Abstract: Spatiotemporal and spatial non-equilibrium patterns in chemical systems can emerge due to the coupling of nonlinear chemical kinetics with the diffusion of reacting particles, with eventual contribution from excitable characteristics. All these phenomena are explainable in terms of the assumption of the isothermal conditions. In our searches for new mechanisms underlying the spatiotemporal instabilities in aqueous media we studied several chemical systems in which hydrogen peroxide was an oxidant for various sulfur-containing species. In one of these systems, containing hydrogen peroxide and thiocyanates as the main reactants [1], which produces sustained oscillations, we discovered the emergence of luminescent patterns. Based on experimental studies and numerical modeling of the reaction kinetics, we found that the observed patterns were essentially the phase waves, caused by the spatially inhomogenous distribution of the solution temperature which affected the local frequency of oscillations. This finding allowed us to take control over the evolution of these phase waves by externally imposed temperature gradient applied to quasi 1-dimensional thin-layer reactor [2]. The second chemical system, containing hydrogen peroxide and thiosulfates, produces only a single oscillatory peak, but in the presence of externally imposed temperature gradient became a source of color front progressing along the reactor. The mechanistic reason for the observed instability is again the dependence of the local chemical reaction kinetics on temperature, i.e. the thermokinetic coupling. Also in this case the experimental findings were successfully reproduced by numerical modeling [3]. We consider these phenomena the novel and rather unique examples of instabilities caused by thermokinetic coupling in liquid media, instead of typical isothermal reaction-diffusion coupling. References: [1] M. Orbán, J. Am. Chem. Soc., 108 (1986) 6893 [2] A. Wiśniewski, M. T. Gorzkowski, K. Pekala, M. Orlik, J. Phys. Chem. A, 117 (2013) 11155 [3] M. Jędrusiak, M. Orlik, J. Phys. Chem. B, 120 (2016) 3169

Abstract: The search for scale-bridging relations in the deformation of amorphous materials presents a current challenge with tremendous applications in material science, engineering and geology. While generic features in the flow and microscopic dynamics support the idea of a universal scaling theory of deformation, direct microscopic evidence remains poor. We study the evolution of slowly sheared granular systems deforming via discrete strain bursts (slips). The granular sample consisting of 105 hard spheres is subjected to applied shear and studied with the combination of two techniques – precise stress-strain measurements and 3D laser sheet imaging. Fluctuations in the stress-strain profile allow us to calculate the magnitude of small internal slip avalanches occurring in the sample due to the shear. 3D laser sheet imaging allows us to visualize each individual slip event, estimate its spatial distribution and connect it to fluctuation in the stress-strain curve. By combining macroscopic force fluctuation measurements with internal strain imaging, we demonstrate the existence of robust scaling relations from particle-scale to macroscopic flow [1]. The presence of the power-law distributions characterizing the spatial and temporal properties of the avalanches suggests the presence of the externally induced critical state in the system. Moreover by building the 3D-map of the critical stress distribution through the system we observe a strongly connected complex network spanning through the whole sample. At a certain critical point the external stress distributed through such network can lead to a creation of a system-wide avalanche resulting in a complete system failure/reconfiguration. These experimental results pave the way to a new universal theory of deformation allowing prediction and possibly prevention of the large avalanches and their negative effects. [1] D.V. Denisov, K.A. Lorincz, J. T. Uhl, K. A. Dahmen & P. Schall, “Universality of slip avalanches in flowing granular matter”, Nature Communications 7, 10641 (2016).

Abstract: Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks’ structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve global and local statistics associated with the nodes’ embedding in a metric space. Comparing the original network’s and the resulting surrogates’ global characteristics allows to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes’ spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology.

Abstract: Randomization techniques deal with the controlled destruction of given temporal or topological structures in complex networks. This is done by resampling certain motifs of the original (empirical) temporal network, such as the edges between nodes or the temporal order of interactions. By comparing how a given dynamical process evolves on the randomized network with how it evolves on the original network, we may identify how the different characteristics affect the dynamical process. Randomization techniques provide a powerful tool for the study of dynamical processes on temporal networks. They may be applied in very general settings as they are purely numerical and non-parametric. They may notably be applied to systems for which no realistic model exists, which is the case for most real systems. A multitude of different randomization techniques exists [Holme, EPJB (2015)], each destroying certain characteristics while preserving others. However, no general procedure exists for their application. Researchers are thus confronted with the non-trivial problem of how to choose/develop techniques and in which order to apply them to be able to identify the important characteristics for each given dynamical phenomenon and dataset under study. As a first step towards a general methodology for randomization-based inference, we propose a taxonomy of existing randomization techniques, based on their methodological nature, their effect on dynamical and topological characteristics of temporal networks, and their known effects on dynamical processes taking place on the networks. This collection should help researches wanting to apply randomization techniques to the study of a given phenomena, providing guidelines for which techniques to apply to most effectively divide the space of possibilities. It is our hope that it may serve as a starting point for the development of a principled randomization-based approach for the characterization of general dynamical networked systems.

Abstract: The dynamics of how people collectively visit different places in cities determines the population’s mixing rate and ultimately drives the socio-economic development of urban areas. Despite the crucial role of the temporal dimension of movement, the laws of attraction to locations that give rise to 'pulsating' population flows with varying frequencies of visitation have remained elusive. In this paper we show the existence of a surprisingly simple scaling function that directly connects i) the number of people attracted to a location, ii) their travel distance from home and iii) their visiting frequency. By combining first principles calculations with dimensional arguments, we find that the collective influx of individuals decreases with the product of travel distance and visiting frequency in form of a power law (slope ≈ -2). This hitherto hidden regularity allows for the prediction of the frequency-distance distribution by just counting the total number of visitors to a given location. The trajectories derived from anonymized mobile phone records of millions of individuals in various countries worldwide confirm that empirical population flows obey the derived scaling function in virtually all tested areas. This suggests that the collective visitation dynamics follow the same underlying principles, regardless of the detailed cultural, socio-economic and infrastructural conditions. Finally, we show how deviations from the inverse square law allow for the identification of locations that trigger significantly more (or less) traffic than should be expected from the total visitor counts. The derived scaling function thus provides an appropriate baseline for the identification of unusual hotspots of activity or under-performing regions in need of stimulation. The revealed dynamics places an important constraint on any theory of human spatial organization, and provides a microscopic basis for traffic forecasting, urban planning and epidemiology.