Characterisation of micromechanical properties using advanced techniques

Extended abstract of a paper presented at Microscopy and Microanalysis 2012 in Phoenix, Arizona, USA, July 29 - August 2, 201

Better Training using Weight-Constrained Stochastic Dynamics

We employ constraints to control the parameter space of deep neural networks throughout training. The use of customized, appropriately designed constraints can reduce the vanishing/exploding gradients problem, improve smoothness of classification boundaries, control weight magnitudes and stabilize deep neural networks, and thus enhance the robustness of training algorithms and the generalization capabilities of neural networks. We provide a general approach to efficiently incorporate constraints into a stochastic gradient Langevin framework, allowing enhanced exploration of the loss landscape. We also present specific examples of constrained training methods motivated by orthogonality preservation for weight matrices and explicit weight normalizations. Discretization schemes are provided both for the overdamped formulation of Langevin dynamics and the underdamped form, in which momenta further improve sampling efficiency. These optimization schemes can be used directly, without needing to adapt neural network architecture design choices or to modify the objective with regularization terms, and see performance improvements in classification tasks.Comment: ICML 2021 camera-ready. arXiv admin note: substantial text overlap with arXiv:2006.1011

Synchrotron X-Rays for Microstructural Investigations of Advanced Reactor Materials

X-rays from synchrotron beamlines provide a powerful tool for materials analysis in circumstances where long-term materials degradation under complex loading conditions (e.g., temperature, irradiation, and stress) becomes important. This may occur for advanced gas cooled reactors. Synchrotron X-rays can help to improve lifetime assessments by providing a more in-depth understanding of microstructural damage. This article summarizes results of X-ray absorption fine spectrum analysis and X-ray magnetic circular dichroism synchrotron techniques. They were employed to evaluate various microstructural features, which are important in understanding the lifetime of materials exposed to extreme conditions. Dispersoid strengthening by yttria particles, conditions that produce nanocrystal Zircaloy, and the role of magnetism on the stability of ferritic steels were taken as example

Characterization of Irradiation Damage of Ferritic ODS Alloys with Advanced Micro-Sample Methods

Oxide dispersion strengthened (ODS) steels are candidate materials for advanced electric energy and heat generation plants (nuclear, fossil). Understanding the degradation of mechanical properties of these alloys as a result of service exposure is necessary for safe design. For advanced nuclear applications combinations of temperature, irradiation and stress are important damage conditions. They are studied either with neutron irradiated samples (often highly active) or with ion-irradiated samples (irradiation damage often limited to only a few micrometer deep areas). High activity of samples and limited sample volume claim to subsized samples like nano-indentation, micro-pillar compression or thin strip creep testing. Irradiation hardening and irradiation creep were studied with these methods. Ferritic ODS steels with 19% chromium were investigated. The materials were studied in qualities differing in grain sizes and in sizes of the dispersoids. Irradiation was performed in an accelerator using He-ions. Irradiation damage profiles could be well analyzed with indentation. Yield stress determined with compression tests of single-crystal micropillars was well comparable with tension tests performed along the same crystallographic orientation. Irradiation creep of samples with different sizes of dispersoids revealed only a small influence of particle size being is in contrast with thermal creep but consistent with expectations from other investigation

Effective models and numerical homogenization methods for long time wave propagation in heterogeneous media

Modeling wave propagation in highly heterogeneous media is of prime importance in engineering applications of diverse nature such as seismic inversion, medical imaging or the design of composite materials. The numerical approximation of such multiscale physical models is a mathematical challenge. Indeed, to reach an acceptable accuracy, standard numerical methods require the discretization of the whole medium at the microscopic scale, which leads to a prohibitive computational cost. Homogenization theory ensures the existence of a homogenized wave equation, obtained from the original problem by a limiting process. As this equation does not depend on the microscopic scale, it is a good target for numerical methods. Unfortunately, for general media, the homogenized equation may not be unique and no formulas are available for its effective data. %Diverse numerical strategies have been developed to approximate a homogenized solution. Nevertheless, such formulas are known for media described by a locally periodic tensor. In that case, or more generally for problems with scale separation, methods such as the finite element heterogeneous multiscale method (FE-HMM) are proved to efficiently approximate the homogenized solution. For wave propagation in heterogeneous media, however, it is known that at large timescales the homogenized solution fails to describe the dispersive behavior of the original wave. Hence, a new equation that captures this dispersion is needed. In this thesis, we study such effective equations for long time wave propagation in heterogeneous media. The first result that we present holds in periodic media. Using the technique of asymptotic expansion, we obtain the characterization of a whole family of equations that describes the long time dispersive effects of the oscillating wave. The validity of our derivation is ensured by rigorous a priori error estimates. We also derive a numerical procedure for the computation of the tensors involved in the first order effective equations. This leads to a numerical homogenization method for long time wave propagation in periodic media. The second result that we present generalizes the procedure for deriving effective equations to arbitrary timescales. This generalization is also useful, for example, for the homogenization of the wave equation with high frequency initial data. We also provide a numerical procedure allowing to compute effective tensors of arbitrary order. The third result is the generalization of the family of first order effective equations from periodic to locally periodic media. A rigorous a priori error analysis is also derived in this situation. This constitutes the first analysis of effective models for the long time approximation of the wave equation in locally periodic media. In a second part of the thesis, we derive numerical homogenization methods for the long time approximation of the wave equation in locally periodic media. In one dimension, we analyze a modification of the FE-HMM called the FE-HMM-L. In higher dimensions, we design a spectral homogenization method. For both methods, we prove error estimates valid for large timescales and in arbitrarily large spatial domains. In particular, we show that these numerical homogenization methods converge to effective solutions that approximate the highly oscillatory wave equation over long time

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

A family of effective equations that capture the long time dispersive effects of wave propagation in heterogeneous media in an arbitrary large periodic spatial domain Omega subset of R-d is proposed and analyzed. For a wave equation with highly oscillatory periodic spatial tensors of characteristic length epsilon, we prove that the solution of any member of our family of effective equations is epsilon-close to the true oscillatory wave over a time interval of length T-epsilon = O(epsilon(-2)) in a norm equivalent to the L-infinity(0, T-epsilon; L-2(Omega)) norm. We show that the previously derived effective equation in [T. Dohnal, A. Lamacz and B. Schweizer, Bloch-wave homogenization on large time scales and dispersive effective wave equations, Multiscale Model. Simulat. 12 (2014) 488-513] belongs to our family of effective equations. Moreover, while Bloch wave techniques were previously used, we show that asymptotic expansion techniques give an alternative way to derive such effective equations. An algorithm to compute the tensors involved in the dispersive equation and allowing for efficient numerical homogenization methods over long time is proposed

A priori error analysis of the finite element heterogeneous multiscale method for the wave equation in heterogeneous media over long time

A fully discrete a priori analysis of the finite element heterogeneous multiscale method introduced in [A. Abdulle, M. Grote, and C. Stohrer, Multiscale Model. Simul., 12, 2014, pp. 1135-1166] for the wave equation with highly oscillatory coefficients over long time is presented. A sharp a priori convergence rate for the numerical method is derived for long time intervals. The effective model over long time is a Boussinesq-type equation that has been shown to approximate the one-dimensional multiscale wave equation with epsilon-periodic coefficients up to time O(epsilon(-2)) in [A. Lamacz, Math. Models Methods Appl. Sci., 21, 2011, pp. 1871-1899]. In this paper we also revisit this result by deriving and analyzing a family of effective Boussinesq-type equations for the approximation of the multiscale wave equation that depends on the normalization chosen for certain micro functions used to define the macroscopic models