A hyperbolic model for the effects of urbanization on air pollution

Barbera, Elvira; Currò, Carmela; Valenti, Giovanna

doi:10.1016/j.apm.2009.10.030

Cited by 60 publications

(28 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Away from the fold curve, the normally hyperbolic manifolds S a and S r deform smoothly to locally invariant manifolds S a,ε and S r,ε , respectively, and the slow flow on these manifolds is a smooth, O(ε) perturbation of the flow on S. Hence, the singular Type I waves Γ established in Lemma 2.5 will perturb to nearby Type I waves Γ ε of the full system (1.6), connecting (1,0) to (u ∞ , 0). Note that since u ∞ is a free parameter, we in fact have a family of possible end states.…”

Section: Uniqueness Of Heteroclinic Orbitsmentioning

confidence: 99%

“…In general, solution trajectories cannot cross this wall of singularities except at the point P (u, w) = Q(u, w) = 0, called the hole in the wall, where the indeterminate form means that the system is no longer singular. Since the discovery of these walls of singularities, they have been studied in a variety of biological (and other) applications [1,18,19,20,22,23,24,25,29]. These studies (beginning with [24]) have led to the discovery of the possibility of both smooth and shock-fronted traveling wave solutions, arising as a result of the singular behavior in the phase plane.…”

Section: Shock-fronted Traveling Wavesmentioning

confidence: 99%

See 1 more Smart Citation

Existence of Traveling Wave Solutions for a Model of Tumor Invasion

Harley¹,

Heijster²,

Marangell³

et al. 2014

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

Abstract. The existence of traveling wave solutions to a haptotaxis dominated model is analyzed. A version of this model has been derived in Perumpanani et al. [Phys. D, 126 (1999), pp. 145-159] to describe tumor invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analyzed using geometric singular perturbation theory. We prove the existence of three types of physically realistic traveling wave solutions in the case of small diffusion. These solutions reduce to the no-diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth traveling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the traveling wave solutions, is also discussed.

show abstract

Section: Uniqueness Of Heteroclinic Orbitsmentioning

confidence: 99%

Section: Shock-fronted Traveling Wavesmentioning

confidence: 99%

Existence of Traveling Wave Solutions for a Model of Tumor Invasion

Harley¹,

Heijster²,

Marangell³

et al. 2014

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

show abstract

“…In comparison with economic and societal research, the ecological and environmental issues in urbanization research have a high priority throughout Wang et al [8]'s paper. About one fifth of papers were in this category and looked at such aspects as the effects of air pollution and the urban thermal environment [31][32][33], the water environment [34][35][36] and the soil environment [37,38]. From this review, it could be seen that urbanization research has a wide range of concerns, and is a complicated system made up of many intertwined and interrelated subsystems, such as, housing and infrastructure, social life, regional economies, the ecological environment, and related policies and regulations, which are organized and managed by a meta-synthesis system.…”

Section: Literature Reviewmentioning

confidence: 99%

An Integrated Approach to Modelling the Economy-Society-Ecology System in Urbanization Process

Liu

Luo

2014

Sustainability

View full text Add to dashboard Cite

Urbanization has become a key part of social and economic progress in the 21st Century, but achieving healthy and safe urban development has a long way to go for many developed and developing countries. Urbanization has been recognized as a complex ecosystem which is affected by economic, social, and ecological factors. With this in mind, this paper looks at many factors to first evaluate based on the matter-element (ME) method and then model an Economy-Society-Ecology (ESE) subsystem using a hybrid method by a fuzzy analytical hierarchy process (FAHP), and then by using the entropy method (EM) to determine the relevant index weights. To avoid subjectivity when defining the model's boundaries, the technique for order preference by similarity to an ideal solution (TOPSIS) is introduced. Then, a coupling coordination degree model focusing on the degree of coordination in the ESE subsystem is established. Panel data collected from 2003 to 2012 for Chengdu, China, is then simulated to analyze the development process. The results show that: (1) The quality of urbanization continues to improve and the phasic features are presented; (2) The sensitivity analysis of subsystem weight shown that it had less effect on the coupling coordinated system; (3) The coordination in the ESE subsystem has also improved. However, the development rate of the economic subsystem is greater than that of the societal and ecological subsystem. The approach used here therefore, is shown to provide a promising basis for policy-making to support healthy urban development.

show abstract

“…The research covers a number of disciplines, including ecology, geography, management, economics and environmental studies (Kennedy et al, 2011;Satterthwaite, 2008;Salim and Shafiei, 2014;Scholz and Binder, 2011). Case studies have been conducted on a variety of countries and regions, including Europe, the US, Russia and China (Barbera et al, 2010;Alnawaiseh et al, 2015;Zanella et al, 2014;Bao and Fang, 2007), with a tendency to look at watersheds, ecologically vulnerable areas, urbanized areas and metropolitan areas (Fang, 2015a;Zawar-Reza et al, 2010;Meerow and Newell, 2015). Studies have taken as their scope the world, countries, provinces, cities and parts of cities, with the main focus being cities (Luo et al, 2009;Yang et al, 2015;Anderson and O'farrell, 2012;Brown, 2012).…”

Section: The Interactive Coupling Effect Between Urbanization and Thementioning

confidence: 99%

International progress and evaluation on interactive coupling effects between urbanization and the eco-environment

2016

View full text Add to dashboard Cite

Global urbanization is exerting severe stress and having far-reaching impacts on the eco-environment, and yet there exists a complex non-linear coupling relationship between the two. Research on the interactive coupling effect between urbanization and the eco-environment will be a popular area of study and frontier in international earth system science and sustainability science in the next 10 years, while also being a high-priority research topic of particular interest to international organizations. This paper systematically collates and summarizes the international progress made in research on interactive coupling theory, coupling relationships, coupling mechanisms, coupling laws, coupling thresholds, coupling models and coupling optimization decision support systems. The research shows that urbanization and eco-environment interactive coupling theories include the Kuznets curve theory, telecoupling theory, planetary boundaries theory, footprint family theory and urban metabolism theory; most research on interactive coupling relationships is concerned with single-element coupling relationships, such as those between urbanization and water, land, atmosphere, climate change, ecosystems and biodiversity; the majority of research on interactive coupling mechanisms and laws focuses on five research paradigms, including coupled human and nature systems, complex social-ecological systems, urban ecosystems, social-economic-natural complex ecosystems, and urbanization development and eco-environment constraint ring; the majority of interactive coupling simulations use STIRPAT models, coupling degree models, multi-agent system models and big data urban computer models; and research has been carried out on urbanization and eco-environment coupling thresholds, coercing risk and optimal decision support systems. An objective evaluation of progress in international research on interactive coupling between urbanization and the eco-environment suggests that there are six main research focal points and six areas lacking research: a lot of research exists on macroscopic coupling effects, with little research on urban agglomeration and scale coupling effects; considerable research exists on sin-

show abstract

A hyperbolic model for the effects of urbanization on air pollution

Cited by 60 publications

References 20 publications

Existence of Traveling Wave Solutions for a Model of Tumor Invasion

Existence of Traveling Wave Solutions for a Model of Tumor Invasion

An Integrated Approach to Modelling the Economy-Society-Ecology System in Urbanization Process

International progress and evaluation on interactive coupling effects between urbanization and the eco-environment

Contact Info

Product

Resources

About