Leadership When It Matters Most Lessons on Influence from In Extremis Contexts

None of us would study or read about leadership if we did not think that leadership is important to people. Assuming that leadership is, indeed, important to people, it then follows that it is most important when people\u27s lives are at risk. This chapter is a discussion of the most important niche in leadership thinking and analysisleader influence in dangerous contexts. There is social benefit to such a discussion. When one adds up the publicly released figures for numbers of active duty military personnel, law enforcement officers, and firefighters-all people who live and work in dangerous contexts-the total is in the millions. Adding mountain climbers, skydivers, and other extreme sports enthusiasts to the list swells this figure. Not to be overlooked are ordinary individuals suddenly and unexpectedly thrust into a dangerous circumstance (for example, shootings, floods, mine disasters, airline incidents) where leadership matters or could have mattered. Dangerous contexts are ubiquitous, and leadership during them can make a difference

On the necessity and a generalized conceptual model for the consideration of large strains in rock mechanics

This contribution presents a generalized conceptual model for the finite element solution of quasi-static isothermal hydro-mechanical processes in (fractured) porous media at large strains. A frequently used averaging procedure, known as Theory of Porous Media, serves as background for the complex multifield approach presented here. Within this context, a consistent representation of the weak formulation of the governing equations (i.e., overall balance equations for mass and momentum) in the reference configuration of the solid skeleton is preferred. The time discretization and the linearization are performed for the individual variables and nonlinear functions representing the integrands of the weak formulation instead of applying these conceptual steps to the overall nonlinear system of weighted residuals. Constitutive equations for the solid phase deformation are based on the multiplicative split of the deformation gradient allowing the adaptation of existing approaches for technical materials and biological tissues to rock materials in order to describe various inelastic effects, growth and remodeling in a thermodynamically consistent manner. The presented models will be a feature of the next version of the scientific open-source finite element code OpenGeoSys developed by an international developer and user group, and coordinated by the authors

A modified combined active-set Newton method for solving phase-field fracture into the monolithic limit

In this work, we examine a numerical phase-field fracture framework in which the crack irreversibility constraint is treated with a primal-dual active set method and a linearization is used in the degradation function to enhance the numerical stability. The first goal is to carefully derive from a complementarity system our primal-dual active set formulation, which has been used in the literature in numerous studies, but for phase-field fracture without its detailed mathematical derivation yet. Based on the latter, we formulate a modified combined active-set Newton approach that significantly reduces the computational cost in comparison to comparable prior algorithms for quasi-monolithic settings. For many practical problems, Newton converges fast, but active set needs many iterations, for which three different efficiency improvements are suggested in this paper. Afterwards, we design an iteration on the linearization in order to iterate the problem to the monolithic limit. Our new algorithms are implemented in the programming framework pfm-cracks [T. Heister, T. Wick; pfm-cracks: A parallel-adaptive framework for phase-field fracture propagation, Software Impacts, Vol. 6 (2020), 100045]. In the numerical examples, we conduct performance studies and investigate efficiency enhancements. The main emphasis is on the cost complexity by keeping the accuracy of numerical solutions and goal functionals. Our algorithmic suggestions are substantiated with the help of several benchmarks in two and three spatial dimensions. Therein, predictor-corrector adaptivity and parallel performance studies are explored as well.Comment: 49 pages, 45 figures, 9 table

On the term and concepts of numerical model validation in geoscientific applications

Modeling and numerical simulation of the coupled physical and chemical processes observed in the subsurface are the only options for long-term analyses of complex geological systems. This contribution discusses some more general aspects of the (dynamic) process modeling for geoscientific applications including reflections about the slightly different understanding of the terms model and model validation in different scientific communities, and about the term and methods of model calibration in the geoscientifc context. Starting from the analysis of observations of a certain part of the perceived reality, the process of model development comprises the establishment of the physical model characterizing relevant processes in a problem-oriented manner, and subsequently the mathematical and numerical models. Considering the steps of idealization and approximation in the course of model development, Oreskes et al. [1] state that process and numerical models can neither be verified nor validated in general. Rather the adequacy of models with specific assumptions and parameterizations made during model set-up can be confirmed. If the adequacy of process models with observations can be confirmed using lab as well as field tests and process monitoring, the adequacy of numerical models can be confirmed using numerical benchmarking and code comparison. Model parameters are intrinsic elements of process and numerical models, in particular constitutive parameters. As they are often not directly measurable, they have to be established by solving inverse problems based on an optimal numerical adaptation of observation results. In addition, numerical uncertainty analyses should be an obligatory part of numerical studies for critical real world applications

Numerical Methods for Algorithmic Systems and Neural Networks

These lecture notes are devoted to numerical concepts and solution of algorithmic systems and neural networks. The course is divided into four parts: traditional AI (artificial intelligence), deep learning in neural networks, applications to (and with) differential equations, and project work. Throughout this course an emphasis is on mathematical ingredients from which several are rigorously proven. In the project work, the participants usually form groups and work together on a given problem to train themselves on mathematical modeling, design of algorithms, implementation, and analysis and intepretation of the simulation results

Online Bit Flip Detection for In-Memory B-Trees on Unreliable Hardware

Hardware vendors constantly decrease the feature sizes of integrated circuits to obtain better performance and energy efficiency. Due to cosmic rays, low voltage or heat dissipation, hardware -- both processors and memory -- becomes more and more unreliable as the error rate increases. From a database perspective bit flip errors in main memory will become a major challenge for modern in-memory database systems, which keep all their enterprise data in volatile, unreliable main memory. Although existing hardware error control techniques like ECC-DRAM are able to detect and correct memory errors, their detection and correction capabilities are limited. Moreover, hardware error correction faces major drawbacks in terms of acquisition costs, additional memory utilization, and latency. In this paper, we argue that slightly increasing data redundancy at the right places by incorporating context knowledge already increases error detection significantly. We use the B-Tree -- as a widespread index structure -- as an example and propose various techniques for online error detection and thus increase its overall reliability. In our experiments, we found that our techniques can detect more errors in less time on commodity hardware compared to non-resilient B-Trees running in an ECC-DRAM environment. Our techniques can further be easily adapted for other data structures and are a first step in the direction of resilient database systems which can cope with unreliable hardware

Modeling, Discretization, Optimization, and Simulation of Phase-Field Fracture Problems

This course is devoted to phase-field fracture methods. Four different sessions are centered around modeling, discretizations, solvers, adaptivity, optimization, simulations and current developments. The key focus is on research work and teaching materials concerned with the accurate, efficient and robust numerical modeling. These include relationships of model, discretization, and material parameters and their influence on discretizations and the nonlinear (Newton-type methods) and linear numerical solution. One application of such high-fidelity forward models is in optimal control, where a cost functional is minimized by controlling Neumann boundary conditions. Therein, as a side-project (which is itself novel), space-time phase-field fracture models have been developed and rigorously mathematically proved. Emphasis in the entire course is on a fruitful mixture of theory, algorithmic concepts and exercises. Besides these lecture notes, further materials are available, such as for instance the open-source libraries pfm-cracks and DOpElib. The prerequisites are lectures in continuum mechanics, introduction to numerical methods, finite elements, and numerical methods for ODEs and PDEs. In addition, functional analysis (FA) and theory of PDEs is helpful, but for most parts not necessarily mandatory. Discussions with many colleagues in our research work and funding from the German Research Foundation within the Priority Program 1962 (DFG SPP 1962) within the subproject Optimizing Fracture Propagation using a Phase-Field Approach with the project number 314067056 (D. Khimin, T. Wick), and support of the French-German University (V. Kosin) through the French-German Doctoral college ``Sophisticated Numerical and Testing Approaches" (CDFA-DFDK 19-04) is gratefully acknowledged

Orthogonal decomposition of anisotropic constitutive models for the phase field approach to fracture

We propose a decomposition of constitutive relations into crack-driving and persistent portions, specifically designed for materials with anisotropic/orthotropic behavior in the phase field approach to fracture to account for the tension-compression asymmetry. This decomposition follows a variational framework, satisfying the orthogonality condition for anisotropic materials. This implies that the present model can be applied to arbitrary anisotropic elastic behavior in a three-dimensional setting. On this basis, we generalize two existing models for tension-compression asymmetry in isotropic materials, namely the volumetric-deviatoric model and the no-tension model, towards materials with anisotropic nature. Two benchmark problems, single notched tensile shear tests, are used to study the performance of the present model. The results can retain the anisotropic constitutive behavior and the tension-compression asymmetry in the crack response, and are qualitatively in accordance with the expected behavior for orthotropic materials. Furthermore, to study the direction of maximum energy dissipation, we modify the surface integral based energy release computation, $G_\theta$, to account only for the crack-driving energy. The computed energies with our proposed modifications predict the fracture propagation direction correctly compared with the standard G-theta method

Simultaneous flow of water and air across the land surface during runoff

This paper presents an inter-compartment boundary condition for the simulation of surface runoff, soil moisture, and soil air as a coupled system of partial differential equations. The boundary condition is based on a classic leakance approach to balance water between differently mobile regions such as the land surface and subsurface. Present work applies leakances to transfer water and air simultaneously through the land surface for soils, which are connected by an air flux with a steady atmosphere. Shallow flow and two phase flow in a porous medium are sequential calculated in an iteration loop. General criteria are stated to guarantee numerical stability in the coupling loop and for leakances to control inter-compartment fluid fluxes. Using the leakance approach, a numerical model captures typical feedbacks between surface runoff and soil air in near-stream areas. Specifically, displacement of water and air in soils is hampered at full-water saturation over the land surface resulting in enhanced surface runoff in the test cases. Leakance parameters permit the simulation of air out-breaks with reference to air pressures, which fluctuate in the shallow subsurface between two thresholds