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

"Water-free" computer model for fluid bilayer membranes

We use a simple and efficient computer model to investigate the physical properties of bilayer membranes. The amphiphilic molecules are modeled as short rigid trimers with finite range pair interactions between them. The pair potentials have been designed to mimic the hydrophobic interactions, and to allow the simulation of the membranes without the embedding solvent as if the membrane is in vacuum. We find that upon decreasing the area density of the molecules the membrane undergoes a solid-fluid phase transition, where in the fluid phase the molecules can diffuse within the membrane plane. The surface tension and the bending modulus of the fluid membranes are extracted from the analysis of the spectrum of thermal undulations. At low area densities we observe the formation of pores in the membrane through which molecules can diffuse from one layer to the other. The appearance of the pores is explained using a simple model relating it to the area dependence of the free energy.Comment: 12 pages, 8 figures, to appear in J. Chem. Phy

Enhancing pantograph-catenary dynamic performance using an inertance-integrated damping system

For modern electrical rail systems, the pantograph-catenary dynamic performance is one of the most critical challenges. Too much fluctuation in contact forces leads to either accelerated wear of the contacting components or losses of contact and, consequently, arcing. In this work, inertance-integrated pantograph damping systems are investigated with the objective of reducing the contact force standard deviation. Firstly, a multibody pantograph model is developed with its accuracy compared with experimental data. The model is improved through the calibration of the pantograph head suspension parameters and the introduction of both non-ideal joint and flexibility effects. Using the calibrated model, beneficial inertance-integrated damping systems are identified for the pantograph suspension. The results show that the configuration with one inerter provides the best performance among other candidate layouts and contends a 40% reduction of the maximum standard deviation of the contact force over the whole operating speed range in the numerical modelling scenario analysed. Considering the identified configuration, time-domain analysis and modal analysis are investigated. It has been shown that the achieved improvement is due to the fact that with the beneficial inertance-integrated damping system, the first resonance frequency of the pantograph system coincides with the natural frequency of the catenary system.info:eu-repo/semantics/publishedVersio