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Model Name Model Type Description Author Use Cases
Social-force pedestrian interaction model Pedestrian Dynamics "Social-force pedestrian interaction model: Treats pedestrians as particles driven by attractive/repulsive social forces"" from goals, other people, and obstacles, combining desired velocity with interaction forces to produce realistic collision avoidance and emergent crowd patterns like lane formation.""" N/A N/A
Cellular automaton crowd simulation Pedestrian Dynamics "Cellular automaton crowd simulation: Discretizes space into a grid of cells; pedestrians move stepwise between cells based on local transition rules and neighbor occupancy, enabling computationally efficient simulation of large crowds with emergent flow behavior." N/A Railway station passenger movement, Airport terminal circulation
Lattice-gas pedestrian flow model Pedestrian Dynamics "Lattice-gas pedestrian flow model: Represents pedestrians as particles hopping between lattice sites with exclusion rules, using statistical mechanics analogies to model density-dependent flow, jamming, and phase transitions in pedestrian traffic." N/A Corridor bidirectional traffic, Large public event crowd movement
Floor-field movement probability method Pedestrian Dynamics "Floor-field movement probability method: Uses static and dynamic ""floor fields"" (potential-like scalar fields) to assign transition probabilities to neighboring cells, guiding pedestrians toward exits while reproducing herding and lane-formation effects." N/A Smoke-filled building evacuation, Shopping mall evacuation planning
Velocity-obstacle collision avoidance Pedestrian Dynamics "Velocity-obstacle collision avoidance: Computes the set of velocities that would lead to future collisions with obstacles or agents, then selects a collision-free velocity, enabling reactive, geometry-based avoidance for multiple moving agents." N/A Autonomous robot navigation among pedestrians, Airport concourse pedestrian guidance
Rule-based stepping dynamics Pedestrian Dynamics "Rule-based stepping dynamics: Governs pedestrian movement through explicit heuristic rules (e.g., avoid collisions, maintain spacing, follow leaders) rather than continuous forces or optimization, offering interpretable but simplified behavioral logic." N/A Sidewalk pedestrian simulation, Museum or exhibition visitor movement
Optimal-velocity crowd movement model Pedestrian Dynamics "Optimal-velocity crowd movement model: Adapts car-following theory to pedestrians, where each agent adjusts speed toward an ""optimal velocity"" determined by spacing to neighbors ahead, producing stop-and-go and stability phenomena." N/A Pedestrian flow through corridors, Festival entrance throughput analysis
Centrifugal force pedestrian model Pedestrian Dynamics "Centrifugal force pedestrian model: Extends social-force concepts with velocity-dependent repulsive forces resembling centrifugal effects, improving realism of avoidance maneuvers and reducing unrealistic oscillations seen in basic force models." N/A High-density bottleneck evacuation, Subway platform crowd movement
Gradient-based navigation potential Pedestrian Dynamics "Gradient-based navigation potential: Guides agents by following the negative gradient of a scalar potential field representing distance-to-goal or cost, similar to potential-field robotics navigation." N/A Hospital evacuation routing, Indoor wayfinding in large buildings
Continuum hydrodynamic crowd model Pedestrian Dynamics "Continuum hydrodynamic crowd model: Treats crowds as a continuous fluid governed by conservation laws (mass, momentum), using PDEs analogous to gas/fluid dynamics to model large-scale density and flow patterns." N/A Mass gathering crowd management, City-scale pedestrian flow prediction
Shortest-path navigation model Pedestrian Dynamics "Shortest-path navigation model: Routes agents along geodesically shortest paths to their destination, typically computed via graph search or continuum shortest-path algorithms, ignoring dynamic congestion effects." N/A Building wayfinding analysis, Transit station route planning
Dynamic potential field routing Pedestrian Dynamics "Dynamic potential field routing: Updates navigation potential fields in real time based on current crowd density, allowing agents to reroute around congestion dynamically rather than following fixed shortest paths." N/A Adaptive evacuation under blocked exits, Dynamic rerouting in transportation hubs
Discrete event pedestrian transition model Pedestrian Dynamics "Discrete event pedestrian transition model: Simulates pedestrian state changes (position, activity) as discrete events triggered asynchronously rather than fixed time steps, useful for efficient large-scale or queue-based simulations." N/A Elevator and stair utilization, Security checkpoint processing
Elliptical repulsive forces model Pedestrian Dynamics "Elliptical repulsive forces model: Modifies social-force repulsion to use elliptical rather than circular interaction zones, accounting for anisotropic personal space that depends on relative walking direction." N/A Bidirectional corridor traffic, Dense urban sidewalk simulation
Panic-driven escape behavior model Pedestrian Dynamics "Panic-driven escape behavior model: Incorporates psychological stress and herding instincts into movement equations during emergencies, capturing faster, less rational movement and increased physical pushing under panic conditions." N/A Fire evacuation analysis, Stadium panic scenario assessment
Queue formation and service-rate model Pedestrian Dynamics "Queue formation and service-rate model: Models pedestrians waiting in line using queueing theory, characterizing arrival and service rates to predict wait times, queue length, and bottleneck throughput." N/A Airport security queues, Theme park attraction queues
Lane-formation emergent pattern model Pedestrian Dynamics "Lane-formation emergent pattern model: Captures self-organized lane segregation in bidirectional pedestrian flows as an emergent outcome of local avoidance interactions, without explicitly programming lane behavior." N/A Opposing pedestrian streams in corridors, Crosswalk flow optimization
Boundary repulsion wall-force method Pedestrian Dynamics "Boundary repulsion wall-force method: Adds repulsive forces from walls and obstacles that increase sharply near boundaries, preventing pedestrians from penetrating physical barriers in force-based simulations." N/A Narrow hallway navigation, Tunnel evacuation modeling
Stochastic step-choice Markov model Pedestrian Dynamics "Stochastic step-choice Markov model: Models each pedestrian's next step as a probabilistic choice among neighboring cells, governed by a Markov process with transition probabilities dependent on local conditions." N/A Pedestrian route choice under uncertainty, Visitor movement in shopping centers
Discomfort-field gradient navigation Pedestrian Dynamics "Discomfort-field gradient navigation: Guides pedestrians away from crowded or uncomfortable regions using a discomfort potential field, balancing goal-directed movement against avoidance of unpleasant proximity to others." N/A Hazard avoidance during evacuations, Construction-zone pedestrian routing
Floor-friction bottleneck model Pedestrian Dynamics "Floor-friction bottleneck model: Represents reduced flow capacity at bottlenecks (doors, corridors) using friction-like resistance terms that capture pushing, clogging, and capacity-drop phenomena." N/A Exit door congestion analysis, Narrow passage evacuation studies
Pedestrian gap-acceptance crossing model Pedestrian Dynamics "Pedestrian gap-acceptance crossing model: Models decisions to cross traffic or merge into flow based on acceptable gap sizes between vehicles or other pedestrians, common in mixed traffic modeling." N/A Unsignalized street crossings, Shared-space traffic analysis
Anticipatory collision-avoidance dynamics Pedestrian Dynamics "Anticipatory collision-avoidance dynamics: Extends avoidance models by predicting future trajectories of neighbors and adjusting current movement preemptively, reducing last-moment evasive maneuvers." N/A Crowded sidewalk simulation, Human-aware robot navigation
Energy-based minimization of walking effort Pedestrian Dynamics "Energy-based minimization of walking effort: Derives pedestrian trajectories by minimizing a cost functional representing physical or cognitive walking effort, akin to variational or optimal-control formulations." N/A Campus pedestrian route planning, Accessibility analysis for mobility-impaired users
Continuum-discrete hybrid pedestrian model Pedestrian Dynamics "Continuum discrete hybrid pedestrian model: Combines continuum flow modeling in dense regions with discrete agent-based modeling in sparse regions, balancing computational efficiency and individual-level detail." N/A City-scale evacuation with local detail, Multi-terminal airport passenger movement
Pressure-based crowd compression model Pedestrian Dynamics "Pressure-based crowd compression model: Models high-density crowd crushes using pressure analogous to compressible fluids, capturing dangerous compression forces and stampede dynamics in extreme density events." N/A Stampede risk assessment, Pilgrimage crowd safety analysis
Density-dependent speed adaptation Pedestrian Dynamics "Density-dependent speed adaptation: Adjusts individual walking speed as a function of local crowd density, reproducing empirical fundamental diagrams relating flow, density, and speed." N/A Transit station congestion prediction, Festival crowd management
Pedestrian-vehicle interaction model Pedestrian Dynamics "Pedestrian-vehicle interaction model: Jointly simulates pedestrians and vehicles sharing space, capturing yielding, negotiation, and collision-avoidance behaviors at crossings or shared zones." N/A Urban crosswalk safety analysis, Shared street design evaluation
Counterflow lane-splitting model Pedestrian Dynamics "Counterflow lane-splitting model: Specifically models bidirectional pedestrian streams splitting into interleaved lanes to minimize head-on conflicts, an emergent self-organization phenomenon." N/A Bidirectional subway corridor design, Emergency evacuation with opposing flows
Random-walk pedestrian diffusion model Pedestrian Dynamics "Random-walk pedestrian diffusion model: Represents pedestrian movement as a stochastic random walk with directional bias toward goals, useful for modeling exploratory or low-structure movement." N/A Casual park visitor movement, Pedestrian dispersion after public events
Brownian dynamics Pedestrian Dynamics "Brownian dynamics: Simulates particle motion under random thermal-like forces plus drag and external forces, neglecting inertia (overdamped), widely used for colloidal, molecular, or crowd-analogy systems." N/A Microscopic pedestrian diffusion studies, Crowd mixing and dispersion analysis
Optimal Steps Model Pedestrian Dynamics "Optimal Steps Model: A continuous-space pedestrian model where agents choose discrete stepping targets that optimize a stride based on speed and direction preferences, avoiding grid artifacts of cellular automata." N/A Detailed building evacuation simulation, Cruise ship boarding and disembarkation optimization
Spring dashpot contact force law Discrete Element Methods "Spring dashpot contact force law: Models particle contact force as a linear spring (elastic) plus dashpot (viscous damping) combination, standard in discrete element method simulations of granular contact." N/A Pharmaceutical tablet mixing, Granular material handling in hoppers
Hookean elastic collision model Discrete Element Methods "Hookean elastic collision model: Represents particle deformation during contact using linear (Hookean) spring force proportional to overlap, providing simple elastic restitution in granular simulations." N/A Ball mill particle collisions, Granular flow in chutes
Hertz Mindlin normal contact model Discrete Element Methods "Hertz Mindlin normal contact model: Combines nonlinear Hertzian normal contact stiffness with Mindlin tangential shear theory, standard in DEM for realistic elastic sphere-sphere contact mechanics." N/A Soil and rock mechanics, Powder compaction processes
Nonlinear Hertzian deformation update Discrete Element Methods "Nonlinear Hertzian deformation update: Updates contact force using Hertz's nonlinear elastic contact theory, where force scales as overlap to the 3/2 power, more physically accurate than linear springs." N/A Rock fragmentation simulation, Bearing contact analysis
Coulomb friction tangential force model Discrete Element Methods "Coulomb friction tangential force model: Limits tangential contact force by a friction coefficient times normal force, preventing unphysical sliding resistance in particle or granular contact simulations." N/A Conveyor belt bulk material transport, Landslide and debris flow simulation
Tangential history-dependent contact model Discrete Element Methods "Tangential history-dependent contact model: Tracks accumulated tangential displacement history at a contact point to compute elastic shear force, capturing stick-slip and pre-sliding behavior more accurately than instantaneous models." N/A Powder blending, Railway ballast behavior
Rolling resistance torque formulation Discrete Element Methods "Rolling resistance torque formulation: Adds a resisting torque opposing particle rolling motion, representing energy dissipation from contact deformation asymmetry not captured by translational friction alone." N/A Pebble-bed nuclear reactor fuel motion, Gravel transport simulation
Simplified drag-force particle update Discrete Element Methods Simplified drag-force particle update: Applies a simplified linear or quadratic drag force proportional to relative velocity to update particle motion in a surrounding fluid medium. N/A Pneumatic conveying systems, Dust transport in industrial equipment
Stokes drag sedimentation model Discrete Element Methods Stokes drag sedimentation model: Uses Stokes' law (drag proportional to velocity for low Reynolds number) to model settling of small particles under gravity in viscous fluid. N/A Sediment settling in water treatment, Aerosol particle settling
JKR (Johnson-Kendall-Roberts) adhesive contact model Discrete Element Methods "JKR (Johnson Kendall Roberts) adhesive contact model: Extends Hertz contact theory to include surface adhesion energy, describing sticking behavior between soft, highly adhesive particles at contact." N/A Fine powder agglomeration, Pharmaceutical powder processing
DMT (Derjaguin-Muller-Toporov) adhesive contact model Discrete Element Methods "DMT (Derjaguin Muller Toporov) adhesive contact model: Models adhesive contact for stiff particles with long-range low adhesion forces, complementary to JKR theory which suits softer, high-adhesion contacts." N/A Toner particle interactions, MEMS surface contact analysis
Maugis-Dugdale cohesive contact model Discrete Element Methods "Maugis Dugdale cohesive contact model: Provides a unified adhesive contact theory bridging JKR and DMT regimes using a cohesive zone approach, parameterized by a transition parameter for particle stiffness/adhesion." N/A Microparticle adhesion studies, Soft material contact mechanics
Linear spring-Coulomb slip model Discrete Element Methods "Linear spring Coulomb slip model: Combines linear tangential spring stiffness with a Coulomb friction slip limit, a common simplified tangential contact law in discrete element simulations." N/A Bulk grain storage simulation, Industrial mixer performance
Viscoelastic Kelvin-Voigt contact model Discrete Element Methods "Viscoelastic Kelvin Voigt contact model: Represents contact material as a spring and dashpot in parallel, capturing simultaneous elastic and viscous dissipation during particle collision." N/A Polymer pellet handling, Rubber particle impact analysis
Maxwell viscoelastic contact formulation Discrete Element Methods "Maxwell viscoelastic contact formulation: Models contact material as spring and dashpot in series, representing stress relaxation behavior distinct from Kelvin-Voigt's simultaneous elastic-viscous response." N/A Asphalt aggregate compaction, Viscoelastic particle collision studies
Walton-Braun inelastic collision model Discrete Element Methods Walton Braun inelastic collision model: Uses different loading/unloading stiffness for normal contact force to capture energy loss and permanent deformation in inelastic particle collisions. N/A Granular impact experiments, Ball milling efficiency analysis
Thornton elasto-plastic contact model Discrete Element Methods "Thornton elasto-plastic contact model: Extends Hertzian contact with a yield criterion, transitioning from elastic to plastic deformation regime once contact stress exceeds a threshold, capturing permanent indentation." N/A Metal powder additive manufacturing, Cold powder compaction
Elasto-plastic Hertzian contact model Discrete Element Methods "Elasto-plastic Hertzian contact model: Combines Hertz elastic theory with plastic flow beyond a yield point, modeling both reversible and irreversible deformation during particle impact." N/A Ceramic powder pressing, High-pressure particle compaction
Brilliantov–Pöschel contact law Discrete Element Methods "Brilliantov P schel contact law: A viscoelastic contact model deriving damping force from material viscosity, producing velocity-dependent restitution coefficients consistent with granular gas theory." N/A Planetary ring particle collisions, Granular gas simulations
Cattaneo-Mindlin partial slip model Discrete Element Methods "Cattaneo Mindlin partial slip model: Describes tangential contact with a mix of stick (elastic) and slip (frictional) regions within the contact area, refining pure Coulomb friction assumptions." N/A Wheel–rail contact mechanics, Fretting wear prediction
Rate-and-state friction law Discrete Element Methods "Rate-and-state friction law: Models friction coefficient as dependent on sliding rate and an evolving state variable, capturing stick-slip and frictional memory effects in geophysical and granular contexts." N/A Earthquake fault gouge simulation, Geotechnical slope stability
Mindlin-Deresiewicz tangential contact model Discrete Element Methods "Mindlin Deresiewicz tangential contact model: A detailed incremental tangential contact theory accounting for partial slip and loading history, more rigorous than simplified Cattaneo Mindlin approximations." N/A Railway ballast deformation, Granular shear testing
Rolling friction viscous damping model Discrete Element Methods "Rolling friction viscous damping model: Applies a velocity-proportional viscous damping torque to resist rolling motion, an alternative to Coulomb-type rolling resistance formulations." N/A Rotary drum mixers, Pebble transport systems
Torsional resistance contact model Discrete Element Methods "Torsional resistance contact model: Adds resistance to relative twisting (spin) between contacting particles about the contact normal axis, capturing an often-neglected rotational degree of freedom." N/A Screw conveyor particle transport, Rotary kiln granular motion
Cohesive zone traction-separation model Discrete Element Methods "Cohesive zone traction separation model: Defines a traction-separation relationship describing progressive bond weakening and failure as contacting surfaces separate, common in fracture and adhesive contact modeling." N/A Composite material fracture, Rock crack propagation
Lennard-Jones surface adhesion contact model Discrete Element Methods Lennard-Jones surface adhesion contact model: Applies the Lennard-Jones potential to model short-range van der Waals attraction and repulsion between particle surfaces near contact. N/A Nanoparticle self-assembly, Fine particle adhesion studies
Capillary bridge force model (liquid-mediated contact) Discrete Element Methods "Capillary bridge force model (liquid-mediated contact): Models attractive force from a liquid meniscus bridging two particles, relevant for wet granular materials where capillary forces dominate cohesion." N/A Wet granulation in pharmaceuticals, Moist soil mechanics
Lubrication force contact model (thin-film hydrodynamic interaction) Discrete Element Methods "Lubrication force contact model (thin-film hydrodynamic interaction): Captures viscous resistance from thin fluid films between near-contacting particles, important in dense suspensions before direct solid contact occurs." N/A Slurry transport, Dense suspension rheology
Basset history force model Discrete Element Methods "Basset history force model: Accounts for the unsteady viscous drag history on an accelerating particle in fluid, adding a memory term to the equation of motion beyond simple drag." N/A Sediment resuspension, Particle transport in unsteady flows
Non-spherical particle contact model (ellipsoidal contact formulation) Discrete Element Methods "Non-spherical particle contact model (ellipsoidal contact formulation): Extends contact mechanics to non-spherical shapes like ellipsoids, using geometric overlap algorithms to compute realistic contact forces for irregular particles." N/A Wood chip handling, Grain and seed storage analysis
Penalty-based contact enforcement method Discrete Element Methods "Penalty-based contact enforcement method: Enforces non-penetration between contacting bodies by applying a proportional restoring force when overlap occurs, simple but requires tuning stiffness to avoid instability." N/A Finite element contact simulation, Deformable particle interaction modeling
Lagrange multiplier contact constraint model Discrete Element Methods "Lagrange multiplier contact constraint model: Enforces exact non-penetration using Lagrange multipliers as constraint forces, avoiding penetration but requiring solution of a constrained system each step." N/A Precision contact mechanics, Structural impact simulation
Augmented Lagrangian contact formulation Discrete Element Methods Augmented Lagrangian contact formulation: Combines penalty and Lagrange multiplier methods to enforce contact constraints accurately while improving numerical convergence and reducing penetration compared to pure penalty methods. N/A Metal forming simulation, Tire-road contact analysis
Mortar finite element contact method Discrete Element Methods "Mortar finite element contact method: A finite-element technique for enforcing contact conditions across non-matching meshes using mortar (interface) elements, ensuring accurate force transfer between bodies." N/A Gear tooth contact analysis, Complex structural contact mechanics
Damped oscillator particle model Discrete Element Methods "Damped oscillator particle model: Represents particle interaction as a damped harmonic oscillator, combining elastic restoring force and damping to simulate vibration decay during contact events." N/A Particle vibration studies, Impact damping material design
Impulse-based collision resolution method Discrete Element Methods "Impulse-based collision resolution method: Resolves collisions by applying instantaneous velocity-changing impulses computed from conservation of momentum and restitution, common in real-time physics engines." N/A Robotic bin-picking simulation, Rigid-body granular collisions
Penalty-force method for contacts Discrete Element Methods "Penalty-force method for contacts: General term for contact resolution via continuous restoring forces proportional to interpenetration depth, trading physical accuracy for computational simplicity." N/A DEM-FEM coupled simulations, Mechanical assembly contact analysis
Discrete collision timing model Discrete Element Methods "Discrete collision timing model: Detects and resolves collisions at exact computed collision times rather than fixed time steps, improving accuracy for fast-moving or rigid-body simulations." N/A Event-driven granular gas simulation, Sparse particle collision prediction
Soft-sphere interaction force formulation Discrete Element Methods "Soft-sphere interaction force formulation: Allows particles to overlap slightly and computes contact force from overlap magnitude, standard in DEM for deformable-like granular particle interactions." N/A Powder mixing and blending, Granular flow in silos
Hard-sphere collision dynamics Discrete Element Methods "Hard-sphere collision dynamics: Treats particles as perfectly rigid, non-deforming spheres whose collisions are instantaneous and governed by conservation laws and a restitution coefficient." N/A Molecular-scale granular gases, Dilute particulate flow simulation
Drag lift aerodynamic particle model Discrete Element Methods "Drag lift aerodynamic particle model: Models both drag and lift forces on particles moving through fluid, important for simulating particle trajectories in airflow or spray dynamics." N/A Cyclone separator design, Windblown dust transport
Rotational drag torque evolution Discrete Element Methods "Rotational drag torque evolution: Applies a torque proportional to angular velocity relative to surrounding fluid, damping particle spin due to viscous resistance." N/A Fluidized bed reactors, Aerosol particle rotation studies
Particle wall impact restitution method Discrete Element Methods "Particle wall impact restitution method: Computes post-impact velocity of a particle striking a wall using a coefficient of restitution, capturing energy loss during rigid boundary collisions." N/A Pneumatic conveying pipe design, Crusher and mill impact analysis
Energy-dissipative collision model Discrete Element Methods "Energy-dissipative collision model: General framework where collision forces are tuned to dissipate kinetic energy consistent with observed inelastic behavior, used across granular and molecular simulations." N/A Protective ballast design, Granular shock absorption systems
Interparticle cohesion force model Discrete Element Methods "Interparticle cohesion force model: Adds attractive forces between particles independent of adhesion mechanisms like liquid bridges, representing generic cohesive bonding in fine powders or clays." N/A Powder caking prediction, Lunar or asteroid regolith simulation
Shear-rate dependent contact damping Discrete Element Methods "Shear-rate dependent contact damping: Varies contact damping coefficient based on local shear rate, capturing rate-dependent dissipation seen in dense granular flows." N/A Dense slurry transport, High-shear powder mixing
Centripetal motion under curved trajectory N-Body "Centripetal motion under curved trajectory: Computes the force required to maintain circular or curved motion, used when modeling particles or bodies constrained to curved paths." N/A Satellite orbital trajectory prediction, Circular particle accelerator beam dynamics
Electrostatic Coulomb force model N-Body "Electrostatic Coulomb force model: Computes pairwise forces between charged particles using Coulomb's inverse-square law, foundational for plasma, colloidal, and molecular electrostatics simulations." N/A Plasma particle simulation, Charged aerosol dynamics
Magnetic dipole-dipole interaction model N-Body "Magnetic dipole dipole interaction model: Calculates forces and torques between magnetized particles based on dipole field interactions, relevant for magnetorheological fluids and magnetic granular systems." N/A Ferrofluid behavior simulation, Magnetic nanoparticle self-assembly
Particle mesh hybrid model N-Body "Particle mesh hybrid model: Combines direct particle-particle force calculation at short range with mesh-based (grid) solvers for long-range forces, improving computational efficiency in large N-body systems." N/A Galaxy formation simulation, Large-scale plasma dynamics
Post-Newtonian correction modeling N-Body "Post-Newtonian correction modeling: Adds relativistic correction terms to Newtonian gravity equations, important for high-precision orbital dynamics near massive bodies like in general relativity applications." N/A Binary neutron star orbital evolution, Black hole inspiral simulations
Softened-gravity potential method N-Body Softened-gravity potential method: Modifies the gravitational potential with a softening length to avoid numerical singularities during close particle encounters in N-body simulations. N/A Star cluster evolution, Dark matter halo simulations
Smoothed particle hydrodynamics coupling N-Body "Smoothed particle hydrodynamics coupling: Couples a meshless Lagrangian fluid method (SPH), where fluid properties are interpolated from neighboring particles, with other solvers for multiphysics simulation." N/A Star formation in molecular clouds, Astrophysical gas cloud collisions
Multi-zone mesh refinement dynamics N-Body "Multi-zone mesh refinement dynamics: Dynamically refines computational mesh resolution in regions of interest (e.g., high density or gradient) while coarsening elsewhere to balance accuracy and efficiency." N/A Planet formation simulations, Supernova remnant evolution
Collisional N-body scattering approach N-Body "Collisional N-body scattering approach: Explicitly tracks close gravitational encounters and scattering events between bodies, essential for star cluster dynamics where two-body relaxation matters." N/A Dense star cluster evolution, Planetesimal collision studies
Monte Carlo stellar-dynamics method N-Body Monte Carlo stellar-dynamics method: Uses statistical Monte Carlo sampling of orbital and encounter probabilities to evolve large stellar systems more efficiently than direct N-body integration. N/A Globular cluster evolution, Galactic nucleus relaxation studies
Hybrid Monte Carlo N-body scheme N-Body "Hybrid Monte Carlo N-body scheme: Combines Monte Carlo statistical sampling with direct dynamical integration for select interactions, balancing speed and accuracy in large-scale stellar simulations." N/A Galaxy merger simulations, Dense stellar system evolution
GPU-accelerated force computation N-Body "GPU-accelerated force computation: Leverages parallel GPU hardware to compute pairwise or mesh-based forces rapidly, enabling large-scale particle or N-body simulations within practical runtimes." N/A Billion-particle cosmological simulations, Real-time gravitational N-body computation
Cosmological large-scale structure integration N-Body Cosmological large-scale structure integration: Simulates gravitational evolution of matter (including dark matter) across cosmological volumes and time to model galaxy and structure formation. N/A Cosmic web formation, Dark matter distribution evolution
Comoving-coordinate expansion model N-Body "Comoving-coordinate expansion model: Uses coordinates that expand with the universe to simplify equations of motion in cosmological simulations, removing background Hubble expansion from particle dynamics." N/A Expanding universe simulations, Large-scale galaxy evolution
Tidal-force perturbation modeling N-Body "Tidal-force perturbation modeling: Computes differential gravitational forces across an extended body from a nearby massive object, modeling tidal stretching, disruption, or orbital perturbation effects." N/A Moon–planet orbital evolution, Galaxy interaction and tidal tail formation
Multi-mass tracer particle scheme N-Body "Multi-mass tracer particle scheme: Uses particles of varying mass resolution to represent different regions (e.g., higher resolution near a target object) in large-scale simulations, improving efficiency." N/A Dark matter tracer studies, Pollutant transport in particle-based environmental models
Stochastic force-fluctuation model N-Body "Stochastic force-fluctuation model: Adds random fluctuating forces to particle dynamics representing unresolved sub-grid processes, akin to a Langevin-type noise term in physical simulations." N/A Brownian gravitational relaxation, Turbulent particle transport with random perturbations
Hybrid tree FMM gravitational solver N-Body Hybrid tree FMM gravitational solver: Combines tree-code (hierarchical grouping) and fast multipole method algorithms to efficiently compute long-range gravitational forces with reduced computational complexity. N/A Large star cluster simulations, Cosmological N-body simulations with millions of bodies
Multi-physics N-body coupling method N-Body "Multi-physics N-body coupling method: Integrates gravitational N-body dynamics with additional physics (hydrodynamics, radiation, chemistry) within a unified simulation framework for astrophysical or engineering applications." N/A Dust–gas interactions in protoplanetary disks, Plasma–particle coupled simulations
High-order variational integrator N-Body "High-order variational integrator: Uses numerical integration schemes derived from discrete variational principles to preserve energy and symplectic structure over long-term simulations, improving stability." N/A Long-term planetary orbit stability analysis, Space mission trajectory propagation
Agent-based walking behavior model Agent-Based Modelling "Agent-based walking behavior model: Simulates individual pedestrians as autonomous agents with internal decision rules governing perception, goal-setting, and movement, capturing heterogeneous individual behavior." N/A Urban sidewalk pedestrian simulation, Airport terminal passenger movement
Group-cohesion behavioral model Agent-Based Modelling "Group-cohesion behavioral model: Models pedestrians moving in social groups (families, friends) that maintain proximity and coordinated movement, affecting overall flow and spatial distribution." N/A Family evacuation from public buildings, Tourist group movement in museums and theme parks
Leader-follower movement dynamics Agent-Based Modelling "Leader follower movement dynamics: Simulates a subset of agents (leaders) guiding movement while followers adjust trajectories relative to leaders, common in evacuation or herd behavior modeling." N/A Guided emergency evacuations, Military squad and search-and-rescue team movement
Vision-based obstacle avoidance scheme Agent-Based Modelling "Vision-based obstacle avoidance scheme: Uses simulated field-of-view perception to detect obstacles and other agents, informing avoidance decisions based on visible rather than omnidirectional information." N/A Autonomous pedestrian navigation in cluttered environments, Human-aware mobile robot navigation
Cognitive map route-choice model Agent-Based Modelling "Cognitive map route-choice model: Represents pedestrians' internal spatial knowledge (cognitive maps) used to plan routes, capturing route preference and wayfinding behavior beyond simple shortest-path logic." N/A Wayfinding in hospitals and shopping malls, Visitor navigation in university campuses and museums
Multi-agent reinforcement learning navigation Agent-Based Modelling "Multi-agent reinforcement learning navigation: Trains agents via reinforcement learning to learn navigation policies that optimize rewards like reaching goals quickly while avoiding collisions, adapting through experience." N/A Adaptive evacuation route optimization, Autonomous robot fleet coordination in warehouses
Emotional contagion evacuation model Agent-Based Modelling "Emotional contagion evacuation model: Simulates spread of emotional states (fear, urgency) between nearby agents during evacuation, influencing speed and decision-making as panic propagates through a crowd." N/A Fire and smoke emergency evacuation, Crowd panic analysis during stadium or concert emergencies
Social-group formation and dispersion model Agent-Based Modelling "Social-group formation and dispersion model: Models dynamic formation, maintenance, and breakup of social groups within crowds based on proximity, relationships, and environmental constraints." N/A Passenger group behavior in airports and transit stations, Crowd dynamics during festivals and public events
Harmonic bond-stretch potential Molecular Dynamics "Harmonic bond-stretch potential: Models covalent bond stretching energy as a quadratic (harmonic) function of bond length deviation from equilibrium, standard in molecular mechanics force fields." N/A Polymer chain deformation, Protein molecular dynamics
Lennard-Jones pair interaction model Molecular Dynamics "Lennard-Jones pair interaction model: Describes non-bonded van der Waals interactions with a potential combining short-range repulsion and longer-range attraction, widely used in molecular simulations." N/A Noble gas simulations, Liquid–vapor phase transition studies
Buckingham exponential-6 potential Molecular Dynamics "Buckingham exponential-6 potential: An alternative non-bonded interaction model using an exponential repulsive term plus an attractive inverse-sixth-power term, avoiding Lennard-Jones's overly steep repulsion." N/A Ionic crystal simulation, Ceramic material modeling
Morse bond energy function Molecular Dynamics "Morse bond energy function: Models bond stretching with an anharmonic exponential potential allowing bond dissociation, more physically realistic than harmonic potentials for large displacements." N/A Molecular vibration analysis, Chemical bond dissociation studies
Harmonic angle-bending potential Molecular Dynamics "Harmonic angle-bending potential: Represents molecular bond-angle deformation energy as a quadratic function of angle deviation from equilibrium value, part of standard force field bonded terms." N/A Protein conformational dynamics, Polymer flexibility analysis
Fourier torsional rotation potential Molecular Dynamics "Fourier torsional rotation potential: Models dihedral/torsional rotation energy using a Fourier series of cosine terms, capturing periodic energy barriers to bond rotation in molecules." N/A Protein side-chain rotation, Organic molecule conformational studies
OPLS all-atom force field model Molecular Dynamics "OPLS all-atom force field model: A widely used molecular mechanics force field parameterized for accurate reproduction of liquid-state thermodynamic properties, covering bonded and non-bonded interactions." N/A Drug–protein binding simulations, Organic solvent simulations
AMBER biomolecular force field Molecular Dynamics "AMBER biomolecular force field: A force field family optimized for proteins, nucleic acids, and biomolecules, providing parameters for bonded and non-bonded interactions in biomolecular simulations." N/A Protein folding, DNA and RNA dynamics
CHARMM coarse-grained model Molecular Dynamics "CHARMM coarse-grained model: A reduced-resolution variant of the CHARMM force field grouping atoms into larger interaction sites, enabling simulation of larger biomolecular systems over longer timescales." N/A Membrane protein simulations, Lipid bilayer dynamics
GROMOS classical potential set Molecular Dynamics "GROMOS classical potential set: A force field emphasizing united-atom representations (implicit hydrogens) for efficient biomolecular and liquid simulations, particularly common in European simulation software." N/A Biomolecular solution simulations, Enzyme dynamics
ReaxFF reactive bond dynamics Molecular Dynamics "ReaxFF reactive bond dynamics: A reactive force field allowing bonds to form and break dynamically based on bond order, enabling simulation of chemical reactions within molecular dynamics." N/A Combustion chemistry, Battery material degradation
COMB charge-optimized many-body potential Molecular Dynamics "COMB charge-optimized many-body potential: A reactive potential incorporating variable atomic charges and many-body terms to model complex bonding environments including metals, oxides, and interfaces." N/A Metal–ceramic interface modeling, Oxidation and corrosion simulations
EAM embedded-atom metallic potential Molecular Dynamics "EAM embedded-atom metallic potential: Models metallic bonding using an embedding energy function of local electron density plus pairwise terms, well-suited for simulating metals and alloys." N/A Metal deformation and dislocation motion, Nanocrystalline metal mechanics
MEAM modified embedded-atom method Molecular Dynamics "MEAM modified embedded-atom method: Extends EAM with angular-dependent terms to capture directional bonding, improving accuracy for covalent and complex metallic systems." N/A Alloy mechanical behavior, Fracture of metallic materials
Stillinger Weber silicon potential Molecular Dynamics Stillinger Weber silicon potential: A widely used empirical potential combining two- and three-body terms to model covalent bonding and tetrahedral geometry in silicon and similar materials. N/A Silicon crystal growth, Semiconductor defect analysis
AIREBO (Adaptive Intermolecular Reactive Empirical Bond Order) potential Molecular Dynamics "AIREBO (Adaptive Intermolecular Reactive Empirical Bond Order) potential: Combines reactive bond-order bonding terms with non-bonded and torsional interactions, commonly used for hydrocarbons and carbon nanostructures." N/A Carbon nanotube mechanics, Graphene fracture simulations
REBO (Reactive Empirical Bond Order) potential Molecular Dynamics "REBO (Reactive Empirical Bond Order) potential: Models covalent bonding in hydrocarbons using bond-order terms that adapt to local atomic environment, allowing bond formation and breaking." N/A Hydrocarbon reaction dynamics, Carbon material deformation
Brenner bond-order potential (2nd generation REBO) Molecular Dynamics Brenner bond-order potential (2nd generation REBO): An improved bond-order potential for carbon-based systems with refined parameters for better mechanical and thermal property prediction over the original REBO. N/A Diamond and graphite mechanics, Carbon nanostructure simulation
Morse pair potential Molecular Dynamics "Morse pair potential: A pairwise interatomic potential capturing bond stretching and dissociation using an exponential form, applicable to diatomic and simple crystal simulations." N/A Metal cluster simulations, Diatomic molecular interactions
Buckingham (exp-6) potential Molecular Dynamics "Buckingham (exp-6) potential: Non-bonded pair potential combining exponential repulsion and inverse-sixth attraction, often used for ionic and ceramic material simulations." N/A Mineral crystal modeling, Oxide material simulations
Bornâ-Mayer-Huggins potential Molecular Dynamics "Born Mayer Huggins potential: An ionic crystal potential combining short-range exponential repulsion with Coulomb electrostatics and van der Waals terms, used for alkali halides and oxides." N/A Ionic solids, Ceramic lattice simulations
ZBL (Ziegler-Biersack-Littmark) universal potential Molecular Dynamics "ZBL (Ziegler Biersack Littmark) universal potential: A universal short-range repulsive potential for high-energy atomic collisions, commonly used to describe close-range interactions in radiation damage simulations." N/A Ion implantation in solids, Radiation damage simulations
Finnis-Sinclair potential Molecular Dynamics "Finnis Sinclair potential: A many-body metallic potential similar to EAM, using a density-dependent cohesive term plus pairwise repulsion to model transition metal bonding." N/A Metallic crystal plasticity, Grain boundary behavior
Gupta many-body potential Molecular Dynamics "Gupta many-body potential: A tight-binding-derived many-body potential for metals based on second-moment approximation, commonly used for nanoparticle and cluster simulations." N/A Metal nanoparticle formation, Metallic cluster stability
Sutton-Chen many-body potential Molecular Dynamics "Sutton Chen many-body potential: A metallic potential incorporating an attractive many-body density term and repulsive pair term, tuned to reproduce elastic and surface properties of metals." N/A Metallic surface diffusion, Nanoparticle growth
Tight-Binding (TB) potential models Molecular Dynamics "Tight-Binding (TB) potential models: Approximate quantum mechanical bonding using simplified electronic Hamiltonians with parameterized hopping integrals, balancing accuracy and computational cost between DFT and classical potentials." N/A Semiconductor electronic structure, Nanomaterial simulations
SCC-DFTB (Self-Consistent Charge Density Functional Tight Binding) Molecular Dynamics "SCC-DFTB (Self-Consistent Charge Density Functional Tight Binding): An efficient quantum-based method combining tight-binding approximations with self-consistent charge corrections, enabling faster-than-DFT electronic structure calculations." N/A Large biomolecule quantum simulations, Organic electronic materials
EDIP (Environment-Dependent Interatomic Potential) Molecular Dynamics "EDIP (Environment-Dependent Interatomic Potential): A bonding potential where interaction parameters depend on local atomic coordination environment, improving transferability for covalent materials like silicon and carbon." N/A Silicon fracture analysis, Amorphous silicon structure
BOP (Analytical Bond-Order Potential) Molecular Dynamics BOP (Analytical Bond-Order Potential): A quantum-mechanically derived bond-order potential providing accurate directional bonding for covalent and metallic systems with reduced computational cost versus full quantum methods. N/A Covalent crystal fracture, Semiconductor defect evolution
SNAP (Spectral Neighbor Analysis Potential) Molecular Dynamics SNAP (Spectral Neighbor Analysis Potential): A machine-learning interatomic potential using bispectrum components of local atomic environments fit via linear regression to quantum-mechanical reference data. N/A High-accuracy metallic alloy simulation, Defect evolution in crystalline materials
GAP (Gaussian Approximation Potential) Molecular Dynamics GAP (Gaussian Approximation Potential): A machine-learning potential using Gaussian process regression on atomic environment descriptors to predict energies and forces with near-quantum accuracy. N/A Machine-learned materials modeling, Phase transformation simulations
Neural Network Potentials (e.g. Molecular Dynamics "Neural Network Potentials: Machine-learning potentials using neural networks trained on quantum-mechanical data to predict atomic energies and forces, enabling accurate large-scale simulations." N/A Accurate molecular dynamics of complex molecules, Catalytic reaction simulations
DeepMD / Deep Potential Molecular Dynamics Molecular Dynamics "DeepMD / Deep Potential Molecular Dynamics: A deep-learning framework generating interatomic potentials from ab initio data, achieving near-DFT accuracy at classical molecular dynamics computational cost." N/A Large-scale atomistic materials simulation, Liquid water and electrolyte modeling
Machine-Learned Moment Tensor Potential (MTP) Molecular Dynamics "Machine-Learned Moment Tensor Potential (MTP): Represents atomic interactions using tensor-based local environment descriptors fit via machine learning, offering efficient, accurate potentials for diverse materials." N/A Alloy phase stability, High-throughput materials discovery
Drude polarizable force field Molecular Dynamics "Drude polarizable force field: Adds auxiliary charged ""Drude"" particles attached to atoms via springs to model electronic polarizability, improving accuracy of electrostatic interactions in classical simulations." N/A Ion transport in biological channels, Electrolyte solution simulations
AMOEBA polarizable force field Molecular Dynamics "AMOEBA polarizable force field: Incorporates atomic multipoles and induced dipoles for polarizable electrostatics, offering higher accuracy than fixed-charge force fields for biomolecular and material systems." N/A Protein–ligand binding affinity, Water structure and dynamics
ClayFF force field (for layered silicates) Molecular Dynamics "ClayFF force field: A force field parameterized specifically for layered clay minerals and hydroxides, modeling structural, electrostatic, and hydration interactions in clay systems." N/A Clay mineral swelling, Soil contaminant transport
COMPASS force field Molecular Dynamics "COMPASS force field: A condensed-phase optimized force field for atomistic simulation, parameterized for accurate prediction of properties across organic and inorganic materials." N/A Polymer material design, Organic crystal simulation
Dreiding generic force field Molecular Dynamics "Dreiding generic force field: A simple, generic force field applicable broadly across organic, biological, and main-group inorganic molecules, useful for quick structural predictions." N/A Molecular crystal prediction, Porous material (MOF) modeling
Adaptive intermolecular reactive force field Molecular Dynamics "Adaptive intermolecular reactive force field: Refers generally to reactive force fields (like ReaxFF/AIREBO) that adapt bonding based on atomic environment, allowing chemical reactions during simulation." N/A Catalytic surface reactions, Reactive polymer degradation
Long-range Ewald summation technique Molecular Dynamics "Long-range Ewald summation technique: Computes electrostatic interactions in periodic systems by splitting the sum into rapidly converging real-space and reciprocal-space components, avoiding truncation errors." N/A Ionic crystal electrostatics, Electrolyte molecular simulations
Particle mesh Ewald electrostatics Molecular Dynamics Particle mesh Ewald electrostatics: An efficient variant of Ewald summation using fast Fourier transforms on a mesh grid to compute long-range electrostatics with reduced computational scaling. N/A Protein folding simulations, DNA–protein interaction modeling
Smooth particle mesh Ewald solver Molecular Dynamics "Smooth particle mesh Ewald solver: An enhanced particle mesh Ewald method using smooth interpolation functions for charge assignment, improving accuracy and efficiency in large-scale molecular simulations." N/A Large biomolecular simulations, Membrane protein electrostatics
Hybrid quantum classical QM/MM method Molecular Dynamics "Hybrid quantum classical QM/MM method: Combines quantum mechanical treatment of a reactive region with classical molecular mechanics for the surrounding environment, balancing accuracy and computational feasibility." N/A Enzyme reaction mechanisms, Drug metabolism simulations
Coarse-grained bead spring polymer model Molecular Dynamics "Coarse-grained bead spring polymer model: Represents polymer chains as connected beads with spring-like bonds, reducing atomic detail to simulate large-scale polymer dynamics efficiently." N/A Polymer melt rheology, DNA coarse-grained simulations
Dissipative particle dynamics approach Molecular Dynamics Dissipative particle dynamics approach: A coarse-grained simulation method using soft pairwise forces plus dissipative and random forces to model mesoscale fluid and soft-matter dynamics while conserving momentum. N/A Soft matter and colloid simulation, Cell membrane dynamics
Brownian dynamics overdamped evolution Molecular Dynamics "Brownian dynamics overdamped evolution: Simulates particle motion in the overdamped (inertialess) limit under random thermal forces and drag, appropriate for slow diffusive processes in viscous media." N/A Protein diffusion in solution, Nanoparticle transport in fluids
Energy-minimized initial structure relaxation Molecular Dynamics "Energy-minimized initial structure relaxation: Refers to computationally adjusting an initial atomic or particle configuration to a local energy minimum before dynamic simulation, removing unphysical strain or overlaps. " N/A Molecular structure preparation before MD, Crystal defect relaxation prior to simulation
CALM Pedestrian Dynamics The CALM model is designed to simulate movement of a crowd in constrained linear passageways such as boarding or deplaning an aircraft. CALM can superimpose a disease spread model over the pedestrian model. N/A N/A
SPED Pedestrian Dynamics The SPED model is designed to simulate movement of a crowd in constrained linear passageways such as boarding or deplaning an aircraft or moving through a security line. SPED can superimpose a disease spread model over the pedestrian model. N/A N/A
Crociani-Lämmel-Park-Vizzari Molecular Dynamics This is a Multi-scale model. It is a high-resolution model of Statin Island ferry boarding areas. It was used to find excessive congestion in boarding areas (boarding and unboarding) make boarding/unboarding more efficient by reorganizing those spaces. This work was performed in collaboration with people in the New York department of transportation in order to provide support for decision-makers. N/A N/A
Vizzari-Crociani-Bandini Agent-Based Modelling The Vizzari-Crociani-Bandini model is a way finding model. It simulates path planning in individuals. It is an Agent based floor field model. It helpps answer the question of how simulated individuals choose among multiple paths. Variables including congestion and imitation of others are factors. It is a small scale scenario modeling individual preferences. N/A N/A
Harweg-Bachman-Weichert Pedestrian Dynamics The goal of this work is to provide an agent-based numerical simulation of pedestrian dynamics in order to assess the behavior of pedestrians in public places in the context of contact transmission of infectious diseases like COVID-19. It is also used to gather insights about exposure times and the overall effectiveness of distancing measures. N/A N/A
Crociani-Zeng-Vizzari-Bandini Pedestrian Dynamics This is a model pertaining to the presence of groups moving together. It assumes individuals will not get too far from each other. This model has implications on path selection based upon desired velocity and other parameter. Corridors are 15 meters x 2.5 meters with open spaces. There are flows in one direction and counterflows. Pedestrian densities may be varied. N/A N/A
Vizzari-Cecconello Agent-Based Modelling This is a multi-agent reinforcement learning model. Pedestrians are in a system and explore different ways to behave and get rewards such as reaching the final destination. This modeling scheme produces behavioral models of plausible behaviors. N/A N/A

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