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SUMMARY:Seminar series on Coagulation and fragmentation dynamics
DTSTART:20260929T080000Z
DTEND:20261020T150000Z
DTSTAMP:20261015T235400Z
UID:indico-event-16068@indico.math.cnrs.fr
DESCRIPTION:A short series of seminars will run throughout the fall 2026. 
 The seminars will run in a hybrid format\, taking place at the Institut de
  Mathématiques de Toulouse and streamed on the links given below. Each se
 minar lasts 1 hour\, including questions.\n \n\n\n\n29 Sep\n11:15 a.m.\nI
 nmaculada Berral(University of Granada)\n \nQuantitative Metastability in
  the Linear Becker–Döring Equations\n \n\n\n6 Oct\n11:15 a.m.\nEugenia
  Franco (University of Bonn)\nLink to the streaming\nLong-time behaviour o
 f a two-component coagulation model for rouleau formation\n \n\n\n20 Oct\
 n9:50 a.m.\nMarina Ferreira (University of Toulouse\, CNRS)\n \nLocalizat
 ion and fluctuations in non-equilibrium multicomponent coagulating systems
 \n \n\n\n\n \nAbstracts:\nInmaculada Berral: Quantitative Metastability 
 in the Linear Becker–Döring Equations\nThe Becker–Döring equations d
 escribe the dynamics of cluster formation and have long been known to exh
 ibit metastable behaviour near the critical monomer concentration. In the
  linear setting\, where the monomer concentration is fixed\, Penrose [3\,
  2] and Kreer [1] established fundamental results on the metastable regim
 e and the long-time behaviour of solutions. In this talk\, we revisit thi
 s metastable behaviour from a quantitative perspective. We study the conve
 rgence of solutions to equilibrium in the subcritical and supercritical r
 egimes and obtain explicit estimates for the exponential relaxation rate. 
 Our approach combines entropy methods with discrete Hardy inequalities an
 d relates the convergence rate to the spectral properties of the associat
 ed linear operator.We show that\, as the critical concentration is approac
 hed\, the relaxation rate becomes small\, providing a quantitative descri
 ption of the metastable time scale. In the supercritical regime\, we also
  identify the role of the critical cluster size and the exponentially sma
 ll flux through it\, which provides a natural interpretation of the slow 
 relaxation.\n \nEugenia Franco: Long-time behaviour of a two-component co
 agulation model for rouleau formation\nWe study a two-component coagulatio
 n equation that models the aggregation of rouleaux in blood. We consider 
 product kernels that have homogeneity 2 and we characterize the initial d
 ata that lead to gelation. We prove that\, when gelation occurs\, the solu
 tion to the two-componentcoagulation equation localizes along a direction 
 of the space of cluster as t approaches the gelation time 0<T∗ <∞. Th
 e localization direction is determined by the initial datum. We also prove
  that the solutionconverges to a self-similar solution along the direction
  of localization.\n \nMarina Ferreira: Localization and fluctuations in n
 on-equilibrium multicomponent coagulating systems\nWe consider the multico
 mponent Smoluchowski coagulation equation under non-equilibrium conditions
  induced either by a source term or via a constant flux constraint. We pro
 ve that the corresponding stationary non-equilibrium solutions have a univ
 ersal localization property: they asymptotically localize into a direction
  determined by the source or by a flux constraint. As a consequence\, the 
 ratio between monomers of a given type to the total number of monomers in 
 the cluster becomes ever closer to a predetermined ratio as the cluster si
 ze is increased. Moreover\, under an extra symmetry assumption on the coag
 ulation kernel\, the fluctuations around the localization direction of the
  quotient of the multicomponent solution and the one-component solution co
 nverge to a multivariate Gaussian probability density function\, which is 
 independent of the coagulation kernel. \n \n\nhttps://indico.math.cnrs.f
 r/event/16068/
URL:https://indico.math.cnrs.fr/event/16068/
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