Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks

Ronellenfitsch, Henrik; Katifori, Eleni

doi:10.1103/physrevlett.117.138301

Cited by 121 publications

(144 citation statements)

References 41 publications

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“…We consider linear supply network models, where the flow between two adjacent nodes is proportional to the difference of the nodal potential, pressure or voltage phase angle. Linear models are applied to hydraulic networks [31], vascular networks of plants and animals [28,[32][33][34][35], economic inputoutput networks [36] as well as electric power grids [37][38][39][40][41][42]. The linearity allows to obtain several rigorous bounds for flow rerouting in general network topologies and to solve special cases fully analytically.…”

Section: Introductionmentioning

confidence: 99%

Non-local impact of link failures in linear flow networks

et al. 2019

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The failure of a single link can degrade the operation of a supply network up to the point of complete collapse. Yet, the interplay between network topology and locality of the response to such damage is poorly understood. Here, we study how topology affects the redistribution of flow after the failure of a single link in linear flow networks with a special focus on power grids. In particular, we analyze the decay of flow changes with distance after a link failure and map it to the field of an electrical dipole for lattice-like networks. The corresponding inverse-square law is shown to hold for all regular tilings. For sparse networks, a long-range response is found instead. In the case of more realistic topologies, we introduce a rerouting distance, which captures the decay of flow changes better than the traditional geodesic distance. Finally, we are able to derive rigorous bounds on the strength of the decay for arbitrary topologies that we verify through extensive numerical simulations. Our results show that it is possible to forecast flow rerouting after link failures to a large extent based on purely topological measures and that these effects generally decay with distance from the failing link. They might be used to predict links prone to failure in supply networks such as power grids and thus help to construct grids providing a more robust and reliable power supply.

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Section: Introductionmentioning

confidence: 99%

Non-local impact of link failures in linear flow networks

et al. 2019

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“…Blood circulation, secondary branching, remodeling and pruning of capillaries [22,23] are not considered in this mesoscopic model, nor are microscopic features such as cell size, shape and cellular mechanics [4,18]. The purpose of this paper is to show that the reduction of complex stochastic angiogenesis dynamics to the simpler soliton description of the angiogenic network allows incorporation of other transport mechanisms in addition to chemotaxis.…”

Section: Discussionmentioning

confidence: 99%

“…It is known that capillaries with insufficient blood circulation may atrophy and disappear. Pruning such blood vessels is an important mechanism to achieve a hierarchical vascular network with optimized transport, as recent global optimization and adaptation algorithms have shown for a number of biological vascular systems [23,24].…”

Section: Introductionmentioning

confidence: 99%

Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis

Bonilla

Carretero

Terragni

2017

Entropy

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Abstract:In this work, we present a numerical study of the influence of matrix degrading enzyme (MDE) dynamics and haptotaxis on the development of vessel networks in tumor-induced angiogenesis. Avascular tumors produce growth factors that induce nearby blood vessels to emit sprouts formed by endothelial cells. These capillary sprouts advance toward the tumor by chemotaxis (gradients of growth factor) and haptotaxis (adhesion to the tissue matrix outside blood vessels). The motion of the capillaries in this constrained space is modelled by stochastic processes (Langevin equations, branching and merging of sprouts) coupled to continuum equations for concentrations of involved substances. There is a complementary deterministic description in terms of the density of actively moving tips of vessel sprouts. The latter forms a stable soliton-like wave whose motion is influenced by the different taxis mechanisms. We show the delaying effect of haptotaxis on the advance of the angiogenic vessel network by direct numerical simulations of the stochastic process and by a study of the soliton motion.

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“…Found everywhere in nature, the intricate structures generated by fractal growth usually emerge from non-trivial self-organizing and self-assembling pattern formation 1–4 . One striking feature of these systems is the morphological transition they undergo as a result of the interplay between entropic and energetic processes in their growth dynamics, that ultimately manifest themselves in the geometry of their structure 5 .…”

Section: Introductionmentioning

confidence: 99%

Universal fractality of morphological transitions in stochastic growth processes

Nicolás-Carlock

Carrillo-Estrada

Dossetti

2017

Sci Rep

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Stochastic growth processes give rise to diverse and intricate structures everywhere in nature, often referred to as fractals. In general, these complex structures reflect the non-trivial competition among the interactions that generate them. In particular, the paradigmatic Laplacian-growth model exhibits a characteristic fractal to non-fractal morphological transition as the non-linear effects of its growth dynamics increase. So far, a complete scaling theory for this type of transitions, as well as a general analytical description for their fractal dimensions have been lacking. In this work, we show that despite the enormous variety of shapes, these morphological transitions have clear universal scaling characteristics. Using a statistical approach to fundamental particle-cluster aggregation, we introduce two non-trivial fractal to non-fractal transitions that capture all the main features of fractal growth. By analyzing the respective clusters, in addition to constructing a dynamical model for their fractal dimension, we show that they are well described by a general dimensionality function regardless of their space symmetry-breaking mechanism, including the Laplacian case itself. Moreover, under the appropriate variable transformation this description is universal, i.e., independent of the transition dynamics, the initial cluster configuration, and the embedding Euclidean space.

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Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks

Cited by 121 publications

References 41 publications

Non-local impact of link failures in linear flow networks

Non-local impact of link failures in linear flow networks

Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis

Universal fractality of morphological transitions in stochastic growth processes

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