Abstract
A Johnson—Mehl tessellation arises as a random division of a given bounded region in a d-dimensional Euclidean space, generated by a stochastic birth-and-growth process, also known as a germ-grain process in stochastic geometry. A typical example is the crystallization of a polymer from an amorphous liquid phase by cooling; in this case a grain (crystal) is formed by growth of a germ (nucleus) born at a random time and space location.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
L. Ambrosio, N. Fusco, D. PallaraFunctions of Bounded Variation and Free Discontinuity ProblemsOxford Clarendon Press, 2000.
A.J. Baddeley, Acrash course in stochastic geometryin Stochastic Geometry. Likelihood and Computation (O.E. Barndorff-Nielsen et al. Eds.), Chapman&Hall/CRC, Boca Raton, 1999.
V. Capasso, R. Escobedo, C. SalaniMoving bands and moving boundaries for an hybrid model of crystallization of polymers.In this volume (2003).
V. Capasso, A. MichelettiLocal spherical contact distribution function and local mean densities for inhomogeneous random sets. Stochastics and Stoch. Rep. 71(2000), 51–67.
V. Capasso, A. MichelettiThe hazard function of an inhomogeneous birth-andgrowth process.Preprint n.39/2001, Dip. di Matematica, Universita’ di Milano, 2001.
V.Capasso, A.Micheletti, M.BurgerDensities of n-facets of incomplete Johnson-Mehl tessellations generated by inhomogeneous birth-and-growth processes.Quaderno n. 38/2001, Dip. di Matematica, Università di Milano.
V.Capasso, Ed.Mathematical Modelling for Polymer Processing. Polymerization Crystallization ManufacturingSpringer, 2002.
Johnson, W.A., Mehl, R.F.Reaction Kinetics in processes of nucleation and growth.Trans. A.I.M.M.E.135(1939), 416–458.
J.L.MeijeringInterface area edge length,and number of vertices in crystal aggregates with random nucleation. Philips Res. Rep. 8 (1953), 270–290.
A. MichelettiThe surface density of a random Johnson-Mehl tessellationQuaderno n. 17/2001, Dip. di Matematica, Università di Milano, 2001.
A. Micheletti, V. Capasso, G. EderThe density of the n-facets of an incomplete Johnson-Mehl tessellation.Preprint of the Institute for Industrial Mathematics, Johannes-Kepler University of Linz (Austria), 1997.
J. MollerRandom Johnson-Mehl tessellations. Adv. Appl. Prob. 24 (1992), 814–844.
J. MollerTopics in Voronoi and Johnson-Mehl tessellations in Stochastic Geometry. Likelihood and Computation (O.E. Barndorff-Nielsen et al. Eds.), Chapman&Hall/CRC, Boca Raton, 1999.
Stoyan, D., Kendall, W.S., MeckeJ. Stochastic Geometry and its ApplicationJohn Wiley & Sons, New York, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Basel AG
About this paper
Cite this paper
Micheletti, A., Capasso, V. (2003). The Stochastic Geometry of the Crystallization Process of Polymers. In: Colli, P., Verdi, C., Visintin, A. (eds) Free Boundary Problems. ISNM International Series of Numerical Mathematics, vol 147. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7893-7_16
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7893-7_16
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9613-9
Online ISBN: 978-3-0348-7893-7
eBook Packages: Springer Book Archive