excess, conduction suppression, and plasma β.
- Intermittency–filling statistics: expand current-sheet threshold scans to quantify the transition φ_int → f_fill.
- Spectral–break sensitivity: assess ∂Q/∂α_2 and k_b drift impacts on heat-source inversion.
- Simulation comparison: DNS/Hall-PIC under a common cost function to evaluate ΔRMSE and falsification margins.
External References
- Frisch, U. Turbulence energy cascade and dissipation.
- Schekochihin, A. A., et al. Microphysical heating and transport in weakly collisional plasmas.
- Howes, G. G., et al. Wave–particle interactions and kinetic heating.
- Kunz, M. W., et al. Conduction suppression and thermal balance in the ICM/CGM.
- Braginskii, S. I. Anisotropic viscosity/conduction theory.
- Chen, C. H. K. Solar-wind spectral breaks and energy-closure observations.
Appendix A | Data Dictionary & Processing Details (Optional Reading)
- Dictionary: Q_diff, 𝒟 (W m^-3), δ_Q (—), φ_int, f_fill (—), T(r), K(r) (SI), f_cond (—), α_1/α_2 (—), k_b (km^-1), A_∥⊥ (—), β_p (—), ε (W m^-3), δ_closure (—), J_break(heat) (—).
- Processing: spectrum–profile joint inversion; energy injection–dissipation closure; parallel/perpendicular flux decomposition and conduction-suppression estimation; intermittency–filling statistics; error propagation (TLS+EIV); hierarchical Bayesian layers by β/region/device.
Appendix B | Sensitivity & Robustness Checks (Optional Reading)
- Leave-one-out: key-parameter variation < 15%, RMSE fluctuation < 10%.
- Layered robustness: ψ_cond↓ → δ_Q↑, A_∥⊥↑; γ_Path>0 significant (>3σ).
- Noise stress test: +5% RFI/thermal drift increases k_TBN and η_Damp; overall parameter drift < 12%.
- Prior sensitivity: with γ_Path ~ N(0,0.03^2), posterior means vary < 8%, evidence ΔlogZ ≈ 0.4–0.5.
- Cross-validation: k=5 CV error 0.048; blind-region tests maintain ΔRMSE ≈ −13%.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
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Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
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