Research
Research areas
My research is primarily in applied analysis. I use and develop tools from
- Calculus of Variations,
- Theory of PDEs,
- Numerical Analysis,
for the purpose of applications. The main applications areas at the moment are
- Effective Theories in Material Sciences,
- Properties of Crystalline Materials,
- Computational Methods for Crystalline Materials.
Recent Publications
- Incompleteness of Sinclair-type continuum flexible boundary conditions for atomistic fracture simulations. Julian Braun, Maciej Buze, 2024. [preprint]
- Higher Order Far-Field Boundary Conditions for Crystalline Defects. Julian Braun, Christoph Ortner, Yangshuai Wang, Lei Zhang, 2022. [preprint]
- Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect. Julian Braun, Thomas Hudson, Christoph Ortner, Arch Rational Mech Anal 245, 1437–1490, 2022. [open access]
- An atomistic derivation of von-Kármán plate theory. Julian Braun, Bernd Schmidt, Networks and Heterogeneous Media, 17(4): 613-644, 2022. [website], [preprint]
- Sharp Uniform Convergence Rate of the Supercell Approximation of a Crystalline Defect. Julian Braun, Christoph Ortner. SIAM Journal on Numerical Analysis, 58:1, 279-297, 2020. [website], [preprint]
- Thermodynamic Limit of the Transition Rate of a Crystalline Defect. Julian Braun, Manh Hong Duong, Christoph Ortner. Arch Rational Mech Anal 238, 1413–1474, 2020. [website], [preprint]
- The Effect of Crystal Symmetries on the Locality of Screw Dislocation Cores. Julian Braun, Maciej Buze, Christoph Ortner, SIAM Journal on Mathematical Analysis, 51:2, 1108-1136, 2019. [website], [preprint]
- Connecting Atomistic and Continuous Models of Elastodynamics. Julian Braun, Arch Rational Mech Anal 224, 907–953, 2017. [website], [preprint]
- Existence and Convergence of Solutions of the Boundary Value Problem in Atomistic and Continuum Nonlinear Elasticity Theory. Julian Braun, Bernd Schmidt, Calc. Var. 55, 125, 2016. [website], [preprint]
- On the passage from atomistic systems to nonlinear elasticity theory. Julian Braun, Bernd Schmidt, Networks and Heterogeneous Media, 8(4): 879-912, 2013. [website], [preprint]