ICMS

Mar 30, 2009 - Apr 3, 2009

14 India Street, Edinburgh EH3 6EZ

Organisers

Name	Institution
Abdulle, Assyr	EPFL (Swiss Federal Institute of Technology)
Enguist, Bjorn	The University of Texas at Austin
Stuart, Andrew	University of Warwick

 

Multiscale or multi-physics modelling play a major role in the modelling of many important problems arising in the geosciences, atmospheric sciences, physical sciences, chemistry, biology and medicine. The past few years has seen new mathematical and computational frameworks emerging to address the challenge of multiscale computation. However, many major problems need still to be addressed and we will focus in this workshop on the issues of adaptivity, robustness and complexity in multiscale modeling and computation.

The purpose of the meeting is to bring together experts (both international leaders and promising young researchers) from several mathematical communities (a posteriori analysis, computational methods for stochastic and multiscale problems, homogenization) and provide an unique opportunity for exchange of ideas, presentation and dissemination of new results likely to contribute to a better understanding of the aforementioned challenging issues.

Numbers will be limited and participation is by invitation only.

This workshop is supported by:

EPSRC
SFC
LMS
Edinburgh Mathematical Society
Glasgow Mathematical Journal Trust

PDF file of full report.

Arrangements

Participation
Participation is by invitation only. The workshop will begin on Monday 30 March and finish on Friday 3 April 2009.

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one. If you do require a visa, ICMS can provide a signed invitation letter.

Venue
The workshop will take place at the head-quarters of ICMS, 14 India Street, Edinburgh. This house is the birthplace of James Clerk Maxwell and is situated in the historic New Town of Edinburgh, near the city centre.

The ICMS travel pages contain advice on how to travel to Edinburgh. For local information the finding ICMS page shows the location of ICMS and contains useful maps of the city centre.

The seminar room at ICMS has 4 whiteboards, 2 overhead projectors, a data projector and laptop. If you are giving a talk we ask that you use our ICMS laptop and bring your talk on a memory stick or CD. If you wish your talk to be pre-loaded onto our laptop, you may email it in advance to Johanna Kytöharju .

Wireless access is available throughout the ICMS building. There are also 4 public PCs which may be used at any time for internet access and to check email.

Accommodation
ICMS will arrange single en-suite rooms in local guest houses for those who require it. Accommodation is typically about 15 to 30 minutes walk from ICMS. Participants are also free to make their own arrangements and may claim back the cost, with receipts, up to a maximum of £65.00 a night for up to 6 nights. A list of Edinburgh accommodation of various sorts and prices is available here . Sections 1-3 are particularly relevant.

Meals and Refreshments
There will be an informal wine reception after the close of lectures on Monday 30 March.

Morning and afternoon refreshments will be provided on each day of the workshop.

Buffet lunches will be provided on only Monday 30 March, Wednesday 1 April and Friday 3 April at no cost to participants. For the remainder of the days, participants are free to go out for lunch and explore the many cafés, sandwich shops, restaurants and bars nearby. On arrival we will provide you with a ‘welcome’ pack which will contain information about eating places nearby.

On Tuesday 31 March a mezze style evening meal will be provided in Nargile Turkish Restaurant, 73 Hanover Street, at 19.00. The workshop dinner will take place at 19.00 at The Magnum Restaurant, 1 Albany Street, on the evening of Thursday 2 April. The workshop grant will cover the cost of these meals.

Registration
Registration will take place on Monday 30 March from 9.00 to 10.30 at ICMS.

Financial Arrangements
Unless otherwise specified in your invitation letter, the workshop grant will cover the cost of your bed and breakfast accommodation, tea/coffee throughout the workshop, lunch on Monday, Wednesday and Friday only, the wine reception, the informal supper on Tuesday and the Workshop Dinner on Thursday evening.

If we have agreed to pay some of your travel costs, you will be informed by email. Reimbursement will take place after the workshop. At Registration you will be given an expenses claim form and this should be submitted to ICMS, with receipts and bank details. Please note that we cannot reimburse any item without a receipt.

Programme

EACH TALK IS FOLLOWED BY A 10 MINUTE DISCUSSION.

Monday 30 March

09.00 - 10.30	Registration
10.30 - 11.05	Mitchell Luskin (University of Minnesota) Predictive and efficient quasicontinuum methods
11.15 - 11.50	Pingbing Ming (Chinese Academy of Sciences) Understanding quasicontinuum method: numerical analysis and beyond
12.00 - 14.00	Buffet lunch
14.00 - 14.35	Serge Prudhomme (The University of Texas at Austin) Error estimation and adaptivity for atomistic-to-continuum coupling methods
14.45 - 15.20	Ping Lin (University of Dundee) The quasi-continuum approximation and virtual internal bond model for material fracture
15.30 - 16.00	Tea/Coffee
16.00 - 16.35	Valery Smyshlyaev (University of Bath) Homogenisation with "partial" degeneracies and applications
17.00 - 18.00	Wine reception at ICMS, 14 India Street

 

Tuesday 31 March

09.00 - 09.35	Greg Pavliotis (Imperial College London) Parameter estimation for multiscale diffusions
09.45 - 10.20	Kostas Zygalakis (University of Oxford) On the existence of modified equations for stochastic differential equations
10.30 - 11.00	Tea/Coffee
11.00 - 11.35	Omar Lakkis (University of Sussex) Error control via elliptic reconstruction in some evolution equations
11.45 - 12.20	Gabriel Stoltz (École Nationale des Ponts et Chaussées) Adaptive methods for computational statistical physics
12.30 - 14.00	Lunch
14.00 - 14.35	Phaedon-Stelios Koutsourelakis (Cornell University) Bayesian reduced-order models for multiscale dynamical systems
14.45 - 15.20	Liliana Borcea (Rice University) Filtering random effects in imaging
15.30 - 16.00	Tea/Coffee
16.00 - 16.35	Ibrahim Fatkullin (University of Arizona) A computational strategy for multiscale systems with application to Lorenz 96 model
19.00 -	Informal evening meal at Nargile Turkish Restaurant, 73 Hanover Street

 

Wednesday 1 April

09.00 - 09.35	Bjorn Enguist (The University of Texas at Austin) Analysis of heterogeneous multiscale methods
09.45 - 10.20	Marcus Grote (University of Basel) Finite element heterogeneous multiscale method for the wave equation
10.30 - 11.00	Tea/Coffee
11.00 - 11.35	Olof Runborg (Royal Institute of Technology) A multiscale method for the wave equation in heterogeneous medium
11.45 - 12.20	Richard Sharp (Carnegie Mellon University) Macroscopic variables for numerical multiscale methods: applications to highly oscillatory ODEs
12.30 - 13.05	Richard Tsai (The University of Texas at Austin) Numerical multiscale algorithms for highly oscillatory ODEs
13.15 - 14.30	Buffet lunch - Knowledge transfer networking event

 

Thursday 2 April

09.00 - 09.35	Rob Stevenson (Universiteit van Amsterdam) Adaptive tensor product wavelet methods
09.45 - 10.20	Rob Scheichl (University of Bath) Multilevel iterative solvers versus upscaling/multiscale techniques
10.30 - 11.00	Tea/Coffee
11.00 - 11.35	Ivan Graham (University of Bath) A new multiscale finite element method for high-contrast elliptic interface problems
11.45 - 12.20	Alain Damlamian (Université Paris 12, Val de Marne) The unfolding method as a way to homogenize known results
12.30 - 14.00	Lunch
14.00 - 14.35	Yalchin Efendiev (Texas A&M University) Mixed multiscale finite element method using limited global information
14.45 - 15.20	Christoph Schwab (ETH Zurich) Sparse adaptive tensor FEM for elliptic periodic multiscale problems
15.30 - 16.00	Tea/Coffee
16.00 - 16.35	Viet Ha Hoang (Nanyang Technological University) Sparse finite element method for periodic multiscale nonlinear monotone problems
19.00 -	Workshop dinner at The Magnum Restaurant, 1 Albany Street

 

Friday 3 April

09.00 - 09.35	Ben Leimkuhler (University of Edinburgh) Controlled variable molecular dynamics
09.45 - 10.20	Pingwen Zhang (Peking University) Nucleation and boundary layer in diblock copolymer SCFT model
10.30 - 11.00	Tea/Coffee
11.00 - 11.35	Tiejun Li (Peking University) Hybrid methods in simulating chemical kinetic systems
11.45 - 12.20	Tony Lelievre (École Nationale des Ponts et Chaussées) Multiscale models for viscoelastic fluids and longtime behaviour
12.30 -	Buffet lunch and close of workshop

Presentations:

Presentation Details
Borcea, Liliana
Filtering random effects in imaging
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Objects that are buried deep in heterogeneous media produce faint echoes which are difficult to distinguish from the backscattered field. Sensor array imaging in such media cannot work unless we filter out the backscattered echoes and enhance the coherent arrivals that carry information about the objects that we wish to image. The question is how to do the filtering without prior information about the location of the objects and with no knowledge of the fluctuations of the wave speed in the medium, which we model with random processes. I will discuss two filtering approaches. The first one is specialised to randomly layered media and has a complete theory. The second one is less understood from the theoretical point of view, but it extends to more general random media.
Damlamian, Alain
The unfolding method as a way to homogenize known results
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We show how the periodic unfolding method can be seen as tool to homogenize already known results in a simple and unified way.
Efendiev, Yalchin
Mixed multiscale finite element method using limited global information
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In this talk, I will describe mixed multiscale finite element methods and their applications to porous media flows. For problems without scale separation, some type of global information is needed. I will talk about the use of approximate global information based on partial upscaling. The application of these methods to stochastic porous media will be described.
Enguist, Bjorn
Analysis of heterogeneous multiscale methods
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TBA
Fatkullin, Ibrahim
A computational strategy for multiscale systems with application to Lorenz 96 model
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I will discuss numerical schemes for systems with multiple spatio-temporal scales and illustrate them on a specific example of a moderately large deterministic system displaying chaotic behavior (Lorenz 96 model). A particular attention will be paid to issues like consistency, accuracy, efficiency, the role of possible hidden slow variables, as well as to additional effects arising on the diffusive time-scale. This is a joint work with Eric Vanden-Eijnden.
Graham, Ivan
A new multiscale finite element method for high-contrast elliptic interface problems
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We introduce a new multiscale finite element method which is able to accurately capture solutions of elliptic interface problems with high contrast coefficients by using only coarse quasiuniform meshes, and without resolving the interfaces. A typical application would be the modelling of flow in a porous medium containing a number of inclusions of relatively low permeability, embedded in a matrix of relatively high permeability. Our method is H1- conforming, with degrees of freedom at the nodes of a triangular mesh and requires the solution of subgrid problems for the basis functions on elements which straddle the coefficient interface, but uses standard linear approximation otherwise. A key point is the introduction of novel coefficient-dependent boundary conditions for the subgrid problems. Under moderate assumptions, we prove that our methods have (optimal) convergence rate of O(h) in the energy norm and O(h^2) in the L_2 norm where h is the (coarse) mesh diameter and the hidden constants in these estimates are independent of the coefficient "contrast''. The proof does not depend on perodicity or any homogenisation argument. This is joint work with Jay Chu and Tom Hou of Caltech.
Grote, Marcus
Finite Element Heterogeneous Multiscale Method for the Wave Equation
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Following previous work of Abdulle, E, and Engquist (2003, 2005), we propose a finite element heterogeneous multiscale method for the simulation of time dependent waves propagating through a medium with rapidly varying sound speed. Here the fine scales for the problem are accounted for in the stiffness matrix at the coarse scale by solving micro-problems with a scale-independent fixed-size within each macro-element. A priori error estimates of the fully discrete method, which include the discretization errors from the macro- and the microproblems, are derived. Numerical examples illustrate the theoretical convergence rates and the usefulness of our approach.
Hoang, Viet Ha
Sparse finite element method for periodic multiscale nonlinear monotone problems
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A sparse tensor product Finite Element method is developed for the high dimensional limiting problems obtained by applying the multiscale convergence to a multiscale non-linear monotone problem in $R^d$. The limiting problem is posed in a product space, so tensor product FE spaces are used for discretization. This sparse FE method requires essentially the same number of degrees of freedom to achieve essentially equal accuracy to that of a standard FE method of a partial differential equation in $R^d$.
Koutsourelakis, Phaedon-Stelios
Bayesian reduced-order models for multiscale dynamical systems
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This talk involves the derivation of reduced-order models for high-dimensional, multiscale dynamical systems. Such systems appear in several problems in computational physics and their direct simulation over long time periods is generally impractical or infeasible. Despite the high dimensionality of the observables, there generally exist a few generalized reaction coordinates that can be used to track the evolution of the system, which can nevertheless vary with time in terms of their number and their relation with the observables. We adopt a data-driven approach that makes use of observables obtained from computer simulations and/or experiments and adopt a Bayesian framework for the structural identification and prediction of such systems. At the core of the proposed methodology lie simple models which are viewed as experts that explain (and potentially predict) the high dimensional observables in a partial and approximate manner. It is the combination of these experts through appropriate probabilistic modeling that gives rise to a sparse and accurate lower-order representation.
Lakkis, Omar
Computing the stochastic Allen - Cahn problem
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Our main goal is the numerical approximation of the Allen-Cahn problem with additive white noise in one-dimensional space. The main difficulty for a rigorous numerical discretization of this SPDE, which is an important model for more complicated phase separation descriptions, is the presence of the time-space white noise as a forcing term. The discretization has to be conducted in two stages: (1) regularize the white noise and study the regularized problem, (2) approximate the regularized problem and derive a finite element Monte Carlo simulation scheme. We then have to relate our numerical results to theoretical results from the probabilistic analysis of scaling limits conducted mainly by Funaki and Brassesco, De Masi & Presutti in the 1990's [KKL07]. Time allowing I shall review recent advances on the topic where we analyze the behavior of one and multiple interfaces when the interface thickness parameter does not approach the limit. Asymptotic analysis shows that the stochastic solution and its approximation remain "close" to a set of functions where the interface makes sense. This is particularly useful to relate numerical results to theory and it has the potential to define stochastic diffuse interfaces in dimensions higher than 1 [KLR09]. Based on joint work with: G. Kossioris (Crete, Greece), M. Katsoulakisd (Amherst, Massachussets) and M. Romito (Florence, Italy).
Leimkuhler, Ben
Controlled variable molecular dynamics
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For molecular dynamics to be useful for recovering macroscopically - relevant information (e.g. thermodynamic averages), it must be regulated by auxiliary control laws such as thermostats and barostats. In this talk I will discuss some examples of such controls, focusing primarily on thermostats. Several types of mixed stochastic-dynamic methods will be presented. This talk describes joint work with Emad Noorizadeh and Sebastian Reich.
Lelievre, Tony
Multiscale models for viscoelastic fluids and longtime behaviour
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We will present recent results concerning the longtime behaviour of some micro-macro and macroscopic models for complex fluids. Micro-macro models (like the dumbbell model for polymeric fluids) couple a fine description of the microstructures evolving in the fluid, with the classical conservations laws of fluid mechanics. Macroscopic models (like the Oldroyd-B model) are based on phenomenological laws for the stress tensor within the fluid. The study of the longtime behaviour for these models gives some insight on the dissipation mechanisms. We will also discuss some numerical schemes which satisfy similar longtime behaviour.
Li, Tiejun
Hybrid methods in simulating chemical kinetic systems
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I will talk about the hybrid methods for simulation multiscale chemical kinetic systems. In which, the species will be partitioned into continuous and discrete types. The stiff solver is applied in different regimes.
Lin, Ping
The quasi-continuum approximation and virtual internal bond model for material fracture
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Recently much attention has been paid to a so-called quasi-continuum approximation in multi-scale material simulation. I will briefly introduce the method (based on an adaptive finite element idea) and results of convergence analysis for the steady state case and comment on when the method may fail. Then I will consider a simple generalization of the method to a zero-temperature dynamical case assuming nearest neighbor interactions. We will relate the discrete atomistic model to the continuous virtual internal bond model which is a nonlinear wave equation of mixed type. We can construct the solution of its Riemann problem and use it to justify or guide our study of numerical methods. Our numerical simulation for a fracture example indicates that the method may be reliable at the early stage of the fracture. Model improvement is needed for a longer time fracture simulation.
Luskin, Mitchell
Predictive and efficient quasicontinuum methods
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The development of predictive and efficient atomistic-to-continuum computational methods requires an analysis of the error and efficiency of its many components - coupling method, model and mesh adaptivity, and solution methods - and their integration into an effective algorithm. There are many choices available for the interaction between the representative atoms of the quasicontinuum method, especially between those in the atomistic and continuum regions, which has led to the development of a variety of quasicontinuum approximations. We will present criteria for determining a good choice of quasicontinuum approximation that considers trade-offs between accuracy and algorithmic efficiency. Our criteria are based on the effect of the coupling error on the goal of the computation, on the integration of the quasicontinuum approximation with model and mesh adaptivity, and on the development of efficient iterative solution methods. Joint Work with Marcel Arndt, Matthew Dobson, and Christoph Ortner
Ming, Pingbing
Understanding quasicontinuum method: numerical analysis and beyond
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In this talk, I will report some recent work for the mathematically understanding of quasicontinuum method, which is among the most successful multiscale methods for modelling the mechanical deformation of solids. The stability and accuracy of nonlocal quasicontinuum method will be discussed in the framework of the classical numerical analysis together with recent results in the understanding of the bridge between the atomistic and the continuum model of the crystalline solids.
Pavliotis, Greg
Parameter estimation for multiscale diffusions
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We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized single-scale model to suchmultiscale data. We demonstrate, numerically and analytically, that if the data is sampled too finely then the parameter fit will fail, in that the correct parameters in the homogenized model are not identified. We also show, numerically and analytically, that if the data is subsampled at an appropriate rate then it is possible to estimate the coefficients of the homogenized model correctly. We also show that subsampling combined with appropriate averaging of the data reduces the variance and leads to an efficient estimator.
Prudhomme, Serge
Error estimation and adaptivity for atomistic-to-continuum coupling methods
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We will present some recent progress on the development of an adaptive strategy for the control of modeling error in atomic-to-continuum coupled simulations. The method is based on the Arlequin framework that considers an overlap region to couple the continuum and molecular models. A goal-oriented adaptive strategy is used in order to determine the optimal position of the overlap so as to reduce the modeling errors in quantities of interests within preset levels of accuracy.
Runborg, Olof
A multiscale method for the wave equation in heterogeneous medium
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We consider the wave equation in a medium with a rapidly varying speed of propagation. We construct a multiscale scheme based on the heterogeneous multiscale method, which can compute the correct coarse behavior of wave pulses traveling in the medium, at a computational cost essentially independent of the size of the small scale variations. This is verified by theoretical results and numerical examples.
Scheichl, Rob
Multilevel iterative solvers versus upscaling/multiscale techniques
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In this talk we compare multilevel iterative solvers and certain upscaling/multiscale techniques for elliptic PDEs with highly variable coefficients. These arise in practice, for example, in the computation of flow in heterogeneous porous media, in both the deterministic and (Monte-Carlo simulated) stochastic cases. When there is no a priori scale separation, standard multiscale techniques require the solution of local "cell" problems in each cell, leading to a computational complexity that can be no better than linear in N, where N is the number of unknowns on the subgrid (globally). Moreover, except for the periodic case, no theory is yet available that analyses the dependency of the accuracy of the upscaled solutions on the coefficient variation. Multilevel iterative methods, such as multigrid or domain decomposition, on the other hand, lead to a similar computational cost with respect to subgrid size (i.e. O(N)), but here the computational cost will in general depend on the coefficient variation. In a series of recent papers we have analysed, both numerically and theoretically, various simple variants of multigrid and domain decomposition methods that are robust to strong coefficient variation. Their similarity to various multiscale techniques provides guidelines for the design of robust multiscale techniques and theoretical tools for their analysis. Neverthless, the findings suggest also that in the highly heterogeneous coefficient case multilevel iterative methods may be preferable to current multiscale techniques. This is joint work with I.G. Graham, J. Van lent (both Bath), and C. Pechstein (Linz).
Schwab, Christoph
Sparse adaptive tensor FEM for elliptic periodic multiscale problems
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Periodic multiscale problems with n>1 separated scales in a physical domain of dimension d can be reformulated as one-scale problems in a tensor product domain of dimension nd, thereby trading the complexity issue of scale resolution in direct simulation for the curse of dimension. We propose overcoming the latter by sparse adaptive tensor product Finite Element discretization of the high-dimensional one-scale problem. We present some results and more open problems in the numerical analysis of this approach for linear and nonlinear PDEs.
Sharp, Richard
Macroscopic variables for numerical multiscale methods: applications to highly oscillatory ODEs
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Methods within the framework of the heterogeneous multiscale methods compute, simultaneously, microscopic and macroscopic solutions to a problem for which only the microscopic dynamics are known. The macroscopic solution is updated by choosing macroscopic state variables and deriving the effective force on these variables from the local microscopic solution. The macroscopic solution is then used to reinitialize the microscopic system. Such methods are applicable to a wide array of systems, for example schooling fish, annealing crystalline networks, and certain molecular dynamics simulations. It is essential to know whether the chosen macroscopic state variables provide enough information to produce a macroscopic solution consistent with the solution of the microscopic model. We apply a Heterogeneous Multiscale Method style algorithm to highly oscillatory ODEs, and use local time averages of the original system variables as the macroscopic variables. These variables are simple to produce and understand, and it can be shown that they are sufficient to close the microscopic/macroscopic loop in certain cases.
Smyshlyaev, Valery
Homogenisation with "partial" degeneracies and applications
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We consider homogenization problems for a generic class of (scalar or vector) operators with "partial" degeneracy in the (tensorial) coefficients. The employed tools are those of "non-classical" (high contrast type) homogenisation. This leads to interesting effect physically (for example allowing "directional localisation", with no wave propagation in certain directions), and mathematically allows treating form a unified perspective "classical", high-contrast homogenizations and intermediate cases. We discuss some related analytic issues, including the need to develop appropriate versions of two-scale convergence and of the theory of compensated compactness.
Stevenson, Rob
Adaptive tensor product wavelet methods
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Sparse grid or hyperbolic cross approximations based on a tensor product of multiscale bases converge with a rate equal to the worst rate of the individual factors. In particular, the rate does not deteriorate with the number of factors. This result holds true when the function to be approximated has bounded mixed derivatives of certain higher order. In cases of interest, this regularity condition is not necessarily fulfilled as we will demonstrate for the example of Poisson's problem with a general smooth right hand side. Above regularity condition can be drastically reduced by considering best $N$-term approximation from the tensor product basis. Moreover, when the function to be approximated is given as the solution of an operator equation, the rate of best $N$-term approximation can be realized by adaptive wavelet methods. As applications, we will discuss in some detail the solution of Poisson's problem in high space dimensions, and that of parabolic evolution equations in simultaneous space-time variational formulation.
Stoltz, Gabriel
Adaptive methods for computational statistical physics
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I will present the mathematical analysis of two instances of nonlinear stochastic dynamics used in molecular dynamics to efficiently compute averages properties as predicted by statistical physics: (i) the adaptive biasing force method in the context of free energy computations; (ii) a method to sample the configurations of a system with a constraint holding in average. In both cases, the proofs of convergence rely on entropy estimates, and some applications to physical systems are proposed.
Tsai, Richard
Numerical multiscale algorithms for highly oscillatory ODEs
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A multiscale method for computing the effective slow behavior of a system of weakly coupled general oscillators is presented. The oscillators may be either in the form of a periodic solution or a stable limit cycle. Furthermore, the oscillators may be in resonance with one another and thereby generate some hidden slow dynamics. The proposed method relies on correctly tracking a set of slow variables that is sufficient to approximate any variable and functional that are slow under the dynamics of the ODE. The technique is more efficient than existing methods and its advantages are demonstrated with examples. The algorithm follows the framework of the heterogeneous multiscale method.
Zhang, Pingwen
Nucleation and boundary layer in diblock copolymer SCFT model
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The phase diagram of the equilibrium states and the stability of the possible microstructures are both important for polymer scientists. The phase behavior of a diblock copolymer system could be studied through self-consistent mean field theory (SCFT). We extensively study the boundary layer of a diblock copolymer melt confined system using compressible self-consistent mean-field theory. We discover the boundary layer profile and its thickness are only determined by boundary potential and compressible parameter. We have also investigated several effects due to the confinement of polymer melts by impenetrable hard surfaces in the self-consistent field calculations. We will also introduce a numerical method to study the nucleation in copolymer melts. Nucleation is the decay of a metastable state via the thermally activated formation and subsequent growth of droplets of the equilibrium phase. We will consider the nucleation in diblock copolymer melts, whose equilibrium phases are well understood. We apply a new numerical method, called the string method, to compute the minimum energy path (MEP). Then from the MEP, we find the size and shape of the critical droplet and the free-energy barrier to nucleation.
Zygalakis, Kostas
On the existense of modified equations for stochastic differential equations
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In this talk we describe a general framework for deriving modified equations for stochastic differential equations with respect to weak convergence. Results are presented for a variety of first order methods, such as Euler-Maryama, Milstein and symplectic Euler. Existence of higher order modified equations is also discussed.

Participants

Name	Institution
Abdulle, Assyr	EPFL (Swiss Federal Institute of Technology)
Ainsworth, Mark	University of Strathclyde
Borcea, Liliana	Rice University
Cliffe, Andrew	University of Nottingham
Damlamian, Alain	Université Paris 12 Val de Marne
Efendiev, Yalchin	Texas A&M University
Enguist, Bjorn	The University of Texas at Austin
Fatkullin, Ibrahim	University of Arizona
Ferro, Maria	Università di Napoli 'Federico II'
Gelder, David	Mathematics for Manufacturers
Graham, Ivan	University of Bath
Grote, Marcus	University of Basel
Hoang, Viet Ha	Nanyang Technological University
Koutsourelakis, Phaedon-Stelios	Cornell University
Lakkis, Omar	University of Sussex
Leimkuhler, Ben	University of Edinburgh
Lelievre, Tony	École Nationale des Ponts et Chaussées
Li, Tiejun	Peking University
Lin, Ping	University of Dundee
Liu, Yi G	AWE plc
Lord, Gabriel	Heriot-Watt University
Luskin, Mitchell	University of Minnesota
Ming, Pingbing	Chinese Academy of Sciences
Nguetseng, Gabriel	University of Yaoundé I
Nonnenmacher, Achim	EPFL (Swiss Federal Institute of Technology)
Noorizadeh, Emad	University of Edinburgh
Pavliotis, Greg	Imperial College London
Prudhomme, Serge	The University of Texas at Austin
Runborg, Olof	Royal Institute of Technology
Scheichl, Rob	University of Bath
Schwab, Christoph	ETH Zurich
Sharp, Richard	Carnegie Mellon University
Sickenberger, Thorsten	Heriot-Watt University
Smyshlyaev, Valery	University of Bath
Stevenson, Rob	Universiteit van Amsterdam
Stoltz, Gabriel	École Nationale des Ponts et Chaussées
Stuart, Andrew	University of Warwick
Tsai, Richard	The University of Texas at Austin
Zhang, Pingwen	Peking University
Zygalakis, Kostas	University of Oxford