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Material Science Examples

This directory contains examples applying DeepCausality to Material Science and Metamaterials. These examples demonstrate advanced physics simulations using the framework's topology, multivector algebra, and causal intervention capabilities.

Quick Start

Run any example from the repository root:

cargo run -p material_examples --example <example_name>

Examples Overview

Example Domain Description
hyperlens Metamaterials Super-resolution imaging using hyperbolic dispersion
topological_insulator Quantum Materials Chern number calculation for topological phase classification
structural_health_monitor Smart Materials Decentralized monitoring with autonomous causal interventions

Common Patterns

1. Metric for Material Properties

Different materials have different "signatures" that determine how waves propagate:

  • Euclidean: Standard vacuum/dielectric
  • Minkowski: Relativistic spacetime
  • Generic(p, q, r): Anisotropic/Hyperbolic metamaterials
use deep_causality_multivector::Metric;

let vacuum = Metric::Euclidean(3);           // (+++)
let hyperbolic = Metric::Generic { p: 1, q: 2, r: 0 }; // (+−−)

2. Manifold<T> & Graph<T> for Topology

  • Manifold: Continuous surfaces with differential structure (hyperlens geometry).
  • Graph: Discrete networks (structural lattices, molecular bonds).

3. Intervenable for Active Materials

Smart materials that can autonomously respond to stimuli use the Intervenable trait to formally separate:

  • Observation (what is happening)
  • Intervention (what we force to happen)
  • Counterfactual (what would have happened otherwise)

Run Commands

Example Command
Hyperlens cargo run -p material_examples --example hyperlens_example
Topological Insulator cargo run -p material_examples --example topological_insulator_example
Structural Health Monitor cargo run -p material_examples --example structural_health_monitor_example

Crates Used

  • deep_causality_multivector: Geometric Algebra for anisotropic field representations.
  • deep_causality_topology: Graph, Manifold, SimplicialComplex for structural modeling.
  • deep_causality_num: High-precision Complex number arithmetic for quantum calculations.
  • deep_causality_core: PropagatingEffect, Intervenable for monadic state and interventions.

Adding New Examples

  1. Create a new directory under examples/: examples/<your_example>/
  2. Add main.rs and README.md
  3. Register in Cargo.toml: 
    [[example]]
name = "your_example"
path = "examples/<your_example>/main.rs"