ReferenceAvailable
Electric Currents
Conductive and capacitive electric-current conservation in frequency-domain media.
Reference
| Field | Value | Description |
|---|---|---|
| constraints | [] | — |
| coupled_runtime | null | — |
| differentiable_runtime | {"certification":"ElectricCurrentsStationaryScalarRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":[],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["ec.V"],"value_kind":"field"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["ec.energy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["ec.compliance"],"value_kind":"scalar-global"}],"residual_owner":"ElectricCurrents.element_residual","state_fields":["V"],"supported_objective_symbols":{"coordinate":["ec.V","ec.energy","ec.compliance"],"material":["ec.V","ec.energy","ec.compliance"],"topology":["ec.V","ec.energy","ec.compliance"]},"topology_expression_gradient":true} | — |
| dynamic_outputs | [] | — |
| equation_summary | div((sigma + i*omega*epsilon)*grad(V)) = 0 | — |
| frequency_domain_runtime | {"certification":"ElectricCurrentsComplexScalarRuntime","operator_terms":[{"angular_frequency_power":0,"coefficient":"conductivity","phase":"real"},{"angular_frequency_power":1,"coefficient":"permittivity","phase":"imaginary"}],"runtime":"scalar-complex-gradient","state_fields":["V"],"supports_sweep":true} | — |
| metadata | {"releaseSupport":{"certifiedStudies":["stationary","frequency-domain"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Available.","selectable":true}} | — |
| preferred_material | null | — |
| schema_version | 0.1.0 | — |
| stateVariables | [{"adjointDescription":"The real stationary conductivity operator supports the shared scalar adjoint; complex frequency-domain adjoints are not certified.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"ec.V","complexValued":true,"componentDescriptions":["Electric-potential phasor"],"componentNames":["V"],"componentSymbols":["ec.V"],"components":1,"description":"Complex electric-potential phasor.","differentiability":"analytic","displayName":"Electric potential","finiteElementSpace":"H1-P1","initialValue":"0","location":"node","name":"V","namingPolicy":"fixed","quantityId":"ec.V","rank":"scalar","role":"state","runtimeEvidence":{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","provider":"ElectricCurrents.element_residual"},"symbolPattern":null,"unit":"V"}] | — |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: inverse potential scaling with conductivity for a fixed volume-current source"},{"certified":true,"differentiability":"exact-ad","kind":"frequency-domain","reason":"september-2026-classroom verified contract: terminal-current conservation and analytical complex-admittance frequency ratio"}] | — |
| transient_runtime | null | — |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(ec.V)), (conductivity+i*angularFrequency*permittivity)*grad(ec.V))","name":"ec.current-conservation","test_field":"ec.V"}] | — |
| category | AC/DC | — |
| description | Conductive and capacitive electric-current conservation in frequency-domain media. | — |
| dimensions | [3] | — |
| display_name | Electric Currents | — |
| kind | Electric Currents | — |
| namespace | ec | — |
| status | certified | — |
| visible | true | — |
Conductive and capacitive electric-current conservation in frequency-domain media.
Contract
| Property | Value |
|---|---|
| constraints | [] |
| coupled_runtime | null |
| differentiable_runtime | {"certification":"ElectricCurrentsStationaryScalarRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":[],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"suppor... |
| dynamic_outputs | [] |
| equation_summary | div((sigma + i*omega*epsilon)*grad(V)) = 0 |
| frequency_domain_runtime | {"certification":"ElectricCurrentsComplexScalarRuntime","operator_terms":[{"angular_frequency_power":0,"coefficient":"conductivity","phase":"real"},{"angular_frequency_power":1,"coefficient":"permittivity","phase":"imaginary"}],"runtime":"scalar-complex-gradient","state_fields":["V"],"supports_sweep":true} |
| metadata | {"releaseSupport":{"certifiedStudies":["stationary","frequency-domain"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Available.","selectable":true}} |
| preferred_material | null |
| schema_version | 0.1.0 |
| stateVariables | [{"adjointDescription":"The real stationary conductivity operator supports the shared scalar adjoint; complex frequency-domain adjoints are not certified.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"ec.V","complexValued":true,"componentDescriptions":["Electric-potential phasor"],"componentNames":["V"],"componentSymbols":["ec.V"],"components":1,"description":"Complex electric-potential phasor.","differentiability":"analytic","displayName":"Electric potenti... |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: inverse potential scaling with conductivity for a fixed volume-current source"},{"certified":true,"differentiability":"exact-ad","kind":"frequency-domain","reason":"september-2026-classroom verified contract: terminal-current conservation and analytical complex-admittance frequency ratio"}] |
| transient_runtime | null |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(ec.V)), (conductivity+i*angularFrequency*permittivity)*grad(ec.V))","name":"ec.current-conservation","test_field":"ec.V"}] |
| category | AC/DC |
| description | Conductive and capacitive electric-current conservation in frequency-domain media. |
| dimensions | [3] |
| display_name | Electric Currents |
| kind | Electric Currents |
| namespace | ec |
| status | certified |
| visible | true |