Self-organized escape processes of linear chains in nonlinear potentials

An enhancement of localized nonlinear modes in coupled systems gives rise to a novel type of escape process. We study a spatially one dimensional set-up consisting of a linearly coupled oscillator chain of $N$ mass-points situated in a metastable nonlinear potential. The Hamilton-dynamics exhibits breather solutions as a result of modulational instability of the phonon states. These breathers localize energy by freezing other parts of the chain. Eventually this localised part of the chain grows in amplitude until it overcomes the critical elongation characterized by the transition state. Doing so, the breathers ignite an escape by pulling the remaining chain over the barrier. Even if the formation of singular breathers is insufficient for an escape, coalescence of moving breathers can result in the required concentration of energy. Compared to a chain system with linear damping and thermal fluctuations the breathers help the chain to overcome the barriers faster in the case of low damping. With larger damping, the decreasing life time of the breathers effectively inhibits the escape process.Comment: 14 pages, 13 figure

A High-Level Programming Language for Modelling the Earth

Computational models based on the solution of partial differential equations (PDEs) play a key role in Earth systems simulations. The software implementing these models depends on the discretisation method, data structures and the computer architecture. For this reason, it is difficult for scientists to implement new models without strong software engineering skills. In this paper, we present a computational modeling language (escript) based on the object-oriented scripting language (Python). This language, is designed to implement PDE-based models with a high degree of abstraction from the underlying discretization techniques and their implementation. The main components of escript are the Data class objects which handle data with a spatial distribution and the linearPDE class which define linear PDEs to be solved in each step of a time integration or non-linear iteration scheme. As an example we will discuss the solution of the Lame equation and the implementation of a quasi-static model for crustal fault systems

esys-escript 5.6

Escript is a programming tool for implementing mathematical models in python using the finite element method (FEM). As users do not access the data structures it is very easy to use and scripts can run on desktop computers as well as highly parallel supercomputer without changes. Application areas for escript include earth mantle convection, geophysical inversion, earthquakes, porous media flow, reactive transport, plate subduction, erosion, and tsunamis

esys-escript 5.5

Escript is a programming tool for implementing mathematical models in python using the finite element method (FEM). As users do not access the data structures it is very easy to use and scripts can run on desktop computers as well as highly parallel supercomputer without changes. Application areas for escript include earth mantle convection, geophysical inversion, earthquakes, porous media flow, reactive transport, plate subduction, erosion, and tsunamis

Thermal Effects in the Evolution of Initially Layered Mantle Material

A simplied model for anisotropic mantle convection based on a novel class of rheologies, originally developed for folding instabilities in multilayered rock, is extended through the introduction of a thermal anisotropy dependent on the local layering. To examine the eect of the thermal anisotropy on the evolution of mantle material, a parallel implementation of this model was undertaken using the Escript modelling toolkit and the Finley nite element computational kernel. For the cases studied, there appears to little if any eect. For comparative purposes, the eects of anisotropic shear viscosity and the introduced thermal anisotropy are also presented. These results contribute to the characterisation of viscous anisotropic mantle convection subject to variation in thermal conductivities and shear viscosities

Non-Newtonian Effects in Simple Models of Mantle Convection

One of the difficulties with self consistent plate-mantle models capturing multiple physical features, such as elasticity, non-Newtonian flow properties, and temperature dependence, is that the individual behaviours cannot be considered in isolation. For instance, if a viscous mantle convection model is generalized idealistically to include hypo-elasticity, then problems based on Earth-like Rayleigh numbers exhibit almost insurmountable numerical stability issues due to spurious softening associated with the co-rotational stress terms. These difficulties can be avoided if a stress limiter is introduced in the form of a power law rheology or yield criterion. A general Eulerian model is discussed and it is shown that the basic convection modes of a cooling planet are reproduced

Numerical Modelling with Python and XML

In this paper we continue the development of our Python-based package for the solution of partial differential equations using spatial discretization techniques such as the finite element method (FEM), but we take it to a higher level using two approaches: First we define a "Model" class object which makes it easy to break down a complex simulation into simpler sub-models, which then can be linked together into a highly efficient whole. Second, we implement an XML schema in which we can save an entire simulation. Thisn allows implementing check-pointing and also graphical user interfaces to enable non-programmers to use models developed for their research. All this is built upon our escript module, which makes it easy to develop numerical models in a very abstract way while using the computational components implemented in C and C++ to achieve extreme high-performance for time-intensive calculations