May 2010 - Digital Minute Issue 2

This issue features information about global repositories, as well as visits to our Digital Commons by country

Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains

It is well established that the solitary waves of FPU-type chains converge in the high-energy limit to traveling waves of the hard-sphere model. In this paper we establish improved asymptotic expressions for the wave profiles as well as an explicit formula for the wave speed. The key step in our approach is the derivation of an asymptotic ODE for the appropriately rescaled strain profile.Comment: revised version with corrected typos; 25 pages, several figure

Sparse bayesian polynomial chaos approximations of elasto-plastic material models

In this paper we studied the uncertainty quantification in a functional approximation form of elastoplastic models parameterised by material uncertainties. The problem of estimating the polynomial chaos coefficients is recast in a linear regression form by taking into consideration the possible sparsity of the solution. Departing from the classical optimisation point of view, we take a slightly different path by solving the problem in a Bayesian manner with the help of new spectral based sparse Kalman filter algorithms

Inverse problems and uncertainty quantification

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.Comment: 25 pages, 17 figures. arXiv admin note: text overlap with arXiv:1201.404