| time, location: |
tba; block course possible
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| learnweb: |
SeminarFriedrichWirth-2020_2
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| contents: |
We plan to have talks about analytical and numerical topics on structures from materials science, e.g. crystallization results (that atoms arrange in crystals), atomistic-to-continuum coupling (numerics in which some regions are resolved at atomistic scale), results and simulations on dislocations and similar structures in materials, results on carbonanostructures (such as fullerenes). Techniques range from numerical analysis via the calculus of variations all the way to discrete mathematics.
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| prerequisites: |
Analysis I-III, some knowledge in numerics/differential equations/variational calculus is helpful.
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| initial meeting: |
The first meeting takes place October 28, 2020, 14:00 via zoom.
Login data: Meeting-ID: 839 1651 5225, Kenncode: 7gThm9
In case you are interested in the seminar, please already now send an e-mail to the lecturer. If you already would like to find a topic or even start working before October, this is also possible (again just send an e-mail).
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| assessment: |
45-minute seminar talk and written report (ca. 7-page handout, to be presented and discussed with the lecturer ca. 10 days before the talk, to allow for improvements and further assistance)
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| topics: |
The following list of articles gives an impression of possible topics:
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Crystallization:
Friesecke, De Luca: Crystallization in Two Dimensions and a Discrete GaussBonnet Theorem
Mainini, Piovano, Stefanelli: Finite Crystallization in the Square Lattice
Schmidt: Ground states of the 2D sticky disc model: fine properties and N3/4 law for the deviation from the asymptotic Wulff shape
Theil: A Proof of Crystallization in Two Dimensions
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Coupling of atomistic and continuum models:
Braides, Solci, Vitali: A derivation of linear elastic energies from pair-interaction atomistic systems
Blanc, Le Bris, Lions: Atomistic to continuum limits for computational materials science
Au Yeung, Friesecke, Schmidt: Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape
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Numerical methods for coupling of atomistic and continuum models:
wie Textbuch: Luskin, Ortner: Atomistic-to-continuum-coupling
Dedner, Ortner, Wu: Coupling atomistic, elasticity and boundary element models
Ortner, Shapeev, Zhang: (In-)stability and stabilisation of qnl-type atomistic-to-continuum coupling methods
Wang, Chen, Liao, Ortner, Wang, Zhang: A posteriori error estimates for adaptive qm/mm coupling methods
Salvalaglio, Voigt, Elder: Closing the gap between atomic-scale lattice deformations and continuum elasticity
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Stability of molecules:
Friedrich, Piovano, Stefanelli: The geometry of C60: A rigorous approach via Molecular Mechanics
Friedrich, Mainini, Piovano, Stefanelli: Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule
Betermin, Friedrich, Stefanelli: Angle-rigidity for Z^2 configurations
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Stability of crystal defects:
Ehrlacher, Ortner, Shapeev: Analysis of boundary conditions for crystal defect atomistic simulations
Hudson, Ortner: Analysis of stable screw dislocation configurations in an anti-plane lattice model
Buze, Hudson, Ortner: Analysis of cell size effects in atomistic crack propagation
Nitschke, Reuther, Voigt: Liquid crystals on deformable surfaces
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Parameterfitting for atomistic and quantum systems:
van der Oord, Dusson, Csanyi, Ortner: Regularised atomic body-ordered permutation-invariant polynomials for the construction of interatomic potentials
Bachmayr, Csanyi, Dusson, Etter, van der Oord, Ortner: Approximation of potential energy surfaces with spherical harmonics
Onat, Ortner, Kermode: Sensitivity and dimensionality of atomic environment representations used for machine learning interatomic potentials
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| talks: |
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