Smoluchowski coagulation equation
E52850
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Smoluchowski coagulation equation canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T412551 — 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: Smoluchowski coagulation equation Context triple: [Marian Smoluchowski, knownFor, Smoluchowski coagulation equation]
-
A.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
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B.
On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat
"On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat" is Albert Einstein’s 1905 paper that provided a theoretical explanation of Brownian motion, offering strong evidence for the existence of atoms and molecules.
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C.
Stokes–Einstein relation
The Stokes–Einstein relation is a fundamental equation in statistical physics that links the diffusion coefficient of a particle in a fluid to its size, the fluid’s viscosity, and temperature.
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D.
Boltzmann equation
The Boltzmann equation is a fundamental kinetic theory equation that describes the statistical behavior and time evolution of a dilute gas or particle distribution in phase space due to streaming and collisions.
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E.
Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
- 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: Smoluchowski coagulation equation Target entity description: 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.
-
A.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
B.
On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat
"On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat" is Albert Einstein’s 1905 paper that provided a theoretical explanation of Brownian motion, offering strong evidence for the existence of atoms and molecules.
-
C.
Stokes–Einstein relation
The Stokes–Einstein relation is a fundamental equation in statistical physics that links the diffusion coefficient of a particle in a fluid to its size, the fluid’s viscosity, and temperature.
-
D.
Boltzmann equation
The Boltzmann equation is a fundamental kinetic theory equation that describes the statistical behavior and time evolution of a dilute gas or particle distribution in phase space due to streaming and collisions.
-
E.
Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
integro-differential equation
ⓘ
kinetic equation ⓘ model in statistical physics ⓘ |
| appliesTo |
aerosols
ⓘ
cloud microphysics ⓘ colloidal suspensions ⓘ gelation phenomena ⓘ planetary formation models ⓘ polymerization processes ⓘ |
| assumes |
mean-field approximation
ⓘ
pairwise particle collisions ⓘ spatial homogeneity ⓘ |
| canExhibit | gelation transition ⓘ |
| describes |
binary collisions between particles
ⓘ
cluster aggregation ⓘ particle coagulation ⓘ time evolution of cluster size distribution ⓘ |
| feature |
gain term due to aggregation
ⓘ
loss term due to aggregation ⓘ nonlinear integral term ⓘ |
| field |
applied mathematics
ⓘ
physical chemistry ⓘ soft matter physics ⓘ statistical physics ⓘ |
| hasSolutionType |
scaling solutions
ⓘ
self-similar solutions ⓘ |
| hasSpecialCase |
additive kernel coagulation model
ⓘ
constant kernel coagulation model ⓘ multiplicative kernel coagulation model ⓘ |
| hasVariable |
cluster size distribution
ⓘ
particle concentration as a function of size and time ⓘ |
| influenced | modern coagulation-fragmentation theory ⓘ |
| involves | collision rate between particles ⓘ |
| mathematicalForm | integro-differential equation in time and cluster size ⓘ |
| namedAfter | Marian Smoluchowski ⓘ |
| originatedIn | early 20th century ⓘ |
| relatedTo |
Boltzmann equation
ⓘ
Fokker–Planck equation ⓘ
surface form:
Smoluchowski diffusion equation
fragmentation equations ⓘ population balance equations ⓘ |
| requires | initial cluster size distribution ⓘ |
| studiedIn |
non-equilibrium statistical mechanics
ⓘ
probability theory ⓘ stochastic processes ⓘ |
| usedFor |
analyzing aggregation kinetics
ⓘ
modeling cluster growth ⓘ predicting particle size distributions ⓘ |
| uses | coagulation kernel ⓘ |
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: Smoluchowski coagulation equation Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.