Search

We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the real-variable system. However, synchrony persists in the form of \textit{complex locked states} for coupling strengths $K$ below the transition $K^{(\text{pl})}$ to classical \textit{phase locking}. Stable complex locked states indicate a locked sub-population of zero mean frequency in the real-variable model and their imaginary parts help identifying which units comprise that sub-population. We uncover a second transition at $K'

The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost five decades of research, many questions remain open, in particular for finite-size systems. Here, we generalize recent work [Phys. Rev. Lett. 130, 187201 (2023)] on the finite-size Kuramoto model with its state variables analytically continued to the complex domain and also complexify its system parameters. Intriguingly, systems of two units with purely imaginary coupling do not actively synchronize even for arbitrarily large magnitudes of the coupling strengths, $|K| \rightarrow \infty$, but exhibit conservative dynamics with asynchronous rotations or librations for all $|K|$. For generic complex coupling, both, traditional phase-locked states and asynchronous states generalize to complex locked states, fixed points off the real subspace that exist even for arbitrarily weak coupling. We analyze a new collective mode of rotations exhibiting finite, yet arbitrarily large rotation numbers. Numerical simulations for large networks indicate a novel form of discontinuous phase transition. We close by pointing to a range of exciting questions for future research.

Filamentation has extensively been explored and is well understood at repetition rates <1 kHz due to the typical availability of multi-mJ laser systems at a moderate average power. The advent of high-power Yb-lasers opened new possibilities for filamentation research. However, so far, high average power Yb systems have mostly been explored to increase the driving pulse energy to several hundreds of mJ and not at significantly higher repetition rates. In this paper, we study, for the first time, long filaments at unprecedented high repetition rates of 10, 40, and 100 kHz using a 500-W Yb-doped thin-disk amplifier driver operating with sub-700 fs pulses. We compare the filament length, density hole, and fluorescence at a constant peak power but different repetition rates and find a strong dependence on filament length and density depletion with repetition rate. Our analysis reveals the emergence of a significant stationary density depletion at repetition rates of 40 and 100 kHz. The corresponding reduction in the breakdown threshold by increasing the laser repetition rate observed in our study signifies a promising avenue for enhancing the efficiency and reliability of electric discharge triggering in various scenarios. Using capacitive plasma probe measurements, we address the limitations of fluorescence imaging-based measurements and demonstrate a systematic underestimation of filament length. This work contributes to a deeper understanding of the interplay between laser repetition rates, filamentation, and heat-driven density depletion effects from high-repetition-rate high-power laser systems and will contribute to guiding future research, making use of filaments at high repetition rates.

The adoption of battery electric vehicles (BEVs) may significantly reduce greenhouse gas emissions caused by road transport. However, there is wide disagreement as to how soon battery electric vehicles will play a major role in overall transportation. Focusing on battery electric passenger cars, we here analyze BEV adoption across 17 individual countries, Europe, and the World, and consistently find exponential growth trends. Modeling-based estimates of future adoption given past trends suggests system-wide adoption substantially faster than typical economic analyses have proposed so far. For instance, we estimate the majority of passenger cars in Europe to be electric by about 2031. Within regions, the predicted times of mass adoption are largely insensitive to model details. Despite significant differences in current electric fleet sizes across regions, their growth rates consistently indicate fast doubling times of approximately 15 months, hinting at radical economic and infrastructural consequences in the near future.

Ride sharing services combine trips of multiple users in the same vehicle and may provide more sustainable transport than private cars. As mobility demand varies during the day, the travel times experienced by passengers may substantially vary as well, making the service quality unreliable. We show through model simulations that such travel time fluctuations may be drastically reduced by stop pooling. Having users walk to meet at joint locations for pick-up or drop-off allows buses to travel more direct routes by avoiding frequent door-to-door detours, especially during high demand. We in particular propose adaptive stop pooling by adjusting the maximum walking distance to the temporally and spatially varying demand. The results highlight that adaptive stop pooling may substantially reduce travel time fluctuations while even improving the average travel time of ride sharing services, especially for high demand. Such quality improvements may in turn increase the acceptance and adoption of ride sharing services.

Ridepooling combines trips of multiple passengers in the same vehicle and may thereby provide a more sustainable option than transport by private cars. The efficiency and sustainability of ridepooling is typically quantified by key performance indicators such as the average vehicle occupancy or the total distance driven by all ridepooling vehicles relative to individual transport. However, even if the average occupancy is high and rides are shared, ridepooling services may increase the total distance driven due to additional detours and deadheading. Moreover, these key performance indicators are difficult to predict without large-scale simulations or actual ridepooling operation. Here, we propose a dimensionless parameter to estimate the sustainability of ridepooling by quantifying the load on a ridepooling service, relating characteristic timescales of demand and supply. The load bounds the relative distance driven and uniquely marks the break-even point above which the total distance driven by all vehicles of a ridepooling service falls below that of motorized individual transport. Detailed event-based simulations and a comparison with empirical observations from a ridepooling pilot project in a rural area of Germany validate the theoretical prediction. Importantly, the load follows directly from a small set of aggregate parameters of the service setting and is thus predictable a priori. The load may thus complement standard key performance indicators and simplify planning, operation and evaluation of ridepooling services.

Understanding the structure and formation of networks is a central topic in complexity science. Economic networks are formed by decisions of individual agents and thus not properly described by established random graph models. In this article, we establish a model for the emergence of trade networks that is based on rational decisions of individual agents. The model incorporates key drivers for the emergence of trade, comparative advantage and economic scale effects, but also the heterogeneity of agents and the transportation or transaction costs. Numerical simulations show three macroscopically different regimes of the emerging trade networks. Depending on the specific transportation costs and the heterogeneity of individual preferences, we find centralized production with a star-like trade network, distributed production with all-to-all trading or local production and no trade. Using methods from statistical mechanics, we provide an analytic theory of the transitions between these regimes and estimates for critical parameters values., Comment: 25 pages, 7 figures

It was recently demonstrated that laser filamentation was able to generate an optically transparent channel through cloud and fog for free-space optical communications applications. However, no quantitative measurement of the interaction between the laser-induced shockwave and the aerosol particles was carried out so far, leaving the precise nature of the clearing mechanism up for discussion. A critical question was the maximum distance at which the filament could still act on the aerosol particle. Distances widely exceeding the filament diameter and its energy reservoir exclude other potential clearing effects like shattering or explosion by direct exposure to the laser. Here, we quantify the force exerted by the shockwave on a single aerosol microparticle. The force is measured by observing the ejection and displacement of the particle when trapped in an optical tweezer. We demonstrate that even for distances ranging from 1.5 mm to 5.5 mm away from the filament, thus widely exceeding the filamentary region, an acoustic force of 500 pN to 8 nN (depending on the initial laser power) acts on the aerosol particle and expels it away from the optical trap., Comment: 12 pages in total with 4 figures. Supplementary material is attached to the manuscript

Standard epidemic models exhibit one continuous, second order phase transition to macroscopic outbreaks. However, interventions to control outbreaks may fundamentally alter epidemic dynamics. Here we reveal how such interventions modify the type of phase transition. In particular, we uncover three distinct types of explosive phase transitions for epidemic dynamics with capacity-limited interventions. Depending on the capacity limit, interventions may (i) leave the standard second order phase transition unchanged but exponentially suppress the probability of large outbreaks, (ii) induce a first-order discontinuous transition to macroscopic outbreaks, or (iii) cause a secondary explosive yet continuous third-order transition. These insights highlight inherent limitations in predicting and containing epidemic outbreaks. More generally our study offers a cornerstone example of a third order explosive phase transition in complex systems., Comment: Main manuscript: 5 pages, 3 figures; Supplemental material: 27 pages, 13 figures

Electric currents circulating between charged clouds and the earth surface during lightning discharges are responsible for considerable damages and casualties. It is therefore important to develop better protection methods in addition to the traditional Franklin rod. Here we present the first demonstration that filaments formed by short and intense laser pulses can guide lightning discharges over considerable distances. We believe that this experimental breakthrough will lead to progress in lightning protection and lightning physics. An experimental campaign was carried out on the S\"antis Mountain in Northeastern Switzerland during the Summer of 2021 with a high repetition rate terawatt laser. The guiding of an upward negative lightning leader over a distance of 50 m was recorded by two separate high-speed cameras. The guiding of negative lightning leaders by laser filaments was corroborated in three other instances by VHF interferometric measurements, and the number of X-ray bursts detected during guided lightning events was significantly increased. While this research field has been very active for more than 20 years with many research groups around the world working to achieve this goal, this result demonstrates lightning guiding by lasers, which may lead to the development of a laser lightning rod. This work paves the way for new atmospheric applications of ultrashort lasers and represents a significant step forward in the development of a laser based lightning protection for airports, launchpads or large infrastructures., Comment: Laser-guided lightning. Nat. Photon. (2023)

Electric vehicles may dominate motorized transport in the next decade, yet the impact of the collective dynamics of electric mobility on long-range traffic flow is still largely unknown. We demonstrate a type of congestion that arises if charging infrastructure is limited or electric vehicle density is high. This congestion emerges solely through indirect interactions at charging infrastructure by queue-avoidance behavior that - counterintuitively - induces clustering of occupied charging stations and phase separation of the flow into free and congested stations. The resulting congestion waves always propagate forward in the direction of travel, in contrast to typically backward-propagating congestion waves known from traditional traffic jams. These results may guide the planning and design of charging infrastructure and decision support applications in the near future.

Ride-pooling (or ride-sharing) services combine trips of multiple customers along similar routes into a single vehicle. The collective dynamics of the fleet of ride-pooling vehicles fundamentally underlies the efficiency of these services. In simplified models, the common features of these dynamics give rise to scaling laws of the efficiency that are valid across a wide range of street networks and demand settings. However, it is unclear how constraints of the vehicle fleet impact such scaling laws. Here, we map the collective dynamics of capacity-constrained ride-pooling fleets to services with unlimited passenger capacity and identify an effective fleet size of available vehicles as the relevant scaling parameter characterizing the dynamics. Exploiting this mapping, we generalize the scaling laws of ride-pooling efficiency to capacity-constrained fleets. We approximate the scaling function with a queueing theoretical analysis of the dynamics in a minimal model system, thereby enabling mean-field predictions of required fleet sizes in more complex settings. These results may help to transfer insights from existing ride-pooling services to new settings or service locations.

Cycling is a crucial part of sustainable urban transportation. Promoting cycling critically relies on a sufficiently developed bicycle infrastructure. However, designing efficient bike path networks constitutes a complex problem that requires balancing multiple constraints while still supporting all cycling demand. Here, we propose a framework to create families of efficient bike path networks by explicitly taking into account the demand distribution and cyclists' route choices based on safety preferences. By reversing the network formation process and iteratively removing bike paths from an initially complete bike path network and continually updating cyclists' route choices, we create a sequence of networks that is always adapted to the current cycling demand. We illustrate the applicability of this demand-driven planning scheme for two cities. A comparison of the resulting bike path networks with those created for homogenized demand enables us to quantify the importance of the demand distribution for network planning. The proposed framework may thus enable quantitative evaluation of the structure of current and planned bike path networks and support the demand-driven design of efficient infrastructures.

Ride sharing - the bundling of simultaneous trips of several people in one vehicle - may help to reduce the carbon footprint of human mobility. However, standard door-to-door ride sharing services trade reduced route length for increased user travel times and come with the burden of many stops and detours to pick up individual users. Requiring some users to walk to nearby shared stops reduces detours, but could become inefficient if spatio-temporal demand patterns do not well fit the stop locations. Here, we present a simple computational model of dynamic stop pooling with flexible stop positions, and analyze its influence on the performance of ride sharing services. We find that dynamic stop pooling does a-priori not save route length, but occupancy. Intriguingly, it also reduces the travel time although users walk parts of their trip. Together, dynamic stop pooling may break the trade-off between route lengths and travel time in door-to-door ride sharing, thus enabling higher sustainability and service quality., Comment: 10 pages, 6 figures

Scaling arguments provide valuable analysis tools across physics and complex systems yet are often employed as one generic method, without explicit reference to the various mathematical concepts underlying them. A careful understanding of these concepts empowers us to unlock their full potential., Comment: 8 pages, 1 figure

Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically, in two dimensions, repeating an isotropic rotation twice maps a given point on the two-dimensional unit sphere (the unit circle) uniformly at random to any point on the unit sphere, reflecting a statistical symmetry as expected. In contrast, in three and higher dimensions, a point is mapped more often closer to the original point than a uniform distribution predicts. Curiously, in the limit of the dimension $d \rightarrow \infty$, a symmetric distribution is approached again. We intuitively explain the emergence of this asymmetry and why it disappears in higher dimensions by disentangling isotropic rotations into a sequence of partial actions. The asymmetry emerges in two qualitatively different forms and for a wide range of general random operations relevant in complex systems modeling, including repeated continuous and discrete rotations, roto-reflections and general orthogonal transformations, Comment: 6 pages, 5 figures

Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they transiently alter. The maximum state changes at those units and the timings of these changes constitute key characteristics of such transient response dynamics. However, even for linear dynamical systems it is not possible to analytically determine time and amplitude of the maximal response of a unit to a perturbation. Here, we propose to extract approximate peak times and amplitudes from effective expectation values used to characterize the typical time and magnitude of the response of a unit by interpreting the system's response as a probability distribution over time. We derive analytic estimators for the peak response based on these expectation value measures in linearized systems operating close to a stable fixed point. These estimators can be expressed in terms of the inverse of the system's Jacobian. We obtain identical results with different approximations for the response dynamics, indicating that these estimators become exact in the limit of weak coupling. Furthermore, the results suggest that perturbations spread ballistically in networks with diffusive coupling., Comment: 15 pages, 7 figures

The capacity of a street segment quantifies the maximal density of vehicles before congestion arises. Here we show in a simple mathematical model that fluctuations in the instantaneous number of vehicles entering a street segment are sufficient to induce persistent congestion. Congestion emerges even if the average flow is below the segment's capacity where congestion is absent without fluctuations. We explain how this fluctuation-induced congestion emerges due to a self-amplifying reduction of the average vehicle velocities., Comment: 5 pages, 2 figures. Findings, December 2020

Although routing applications increasingly affect individual mobility choices, their impact on collective traffic dynamics remains largely unknown. Smart communication technologies provide accurate traffic data for choosing one route over other alternatives, yet inherent delays undermine the potential usefulness of such information. Here we introduce and analyze a simple model of collective traffic dynamics which result from route choice relying on outdated traffic information. We find for sufficiently small information delays that traffic flows are stable against perturbations. However, delays beyond a bifurcation point induce self-organized flow oscillations of increasing amplitude -- congestion arises. Providing delayed information averaged over sufficiently long periods of time or, more intriguingly, reducing the number of vehicles adhering to the route recommendations may prevent such delay-induced congestion. We reveal the fundamental mechanisms underlying these phenomena in a minimal two-road model and demonstrate their generality in microscopic, agent-based simulations of a road network system. Our findings provide a way to conceptually understand system-wide traffic dynamics caused by broadly used non-instantaneous routing information and suggest how resulting unintended collective traffic states could be avoided., Comment: 12 pages, 9 figures; additional appendix section, included link to code and data

Symmetry breaking ubiquitously occurs across complex systems, from phase transition in statistical physics to self-organized lane formation in pedestrian dynamics. Here, we uncover spontaneous symmetry breaking in a simple model of ride-sharing adoption. We analyze how collective interactions among ride-sharing users to avoid detours in shared rides give rise to spontaneous symmetry breaking and pattern formation in the adoption dynamics. These dynamics result in bistability of high homogeneous and partial heterogeneous adoption states, potentially limiting the population-wide adoption of ride-sharing. Our results provide a framework to understand real-world adoption patterns of ride-sharing in complex urban settings and support the (re)design of ride-sharing services and incentives for sustainable shared mobility.

Ride-sharing - the combination of multiple trips into one - may substantially contribute towards sustainable urban mobility. It is most efficient at high demand locations with many similar trip requests. However, here we reveal that people's willingness to share rides does not follow this trend. Modeling the fundamental incentives underlying individual ride-sharing decisions, we find two opposing adoption regimes, one with constant and another one with decreasing adoption as demand increases. In the high demand limit, the transition between these regimes becomes discontinuous, switching abruptly from low to high ride-sharing adoption. Analyzing over 360 million ride requests in New York City and Chicago illustrates that both regimes coexist across the cities, consistent with our model predictions. These results suggest that even a moderate increase in the financial incentives may have a disproportionately large effect on the ride-sharing adoption of individual user groups.

Digital technology is fundamentally transforming human mobility. Route choices in particular are greatly affected by the availability of traffic data, increased connectivity of data sources and cheap access to computational resources. Digital routing technologies promise more efficient route choices for the individual and a reduction of congestion for cities. Yet, it is unclear how widespread adoption of such technologies actually alters the collective traffic flow dynamics on complex street networks. Here, we answer this question for the dynamics of urban commuting under digital route choice support. Building on the class of congestion games we study the evolution of commuting behavior as a fraction of the population relies on, but also contributes to, crowdsourced traffic information. The remainder of the population makes their route choices based on personal experience. We show how digital route choice support may cause a separation of commuter flows into technology and non-technology users along different routes. This collective behavior may fuel systemic inefficiencies and lead to an increase of congestion as a consequence. These results highlight new research directions in the field of algorithmic design of route choice decision support protocols to help fight congestion, emissions and other systemic inefficiencies in the course of increasing urbanization and digitization.

Few African countries have reported COVID-19 case numbers above $1\,000$ as of April 18, 2020, with South Africa reporting $3\,034$ cases being hit hardest in Sub-Saharan Africa. Several African countries, especially South Africa, have already taken strong non-pharmaceutical interventions that include physical distancing, restricted economic, educational and leisure activities and reduced human mobility options. The required strengths and overall effectiveness of such interventions, however, are debated because of simultaneous but opposing interests in most African countries: strongly limited health care capacities and testing capabilities largely conflict with pressured national economies and socio-economic hardships on the individual level, limiting compliance to intervention targets. Here we investigate implications of interventions on the COVID-19 outbreak dynamics, focusing on South Africa before and after the national lockdown enacted on March 27, 2020. Our analysis shows that initial exponential growth of existing case numbers is consistent with doubling times of about $2.5$ days. After lockdown, the growth remains exponential, now with doubling times of 18 days, but still in contrast to subexponential growth reported for Hubei/China after lockdown. Moreover, a scenario analysis of a computational data-driven agent based mobility model for the Nelson Mandela Bay Municipality (with $1.14$ million inhabitants) hints that keeping current levels of intervention measures and compliance until the end of April is of insufficient length and still too weak, too unspecific or too inconsistently complied with to not overload local intensive care capacity. Yet, enduring, slightly stronger, more specific interventions combined with sufficient compliance may constitute a viable option for interventions for regions in South Africa and potentially for large parts of the African continent., Comment: 16 pages including 3 Figures and Executive Summary

COVID-19 has spread from China across Europe and the United States and has become a global pandemic. In countries of the Global South, due to often weaker socioeconomic options and health care systems, effective local countermeasures remain debated. We combine large-scale socioeconomic and traffic survey data with detailed agent-based simulations of local transportation to analyze COVID-19 spreading in a regional model for the Nelson Mandela Bay Municipality in South Africa under a range of countermeasure scenarios. The simulations indicate that any realistic containment strategy, including those similar to the one ongoing in South Africa, may yield a manifold overload of available intensive care units (ICUs). Only immediate and the most severe countermeasures, up to a complete lock-down that essentially inhibits all joint human activities, can contain the epidemic effectively. As South Africa exhibits rather favorable conditions compared to many other countries of the Global South, our findings constitute rough conservative estimates and may support identifying strategies towards containing COVID-19 as well as any major future pandemics in these countries., Comment: including 3 Figures and Supplementary Material

High intensity laser filamentation in air has recently demonstrated that, through plasma generation and its associated shockwave, fog can be cleared around the beam, leaving an optically transparent path to transmit light. However, for practical applications like free-space optical communication (FSO), channels of multi-centimeter diameters over kilometer ranges are required, which is extremely challenging for a plasma based method. Here we report a radically different approach, based on quantum control. We demonstrate that fog clearing can also be achieved by producing molecular quantum wakes in air, and that neither plasma generation nor filamentation are required. The effect is clearly associated with the rephasing time of the rotational wave packet in N2.Pump excitation provided in the form of resonant trains of 8 pulses separated by the revival time are able to transmit optical data through fog with initial extinction as much as -6 dB.

Dynamic pricing schemes are increasingly employed across industries to maintain a self-organized balance of demand and supply. However, throughout complex dynamical systems, unintended collective states exist that may compromise their function. Here we reveal how dynamic pricing may induce demand-supply imbalances instead of preventing them. Combining game theory and time series analysis of dynamic pricing data from on-demand ride-hailing services, we explain this apparent contradiction. We derive a phase diagram demonstrating how and under which conditions dynamic pricing incentivizes collective action of ride-hailing drivers to induce anomalous supply shortages. By disentangling different timescales in price time series of ride-hailing services at 137 locations across the globe, we identify characteristic patterns in the price dynamics reflecting these anomalous supply shortages. Our results provide systemic insights for the regulation of dynamic pricing, in particular in publicly accessible mobility systems, by unraveling under which conditions dynamic pricing schemes promote anomalous supply shortages., Comment: Main manuscript is 21 pages (incl. methods) with 4 figures. Appendix contains detailed description of the data and methods and additional examples

Input-Output analysis describes the dependence of production, demand and trade between sectors and regions and allows to understand the propagation of economic shocks through economic networks. A central challenge in practical applications is the availability of data. Observations may be limited to the impact of the shocks in few sectors, but a complete picture of the origin and impacts would be highly desirable to guide political countermeasures. In this article we demonstrate that a shock in the final demand in few sectors can be fully reconstructed from limited observations of production changes. We adapt three algorithms from sparse signal recovery and evaluate their performance and their robustness to observation uncertainties., Comment: 10 pages, 4 figures, conference proceeding for CompleNet 2020

Ride-sharing may substantially contribute to future-compliant sustainable mobility, both in urban and rural areas. The service quality of ride-sharing fleets jointly depends on the topology of the underlying street networks, the spatio-temporal demand distributions, and the dispatching algorithms. Yet, efficiency of ride-sharing services is typically quantified by economic or ecological ad-hoc measures that do not transfer to new service regions with different characteristics. Here we derive a generic measure of ride-sharing efficiency based on the intrinsic ride-sharing dynamics that follows a universal scaling law across network topologies. We demonstrate that the same scaling holds across street networks of distinct topologies, including cities, islands and rural areas, and is insensitive to modifying request distributions and dispatching criteria. These results further our understanding of the collective dynamics of ride-sharing fleets and may enable quantitative evaluation of conditions towards increasing the feasibility of creating or transferring ride-sharing services to previously unserviced regions.

Quantifying the importance and power of individual nodes depending on their position in socio-economic networks constitutes a problem across a variety of applications. Examples include the reach of individuals in (online) social networks, the importance of individual banks or loans in financial networks, the relevance of individual companies in supply networks, and the role of traffic hubs in transport networks. Which features characterize the importance of a node in a trade network during the emergence of a globalized, connected market? Here we analyze a model that maps the evolution of trade networks to a percolation problem. In particular, we focus on the influence of topological features of the node within the trade network. Our results reveal that an advantageous position with respect to different length scales determines the success of a node at different stages of globalization and depending on the speed of globalization.

Titanium is the base material for a number of technologically important alloys for energy conversion and structural applications. Atomic-scale studies of Ti-based metals employing first-principles methods, such as density functional theory, are limited to ensembles of a few hundred atoms. To perform large-scale and/or finite temperature simulations, computationally more efficient interatomic potentials are required. In this work, we coarse grain the tight-binding (TB) approximation to the electronic structure and develop an analytic bond-order potential (BOP) for Ti by fitting to the energies and forces of elementary deformations of simple structures. The BOP predicts the structural properties of the stable and defective phases of Ti with a quality comparable to previous TB parametrizations at a much lower computational cost. The predictive power of the model is demonstrated for simulations of martensitic transformations.

The enigmatic coupling between electronic and magnetic phenomena was one of the riddles propelling the development of modern electromagnetism. Today, the fully controlled electric field evolution of ultrashort laser pulses permits the direct and ultrafast control of electronic properties of matter and is the cornerstone of light-wave electronics. In sharp contrast, because there is no first order interaction between light and spins, the magnetic properties of matter can only be affected indirectly on the much slower tens-of-femtosecond timescale in a sequence of optical excitation followed by the rearrangement of the spin structure. Here we record an orders of magnitude faster magnetic switching with sub-femtosecond response time by initiating optical excitations with near-single-cycle laser pulses in a ferromagnetic layer stack. The unfolding dynamics are tracked in real-time by a novel attosecond time-resolved magnetic circular dichroism (atto-MCD) detection scheme revealing optically induced spin and orbital momentum transfer (OISTR) in synchrony with light field driven charge relocation. In tandem with ab-initio quantum dynamical modelling, we show how this mechanism provides simultaneous control over electronic and magnetic properties that are at the heart of spintronic functionality. This first incarnation of attomagnetism observes light field coherent control of spin-dynamics in the initial non-dissipative temporal regime and paves the way towards coherent spintronic applications with Petahertz clock rates., Comment: 12 pages, 3+1 figures

Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network growth processes. Real networks not only grow but often also restructure, yet common network restructuring processes, such as small world rewiring, do not exhibit phase transitions. Here, we uncover a class of intrinsically discontinuous transitions emerging in network restructuring processes controlled by \emph{adhesion} -- the preference of a chosen link to remain connected to its end node. Deriving a master equation for the temporal network evolution and working out an analytic solution, we identify genuinely discontinuous transitions in non-growing networks, separating qualitatively distinct phases with monotonic and with peaked degree distributions. Intriguingly, our analysis of heuristic data indicates a separation between the same two forms of degree distributions distinguishing abstract from face-to-face social networks., Comment: 6 pages incl. references, accepted at Physical Review Letters

Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks experiencing perturbations. Still, how local disturbances spread across networks is not yet quantitatively understood. Here we analyze generic spreading dynamics in deterministic network dynamical systems close to a given operating point. Standard dynamical systems' theory does not explicitly provide measures for arrival times and amplitudes of a transient, spreading signal because it focuses on invariant sets, invariant measures and other quantities less relevant for transient behavior. We here change the perspective and introduce effective expectation values for deterministic dynamics to work out a theory explicitly quantifying when and how strongly a perturbation initiated at one unit of a network impacts any other. The theory provides explicit timing and amplitude information as a function of the relative position of initially perturbed and responding unit as well as on the entire network topology., Comment: 9 pages and 4 figures main manuscript 9 pages and 3 figures appendix

The emergence of large-scale connectivity underlies the proper functioning of many networked systems, ranging from social networks and technological infrastructure to global trade networks. Percolation theory characterizes network formation following stochastic local rules, while optimization models of network formation assume a single controlling authority or one global objective function. In socio-economic networks, however, network formation is often driven by individual, locally optimal decisions. How such decisions impact connectivity is only poorly understood to date. Here, we study how large-scale connectivity emerges from decisions made by rational agents that individually minimize costs for satisfying their demand. We establish that the solution of the resulting nonlinear optimization model is exactly given by the final state of a local percolation process. This allows us to systematically analyze how locally optimal decisions on the micro-level define the structure of networks on the macroscopic scale., Comment: 6 pages, 5 figures and an additional 23 pages, 10 figures appendix/supplement. See also ancillary files for data

Connectivity - or the lack thereof - is crucial for the function of many man-made systems, from financial and economic networks over epidemic spreading in social networks to technical infrastructure. Often, connections are deliberately established or removed to induce, maintain, or destroy global connectivity. Thus, there has been a great interest in understanding how to control percolation, the transition to large-scale connectivity. Previous work, however, studied control strategies assuming unlimited resources. Here, we depart from this unrealistic assumption and consider the effect of limited resources on the effectiveness of control. We show that, even for scarce resources, percolation can be controlled with an efficient intervention strategy. We derive this strategy and study its implications, revealing a discontinuous transition as an unintended side-effect of optimal control., Comment: 5 pages, 4 figures, additional supplemental material (19 pages)

We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the introduced order parameters capture all transitions from incoherence over phase locking to full synchrony for arbitrary, finite networks. We then introduce an alternative, universal order parameter that accurately tracks the degree of partial phase locking and synchronization, adapting the traditional definition to account for the network topology and its influence on the phase coherence of the oscillators. We rigorously proof that this order parameter is strictly monotonously increasing with the coupling strength in the phase locked state, directly reflecting the dynamic stability of the network. Furthermore, it indicates the onset of full phase locking by a diverging slope at the critical coupling strength. The order parameter may find applications across systems where different types of synchrony are possible, including biological networks and power grids., Comment: 8 pages, 4 figures

Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them -- a phenomenon termed "generalized synchronization." Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.

Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order parameter [Chen et al., Phys. Rev. Lett. 112, 155701 (2014)]. Here we report the discovery of macrotransition cascades which follow percolation. The order parameter grows in discrete macroscopic steps with positions that can be randomly distributed even in the thermodynamic limit. These transition positions are, however, correlated and follow scaling laws which arise from discrete scale invariance and non self-averaging, both traditionally unrelated to percolation. We reveal the discrete scale invariance in ensemble measurements of these non self-averaging systems by rescaling of the individual realizations before averaging., Comment: 8 pages, 8 figures

Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently uncoupling them. Specifically, systems coupled only in a fraction of their state space may synchronize even if fully coupled they do not. Although, for many standard systems, coupling strengths need to be bounded to ensure synchrony, transient uncoupling removes this bound and thus enables synchronization in an infinite range of effective coupling strengths. The presented coupling scheme thus opens up the possibility to induce synchrony in (biological or technical) systems whose parameters are fixed and cannot be modified continuously., Comment: 5 pages, 6 figures

We report the discovery of a discrete hierarchy of micro-transitions occurring in models of continuous and discontinuous percolation. The precursory micro-transitions allow us to target almost deterministically the location of the transition point to global connectivity. This extends to the class of intrinsically stochastic processes the possibility to use warning signals anticipating phase transitions in complex systems., Comment: 5 pages, 4 figures (main text) + 14 figures and 8 figures (supplementary materials). Accepted for publication by Physical Review Letters

Crackling noise is a common feature in many systems that are pushed slowly, the most familiar instance of which is the sound made by a sheet of paper when crumpled. In percolation and regular aggregation clusters of any size merge until a giant component dominates the entire system. Here we establish `fractional percolation' where the coalescence of clusters that substantially differ in size are systematically suppressed. We identify and study percolation models that exhibit multiple jumps in the order parameter where the position and magnitude of the jumps are randomly distributed - characteristic of crackling noise. This enables us to express crackling noise as a result of the simple concept of fractional percolation. In particular, the framework allows us to link percolation with phenomena exhibiting non-self-averaging and power law fluctuations such as Barkhausen noise in ferromagnets., Comment: non-final version, for final see Nature Communications homepage