Cahn–Hilliard equation
E574814
fourth-order partial differential equation
mathematical model of phase separation
partial differential equation
phase-field model
The Cahn–Hilliard equation is a nonlinear partial differential equation that models phase separation and coarsening in binary mixtures and other systems undergoing spinodal decomposition.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Cahn–Hilliard equation canonical | 5 |
| Cahn–Hilliard free energy functional | 1 |
| Cahn–Hilliard theory of phase separation | 1 |
| “Spinodal Decomposition” | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6214872 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cahn–Hilliard equation Context triple: [John W. Cahn, knownFor, Cahn–Hilliard equation]
-
A.
Smoluchowski coagulation equation
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
-
B.
Stefan problem
The Stefan problem is a classical mathematical model in heat transfer that describes how phase-change boundaries, such as the interface between ice and water, move over time.
-
C.
Monge–Ampère equation
The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
-
D.
Charney equation
The Charney equation is a fundamental quasi-geostrophic equation in atmospheric dynamics that describes large-scale Rossby waves and mid-latitude weather patterns on a rotating planet.
-
E.
Gibbs dividing surface
The Gibbs dividing surface is an idealized mathematical interface in thermodynamics used to separate phases and define interfacial properties such as surface tension and adsorption.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Cahn–Hilliard equation Target entity description: The Cahn–Hilliard equation is a nonlinear partial differential equation that models phase separation and coarsening in binary mixtures and other systems undergoing spinodal decomposition.
-
A.
Smoluchowski coagulation equation
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
-
B.
Stefan problem
The Stefan problem is a classical mathematical model in heat transfer that describes how phase-change boundaries, such as the interface between ice and water, move over time.
-
C.
Monge–Ampère equation
The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
-
D.
Charney equation
The Charney equation is a fundamental quasi-geostrophic equation in atmospheric dynamics that describes large-scale Rossby waves and mid-latitude weather patterns on a rotating planet.
-
E.
Gibbs dividing surface
The Gibbs dividing surface is an idealized mathematical interface in thermodynamics used to separate phases and define interfacial properties such as surface tension and adsorption.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
fourth-order partial differential equation
ⓘ
mathematical model of phase separation ⓘ partial differential equation ⓘ phase-field model ⓘ |
| appliesTo |
spinodally unstable mixtures
ⓘ
systems with conserved order parameter ⓘ |
| basedOn |
Ginzburg–Landau free energy functional
ⓘ
linked to:
Ginzburg–Landau theory of superconductivity
variational principles ⓘ |
| describes |
coarsening dynamics
ⓘ
conserved order parameter dynamics ⓘ diffusion-driven phase separation ⓘ phase separation in binary mixtures ⓘ spinodal decomposition ⓘ |
| field |
applied mathematics
ⓘ
computational physics ⓘ materials science ⓘ statistical physics ⓘ thermodynamics ⓘ |
| governs |
evolution of composition field
ⓘ
evolution of order parameter field ⓘ |
| hasCharacteristic |
double-well free energy density
ⓘ
fourth-order spatial derivatives ⓘ gradient-flow structure ⓘ mass-conserving dynamics ⓘ nonlinear chemical potential ⓘ |
| hasComponent |
bulk free energy density
ⓘ
gradient energy coefficient ⓘ mobility coefficient ⓘ |
| hasForm |
conservation law for order parameter
ⓘ
time derivative equals Laplacian of chemical potential ⓘ |
| namedAfter |
John E. Hilliard
ⓘ
John W. Cahn ⓘ |
| publishedIn | Acta Metallurgica ⓘ |
| relatedTo |
Allen–Cahn equation
ⓘ
Model B in Hohenberg–Halperin classification ⓘ phase-field models of solidification ⓘ |
| solvedBy |
finite difference methods
ⓘ
finite element methods ⓘ spectral methods ⓘ |
| usedIn |
binary fluid mixtures
ⓘ
image inpainting ⓘ lithium-ion battery modeling ⓘ microstructure evolution modeling ⓘ multiphase flow modeling ⓘ polymer blend phase separation ⓘ spinodal decomposition in alloys ⓘ topology optimization ⓘ |
| yearProposed | 1958 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Cahn–Hilliard equation Description of subject: The Cahn–Hilliard equation is a nonlinear partial differential equation that models phase separation and coarsening in binary mixtures and other systems undergoing spinodal decomposition.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.