Validation media

The README only keeps a compact visual teaser. Detailed media context belongs here so each visual carries its claim level, source path, equations, and literature anchor. These assets are either generated from MHX validation gates or explicitly labeled theory schematics; none are production nonlinear plasmoid claims.

README media scope

The README should stay concise and show only landing-page media from docs/_static/readme/: solver-generated Harris-sheet reconnection movies with magnetic-flux contours, solver-generated reduced-MHD Orszag–Tang nonlinear movies, and one compact Harris tearing layer sweep. Detailed benchmark command catalogs, validation figure galleries, artifact inventories, CI output checklists, production-run chunking details, neural-ODE outputs, plugin walkthroughs, still figures, and scaffold comparisons belong in the documentation pages where they can carry tolerances, commands, claim boundaries, and maintenance context.

Residual-flux media policy

Public-facing double-Harris media must not rely on raw total-flux movies alone. The total magnetic flux is visually dominated by the static equilibrium sheet, so reviewer-facing media should pair any raw flux/current movie with at least one of:

• a residual-flux movie or panel, \(\Delta\psi=\psi_\mathrm{perturbed}-\psi_\mathrm{base}\);

• reconnected-flux and island-width proxy histories from the validation JSON;

• a promotion or local gate summary that states gate_ready, production_claim_ready, and the declared claim_level_if_passed.

The residual-flux view is visualization policy, not a stronger physics claim: it makes the seeded reconnecting response visible while the claim level remains bounded by the manifest and promotion gate. The standalone reviewer example that follows this policy is reproduced with:

MHX_EXAMPLE_FAST=1 \
MHX_EXAMPLE_OUTDIR_ROOT=outputs/reviewer/examples \
python examples/publication_double_harris_reconnection.py

It writes outputs/reviewer/examples/double_harris_reconnection/figures/publication_double_harris_delta_flux.gif alongside the raw flux/current movies, summary figure, manifest.json, and validation.json.

At-a-glance media table

Asset	What it shows	Claim boundary and anchor
	Single-sheet Harris reconnection zoom from a 128×128, t_end=160 GPU validation bundle: residual reconnecting flux \(\Delta\psi\) with total magnetic-flux/Az contours and diagnostic X/O annotations.	Solver-generated validation media anchored to the Harris current-sheet and FKR tearing picture; the markers are diagnostic annotations, not separatrix-event labels or converged Rutherford/plasmoid evidence.
	Full-domain periodic double-Harris view from the same bundle, showing residual current \(\Delta j_z\) across both sheets with total flux contours.	Solver-generated validation media; useful for morphology QA before larger seed, duration, and resolution sweeps.
	64×64, t_end=80 forced-turbulence current-sheet replay: current density with magnetic-flux contours and reconnection-rate proxy diagnostics.	Pedagogical 2-D reduced-MHD validation media anchored to turbulent-reconnection literature; not a 3-D LV99 fast-reconnection production test.
	64×64, t_end=8 decaying reduced-MHD turbulence replay with current filaments and flux contours.	Solver-generated nonlinear validation media; useful for turbulence morphology and current-sheet diagnostics, not converged turbulence statistics.
	Current-density filament formation from a 96×96, t_end=10 reduced-MHD Orszag–Tang replay.	Solver-generated validation media; nonlinear reduced-MHD cascade evidence, not a compressible shock-capturing full-MHD result.
	Vorticity roll-up from the same Orszag–Tang replay.	Solver-generated validation media with energy, divergence, and high-wavenumber-fraction gates.
	Flux-function deformation and dissipative mixing from the same Orszag–Tang replay.	Solver-generated validation media; useful as a nonlinear example for new users.
	Direct Harris-sheet eigenproblem: growth decreases with \(S\) while the resonant flow/current layer narrows.	Solver-generated validation media from mhx benchmark linear-tearing-layer; anchored to classical tearing localization from FKR 1963 and the reduced-MHD Harris eigenproblem used by MacTaggart 2019.
	Schematic Sweet-Parker sheet fragmentation with \(\gamma_{\max}\tau_A\propto S^{1/4}\) and \(k_{\max}L\propto S^{3/8}\).	Theory schematic only; anchored to Loureiro, Schekochihin & Cowley 2007, not a nonlinear MHX plasmoid result.
	Synthetic magnetic-flux eddies, current filaments, and an animated cascade guide.	Theory/pedagogy schematic only; not a nonlinear MHX turbulence simulation.
	Historical committed validation replay at 64×64, showing magnetic-flux evolution over t_end=30; README landing-page media now uses the longer 128×128, t_end=160 GPU validation bundle documented below.	Validation bridge from Harris tearing to longer nonlinear campaigns; bounded evidence, not converged Rutherford/plasmoid production.
	Same seeded run through fixed-scale out-of-plane current density.	Checks current-density visualization and dissipative nonlinear replay before aspect-ratio, seed, and resolution sweeps.
	FAST resolution/time-step sweep for the seeded periodic double-Harris replay.	Convergence scaffold that gates spread in early growth/amplification before any production Rutherford/plasmoid claim.
	Restartable Rutherford executor chunk with fixed-scale magnetic flux.	Execution-path validation for the chunked production runner; not completed nonlinear production evidence.
	Same executor chunk through current density, using fixed color limits.	Checks the movie/artifact lane and the current-density visualization contract.

Still validation figures live on the physics validation, long-run evidence, and publication checklist pages where they can be interpreted with equations, tolerances, and source links.

README Harris-sheet reconnection previews

The README Harris pair is regenerated from the preferred GPU validation bundle when present, then from the longest available seeded periodic double-Harris history under outputs/readme_media/, outputs/long_runs/, outputs/docs_validation/, or outputs/ci/. The current release media were regenerated from outputs/campaigns/gpu_nonlinear_20260522_085049/double_harris_long_n128_t160, a 128×128, t_end=160 validation bundle chosen for visible residual response rather than production convergence:

RUN_DIR=outputs/campaigns/gpu_nonlinear_20260522_085049

mhx benchmark double-harris-long-run \
  --outdir "$RUN_DIR/double_harris_long_n128_t160" \
  --nx 128 --ny 128 --width 0.36 --eta 0.0045 --nu 0.0045 \
  --perturbation-amplitude 0.004 --mode-x 2 --mode-y 1 \
  --dt 0.02 --t-end 160 --save-every 100 \
  --fit-start 0 --fit-stop 16 \
  --min-early-growth-rate 1e-9 \
  --min-max-growth-factor 1.000000001 \
  --min-reconnected-flux-amplification 1.000000001 \
  --min-island-width-amplification 1.000000001 \
  --movies

python examples/make_readme_media.py

The underlying periodic double-Harris field is the spectral analogue of a Harris sheet:

\[ B_y(x)=B_0\left[ \tanh\left(\frac{x-L_x/4}{a}\right) -\tanh\left(\frac{x-3L_x/4}{a}\right)-1 \right], \]

with a tearing-like seed

\[ \delta\psi(y,0)=\epsilon \cos(2\pi y/L_y). \]

The single-sheet README movie uses residual reconnecting flux \(\Delta\psi=\psi_\mathrm{perturbed}-\psi_\mathrm{base}\) as the color field and overlays total magnetic-flux (Az/ψ) contours. The full-domain companion uses residual current \(\Delta j_z=-\nabla^2\Delta\psi\) with the same total-flux contour context. The single-sheet movie rotates the view into standard current-sheet coordinates: horizontal is the sheet direction and vertical is the normal coordinate. The X/O labels are generated by the MHX critical-point detector: local minima of \(|\nabla\psi|\) are classified by the Hessian determinant, with saddle points marked as X and elliptic extrema marked as O. The detector now supports sub-cell quadratic Newton refinement for smooth fields; README labels remain diagnostic annotations rather than claimed separatrix topology.

This media is literature-anchored to the Harris equilibrium (Harris 1962) and the classical tearing instability picture (Furth, Killeen & Rosenbluth 1963). The validation manifest confirms finite histories, positive early perturbation growth, visible nonlinear amplification, response amplification, X/O counts, and dissipative total energy. mhx benchmark double-harris-promotion-check now marks the boundary between single-run media and convergence-backed validation evidence. It remains claim_level = "validation" until broader seed, aspect-ratio, Lundquist-number, and duration sweeps are attached. When the same data are used for reviewer/publication media, include the residual flux \(\psi_\mathrm{perturbed}-\psi_\mathrm{base}\) or the reconnected-flux proxy next to these raw total-field movies; raw total flux is not sufficient by itself because the equilibrium sheet can visually mask the seeded response.

Visual QA artifacts are written next to the README movies:

• docs/_static/readme/readme_media_visual_qa.json

• docs/_static/readme/double_harris_flux_snapshots.png

• docs/_static/readme/double_harris_current_snapshots.png

• docs/_static/readme/double_harris_current_sheet_snapshots.png

Source links:

• Current-sheet validation implementation

• Current-sheet tests

• README media generator

Decaying and forced MHD turbulence

The README now includes two solver-generated turbulence examples. They are designed to be pedagogical, deterministic, and cheap enough to regenerate, not to replace high-Re turbulence production campaigns.

The decaying case starts from a band-limited broadband reduced-MHD state,

\[ \psi(x,y,0)=A_\psi\sum_{k_{\min}\le |{\bf k}|\le k_{\max}} |{\bf k}|^{-5/6}\cos({\bf k}\cdot{\bf x}+\alpha_{\bf k}), \]

with an analogous stream function for the initial flow. It then evolves the standard resistive-viscous reduced-MHD equations and checks finite histories, dissipative total energy, current-sheet activity, high-wavenumber transfer, and \(\nabla\cdot\mathbf{B}_\perp=0\).

The forced current-sheet case adds the same kind of deterministic broadband flow/flux perturbation to a periodic double-Harris sheet and applies a static large-scale vorticity forcing. It records a reconnection proxy based on the absolute detected X/O flux separation, \(|\langle\psi_O\rangle-\langle\psi_X\rangle|\), and its finite-difference time derivative. This is anchored to 2-D turbulent reconnection diagnostics such as Servidio et al. 2009 and to the broader turbulent-reconnection program of Lazarian & Vishniac 1999 and Kowal et al. 2009, but MHX does not claim a 3-D LV99 fast-reconnection result from this 2-D validation example.

mhx benchmark decaying-turbulence \
  --outdir outputs/readme_media/decaying_mhd_turbulence_64_t8 \
  --nx 64 --ny 64 --eta 2e-2 --nu 2e-2 \
  --dt 1e-2 --t-end 8 --save-every 40

mhx benchmark forced-turbulent-reconnection \
  --outdir outputs/readme_media/forced_turbulent_reconnection_64_t80_wide \
  --nx 64 --ny 64 --width 0.35 --eta 1e-3 --nu 1e-3 \
  --perturbation-amplitude 1e-1 \
  --turbulent-flux-amplitude 1e-1 \
  --turbulent-flow-amplitude 1e-1 \
  --forcing-amplitude 2e-2 \
  --dt 2e-2 --t-end 80 --save-every 100 \
  --max-relative-energy-growth 30.0

python examples/make_readme_media.py

Source links:

• Turbulence benchmark implementation

• Turbulence tests

• Critical-point diagnostics

Orszag–Tang nonlinear reduced-MHD vortex

The README now includes a second nonlinear solver-generated example: an incompressible reduced-MHD adaptation of the Orszag–Tang vortex. The classic test was introduced for two-dimensional MHD turbulence by Orszag & Tang 1979 and is widely used as an MHD-code stress test; full compressible variants develop shocks, while MHX currently uses the reduced-MHD periodic vortex to exercise nonlinear advection, magnetic tension, dissipation, current-density diagnostics, and movie generation.

MHX uses

\[ \phi(x,y,0)=\cos x+\cos y,\qquad \psi(x,y,0)=\cos y+\frac{1}{2}\cos 2x, \]

so that, with the MHX convention \(\mathbf{v}_\perp=(\partial_y\phi,-\partial_x\phi)\) and \(\mathbf{B}_\perp=(\partial_y\psi,-\partial_x\psi)\),

\[ \mathbf{v}_\perp=(-\sin y,\sin x),\qquad \mathbf{B}_\perp=(-\sin y,\sin 2x). \]

The committed README media were regenerated from a 96×96, t_end=10 run:

mhx benchmark orszag-tang \
  --outdir outputs/readme_media/orszag_tang_vortex_96_t10 \
  --nx 96 --ny 96 --t-end 10 --save-every 40 --movies

python examples/make_readme_media.py

The validation gates check finite arrays, monotone resistive-viscous energy decay, nonzero net dissipation, growth of current/vorticity high-wavenumber fractions, and preservation of \(\nabla\cdot\mathbf{B}_\perp=0\) by construction. The QA manifest records the peak high-wavenumber fractions and energy drop.

Source links:

• Orszag–Tang benchmark implementation

• Orszag–Tang tests

• README media generator

Harris tearing layer sweep

This GIF is generated from mhx benchmark linear-tearing-layer. It uses the direct finite-domain Harris-sheet eigenproblem and shows the FAST validation trend: increasing Lundquist number reduces the growth rate and narrows the localized flow/current response near the resonant surface. The anchor is the classical tearing-mode picture from Furth, Killeen & Rosenbluth and the reduced-MHD Harris eigenproblem used in the MacTaggart validation papers.

Source links:

• Layer benchmark implementation

• Layer validation tests

• README media generator

Sweet-Parker plasmoid scaling schematic

This GIF is an explicitly labeled theory schematic, not a nonlinear MHX solver result. It visualizes the Loureiro-Schekochihin-Cowley Sweet-Parker plasmoid scalings

\[ \gamma_{\max}\tau_A\propto S^{1/4},\qquad k_{\max}L\propto S^{3/8}. \]

The purpose is pedagogic: readers should immediately see the literature target that future nonlinear MHX plasmoid runs must recover.

Source links:

• Schematic generator

• Analytic scaling gate

• Scaling validation tests

MHD turbulence cascade schematic

This GIF is explicitly schematic. It combines synthetic magnetic-flux eddies, current filaments, and a \(k^{-5/3}\) guide curve to communicate the kind of turbulent MHD morphology future high-Re campaigns should target. The exponent is used as a recognizable inertial-range guide, not as a validation result. Classical reference points include Kraichnan 1958, the Iroshnikov–Kraichnan phenomenology summarized in Verma 2004, and anisotropic strong-MHD-turbulence ideas associated with Goldreich–Sridhar as discussed in modern reviews such as Schekochihin 2009.

Nonlinear validation movies

The periodic double-Harris long-run movie pair is generated by:

mhx benchmark double-harris-long-run \
  --outdir outputs/benchmarks/periodic_double_harris_seeded_long_run \
  --nx 96 --ny 96 --t-end 120 --save-every 300 --fit-stop 10 --movies

It visualizes the validation bridge documented in physics validation. The run advances a base periodic double-Harris sheet and a seeded copy, then tracks normalized perturbation growth, total energy, kinetic energy, peak current, and current-density frames. It remains claim_level = "validation" until convergence, seed, aspect-ratio, and duration sweeps are attached.

The restartable Rutherford executor movie pair is generated by:

mhx campaign rutherford-execute \
  outputs/campaigns/rutherford_production_plan \
  --max-steps 128 --movies

It validates fixed-scale flux/current movie writing, checkpoint metadata, and manifested artifacts for a production executor chunk. A chunk or completed duration run remains validation-level unless --allow-production-claim is used after the planned duration completes, execution checks pass, and mhx campaign rutherford-promotion-check writes a passing promotion-readiness report with convergence, seed-QI, movie, geometry, energy-budget, divergence, and X/O-count evidence.

Source links:

• Current-sheet validation implementation

• Production executor implementation

• Current-sheet tests

• Production executor tests

Latest GPU validation media status

The latest bounded GPU validation bundle is outputs/campaigns/gpu_nonlinear_20260522_085049/double_harris_long_n128_t160. Its raw fixed-scale flux/current movies and residual-flux audit movie are:

• figures/periodic_double_harris_flux.gif

• figures/periodic_double_harris_current.gif

• figures/gpu_long_delta_flux_validation.gif

The local promotion gate summary reports gate_ready = true and production_claim_ready = false. The passed gates cover duration, one 64/96/128 convergence bundle, X/O counts, reconnecting-flux amplification, island-width amplification, fixed-scale movies, and manifests. It remains validation media because the attached promotion report declares claim_level_if_passed = "validation", not production.

Recreate the local gate summary without asserting a production claim:

python tools/nonlinear_campaign_evidence.py \
  --campaign-dir outputs/campaigns/gpu_nonlinear_20260522_085049/double_harris_long_n128_t160 \
  --output-json outputs/campaigns/gpu_nonlinear_20260522_085049/double_harris_long_n128_t160/promotion_gate_summary.json \
  --output-md outputs/campaigns/gpu_nonlinear_20260522_085049/double_harris_long_n128_t160/promotion_gate_summary.md

Regenerate the README teaser movies with:

python examples/make_readme_media.py

The generated files are intentionally compact:

• docs/_static/readme/double_harris_reconnection.gif

• docs/_static/readme/double_harris_current_sheet.gif

• docs/_static/readme/forced_turbulent_reconnection.gif

• docs/_static/readme/decaying_mhd_turbulence_current.gif

• docs/_static/readme/orszag_tang_current.gif

• docs/_static/readme/orszag_tang_vorticity.gif

• docs/_static/readme/orszag_tang_flux.gif

• docs/_static/readme/harris_layer_sweep.gif

• docs/_static/readme/plasmoid_scaling_schematic.gif

• docs/_static/readme/mhd_turbulence_cascade.gif