Schutte C.,Mathematics Institute |
Wulkow M.,CiT GmbH
Macromolecular Reaction Engineering | Year: 2010
Population balance models describing not only the chain-length distribution of a polymer but also additional properties like branching or composition are still difficult to solve numerically. For simulation of such systems two essentially different approaches are discussed in the literature: deterministic solvers based on rate equations and stochastic Monte-Carlo (MC) strategies based on chemical master equations. The paper presents a novel hybrid approach to polymer reaction kinetics that combines the best of these two worlds. We discuss the theoretical conditions of the algorithm, describe its numerical realization, and show that, if applicable, it is more efficient than full-scale MC approaches and leads to more detailed information in additional property indices than deterministic solvers. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Ochoa J.G.D.,Pelargusstr. 2 |
Wulkow M.,CiT GmbH
International Journal of Modern Physics C | Year: 2012
The damage of DNA chains by environmental factors like radiation or chemical pollutants is a topic that has been frequently explored from an experimental and a theoretical perspective. Such damages, like the damage of the strands of a DNA chain, are toxic for the cell and can induce mutagenesis or apoptosis. Several models make strong assumptions for the distribution of damages; for instance a frequent supposition is that these damages are Poisson distributed. [L. Ma, J. J. Wagner, W. Hu, A. J. Levine and G. A. Stolovitzki, Proc. Natl. Acad. Sci.PNAS 102, 14266 (2005).] Only few models describe in detail the damage and the mechanisms associated to the formation and evolution of this damage distribution [H. Nikjoo, P. O'neill and D. T. Goodhead, Radiat. Res. 156, 577 (2001).] Nevertheless, such models do not include the repair processes which are continuously active inside the cell. In this work we present a novel model, based on a depolymerization process, describing the distribution of damages on DNA chains coupled to the dynamics associated to its repair processes. The central aim is not to give a final and comprehensive model, but a hint to represent in more detail the complex dynamics involved in the damage and repair of DNA. We show that there are critical parameters associated to this repair process, in particular we show how critical doses can be relevant in deciding whether the cell continues its repair process or starts apoptosis. We also find out that the damage concentration is related to the dose via a power law relation. © 2012 World Scientific Publishing Company.
Nikitin A.N.,Free University of Berlin |
Nikitin A.N.,Institute on Laser and Information Technologies |
Wulkow M.,CiT GmbH |
Schutte C.,Free University of Berlin
Macromolecular Theory and Simulations | Year: 2013
The modeling approach called "numerical fractionation" has been incorporated into a PREDICI model to simulate crosslinking copolymerization. In order to take inhomogeneities of the considered copolymerization into account, the kinetic parameters of the model are proposed to be different for each generation of the numerical fractionation. Using this approach the chain-length dependence of the termination has been incorporated into the model so that even the method of moments could be applied to study crosslinking copolymerization. The styrene/m-divinylbenzene crosslinking copolymerization at low crosslinker content has been simulated. The chain-length dependence of the termination has been found to accelerate the gel point in monovinyl/divinyl copolymerization and must be taken into account for a correct description of the gel points. The modeling approach called "numerical fractionation" has been incorporated into a PREDICI model to simulate crosslinking copolymerization. The kinetic parameters of the model are proposed to be different for each generation of the numerical fractionation. The styrene/m-divinylbenzene copolymerization at low content of the crosslinker is simulated. The chain-length dependence of the termination is found to accelerate the gel point in monovinyl/divinyl copolymerization. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Ali Parsa M.,Queens University |
Kozhan I.,CiT GmbH |
Kozhan I.,Free University of Berlin |
Wulkow M.,CiT GmbH |
Hutchinson R.A.,Queens University
Macromolecular Theory and Simulations | Year: 2014
The distribution of functional groups in polymer chains produced in radical copolymerization by starved-feed semibatch operation is simulated using three different methodologies. Even under perfect control of the overall copolymer composition, a significant fraction of the polymer chains produced contain no functionality. A deterministic model is formulated to separately track the homopolymer chains that are produced without the desired functionality, a Monte Carlo (MC) model is written to represent the system, and a hybrid deterministic/MC approach is taken using new capabilities within the software package PREDICI. The advantages and disadvantages of each approach are discussed. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.