Bergische Universität Wuppertal Fakultät für Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis (AMNA)

People Research Publications Teaching

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Im Modellierungsseminar diskutieren wir Fragestellungen der Physik, der Biologie, der Geologie, der Wirtschaft ... und lernen dadurch die Mathematik von einer völlig neuen Seite kennen: Mathematik ist in vielen Bereichen unseres Lebens enthalten!

Im diesem Modellierungsseminar diskutieren und lösen die TeilnehmerInnen in Kleingruppen mit Hilfe der Mathematik Probleme und Phänomene aus der Biologie (Räuber-Beute Modelle, Muster in Tierfellen, usw. ). Die im Seminar erhaltenen Modelle werden anhand von frei zugänglichen Daten kalibriert. Sie erlauben einen Ausblick auf die (mögliche) zukünftige Entwicklungen und auch den Einfluss von Parametern auf die Problemgrössen.

Dieses Seminar steht in gleicher Weise MathematikerInnen, WirtschaftsmathematikerInnen, LehramtskandidatInnen und IngenieurInnen offen.

Schwerpunkt dieses Seminar werden nichtlineare gewöhnliche bzw. partielle Differentialgleichungen (Modellierung, Analysis und Numerik) sein.

Die Daten zur Kalibrierung der Modelle wurden uns vom Statistischen Bundesamt Deutschland, Zweigstelle Bonn zur Verfügung gestellt.

Literatur:

• J. Banasiak, M. Lachowicz, Methods of Small Parameter in Mathematical Biology, Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Basel, 2014.
• E. Beltrami, Von Krebsen und Kriminellen. Mathematische Modelle in Biologie und Soziologie, Vieweg 1993.
• F. Brauer, C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Texts in Applied Mathematics 40, Springer, 2012.
• C.S. Chou, A. Friedman, Introduction to Mathematical Biology, Springer Undergraduate Texts in Mathematics and Technology, Springer, 2016.
• A. Goriely, The Mathematics and Mechanics of Biological Growth, Interdisciplinary Applied Mathematics 45, Springer, 2017.
• K.P. Hadeler, Topics in Mathematical Biology, Lecture Notes on Mathematical Modelling in the Life Sciences, Springer, 2018.
• J. Istas, Mathematical Modeling for the Life Sciences, Universitext, Springer, 2005.
• D.S. Jones, M. Plank, B.D. Sleeman, Differential Equations and Mathematical Biology, Second Edition, Chapman & Hall/CRC Mathematical and Computational Biology, 2009.
• I.Z. Kiss, J.C. Miller, P.L. Simon, Mathematics of Epidemics on Networks - From Exact to Approximate Models, Interdisciplinary Applied Mathematics 46, Springer 2017.
• S.A. Levin, G.T. Hallam, L.J. Gross (eds.), Applied Mathematical Ecology, Biomathematics 18, Springer 1989.
• M.A. Lewis, S.V. Petrovskii, J.R. Potts, The Mathematics Behind Biological Invasions, Interdisciplinary Applied Mathematics 44, Springer 2016.
• P. Magal, S. Ruan (eds.), Structured Population Models in Biology and Epidemiology, Mathematical Biosciences Subseries, Springer, 2008.
• M. Martcheva, An Introduction to Mathematical Epidemiology, Texts in Applied Mathematics 61, Springer, 2015.
• J. Müler, C. Kuttler, Methods and Models in Mathematical Biology: Deterministic and Stochastic Approaches, Lecture Notes on Mathematical Modelling in the Life Sciences, Springer, 2015.
• J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989.
• J.D. Murray, Mathematical Biology : I. An Introduction, Interdisciplinary Applied Mathematics, Springer, 2002.
• J.D. Murray, Mathematical Biology : II. Spatial Models and Biomedical Applications, Interdisciplinary Applied Mathematics, Springer, 2003.
• J.W. Prüß, R. Schnaubelt, R. Zacher, Mathematische Modelle in der Biologie. Deterministische homogene Systeme, Birkhäuser, 2008.
• R.W. Shonkwiler, J. Herod, Mathematical Biology - An Introduction with Maple and Matlab, Undergraduate Texts in Mathematics, Springer 2009.
• S.H. Strogatz, Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, 2001.
• F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Universitext, Springer, 1996.

  Tierfelle : Musterbildung in Reaktions-Diffusions Gleichungen

Wie modelliert man die Entstehung von Streifen oder Flecken bei Tierfellen?

• J.D. Murray, How the leopard gets its spots, Scientific American, March 1988, p. 80.
• J.D. Murray, Mathematical Biology, Springer, 1989, Kapitel 14.
• A. Gierer, H. Meinhardt, A theory of biological pattern formation. Kybernetik 12 (1972), 30-39.

Wie

• A. Ghasemabadi, Stability and bifurcation in a generalized delay prey-predator model, Nonlinear Dyn. 90 (2017), 2239-2251.
• P. Magal, S. Ruan (eds.), Structured Population Models in Biology and Epidemiology, Mathematical Biosciences Subseries, Springer, 2008.
• D. Ludwig, D.D. Jones, C.S. Holling, Qualitative Analysis of Insect Outbreaks Systems: The Spruce Budworms and Forrest, Journal of Animal Ecology 47 (1978), 315-322
• P. Arriola, I. Mijares-Bernal, J.A. Ortiz-Navarro, R.A. Saenz, Dynamics of the Spruce Budworm Population Under the Action of Predation and Insecticides, Working paper BU-1517-M, 2000.
• Insect Outbreak Model: Spruce Budworm, Chapter 1.2 in: J.D. Murray, Mathematical Biology, Springer, 1989.
• J. Gani, R.J. Swift, Prey-predator models with infected prey and predators, Discrete & Continuous Dynamical Systems - A 33 (2013), 5059-5066.
• J.C. Marques, H. Malchow, L.A.D. Rodrigues, D.C. Mistro, The effects of demographic noise on pattern formation in a space- and time-discrete predator-prey system with strong Allee effect in the prey. Bulletin of Mathematical Biology, submitted, 2017.

Wie

• C.W. Clark, Bioeconomic Modeling and Resource Management, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• R. McKelvey, Common Property and the Conservation of Natural Resources, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• M. Mangel, Information and Area-Wide Control in Agricultural Ecology, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.

Wie

• H.W. Hethcote, Three Basic Epidemiological Models, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• A.P. Dobson, The Population Boilogy of Parasitic Helminths in Animal Populations, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• J.L. Aron, Simple Versus Complex Epidemiological Models, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• H.W. Hethcote, S.A. Levin, Periodicity in Epidemiological Models, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.

Wie modelliert man Röteln oder humane Rotaviren?

• G.González-Parra, H.M. Dobrovolny, D.F. Aranda, B. Chen-Charpentier, R.A. Guerrero Rojas, Quantifying rotavirus kinetics in the REH tumor cell line using in vitro data, Virus Research 244 (2018), 53-63.
• H.W. Hethcote, Rubella, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• W.-M. Liu, S.A. Levin, Influenza and Some Related Mathematical Models, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• C. Castillo-Chavez, Review of Recent Models of HIV/AIDS Transmission, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• R.M. May, R.M. Anderson, The Transmission Dynamics of Human Immunodeficiency Virus (HIV), In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.

Wie

• S.A. Levin, Models in Ecotoxicology: Methodological Aspects, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• R.V. Thomann, Deterministic and Statistical Models of Chemical Fate in Aquatic Systems, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• R.R. Lassiter, S.A.L.M. Kooijman, Effects of Toxicants on Aquatic Populations, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.

Wie

• L.J. Gross, Mathematical Models in Plant Biology: An Overview, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• J. Impagliazzo, Stable Population Theory and Applications, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• R.M. Nisbet, W.S.C. Gurney, J.A.J. Metz, Stage Structure Models Applied in Evolutionary Ecology, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.
• C. Castillo-Chavez, Some Applications of Structured Models in Population Dynamics, In: S.A. Levin, T.G. Hallam, L.J. Gross (eds.) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, 1989.

Wie modelliert man ...

• M.J. Poulin, P.J. Liang, P.A. Robbins, Dynamics of the cerebral blood flow response to step changes in end-tidal PCO2 and PO2 in humans, J. Appl. Physiol. 81 (1996), 1084-1095.
• M.J. Poulin, P.J. Liang, P.A. Robbins. Fast and slow components of cerebral blood flow response to step decreases in end-tidal PCO2 in humans, J. Appl. Physiol. 85 (1998), 388-397.

Wie modelliert man ...

• Continuous Population Models for Single Species, in: J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989, Kapitel 1, pp. 1-43.
• L. Garnier, F. Simon-Plas, P. Thuleau, J.-P. Agnel, J.-P. Blein, R. Ranjeva, J.-L. Montillet, Cadmium affects tobacco cells by a series of three waves of reactive oxygen species that contribute to cytotoxicity, Plant, Cell & Environment 29(10) (2006), 1956-1969.
• H. Safuan, I.N. Towers, Z. Jovanoski , H.S. Sidhu, A simple model for the total microbial biomass under occlusion of healthy human skin, 19th International Congress on Modelling and Simulation, Perth, Australia, December 12-16, 2011, pp. 733-739.
• K.E. Emmert, P. White, K. Sims, Continuous-time, stage-structured, multiple-species model with applications to amphibians, Applied Mathematics and Computation 216(4) (2010), 1109-1121.

Wie modelliert man ...

• Discrete Population Models for Single Species, in: J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989, Kapitel 2.
• A. Georgescu, L. Palese, G. Raguso, Dynamical Approach in Biomathematics, ROMAI J., 2, 2(2006), 63-76.

Wie modelliert man ...

• Models for Interacting Populations, in: J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989, Kapitel 3.
• A. Saikh, N.H. Gazi, Mathematical analysis of a predator-prey eco-epidemiological system under the reproduction of infected prey, J. Appl. Math. Comput. (2017).
• S.H.A. Khoshnaw, Dynamic Analysis of a Predator and Prey Model with Some Computational Simulations, arXiv.org, September 2017.
• A. Ben Saad, O. Boubaker, A New Fractional-Order Predator-Prey System with Allee Effect, in: A. Azar, S. Vaidyanathan, A. Ouannas (eds), Fractional Order Control and Synchronization of Chaotic Systems. Studies in Computational Intelligence, vol 688. Springer, 2017, pp. 857-877.

Wie modelliert man bei Schildkröten, Eidechsen und Krokodilen.

• Temperature-Dependent Sex Determination (TSD): Crocodilian Survivorship, Chapter 4 in: J.D. Murray (ed.), Mathematical Biology, Interdisciplinary Applied Mathematics 17, Springer, 1993.
• J.W. Lang, H.V. Andrews, Temperature-dependent sex determination in crocodilians, Journal of Experimental Zoology 270(1) (1994), 28-44.
• M.A. Ewert, D.R. Jackson, C.E. Nelson, Patterns of temperature-dependent sex determination in turtles, Journal of Experimental Zoology 270(1) (1994), 3-15.
• D.E. Woodward, J.D. Murray, On the effect of temperature-dependent sex determination on sex ratio and survivorship in crocodilians, Proc. R. Soc. Lond. B: Biological Sciences Volume 252, Issue 1334, 149-155
• N. Pezaro, J.S. Doody, M.B. Thompson, The ecology and evolution of temperature-dependent reaction norms for sex determination in reptiles: a mechanistic conceptual model, Biological Reviews 92(3) (2017), 1348-1364.
• M.V.P. Marcó, P. Leiva, J.L. Iungman et al., New Evidence Characterizing Temperature-dependent Sex Determination in Broad-snouted Caiman, Caiman latirostris, Herpetological Conservation and Biology 12 (2017), 78-84.
• A.H. Escobedo-Galván, M.A. López-Luna, F.G. Cupul-Magaña, Thermal fluctuation within nests and predicted sex ratio of Morelet's Crocodile, Journal of Thermal Biology 58 (2016), 23-28.
• R.-J. Spencer, F.J. Janzen, A novel hypothesis for the adaptive maintenance of environmental sex determination in a turtle, Proc. R. Soc. B 281: 20140831.

Wie modelliert man ...

• Reaction Kinetics, in: J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989, Kapitel 6.
• B. Emerick, G. Schleiniger, B.M. Boman, Multi-scale modeling of APC and β-catenin regulation in the human colonic crypt, Journal of Mathematical Biology (2018), 1-34.

Wie modelliert man ...

• Biological Oscillators and Switches, in: J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989, Kapitel 7.
• C. Monzel,C. Vicario, J. Piehler, M. Coppey, M. Dahan, Magnetic control of cellular processes using biofunctional nanoparticles, Chemical Science, (2017), 8, 7330.
• A. Mogilner, R. Wollman, W.F. Marshall, Quantitative Modeling in Cell Biology: What Is It Good for?, Developmental Cell 11(3) (2006), 279-287.
• H. Ben Amor, N. Glade, C. Lobos, et al., The Isochronal Fibration: Characterization and Implication in Biology, Acta Biotheoretica 58(2-3) (2010), 121-142.

Wie modelliert man ...

• Belousov-Zhabotinskii Oscillating Reactions, in: J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989, Kapitel 8.
• M. Orlik, Introduction to the dynamic self-organization of chemical systems Part II: Dynamic instabilities in selected chemical systems, ChemTexts (2017) 3: 11.
• S.N. Menon, S. Sinha, "Defective" logic: Using spatiotemporal patterns in coupled relaxation oscillator arrays for computation, 2014 International Conference on Signal Processing and Communications (SPCOM), Bangalore, 2014, pp. 1-6.
• A.S. KovalenkoL. P. TikhonovaK. B. Yatsimirskii, Effect of molecular oxygen on concentration autooscillations and autowaves in the Belousov-Zhabotinskii reaction, Theoretical and Experimental Chemistry 24(6) (1988), 633-638.

Epidemische Modelle für die Beschreibung der Dynamik ansteckender Krankheiten (z.B. Grippe, HIV, Ebola) basieren auf Differentialgleichungs-Systemen vom SIR (Susceptible-Infected-Recovered) Typ. Sie können auch eine Struktur (z.B. Alter, Raum) berücksichtigen, was zu partiellen Differentialgleichungen mit Integraltermen (PIDE) und evtl. auch stochastischen Termen (Unsicherheiten) führt.
Neben der mathematischen Modellierung soll auch die Dynamik mithilfe von numerischen Simulationen und Werkzeugen aus der Analysis untersucht werden.

• Dynamics of Infectious Diseases: Epidemic Models and AIDS, in: J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989, Kapitel 10.

Wie modelliert man ...

• Reaction Diffusion, Chemotaxis, and Nonlocal Mechanisms, in: J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989, Kapitel 11.
• J. Elias, Trend to Equilibrium for a Reaction-Diffusion System Modelling Reversible Enzyme Reaction, Bulletin of Mathematical Biology 80(1) (2018), 104-129.
• M.C. Getz, J.A. Nirody, P. Rangamani, Stability analysis in spatial modeling of cell signaling, Wiley Interdisciplinary Reviews: Systems Biology and Medicine 10(1) (2018), e1395.
• M. Khalil, A.A.M. Arafa, A. Sayed, A variable fractional order network model of zika virus, Journal of Fractional Calculus and Applications 9(1) (2018), 204-221.
• R. Altmann, A. Ostermann, Splitting methods for constrained diffusion-reaction systems, Computers & Mathematics with Applications 74(5) (2017), 962-976.

Wie modelliert man ...

• Oscillator-Generated Wave Phenomena and Central Pattern Generators, in: J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989, Kapitel 12.
• A. Bell, A Resonance Approach to Cochlear Mechanics, PLoS ONE 7(11) (2012), e47918.
• F.A. Sarria-S, B.D. Chivers, C.D. Soulsbury, F. Montealegre-Z, Non-invasive biophysical measurement of travelling waves in the insect inner ear, The Royal Society Open Science 4(5) (2017).

Wie modelliert man ...

• Biological Waves: Single-Species Models, in: J.D. Murray, Mathematical Biology, Biomathematics Texts, Springer, 1989, Kapitel 13.
• V.E. Deneke, S. Di Talia, Chemical waves in cell and developmental biology, The Journal of Cell Biology 217(2) (2018).

Wie modelliert man

• J. Keener, J. Sneyd, Mathematical Physiology, Interdisciplinary Applied Mathematics 8/2, Springer Verlag, 2009. Kapitel 23.
• A. Hudspeth, Mechanical amplification of stimuli by hair cells, Curr. Op. Neurobiol. 7 (1997), 480.
• P. Martin et al., Comparison of a hair bundle's spontaneous oscillations with its response to mechanical stimulation reveals the underlying active process, PNAS 98, 25 (2001), 14380.
• B. Nadrowski et al., Active hair-bundle motility harness noise to operate near an optimum of mechanosensitivity, PNAS 101,33 12195 2004.

Wie modelliert man

• J. Keener, J. Sneyd, Mathematical Physiology, Interdisciplinary Applied Mathematics 8/2, Springer Verlag, 2009. Kapitel 11, 14.
• D. Noble, Modelling the heart: from genes to cells to the whole organ, Science 295 (2002), 1678-1682.
• M.R. Guevara, A. Shrier, L. Glass, Phase-locked rhythms in periodically stimulated heart cell aggregates, Amer. J. Physiol. 254 (Heart Circ. Physiol. 23), H1-H10 (1988)..

Wie modelliert man ein positives emotionales Verhältnis zu Entführern?

• M.J. Piotrowska, J. Gorecka, U. Forys, The role of optimism and pessimism in the dynamics of emotional states, Discrete & Continuous Dynamical Systems - Series B. Jan. 2018, Vol. 23, Issue 1, 401-423.

Wie macht man Prognosen zu Scheidungen?

• J. Cook, R. Tyson, J. White, R. Rushe, J. Gottman, J. Murray, Mathematics of Marital Conflict: Qualitative Dynamic Mathematical Modelling of Marital Interaction, Journal of Family Psychology 8 (1995), 110-130.
• J.M. Gottman, Mathematics of Marriage: Dynamic Nonlinear Models, Bradford Books, 2005.
• J. Gottman, C. Swanson, K. Swanson, A General Systems Theory of Marriage: Nonlinear Difference Equation Modeling of Marital Interaction, Personality and Social Psychology Review, 2002.
• Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage Repair, In: J.D. Murray (ed.) Mathematical Biology. Interdisciplinary Applied Mathematics 17, Springer, 1993, pp 146-174.

• N. Bielczyk, M. Bodnar, U. Foryś, Delay can stabilize: Love affairs dynamics, Applied Mathematics and Computation, 219 (2012), 3923-3937.
• N. Bielczyk, U. Foryś, T. Platkowski, Dynamical models of dyadic interactions with delay, J. Math. Soc., 37 (2013), 223-249.
• D.H. Felmlee, D.F. Greenberg, A dynamic systems model of dyadic interaction, Journal of Mathematical Sociology, 23 (1999), 155-180.
• J.M. Gottman, J.D. Murray, C.C. Swanson, R. Tyson, K.R. Swanson, The Mathematics of Marriage: Dynamic Nonlinear Models, MIT Press, Cambridge, 2002.
• D. Kahneman, A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291.
• L. Liebovitch, V. Naudot, R. Vallacher, A. Nowak, L. Biu-Wrzosinska, P. Coleman, Dynamics of two-actor cooperation-competition conflict models, Physica A, 387 (2008), 6360-6378.
• S. Rinaldi, Love dynamics: The case of linear couples, Applied Mathematics and Computation, 95 (1998), 181-192.
• S. Rinaldi, F. Della Rosa, F. Dercole, Love and appeal in standard couples, International Journal of Bifurcation and Chaos, 20 (2010), 3473-3485.
• S. Rinaldi, A. Gragnani, Love dynamics between secure individuals: A modeling approach, Nonlinear Dynamics, Psychology, and Life Sciences, 2 (1998), 283-301.
• S. Rinaldi, P. Landi, F. Della Rosa, Small discoveries can have great consequences in love affairs: The case of beauty and the beast, International Journal of Bifurcation and Chaos, 23 (2013), 1330038, 8pp.
• S. Rinaldi, P. Landi, F. Della Rossa, Temporary bluffing can be rewarding in social systems: The case of romantic relationships, The Journal of Mathematical Sociology, 39 (2015), 203-220.
• S. Rinaldi, F. Della Rossa, P. Landi, A mathematical model of pride and prejudice?, Nonlinear dynamics, psychology, and life sciences, 18 (2014), 199-211.
• S. Rinaldi, F. Rossa Della, F. Dercole, A. Gragnani, P. Landi, Modeling Love Dynamics, vol. 89 of World Scientific Series on Nonlinear Science Series A, World Scientific Publishing Co.Pte. Ltd., 2016.
• S. Strogatz, Love affairs and differential equations, Math. Magazine, 65 (1988), p.35.
• S. Strogatz, Nonlinear Dynamics and Chaos, Westwiev Press, 1994.

• H.T. Banks, Modeling and control in the biomedical sciences, Berlin: Springer-Verlag, 1975.
• H.T. Banks, K. Bekele-Maxwell, R.A. Everett, L. Stephenson, S. Shao, J. Morgenstern, Dynamic modeling of problem drinkers undergoing behavioral treatment, Bulletin of Mathematical Biology, 79(6), (2016), 1254-1273.
• H.T. Banks, S. Hu, W.C. Thompson, Modeling and inverse problems in the presence of uncertainty, Boca Raton: CRC Press, 2014.
• H.T. Banks, K.L. Rehm, K. L. Sutton, C. Davis, L. Hail, A. Kuerbis, J. Morgenstern, Dynamic modeling of behavior change, Quarterly of Applied Mathematics, 72(2), (2014), 209-251.
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• K. Bekele-Maxwell, R.A. Everett, S. Shao, A. Kuerbis, L. Stephenson, H.T. Banks, J. Morgenstern, Dynamical Systems Modeling to Identify a Cohort of Problem Drinkers with Similar Mechanisms of Behavior Change, Journal for Person-Oriented Research 2017, 3(2), 101-118. DOI: 10.17505/jpor.2017.09
• K.B. Carey, J.M. Henson, M.P. Carey, S.A. Maisto, Perceived norms mediate effects of a brief motivational intervention for sanctioned college drinkers, Clinical Psychology: Science and Practice, 17(1), (2010), 58-71.
• S.M. Chow, E.L. Hamaker, F. Fujita, S.M. Boker, Representing time-varying cyclic dynamics using multiple-subject state-space models, British Journal of Mathematical and Statistical Psychology, 62(3), (2009), 683-716.
• S.M. Chow, N. Ram, S.M. Boker, F. Fujita, G. Clore, Emotion as a thermostat: representing emotion regulation using a damped oscillator model, Emotion, 5(2), (2005), 208-225. doi: 10.1037/1528-3542.5.2.208
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• J. Morgenstern, A. Kuerbis, A. Chen, C.W. Kahler, D.A. Bux, H. Kranzler, A randomized clinical trial of naltrexone and behavioral therapy for problem drinking men-who-have-sex-with-men, Journal of Consulting and Clinical Psychology, 80(5), (2012), 863-875.
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• J.E. Macías-Díaz, A. Puri, A numerical method with properties of consistency in the energy domain for a class of dissipative nonlinear wave equations with applications to a Dirichlet boundary-value problem, Z. Angew. Math. 88 (2008), 828-846.
• J.E. Macías-Díaz, A. Puri, On some explicit non-standard methods to approximate nonnegative solutions of a weakly hyperbolic equation with logistic nonlinearity, Int. J. Comput. Math. 88 (2011), 3308-3323.
• J.E. Macías-Díaz, J. Ruiz-Ramírez, A non-standard symmetry-preserving method to compute bounded solutions of a generalized Newell-Whitehead-Segel equation, Appl. Numer. Math. 61 (2011), 630-640.
• I.E. Medina-Ramírez, J.E. Macías-Díaz, On a fully discrete finite-difference approximation of a nonlinear diffusion-reaction model in microbial ecology, Int. J. Comput. Math. 90(9), (2013), 1915-1937.
• R.E. Mickens, P.M. Jordan, A positivity-preserving nonstandard finite difference scheme for the damped wave equation, Numer. Methods Partial Differential Equations 20 (2004), 639-649.
• R.E. Mickens, P.M. Jordan, A new positivity-preserving nonstandard finite difference scheme for the DWE, Numer. Methods Partial Differential Equations 21 (2005), 976-985.
• Y. Morinishi, T. Lund, O. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 143 (1998), 90-124.
• M. Morlighem, E. Rignot, H. Seroussi, E. Larour, H.B. Dhia, and D. Aubry, A mass conservation approach for mapping glacier ice thickness, Geophys. Res. Lett. 38 (2011), L19503.
• J. Ruiz-Ramírez, J.E. Macías-Díaz, A finite-difference scheme to approximate non-negative and bounded solutions of a FitzHugh-Nagumo equation, Int. J. Comput. Math. 88 (2011), 3186-3201.
• J.H. Seo, R. Mittal, A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations, J. Comput. Phys. 230 (2011), 7347-7363.
• R. Shukla, M. Tatineni, X. Zhong, Very high-order compact finite difference schemes on non-uniform grids for incompressible Navier-Stokes equations, J. Comput. Phys. 224 (2007), 1064-1094.
• R. Shukla, X. Zhong, Derivation of high-order compact finite difference schemes for non-uniform grid using polynomial interpolation, J. Comput. Phys. 204 (2005), 404-429.
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Scheinkriterium:

  Präsentation

• Erläuterung des Anwendungsproblems
• Mathematische Modellierung (evtl. mehrstufig)
• Lösung / Analyse / Numerik
• Diskussion der Resultate und ihrer Relevanz für die Anwendung
• Für die Präsentation wird Prosper bzw. HA-Prosper oder ifmslide oder PPower4 oder Beamer empfohlen
  ( Verschiedene Präsentationsprogramme)
• Evtl. numerische Simulationen (möglichst in Matlab, Scilab oder Octave)
  Schriftliche Ausarbeitung (ca. 10 Seiten, inkl. Beispiele)
  Regelmässige Teilnahme am Seminar

Vorkenntnisse: Basiswissen mathematischer Grundvorlesungen wird vorausgesetzt.

Didaktische Vortragstipps:

• M. Lehn, Wie halte ich einen Seminarvortrag, (pdf-file)
• S.P. Jones, How to write a good research paper and give a good research talk
• I. Parberry, How to present a paper in theoretical computer science: A speaker's guide for students, Bulletin of the EATCS,(37), 1989.
• S.P. Jones, J. Launchbury, J. Hughes, How to give a good research talk, SIGPLAN Notices 28(11), November 1993.
• G. Aiglstorfer, A short guide for students talks and papers, TU Munich, 2004.
• H. Kraft, Das Verfassen und Präsentieren wissenschaftlicher Arbeiten, TU Munich, 2006.