# Search result: Catalogue data in Spring Semester 2020

Mathematics Master | ||||||

Application Area Only necessary and eligible for the Master degree in Applied Mathematics. One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area. | ||||||

Material Modelling and Simulation | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|---|

327-2201-00L | Transport Phenomena II | W | 5 credits | 4G | J. Vermant | |

Abstract | Numerical and analytical methods for real-world "Transport Phenomena"; atomistic understanding of transport properties based on kinetic theory and mesoscopic models; fundamentals, applications, and simulations | |||||

Learning objective | The teaching goals of this course are on five different levels: (1) Deep understanding of fundamentals: kinetic theory, mesoscopic models, ... (2) Ability to use the fundamental concepts in applications (3) Insight into the role of boundary conditions (4) Knowledge of a number of applications (5) Flavor of numerical techniques: finite elements, lattice Boltzmann, ... | |||||

Content | Thermodynamics of Interfaces Interfacial Balance Equations Interfacial Force-Flux Relations Polymer Processing Transport Around a Sphere Refreshing Topics in Equilibrium Statistical Mechanics Kinetic Theory of Gases Kinetic Theory of Polymeric Liquids Transport in Biological Systems Dynamic Light Scattering | |||||

Lecture notes | The course is based on the book D. C. Venerus and H. C. Öttinger, A Modern Course in Transport Phenomena (Cambridge University Press, 2018) | |||||

Literature | 1. D. C. Venerus and H. C. Öttinger, A Modern Course in Transport Phenomena (Cambridge University Press, 2018) 2. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd Ed. (Wiley, 2001) 3. Deen,W. Analysis of Transport Phenomena, Oxford University Press, 2012 4. R. B. Bird, Five Decades of Transport Phenomena (Review Article), AIChE J. 50 (2004) 273-287 | |||||

Prerequisites / Notice | Complex numbers. Vector analysis (integrability; Gauss' divergence theorem). Laplace and Fourier transforms. Ordinary differential equations (basic ideas). Linear algebra (matrices; functions of matrices; eigenvectors and eigenvalues; eigenfunctions). Probability theory (Gaussian distributions; Poisson distributions; averages; moments; variances; random variables). Numerical mathematics (integration). Statistical thermodynamics (Gibbs' fundamental equation; thermodynamic potentials; Legendre transforms; Gibbs' phase rule; ergodicity; partition functions; Einstein's fluctuation theory). Linear irreversible thermodynamics (forces and fluxes; Fourier's, Newton's and Fick's laws for fluxes). Hydrodynamics (local equilibrium; balance equations for mass, momentum, energy and entropy). Programming and simulation techniques (Matlab, Monte Carlo simulations). | |||||

151-0515-00L | Continuum Mechanics 2 | W | 4 credits | 2V + 1U | E. Mazza, R. Hopf | |

Abstract | An introduction to finite deformation continuum mechanics and nonlinear material behavior. Coverage of basic tensor- manipulations and calculus, descriptions of kinematics, and balance laws . Discussion of invariance principles and mechanical response functions for elastic materials. | |||||

Learning objective | To provide a modern introduction to the foundations of continuum mechanics and prepare students for further studies in solid mechanics and related disciplines. | |||||

Content | 1. Tensors: algebra, linear operators 2. Tensors: calculus 3. Kinematics: motion, gradient, polar decomposition 4. Kinematics: strain 5. Kinematics: rates 6. Global Balance: mass, momentum 7. Stress: Cauchy's theorem 8. Stress: alternative measures 9. Invariance: observer 10. Material Response: elasticity | |||||

Lecture notes | None. | |||||

Literature | Recommended texts: (1) Nonlinear solid mechanics, G.A. Holzapfel (2000). (2) An introduction to continuum mechanics, M.B. Rubin (2003). |

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