# Suchergebnis: Katalogdaten im Frühjahrssemester 2018

Physik Bachelor | ||||||

Auswahl an Lehrveranstaltungen aus höheren Semestern | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|---|

401-0674-00L | Numerical Methods for Partial Differential EquationsNot meant for BSc/MSc students of mathematics. | W | 8 KP | 4V + 2U + 1A | R. Hiptmair | |

Kurzbeschreibung | Derivation, properties, and implementation of fundamental numerical methods for a few key partial differential equations: convection-diffusion, heat equation, wave equation, conservation laws. Implementation in C++ based on a finite element library. | |||||

Lernziel | Main skills to be acquired in this course: * Ability to implement advanced numerical methods for the solution of partial differential equations efficiently. * Ability to modify and adapt numerical algorithms guided by awareness of their mathematical foundations. * Ability to select and assess numerical methods in light of the predictions of theory * Ability to identify features of a PDE (= partial differential equation) based model that are relevant for the selection and performance of a numerical algorithm. * Ability to understand research publications on theoretical and practical aspects of numerical methods for partial differential equations. * Skills in the efficient implementation of finite element methods on unstructured meshes. This course is neither a course on the mathematical foundations and numerical analysis of methods nor an course that merely teaches recipes and how to apply software packages. | |||||

Inhalt | 1 Case Study: A Two-point Boundary Value Problem 1.1 Introduction 1.2 A model problem 1.3 Variational approach 1.4 Simplified model 1.5 Discretization 1.5.1 Galerkin discretization 1.5.2 Collocation [optional] 1.5.3 Finite differences 1.6 Convergence 2 Second-order Scalar Elliptic Boundary Value Problems 2.1 Equilibrium models 2.1.1 Taut membrane 2.1.2 Electrostatic fields 2.1.3 Quadratic minimization problems 2.2 Sobolev spaces 2.3 Variational formulations 2.4 Equilibrium models: Boundary value problems 3 Finite Element Methods (FEM) 3.1 Galerkin discretization 3.2 Case study: Triangular linear FEM in two dimensions 3.3 Building blocks of general FEM 3.4 Lagrangian FEM 3.4.1 Simplicial Lagrangian FEM 3.4.2 Tensor-product Lagrangian FEM 3.5 Implementation of FEM in C++ 3.5.1 Mesh file format (Gmsh) 3.5.2 Mesh data structures (DUNE) 3.5.3 Assembly 3.5.4 Local computations and quadrature 3.5.5 Incorporation of essential boundary conditions 3.6 Parametric finite elements 3.6.1 Affine equivalence 3.6.2 Example: Quadrilaterial Lagrangian finite elements 3.6.3 Transformation techniques 3.6.4 Boundary approximation 3.7 Linearization [optional] 4 Finite Differences (FD) and Finite Volume Methods (FV) [optional] 4.1 Finite differences 4.2 Finite volume methods (FVM) 5 Convergence and Accuracy 5.1 Galerkin error estimates 5.2 Empirical Convergence of FEM 5.3 Finite element error estimates 5.4 Elliptic regularity theory 5.5 Variational crimes 5.6 Duality techniques [optional] 5.7 Discrete maximum principle [optional] 6 2nd-Order Linear Evolution Problems 6.1 Parabolic initial-boundary value problems 6.1.1 Heat equation 6.1.2 Spatial variational formulation 6.1.3 Method of lines 6.1.4 Timestepping 6.1.5 Convergence 6.2 Wave equations [optional] 6.2.1 Vibrating membrane 6.2.2 Wave propagation 6.2.3 Method of lines 6.2.4 Timestepping 6.2.5 CFL-condition 7 Convection-Diffusion Problems 7.1 Heat conduction in a fluid 7.1.1 Modelling fluid flow 7.1.2 Heat convection and diffusion 7.1.3 Incompressible fluids 7.1.4 Transient heat conduction 7.2 Stationary convection-diffusion problems 7.2.1 Singular perturbation 7.2.2 Upwinding 7.3 Transient convection-diffusion BVP 7.3.1 Method of lines 7.3.2 Transport equation 7.3.3 Lagrangian split-step method 7.3.4 Semi-Lagrangian method 8 Numerical Methods for Conservation Laws 8.1 Conservation laws: Examples 8.2 Scalar conservation laws in 1D 8.3 Conservative finite volume discretization 8.3.1 Semi-discrete conservation form 8.3.2 Discrete conservation property 8.3.3 Numerical flux functions 8.3.4 Montone schemes 8.4 Timestepping 8.4.1 Linear stability 8.4.2 CFL-condition 8.4.3 Convergence 8.5 Higher order conservative schemes [optional] 8.5.1 Slope limiting 8.5.2 MUSCL scheme 8.6. FV-schemes for systems of conservation laws [optional] | |||||

Skript | Lecture documents and classroom notes will be made available to the audience as PDF. | |||||

Literatur | Chapters of the following books provide supplementary reading (detailed references in course material): * D. Braess: Finite Elemente, Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie, Springer 2007 (available online). * S. Brenner and R. Scott. Mathematical theory of finite element methods, Springer 2008 (available online). * A. Ern and J.-L. Guermond. Theory and Practice of Finite Elements, volume 159 of Applied Mathematical Sciences. Springer, New York, 2004. * Ch. Großmann and H.-G. Roos: Numerical Treatment of Partial Differential Equations, Springer 2007. * W. Hackbusch. Elliptic Differential Equations. Theory and Numerical Treatment, volume 18 of Springer Series in Computational Mathematics. Springer, Berlin, 1992. * P. Knabner and L. Angermann. Numerical Methods for Elliptic and Parabolic Partial Differential Equations, volume 44 of Texts in Applied Mathematics. Springer, Heidelberg, 2003. * S. Larsson and V. Thomée. Partial Differential Equations with Numerical Methods, volume 45 of Texts in Applied Mathematics. Springer, Heidelberg, 2003. * R. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, UK, 2002. However, study of supplementary literature is not important for for following the course. | |||||

Voraussetzungen / Besonderes | Mastery of basic calculus and linear algebra is taken for granted. Familiarity with fundamental numerical methods (solution methods for linear systems of equations, interpolation, approximation, numerical quadrature, numerical integration of ODEs) is essential. Important: Coding skills and experience in C++ are essential. Homework assignments involve substantial coding, partly based on a C++ finite element library. The written examination will be computer based and will comprise coding tasks. | |||||

402-0714-00L | Astro-Particle Physics II | W | 6 KP | 2V + 1U | A. Biland | |

Kurzbeschreibung | This lecture focuses on the neutral components of the cosmic rays as well as on several aspects of Dark Matter. Main topics will be very-high energy astronomy and neutrino astronomy. | |||||

Lernziel | Students know experimental methods to measure neutrinos as well as high energy and very high energy photons from extraterrestrial sources. They are aware of the historical development and the current state of the field, including major theories. Additionally, they understand experimental evidences about the existence of Dark Matter and selected Dark Matter theories. | |||||

Inhalt | a) short repetition about 'charged cosmic rays' (1st semester) b) High Energy (HE) and Very-High Energy (VHE) Astronomy: - ongoing and near-future detectors for (V)HE gamma-rays - possible production mechanisms for (V)HE gamma-rays - galactic sources: supernova remnants, pulsar-wind nebulae, micro-quasars, etc. - extragalactic sources: active galactic nuclei, gamma-ray bursts, galaxy clusters, etc. - the gamma-ray horizon and it's cosmological relevance c) Neutrino Astronomy: - atmospheric, solar, extrasolar and cosmological neutrinos - actual results and near-future experiments d) Dark Matter: - evidence for existence of non-barionic matter - Dark Matter models (mainly Supersymmetry) - actual and near-future experiments for direct and indirect Dark Matter searches | |||||

Skript | See: Link | |||||

Literatur | See: Link | |||||

Voraussetzungen / Besonderes | This course can be attended independent of Astro-Particle Physics I. | |||||

402-0742-00L | Energy and Environment in the 21st Century (Part II) | W | 6 KP | 2V + 1U | M. Dittmar | |

Kurzbeschreibung | Despite the widely used concepts of sustainability and sustainable development, one remarks the absence of a scientific definition. In this lecture we will discuss, based on the natural laws and the scientific method, various proposed concepts for a development towards sustainability. | |||||

Lernziel | A scientifically useful definition of sustainability? Unsustainable aspects of our lifestyle and our society? (unsustainable use of ressources, environmental destruction and climate change, mass extinctions etc) How long can humanity continue on its current unsustainable path, what are the possible consequences? Historical examples of society collapse. What can we learn from them. Existing Gedanken models/experiments (like Permaculture) promise to transform the human society into the direction of sustainability. If these ideas would theoretically transform our global society into a sustainable one, what are the large scale limitations and why do we not yet follow these ideas? | |||||

Inhalt | Introduction ``sustainability" (24.2.); Population Dynamik (3.3.); finite (energy)-resources (10.3.); waste problems (17.3.); water, soil and industrial agriculture (24.3.); biodiversity (31.3.); (un)-sustainable development (7.4./28.4./5.5); example for sustainable systems (12.5./19.5.); human nature, Ethics and earth-care(?) (26.5./2.6.) | |||||

Skript | Web page: Link | |||||

Literatur | for example: Environmental Physics (Boeker and Grandelle) A prosperous way down: Principles and Policies (H. Odum and E. Odum) | |||||

Voraussetzungen / Besonderes | Basic knowledge of the ``physics laws" governing todays energy system and it use to deliver ``useful" work for our life (laws of energie conservation and of the energy transformation to do work). Interest to learn about the problems (and possible solutions) related to the transition from an unsustainable use of renewable and non renewable (energy) resources to a sustainable system using scientific method. | |||||

401-3532-08L | Differential Geometry II | W | 10 KP | 4V + 1U | D. A. Salamon | |

Kurzbeschreibung | Introduction to Differential Topology, including degree theory and intersection theory; Differential forms, including deRham cohomology and Poincare duality; Vector bundles, including Thom isomorphism and Euler number. | |||||

Lernziel | The aim of this course is to give an introduction to Differential Topology including the degree of a mapping and intersection theory, differential forms including deRham cohomology and Poincare duality, and vector bundles including the Thom isomorphism theorem. | |||||

Inhalt | Introduction to Differential Topology, including the mod-2 degree, orientation and the Brouwer degree, Poincare-Hopf Theorem, the Pontryagin construction, Hopf Degree Theorem., intersection theory, Lefschetz numbers; Differential forms, Stokes, Cartan's formula, deRham cohomology, Mayer-Vietoris, Poincare duality, Euler characteristic, Degree Theorem, Gauss-Bonnet, Moser isotopy, Cech-DeRham complex and finite-dimensionality; Vector bundles, Thom isomorphism, Euler number. | |||||

Literatur | - J. Milnor, Topology from the Differential Viewpoint. Univ Virginia Press, 1969. - V. Guillemin, A. Pollack, Differential Topology. Prentice-Hall, 1974. - R. Bott, L.W. Tu, Differential Forms in Algebraic Topology, Springer, 1982. - J. Robbin, D. Salamon, Introduction to Differential Topology, in preparation. Link | |||||

Voraussetzungen / Besonderes | Prerequisite is a working knowledge of the introductory material in Differential Geometry I, including smooth manifolds, tangent bundles, vector fields and flows. see Link | |||||

402-0343-00L | Physics Against Cancer: The Physics of Imaging and Treating Cancer | W | 6 KP | 2V + 1U | A. J. Lomax, U. Schneider | |

Kurzbeschreibung | Radiotherapy is a rapidly developing and technology driven medical discipline that is heavily dependent on physics and engineering. In this lecture series, we will review and describe some of the current developments in radiotherapy, particularly from the physics and technological view point, and will indicate in which direction future research in radiotherapy will lie. | |||||

Lernziel | Radiotherapy is a rapidly developing and technology driven medical discipline that is heavily dependent on physics and engineering. In the last few years, a multitude of new techniques, equipment and technology have been introduced, all with the primary aim of more accurately targeting and treating cancerous tissues, leading to a precise, predictable and effective therapy technique. In this lecture series, we will review and describe some of the current developments in radiotherapy, particularly from the physics and technological view point, and will indicate in which direction future research in radiotherapy will lie. Our ultimate aim is to provide the student with a taste for the critical role that physics plays in this rapidly evolving discipline and to show that there is much interesting physics still to be done. | |||||

Inhalt | The lecture series will begin with a short introduction to radiotherapy and an overview of the lecture series (lecture 1). Lecture 2 will cover the medical imaging as applied to radiotherapy, without which it would be impossible to identify or accurately calculate the deposition of radiation in the patient. This will be followed by a detailed description of the treatment planning process, whereby the distribution of deposited energy within the tumour and patient can be accurately calculated, and the optimal treatment defined (lecture 3). Lecture 4 will follow on with this theme, but concentrating on the more theoretical and mathematical techniques that can be used to evaluate different treatments, using mathematically based biological models for predicting the outcome of treatments. The role of physics modeling, in order to accurately calculate the dose deposited from radiation in the patient, will be examined in lecture 5, together with a review of mathematical tools that can be used to optimize patient treatments. Lecture 6 will investigate a rather different issue, that is the standardization of data sets for radiotherapy and the importance of medical data bases in modern therapy. In lecture 7 we will look in some detail at one of the most advanced radiotherapy delivery techniques, namely Intensity Modulated Radiotherapy (IMRT). In lecture 8, the two topics of imaging and therapy will be somewhat combined, when we will describe the role of imaging in the daily set-up and assessment of patients. Lecture 9 follows up on this theme, in which a major problem of radiotherapy, namely organ motion and changes in patient and tumour geometry during therapy, will be addressed, together with methods for dealing with such problems. Finally, in lectures 10-11, we will describe in some of the multitude of different delivery techniques that are now available, including particle based therapy, rotational (tomo) therapy approaches and robot assisted radiotherapy. In the final lecture, we will provide an overview of the likely avenues of research in the next 5-10 years in radiotherapy. The course will be rounded-off with an opportunity to visit a modern radiotherapy unit, in order to see some of the techniques and delivery methods described in the course in action. | |||||

Voraussetzungen / Besonderes | Although this course is seen as being complimentary to the Medical Physics I and II course of Dr Manser, no previous knowledge of radiotherapy is necessarily expected or required for interested students who have not attended the other two courses. | |||||

402-0787-00L | Therapeutic Applications of Particle Physics: Principles and Practice of Particle Therapy | W | 6 KP | 2V + 1U | A. J. Lomax | |

Kurzbeschreibung | Physics and medical physics aspects of particle physics Subjects: Physics interactions and beam characteristics; medical accelerators; beam delivery; pencil beam scanning; dosimetry and QA; treatment planning; precision and uncertainties; in-vivo dose verification; proton therapy biology. | |||||

Lernziel | The lecture series is focused on the physics and medical physics aspects of particle therapy. The radiotherapy of tumours using particles (particularly protons) is a rapidly expanding discipline, with many new proton and particle therapy facilities currently being planned and built throughout Europe. In this lecture series, we study in detail the physics background to particle therapy, starting from the fundamental physics interactions of particles with tissue, through to treatment delivery, treatment planning and in-vivo dose verification. The course is aimed at students with a good physics background and an interest in the application of physics to medicine. | |||||

Voraussetzungen / Besonderes | The former title of this course was "Medical Imaging and Therapeutic Applications of Particle Physics". | |||||

402-0673-00L | Physics in Medical Research: From Humans to Cells | W | 6 KP | 2V + 1U | B. K. R. Müller | |

Kurzbeschreibung | The aim of this lecture series is to introduce the role of physics in state-of-the-art medical research and clinical practice. Topics to be covered range from applications of physics in medical implant technology and tissue engineering, through imaging technology, to its role in interventional and non-interventional therapies. | |||||

Lernziel | The lecture series is focused on applying physics in diagnosis, planning, and therapy close to clinical practice and fundamental medical research. Beside a general overview the lectures give a deep insight into selected techniques, which will help the students to apply the knowledge to related techniques. In particular, the lectures will elucidate the physics behind the X-ray imaging currently used in clinical environment and contemporary high-resolution developments. It is the goal to visualize and quantify microstructures of human tissues and implants as well as their interface. Ultrasound is not only used for diagnostic purposes but includes therapeutic approaches such as the control of the blood-brain barrier under MR-guidance. Physicists in medicine are working on modeling and simulation. Based on the vascular structure in cancerous and healthy tissues, the characteristic approaches in computational physics to develop strategies against cancer are presented. In order to deliberately destroy cancerous tissue, heat can be supplied or extracted in different manner: cryotherapy (heat conductivity in anisotropic, viscoelastic environment), radiofrequency treatment (single and multi-probe), laser application, and proton therapy. Medical implants play an important role to take over well-defined tasks within the human body. Although biocompatibility is here of crucial importance, the term is insufficiently understood. The aim of the lectures is the understanding of biocompatibility performing well-defined experiments in vitro and in vivo. Dealing with different classes of materials (metals, ceramics, polymers) the influence of surface modifications (morphology and surface coatings) are key issues for implant developments. Mechanical stimuli can drastically influence soft and hard tissue behavior. The students should realize that a physiological window exists, where a positive tissue response is expected and how the related parameter including strain, frequency, and resting periods can be selected and optimized for selected tissues such as bone. For the treatment of severe incontinence artificial smart muscles have to be developed. The students should have a critical look at promising solutions and the selection procedure as well as realize the time-consuming and complex way to clinical practice. The course will be completed by a visit of advanced facilities within a leading Swiss hospital. | |||||

Inhalt | This lecture series will cover the following topics: Introduction: Imaging the human body down to individual cells Development of artificial muscles X-ray-based computed tomography in clinics and related medical research High-resolution micro computed tomography Phase tomography using hard X-rays in biomedical research Metal-based implants and scaffolds Natural and synthetic ceramics for implants and regenerative medicine Biomedical simulations Polymers for medical implants From open surgery to non-invasive interventions - Physical approaches in medical imaging Dental research Focused Ultrasound and its clinical use Applying physics in medicine: Benefitting patients | |||||

Skript | Link login and password to be provided during the lecture | |||||

Voraussetzungen / Besonderes | Students from other departments are very welcome to join and gain insight into a variety of sophisticated techniques for the benefit of patients. No special knowledge is required. Nevertheless, gaps in basic physical knowledge will result in additional efforts. | |||||

» Wahlfächer (Physik Master) |

- Seite 1 von 1