An iterative method for the approximation of fibers in slow-fast systems

In this paper we extend a method for iteratively improving slow manifolds so that it also can be used to approximate the fiber directions. The extended method is applied to general finite dimensional real analytic systems where we obtain exponential estimates of the tangent spaces to the fibers. The method is demonstrated on the Michaelis-Menten-Henri model and the Lindemann mechanism. The latter example also serves to demonstrate the method on a slow-fast system in non-standard slow-fast form. Finally, we extend the method further so that it also approximates the curvature of the fibers.Comment: To appear in SIAD

Implicit Methods for Equation-Free Analysis: Convergence Results and Analysis of Emergent Waves in Microscopic Traffic Models

We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time stepper converges to the true dynamics on the slow manifold within an error that is exponentially small with respect to the small parameter measuring time scale separation. Second, we apply this result to the idealized traffic modeling problem of phantom jams generated by cars with uniform behavior on a circular road. The traffic jams are waves that travel slowly against the direction of traffic. Equation-free analysis enables us to investigate the behavior of the microscopic traffic model on a macroscopic level. The standard deviation of cars' headways is chosen as the macroscopic measure of the underlying dynamics such that traveling wave solutions correspond to equilibria on the macroscopic level in the equation-free setup. The collapse of the traffic jam to the free flow then corresponds to a saddle-node bifurcation of this macroscopic equilibrium. We continue this bifurcation in two parameters using equation-free analysis.Comment: 35 page

Wavevector-dependent optical properties from wavevector-independent proper conductivity tensor

We discuss the calculation of the refractive index by means of the ab initio scalar dielectric function and point out its inherent limitations. To overcome these, we start from the recently proposed fundamental, microscopic wave equation in materials in terms of the frequency- and wavevector-dependent dielectric tensor, and investigate under which conditions the standard treatment can be justified. Thereby, we address the question of neglecting the wavelength dependence of microscopic response functions. Furthermore, we analyze in how far the fundamental, microscopic wave equation is equivalent to the standard wave equation used in theoretical optics. In particular, we clarify the relation of the "effective" dielectric tensor used there to the microscopic dielectric tensor defined in ab initio physics.Comment: consistent with published version in Eur. Phys. J. B (2020

Efficient computation of quasiperiodic oscillations in nonlinear systems with fast rotating parts

We present a numerical method for the investigation of quasiperiodic oscillations in applications modeled by systems of ordinary differential equations. We focus on systems with parts that have a significant rotational speed. An important element of our approach is to change coordinates into a co-rotating frame. We show that this leads to a dramatic reduction of computational effort in the case that gravitational forces can be neglected. As a practical example we study a turbocharger model for which we give a thorough comparison of results for a model with and without gravitational forces

Local transport measurements on epitaxial graphene

Growth of large-scale graphene is still accompanied by imperfections. By means of a four-tip STM/SEM the local structure of graphene grown on SiC(0001) was correlated with scanning electron microscope images and spatially resolved transport measurements. The systematic variation of probe spacings and substrate temperature has clearly revealed two-dimensional transport regimes of Anderson localization as well as of diffusive transport. The detailed analysis of the temperature dependent data demonstrates that the local on-top nano-sized contacts do not induce significant strain to the epitaxial graphene films.Comment: 3 figure

Continuation with Non-invasive Control Schemes: Revealing Unstable States in a Pedestrian Evacuation Scenario

This paper presents a framework to perform bifurcation analysis in laboratory experiments or simulations. We employ control-based continuation to study the dynamics of a macroscopic variable of a microscopically defined model, exploring the potential viability of the underlying feedback control techniques in an experiment. In contrast to previous experimental studies that used iterative root-finding methods on the feedback control targets, we propose a feedback control law that is inherently non-invasive. That is, the control discovers the location of equilibria and stabilizes them simultaneously. We call the proposed control zero-in-equilibrium feedback control and we prove that it is able to stabilize branches of equilibria, except at singularities of codimension n+1, where n is the number of state space dimensions the feedback can depend on. We apply the method to a simulated evacuation scenario were pedestrians have to reach an exit after maneuvering left or right around an obstacle. The scenario shows a hysteresis phenomenon with bistability and tipping between two possible steady pedestrian flows in microscopic simulations. We demonstrate for the evacuation scenario that the proposed control law is able to uniformly discover and stabilize steady flows along the entire branch, including points where other non-invasive approaches to feedback control become singular.Comment: submitted (34 pages 12 figures

Use Your Strategic Entrepreneurs to Build Your Strategic Partnerships

Internationalisation through strategic partnerships is a goal for many higher education institutions and their upper-level management teams. Yet for institutional objectives to truly flourish, they should get the most out of the various skills that different actors bring to be table. This piece explores the interesting role that can be played by resourceful academic staff in materialising institutional, and individual, aims