Wave propagation in fractal trees. Mathematical and numerical issues

Joly, Patrick; Kachanovska, Maryna; Semin, Adrien

doi:10.3934/nhm.2019010

Cited by 13 publications

(12 citation statements)

References 27 publications

(56 reference statements)

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“…The assumption (3.39) of Proposition 3.18 says that M n is independent of j. Consider the case of a self-similar p-adic tree[16,17], namely assume that there exist p direct similitudes σ 0 , σ 1 , . .…”

mentioning

confidence: 99%

Density and trace results in generalized fractal networks

Nicaise

Semin

2018

ESAIM: M2AN

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mentioning

confidence: 99%

Density and trace results in generalized fractal networks

Nicaise

Semin

2018

ESAIM: M2AN

Self Cite

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“…Models of flows in networks can contain numerous differential equations. As a consequence, one often has to solve these equations numerically [ 265 , 266 , 267 , 268 , 269 , 270 , 271 , 272 , 273 , 274 , 275 , 276 ]. There are cases in which the corresponding model equations are not large in number, or we are interested in the situation in just one or several nodes of the network.…”

Section: Models Of Network Flows Containing Differential Equationsmentioning

confidence: 99%

Flows of Substances in Networks and Network Channels: Selected Results and Applications

Dimitrova

2022

Entropy

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This review paper is devoted to a brief overview of results and models concerning flows in networks and channels of networks. First of all, we conduct a survey of the literature in several areas of research connected to these flows. Then, we mention certain basic mathematical models of flows in networks that are based on differential equations. We give special attention to several models for flows of substances in channels of networks. For stationary cases of these flows, we present probability distributions connected to the substance in the nodes of the channel for two basic models: the model of a channel with many arms modeled by differential equations and the model of a simple channel with flows of substances modeled by difference equations. The probability distributions obtained contain as specific cases any probability distribution of a discrete random variable that takes values of 0,1,…. We also mention applications of the considered models, such as applications for modeling migration flows. Special attention is given to the connection of the theory of stationary flows in channels of networks and the theory of the growth of random networks.

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“…One can readily formulate wave equations on large metric graphs by specifying relevant boundary conditions and rules at each junction. For example, Joly et al [82] recently examined wave propagation of the standard linear wave equation on fractal trees. Because many natural real-life settings are spatially embedded (e.g., wave propagation in granular materials [101,129] and traffic-flow patterns in cities), it will be particularly valuable to examine wave dynamics on (both synthetic and empirical) spatially-embedded networks [9].…”

Section: Metric Graphs and Waves On Networkmentioning

confidence: 99%

Nonlinearity + Networks: A 2020 Vision

Porter¹

2019

Preprint

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I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics include temporal networks (in which the entities and/or their interactions change in time), stochastic and deterministic dynamical processes on networks, adaptive networks (in which a dynamical process on a network is coupled to dynamics of network structure), and network structure and dynamics that include "higher-order" interactions (which involve three or more entities in a network). I draw examples from a variety of scenarios, including contagion dynamics, opinion models, waves, and coupled oscillators.

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Wave propagation in fractal trees. Mathematical and numerical issues

Cited by 13 publications

References 27 publications

Density and trace results in generalized fractal networks

Density and trace results in generalized fractal networks

Flows of Substances in Networks and Network Channels: Selected Results and Applications

Nonlinearity + Networks: A 2020 Vision

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