A complete analytical solution to the integro‐differential model describing the nucleation and evolution of ellipsoidal particles

DOI10.1002/mma.7927zbMath1527.82057OpenAlexW3209069854MaRDI QIDQ6087651

Margarita A. Nikishina, Dmitri V. Alexandrov

Publication date: 12 December 2023

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.7927

zbMATH Keywords

integro-differential equationsphase transformationssaddle-point methodsupersaturated solutionsapplied mathematical modeling

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Statistical mechanics of liquids (82D15) Integro-partial differential equations (35R09)

Cites Work

• Unnamed Item
• Unnamed Item
• Directional solidification of binary melts with a non-equilibrium mushy layer
• Nucleation and particle growth with fluctuating rates at the intermediate stage of phase transitions in metastable systems
• Transient nucleation kinetics of crystal growth at the intermediate stage of bulk phase transitions
• A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals
• Nucleation and evolution of spherical crystals with allowance for their unsteady-state growth rates
• The shape of dendritic tips
• Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics
• Dissolution of polydisperse ensembles of crystals in channels with a forced flow
• From nucleation and coarsening to coalescence in metastable liquids
• Mathematical modeling of the growth of ellipsoidal crystals in metastable melts and solutions
• The influence of Brownian coagulation on the particle-size distribution function in supercooled melts and supersaturated solutions
• On the theory of the unsteady-state growth of spherical crystals in metastable liquids
• Effects of nonlinear growth rates of spherical crystals and their withdrawal rate from a crystallizer on the particle-size distribution function
• On the theory of crystal growth in metastable systems with biomedical applications: protein and insulin crystallization
• Phase transformations in metastable liquids combined with polymerization
• Relaxation dynamics of the phase transformation process at its ripening stage
• Nucleation and crystal growth in binary systems
• On the theory of transient nucleation at the intermediate stage of phase transitions

This page was built for publication: A complete analytical solution to the integro‐differential model describing the nucleation and evolution of ellipsoidal particles