@article{HungenbergSchwedeWulkowetal.2021, author = {Hungenberg, Klaus-Dieter and Schwede, Christian and Wulkow, Michael and Wulkow, Niklas}, title = {Determination of reactivity ratios for acrylic acid and its dimer from classical parameter estimation and Bayesian approach}, journal = {Canadian Journal of Chemical Engineering}, doi = {https://doi.org/10.1002/cjce.24330}, pages = {1 -- 10}, year = {2021}, abstract = {The reactivity ratios of acrylic acid (AA, M1) and its dimer beta-acroyloxypropionic acid (diAA, M2) are determined from cumulative copolymerization data by two different methods: classical parameter estimation (PE) by minimizing the objective function and a Bayesian analysis. Classical PE gives r1 =0.74 and r2 = 1.23 at the minimum of the residual. From the Bayesian analysis, the probability distribution of the parameter sets is obtained, revealing the existence of parameter sets with rather the same probability. The influence of the number of data and the size of the measurement error are discussed.}, language = {en} } @article{WulkowTelgmannHungenbergetal.2021, author = {Wulkow, Niklas and Telgmann, Regina and Hungenberg, Klaus-Dieter and Sch{\"u}tte, Christof and Wulkow, Michael}, title = {Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples}, volume = {30}, journal = {Macromolecular Theory and Simulations}, doi = {10.1002/mats.202100017}, year = {2021}, abstract = {Two different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two-article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered.}, language = {en} } @misc{DeuflhardHuisingaJahnkeetal.2007, author = {Deuflhard, Peter and Huisinga, Wilhelm and Jahnke, Tobias and Wulkow, Michael}, title = {Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9471}, number = {07-04}, year = {2007}, abstract = {\begin{abstract} In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signalling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equat ion, also known as the chemical master equation (CME). Up to now, the CME has almost exclusively been treated by Monte-Carlo techniques, the most prominent of which is the simulation algorithm suggest ed by Gillespie in 1976. Since this algorithm requires an update for each single reaction event, realizations can be computationally very costly. As an alternative, we here propose a novel approach, which focuses on the discrete partial differential equation (PDE) structure of the CME and thus allows to adopt ideas from adaptive discrete Galerkin methods (as designed by two of the present authors in 1989), which have proven to be highly efficient in the mathematical modelling of polyreaction kinetics. Among the two different options of discretizing the CME as a discrete PDE, the method of lines approach (first space, then time) and the Rothe method (first time, then space), we select the latter one for clear theoretical and algorithmic reasons. First numeric al experiments at a challenging model problem illustrate the promising features of the proposed method and, at the same time, indicate lines of necessary further research. \end{abstract}}, language = {en} } @article{HornWulkow2005, author = {Horn, H. and Wulkow, Michael}, title = {Simulation von Wachstum und Abtrag der Biomasse - Eine exemplarische Betrachtung f{\"u}r eine 2D-Modellierung}, volume = {77}, journal = {Chem. Ing. Technik}, number = {4}, pages = {418 -- 424}, year = {2005}, language = {en} } @article{HornWulkow1996, author = {Horn, H. and Wulkow, Michael}, title = {Modellierung von Einleitungen in kleine Fließgew{\"a}sser}, volume = {137}, journal = {gwf Wasser Abwasser}, year = {1996}, language = {en} } @article{HuisingaTelgmannWulkow2006, author = {Huisinga, Wilhelm and Telgmann, R. and Wulkow, Michael}, title = {The virtual lab approach to pharmacokinetic}, volume = {11}, journal = {Drug Discov Today}, pages = {800 -- 805}, year = {2006}, language = {en} } @article{HungenbergChenZhangetal.2001, author = {Hungenberg, K.-D. and Chen, C.-C. and Zhang, F. and Wulkow, Michael and Stubbe, G. and Nieken, U.}, title = {Design of Polymer Processes Using the Coupling of Commercial Simulation Packages Polymers Plus and PREDICI}, volume = {137}, journal = {DECHEMA Monographs}, pages = {237 -- 245}, year = {2001}, language = {en} } @article{HungenbergKnollWulkow1997, author = {Hungenberg, K.-D. and Knoll, K. and Wulkow, Michael}, title = {Absolute Propagation Rate Coefficients in Radical Polymerization from Gel Permeation Chromatography of Polymers Produced by Intermittent Initiation}, volume = {6}, journal = {Macromol. Theory Simul.}, year = {1997}, language = {en} } @article{IedemaWulkowHoefsloot2007, author = {Iedema, P. and Wulkow, Michael and Hoefsloot, H.}, title = {Conditional Monte Carlo sampling to find branching architectures of polymers from radical polymerizations with transfer to polymer and recombination termination}, volume = {48}, journal = {Polymer}, number = {6}, pages = {1770 -- 1784}, year = {2007}, language = {en} } @article{IedemaWulkowHoefsloot:2000, author = {Iedema, P. and Wulkow, Michael and Hoefsloot:, H.}, title = {Modeling Molecular Weight and Degree of Branching Distribution of low density Polyethylene}, volume = {33}, journal = {Macromolecules}, pages = {7173 -- 7184}, year = {2000}, language = {en} } @article{KatzerPauerMoritzetal.2012, author = {Katzer, J. and Pauer, W. and Moritz, H.-U. and Wulkow, Michael}, title = {Thermal polymerization of styrene Part B}, volume = {6}, journal = {Macromol. React. Eng}, pages = {225 -- 238}, year = {2012}, language = {en} } @article{LinGrimmWulkowetal.2008, author = {Lin, P.-J. and Grimm, L. and Wulkow, Michael and Hempel, D. and Krull, R.}, title = {Population Balance Modeling of the Conidial Aggregation of Aspergillus niger}, volume = {99}, journal = {Biotechnology and Bioengineering}, number = {2}, pages = {341 -- 350}, year = {2008}, language = {en} } @article{MuellerYanWulkow1997, author = {M{\"u}ller, A. and Yan, D. and Wulkow, Michael}, title = {Molecular Parameters of Hyperbranched Polymers Made by Self-condensing Vinyl Polymerization, 1. Molecular weight distribution}, volume = {30}, journal = {Macromolecules}, pages = {7015}, year = {1997}, language = {en} } @article{OchoaWulkow2012, author = {Ochoa, J.G. and Wulkow, Michael}, title = {DNA damages as a Depolymerization Process}, volume = {23}, journal = {International Journal of Modern Physics C}, number = {03}, pages = {1250018 -- 1}, year = {2012}, language = {en} } @article{ReuterKrauseWulkowetal.2003, author = {Reuter, H. and Krause, G. and Wulkow, Michael and M{\"o}nig, A. and Horn, H.}, title = {A water quality management tool for river basins}, volume = {48}, journal = {Wat. Sci. Techn.}, number = {10}, pages = {47 -- 53}, year = {2003}, language = {en} } @article{ReynhoutMeuldijkDrinkenburgetal.2005, author = {Reynhout, X. and Meuldijk, J. and Drinkenburg, B. and Iedema, P. and Wulkow, Michael}, title = {A Novel Method to Model Emulsion Polymerization Kinetics}, volume = {44}, journal = {Polymer-Plastics Tech. Eng.}, number = {4}, pages = {707 -- 740}, year = {2005}, language = {en} } @article{SchmidtBuschLilgeetal.2005, author = {Schmidt, Christian-Ulrich and Busch, Markus and Lilge, Dieter and Wulkow, Michael}, title = {Detailed Molecular Structure Modeling - A Path Forward to Designing Application Properties of ldPE}, volume = {290}, journal = {Macromolecular Materials and Engineering}, pages = {404}, year = {2005}, language = {en} } @article{SchuetteWulkow2010, author = {Sch{\"u}tte, Christof and Wulkow, Michael}, title = {A hybrid Galerkin-Monte-Carlo approach to higher-dimensional population balances in polymerization kinetics}, volume = {4}, journal = {Macromol. React. Eng.}, pages = {562 -- 577}, year = {2010}, language = {en} } @article{TeichmannLiebeltReuschenbachetal.2001, author = {Teichmann, L. and Liebelt, U. and Reuschenbach, P. and Wulkow, Michael and Horn, H.}, title = {Two dimensional simulation of mass transport and nitrification in the river Rhine}, volume = {1}, journal = {Eng. Life Sci.}, number = {4}, pages = {145 -- 149}, year = {2001}, language = {en} } @article{Wulkow2008, author = {Wulkow, Michael}, title = {Feature article - Computer Aided Modeling of Polymer Reaction Engineering - The Status of Predici, 1 - Simulation}, volume = {2}, journal = {Macromol. React. Eng.}, pages = {461 -- 494}, year = {2008}, language = {en} } @article{Wulkow1996, author = {Wulkow, Michael}, title = {Feature article - The Simulation of Molecular Weight Distributions in Polyreaction Kinetics by Discrete Galerkin Methods}, volume = {5}, journal = {Macromol. Theory Simul.}, pages = {393 -- 416}, year = {1996}, language = {en} } @article{WulkowBuschDavisetal.2004, author = {Wulkow, Michael and Busch, Markus and Davis, Thomas P. and Barner-Kowollik, Christopher}, title = {Implementing the Reversible Addition Fragmentation Chain Transfer (RAFT) Process in Predici.}, volume = {42}, journal = {Journal of Polymer Science}, pages = {1441}, year = {2004}, language = {en} }