Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Semantics of multi-mode DAE systems

Deliverable D.4.1.1 of the ITEA2 Modrio collaborative projectHybrid systems modelers exhibit a number of difficulties related to the mix of continuous and discrete dynamics and sensitivity to the discretization scheme. Modular modeling, where subsystems models can be simply assembled with no rework, calls for using Differential Algebraic Equations (DAE). In turn, DAE are strictly more difficult than ODE. They require sophisticated pre-processing using various notions of index before they can be submitted to a solver. In this report we study some fundamental issues raised by the modeling and simulation of hybrid systems involving DAEs. The objective of this work is to serve for the evolution and the design of future releases of the Modelica language for such systems. We focus on the following questions: * What is the proper notion of index for a hybrid DAE system? * What are the primitive statements needed for a DAE hybrid systems modeler? The differentiation index for DAE explicitly relies on everything being differentiable. Therefore, generalizations to hybrid systems must be done with caution. We propose relying on non-standard analysis for this. Non-standard analysis formalizes differential equations as discrete step transition systems with infinitesimal time basis. We can thus bring hybrid DAE systems to their nonstandard form, where the notion of difference index can be firmly used. From this study, general hints for future releases of Modelica can be drawn

Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report

This Report summarizes the proceedings of the 2015 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt with (I) new developments relevant for high precision Standard Model calculations, (II) the new PDF4LHC parton distributions, (III) issues in the theoretical description of the production of Standard Model Higgs bosons and how to relate experimental measurements, (IV) a host of phenomenological studies essential for comparing LHC data from Run I with theoretical predictions and projections for future measurements in Run II, and (V) new developments in Monte Carlo event generators.Comment: Proceedings of the Standard Model Working Group of the 2015 Les Houches Workshop, Physics at TeV Colliders, Les Houches 1-19 June 2015. 227 page