Stress distribution during neck formation : an approximate theory

In this paper we investigate the effects of deformation of a metal specimen, which is either a plate or a cylindrical rod in our case. In particular we study neck formation in tensile loading of a plastic metal. We try to generalize the work of Bridgman, who considered a purely two-dimensional geometry, to an effective theory that takes into account some essential three dimensional characteristics. That extending the description of neck formation to three dimensions is necessary was illustrated by recent experimental findings of [1]. We have studied existing models from the literature that describe necking for plates and cylinders to identify the consequences of the crucial assumption of uniform in-plane stress. We also developed a new model that we have not yet been able to analyze. Finally, using work of [4] in which a power law relation between the von Mises stress and the effective strain is used, a perturbation analysis for a simple flat geometry was performed. The perturbation analysis offers a good starting point for generalizing the work of Bridgman to three dimensions. Keywords: Neck formation, von Mises stress, tensile pulling, plane stress assumptio

A Case Study in the Future Challenges in Electricity Grid Infrastructure

The generation by renewables and the loading by electrical vehicle charging imposes severe challenges in the redesign of today’s power supply systems. Indeed, accommodating these emerging power sources and sinks requires traditional power systems to evolve from rigid centralized unidirectional architectures to intelligent decentralized entities allowing a bidirectional power flow. In the case study proposed by ENDINET, we investigate how the penetration of solar panels and of battery charging stations on large scale affects the voltage quality and loss level in a distribution network servicing a residential area in Eindhoven, NL. In our case study we take the average household load during summer and winter into account and consider both a radial and meshed topology of the network. Our study results for both topologies considered in a quantification of the levels of penetration and a strategy for electrical vehicle loading strategy that meet the voltage and loss requirements in the network

Correcting Numerical Simulations for Known Expectations

Predictions of the future climate require long-time simulation of a chaotic dynamical system. This poses a challenge for numerical simulations, as these do not necessarily capture the correct long-term behaviour of chaotic systems. This problem is exacerbated by the wide range of length scales present in atmospheric and oceanic dynamics. The modeling choices for small scale processes have a large impact on long term statistics of the scales of interest. This thesis studies the dynamics of two different fluid models as a proxy for atmospheric dynamics: a point vortex flow on the sphere and two-dimensional turbulent flow on a torus. We apply gentle dynamical perturbations commonly used in molecular dynamics to these fluid dynamics problems as a means for improving the statistical veracity of low fidelity simulations. For the point vortex system we study a system consisting of both strong and weak vortices. The strong vortex dynamics are mildly influenced by the weak vortices on a short time scale, but the presence of the weak vortices introduces a variability in the strong vortex energy. We mimic this behaviour in a model with only the strong vortices by gentle perturbations to the equations of motion. The perturbations have a stochastic forcing such that the modified dynamics ergodically sample an invariant measure consistent with observations from the strong vortex system in contact with the weak vortices. We choose the invariant measure as the minimal entropy density consistent with observations. The required Lagrange multipliers can be computed either a priori using a sample set in some prior distribution, or they can be computed on-the-fly using the simulation history as an ensemble. The latter method allows the observations to be updated during runtime, providing the opportunity for data-assimilation. We construct a Poisson integration method for the aforementioned point vortex dynamics by splitting the Hamiltonian into its constituent vortex pair terms. The method provides exact solutions to a Poisson system with the same bracket as the original dynamical system, but with a modified Hamiltonian function. Different orderings of the pairwise interactions are considered and are also used for the construction of higher order methods. The energy and momentum conservation of the splitting schemes is demonstrated for several test cases. For particular orderings of the pairwise interactions, the schemes allow scalable parallelization. This results in a linear -- as opposed to quadratic -- scaling of computation time with system size. We also explore the direct modification of the pseudo-spectral truncation of two-dimensional, incompressible fluid dynamics on a torus to maintain a prescribed kinetic energy spectrum. The method provides a means of simulating fluid states with defined spectral properties, for the purpose of matching simulation statistics to given information, arising from observations, theoretical predictions or high fidelity simulations. In the scheme outlined here, Nos\'{e}-Hoover thermostats -- commonly used in molecular dynamics -- are introduced as feedback controls applied to energy bands of the Fourier-discretized Navier-Stokes equations. As we demonstrate in numerical experiments, the dynamical properties -- quantified using autocorrelation functions -- are only modestly perturbed by our device, while ensemble dispersion is significantly enhanced in comparison with simulations of a corresponding truncation using hyperviscosity

Numerical Time Integration of Stochastic Differential Equations

Most mathematical models used in science and engineering rely on empirical constants and these are usually assumed to have some deterministic value. In reality however these values are subject to stochastic distribution. Be it due to measurement inaccuracy or be it due to physical variance of the parameter, this distribution is ideally not ignored but considered by the model. Such a model will yield a more complete picture of the physical process, inherently improving it. The same can be said for the initial and boundary conditions of any model.Aerospace Engineerin

Statistical modelling of pre-impact velocities in car crashes

The law wants to determine if any party involved in a car crash is guilty. The Dutch court invokes the expertise of the Netherlands Forensic Institute (NFI) to answer this question. We discuss the present method of the NFI to determine probabilities on pre-impact car velocities, given the evidence from the crash scene. A disadvantage of this method is that it requires a prior distribution on the velocities of the cars involved in the crash. We suggest a different approach, that of statistical significance testing, which can be carried out without a prior. We explain this method, and apply it to a toy model. Finally, a sensitivity analysis is performed on a simple two-car collision model

Statistical modelling of pre-impact velocities in car crashes

The law wants to determine if any party involved in a car crash is guilty. The Dutch court invokes the expertise of the Netherlands Forensic Institute (NFI) to answer this question. We discuss the present method of the NFI to determine probabilities on pre-impact car velocities, given the evidence from the crash scene. A disadvantage of this method is that it requires a prior distribution on the velocities of the cars involved in the crash. We suggest a different approach, that of statistical significance testing, which can be carried out without a prior. We explain this method, and apply it to a toy model. Finally, a sensitivity analysis is performed on a simple two-car collision model

Statistical Modelling of Pre-Impact Velocities in Car Crashes

The law wants to determine if any party involved in a car crash is guilty. The Dutch court invokes the expertise of the Netherlands Forensic Institute (NFI) to answer this question. We discuss the present method of the NFI to determine probabilities on pre-impact car velocities, given the evidence from the crash scene. A disadvantage of this method is that it requires a prior distribution on the velocities of the cars involved in the crash. We suggest a different approach, that of statistical significance testing, which can be carried out without a prior. We explain this method, and apply it to a toy model. Finally, a sensitivity analysis is performed on a simple two-car collision model

Stress distribution during neck formation : an approximate theory

In this paper we investigate the effects of deformation of a metal specimen, which is either a plate or a cylindrical rod in our case. In particular we study neck formation in tensile loading of a plastic metal. We try to generalize the work of Bridgman, who considered a purely two-dimensional geometry, to an effective theory that takes into account some essential three dimensional characteristics. That extending the description of neck formation to three dimensions is necessary was illustrated by recent experimental findings of [1]. We have studied existing models from the literature that describe necking for plates and cylinders to identify the consequences of the crucial assumption of uniform in-plane stress. We also developed a new model that we have not yet been able to analyze. Finally, using work of [4] in which a power law relation between the von Mises stress and the effective strain is used, a perturbation analysis for a simple flat geometry was performed. The perturbation analysis offers a good starting point for generalizing the work of Bridgman to three dimensions. Keywords: Neck formation, von Mises stress, tensile pulling, plane stress assumptio

Statistical modelling of pre-impact velocities in car crashes

The law wants to determine if any party involved in a car crash is guilty. The Dutch court invokes the expertise of the Netherlands Forensic Institute (NFI) to answer this question. We discuss the present method of the NFI to determine probabilities on pre-impact car velocities, given the evidence from the crash scene. A disadvantage of this method is that it requires a prior distribution on the velocities of the cars involved in the crash. We suggest a different approach, that of statistical significance testing, which can be carried out without a prior. We explain this method, and apply it to a toy model. Finally, a sensitivity analysis is performed on a simple two-car collision model