Discover how plasma tendril models simulate dielectric breakdown, electric potential fields, and organic branching mechanics in ionized gases.

https://youtu.be/gxd5ahTl8EQ

<aside> ๐Ÿ‘

  1. https://payhip.com/b/BacMg
  2. https://www.instagram.com/reel/DdlPmyBSPf0/?utm_source=ig_web_copy_link
  3. https://bsky.app/profile/researcherdean.bsky.social/post/3mw3sqzzznc2c
  4. https://via-dean.gitbook.io/all/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/from-laplace-fields-to-lightning-strikes-how-plasma-tendrils-form
  5. https://hackmd.io/@bafMjVSBQ6e7vlO7NdkhXA/HJB14Tl5fg </aside>

๐ŸƒLaplacian Dielectric Breakdown & Exponent-Driven Morphology Study

Reflect the investigation into how changing growth exponents alters filament structure under Laplace field conditions.

<aside> ๐Ÿ‘

  1. http://youtube.com/post/Ugkxj35grk994LyYnoYG3RHsi0qRRBbe69XY?si=EnIGOIwcHsLeYTOv
  2. https://pin.it/2Nr0wN9WS
  3. https://hackmd.io/@bafMjVSBQ6e7vlO7NdkhXA/HJB14Tl5fg
  4. https://via-dean.gitbook.io/all/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/from-laplace-fields-to-lightning-strikes-how-plasma-tendrils-form </aside>

<aside> <img src="/icons/download_yellow.svg" alt="/icons/download_yellow.svg" width="40px" />

๐Ÿ„Deliverables 27

From Laplace Fields to Lightning Strikes: How Plasma Tendrils Form

https://payhip.com/b/BacMg

Documents

Exploration Frontiers

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    'primaryBorderColor': '#38bdf8',
    'lineColor': '#94a3b8',
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    'tertiaryColor': '#0b0f19',
    'edgeLabelBackground': '#1e293b',
    'fontFamily': 'inter, system-ui, sans-serif'
  }
}}%%
graph TD
    %% Core Domain Node %%
    Start["โšก <b>Current Research Domain</b><br/>Computational Plasma DBM Modeling"]:::current

    %% Baseline Pipeline %%
    subgraph Baseline ["<b>๐Ÿ“Œ Current Pipeline</b>"]
        SolveLaplace("๐Ÿงฎ <b>Field Solver Method</b><br/>Iterative SOR Field Solver<br/><i>โˆ‡ยฒฯ• = 0</i>"):::current
        Growth("๐ŸŒฑ <b>Growth Mechanism</b><br/>Stochastic Filament Growth<br/><i>P โˆ ฮฆโฟ</i>"):::current
        Anim("๐Ÿ“Š <b>Visualization Output</b><br/>Matplotlib Animations<br/><i>61x61 to 121x121 Grid</i>"):::current
    end

    %% Decision Nodes %%
    OptimizeDec{"<b>Performance<br/>Constraint?</b>"}:::decision
    PhysicsDec{"<b>Physics<br/>Expansion?</b>"}:::decision
    AnalyzeDec{"<b>Analysis<br/>Goal?</b>"}:::decision

    %% Future Pathways Subgraphs %%
    subgraph Acceleration ["<b>๐Ÿš€ Acceleration & Scaling</b>"]
        Grid("<b>Adaptive Mesh Refinement</b><br/>& GPU Porting"):::accentGreen
        Solver3D("<b>3D DBM Extensions</b><br/><i>NxNxN Grid</i>"):::accentGreen
    end

    subgraph AdvancedPhysics ["<b>๐Ÿ”ฌ Advanced Physics Modeling</b>"]
        NewMedia("<b>Non-Uniform Dielectrics</b><br/>& Gas Dynamics"):::accentAmber
        Poisson("<b>Poisson Solver Integration</b><br/><i>โˆ‡ยฒฯ• = -ฯ/ฮตโ‚€</i>"):::accentAmber
    end

    subgraph QuantAnalysis ["<b>๐Ÿ“ˆ Quantitative Analysis</b>"]
        Fractal("<b>Quantitative Fractal</b><br/>Dimension Analysis"):::accentPink
    end

    %% Flow Connections %%
    Start --> SolveLaplace
    SolveLaplace --> Growth
    Growth --> Anim

    Start -.-> OptimizeDec
    Start -.-> PhysicsDec
    Start -.-> AnalyzeDec

    OptimizeDec -- "Yes" --> Grid
    Grid --> Solver3D

    PhysicsDec -- "Physical Media" --> NewMedia
    NewMedia --> Poisson

    AnalyzeDec -- "Yes" --> Fractal

    %% Custom Node Styling %%
    classDef current fill:#1e293b,stroke:#38bdf8,stroke-width:2px,rx:10,ry:10,color:#f8fafc;
    classDef decision fill:#2e1065,stroke:#c084fc,stroke-width:2px,color:#f3e8ff;
    classDef accentGreen fill:#14532d,stroke:#4ade80,stroke-width:1.5px,rx:8,ry:8,color:#f0fdf4;
    classDef accentAmber fill:#78350f,stroke:#fbbf24,stroke-width:1.5px,rx:8,ry:8,color:#fef3c7;
    classDef accentPink fill:#831843,stroke:#f472b6,stroke-width:1.5px,rx:8,ry:8,color:#fce7f3;

<aside> ๐Ÿ‘

  1. http://youtube.com/post/UgkxDI5jZIPOZAEHEibkv-bZ5Wvr3p8BX11q?si=uzKCW1QW18L7UYL6
  2. https://pin.it/2X73Oi1fg
  3. https://hackmd.io/@bafMjVSBQ6e7vlO7NdkhXA/HJB14Tl5fg
  4. https://www.instagram.com/p/DdnmHNzFJ1o/?utm_source=ig_web_copy_link&stkn=MzRlODBiNWFlZA==
  5. https://via-dean.gitbook.io/all/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/from-laplace-fields-to-lightning-strikes-how-plasma-tendrils-form </aside>

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