Is gelation a singularity or a flow induced instability?
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911401388277760 |
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| author | Dedola, Manuel Cademartiri, Ludovico |
| author_facet | Dedola, Manuel Cademartiri, Ludovico |
| contents | Gelation in the Smoluchowski coagulation equation is commonly interpreted as a finite-time singularity marked by mass loss or moment divergence. We instead characterize gelation as a loss of dynamical stability of the Smoluchowski flow, quantified through the time-dependent spectrum of the Jacobian along the evolving aggregation dynamics. Studying homogeneous kernels $K(i,j)=(ij)^α$ together with the classical Smoluchowski, we show that gelation is consistently preceded by the appearance of positive real eigenvalues, indicating a loss of local dynamical stability. While non-gelling kernels exhibit only transient finite-size effects, gelling kernels display persistent spectral destabilization associated with macroscopic gel formation. Our results identify gelation as a genuine dynamical instability of the Smoluchowski flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18806 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Is gelation a singularity or a flow induced instability? Dedola, Manuel Cademartiri, Ludovico Soft Condensed Matter Adaptation and Self-Organizing Systems Applications Gelation in the Smoluchowski coagulation equation is commonly interpreted as a finite-time singularity marked by mass loss or moment divergence. We instead characterize gelation as a loss of dynamical stability of the Smoluchowski flow, quantified through the time-dependent spectrum of the Jacobian along the evolving aggregation dynamics. Studying homogeneous kernels $K(i,j)=(ij)^α$ together with the classical Smoluchowski, we show that gelation is consistently preceded by the appearance of positive real eigenvalues, indicating a loss of local dynamical stability. While non-gelling kernels exhibit only transient finite-size effects, gelling kernels display persistent spectral destabilization associated with macroscopic gel formation. Our results identify gelation as a genuine dynamical instability of the Smoluchowski flow. |
| title | Is gelation a singularity or a flow induced instability? |
| topic | Soft Condensed Matter Adaptation and Self-Organizing Systems Applications |
| url | https://arxiv.org/abs/2601.18806 |