Wavefronts in Traffic Flows and Crowds Dynamics

Corli, Andrea; Malaguti, Luisa

doi:10.1007/978-3-030-61346-4_8

Cited by 5 publications

(4 citation statements)

References 83 publications

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“…where μ j are the corresponding eigenvalues of L. Therefore, what the authors of [92] have proposed can be though as an index related to the solution of the backward diffusion equation, i.e., negative time, or as a diffusion equation with negative diffusivity D < 0 [65]. There are physical situations in which such negative diffusivity appears [48,140,173,225,226]. For instance, in the simultaneous diffusion of boron and point defect in silicon, the diffusivities of interstitial could be negative [225].…”

Section: Laplacian Estrada Index and Backward Diffusionmentioning

confidence: 99%

The many facets of the Estrada indices of graphs and networks

Estrada

2021

SeMA

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The Estrada index of a graph/network is defined as the trace of the adjacency matrix exponential. It has been extended to other graph-theoretic matrices, such as the Laplacian, distance, Seidel adjacency, Harary, etc. Here, we describe many of these extensions, including new ones, such as Gaussian, Mittag–Leffler and Onsager ones. More importantly, we contextualize all of these indices in physico-mathematical frameworks which allow their interpretations and facilitate their extensions and further studies. We also describe several of the bounds and estimations of these indices reported in the literature and analyze many of them computationally for small graphs as well as large complex networks. This article is intended to formalize many of the Estrada indices proposed and studied in the mathematical literature serving as a guide for their further studies.

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Section: Laplacian Estrada Index and Backward Diffusionmentioning

confidence: 99%

The many facets of the Estrada indices of graphs and networks

Estrada

2021

SeMA

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“…In the ITS, it is necessary to characterise the traffic profile to optimise the road. Consequently, knowing the traffic profile is essential as predictive systems require training and updating based on accurate data [7]. A system that uses the size and speed of vehicles can predict traffic jams, crowds, and infractions, or even adapt lighting to the traffic on the road.…”

Section: Introductionmentioning

confidence: 99%

Low-cost modular devices for on-road vehicle detection and characterisation

Poza-Lujan

Uribe-Chavert

Posadas-Yagüe

2023

Des Autom Embed Syst

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Detecting and characterising vehicles is one of the purposes of embedded systems used in intelligent environments. An analysis of a vehicle’s characteristics can reveal inappropriate or dangerous behaviour. This detection makes it possible to sanction or notify emergency services to take early and practical actions. Vehicle detection and characterisation systems employ complex sensors such as video cameras, especially in urban environments. These sensors provide high precision and performance, although the price and computational requirements are proportional to their accuracy. These sensors offer high accuracy, but the price and computational requirements are directly proportional to their performance. This article introduces a system based on modular devices that is economical and has a low computational cost. These devices use ultrasonic sensors to detect the speed and length of vehicles. The measurement accuracy is improved through the collaboration of the device modules. The experiments were performed using multiple modules oriented to different angles. This module is coupled with another specifically designed to detect distance using previous modules’ speed and length data. The collaboration between different modules reduces the speed relative error ranges from 1 to 5%, depending on the angle configuration used in the modules.

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“…This study clarifies that a discontinuity can develop without dissipation even under the smoothness of all input in the kinematic wave model. Such a phenomenon is intrinsic to first-order quasilinear partial differential equations (FOQLPDEs), including the kinematic wave model, the Kynch's sedimentation model (Bürger and Wendland, 2001), the compressible Euler equations (Chen et al, 2017), and traffic flow models (Corli and Malaguti, 2021). Conversely, treatment of the kinematic wave model not as a FOQLPDE but a Hamilton-Jacobi type leads to inconsistency as in Mean et al (2020).…”

Section: Introductionmentioning

confidence: 99%

Numerical Examples of Non-Dissipative Discontinuous Kinematic Waves in Open Channels

Mean

Unami

Fujihara

2022

Journal of Rainwater Catchment Systems

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The kinematic wave model under the assumption of balanced gravity and friction forces has been applied in open channel hydraulics and surface hydrology. There persists a severe misunderstanding that a discontinuity of a kinematic wave occurs due to a discontinuity of input and then dissipates. This study clarifies that a discontinuity can develop without dissipation under the smoothness of all input. The theory of first-order quasilinear partial differential equations shows that Cauchy problems for the kinematic wave model have unique measurable and bounded solutions, which are possibly discontinuous. Numerical examples are presented to visualize the fundamental properties of discontinuous kinematic waves.

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Wavefronts in Traffic Flows and Crowds Dynamics

Cited by 5 publications

References 83 publications

The many facets of the Estrada indices of graphs and networks

The many facets of the Estrada indices of graphs and networks

Low-cost modular devices for on-road vehicle detection and characterisation

Numerical Examples of Non-Dissipative Discontinuous Kinematic Waves in Open Channels

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