Construct · 2 fields · 2 citations

Where does coarsening collide?

One name. Different field. Different construct. One map.

● jingle · one word, two constructs Nearest construct by meaning·not indexed
coarsening2 CONSTRUCTSOstwald ripeningLIFSHITZ · OSTWALD RIPENGraph coarseningBARKER · GRAPH COARSEN

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1961Ostwald ripening2021Graph coarsening
2026

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Materials Science

Large precipitates grow at the expense of small ones to cut interfacial energy

In materials science, coarsening (Ostwald ripening) is the process by which, in a two-phase mixture, larger particles grow while smaller ones dissolve, reducing the total interfacial energy and raising the average particle size over time. Ilya Lifshitz and Vitaly Slyozov gave the classic diffusion-limited theory in The kinetics of precipitation from supersaturated solid solutions in the Journal of Physics and Chemistry of Solids. The referent is energy-driven growth of a microstructure's features, not the deliberate algorithmic shrinking of a graph.[1]

Unit
One mean particle radius, growing in proportion to the cube root of time
Recovery means
Age a two-phase alloy and watch the mean precipitate size grow while small particles vanish
Measured by
Tracked by microscopy of the particle size distribution; mean radius cubed grows linearly in time

Computer Science

Algorithmically reducing a graph to a smaller one that preserves its structure

In computational science, graph coarsening is the deliberate construction of a smaller graph from a larger one, by aggregating nodes, so the reduced graph preserves key structural or spectral properties and can be solved or analyzed more cheaply, as in multilevel and multigrid methods. Andrew Barker and colleagues develop spectral coarsening in Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation in the SIAM Journal on Scientific Computing. The referent is an engineered reduction of a graph, not the energy-driven growth of particles in an alloy.[2]

Unit
One coarsening level, mapping fine nodes onto coarse aggregates
Recovery means
Take a large graph and build a reduced version by grouping nodes into aggregates
Measured by
Assessed by the coarsening ratio and how well the coarse graph preserves spectra and solutions

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Nearby collisions

Lifshitz-Slyozov-Wagner theory1 fields · 1 citationsanchor · a standalone constructbed armoring1 fields · 1 citationsanchor · a standalone constructcoarsening at random1 fields · 1 citationsanchor · a standalone construct

References

  1. Lifshitz, I. M., & Slyozov, V. V. (1961). The kinetics of precipitation from supersaturated solid solutions. Journal of Physics and Chemistry of Solids, 19(1–2), 35–50. https://doi.org/10.1016/0022-3697(61)90054-3
  2. Barker, A. T., Gelever, S. V., Lee, C. S., Osborn, S. V., & Vassilevski, P. S. (2021). Multilevel spectral coarsening for graph Laplacian problems with application to reservoir simulation. SIAM Journal on Scientific Computing, 43(4), A2737–A2765. https://doi.org/10.1137/19m1296343

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