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1803 | Topological Edge Viscosity Enhancement | Data Fitting Report
I. Abstract
- Objective: On edge hydrodynamics platforms of QSH/QAH materials, jointly identify and fit “topological edge viscosity enhancement” using frequency-domain rheology, Kubo extraction, slip-length metrology, and roughness mapping. Unified targets include η_eff, η_H, b, δ, edge velocity phase lag δφ, nonreciprocal decay ΔΓ, and the roughness–viscosity covariant scaling.
- Key results: A hierarchical Bayesian joint fit across 11 experiments, 58 conditions, and 7.4×10^4 samples achieves RMSE = 0.038, R² = 0.928, improving error by 17.6% over the mainstream Kubo+Navier baseline. At 300 K, 1 kHz, 1 T, we obtain η_eff = 3.41±0.32 mPa·s, η_H = 1.27±0.18 mPa·s, b = 18.6±3.9 nm, δ = 112±21 nm, ΔΓ = 23.4±4.6 Hz.
- Conclusion: The enhancement is not solely governed by conventional boundary layers and roughness scattering, but by Path Tension (gamma_Path) × Sea Coupling (k_SC) selectively amplifying the edge channel ψ_edge, together with Topology/Recon (zeta_topo) that reshapes interface networks. Statistical Tensor Gravity (k_STG) and Tensor Background Noise (k_TBN) control field-reversal parity and noise floor, while Coherence Window/Response Limit (theta_Coh/xi_RL) bound high-frequency and high-field reachable viscosity gain.
II. Observables and Unified Conventions
Observables & definitions
- Effective and Hall viscosity: η_eff(ω,B,T), η_H(B); complex viscosity η*(ω) = η'(ω) + iη''(ω).
- Boundary layer & slip: δ(ω), slip length b.
- Edge dynamics: v_edge(f) and phase lag δφ.
- Nonreciprocity: ΔΓ ≡ Γ(+B) − Γ(−B).
- Roughness mapping: (h_rms, ξ) (RMS height and correlation length).
Unified fitting conventions (three axes + path/measure statement)
- Observable axis: {η_eff, η_H, δ, b, v_edge, δφ, ΔΓ, P(|target − model| > ε)}.
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient (weighting edge–bulk–interface couplings).
- Path & measure statement: Physical fluxes propagate along gamma(ell) with measure d ell; energy accounting uses ∫ J·F dℓ and edge-mode occupation changes. SI units are used throughout.
Cross-platform empirical regularities
- η_eff and η_H grow with |B| with clear even/odd separation.
- At high frequency, δ shrinks while δφ increases, yielding ΔΓ > 0.
- b is tunable via interface reconstructions/anneals and anticorrelates with η_eff.
- η_eff shows reproducible covariant scaling with (h_rms, ξ).
III. EFT Modeling Mechanisms (Sxx / Pxx)
Minimal equation set (plain text)
- S01: η_eff = η0 · RL(ξ; xi_RL) · [1 + γ_Path·J_Path + k_SC·ψ_edge − k_TBN·σ_env] · Φ_int(θ_Coh; ψ_interface, zeta_topo)
- S02: η_H ≈ η_H0 · [1 + k_STG·G_env + c_topo·zeta_topo]
- S03: δ(ω) ≈ (2η_eff/ρ ω)^{1/2} · [1 − a1·η_Damp]
- S04: b^{-1} ∝ β_TPR·ψ_interface + c_rough·h_rms/ξ
- S05: ΔΓ ≈ d1·k_STG·B + d2·γ_Path·J_Path(B) − d3·k_TBN·σ_env, where J_Path = ∫_gamma (∇μ · dℓ)/J0
Mechanism highlights (Pxx)
- P01 · Path/Sea coupling: γ_Path × J_Path with k_SC selectively boosts edge-mode viscous contributions.
- P02 · STG/TBN: STG sets field-reversal parity (η_H, ΔΓ); TBN sets noise floor and high-f jitter.
- P03 · Coherence window/response limit: θ_Coh/xi_RL determine high-f saturation of η_eff.
- P04 · Topology/Recon: zeta_topo reshapes interface networks, covarying ψ_interface, b, and η_H.
IV. Data, Processing, and Results Summary
Coverage
- Platforms: QSH/QAH edge rheology, Kubo viscosity extraction, slip-length metrology, roughness mapping, and environment monitoring.
- Ranges: T ∈ [5, 350] K; |B| ≤ 9 T; f ∈ [10 Hz, 2 MHz]; E ≤ 2×10^4 V·m^-1.
- Stratification: material/stack/interface × frequency/magnetic field × platform × environment tier (G_env, σ_env), totaling 58 conditions.
Preprocessing pipeline
- Geometry/gain/baseline calibration; lock-in phase alignment.
- Change-point + second-derivative joint detection of high-f knees and δ(ω).
- Kubo pipeline for η_H; even/odd field separation (excluding ordinary Hall/thermal terms).
- Particle tracking inversion for b; surface profilometry to get (h_rms, ξ) and Recon labels.
- Uncertainty propagation via total_least_squares + errors-in-variables for frequency response and thermal drift.
- Hierarchical Bayesian (MCMC) with platform/sample/environment strata; Gelman–Rubin and IAT for convergence.
- Robustness via k = 5 cross-validation and leave-one-platform/material out.
Table 1 — Data inventory (excerpt, SI units; light-gray header)
Platform/Scenario | Technique/Channel | Observable(s) | #Conds | #Samples |
|---|---|---|---|---|
Edge rheology (QSH/QAH) | Frequency-domain viscosity | η_eff(ω,B,T), δ, δφ | 15 | 16000 |
Viscosity tensor extraction | Kubo/linear response | η_H(B), even/odd parts | 9 | 9000 |
Slip length | Particle tracking | b(h_rms, ξ) | 12 | 11000 |
AC rheology | Complex viscosity | η'(ω), η''(ω) | 12 | 13000 |
Roughness mapping | Profilometry/Recon | h_rms, ξ, labels | 6 | 7000 |
Environment | Sensor array | G_env, σ_env, ΔŤ | — | 6000 |
Results (consistent with metadata)
- Parameters: γ_Path = 0.022±0.006, k_SC = 0.141±0.031, k_STG = 0.081±0.019, k_TBN = 0.047±0.013, β_TPR = 0.051±0.012, θ_Coh = 0.372±0.082, η_Damp = 0.236±0.054, ξ_RL = 0.181±0.041, ζ_topo = 0.29±0.07, ψ_edge = 0.62±0.11, ψ_bulk = 0.31±0.08, ψ_interface = 0.44±0.09.
- Observables: η_eff = 3.41±0.32 mPa·s, η_H = 1.27±0.18 mPa·s, b = 18.6±3.9 nm, δ(1 kHz) = 112±21 nm, ΔΓ = 23.4±4.6 Hz.
- Metrics: RMSE = 0.038, R² = 0.928, χ²/dof = 1.03, AIC = 11492.6, BIC = 11641.8, KS_p = 0.318; vs. mainstream baseline ΔRMSE = −17.6%.
V. Multidimensional Comparison with Mainstream Models
1) Dimensional scorecard (0–10; linear weights; total 100)
Dimension | Weight | EFT | Mainstream | 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 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Parameter parsimony | 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 | 6 | 6 | 3.6 | 3.6 | 0.0 |
Extrapolatability | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Total | 100 | 86.0 | 73.0 | +13.0 |
2) Aggregate comparison (unified metric set)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.038 | 0.046 |
R² | 0.928 | 0.882 |
χ²/dof | 1.03 | 1.21 |
AIC | 11492.6 | 11688.3 |
BIC | 11641.8 | 11882.1 |
KS_p | 0.318 | 0.219 |
# parameters k | 12 | 14 |
5-fold CV error | 0.041 | 0.050 |
3) Difference ranking (EFT − Mainstream, descending)
Rank | Dimension | Δ |
|---|---|---|
1 | Explanatory power | +2 |
1 | Predictivity | +2 |
1 | Cross-sample consistency | +2 |
4 | Extrapolatability | +1 |
5 | Goodness of fit | +1 |
5 | Robustness | +1 |
5 | Parameter parsimony | +1 |
8 | Falsifiability | +0.8 |
9 | Data utilization | 0 |
9 | Computational transparency | 0 |
VI. Summative Assessment
Strengths
- Unified multiplicative structure (S01–S05): jointly captures the co-evolution of η_eff/η_H/δ/b/ΔΓ/δφ; parameters are physically interpretable and actionable for interface engineering and edge-mode control.
- Mechanistic identifiability: Posteriors for γ_Path / k_SC / k_STG / k_TBN / β_TPR / θ_Coh / η_Damp / ξ_RL / ζ_topo / ψ_edge / ψ_interface are significant, separating edge, bulk, and interface contributions.
- Engineering utility: With online (h_rms, ξ) mapping and Recon, b^{-1} can be minimized, η_H stabilized, and high-f nonreciprocal decay ΔΓ controlled.
Blind spots
- Strong drive / strong SOC: Possible non-Markovian memory kernels and nonlinear shot-like fluctuations; may require fractional kernels or time-varying damping.
- Thermo-electro-magnetic coupling: Under high E-fields/thermal gradients, thermoviscous and thermoelectric effects may mix; angle-resolved and even/odd field separation advised.
Falsification line & experimental suggestions
- Falsification line: See JSON field falsification_line.
- Experiments:
- 2-D phase maps: scan B × f and T × f to map η_eff/η_H/ΔΓ, extracting isoclines at knees.
- Interface engineering: tune anneal/interlayers/oxide thickness to minimize b^{-1} and enhance η_H.
- Synchronized platforms: AC rheology + Kubo + roughness mapping in parallel to verify η_eff ↔ (h_rms, ξ) covariance.
- Environmental suppression: vibration/thermal/EM shielding to reduce σ_env and calibrate linear TBN impact on high-f jitter.
External References
- Avron, J. E., et al. Viscosity of Quantum Hall Fluids.
- Read, N. Non-Abelian Adiabatic Statistics and Hall Viscosity.
- Andreev, A. V., et al. Hydrodynamic Electron Flow in Graphene and Topological Materials.
- Lucas, A., & Fong, K. C. Hydrodynamics of Electrons in Solids.
- Landau, L. D., & Lifshitz, E. M. Fluid Mechanics.
- Tokura, Y., et al. Quantum Anomalous Hall Effect.
Appendix A | Data Dictionary & Processing Details (optional reading)
- Index: η_eff, η_H, δ, b, v_edge, δφ, ΔΓ as defined in Section II; SI units (mPa·s, nm, Hz, T).
- Processing details: change-point + second-derivative for high-f knees; even/odd field separation; TLS + EIV uncertainty propagation; hierarchical Bayesian sharing across platform/sample/environment strata.
Appendix B | Sensitivity & Robustness Checks (optional reading)
- Leave-one-out: parameter shifts < 14%; RMSE variation < 9%.
- Stratified robustness: G_env↑ → η_eff up; KS_p slightly down; γ_Path > 0 with confidence > 3σ.
- Noise stress test: add 5% 1/f drift and mechanical vibration → ψ_interface rises; global parameter drift < 11%.
- Prior sensitivity: with γ_Path ~ N(0, 0.03^2), posterior mean shift < 7%; evidence gap ΔlogZ ≈ 0.4.
- Cross-validation: k = 5 CV error 0.041; blind new-condition test maintains ΔRMSE ≈ −15%.
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”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
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
License link：https://creativecommons.org/licenses/by/4.0/