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This page hosts information about meetings organised through OxMOS. Some photographs of the events are also available.
This workshop both brought the EPSRC-funded OxMOS programme to a close and was the first to be held in the NSF PIRE programme Science at the Triple Point of Mathematics, Mechanics and Materials Science.
Speakers included:
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Further information on accommodation, the programme and registration for the event.
Please click here for further information.
Presentations by:
Bernhard Langwallner Continuum limits of atomistic energies and new computational models of fracture
Yasemin Sengul Well-posedness of dynamics
Kostas Koumatos X-interfaces and nonclassical austenite-martensite interfaces
Tim Squires Models for breast cancer and heart tissue
Professor Lisa Jardine (QMUL)
Chaired by Dr Jim Bennett
Director, Museum of the History of Science, Oxford
6.30 pm, Thursday 7 January 2010
St Anne’s College, Oxford
The evening lecture was cancelled due to travel difficulties as a result of the weather conditions. We apologise for any inconvenience that this may cause you and thank you for your understanding.
There was a 2-day Joint OxMOS Workshop with the MD-Network (Mathematical Challenges of Molecular Dynamics) on 7–8 December 2009 on “Atomistic Models of Solids”.
A 2½-day Joint OxMOS International Conference was held with OCCAM on “New Developments in Elasticity: the Legacy of Robert Hooke” on 6–8 January 2010. Speakers included:
You may download the programme here.
A LMS–EPSRC short course was held between 28 June and 3 July 2009, encompassing aspects of the Mathematics of Materials Science, including Microstructure, Fracture, and Soft and Active Matter, together with a crash-course on basic Elasticity theory. For more details please visit the course webpage.
A workshop on multiscale models was held in the Mathematical Institute on 3 June 2009. For further information please visit the workshop website.
Following the success of the dislocations workshop on 30 September, it was decided to have a follow-up workshop. Dr Gabor Csanyi from Cambridge, an expert on atomistic modelling of dislocations, participated. The meeting was held on Friday 31 October starting at 11.45am. The workshop took place in the 1st floor seminar room in the Gibson Building on the Old Radcliffe Infirmary Site off Woodstock Road.
Outline plan:
3rd October 2008
Mathematical Institute, University of Oxford
Full details are available on this website.
Held in DH Seminar Room 3 on 30 September 2008 at 14:00, with Amit Acharya.
A Posteriori Error Estimates for PDE Constrained Optimization with Pointwise State Constraints, Winnifried Wollner (Heidelberg)
Tuesday, 16 September, 15:30, Gibson Building Seminar Room
This talk was devoted to adaptivity in optimal control of PDEs with special emphasis on barrier methods for pointwise state constraints. The talk was divided into two major parts, first the case of additional pointwise inequality constraints on the state variable, then transfering the results to constraints on the gradient of the state. Each part started with a discussion of necessary optimality conditions and a brief overview about what is known and what is not known concerning a priori analysis. Then a posteriori error estimates for the discretization error as well as for the error from the barrier method were presented. Finally some simple examples were shown to illustrate the behavior of the estimators.
The effective static and dynamic properties of composite media, William Parnell, University of Manchester
Tuesday, 6 May, 15:15, Gibson Building Seminar Room and Wednesday, 21 May, 12:00, DH Seminar Room 3
The effective properties of composite media are defined by the constituent phase properties (elastic moduli, thermal conductivities, etc.), their volume fractions, and their distribution throughout the medium. In the case of constituents distributed periodically, there exist many homogenization theories which can provide exact solutions for the effective properties. However, the case of the effective properties of random media remains largely an open problem.
This talk began by discussing the notion of homogenization as an extension to the continuum assumption and regimes in which it breaks down. It then discussed various approaches to dealing with randomness whilst determining the effective properties of acoustic, thermal and elastic media. In particular it was shown how the effective properties depend on the randomness of the microstructure.
Yield criteria for shape memory materials: convexity conditions and surfaces transport, Christian Lexcellent
Monday, 26 May, 13:30, Gibson Building Seminar Room
The OxMOS one day workshop on ‘Fracture’ was held on Monday 10 March 2008.
Phase field modelling and simulation of some interface problems — Qiang Du, Verne M. Willaman Professor at Penn State University
Monday 14 January, 4pm, DHSR3
An overview of some work on modelling interface/microstructures with curvature dependent energies and also the effect of elasticity on critical nuclei morphology.
High Performance Computational Mechanics in Marenostrum supercomputer — Mariano Vázquez, Barcelona
Monday 21 January, 12 noon, DHSR3
Computational Mechanics (CM) has become a scientific discipline in itself, being High Perfomance Computational Mechanics (HPCM) a key sub-discipline. The effort for the most efficient use of distributed memory machines provides a different perspective to CM scientists relative to a wide range of topics, from the very physics of the problem to solve to the numerical method used. Marenostrum supercomputer is the largest facility in Europe and the 5th in the world (top500.org — Spring 2007). This talk described the research lines in the CASE Dpt. of the BSC applied to Aerospace, Bio-mechanics, Geophysics or Environment, through the development of Alya, the in-house HPCM code for complex coupled problems capable of running efficiently in large distributed memory facilities.
The Gamma-limit of a finite-strain Cosserat model for asymptotically thin domains versus a formal dimensional reduction (Abstract)
11am, Thursday 28th February 2008, Gibson Building Seminar Room
Patrizio Neff (Darmstadt)
Reconstruction of deformations from Cauchy–Green tensors with little regularity (Abstract)
5pm, Monday 3rd March 2008, Mathematical Institute, L3
Sorin Mardare (Zurich)
Carlos Mora-Corral presented a short series of lectures on bifurcation theory. These were held on the following dates from 12–1pm:
The programme for these lectures was as follows:
Lecture 1: Local Bifurcation Theory (I): Theorem of Crandall and Rabinowitz.
Lecture 2: Local Bifurcation Theory (II): Principle of exchange of stability, Lyapunov-Schmidt reduction, Theorem of Ize.
Lecture 3: Introduction to the topological degree: Existence and Uniqueness of the Brouwer degree, Existence and Uniqueness of the Leray-Schauder degree.
Lecture 4: Global Bifurcation Theory: Alternative of Rabinowitz.
Hanus Seiner, Laboratory of Ultrasonic Methods, Institute of Thermomechanics ASCR, Prague, Czech Republic.
10–11 am, 11th September, 2007 in DHSR1 in Maths Institute Annex in Dartington House on Little Clarendon Street.
“Motion of martensitic microstructures: Experimental observation on single crystals of shape memory alloys”.
Abstract: The lecture will summarize results of experimental observation of mobile interfacial microstructures forming between austenite and stabilized martensite in single crystals of Cu-Al-Ni shape memory alloy (SMA) during the shape recovery process. After short introduction to mechanics, crystallography, and thermodynamics of SMAs, the observed microstructures will be described and analyzed. Mathematical description of these microstructures is still an open problem, as the requirement of mobility seems to outweigh the compatibility conditions obeyed in the equilibrium state. The growth mechanisms of each microstructure will be analyzed and formation of rarely observed structures (such as weakly nonclassical interfaces) will be documented.
Zhiping Li, Beijing University.
2.30 am, 11th September 2007 in L1 in the Maths Institute on St Giles.
“Numerical computation of singular minimizers involving the Lavrentiev phenomenon”.
2–5 September 2007
3rd OxMOS Workshop — a joint meeting with MULTIMAT on “Microstructure”. This took place at St Anne’s College, Oxford.
For more information please visit the OxMOS/MULTIMAT workshop page.
Presentations from the Tuesday morning session (login required):
There were three discussion meetings based on aspects of the programme open to all internal project members. The meetings were held in DHSR2 on:
Three informal lunchtime meetings were held in Trinity term 2007 to investigate possible collaborations between OxMOS and other departments throughout the university. Each meeting concentrated on one of the OxMOS themes, and they were held from 1–2 pm in DHSR2 on the following dates:
OxMOS post-doc Christoph Ortner gave a series of lectures on gamma-convergence for the benefit of graduate students and post-docs. They were held at 10–11am on Tuesdays in weeks 3, 5 and 7 of Trinity term 2007 in DHSR2.
OxMOS visitor Casey Richardson gave a talk on his research on 6 June, from 10–11 am in DHSR2:
Fracture Trajectories Based on Crack Fronts
Crack fronts often play a fundamental role in engineering models for fracture, as they are the location of both the growth of cracks and the energy dissipation due to this (quasi-static) growth. However, there has not been a rigorous mathematical definition of crack front, nor well-posed mathematical models using these fronts as the location of growth and dissipation. Here, we give a natural weak definition of crack front and front speed, and consider some models of crack growth where the energy dissipation occurs at the crack front and is a nonlinear function of the front speed, so that the models cannot be reformulated without reference to the fronts. We then analyze one such variational problem in a two dimensional setting, finally showing the existence of an optimal crack path. We then consider another model, which requires fewer constraints on admissible trajectories, but requires relaxation. We show that, even though the model depends superlinearly on the crack speed and includes a penalty on front nucleation, it relaxes to an energy dissipation that is linear in the front speed and has no penalty on nucleation, i.e., a Griffith energy dissipation.
Between 26 April and 17 May a series of lectures was held in the Main Lecture Theatre, the Physical and Theoretical Chemistry Laboratory. The speaker was Professor Michele Parrinello.
Wednesday 18 April 2007
A mini-symposium based on the themes of the OxMOS project took place at the 49th British Applied Mathematics Colloquium, which was held at the University of Bristol, 17–19 April 2007.
Tuesday 13 March 2007
Models of growth and residual stress in biology.
Tissue growth is an important effect in areas such as developmental biology (including plant growth), bone remodelling and cancer. An accurate model of growth is a necessary framework on which to hang biochemical interactions. Moreover, growth causes stress, and it is increasingly being found that a cell’s environment, including the mechanical forces it experiences, can alter gene expression patterns and even affect cell fate. In such cases it becomes even more important to be able to predict the mechanics of growth.
The workshop aims to examine various different approaches to modelling growth and stress generation in biological tissue. Applications considered range from tumour growth to plant growth to the generation of heart beats.
Speakers are drawn from many disciplines, covering theory, experiment and computation. Both discrete (cell-based) and continuous (tissue-based) approaches will be discussed. The programme will allow time for discussion.
Speakers include:
More information can be found on the invitation poster (PDF).
Friday 23 February 2007
2–3 pm, Room 478, Computing Laboratory
Blaise Bourdin
Numerical implementation of variational brittle fracture.
The variational formulation of brittle fracture mechanics relies (in its current state) in computing the time evolution of global minimizers of an energy functional.
In terms of numerical implementation, this is a challlenge, as the energy functional is non-convex. Existing numerical methods typically rely on a time discretization and on constructing evolutions statisfying first order necessary conditions for optimality at each step separately.
I will briefly introduce the model and will focus on its numerical implementation. I particular, I will present a backtracking algorithm based on satisfying an additional necessary condition for optimality of the entire evolution with respect to time. I will give some elements of analysis and will present large scale numerical two and three dimensional numerical experiments. Time-permitting, I will also present experiments based on extensions of the Francfort-Marigo framework, and highlight some of the issues they raise.
Professor Gilles Francfort
Université Paris 13
12 noon, Thursday, 7 December
Lecture Theatre, Oxford University Computing Laboratory,
Wolfson Building, Parks Road, Oxford OX1 3QD
The variational theory of brittle fracture, which has developed in the past few years, is based on the time evolution of global minimizers of the energy functionals. In this talk I will briefly recall the main results, then concentrate on the issues brought about by global minimality and focus on possible alternatives.
There, the theory is far from complete, especially in dimensions greater than one.
New Frontiers in the Mathematics of Solids (OxMOS), which is funded by the Engineering and Physical Sciences Research Council (EPSRC) as a Critical Mass Project, held its Launch Workshop at Oxford on 8 November 2006. Over 50 people from around the country attended the day, with participation coming from a wide range of disciplines, including engineering, material science, biomedicine and, naturally, mathematics. The project co-coordinators are John Ball and Jon Chapman of the Oxford Mathematical Institute and Endre Süli of the Oxford University Computing Laboratory (Comlab).
The day was opened by John Ball who gave an overview of the objectives of the project. “The aim of OxMOS is to revitalize the study of mathematical solid mechanics in the U.K. through a simultaneous attack on three key areas: microstructure morphology; fracture; and applications in medicine. These areas share more or less the same governing equations, those of nonlinear elasticity theory, and we hope that lessons learnt in one area will prove fruitful in the others.”
The three main themes of the project were each represented by two speakers during the day, one approaching the subject from the practical applications and the other from the underlying mathematics.
The morning session concentrated on fracture mechanics and opened with David Hills of the Department of Engineering in Oxford speaking on ‘Recent progress in understanding deformation and fracture of solids at Oxford’. David’s session was twinned with one by Christoph Ortner, one of the post-doctoral researchers working on the OxMOS programme and based at the Comlab. In his presentation ‘Mathematical digressions from fracture mechanics’, Christoph gave a review of a recently developed variational theory of fracture and an outlook of the role of OxMOS.
Lunch was held at St. Anne’s college providing a chance to continue the discussions prompted by the morning sessions.
The first two presentations after lunch looked at the formation of patterns in microstructure in alloys and were chaired by Stefan Müller of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, who also acts as the chair of the OxMOS Steering Committee. David Cockayne of the Department of Materials in Oxford spoke on ‘The visible patterns in microstructure’ illustrating his talk by some fascinating images from his department’s electron microscopes. This was followed by Richard James of the Department of Aerospace Engineering and Mechanics, Minnesota attacking the subject from the mathematical angle in his paper ‘New observations on the origins of hysteresis in phase transformations and metastability in the calculus of variations’.
Following discussions over tea, the final sessions of the day looked at the applications of solid mechanics to medicine. Alison Noble of the Wolfson Medical Vision Laboratory in Oxford spoke on the challenges of understanding, detecting and imaging tumours, especially in the breast and colon, in her presentation ‘Soft tissue imaging and analysis’. Pras Pathmanathan, another OxMOS post-doctoral researcher based at the Comlab, followed this up with some of his doctoral work ‘Predicting tumour location by modelling the deformation of the breast using nonlinear elasticity’.
The day finished at 6.15pm. All the papers had generated good interdisciplinary discussion and participants were encouraged to contact the project manager should they wish to get more involved in collaboration with the OxMOS programme.
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