Atomistic-continuum multiscale modelling of magnetisation dynamics at non-zero temperature

In this article, a few problems related to multiscale modelling of magnetic materials at finite temperatures and possible ways of solving these problems are discussed. The discussion is mainly centred around two established multiscale concepts: the partitioned domain and the upscaling-based methodologies. The major challenge for both multiscale methods is to capture the correct value of magnetisation length accurately, which is affected by a random temperature-dependent force. Moreover, general limitations of these multiscale techniques in application to spin systems are discussed.Comment: 30 page

Graphene and Black Holes: novel materials to reach the unreachable

The case for a dedicated laboratory, to test hep-th models on analogue systems, is briefly made. The focus is on graphene.Comment: 3 pages; invited to talk to the workshop "New Frontiers in Multiscale Modelling of Advanced Materials", ECT*, Trento, June 17-20, 2014; to appear in Frontiers in Material

Multiscale time series modelling with an application to the relativistic electron intensity at the geosynchronous orbit

In this paper, a Bayesian system identification approach to multiscale time series modelling is proposed, where multiscale means that the output of the system is observed at one(coarse) resolution while the input of the system is observed at another (One) resolution. The proposed method identifies linear models at different levels of resolution where the link between the two resolutions is realised via non-overlapping averaging process. This averaged time series at the coarse level of resolution is assumed to be a set of observations from an implied process so that the implied process and the output of the system result in an errors-in-variables ARMAX model at the coarse level of resolution. By using a Bayesian inference and Markov Chain Monte Carlo (MCMC) method, such a modelling framework results in different dynamical models at different levels of resolution at the same time. The new method is also shown to have the ability to combine information across different levels of resolution. An application to the analysis of the relativistic electron intensity at the geosynchronous orbit is used to illustrate the new method

Reducing The Computational Requirements for Simulating Tunnel Fires by Combining Multiscale Modelling and Multiple Processor Calculation

Multiscale modelling of tunnel fires that uses a coupled 3D (fire area) and 1D (the rest of the tunnel) model is seen as the solution to the numerical problem of the large domains associated with long tunnels. The present study demonstrates the feasibility of the implementation of this method in FDS version 6.0, a widely used fire-specific, open source CFD software. Furthermore, it compares the reduction in simulation time given by multiscale modelling with the one given by the use of multiple processor calculation. This was done using a 1200 m long tunnel with a rectangular cross-section as a demonstration case. The multiscale implementation consisted of placing a 30 MW fire in the centre of a 400 m long 3D domain, along with two 400 m long 1D ducts on each side of it, that were again bounded by two nodes each. A fixed volume flow was defined in the upstream duct and the two models were coupled directly. The feasibility analysis showed a difference of only 2% in temperature results from the published reference work that was performed with Ansys Fluent (Colella et al., 2010). The reduction in simulation time was significantly larger when using multiscale modelling than when performing multiple processor calculation (97% faster when using a single mesh and multiscale modelling; only 46% faster when using the full tunnel and multiple meshes). In summary, it was found that multiscale modelling with FDS v.6.0 is feasible, and the combination of multiple meshes and multiscale modelling was established as the most efficient method for reduction of the calculation times while still maintaining accurate results. Still, some unphysical flow oscillations were predicted by FDS v.6.0 and such results must be treated carefully

Multiscale Modelling for Tokamak Pedestals

Pedestal modelling is crucial to predict the performance of future fusion devices. Current modelling efforts suffer either from a lack of kinetic physics, or an excess of computational complexity. To ameliorate these problems, we take a first-principles multiscale approach to the pedestal. We will present three separate sets of equations, covering the dynamics of Edge Lo- calised Modes, the inter-ELM pedestal, and pedestal turbulence, respectively. Precisely how these equations should be coupled to each other are covered in detail. This framework is completely self-consistent; it is derived from first principles by means an asymptotic expansion in appropriate small parameters. The derivation exploits the narrowness of the pedestal region, the smallness of the thermal gyroradius, and the low plasma $\beta$ typical of current pedestal operation to achieve its simplifications. The relationship between this framework and gyrokinetics is analysed, and possibilities to directly match this framework onto multiscale gyrokinetics are explored. A detailed comparison between our model and other models in the literature is performed. Finally, the potential for matching this framework onto an open-field-line region is discussed.Comment: 49 pages; Accepted for publication in the Journal of Plasma Physic

Multiscale functional inequalities in probability: Concentration properties

In a companion article we have introduced a notion of multiscale functional inequalities for functions $X(A)$ of an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. These inequalities are multiscale weighted versions of standard Poincar\'e, covariance, and logarithmic Sobolev inequalities. They hold for all the examples of fields $A$ arising in the modelling of heterogeneous materials in the applied sciences whereas their standard versions are much more restrictive. In this contribution we first investigate the link between multiscale functional inequalities and more standard decorrelation or mixing properties of random fields. Next, we show that multiscale functional inequalities imply fine concentration properties for nonlinear functions $X(A)$. This constitutes the main stochastic ingredient to the quenched large-scale regularity theory for random elliptic operators by the second author, Neukamm, and Otto, and to the corresponding quantitative stochastic homogenization results.Comment: 24 page