Objective "The MUSYX project will develop a rigorous numerical analysis framework for assessing the accuracy of multiscale methods for simulating the dynamics of crystalline defects. The core focus of the research will be the analysis of approximation errors of atomistic-to-continuum (a/c) coupling methods and related multiscale schemes. The rigorous mathematical foundations, which will be the outcome of this work, will also lead to the construction of more robust and more efficient numerical algorithms.The research will be undertaken within four distinct but closely related themes: Theme A: quasistatic evolutions up to and including bifurcation points (defect nucleation and evolution); Theme B: Transition paths, saddles, and transition rates between local minima (defect nucleation and diffusion at finite temperature); Theme C: Computation of defect formation energies within the framework of equilibrium statistical mechanics; Theme D: Fully dynamic problems. The four themes are connected through the focus on crystal defects and model interfaces (e.g. atomistic/continuum).Themes A and B build on and significantly extend the theory of a/c coupling pioneered by the PI, which combines classical techniques of numerical analysis (consistency, stability) with modern concepts of multiscale and atomistic modeling. Theme C aims to develop an analogous theory for multiscale free energy calculations (precisely, defect formation energies). Theme D approaches the analysis of a fully dynamic multiscale scheme by analyzing its qualitative statistical properties." Fields of science natural sciencesphysical sciencesclassical mechanicsstatistical mechanicsnatural sciencescomputer and information sciencescomputational sciencemultiphysicsnatural sciencesmathematicsapplied mathematicsnumerical analysis Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2013-StG See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution THE UNIVERSITY OF WARWICK EU contribution € 1 111 793,28 Address Kirby Corner Road - University House CV4 8UW Coventry United Kingdom See on map Region West Midlands (England) West Midlands Coventry Activity type Higher or Secondary Education Establishments Principal investigator Christoph Ortner (Dr.) Administrative Contact Catherine Cochrane (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all THE UNIVERSITY OF WARWICK United Kingdom EU contribution € 1 111 793,28 Address Kirby Corner Road - University House CV4 8UW Coventry See on map Region West Midlands (England) West Midlands Coventry Activity type Higher or Secondary Education Establishments Principal investigator Christoph Ortner (Dr.) Administrative Contact Catherine Cochrane (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
