physnor 1.0.2

Dart package that use AI(Gemini) to level up your physics knowledge and chat with your Ai physicist!

physnor

PhysNOR is a Dart package that combines a physics-focused AI assistant with a scientific model library for chemistry and engineering calculations. It supports both conversational reasoning with PhysNOR and direct numerical modeling through static scientific classes.

Features

• Physics-focused AI helper for prompt-driven analysis and derivations.
• Static model API for scientific equations and engineering correlations.
• Validation helpers for positive, finite, and thermodynamic inputs.
• Coverage across transport, adsorption, kinetics, thermodynamics, heat transfer, fluids, electrochemistry, and advanced domains.

Getting started

Add the package to your pubspec.yaml:

dependencies:
  physnor: ^1.0.2

Then import the library:

import 'package:physnor/physnor.dart';

AI assistant usage

Basic single-query example:

import 'package:physnor/physnor.dart';

Future<void> main() async {
  final assistant = PhysNOR(apiKey: '<YOUR_GEMINI_API_KEY>');
  assistant.setModel('models/gemini');

  final answer = await assistant.ask(
    'Explain the photoelectric effect with equations and units.',
  );

  print(answer);
}

Chat-style usage:

final messages = [
  {'author': 'user', 'content': 'How does a mass-spring oscillator behave?'},
];

final reply = await assistant.chatAsk(messages);
print(reply);

See example/bin/main.dart for a runnable example.

Scientific model library

The numerical model layer is organized by scientific domain. All models are exposed through the package root, and the API follows a consistent static-call pattern:

final flux = FickFirstLaw.flux(
  diffusionCoefficient: 1e-9,
  concentrationGradient: 1000.0,
);

final qe = LangmuirIsotherm.qe(
  qmax: 500.0,
  kl: 0.25,
  ce: 20.0,
);

1. Transport

Models:

• FickFirstLaw, FickSecondLaw
• EinsteinDiffusion
• StokesEinstein
• MaxwellStefanDiffusion
• KnudsenDiffusion
• DarkenDiffusion
• ThermalDiffusion
• SoretEffect
• DufourEffect
• NernstPlanck
• PoissonNernstPlanck

Usage:

final diffusiveFlux = FickFirstLaw.flux(
  diffusionCoefficient: 1e-9,
  concentrationGradient: 1000.0,
);

final ds = EinsteinDiffusion.msd(
  diffusionCoefficient: 1e-9,
  time: 10.0,
  dimensions: 3,
);

final msf = MaxwellStefanDiffusion.flux(
  diffusionCoefficient: 2.5e-10,
  concentrationDifference: 0.5,
  membraneThickness: 1e-4,
);

2. Adsorption

Models:

• LangmuirIsotherm
• FreundlichIsotherm
• TemkinIsotherm
• BETIsotherm
• SipsIsotherm
• DubininRadushkevichIsotherm
• DubininAstakhovIsotherm
• RedlichPetersonIsotherm
• TothIsotherm
• HalseyIsotherm
• ElovichAdsorption
• FowlerGuggenheimModel

Usage:

final qe = LangmuirIsotherm.qe(
  qmax: 500.0,
  kl: 0.25,
  ce: 20.0,
);

final freundlich = FreundlichIsotherm.qe(
  kf: 15.0,
  n: 1.8,
  ce: 10.0,
);

final bet = BETIsotherm.qe(
  qmax: 200.0,
  k1: 0.5,
  k2: 0.02,
  ce: 5.0,
);

3. Kinetics

Models:

• ArrheniusModel
• FirstOrderKinetics
• SecondOrderKinetics
• PseudoFirstOrder
• PseudoSecondOrder
• ElovichKinetics
• IntraparticleDiffusion
• WeberMorrisModel
• BoydModel
• FilmDiffusion
• BanghamModel

Usage:

final k = ArrheniusModel.rateConstant(
  preExponentialFactor: 1.2e9,
  activationEnergyJmol: 50000.0,
  temperatureK: 298.15,
);

final c = FirstOrderKinetics.concentration(
  initialConcentration: 10.0,
  rateConstant: 0.12,
  time: 5.0,
);

final qt = ElovichKinetics.qt(
  alpha: 2.0,
  beta: 0.5,
  time: 12.0,
);

4. Thermodynamics

Models:

• GibbsFreeEnergy
• VanthoffEquation
• ClapeyronEquation
• ClausiusClapeyron

Usage:

final deltaG = GibbsFreeEnergy.deltaG(
  deltaH: -120000.0,
  deltaS: -250.0,
  temperatureK: 298.15,
);

final k = GibbsFreeEnergy.equilibriumConstant(
  deltaGStandard: -5000.0,
  temperatureK: 298.15,
);

final pressureRatio = ClausiusClapeyron.pressureRatio(
  enthalpyJmol: 40000.0,
  temperatureK: 300.0,
  temperatureDeltaK: 20.0,
);

5. Heat transfer

Models:

• FourierHeatConduction
• NewtonCooling
• StefanBoltzmannRadiation
• PlanckRadiation
• WienDisplacement
• KirchhoffRadiation
• LumpedCapacitance
• BiotNumber
• ThermalDiffusivity

Usage:

final heatFlux = FourierHeatConduction.heatFlux(
  thermalConductivity: 0.8,
  temperatureGradient: 40.0,
);

final tempAtTime = NewtonCooling.temperatureAtTime(
  ambientTemperatureK: 293.15,
  initialTemperatureK: 350.0,
  heatTransferCoefficient: 15.0,
  time: 60.0,
  area: 0.5,
  mass: 2.0,
  specificHeat: 4200.0,
);

6. Fluid dynamics

Models:

• BernoulliEquation
• NavierStokes
• EulerFluidModel
• HagenPoiseuille
• DarcyLaw
• ForchheimerModel
• BrinkmanModel
• StokesFlow
• ReynoldsNumber
• BinghamPlastic
• HerschelBulkley
• PowerLawFluid

Usage:

final flow = HagenPoiseuille.volumetricFlowRate(
  radius: 0.01,
  pressureDrop: 1500.0,
  viscosity: 0.001,
  length: 2.0,
);

final re = ReynoldsNumber.reynoldsNumber(
  density: 1000.0,
  velocity: 0.5,
  diameter: 0.02,
  viscosity: 0.001,
);

7. Electrochemistry

Models:

• NernstEquation
• ButlerVolmer
• TafelEquation
• GouyChapman
• SternModel
• HelmholtzModel
• RandlesSevcik
• CottrellEquation
• DebyeHuckel
• OnsagerTransport

Usage:

final potential = NernstEquation.potential(
  standardPotentialV: 0.0,
  reactionQuotient: 10.0,
  electrons: 1,
  temperatureK: 298.15,
);

final current = ButlerVolmer.currentDensity(
  exchangeCurrentDensity: 1e-4,
  overpotential: 0.1,
  symmetryFactor: 0.5,
  electrons: 1,
);

8. Phase change, polymers, surface science, quantum, radiation, spectroscopy, statistics, and environmental models

Models:

• Phase change: ClausiusClapeyron
• Polymers: PolymerViscosity, MarkHouwink
• Surface science: YoungLaplace, KelvinEquation
• Quantum: ParticleInBox, HarmonicOscillator
• Radiation: BlackbodyRadiation
• Spectroscopy: LambertBeer, RamanShift
• Statistics: GaussianDistribution, BoltzmannDistribution
• Environmental: FirstOrderDecay, EnvironmentalAdsorption

Usage:

final ratio = ClausiusClapeyron.pressureRatio(
  enthalpyJmol: 40000.0,
  temperatureK: 300.0,
  temperatureDeltaK: 20.0,
);

final drift = YoungLaplace.pressureDifference(
  surfaceTension: 0.072,
  radius: 1e-3,
);

final absorbance = LambertBeer.absorbance(
  molarAbsorptivity: 1200.0,
  pathLengthM: 0.01,
  concentrationM: 0.5,
);

final pdf = GaussianDistribution.pdf(
  x: 0.0,
  mean: 0.0,
  sigma: 1.0,
);

Example: full workflow

import 'package:physnor/physnor.dart';

void main() {
  final flux = FickFirstLaw.flux(
    diffusionCoefficient: 1e-9,
    concentrationGradient: 1000.0,
  );

  final qe = LangmuirIsotherm.qe(
    qmax: 500.0,
    kl: 0.25,
    ce: 20.0,
  );

  final arrhenius = ArrheniusModel.rateConstant(
    preExponentialFactor: 1.2e9,
    activationEnergyJmol: 50000.0,
    temperatureK: 298.15,
  );

  final nernst = NernstEquation.potential(
    standardPotentialV: 0.0,
    reactionQuotient: 10.0,
    electrons: 1,
    temperatureK: 298.15,
  );

  print('Fick flux = $flux');
  print('Langmuir qe = $qe');
  print('Arrhenius k = $arrhenius');
  print('Nernst potential = $nernst');
}

License

This package is published under the BSD 3-Clause license.