Particle Simulation Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Particle Simulation Ontology within the Kireth Research Semantic Library. Particle simulation models systems as discrete interacting particles, agents, bodies or material points whose states evolve under forces, fields, collisions, constraints, stochastic processes or continuum approximations. This ontology supports molecular dynamics, N-body systems, discrete element methods, smoothed particle hydrodynamics, particle-in-cell methods, neighbour searching, force accumulation, time integration, collisions, boundary handling, conservation, stability, parallel execution, verification, validation and reproducibility.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Particle Simulation Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Computational Mathematics"
 SPECIALISATION = "Scientific Simulation / Particle Simulation"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/computational-mathematics-ontologies/scientific-simulation/particle-simulation-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = ParticleSimulation
 ENTITY_CLASS = DiscreteParticleSystemSimulationFramework
 PRIMARY_CONTEXT = ScientificSimulation
 DEFINITION = "Particle simulation is the computational evolution of systems represented by discrete particles, agents, bodies or material points whose interactions determine system behaviour."
 SYMBOLIC_FORMS = [
  "m_i * d2x_i/dt2 = F_i",
  "x_i(t+dt)=Integrator(x_i,v_i,F_i,dt)",
  "F_i=sum_j F_ij + F_external",
  "rho_i=sum_j m_j W(|x_i-x_j|,h)"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for particle state, interactions, force models, neighbour search, collisions, particle methods, time integration, conservation, numerical stability and reproducibility."
}

SCOPE {
 INCLUDE = [
  ParticleSimulation,ParticleSystem,DiscreteParticleModel,
  Particle,MaterialPoint,Agent,Body,PointMass,
  ParticleState,ParticlePosition,ParticleVelocity,
  ParticleAcceleration,ParticleMass,ParticleCharge,
  ParticleRadius,ParticleOrientation,AngularVelocity,
  Force,Torque,InteractionForce,PairwiseForce,
  ExternalForce,BodyForce,ConstraintForce,
  Gravity,ElectrostaticForce,MagneticForce,
  ContactForce,FrictionForce,DragForce,
  SpringForce,DampingForce,PotentialForce,
  PairPotential,InteractionPotential,
  LennardJonesPotential,CoulombPotential,
  HarmonicPotential,MorsePotential,
  MolecularDynamics,MD,CoarseGrainedMolecularDynamics,
  NBodySimulation,GravitationalNBody,ChargedNBody,
  BarnesHutAlgorithm,FastMultipoleMethod,
  Treecode,DirectSummation,
  DiscreteElementMethod,DEM,
  GranularSimulation,GranularMaterial,
  ContactModel,HertzContact,HertzMindlinModel,
  LinearSpringDashpot,CoulombFriction,
  CoefficientOfRestitution,FrictionCoefficient,
  SmoothedParticleHydrodynamics,SPH,
  KernelFunction,SmoothingKernel,SmoothingLength,
  KernelSupport,NeighbourParticle,
  DensityEstimate,PressureEstimate,
  SPHGradient,SPHLaplacian,
  WeaklyCompressibleSPH,IncompressibleSPH,
  ParticleInCell,PIC,CloudInCell,CIC,
  ParticleMeshMethod,PM,ParticleParticleParticleMesh,P3M,
  MeshParticleCoupling,ChargeDeposition,
  FieldInterpolation,GridToParticle,ParticleToGrid,
  MaterialPointMethod,MPM,
  FLIP,PICFLIP,APIC,
  VortexParticleMethod,VortexMethod,
  DissipativeParticleDynamics,DPD,
  BrownianDynamics,LangevinDynamics,
  StochasticParticleSimulation,
  RandomForce,ThermalNoise,Diffusion,
  CollisionDetection,CollisionResponse,
  ParticleParticleCollision,ParticleBoundaryCollision,
  HardSphereCollision,SoftSphereCollision,
  EventDrivenParticleSimulation,
  TimeDrivenParticleSimulation,
  ContactResolution,ImpulseResolution,
  PenaltyContact,ConstraintBasedContact,
  NeighbourSearch,NeighbourList,
  VerletList,CellList,LinkedCellMethod,
  SpatialHashing,UniformGrid,
  KDTree,Octree,Quadtree,
  BoundingVolumeHierarchy,BVH,
  CutoffRadius,InteractionRadius,
  SkinDistance,NeighbourListRebuild,
  PeriodicBoundaryCondition,ReflectiveBoundary,
  AbsorbingBoundary,OpenBoundary,
  WallBoundary,GhostParticle,BoundaryParticle,
  ParticleInjection,ParticleDeletion,
  ParticleSplitting,ParticleMerging,
  AdaptiveParticleResolution,
  TimeIntegration,ExplicitIntegrator,
  ImplicitIntegrator,SymplecticIntegrator,
  EulerMethod,RungeKuttaMethod,
  VerletIntegration,VelocityVerlet,
  LeapfrogMethod,BeemanAlgorithm,
  PredictorCorrector,
  AdaptiveTimeStep,FixedTimeStep,
  Stability,CFLCondition,CollisionTimeStep,
  StiffnessTimeStep,ForceTimeScale,
  EnergyConservation,MomentumConservation,
  AngularMomentumConservation,MassConservation,
  ChargeConservation,ConservationError,
  NumericalDamping,EnergyDrift,
  NumericalError,DiscretisationError,
  RoundOffError,StatisticalError,
  FloatingPointArithmetic,MachinePrecision,
  InitialCondition,ParticleInitialisation,
  RandomInitialisation,LatticeInitialisation,
  DistributionSampling,VelocityDistribution,
  MaxwellBoltzmannDistribution,
  Equilibration,Thermostat,
  BerendsenThermostat,NoseHooverThermostat,
  AndersenThermostat,Barostat,
  PressureControl,TemperatureControl,
  Ensemble,NVE,NVT,NPT,
  BoundaryCondition,Domain,SimulationBox,
  PeriodicBox,MinimumImageConvention,
  EwaldSummation,ParticleMeshEwald,PME,
  LongRangeInteraction,ShortRangeInteraction,
  CutoffMethod,TailCorrection,
  ParallelParticleSimulation,
  DomainDecomposition,ParticleDecomposition,
  ForceDecomposition,SpatialDecomposition,
  LoadBalancing,DynamicLoadBalancing,
  GhostParticleExchange,HaloExchange,
  MPI,GPUAcceleration,SIMD,
  DistributedMemory,SharedMemory,
  HighPerformanceComputing,HPC,
  Determinism,RandomSeed,
  Reproducibility,Checkpoint,Restart,
  Trajectory,ParticleTrajectory,
  Snapshot,Frame,OutputSampling,
  Observable,RadialDistributionFunction,RDF,
  MeanSquaredDisplacement,MSD,
  VelocityAutocorrelation,DiffusionCoefficient,
  StructureFactor,Pressure,Temperature,
  KineticEnergy,PotentialEnergy,TotalEnergy,
  StressTensor,VirialStress,
  Verification,CodeVerification,
  SolutionVerification,Validation,
  Benchmark,ReferenceSolution,
  ExperimentalValidation,ConvergenceStudy,
  SensitivityAnalysis,UncertaintyQuantification
 ]
 EXCLUDE_AS_PRIMARY = [
  ContinuumSimulationWithoutDiscreteParticleRepresentation,
  AgentBasedSimulationWithoutPhysicalParticleInteractionSemantics,
  PureGeometricPointCloudProcessingWithoutStateEvolution,
  RenderingParticleEffectsWithoutScientificSimulationSemantics
 ]
 DISAMBIGUATION_RULE = "When system behaviour is computed by evolving discrete interacting particles, bodies or material points, interpret the context as particle simulation."
}

CORE_CONCEPTS {
 ParticleSimulation = "Simulation of a system represented by discrete interacting particles."
 ParticleState = "Set of variables describing a particle at a given time."
 PairwiseInteraction = "Interaction between two particles contributing to system evolution."
 NeighbourSearch = "Procedure identifying nearby particles relevant to local interactions."
 MolecularDynamics = "Particle simulation based on atomistic or coarse-grained force fields."
 DiscreteElementMethod = "Particle method for granular and contacting bodies."
 SmoothedParticleHydrodynamics = "Mesh-free particle approximation of continuum fluid or solid fields."
 ParticleInCell = "Hybrid particle-grid method coupling particle states to field quantities on a mesh."
}

RELATIONS {
 ParticleSimulation --is_child_of--> ScientificSimulation
 ParticleSimulation --contains--> Particle
 Particle --has--> ParticleState
 ParticleState --includes--> Position
 ParticleState --includes--> Velocity
 Particle --experiences--> Force
 PairwiseForce --depends_on--> ParticlePair
 NeighbourSearch --produces--> NeighbourList
 NeighbourList --limits--> InteractionEvaluation
 MolecularDynamics --uses--> InteractionPotential
 DiscreteElementMethod --uses--> ContactModel
 SmoothedParticleHydrodynamics --uses--> KernelFunction
 ParticleInCell --couples--> ParticleAndGrid
 TimeIntegration --advances--> ParticleState
 CollisionDetection --supports--> ParticleCollisionResponse
 DomainDecomposition --supports--> ParallelParticleSimulation
 Verification --checks--> ParticleSimulationResult
 Validation --compares--> SimulationWithEvidence
}

OPERATORS {
 FORCE_ACCUMULATION(i) := sum_j F_ij + F_external_i
 VELOCITY_VERLET_POSITION(x,v,a,dt) := x_next=x+v*dt+0.5*a*dt^2
 VELOCITY_VERLET_VELOCITY(v,a,a_next,dt) := v_next=v+0.5*(a+a_next)*dt
 DENSITY_SPH(i) := sum_j m_j*W(|x_i-x_j|,h)
 NEIGHBOURS(i,r_c) := {j | ||x_i-x_j|| <= r_c}
 KINETIC_ENERGY := sum_i 0.5*m_i*||v_i||^2
 POTENTIAL_ENERGY := sum_interactions U_ij
 TOTAL_MOMENTUM := sum_i m_i*v_i
 RDF(r) := normalised_pair_distance_distribution
}

AXIOMS {
 A1 = "Particle simulation evolves discrete particle states through declared interaction and integration rules."
 A2 = "Neighbour-search accuracy affects force completeness for short-range interactions."
 A3 = "Time-step choice must resolve the fastest relevant interaction scale."
 A4 = "Conservation properties depend on both physical force models and numerical integrators."
 A5 = "Long-range interactions require specialised acceleration or summation methods at scale."
 A6 = "Particle-grid methods require consistent deposition and interpolation semantics."
 A7 = "Parallel particle simulation requires consistent ghost or halo exchange."
 A8 = "Particle-simulation results require explicit force, neighbour, integration, conservation and reproducibility semantics."
}

REASONING {
 R1_CONTEXT = identify(particle_model,dimension,particle_count,interaction_types,boundaries,outputs,accuracy_goal)
 R2_STATE = define(particle_state_variables,masses,charges,radii,material_or_species_properties)
 R3_INTERACTION = choose(pairwise,contact,field,stochastic,short_range_or_long_range_force_models)
 R4_NEIGHBOURS = configure(cutoff,cell_list,Verlet_list,tree_or_BVH_neighbour_search)
 R5_INTEGRATOR = select(Euler,RungeKutta,Verlet,leapfrog,symplectic,implicit_or_event_driven_method)
 R6_BOUNDARY = configure(periodic,reflective,absorbing,wall_or_open_boundary_semantics)
 R7_EXECUTION = evaluate_neighbours_forces_collisions_constraints_and_advance_particles
 R8_MONITOR = track(energy,momentum,mass,temperature,pressure,neighbour_statistics_and_stability)
 R9_PARALLEL = if_large configure(domain_decomposition,ghost_exchange,load_balancing_and_acceleration)
 R10_VALIDATE = check(conservation,convergence,reference_cases,statistics_and_reproducibility)
}

CONSTRAINTS {
 C1 = "A time step that is too large can destabilise stiff particle interactions."
 C2 = "Neighbour lists must be rebuilt before particles move beyond the declared skin margin."
 C3 = "Short-range cutoffs can introduce truncation artefacts if not corrected or smoothed."
 C4 = "Long-range electrostatic or gravitational interactions can dominate computational cost."
 C5 = "DEM contact stiffness can impose severe time-step restrictions."
 C6 = "SPH accuracy depends on particle distribution, kernel choice and smoothing length."
 C7 = "PIC methods can introduce grid heating, interpolation error or numerical diffusion."
 C8 = "Parallel domain decomposition can become imbalanced when particles cluster."
 C9 = "Random thermostats or stochastic forces require seed-aware statistical validation."
 C10 = "Visual plausibility does not establish physical validity or conservation."
}

SEMANTIC_EQUIVALENCE {
 "ParticleSimulation" <=> "ParticleBasedSimulation"
 "MolecularDynamics" <=> "MD"
 "DiscreteElementMethod" <=> "DEM"
 "SmoothedParticleHydrodynamics" <=> "SPH"
 "ParticleInCell" <=> "PIC"
 "ParticleParticleParticleMesh" <=> "P3M"
 "ParticleMeshEwald" <=> "PME"
 "MeanSquaredDisplacement" <=> "MSD"
 "RadialDistributionFunction" <=> "RDF"
}

VALIDATION {
 V1 = "Particle representation and state variables are explicit."
 V2 = "Force, potential or contact models are documented."
 V3 = "Neighbour-search method and cutoff semantics are documented."
 V4 = "Initial and boundary conditions are documented."
 V5 = "Time integrator and time-step policy are documented."
 V6 = "Energy, momentum, mass or other relevant conservation checks are performed."
 V7 = "Convergence or time-step sensitivity is assessed where relevant."
 V8 = "Statistical observables are validated for stochastic or molecular simulations."
 V9 = "Parallel decomposition and ghost-exchange semantics are documented where used."
 V10 = "Results are reproducible under documented configuration, arithmetic and random-seed settings."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 PARTICLE_SIMULATION_DEFINITION = 0.99
 NEIGHBOUR_REASONING = 0.99
 MOLECULAR_DYNAMICS_REASONING = 0.99
 DEM_REASONING = 0.98
 SPH_REASONING = 0.98
 PIC_REASONING = 0.98
 PARALLEL_PARTICLE_REASONING = 0.98
 POLICY = "Reduce confidence when interaction laws, neighbour search, time-step criteria, boundary conditions, particle resolution, long-range treatment or conservation checks are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,ParticleSimulationReasoning,
  ParticleStateReasoning,ForceAccumulationReasoning,
  NeighbourSearchReasoning,MolecularDynamicsReasoning,
  DiscreteElementReasoning,SPHReasoning,PICReasoning,
  NBodyReasoning,LongRangeInteractionReasoning,
  CollisionReasoning,TimeIntegrationReasoning,
  ConservationReasoning,ParallelParticleReasoning,
  StatisticalObservableReasoning,VerificationReasoning,
  ValidationReasoning,ReproducibilityReasoning,
  KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "particle simulation" -> ParticleSimulation
  "particle-based simulation" -> ParticleSimulation
  "MD" -> MolecularDynamics
  "DEM" -> DiscreteElementMethod
  "SPH" -> SmoothedParticleHydrodynamics
  "PIC" -> ParticleInCell
  "P3M" -> ParticleParticleParticleMesh
  "PME" -> ParticleMeshEwald
  "RDF" -> RadialDistributionFunction
  "MSD" -> MeanSquaredDisplacement
 }
}

EXECUTION_RULES {
 E1 = "If a simulation evolves discrete interacting particles, bodies or material points, activate ParticleSimulationOntology."
 E2 = "Define particle state, species or material properties and interaction laws before execution."
 E3 = "Choose neighbour-search and cutoff methods consistent with interaction range."
 E4 = "Choose a time integrator and time step appropriate to the fastest physical scale."
 E5 = "Use specialised long-range methods such as tree, FMM, Ewald or mesh-based methods where required."
 E6 = "Monitor conservation quantities and thermodynamic or statistical observables."
 E7 = "For particle-grid methods, document deposition and interpolation operators."
 E8 = "For parallel simulations, preserve ghost-particle consistency and load balance."
 E9 = "Validate force models, convergence, conservation, statistical behaviour and reproducibility."
}

RECURSION {
 ENTRY = ParticleSimulation
 EXPAND(ParticleSimulation) -> [
  ParticleSystem,DiscreteParticleModel,Particle,MaterialPoint,
  PointMass,ParticleState,ParticlePosition,ParticleVelocity,
  ParticleAcceleration,ParticleMass,ParticleCharge,
  ParticleRadius,ParticleOrientation,Force,Torque,
  PairwiseForce,ExternalForce,Gravity,ElectrostaticForce,
  ContactForce,FrictionForce,DragForce,SpringForce,
  InteractionPotential,LennardJonesPotential,CoulombPotential,
  MolecularDynamics,MD,NBodySimulation,GravitationalNBody,
  BarnesHutAlgorithm,FastMultipoleMethod,Treecode,
  DiscreteElementMethod,DEM,GranularSimulation,
  ContactModel,HertzContact,HertzMindlinModel,
  SmoothedParticleHydrodynamics,SPH,KernelFunction,
  SmoothingLength,DensityEstimate,PressureEstimate,
  ParticleInCell,PIC,CloudInCell,ParticleMeshMethod,
  ParticleParticleParticleMesh,P3M,MaterialPointMethod,
  FLIP,APIC,BrownianDynamics,LangevinDynamics,
  CollisionDetection,ParticleParticleCollision,
  ParticleBoundaryCollision,NeighbourSearch,NeighbourList,
  VerletList,CellList,SpatialHashing,UniformGrid,
  KDTree,Octree,BVH,CutoffRadius,SkinDistance,
  PeriodicBoundaryCondition,ReflectiveBoundary,
  AbsorbingBoundary,GhostParticle,ParticleInjection,
  AdaptiveParticleResolution,TimeIntegration,
  SymplecticIntegrator,RungeKuttaMethod,VerletIntegration,
  VelocityVerlet,LeapfrogMethod,AdaptiveTimeStep,
  EnergyConservation,MomentumConservation,
  AngularMomentumConservation,MassConservation,
  ConservationError,EnergyDrift,ParticleInitialisation,
  VelocityDistribution,Thermostat,NoseHooverThermostat,
  Barostat,NVE,NVT,NPT,SimulationBox,
  MinimumImageConvention,EwaldSummation,
  ParticleMeshEwald,PME,ParallelParticleSimulation,
  DomainDecomposition,LoadBalancing,GhostParticleExchange,
  GPUAcceleration,HPC,RandomSeed,Checkpoint,Trajectory,
  RadialDistributionFunction,RDF,MeanSquaredDisplacement,
  MSD,VelocityAutocorrelation,DiffusionCoefficient,
  StructureFactor,KineticEnergy,PotentialEnergy,
  TotalEnergy,StressTensor,Verification,Validation,
  Benchmark,ReferenceSolution,ConvergenceStudy,
  SensitivityAnalysis,UncertaintyQuantification,Reproducibility
 ]
 EXPAND(ParticleSimulationFamilies) -> [
  MolecularDynamicsSimulation,
  NBodySimulation,
  DiscreteElementSimulation,
  SPHParticleSimulation,
  ParticleInCellSimulation,
  StochasticParticleSimulation,
  ParticleGridHybridSimulation,
  ParallelHighPerformanceParticleSimulation
 ]
 STOP_CONDITION = "Stop when particle state, interaction laws, neighbour search, boundary conditions, integration, conservation, parallel execution, verification and reproducibility are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Scientific Simulation Ontology"
 RELATED_ONTOLOGIES = [
  "Scientific Simulation Ontology",
  "Physical Simulation Ontology",
  "Scientific Computing Ontology 2",
  "Collision Detection Ontology 2",
  "Spatial Partitioning Ontology 2",
  "Numerical Methods Ontology 2",
  "Differential Equation Solver Ontology",
  "Monte Carlo Simulation Ontology",
  "Random Process Ontology",
  "Numerical Stability Ontology 2",
  "Numerical Error Ontology",
  "Floating Point Arithmetic Ontology"
 ]
 ROUTE_RULES = [
  "Particle Simulation -> Scientific Simulation Ontology for parent semantics",
  "Particle Simulation -> Physical Simulation for physics-based particle dynamics",
  "Particle Simulation -> Scientific Computing for scalable execution",
  "Particle Simulation -> Collision Detection for particle contact and impact",
  "Particle Simulation -> Spatial Partitioning for neighbour search",
  "Particle Simulation -> Numerical Methods for integration and approximation",
  "Particle Simulation -> Differential Equation Solver for particle equations of motion",
  "Particle Simulation -> Monte Carlo Simulation for stochastic particle methods",
  "Particle Simulation -> Random Process for Langevin and Brownian dynamics",
  "Particle Simulation -> Numerical Stability for time-step restrictions",
  "Particle Simulation -> Numerical Error for cutoff, integration and statistical error",
  "Particle Simulation -> Floating Point Arithmetic for large-scale accumulation effects"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible particle methods, interaction models or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve particle-state-versus-field-state distinction.",
  "Preserve short-range-versus-long-range interaction distinction.",
  "Preserve force-model-versus-integrator distinction.",
  "Preserve neighbour-search-versus-force-evaluation distinction.",
  "Preserve deterministic-versus-stochastic particle dynamics distinction.",
  "Preserve particle-only-versus-particle-grid distinction.",
  "Preserve local-particle-versus-ghost-particle distinction.",
  "Preserve machine-readable particle-simulation semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Particle simulation computationally evolves discrete interacting particles, bodies or material points."
 INTERACTION_SUMMARY = "Forces may arise from pair potentials, contact laws, long-range fields, drag, constraints or stochastic processes."
 NEIGHBOUR_SUMMARY = "Cell lists, Verlet lists, trees, hashing and BVHs reduce the cost of local interaction discovery."
 METHOD_SUMMARY = "Molecular dynamics, DEM, SPH, PIC, N-body and particle-grid hybrid methods represent distinct particle-simulation families."
 INTEGRATION_SUMMARY = "Velocity-Verlet, leapfrog, Runge-Kutta, symplectic and event-driven schemes advance particle states."
 CONSERVATION_SUMMARY = "Energy, momentum, mass, charge and angular momentum provide important diagnostic invariants."
 VALIDATION_SUMMARY = "Particle simulations should be checked through force-model verification, conservation, resolution and time-step studies, statistical observables, benchmark comparison and reproducibility."
}

FLOW {
 INPUT
 -> detect_particle_simulation_context
 -> identify_particle_model_dimension_particle_count_interactions_boundaries_outputs_accuracy_goal_and_budget
 -> define_particle_state_material_species_mass_charge_radius_and_initial_conditions
 -> select_pairwise_contact_field_stochastic_short_range_or_long_range_interaction_models
 -> configure_cutoff_cell_list_Verlet_list_tree_hash_or_BVH_neighbour_search
 -> select_Euler_RungeKutta_Verlet_leapfrog_symplectic_implicit_or_event_driven_integrator
 -> configure_periodic_reflective_absorbing_wall_or_open_boundaries
 -> evaluate_neighbours_forces_contacts_constraints_and_optional_particle_grid_coupling
 -> advance_particle_states
 -> monitor_energy_momentum_mass_temperature_pressure_stability_and_neighbour_statistics
 -> if_large configure_domain_decomposition_ghost_exchange_load_balancing_GPU_or_other_parallel_acceleration
 -> assess_time_step_resolution_cutoff_statistical_and_finite_precision_error
 -> verify_against_reference_benchmark_or_invariant_evidence
 -> validate_against_experimental_or_observational_data_when required
 -> document_configuration_versions_random_seed_provenance_and_reproducibility
 -> route_to_related_scientific_simulation_physical_simulation_scientific_computing_collision_spatial_partitioning_numerical_methods_differential_equation_Monte_Carlo_random_process_stability_error_and_floating_point_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Particle Simulation Ontology defines computational evolution of discrete interacting particles and material points. It supports particle state variables, pairwise and external forces, Lennard-Jones, Coulomb and contact models, molecular dynamics, N-body methods, Barnes-Hut and fast multipole acceleration, discrete-element and granular simulation, smoothed particle hydrodynamics, particle-in-cell, particle-mesh and material-point methods, stochastic Brownian and Langevin dynamics, neighbour lists, cell lists, Verlet lists, spatial hashing and tree structures, collisions, periodic and wall boundaries, explicit, symplectic, Verlet and leapfrog integration, thermostats and statistical ensembles, Ewald and particle-mesh long-range methods, conservation diagnostics, parallel domain decomposition, ghost-particle exchange, GPU acceleration, RDF, MSD and other observables, verification, validation, uncertainty and reproducibility."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-COMPUTATIONAL-MATHEMATICS-PARTICLE-SIMULATION-ONTOLOGY-V1"
}

}

END_FLOW