An official website of the United States government
This paper provides a framework to evaluate the performance of single and double integrator networks over arbitrary directed graphs. Adopting vehicular network terminology, we consider quadratic performance metrics defined by the L2-norm of position and velocity based response functions given impulsive inputs to each vehicle. We exploit the spectral properties of weighted graph Laplacians and output performance matrices to derive a novel method of computing the closed-form solutions for this general class of performance metrics, which include H2-norm based quantities as special cases. We then explore the effect of the interplay between network properties (such as edge directionality and connectivity) and the control strategy on the overall network performance. More precisely, for systems whose interconnection is described by graphs with normal Laplacian L, we characterize the role of directionality by comparing their performance with that of their undirected counterparts, represented by the Hermitian part of L. We show that, for single-integrator networks, directed and undirected graphs perform identically. However, for double-integrator networks, graph directionality -expressed by the eigenvalues of L with nonzero imaginary part- can significantly degrade performance. Interestingly, in many cases, well-designed feedback can also exploit directionality to mitigate degradation or even improve the performance to exceed that of the undirected case. Finally we focus on a system coherence metric -aggregate deviation from the state average- to investigate the relationship between performance and degree of connectivity, leading to somewhat surprising findings. For example, increasing the number of neighbors on a ω-nearest neighbor directed graph does not necessarily improve performance. Similarly, we demonstrate equivalence in performance between all-to-one and all-to-all communication graphs.
more »
« less
Unique superdiffusion induced by directionality in multiplex networks
Abstract The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer networks while most complex systems in nature exhibit directed interactions. Here, we propose a framework to analyze diffusive dynamics on multilayer networks consisting of at least one directed layer. We rigorously demonstrate that directionality in multilayer networks can fundamentally change the behavior of diffusive dynamics: from monotonic (in undirected systems) to non-monotonic diffusion with respect to the interlayer coupling strength. Moreover, for certain multilayer network configurations, the directionality can induce a unique superdiffusion regime for intermediate values of the interlayer coupling, wherein the diffusion is even faster than that corresponding to the theoretical limit for undirected systems, i.e. the diffusion in the integrated network obtained from the aggregation of each layer. We theoretically and numerically show that the existence of superdiffusion is fully determined by the directionality of each layer and the topological overlap between layers. We further provide a formulation of multilayer networks displaying superdiffusion. Our results highlight the significance of incorporating the interacting directionality in multilevel networked systems and provide a framework to analyze dynamical processes on interconnected complex systems with directionality.
more »
« less
- Award ID(s):
- 1811909
- PAR ID:
- 10362333
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- New Journal of Physics
- Volume:
- 23
- Issue:
- 1
- ISSN:
- 1367-2630
- Page Range / eLocation ID:
- Article No. 013016
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The cytoskeleton–a composite network of biopolymers, molecular motors, and associated binding proteins–is a paradigmatic example of active matter. Particle transport through the cytoskeleton can range from anomalous and heterogeneous subdiffusion to superdiffusion and advection. Yet, recapitulating and understanding these properties–ubiquitous to the cytoskeleton and other out-of-equilibrium soft matter systems–remains challenging. Here, we combine light sheet microscopy with differential dynamic microscopy and single-particle tracking to elucidate anomalous and advective transport in actomyosin-microtubule composites. We show that particles exhibit multi-mode transport that transitions from pronounced subdiffusion to superdiffusion at tunable crossover timescales. Surprisingly, while higher actomyosin content increases the range of timescales over which transport is superdiffusive, it also markedly increases the degree of subdiffusion at short timescales and generally slows transport. Corresponding displacement distributions display unique combinations of non-Gaussianity, asymmetry, and non-zero modes, indicative of directed advection coupled with caged diffusion and hopping. At larger spatiotemporal scales, particles in active composites exhibit superdiffusive dynamics with scaling exponents that are robust to changing actomyosin fractions, in contrast to normal, yet faster, diffusion in networks without actomyosin. Our specific results shed important new light on the interplay between non-equilibrium processes, crowding and heterogeneity in active cytoskeletal systems. More generally, our approach is broadly applicable to active matter systems to elucidate transport and dynamics across scales.more » « less
-
The significance of critical infrastructure systems in maintaining productivity is undeniable. However, such systems remain susceptible to external disturbances and cascading failures. Instead of operating independently, these physical systems, such as transportation and stormwater systems, form an interdependent system. This interdependence, particularly important during flooding, illustrates that the failure of a stormwater system can disrupt traffic networks. To explore the extent of such interdependency, this study investigates the transportation and stormwater networks in Norman, Oklahoma. Using network science theories and concepts of multilayered networks, this paper analyzes these systems, both individually and in combination. The study identifies closely located components in the road and stormwater networks using Moran's I spatial autocorrelation metric. Next, the connectivity of these networks is represented in a graph format to investigate the topological credentials (i.e., rank of relative importance) of the network components (i.e., water inlets, road intersections as nodes, and stormwater conduits, road segments as links). Moreover, such credentials further change by considering the weights of the network components (i.e., average daily traffic, water flow). The proximity-based connectivity considerations between these networks utilizing Moran's I significance score revealed a good indicator of spatial interdependency. When incorporating directionality, the multilayer network analysis highlights that highly central components tend to cluster spatially, unlike the undirected counterpart. The study also identifies vulnerable locations and network components in a combined network setting that differ from the networks in isolation. In doing so, the research reveals new insights governing the complex reliance of transportation systems on neighboring stormwater systems.more » « less
-
Abstract This paper explores the Glauber dynamics of spin systems with asymmetric coupling, a scenario that inherently violates detailed balance, leading to non-equilibrium steady states. By focusing on weighted and heterogeneous networks, we extend the applicability of Glauber models to capture complex real-world interactions, such as those seen in multilayer and hierarchical systems. Under specific assumptions on the coupling matrix, we demonstrate the tractability of these dynamics in the limit as the number of spins approaches infinity. Our results highlight the influence of network topology on dynamic behavior and provide a framework for analyzing stochastic processes in diverse applications, from statistical mechanics to data-driven modeling in applied sciences. The approach also uncovers potential for leveraging non-equilibrium dynamics in machine learning and network analysis.more » « less
-
Abstract Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices.more » « less
