Session P25: Fabric, Knits and Knots II / Complex Networks

String Contraction via Twisting: Ideal and Nonideal Behavior

Strings are an ancient and extremely common tool for force delivery. They may also be used to deliver torque via twisting, according to tension times the rate of length contraction versus twist angle Θ, and this is important for twisted string actuators in robotics as well as for button-on-a-string toys and hand-powered centrifuges. Idealized behavior for length contraction is predicted to be L² = L₀² – (rΘ)² where L₀ is the initial string length and r is its radius. Here we compare this model with data for single, double and triple stranded strings of parachute cords, rattail cord, nylon, kevlar, monofilament fishing line, and metal wire. We also examine deviation from ideality at small and large twist angles in order to probe the internal structure of our strings. At small angles, we see a systematic decrease in the effective cord radius compared to expectation, as individual strands compress into each other, while at large twist angles we see less contraction than expectation due to the coiling of the strands. In all cases, nonideal effects may be quantified by an effective string radius indicative of internal geometry and string-string interaction, which could play a role in the mechanics of real knots and fabrics.   

Contact geometry of equidistant tubes

We consider equilibrium configurations of two flexible tubes arranged in space such that their centrelines are separated by a constant distance. Depending on their configuration, the two centrelines may exhibit single or double contact. We will discuss the contact geometry of one such configuration that exhibits double contact, called the orthogonal clasp, where the two centrelines are assumed to lie in orthogonal planes. Based on this example, we will motivate a “capstan” like equation governing tension decay along the centreline of a flexible tube wrapped around a rigid hook with friction.   

Fibered by fibers: the geometry and elasticity of frustrated filaments

Filamentous and columnar assemblies are a ubiquitous motif in materials, from microscopic and biological materials, like discotic liquid crystals and biopolymer bundles, to familiar macroscopic materials like yarns, cables, and ropes. Ordered ground states in filament bundles, however, are highly geometrically constrained. We show that only two families of filament textures permit equidistance between the constituent filaments: the developable domains, which can bend, but not twist, and the helical domains, which can twist uniformly, but not bend. The elastic response of non-equidistant filament bundles is then frustrated, and cannot adequately be described by a linearized energy. To describe nonequidistant configurations, we derive a geometrically nonlinear, coordinate invariant, gauge-like theory for the elasticity of filamentous materials. Within this framework, we discuss the impact of filament texture on bundle elasticity, and calculate the stable states for non-equidistant bundles with small curvature.   

Disease outbreak as stochastic resonance: interplay between host-seeking behavior and heterogeneous human/vector interactions results in system amplification

We perform phase space analysis on a mathematical model of mosquito-borne disease that incorporates the full mosquito life cycle. We also include the cessation of host-seeking after obtaining a blood meal, and heterogeneous interactions between the human and mosquito populations. We find that under these conditions, stochastic resonance results in the emergence of a dynamic phase of episodic outbreak, where the proportion of the human and mosquito populations susceptible to disease exposure varies wildly from year to year. The results of this work suggest that interventions to screen vector and human populations from disease leads to intermittent exposure to infection, which may lead to these populations becoming more sensitive to outbreaks.   

Impact of initial seeds in cooperative contagion processes

Many types of contagion phenomena are often strongly influenced by cooperative effects among multiple pathogens. When a node has been infected with one of the diseases, the probability of the second disease’s transmission grows, compared to single pathogen spreading. It remains unclear how to predict epidemic outbreaks from the location of the initial seeds. In this work, we modulate the probability of infection depending on the state of nodes taking into account the cooperativity between different pathogens. Defining the transmission probabilities of the first and of the second infecting disease, we derive message-passing equations for cooperative contagion processes. By using the message-passing equations, we assess the impact of seeds in cooperative coinfections and also provide explanation how cooperative epidemic occurs.   

Degree-preserving Network Growth

Real-world networks evolve over time via the addition or removal of vertices and edges. In current network evolution models, vertex degree varies or can even grow arbitrarily, yet there are many networks in which it saturates (e.g., social networks) or is fixed (e.g., chemical complexes), thus requiring an entirely different description. We introduce a novel class of models that encapsulates degree preserving dynamics in the simplest form, resulting in structures significantly different from previous ones. We discuss their properties as function of the evolution of the network's matching number and present several generative models based on this framework, from growing uniform degree distribution graphs to growing random regular graphs, which, to our best knowledge, is the first model of this kind. Within this approach, we also introduce configuration-like models that realize given degree sequences, with tunable degree-mixing properties. Moreover, this process can generate scale-free networks with arbitrary exponents, but without involving any degree-based preferential attachment.   

Synchronization of Coupled Kuramoto Oscillators under Resource Constraints

A fundamental understanding of synchronized behavior in multi-agent systems can be acquired by studying analytically tractable Kuramoto models. Yet, such models typically diverge from many real systems whose dynamics evolve under marked resource constraints. Here we construct a system of coupled Kuramoto oscillators that consume or produce resources as a function of their oscillation frequency. At high coupling, we observe strongly synchronized dynamics, whereas at low coupling, we observe independent oscillator dynamics, as expected. For intermediate coupling which typically induces a partially synchronized state, we demonstrate that the system can exist in either an oscillatory synchronization state or a bistable synchronization state depending on whether the oscillators consume or produce resources, respectively. Relevant for systems as varied as coupled neurons and social groups, our study lays important groundwork for future efforts developing quantitative predictions of synchronized dynamics for systems embedded in environments marked by resource constraints.   

Model reduction of large networked systems using the Manifold Boundary Approximation Method

Complex systems are often described by a network.
Models of these systems are often constructed from physical first principles by accounting for the interaction network among the components.
For large systems, model complexity grows faster than the richness of the available data, leading to many more tunable parameters than can be reliably estimated from measurements.
The resulting models are often sloppy and amenable to effective descriptions in which mechanistic details are intentionally ignored in favor of the relevant collective degrees of freedom governing system behavior.
We consider the case of a small network model from electric power systems and show that sloppiness is manifest in both dynamic and network parameters.
Using techniques of information geometry, we derive reduced models of the network that act as effective theories in cases where only partial system measurements are available using the Manifold Boundary Approximation Method (MBAM).
Leveraging insights from this model, we apply a linearized version of MBAM to a much larger system.
We demonstrate that this method can identify the effective network of interactions, and discuss implications for modeling of other networked systems.   

Path-dependent Dynamics Induced by Rewiring Networks of Kuramoto Oscillators with Inertia

In networks of coupled oscillators, it is of wide interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static networks. However, new questions arise when network structure is time-varying or when the oscillator system is multistable, which can occur by adding an inertial term to the Kuramoto model. While the consequences of evolving topology and multistability have been examined separately, real-world systems such as the brain may exhibit these properties simultaneously. This motivates investigation into how rewiring of network connectivity affects synchronization in systems with multistability, where different paths of network evolution may differentially impact collective behavior. To this end, we study the effects of evolving network topology on coupled Kuramoto oscillators with inertia. We find that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony, and that these changes are robust to a wide range of network perturbations. Our findings suggest that the specific progression of network topology can play a considerable role in modulating the collective behavior of systems evolving on complex networks.   

Distribution of the Sizes of theBblackouts in Power Grids, Synthetic Models, and the Motter and Lai Model under different Dynamical Rules and Criteria of Overload

Studies of the sizes of the blackouts in real grids and computer simulation models of them using the direct current approximation suggest that the resulting blackout sizes are distributed as a power law when using the standard criterion of resilience, the so-called N-1 condition: The grid must safely operate in the event of a failure of any single line. At any stage of the cascade, one of the lines whose load exceeds the maximum values imposed by the N-1 condition fails and immediately all the currents in the grids are redistributed adjusting to the new topology. On the contrary, when the grid is modeled with a uniform tolerance proportional to its initial current for all the nodes and one removes all the overloaded lines simultaneously at each stage of the cascade, the distribution of the sizes of the blackouts is bimodal as in a first the order phase transition, resulting in either a very small blackout or a very large blackout. Here we reconcile both approaches by looking at how the blackout distribution changes with model parameters and different dynamic rules of failure of the overloaded lines. We also study the Motter and Lai model of betweenness overload and find similar results, suggesting that the physical laws of flow are not the determinant factor in the problem.   

Generating individual aging trajectories with a network model

Aging is characterized by the stochastic accumulation of damage. We model this process with a set of health attributes as nodes that interact in a network leading to mortality. Health decline and mortality occur stochastically with a set of complex rates that are trained along with the interaction network using data from observational aging studies. Our model generates synthetic-individuals with health trajectories and lifespan resembling real individuals. The trajectories and lifespans generated with this method also let us model both health events and health interventions so as to better understand their effects on the future health and lifespan of individuals.   

Modeling the Dynamics of Belief in Climate Change with Statistical Physics

We simulate the dynamics of belief in climate change using agents on a social network who update their beliefs according to a classical XY Model Hamiltonian. The initial conditions of the model are set by contemporary empirical insights in the social distribution of climate beliefs (Hornsey et al. 2016). The social network dynamics are inspired by dispersion rules proposed by Galesic and Stein (2019) but extend with additional social and environmental rules. Environmental effects include extreme weather events and disasters. The frequency, spatial-distribution, and intensity of extreme weather events are calibrated with real world data on climate impacts (Siscoet al. 2017). The model enables us to analyse the interactions between social belief dynamics in networks and climate impacts and suggest when and if a consensus about climate change will form in the wake of extreme climate-related weather events.