| |
|
|
This meeting is an intra-network. The main purpose of the
meeting is to foster communication on current research among the network's members. It is also an
opportunity for post-graduates and young researchers to advertise their scientific work and test
its reach on a rather informal and friendly audience, as well as for senior members to lecture
and inform the younger ones about different kinds of research.
The basic format of this meeting is that all participants are treated on an equal footing, and
each person whishing to talk about their work is allocated the same amount of time regardless
of position and status. The time for a talk is 30 minutes plus 15 minutes that can be used for
discussion. Discussion is not necessarily confined to the end of the talk, but can be
interspread in the midst of the talk (for example to clarify a point being exposed) if the
participants and the speaker wish to do so. Due to the informal and small size of the meeting,
this seems to be a constructive fashion of delivering the talks.
The meeting is held at the University of Sussex on Friday 10-Saturday 11 December 2004. The
organisers are Charlie Elliott and Omar Lakkis, from the University of Sussex. Staff, student
and faculty support was kindly provided by Tom Armour, Heather Burton, Yohei Kashima, Vanessa
Styles, Alex Tomasi, Rich Welford, Marc Williams.
Participants
- Imperial College, London
- John Barrett
- Christoph Haselwandter
- Robert Nurnberg
- Grigorios Pavliotis
- Dimitri Vvedensky
- University of Oxford
- Aurelio Arranz
- Benson Muite
- Christoph Ortner
- Endre Suli
- University of Sussex
- Charlie Elliott
- Yohei Kashima
- David Kay
- Omar Lakkis
- Sheila McBeth
- Vanessa Styles
- Shahnaz Taheri
- Alessandro Tomasi
- Richard Welford
Schedule
- Speaker:
- Aurelio Arranz
- Title:
- Discontinuous Galerkin finite element methods for elasticity and crack-propagation problems
- Adbstract:
-
We approximate the solutions to the dynamic Navier-Lamé (Elasticity) equation both in 2D and 3D. Some preliminary results on its application to fully 3D-crack propagation problems are also shown.
- Speaker:
- Christoph Ortner
- Title:
- Free discontinuity problems in fracture mechanics
- Adbstract:
-
I give an overview of a recent model for brittle fracture based on the minimization of energies defined in SBV and outline a moving mesh approach for the discretization of models with free discontinuities.
- Speaker:
- Yohei Kashima
- Title:
- A variational approach to singular diffusion equations
- Adbstract:
-
Some models describing motion of crystal have strong singularity, therefore they do not make sense mathematically in their original forms. We will introduce a method to formulate such singular diffusion equations and consider the behaviour of their solutions defined properly. The singular gradient of cristalline energy can be formulated by a subdifferential of the convex functional in a suitable functional space. By characterising the subdifferential operator, we observe the speed of the solution solving the initial boundary value problem. Especially we apply this method to 4th order singular gradient flow equations and investigate the motion of crystalline surface.
- Speaker:
- Richard Welford
- Title:
- A finite element multigrid solver for the Cahn-Hilliard equation
- Adbstract:
-
A finite element multigrid solver for the Cahn-Hilliard equation is presented which exhibits convergence rates independent of mesh size. Numerical examples are shown which show the superiority of this method over traditional iterative methods such as Gauss-Seidel.
- Speaker:
- Sheila McBeth
- Title:
- The recovery of objects from noisy images
- Adbstract:
-
The state-of-the art Osher-Sole-Vese model for separating digital images into cartoon plus texture is presented. Fourier space is used to show why it is an improvement over the previous Rudin-Osher-Fatemi model. A summary is given of our theoretical results for the model to date. The signal-to-noise ratio is introduced, which quantifies the quality of a restored image. An algorithm is given for choosing the weight parameter in the model when the noise is known. Numerical experiments are presented which demonstrate the superiority of OSV to ROF. The wider relevance of our work is discussed.
- Speaker:
- Grigorios Pavliotis
- Title:
- Modulation equations: stochastic bifurcation in large domains
- Adbstract:
-
We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this approximation also extends to the invariant measures of these equations. Joint work with D. Bloemker and M. Hairer.
- Speaker:
- Dimitri Vvedensky
- Title:
- Morphological evolution of strained epitaxial films
- Adbstract:
-
The morphological evolution of strained epitaxial films is described with a stochastic differential equation obtained from the master equation for the atomistic growth kinetics. The transition rules are based on previous kinetic Monte Carlo simulations that incorporate the effects of strain in local height-dependent energy barriers to adatom hopping, attachment and detachment. Comparisons with previous approaches are made to provide an atomistic interpretation of equations obtained using classical elasticity.
- Speaker:
- Christoph Haselwandter
- Title:
- Multiscale approach to amorphous and homoepitaxial surface growth
- Adbstract:
-
Lattice Langevin equations are derived for lattice models of surface growth. These equations provide an exact description of the lattice models which is suitable for a direct mathematical analysis, such as the passage to the continuum limit, and constitute a computational alternative to kinetic Monte Carlo simulations. These concepts are applied to models for the amorphous and homoepitaxial growth of solids.
- Speaker:
- Omar Lakkis
- Title:
- A finite element method for the stochastic Allen-Cahn equation
- Adbstract:
-
[Joint work with: G. Kossioris (Crete, Greece) and M. Katsoulakis (Amherst, Massachussets).]
I will motivate my talk by first reviewing the background of the stochastic Allen-Cahn equation. Next I will show the difficulties faced upon trying to discretise the equation by traditional finite elements/differences. This is a well-known PDE at a macroscopic level that is subject to microscopic fluctuations that are modelled by the white noise.
It turns out that a good way for the numerician to proceed is first to regularise the white noise that appears in the equation and secondly to approximate numerically the regularised problem. I will expose some recent results that justify this approach. Simplicity of implementation and efficiency being the major goals.
Time allowing, I will give a brief discussion of the interplay the different parameters appearing in the model itself, the regularisation and the numerical approximation.
|
|
|
