Uncertainty quantification of dynamic earthquake rupture simulations.

We present a tutorial demonstration using a surrogate-model based uncertainty quantification (UQ) approach to study dynamic earthquake rupture on a rough fault surface. The UQ approach performs model calibration where we choose simulation points, fit and validate an approximate surrogate model or emulator, and then examine the input space to see which inputs can be ruled out from the data. Our approach relies on the mogp_emulator package to perform model calibration, and the FabSim3 component from the VECMA toolkit to streamline the workflow, enabling users to manage the workflow using the command line to curate reproducible simulations on local and remote resources. The tools in this tutorial provide an example template that allows domain researchers that are not necessarily experts in the underlying methods to apply them to complex problems. We illustrate the use of the package by applying the methods to dynamic earthquake rupture, which solves the elastic wave equation for the size of an earthquake and the resulting ground shaking based on the stress tensor in the Earth. We show through the tutorial results that the method is able to rule out large portions of the input parameter space, which could lead to new ways to constrain the stress tensor in the Earth based on earthquake observations. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

Effective temperature dynamics of shear bands in metallic glasses.

We study the plastic deformation of bulk metallic glasses with shear transformation zone (STZ) theory, a physical model for plasticity in amorphous systems, and compare it with experimental data. In STZ theory, plastic deformation occurs when localized regions rearrange due to applied stress and the density of these regions is determined by a dynamically evolving effective disorder temperature. We compare the predictions of STZ theory to experiments that explore the low-temperature deformation of Zr-based bulk metallic glasses via shear bands at various thermal temperatures and strain rates. By following the evolution of effective temperature with time, strain rate, and temperature through a series of approximate and numerical solutions to the STZ equations, we successfully model a suite of experimentally observed phenomena, including shear-band aging as apparent from slide-hold-slide tests, a temperature-dependent steady-state flow stress, and a strain-rate- and temperature-dependent transition from stick-slip (serrated flow) to steady-sliding (nonserrated flow). We find that STZ theory quantitatively matches the observed experimental data and provides a framework for relating the experimentally measured energy scales to different types of atomic rearrangements.

Stick-slip instabilities and shear strain localization in amorphous materials.

We study the impact of strain localization on the stability of frictional slipping in dense amorphous materials. We model the material using shear transformation zone (STZ) theory, a continuum approximation for plastic deformation in amorphous solids. In the STZ model, the internal state is quantified by an effective disorder temperature, and the effective temperature dynamics capture the spontaneous localization of strain. We study the effect of strain localization on stick-slip instabilities by coupling the STZ model to a noninertial spring slider system. We perform a linear stability analysis to generate a phase diagram that connects the small scale physics of strain localization to the macroscopic stability of sliding. Our calculations determine the values of spring stiffness and driving velocity where steady sliding becomes unstable and we confirm our results through numerical integration. We investigate both homogeneous deformation, where no shear band forms, and localized deformation, where a narrow shear band spontaneously forms and accommodates all of the deformation. Our results show that at a given velocity, strain localization leads to unstable frictional sliding at a much larger spring stiffness compared to homogeneous deformation, and that localized deformation cannot be approximated by a homogeneous model with a narrower material. We also find that strain localization provides a physical mechanism for irregular stick-slip cycles in certain parameter ranges. Our results quantitatively connect the internal physics of deformation in amorphous materials to the larger scale frictional dynamics of stick-slip.

Quantifying optimal accuracy of local primary sequence bioinformatics methods.

MOTIVATION: Traditional bioinformatics methods scan primary sequences for local patterns. It is important to assess how accurate local primary sequence methods can be. RESULTS: We study the problem of donor pre-mRNA splice site recognition, where the sequence overlaps between real and decoy datasets can be quantified, exposing the intrinsic limitations of the performance of local primary sequence methods. We assess the accuracy of primary sequence methods generally by studying how they scale with dataset size and demonstrate that our new primary sequence ranking methods have superior performance.