The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.

Pedestrian dynamics is an interdisciplinary field of research. Psychologists, sociologists, traffic engineers, physicists, mathematicians and computer scientists all strive to understand the dynamics of a moving crowd. In principle, computer simulations offer means to further this understanding. Yet, unlike for many classic dynamical systems in physics, there is no universally accepted locomotion model for crowd dynamics. On the contrary, a multitude of approaches, with very different characteristics, compete. Often only the experts in one special model type are able to assess the consequences these characteristics have on a simulation study. Therefore, scientists from all disciplines who wish to use simulations to analyze pedestrian dynamics need a tool to compare competing approaches. Developers, too, would profit from an easy way to get insight into an alternative modeling ansatz. Vadere meets this interdisciplinary demand by offering an open-source simulation framework that is lightweight in its approach and in its user interface while offering pre-implemented versions of the most widely spread models.

Clock steering is an important discipline within the time and frequency community as well as in cognate disciplines such as global navigation satellite systems (GNSSs). In the latter, clock steering is a mandatory tool for realizations of time scales, which first are typically created by algorithms forming a paper clock. Often, this software solution of a time scale is already sufficient. However, sometimes a realization in the form of a frequency signal is feasible or even necessary. Future GNSSs concepts plan to use composite clocks consisting of several different clocks to achieve synchronization of satellites within one orbit with the system time. In this approach, a real clock output in the microwave regime is indispensable. Therefore, a real clock has to be steered against the paper clock to realize the composite clock. Consequently, steering techniques are an essential piece for obtaining a realization. Besides the number of algorithms to choose from, there are several parameters that need to be defined by the user to achieve the best performance for distinct scenarios. In this paper we compare the realization performance and applicability of two different steering techniques, namely linear-quadratic Gaussian control and pole placement, in a simplified hardware setup. The studied scenario consists of a steerable clock consisting of a micro phase stepper which changes the frequency of the output of an oven-controlled quartz oscillator (OCXO) and a rubidium atomic clock (RB). The OCXO in turn is steered to follow the free-running RB as closely as possible. Steering the output of the OCXO introduces a new process in the clock. As a result, the Allan deviation of the steered clock shows a bump which location is dependent on the chosen control interval and steering technique. This has to be considered for the designated operation. We compare simulations of the clock steering with both techniques to real-data results from our laboratory.

Microscopic crowd simulation can help to enhance the safety of pedestrians in situations that range from museum visits to music festivals. To obtain a useful prediction, the input parameters must be chosen carefully. In many cases, a lack of knowledge or limited measurement accuracy add uncertainty to the input. In addition, for meaningful parameter studies, we first need to identify the most influential parameters of our parametric computer models. The field of uncertainty quantification offers standardized and fully automatized methods that we believe to be beneficial for pedestrian dynamics. In addition, many methods come at a comparatively low cost, even for computationally expensive problems. This allows for their application to larger scenarios. We aim to identify and adapt fitting methods to microscopic crowd simulation in order to explore their potential in pedestrian dynamics. In this work, we first perform a variance-based sensitivity analysis using Sobol’ indices and then crosscheck the results by a derivative-based measure, the activity scores. We apply both methods to a typical scenario in crowd simulation, a bottleneck. Because constrictions can lead to high crowd densities and delays in evacuations, several experiments and simulation studies have been conducted for this setting. We show qualitative agreement between the results of both methods. Additionally, we identify a one-dimensional subspace in the input parameter space and discuss its impact on the simulation. Moreover, we analyze and interpret the sensitivity indices with respect to the bottleneck scenario.

Clock ensembling is a promising concept for future time scale generation as robustness and stability can be considerably improved compared to master clock approaches. While ensembles consisting of the same clock types were already demonstrated to improve robustness of the generated time scale, ensembles using different clock types can clearly benefit from the advantages of the individual single clocks contributing to the time generation process. In particular, the performance of the ensemble time can be improved over a wide range of averaging times by combining clocks exhibiting superior stabilities for distinct time scales. In future, this approach could be used to integrate newly developed clock types such as e.g. optical clocks into a clock ensemble.