2d:null 2e:["$","title",null,{"children":"d3-force-md Documentation | Georgios Varnavides | Observable"}] 33:T630,simulation_nodes=md` # simulation.nodes([nodes]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/simulation.js) If *nodes* is specified, sets the simulation’s nodes to the specified array of objects, initializing their positions, velocities, and forces if necessary, and then [re-initializes](#force_initialize) any bound [forces](#simulation_force); returns the simulation. If *nodes* is not specified, returns the simulation’s array of nodes as specified to the [constructor](#forceSimulation). Each *node* must be an object. The following properties are assigned by the simulation: * \`index\` - the node’s zero-based index into *nodes* * \`mass\` - the node’s mass * \`x\` - the node’s current *x*-position * \`y\` - the node’s current *y*-position * \`vx\` - the node’s current *x*-velocity * \`vy\` - the node’s current *y*-velocity * \`force_x\` - the node’s current *x*-force * \`force_y\` - the node’s current *y*-force The position ⟨*x*,*y*⟩ and velocity ⟨*vx*,*vy*⟩ may be subsequently modified by [forces](#forces) and by the simulation. If either *vx* or *vy* is NaN, the velocity is initialized to ⟨0,0⟩. If either *force_x* or *force_y* is NaN, the force is initialized to ⟨0,0⟩. If either *x* or *y* is NaN, the position is initialized in a [phyllotaxis arrangement](https://observablehq.com/@d3/force-layout-phyllotaxis), so chosen to ensure a deterministic, uniform distribution. If *mass* is NaN, the mass is initialized to 1. `34:T419,lennardJonesPotential_strength = md` # lennardJonesPotential.strength([strength]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/lennardJonesPotential.js) If *strength* is specified, sets the strength accessor to the specified number or function, re-evaluates the strength accessor for each node, and returns this force. Currently, strength merely acts a counter accumulated in the Barnes-Hut implementation. If *strength* is not specified, returns the current strength accessor, which defaults to: \`\`\`js function strength() { return 1; } \`\`\` The strength accessor is invoked for each [node](#simulation_nodes) in the simulation, being passed the *node* and its zero-based *index*. The resulting number is then stored internally, such that the strength of each node is only recomputed when the force is initialized or when this method is called with a new *strength*, and not on every application of the force. `35:T539,lennardJonesPotential_theta = md` # lennardJonesPotential.theta([theta]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/lennardJonesPotential.js) If *theta* is specified, sets the Barnes–Hut approximation criterion to the specified number and returns this force. If *theta* is not specified, returns the current value, which defaults to 0.25. To accelerate computation, this force implements the [Barnes–Hut approximation](http://en.wikipedia.org/wiki/Barnes–Hut_simulation) which takes O(*n* log *n*) per application where *n* is the number of [nodes](#simulation_nodes). For each application, a [quadtree](https://github.com/d3/d3-quadtree) stores the current node positions; then for each node, the combined force of all other nodes on the given node is computed. For a cluster of nodes that is far away, the interatomic potential force can be approximated by treating the cluster as a single, larger node. The *theta* parameter determines the accuracy of the approximation: if the ratio *w* / *l* of the width *w* of the quadtree cell to the distance *l* from the node to the cell’s center of mass is less than *theta*, all nodes in the given cell are treated as a single node rather than individually.`36:T51d,centralPotential_theta=md`# centralPotential.theta([theta]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/centralPotential.js) If *theta* is specified, sets the Barnes–Hut approximation criterion to the specified number and returns this force. If *theta* is not specified, returns the current value, which defaults to 0.25. To accelerate computation, this force implements the [Barnes–Hut approximation](http://en.wikipedia.org/wiki/Barnes–Hut_simulation) which takes O(*n* log *n*) per application where *n* is the number of [nodes](#simulation_nodes). For each application, a [quadtree](https://github.com/d3/d3-quadtree) stores the current node positions; then for each node, the combined force of all other nodes on the given node is computed. For a cluster of nodes that is far away, the interatomic potential force can be approximated by treating the cluster as a single, larger node. The *theta* parameter determines the accuracy of the approximation: if the ratio *w* / *l* of the width *w* of the quadtree cell to the distance *l* from the node to the cell’s center of mass is less than *theta*, all nodes in the given cell are treated as a single node rather than individually.`37:[] 31:{"id":"e4baa573469327ae","slug":"d3-force-md-documentation","title":"d3-force-md Documentation","thumbnail":"9865981cbe39612b2a2fc9028578e60cf214fe5e11e026b3e7f970ead36446d6","access_level":"public","create_time":"$D2021-05-17T17:07:37.522Z","update_time":"$D2021-05-17T20:37:46.601Z","view_time":null,"first_public_time":"$D2021-05-17T18:01:29.083Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"69c521ca096fbf54","login":"gvarnavi","name":"Georgios Varnavides","avatar_url":"https://avatars-next.observableusercontent.com/57bb5cf1c4a2d1352d2dcf9f07e535f6e39eb182bbe2295099a4f46fdde5f613","tier":"starter_2024"},"version":150,"publish_version":150,"role":null,"authored":false,"authors":[{"type":"individual","id":"6649dc029d167559","login":"gvarnavi","name":"Georgios Varnavides","avatar_url":"https://avatars-next.observableusercontent.com/4c6924e984dc3d1f89f81dee4e6fc0ca3ab63880a01338b6b6f64d28bc7321e5","tier":null}],"members":[{"type":"individual","id":"6649dc029d167559","login":"gvarnavi","name":"Georgios Varnavides","avatar_url":"https://avatars-next.observableusercontent.com/4c6924e984dc3d1f89f81dee4e6fc0ca3ab63880a01338b6b6f64d28bc7321e5","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"855921dc8c34ef16","slug":"d3-force-md","title":"d3-force-md","owner":{"id":"69c521ca096fbf54","login":"gvarnavi","name":"Georgios Varnavides"}},"type":"notebook","body":{"title":"d3-force-md Documentation","cells":[{"id":0,"value":"md`\n# d3-force-md Documentation\n\nExtended version of [d3-force](https://github.com/d3/d3-force) to implement a _true_ [velocity Verlet](https://en.wikipedia.org/wiki/Verlet_integration) algorithm and extend built-in forces to account for common interatomic potentials encountered in molecular dynamics simulations.\n\nSee [git repository](https://github.com/gvarnavi/d3-force-md) for full documentation. This notebook documents the differences/additions to the API for easier access.\n\nSee also [examples notebook](https://observablehq.com/@gvarnavi/introduction-to-d3-force-md) for examples.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"md`\n## Importing\nImport \\`d3-force-md\\` as usual with D3 modules.\nSince the module overwrites some definitions from \\`d3-force\\`, make sure you require/import it last.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"d3 = require(\"d3@6\",\"d3-force-md@v2.2.2\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"md`\n## API Reference\n\n- [\\`forceSimulation\\`](#forceSimulation) – **updated** simulation implementing true velocity Verlet.\n- [\\`forceLink\\`](#forceLink) – **updated** force to implement energy-conserving constraints.\n- [\\`forceLennardJonesPotential\\`](#forceLennardJones) – **new** force to implement LJ-type interactions.\n- [\\`forceCentralPotential\\`](#forceCentralPotential) – **new** force to implement interatomic interactions.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"md`\n### Simulation\n(only showing relevant/updated sections, see [git repository](https://github.com/gvarnavi/d3-force-md#forceSimulation) for full documentation)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":35,"value":"forceSimulation=md`\n# d3.forceSimulation([nodes]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/simulation.js)\n\nCreates a new simulation with the specified array of [*nodes*](#simulation_nodes) and no [forces](#simulation_force). If *nodes* is not specified, it defaults to the empty array. The simulator [starts](#simulation_restart) automatically; use [*simulation*.on](#simulation_on) to listen for tick events as the simulation runs. If you wish to run the simulation manually instead, call [*simulation*.stop](#simulation_stop), and then call [*simulation*.tick](#simulation_tick) as desired.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":49,"value":"simulation_dt=md`\n# simulation.dt([dt]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/simulation.js)\n\nIf *dt* is specified, sets the simulation's time-step to the specified number and returns this simulation. If *dt* is not specified, returns the current time-step value, which defaults to 1.\n\nIn molecular dynamics simulations, it is common to set [*dt*](#simulation_dt) to appropriate normalized units. E.g. for interatomic potentials normalized to have a minimum value of -1 at distance of 1, 0.05 is a reasonable initial estimate for the time-step value.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":63,"value":"simulation_alphaDecay=md`\n# simulation.alphaDecay([decay]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/simulation.js)\n\nIn molecular dynamics simulations, it is common to set both [*alphaDecay*](#simulation_alphaDecay) and [*velocityDecay*](#simulation_velocityDecay) to 0.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"simulation_velocityDecay=md`\n# simulation.velocityDecay([decay]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/simulation.js)\n\nIn molecular dynamics simulations, it is common to set both [*alphaDecay*](#simulation_alphaDecay) and [*velocityDecay*](#simulation_velocityDecay) to 0.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":71,"value":"md`\n### Forces\n(only showing relevant/updated sections, see [git repository](https://github.com/gvarnavi/d3-force-md#_force) for full documentation)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":89,"value":"md`#### Links\nThe link force pushes linked nodes together or apart according to the desired [link distance](#link_distance). The strength of the force is proportional to the difference between the linked nodes’ distance and the target distance, similar to a spring force.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":74,"value":"forceLink=md`\n# d3.forceLink([links]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/link.js)\n\nCreates a new link force with the specified *links* and default parameters. If *links* is not specified, it defaults to the empty array.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":86,"value":"link_iterations=md`\n# link.iterations([iterations]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/link.js)\n\nIf *iterations* is specified, sets the number of iterations per application to the specified number and returns this force. If *iterations* is 0, the [force](#forceLink) performs a single energy-conserving iteration (useful for molecular dynamics simulations). If *iterations* > 0, the [force](#forceLink) instead performs [iterative relaxation](https://en.wikipedia.org/wiki/Relaxation_(iterative_method)). If *iterations* is not specified, returns the current iteration count which defaults to 1.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":92,"value":"md`\n#### Lennard-Jones\n\nThe [Lennard-Jones](https://en.wikipedia.org/wiki/Lennard-Jones_potential) (or *nm*-potential, *Mie*-potential) force is a common many-body force in molecular dynamics which applies mutually amongst all [nodes](#simulation_nodes). This implementation considers a general class of Lennard-Jones potentials with varying exponents to model repulsive and attractive forces, and uses quadtrees and the [Barnes–Hut approximation](https://en.wikipedia.org/wiki/Barnes–Hut_simulation) to greatly improve performance; the accuracy can be customized using the [theta](#manyBody_theta) parameter.\n\nUnlike links, which only affect two linked nodes, the interatomic potential force is global: every node affects every other node, even if they are on disconnected subgraphs.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":95,"value":"forceLennardJones=md`\n# d3.forceLennardJonesPotential() · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/lennardJonesPotential.js)\n\nCreates a new lennard-jones force with the default parameters.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":98,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":102,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"lennardJonesPotential_distanceMin=md`\n# lennardJonesPotential.distanceMin([distance]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/lennardJonesPotential.js)\n\nIf *distance* is specified, sets the minimum distance between nodes over which this force is considered. If *distance* is not specified, returns the current minimum distance, which defaults to 0.85. A minimum distance establishes an upper bound on the strength of the force between two nearby nodes, avoiding instability. In particular, it avoids an infinitely-strong force if two nodes are exactly coincident; in this case, the direction of the force is random.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":109,"value":"lennardJonesPotential_distanceMax=md`\n# lennardJonesPotential.distanceMax([distance]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/lennardJonesPotential.js)\n\nIf *distance* is specified, sets the maximum distance between nodes over which this force is considered. If *distance* is not specified, returns the current maximum distance, which defaults to infinity. Specifying a finite maximum distance improves performance and produces a more localized layout.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":112,"value":"lennardJonesPotential_repulsivePower=md`\n# lennardJonesPotential.repulsivePower([n]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/lennardJonesPotential.js)\n\nIf *n* is specified, sets the repulsive exponent in the generalized Lennard-Jones potential, ${tex`f(r)=\\frac{n r^{-m}-m r^{-n}}{m-n}`}. If *n* is not specified, returns the current repulsive exponent, which defaults to 12.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":114,"value":"lennardJonesPotential_attractivePower=md`# lennardJonesPotential.attractivePower([m]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/lennardJonesPotential.js)\n\nIf *m* is specified, sets the attractive exponent in the generalized Lennard-Jones potential, ${tex`f(r)=\\frac{n r^{-m}-m r^{-n}}{m-n}`}. If *m* is not specified, returns the current attractive exponent, which defaults to 6.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":123,"value":"md`\n#### Central-Body\n\nThe [Central-Body](https://en.wikipedia.org/wiki/Classical_central-force_problem) force is a general-purpose interatomic potential force used in molecular dynamics which applies mutually amongst all [nodes](#simulation_nodes). This implementation accepts an interatomic potential function, and uses quadtrees and the [Barnes–Hut approximation](https://en.wikipedia.org/wiki/Barnes–Hut_simulation) to greatly improve performance; the accuracy can be customized using the [theta](#manyBody_theta) parameter.\n\nUnlike links, which only affect two linked nodes, the interatomic potential force is global: every node affects every other node, even if they are on disconnected subgraphs.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":126,"value":"forceCentralPotential=md`# d3.forceCentralPotential() · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/centralPotential.js)\n\nCreates a new central-body force with the default parameters.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":129,"value":"centralPotential_strength=md`# centralPotential.strength([strength]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/centralPotential.js)\n\nIf *strength* is specified, sets the strength accessor to the specified number or function, re-evaluates the strength accessor for each node, and returns this force. Currently, strength merely acts a counter accumulated in the Barnes-Hut implementation. If *strength* is not specified, returns the current strength accessor, which defaults to:\n\n\\`\\`\\`js\nfunction strength() {\n return 1;\n}\n\\`\\`\\`\n\nThe strength accessor is invoked for each [node](#simulation_nodes) in the simulation, being passed the *node* and its zero-based *index*. The resulting number is then stored internally, such that the strength of each node is only recomputed when the force is initialized or when this method is called with a new *strength*, and not on every application of the force.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":132,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":135,"value":"centralPotential_distanceMin=md`# centralPotential.distanceMin([distance]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/centralPotential.js)\n\nIf *distance* is specified, sets the minimum distance between nodes over which this force is considered. If *distance* is not specified, returns the current minimum distance, which defaults to 0.85. A minimum distance establishes an upper bound on the strength of the force between two nearby nodes, avoiding instability. In particular, it avoids an infinitely-strong force if two nodes are exactly coincident; in this case, the direction of the force is random.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":138,"value":"centralPotential_distanceMax=md`# centralPotential.distanceMax([distance]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/centralPotential.js)\n\nIf *distance* is specified, sets the maximum distance between nodes over which this force is considered. If *distance* is not specified, returns the current maximum distance, which defaults to infinity. Specifying a finite maximum distance improves performance and produces a more localized layout.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":141,"value":"centralPotential_potentialFunction=md`# centralPotential.potentialFunction([f]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/centralPotential.js)\n\nIf *f* is specified, sets the interatomic potential function \\`f(r)\\`. If *f* is not specified, returns the current interatomic potential function, which defaults to:\n\\`\\`\\`js\nrho => Math.pow(rho,-12)-2*Math.pow(rho,-6)\n\\`\\`\\`\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":144,"value":"centralPotential_gradientFunction=md`\n# centralPotential.gradientFunction([fp]) · [Source](https://github.com/gvarnavi/d3-force-md/blob/master/src/centralPotential.js)\n\nIf *fp* is specified, sets the interatomic potential gradient function \\`f'(r)/r\\`. If *fp* is not specified, returns the current interatomic potential gradient function, which defaults to:\n\\`\\`\\`js\nrho => 12*(Math.pow(rho,6)-1)/Math.pow(rho,14)\n\\`\\`\\`\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W37","stdlib":"1","titling":"auto"}} 32:"$31:body"