Department of Physics • University of Cologne

Schnakenberg’s paper from 1976 has been foundational to the field of network thermodynamics. Exploiting tools from graph theory and circuit analysis, it provides a geometrical framework to identify the fundamental observables in master-equation dynamics. However, because chemical reactions are usually many-to-many, chemical networks are rather described by hypergraphs, which lack a systematized algebraic treatment and a clear geometric intuition. Here we fill this gap by proposing a framework that reconciles the algebraic and geometric representations of CNRs, allowing one to identify conservative and driving chemical forces. As an application, we propose a reconstruction algorithm for large metabolic networks consistent with Kirchhoff’s Voltage and Current Laws.

In this talk, I will present recent results on the statistical properties of active particles. I will focus on the run-and-tumble particle (RTP) model, which describes the persistent motion of a class of bacteria, including E. coli. In the first part of the talk, I will show that many properties of this model, including the survival probability and the record statistics, are completely universal, i.e., independent of the system's dimension and the speed fluctuations of the particle. In the second part of the talk, I will investigate the position distribution of a single RTP at late times. I will show that, under certain conditions, a condensation transition can be observed in the large-deviation regime where the particle is far from its starting position.

When sufficiently deformed, amorphous solids exhibit irreversible, or plastic, response and eventually fail. Although such behaviour is broadly common to all solids, amorphous solids, or glasses, display disordered microscopic structure, leading to significant differences in how these phenomena may be understood, and to distint statistical mechanical approaches to address them. After a brief overview of glass phenomenology, recent approaches to yielding of amorphous solids is described, with specific focus on the response to cyclic shear deformations. Results from computer simulations of model glasses, as well as theoretical approaches and results will be discussed.

Within the description of correlation functions in dense fluids, the dynamical laws arise from glass-transition singularities. The simplest such singularity yields a master function with a two-step decay. Higher-order singularities allow for logarithmic decay laws, while multiple singularities give rise to complex master functions. While the scenarios with multiple singularities appear relevant for colloids, liquid water, and granular matter, the simple two-step scenario may be identified within simple models that allow for analytical calculations.

The ratchet effect in the colloidal suspension moving in a narrow channel of a periodically varying diameter can be used for particle separation by sizes. We study this phenomenon by mapping the colloid in the channel onto one-dimensional lattice models in which particles stochastically jump between sites with exclusion interaction. Besides allowing multiple occupancy of sites, we consider a mixture of small and big particles as well as complex geometry of the one-dimensional lattice when each site is joined to a lateral pocket. Currents of particles calculated within the mean-field approximation of the master equation approach are compared to Monte Carlo simulations. Phase diagram contains the density domain where the ratchet currents of small and big particles are of opposite directions, thus enabling full size separation

Part A: "A Fine Discrete FFCA Pedestrian Model and Its Application On Evacuation"; Part B: "How Sychronization Improves Pedestrian Traffic by Sound: from Macroscopic to Microscopic"

In the recent years, a growing interest on pedestrian traffic has led to a better knowledge on the movement of large crowds inside public facilities such as transportation hubs and recreational halls. However, there are still many aspects which are unknown and, especially when psychological aspects arise, managing and controlling large crowds is a challenging task. In this talk, classical methods to analyze and measure pedestrian crowds will be introduced and discussed. We will start with the bidirectional flow (for example people moving in a corridor), which, although rather simple, presents most of the characteristics of pedestrian dynamics, in particular regarding the presence of collision avoidance and emergent phenomena (in the form of lanes). Later the discussion will be extended to more complex cases, with the chaotic motion being the least organized. In the presentation a focus will be set on methods to analyze the level of congestion and the intrinsic risk of human crowds by also discussing methods to simulate pedestrian behavior with the aim of predicting future changes. Novel techniques (for example the use of inertial data from portable devices) will be presented showing advantages and limitations compared to classical approaches typically taken for pedestrian traffic and more generally for transportation systems.

We discuss significant events in the recent Renaissance triggered by the enigmatic and elusive, but rich stochastic nonlinear PDE of Kardar, Parisi & Zhang, a celebrated equation whose reach far exceeds its grasp, touching such diverse phenomena as non-equilibrium stochastic growth, extremal paths through disordered landscapes, driven lattice gases & dissipative condensates, as well as the statistics of random matrices & permutations.

Single-file motion in quasi one-dimensional geometry appears in wide-ranging systems, ranging from ion transport in biological channels, fluids absorbed in materials with nanopores, colloidal particles moving along circular grooves to pedestrian dynamics regulated along a line. In this talk, we focus on the steady state density profiles in directed single-file motions of a collection of particles along closed heterogeneous landscapes. Modeling these as asymmetric exclusion processes with heterogeneous hopping rates along a closed ring, we explore generic localised (LDW) and delocalised (DDW) domain walls and delocalisation of LDWs in the steady states. We further show how the interplay between heterogeneity and particle non-conserving Langmuir kinetics leads to a phase transition between a two-phase coexistence and a three-phase coexistence state. We eventually discuss the more generic problem of heterogeneities with arbitrary spatial variation and extract a notion of universality, hitherto unknown, for the steady state density profiles and the associated phase diagrams.

We consider a simplified model of a future European electricity network with a high share of renewable generation. In a cost optimal design of such a system, most of the renewable generation capacity is placed at locations with favorable weather conditions, that is for instance onshore wind in countries bordering the North Sea and solar PV in South European countries. Countries with less favorable renewable generation conditions benefit from this capacity by importing the respective electricity as power flows through the transmission grid. Using flow tracing techniques, which are related to directed diffusion processes on networks, we disentangle the emerging pattern of imports and exports and assign shares of the distributed generation capacity in the European system to the countries which actually make use of them. This procedures yields nodal levelized costs, which incorporate both internal and external generation as well as transmission costs associated with the electricity consumption in a country. Compared to a scenario without transmission, these nodal levelized costs are reduced by about 15% and represent the benefit of cooperation.

GPS data from participating groups in the Cologne Rose Monday parade are analyzed. The preparation of the measured data requires a correction of the data by a specially adapted algorithm for the map-matching method. A higher average velocity is observed for the last participant, the carnival prince, than for the head of the parade. This prince paradox can be explained by the the constant moving vehicle driving ahead of the parade leaving the train path. In addition, the influence of the route on the traffic kinematics of the parade is examined. Some areas can be determined in which the parade shows velocities below or above the average. Based on the results of the data analysis, for the first time a model can be established for parading groups as a modified Nagel-Schreckenberg model. The characteristics observed in the data analysis can be reproduced by this model in simulations. Furthermore, the train group model is expanded in a second simulation in order to adjust the average velocity of the prince.

Granular materials consist of macroscopic, athermal packings of particles which only interact via dissipative contact forces. The systems can adopt different states of aggregation depending on the external driving conditions. The viscosity dependence of a granular fluid will be probed by an active microrheology setup. We demonstrate access to three viscosity regimes depending on the shear rate. In a static granular system we measure the contact forces on grain scale and evaluate the local mechanical heterogeneities in an amorphous and crystalline packing.

Modelling the spread of epidemics on complex networks has led to a number of interesting results in the recent past. Starting with a brief overview, we discuss the characteristic features of the Susceptible-Infected-Removed (SIR) model considered on a network embedded in Euclidean space with random long range interactions chosen following a certain prescription. Numerical simulations suggest a simple form of the cumulative density of infected agents at time t, R(t), depending on the network parameters and the infection probability q. The epidemic dynamics shows the effect of the phase transition occurring in the network. The data for the Ebola outbreak that occurred in 2014-2016 in three countries of West Africa are analysed within a common framework using this model. The predicted form of R(t) is seen to fit well with the data. We also show that in the Euclidean model, appropriate choices of the parameters reproduce the data for the three countries with considerable accuracy. These choices are correlated with population density, control schemes and other factors. Comparing the real data and the results from the model one can also estimate the size of the actual population susceptible to the disease.

The emergence of global structures in networks is at the core of our increasingly connected world, ranging from international trade to the spreading of innovations in social networks. Many of these networks are constructed by individual decisions optimizing connectivity under various constraints, for example people choosing their friends in geographically constrained social networks. Yet, how and under which conditions these local decisions create global structures is hardly understood. We study a general optimization problem modeling the emergence of global interactions in networks in the presence of local feedback and transaction costs over long distances. Related problems arise for economic decisions in trade networks, for biological interactions in the context of cooperation and in social networks for the adoption of innovations. We map a wide range of these global optimization problems to a local percolation model where connectivity increases when the transaction costs in the network decrease. We explain how this transition is affected by the network structure and the local feedback effects: While the transition is discontinuous in compact networks and for strong enough feedback effects, the transition is slow in networks with a large diameter and small feedback effects.

As a by-product of the rising interest in the structural and dynamical characterization of networks in various scientific disciplines, complex network based methods have recently found wide use as an exploratory tool of data analysis across fields. In particular, functional networks encoding essential statistical interrelationships among multivariate time series have proven to be a versatile tool in climate sciences, neurophysiology and various other areas. In my talk, I will focus on some recent applications of functional network analysis in the field of climatology to highlight the potentials as well as ongoing challenges of such "climate network" approaches. As one particular example, I will demonstrate how the El Nino Southern Oscillation, the most prominent mode of tropical climate variability, is reflected in the global correlation structure of surface air temperatures. I will then present a straightforward methodological extension utilizing the idea of coupled networks and their appropriate structural quantification, and demonstrate the application of this idea to studying ocean-atmosphere interdependences in the Northern latitude extratropics during boreal winter.