Materials-Science

Nuclear isotopes, radioactive decay chains, radiation dose, and hazardous chemical substances with toxicological thresholds and unit conversions.

Namespace: CSharpNumerics.Physics.Materials

using CSharpNumerics.Physics.Materials.Nuclear.Isotopes;
using CSharpNumerics.Physics.Materials.Nuclear.Decay;
using CSharpNumerics.Physics.Materials.Nuclear.DecayChains;
using CSharpNumerics.Physics.Materials.Nuclear.RadiationDose;
using CSharpNumerics.Physics.Materials.Chemical;

🧪 Isotopes & Library

// Built-in isotopes
Isotope cs = Isotope.Cs137;           // Cs-137: t½ = 30.17 years
Isotope iodine = Isotope.I131;        // I-131: t½ = 8.02 days

// Lookup by name
Isotope sr = IsotopeLibrary.Get("Sr90");
bool found = IsotopeLibrary.TryGet("Co60", out Isotope co);

// Properties
double halfLife = cs.HalfLifeSeconds;       // ~9.51e8 s
double lambda = cs.Lambda;                   // decay constant (ln2/t½)
double activity = cs.SpecificActivityBqKg;   // Bq per kg
bool stable = Isotope.Ba137.IsStable;        // true

// Filter by element
var caesiumIsotopes = IsotopeLibrary.ByElement(55);  // Z = 55

// Register custom isotope at runtime
IsotopeLibrary.Register(new Isotope("Pu239", 94, 239, 7.6e11, 2.3e9,
    DecayMode.Alpha, 0.0, 4.4e-5, 0));

⚛️ Radioactive Decay

// Simple decay
double a0 = Decay.Activity(massKg: 0.001, Isotope.Cs137);      // initial Bq
double aT = Decay.ActivityAtTime(a0, timeSeconds: 3600, Isotope.Cs137);
double remaining = Decay.RemainingMass(0.001, 3600, Isotope.Cs137);

Decay chains — Bateman equations for sequential decay:

// Decay chain (Bateman equations)
var chain = DecayChain.Cs137Chain();    // Cs137 → Ba137m → Ba137
double[] masses = chain.Evolve(
    initialMasses: new[] { 1.0, 0.0, 0.0 },
    timeSeconds: 3600);

double[] activities = chain.EvolveActivity(
    new[] { 1.0, 0.0, 0.0 }, 3600);  // Bq for each isotope

// I-131 chain
var iChain = DecayChain.I131Chain();   // I131 → Xe131

☢️ Radiation Dose

// Point-source dose rate (inverse-square law)
double svPerHour = RadiationDose.DoseRate(
    activityBq: 1e9, distanceM: 1.0, Isotope.Cs137);

// Ground-shine dose (deposition on surface)
double sv = RadiationDose.GroundShineDose(
    depositionBqM2: 1e6, Isotope.Cs137, timeSeconds: 3600);

// Inhalation dose
double inhDose = RadiationDose.InhalationDose(
    concentrationBqM3: 100,
    breathingRateM3s: RadiationDose.DefaultBreathingRate,
    exposureTimeSeconds: 3600,
    Isotope.Cs137);

🏭 Chemical Materials

Namespace: CSharpNumerics.Physics.Materials.Chemical

Model hazardous chemical substances with toxicological thresholds (IDLH, ERPG, LC50, TLV) and unit conversions (kg/m³ ↔ ppm). Integrates with the GIS dispersion pipeline via .WithMaterial(Materials.Chemical("Cl2")).

Built-in substances

Formula	Name	MW (g/mol)	IDLH (ppm)	ERPG-2 (ppm)	ERPG-3 (ppm)	Phase
Cl₂	Chlorine	70.9	10	3	20	Gas
NH₃	Ammonia	17.0	300	200	1000	Gas
H₂S	Hydrogen Sulfide	34.1	50	30	100	Gas
CH₄	Methane	16.0	N/A*	5000	50000	Gas
C₃H₈	Propane	44.1	2100	5000	17000	Liquefied gas

*Simple asphyxiant — no toxicity-based IDLH.

Substance lookup & custom registration

using CSharpNumerics.Physics.Materials.Chemical;

// Static instances
ChemicalSubstance cl = ChemicalSubstance.Chlorine;
ChemicalSubstance nh3 = ChemicalSubstance.Ammonia;

// Library lookup (case-insensitive)
ChemicalSubstance h2s = ChemicalLibrary.Get("H2S");
bool found = ChemicalLibrary.TryGet("CH4", out ChemicalSubstance methane);

// Properties
double mw = cl.MolarMass;          // 70.906 g/mol
double idlh = cl.IDLH;             // 10 ppm
double erpg2 = cl.ERPG2;           // 3 ppm
double vapDens = cl.VapourDensity;  // 2.49 (heavier than air)

// Register custom substance
ChemicalLibrary.Register(new ChemicalSubstance(
    "COCl2", "Phosgene", "75-44-5",
    98.92, 3.4, 8.3, PhaseAtSTP.Gas,
    idlh: 2, erpg2: 0.5, erpg3: 1.5, lc50: 5,
    tlvTwa: 0.1, tlvStel: 0.3));

Unit conversion (kg/m³ ↔ ppm)

// Convert mass concentration to ppm at 20°C, 1 atm
double ppm = cl.KgM3ToPpm(2.95e-6);   // ≈ 1 ppm
double kgm3 = cl.PpmToKgM3(10);        // IDLH in kg/m³

GIS pipeline integration

using CSharpNumerics.Physics.Materials;

// Attach chemical material to a dispersion scenario
var result = RiskScenario
    .ForGaussianPlume(5.0)
    .FromSource(new Vector(0, 0, 10))
    .WithWind(5, new Vector(1, 0, 0))
    .WithStability(StabilityClass.D)
    .WithMaterial(Materials.Chemical("Cl2"))    // ← chemical
    .OverGrid(new GeoGrid(-500, 500, -500, 500, 0, 100, 50))
    .OverTime(0, 3600, 60)
    .RunSingle();

// Snapshot layers: "ppm" and "toxicDose" (ppm·s)
double[] ppmLayer = result.Snapshots[0].GetLayer("ppm");
double[] toxDose  = result.Snapshots[0].GetLayer("toxicDose");

// IDLH exceedance polygon (Cl2 IDLH = 10 ppm)
var idlhZone = result.GeneratePeakExposurePolygon(10, "ppm");

// ERPG-2 exceedance polygon (3 ppm)
var erpg2Zone = result.GeneratePeakExposurePolygon(3, "ppm");

// Integrated toxic dose polygon
var integratedZone = result.GenerateIntegratedExposurePolygon(
    threshold: 1000, layerName: "toxicDose");  // 1000 ppm·s

🧱 Engineering Materials

The EngineeringMaterial immutable struct bundles thermo-mechanical-electrical properties for multiphysics simulations. The EngineeringLibrary provides common pre-defined materials.

Namespace: CSharpNumerics.Physics.Materials.Engineering

Material Properties

Property	Unit	Description
`ThermalConductivity`	W/(m·K)	Heat conduction coefficient $k$
`SpecificHeat`	J/(kg·K)	Specific heat capacity $c_p$
`Density`	kg/m³	Mass density $\rho$
`DynamicViscosity`	Pa·s	Dynamic viscosity $\mu$
`ElectricPermittivity`	F/m	Dielectric permittivity $\varepsilon$
`YoungsModulus`	Pa	Young's modulus $E$
`PoissonsRatio`	—	Poisson's ratio $\nu$

Computed properties:

Computed	Formula	Description
`ThermalDiffusivity`	$\alpha = k/(\rho c_p)$	Heat diffusion rate
`KinematicViscosity`	$\nu = \mu/\rho$	Flow diffusion rate

Pre-defined Materials

using CSharpNumerics.Physics.Materials.Engineering;

var steel = EngineeringLibrary.Steel;       // E=200 GPa, k=50 W/(m·K)
var al    = EngineeringLibrary.Aluminum;    // E=69 GPa, k=237 W/(m·K)
var cu    = EngineeringLibrary.Copper;      // E=117 GPa, k=401 W/(m·K)
var water = EngineeringLibrary.Water;       // μ=1e-3 Pa·s, ρ=1000 kg/m³
var air   = EngineeringLibrary.Air;         // μ=1.81e-5 Pa·s
var conc  = EngineeringLibrary.Concrete;    // E=30 GPa
var glass = EngineeringLibrary.Glass;       // E=70 GPa

double alpha = steel.ThermalDiffusivity;     // k/(ρ·cp)
double nu    = water.KinematicViscosity;     // μ/ρ

Custom Materials

var titanium = new EngineeringMaterial(
    name: "Titanium",
    thermalConductivity: 21.9,        // W/(m·K)
    specificHeat: 523,                // J/(kg·K)
    density: 4507,                    // kg/m³
    dynamicViscosity: 0,              // not a fluid
    electricPermittivity: 0,
    youngsModulus: 116e9,             // Pa
    poissonsRatio: 0.34);

🌲 Fuel Models (Anderson 13)

The FuelModel readonly struct holds Rothermel fuel parameters. All 13 standard Anderson models are pre-loaded in FuelLibrary.

// All models are in SI units
FuelModel chaparral = FuelLibrary.Get(FuelModelType.Chaparral);
// chaparral.SurfaceAreaToVolumeRatio = 4921 (1/m)
// chaparral.FuelBedDepth             = 1.829 (m)
// chaparral.OvendryFuelLoad          = 3.663 (kg/m²)
// chaparral.MoistureOfExtinction     = 0.20

// Iterate all models
foreach (var fuel in FuelLibrary.All)
    Console.WriteLine($"{fuel.Type}: δ={fuel.FuelBedDepth:F3} m");

// Register a custom fuel model at runtime
FuelLibrary.Register(new FuelModel(
    (FuelModelType)99, "Custom Sage", sigma: 5000,
    delta: 0.5, w0: 1.2, Mx: 0.25, h: 18000));

Model	Type	σ (1/m)	δ (m)	w₀ (kg/m²)	Mₓ
1	Short Grass	11,483	0.305	0.166	0.12
2	Timber/Grass Understory	3,281	0.305	0.897	0.15
3	Tall Grass	4,921	0.762	0.675	0.25
4	Chaparral	6,562	1.829	3.663	0.20
5	Brush	6,562	0.610	0.784	0.20
6	Dormant Brush	5,741	0.762	0.672	0.25
7	Southern Rough	5,741	0.762	0.529	0.40
8	Closed Timber Litter	6,562	0.061	1.121	0.30
9	Hardwood Litter	8,202	0.061	0.327	0.25
10	Timber/Litter Understory	6,562	0.305	1.121	0.25
11	Light Logging Slash	4,921	0.305	1.345	0.15
12	Medium Logging Slash	4,921	0.701	3.363	0.20
13	Heavy Logging Slash	4,921	0.914	5.604	0.25

🔦 Optical Materials

Pre-defined media are available via OpticalMaterialLibrary or the Materials.Optical() factory:

using CSharpNumerics.Physics.Materials;
using CSharpNumerics.Physics.Optics;

var diamond = OpticalMaterialLibrary.Diamond;       // n=2.417
var bk7 = Materials.Optical("CrownGlass");        // factory lookup
var flint = Materials.Optical("SF11");            // n=1.7847, low Abbe -> high dispersion

🌊 Aquatic Contaminants

Pre-loaded contaminant library with decay, adsorption, and toxicity data:

Namespace: CSharpNumerics.Physics.Materials.Water

using CSharpNumerics.Physics.Materials.Water;

// Built-in contaminants: Cs137, Sr90, I131, Benzene, Toluene, Cyanide,
// Mercury, Lead, Arsenic, EColi, Enterococcus, GenericHeat
var cs137 = ContaminantLibrary.Get("Cs-137");
// cs137.HalfLifeSeconds ≈ 9.5×10⁸, cs137.PartitionCoefficient = 1000, etc.

var benzene = AquaticContaminant.Benzene;
bool isConservative = benzene.IsConservative;  // false (has half-life)
double lambda = benzene.DecayConstant;          // ln(2) / t½

// Create a custom contaminant
var custom = new AquaticContaminant("PFOS",
    ContaminantType.Chemical,
    halfLifeSeconds: 0,       // persistent (conservative tracer)
    partitionCoefficient: 10,
    toxicityThresholdMgL: 0.00007,
    lethalThresholdMgL: 50);

ContaminantLibrary.Register(custom);

Pre-defined Contaminants

Contaminant	Type	Half-life	Kd (L/kg)	Toxicity (mg/L)
Cs-137	Radioactive	30.17 yr	1000	0.002
Sr-90	Radioactive	28.8 yr	200	0.008
I-131	Radioactive	8.02 d	10	0.003
Benzene	Chemical	180 d	1.8	0.005
Cyanide	Chemical	∞	0	0.07
Mercury	Chemical	∞	5000	0.001
E. coli	Biological	2 d	0	0.0001

🦠 Biological Materials — Bioaerosol Agents

Namespace: CSharpNumerics.Physics.Materials.Biological

Model biological aerosol agents (viruses, bacteria, spores) with viability decay, unit-mass conversion (kg/m³ ↔ units/m³), and screening-level infectious dose layers. Integrates with the GIS dispersion pipeline via Materials.Biological("Virus").

Agent properties

Property	Description
`Code`	Short identifier for lookup (e.g. `"Virus"`)
`Name`	Human-readable name
`Classification`	`BiologicalAgentClass` enum: `Virus`, `Bacteria`, `Spore`
`TypicalDiameterMicrons`	Representative aerodynamic diameter (µm)
`UnitMassKg`	Mass of one biological unit (kg) — converts kg/m³ → units/m³
`ViabilityHalfLifeSeconds`	Screening half-life for viability in air (seconds)
`IsPersistent`	`true` when viability is treated as non-decaying

Built-in agents

Code	Name	Class	Diameter (µm)	Unit mass (kg)	Viability t½
Virus	Generic Viral Aerosol	Virus	0.12	1 × 10⁻¹⁸	6 h
Bacteria	Generic Bacterial Aerosol	Bacteria	1.5	1 × 10⁻¹⁵	12 h
Spore	Generic Biological Spore	Spore	2.5	3 × 10⁻¹⁵	7 d

Agent lookup & custom registration

using CSharpNumerics.Physics.Materials.Biological;

// Static instances
BiologicalAgent virus = BiologicalAgent.GenericVirus;
BiologicalAgent bacteria = BiologicalAgent.GenericBacteria;
BiologicalAgent spore = BiologicalAgent.GenericSpore;

// Library lookup (case-insensitive, supports aliases)
BiologicalAgent v = BiologicalLibrary.Get("virus");
BiologicalAgent s = BiologicalLibrary.Get("Spores");   // alias
bool found = BiologicalLibrary.TryGet("bacteria", out BiologicalAgent b);

// All registered agents (de-duplicated)
IReadOnlyCollection<BiologicalAgent> all = BiologicalLibrary.All();

// Register custom agent with aliases
BiologicalLibrary.Register(
    new BiologicalAgent(
        code: "Anthrax",
        name: "Bacillus anthracis spore",
        classification: BiologicalAgentClass.Spore,
        typicalDiameterMicrons: 1.5,
        unitMassKg: 1e-15,
        viabilityHalfLifeSeconds: 30 * 24 * 3600),  // 30 days
    "anthrax", "b.anthracis");

Unit conversion (kg/m³ ↔ units/m³)

BiologicalAgent bacteria = BiologicalAgent.GenericBacteria;

// Convert mass concentration to biological units per m³
double units = bacteria.KgM3ToUnitsPerM3(2.5e-12);  // 2500 units/m³
double kgm3  = bacteria.UnitsPerM3ToKgM3(units);    // round-trip

// Viability fraction at a given time
double fraction = bacteria.ViabilityFractionAt(6 * 3600);  // after 6 h

GIS pipeline integration

using CSharpNumerics.Physics.Materials;

// Attach biological material to a dispersion scenario
var sim = new PlumeSimulator(
    2.0, 8, new Vector(1, 0, 0), 50,
    new Vector(0, 0, 50), StabilityClass.D);
sim.Material = Materials.Biological("Bacteria");

var snaps = sim.Run(grid, tf);

// Snapshot layers: "bioUnits", "viableBioUnits", and "infectiousDose"
double[] bioUnits     = snaps[0].GetLayer("bioUnits");
double[] viable       = snaps[0].GetLayer("viableBioUnits");
double[] infectious   = snaps[0].GetLayer("infectiousDose");

The viableBioUnits layer applies exponential viability decay based on the agent's half-life, so viable counts decrease over successive time steps while raw bioUnits reflect total transported mass only.

🧪 Isotopes & Library​

⚛️ Radioactive Decay​

☢️ Radiation Dose​

🏭 Chemical Materials​

🧱 Engineering Materials​

🌲 Fuel Models (Anderson 13)​

🔦 Optical Materials​

🌊 Aquatic Contaminants​

🦠 Biological Materials — Bioaerosol Agents​

Agent properties​

Built-in agents​

Agent lookup & custom registration​

Unit conversion (kg/m³ ↔ units/m³)​

GIS pipeline integration​