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Multi-scale Analysis of variational models in Materials Science - Single View

Basic Information
Type of Course Lecture Long text
Number 104770 Short text
Term SS 2015 Hours per week in term 4
Expected no. of participants Study Year
Max. participants
Credits Assignment enrollment
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Language english
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  Day Time Frequency Duration Room Room-
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Lecturer Status Remarks Cancelled on Max. participants
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Mon. 10:00 to 12:00 weekly 06.04.2015 to 06.07.2015  Einsteinstr. 64 - M B 6 (M 6)        
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Thu. 10:00 to 12:00 weekly 09.04.2015 to 09.07.2015  Einsteinstr. 64 - M B 6 (M 6)        
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Responsible Instructor
Responsible Instructor Responsibilities
Zeppieri, Caterina, Prof. Dr. responsible
Curriculae
Graduation - Curricula Sem ECTS Bereich Teilgebiet
Master - Mathematik (88 105 13) -
Master - Mathematik (88 105 10) -
Exams / Modules
Number of Exam Module
20001 Vorlesung 1 - Master Mathematik Version 2010
20010 Klausur/mündliche Prüfung zu einer Vorlesung/Vorlesungskombination - Master Mathematik Version 2010
17001 Vorlesung 1 - Master Mathematik Version 2013
Assign to Departments
Fachbereich 10 Mathematik und Informatik
Contents
Description

A large variety of physical and mechanical models with variational structure contain small parameters of either constitutive or geometrical nature. The well-known examples include descriptions of fine scale mixtures in composite materials, lattice systems with characteristic atomic scales and, in general, a range of physical models with a microstructure or exhibiting some kind of microscopic phenomenon.

 

Scope of this course is the asymptotic analysis of energies depending on a small parameter from the stand point of global minimization and Gamma-convergence. The development of a general theory will be complemented by many concrete examples arising in Materials Science.

 

Literature

A. Braides: Gamma-convergence for beginners. Oxford Lecture Series in Mathematics and its Applications, 22. Oxford University Press, Oxford, 2002.

Remarks

A large variety of physical and mechanical models with variational structure contain small parameters of either constitutive or geometrical nature. The well-known examples include descriptions of fine scale mixtures in composite materials, lattice systems with characteristic atomic scales and, in general, a range of physical models with a microstructure or exhibiting some kind of microscopic phenomenon.

Scope of this course is the asymptotic analysis of energies depending on a small parameter from the stand point of global minimization and Gamma-convergence. The development of a general theory will be complemented by many concrete examples such as homogenization problems, segmentation problems, phase transition problems, and free discontinuity problems.

Prerequisites

Analysis I - III ( Variationsrechnung ist hilfreich)

Certificates

Um die Vorlesung als Bestanden eintragen zu lassen, benötigen Sie die regelmäßige Teilnahme an der Vorlesung und die Übungen müssen ebenfalls bestanden sein.


Structure Tree
Lecture not found in this Term. Lecture is in Term SS 2015 , Currentterm: WiSe 2022/23