Developing an Aw–Rascle model of traffic flow

Jiang, Weifeng; Wang, Zhen

doi:10.1007/s10665-015-9801-2

Cited by 17 publications

(9 citation statements)

References 20 publications

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“…Previous researchers observed that co-digested KW with other substrates, such as cow manure, sewage sludge results in a higher degradation rate compared to KW alone [12][13][14]. Spices contained in KW may inhibit the degradation process of KW as suggested by previous researchers [15,16].…”

Section: Methane Concentrationmentioning

confidence: 93%

Biogas production from household solid waste-an alternative solid waste treatment for a communal scale

2019

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Current practice in Indonesia shows that Household Solid Waste (HSW) is handled by transferring to landfill site. Meanwhile, around 68% of HSW is composed of biodegradable components, which has potential for biogas production. The current study compares some commercial activators including Green Phosko (GP7) and Effective microorganisms 4 (EM4) with homemade activator in 200 L anaerobic digester equipped with manual mixing for processing kitchen waste (KW). pH and ratio of solid waste to water were set at 8 and 1:2, respectively. Batch experiments show that digester #3 with homemade activator shows superior performance compared to commercial activators. Meanwhile, the digesters with commercial activators show better performance compared to digester control (without activator). Digester #3 produces 1.35 L CH4/kg total solid (TS) and 1.14 L CH4/kg volatile solid (VS). Current work suggests that the homemade activator has the most suitable methanogen bacterium compared to the commercial activators.

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Section: Methane Concentrationmentioning

confidence: 93%

Biogas production from household solid waste-an alternative solid waste treatment for a communal scale

2019

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“…p α = κ α ρ γ denote some kind of pressure, α = L, R, and H(x) is the Heaviside function and κ α denotes the road condition. If κ L = κ R , then system (1.1)-(1.2) becomes the classical Aw-Rascle traffic model, which was introduced by Aw and Rascle [7] and has been widely studied by many authors, see [1,25,34] among others. System (1.1)-(1.2) with κ L = κ R is a model of coupling.…”

Section: )mentioning

confidence: 99%

The resonance behavior for the coupling of two Aw–Rascle traffic models

Wang

2020

Adv Differ Equ

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By studying the Riemann problem for the Aw-Rascle traffic model with different pressure laws, which is the coupling of two one-dimensional hyperbolic systems, we investigate the resonance phenomena. The main difficulty arises from the possible resonance behavior which may result in multiple solutions. We discover a new and interesting phenomenon showing that there exist infinitely many solutions for some certain initial data, which is quite different compared to earlier studies for the isentropic model of a fluid flow in a nozzle with variable cross-section and the shallow water equations with discontinuous topography. In order to overcome this difficulty, we impose the so-called TV-condition to obtain the uniqueness of solution to the Riemann problem. MSC: 35L65; 35J70; 35R35

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“…Introduction. In this paper, we focus on the improved Aw-Rascle-Zhang (IARZ) model [16], ρ t + (ρu) x = 0, (ρ(F (u) + p(ρ))) t + (ρu(F (u) + p(ρ))) x = 0, (1) where 0 < ρ < ρ * and u represent the density, velocity of the traffic flow, respectively. ρ * is the jam density of this traffic flow system.…”

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confidence: 99%

“…According to Lemma 3.1 in [16], if F (u) satisfies the third inequality of (5), there is only one inflection point on the curves of the first family waves in the (ρ, q) plane. Thus the first characteristic family is non-genuinely nonlinear.…”

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confidence: 99%

“…But many traffic engineers and mathematicians, such as Helbing [14], Jin and Zhang [18], discovered non-concave flow-density diagrams in real traffic observation. The IARZ model built by Jiang and Wang [16] was derived from the car-following principle [17] and from the basic principle of traffic flow. The first characteristic field of the IARZ model ( 1) is non-genuinely nonlinear.…”

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confidence: 99%

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The wave interactions of an improved Aw-Rascle-Zhang model with a non-genuinely nonlinear field

Jiang

Chen

et al. 2023

DCDS-B

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<p style='text-indent:20px;'>This work is devoted to the study of the wave interactions of an improved Aw-Rascle-Zhang model with a non-genuinely nonlinear field. The wave interactions between single elementary waves involving the composite wave are analyzed by reviewing the Riemann solutions. Due to the non-genuinely nonlinear field, some new phenomena are found. The rarefaction waves may penetrate the shock waves. As a contact discontinuity interacts with the composite waves, there appear the compression waves which change to a contact discontinuity, then to rarefaction waves. Using the single wave interaction results, we construct the weak solutions of this model with three piecewise constant states. Finally, we give some intuitions to eliminate the "phantom traffic jam".</p>

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Developing an Aw–Rascle model of traffic flow

Cited by 17 publications

References 20 publications

Biogas production from household solid waste-an alternative solid waste treatment for a communal scale

Biogas production from household solid waste-an alternative solid waste treatment for a communal scale

The resonance behavior for the coupling of two Aw–Rascle traffic models

The wave interactions of an improved Aw-Rascle-Zhang model with a non-genuinely nonlinear field

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