
Remote and marginal areas with scarce and vulnerable populations are "comfortable" settings and suitable places for the development of new extractive activities for energy production. Fracking and modern windmills are often controversial activities in marginal areas for native and local populations, with varying political positions from local elites. The new scalar policies associated with the energy project introduce some of the resistance strategies in the form of more than human geographies or hybrid spatial relationships that characterize recent human geography. This paper explores and suggests possible ways of integrating local interests with regional or national policies based on the "health" of marginal populations, marginal rather than human materiality's and marginal more-than-human.
Citation: Angel Paniagua. Use and abuse of the planet in non-rich regions: histories of fracking and windmills in a more than human geographical perspective[J]. AIMS Geosciences, 2022, 8(1): 1-15. doi: 10.3934/geosci.2022001
[1] | Rubayyi T. Alqahtani, Jean C. Ntonga, Eric Ngondiep . Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms. AIMS Mathematics, 2023, 8(4): 9265-9289. doi: 10.3934/math.2023465 |
[2] | Abdulhamed Alsisi . The powerful closed form technique for the modified equal width equation with numerical simulation. AIMS Mathematics, 2025, 10(5): 11071-11085. doi: 10.3934/math.2025502 |
[3] | Kamel Mohamed, H. S. Alayachi, Mahmoud A. E. Abdelrahman . The mR scheme to the shallow water equation with horizontal density gradients in one and two dimensions. AIMS Mathematics, 2023, 8(11): 25754-25771. doi: 10.3934/math.20231314 |
[4] | Mingming Li, Shaoyong Lai . The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi model. AIMS Mathematics, 2024, 9(1): 1772-1782. doi: 10.3934/math.2024086 |
[5] | Mohammad Alqudah, Safyan Mukhtar, Haifa A. Alyousef, Sherif M. E. Ismaeel, S. A. El-Tantawy, Fazal Ghani . Probing the diversity of soliton phenomena within conformable Estevez-Mansfield-Clarkson equation in shallow water. AIMS Mathematics, 2024, 9(8): 21212-21238. doi: 10.3934/math.20241030 |
[6] | Christelle Dleuna Nyoumbi, Antoine Tambue . A fitted finite volume method for stochastic optimal control problems in finance. AIMS Mathematics, 2021, 6(4): 3053-3079. doi: 10.3934/math.2021186 |
[7] | Mostafa M. A. Khater, S. H. Alfalqi, J. F. Alzaidi, Samir A. Salama, Fuzhang Wang . Plenty of wave solutions to the ill-posed Boussinesq dynamic wave equation under shallow water beneath gravity. AIMS Mathematics, 2022, 7(1): 54-81. doi: 10.3934/math.2022004 |
[8] | M. Mossa Al-Sawalha, Rasool Shah, Adnan Khan, Osama Y. Ababneh, Thongchai Botmart . Fractional view analysis of Kersten-Krasil'shchik coupled KdV-mKdV systems with non-singular kernel derivatives. AIMS Mathematics, 2022, 7(10): 18334-18359. doi: 10.3934/math.20221010 |
[9] | Youngjin Hwang, Jyoti, Soobin Kwak, Hyundong Kim, Junseok Kim . An explicit numerical method for the conservative Allen–Cahn equation on a cubic surface. AIMS Mathematics, 2024, 9(12): 34447-34465. doi: 10.3934/math.20241641 |
[10] | Jean-Paul Chehab, Denys Dutykh . On time relaxed schemes and formulations for dispersive wave equations. AIMS Mathematics, 2019, 4(2): 254-278. doi: 10.3934/math.2019.2.254 |
Remote and marginal areas with scarce and vulnerable populations are "comfortable" settings and suitable places for the development of new extractive activities for energy production. Fracking and modern windmills are often controversial activities in marginal areas for native and local populations, with varying political positions from local elites. The new scalar policies associated with the energy project introduce some of the resistance strategies in the form of more than human geographies or hybrid spatial relationships that characterize recent human geography. This paper explores and suggests possible ways of integrating local interests with regional or national policies based on the "health" of marginal populations, marginal rather than human materiality's and marginal more-than-human.
Hydraulic jumps are frequently observed in lab studies, river flows, and coastal environments. The shallow water equations, commonly known as Saint-Venant equations, have important applications in oceanography and hydraulics. These equations are used to represent fluid flow when the depth of the fluid is minor in comparison to the horizontal scale of the flow field fluctuations [1]. They have been used to simulate flow at the atmospheric and ocean scales, and they have been used to forecast tsunamis, storm surges, and flow around constructions, among other things [2,3]. Shallow water is a thin layer of constant density fluid in hydrostatic equilibrium that is bordered on the bottom by a rigid surface and on the top by a free surface [4].
Nonlinear waves have recently acquired importance due to their capacity to highlight several complicated phenomena in nonlinear research with spirited applications [5,6,7,8]. Teshukov in [9] developed the equation system that describes multi-dimensional shear shallow water (SSW) flows. Some novel solitary wave solutions for the ill-posed Boussinesq dynamic wave model under shallow water beneath gravity were constructed [10]. The effects of vertical shear, which are disregarded in the traditional shallow water model, are included in this system to approximate shallow water flows. It is a non-linear hyperbolic partial differential equations (PDE) system with non-conservative products. Shocks, rarefactions, shear, and contact waves are all allowed in this model. The SSW model can capture the oscillatory character of turbulent hydraulic leaps, which corrects the conventional non-linear shallow water equations' inability to represent such occurrences [11]. Analytical and numerical techniques for solving such problems have recently advanced; for details, see [12,13,14,15,16,17] and the references therein.
The SSW model consists of six non-conservative hyperbolic equations, which makes its numerical solution challenging since the concept of a weak solution necessitates selecting a path that is often unknown. The physical regularization mechanism determines the suitable path, and even if one knows the correct path, it is challenging to construct a numerical scheme that converges to the weak solution since the solution is susceptible to numerical viscosity [18].
In the present work, we constructed the generalized Rusanov (G. Rusanov) scheme to solve the SSW model in 1D of space. This technique is divided into steps for predictors and correctors [19,20,21,22,23]. The first one includes a numerical diffusion control parameter. In the second stage, the balance conservation equation is retrieved. Riemann solutions were employed to determine the numerical flow in the majority of the typical schemes. Unlike previous schemes, the interesting feature of the G. Rusanov scheme is that it can evaluate the numerical flow even when the Riemann solution is not present, which is a very fascinating advantage. In actuality, this approach may be applied as a box solver for a variety of non-conservative law models.
The remainder of the article is structured as follows. Section 2 offers the non-conservative shear shallow water model. Section 3 presents the structure of the G. Rusanov scheme to solve the 1D SSW model. Section 4 shows that the G. Rusanov satisfies the C-property. Section 5 provides several test cases to show the validation of the G. Rusanov scheme versus Rusanov, Lax-Friedrichs, and reference solutions. Section 6 summarizes the work and offers some conclusions.
The one-dimensional SSW model without a source term is
∂W∂t+∂F(W)∂x+K(W)∂h∂x=S(W), | (2.1) |
W=(hhv1hv2E11E12E22),F(W)=(hv1R11+hv21+gh22R12+hv1v2(E11+R11)v1E12v1+12(R11v2+R12v1)E22v1+R12v2), |
K(W)=(000ghv112ghv20),S(W)=(0−gh∂B∂x−Cf|v|v1−Cf|v|v2−ghv1∂B∂x+12D11−Cf|v|v21−12ghv2∂B∂x+12D12−Cf|v|v1v212D22−Cf|v|v22), |
while R11 and R12 are defined by the following tensor Rij=hpij, and also, E11, E12 and E22 are defined by the following tensor Eij=12Rij+12hvivj with i≥1,j≤2. We write the previous system 2.1 in nonconservative form with non-dissipative (Cf=0,D11=D12=D22=0), see [24], which can be written as follows
∂W∂t+(∇F(W)+C(W))∂W∂x=S1(W). | (2.2) |
Also, we can write the previous system as the following
∂W∂t+A(W)∂W∂x=S1(W) | (2.3) |
with
A(W)=[010000gh00200000020−3E11v1h+2v31+ghv23E11h−3v2103v100−2E12v1h−E11v2h+2v21v2+ghv222E12h−2v1v2E11h−v21v22v10−E22v1h−2E12v2h+v22v1E22h+v222E12h−2v2v102v2v1] |
and
S1(W)=(0−gh∂B∂x0−ghv1∂B∂x−12ghv2∂B∂x0). |
System (2.3) is a hyperbolic system and has the following eigenvalues
λ1=λ2=v1,λ3=v1−√2E11h−v21,λ4=v1+√2E11h−v21, |
λ5=v1−√gh+3(v21−2E11h),λ6=v1+√gh+3(v21−2E11h). |
In order deduce the G. Rusanov scheme, we rewrite the system (2.1) as follows
∂W∂t+∂F(W)∂x=−K(W)∂h∂x+S1(W)=Q(W). | (3.1) |
Integrating Eq (3.1) over the domain [tn,tn+1]×[xi−12,xi+12] gives the finite-volume scheme
Wn+1i=Wni−ΔtΔx(F(Wni+1/2)−F(Wni−1/2))+ΔtQin | (3.2) |
in the interval [xi−1/2,xi+1/2] at time tn. Wni represents the average value of the solution W as follows
Wni=1Δx∫xi+1/2xi−1/2W(tn,x)dx, |
and F(Wni±1/2) represent the numerical flux at time tn and space x=xi±1/2. It is necessary to solve the Riemann problem at xi+1/2 interfaces due to the organization of the numerical fluxes. Assume that for the first scenario given below, there is a self-similar Riemann problem solution associated with Eq (3.1)
W(x,0)={WL,ifx<0,WR,ifx>0 | (3.3) |
is supplied by
W(t,x)=Rs(xt,WL,WR). | (3.4) |
The difficulties with discretization of the source term in (3.2) could arise from singular values of the Riemann solution at the interfaces. In order to overcome these challenges and reconstruct a Wni+1/2 approximation, we created a finite-volume scheme in [19,20,21,22,23,25,26,27] for numerical solutions of conservation laws including source terms and without source terms. The principal objective here is building the intermediate states Wni±1/2 to be utilized in the corrector stage (3.2). The following is obtained by integrating Eq (3.1) through a control volume [tn,tn+θni+1/2]×[x−,x+], that includes the point (tn,xi+1/2), with the objective to accomplish this:
∫x+x−W(tn+θni+1/2,x)dx=Δx−Wni+Δx+Wni+1−θni+1/2(F(Wni+1)−F(Wni))+θni+1/2(Δx−−Δx+)Qni+12 | (3.5) |
with Wni±1/2 denoting the approximation of Riemann solution Rs across the control volume [x−,x+] at time tn+θni+1/2. While calculating distances Δx− and Δx+ as
Δx−=|x−−xi+1/2|,Δx+=|x+−xi+1/2|, |
Qni+12 closely resembles the average source term Q and is given by the following
Qni+12=1θni+12(Δx−+Δx+)∫tn+θni+12tn∫x+x−Q(W)dtdx. | (3.6) |
Selecting x−=xi, x+=xi+1 causes the Eq (3.5) to be reduced to the intermediate state, which given as follows
Wni+1/2=12(Wni+Wni+1)−θni+1/2Δx(F(Wni+1)−F(Wni))+θni+12Qni+12, | (3.7) |
where the approximate average value of the solution W in the control domain [tn,tn+θni+1/2]×[xi,xi+1] is expressed by Wni+1/2 as the following
Wni+1/2=1Δx∫xi+1xiW(x,tn+θni+1/2)dx | (3.8) |
by selecting θni+1/2 as follows
θni+1/2=αni+1/2ˉθi+1/2,ˉθi+1/2=Δx2Sni+1/2. | (3.9) |
This choice is contingent upon the results of the stability analysis[19]. The following represents the local Rusanov velocity
Sni+1/2=maxk=1,...,K(max(∣λnk,i∣,∣λnk,i+1∣)), | (3.10) |
where αni+1/2 is a positive parameter, and λnk,i represents the kth eigenvalues in (2.3) evaluated at the solution state Wni. Here, in our case, k=6 for the shear shallow water model. One can use the Lax-Wendroff technique again for αni+1/2=ΔtΔxSni+1/2. Choosing the slope αni+1/2=˜αni+1/2, the proposed scheme became a first-order scheme, where
˜αni+1/2=Sni+1/2sni+1/2, | (3.11) |
and
sni+1/2=mink=1,...,K(max(∣λnk,i∣,∣λnk,i+1∣)). | (3.12) |
In this case, the control parameter can be written as follows:
αni+1/2=˜αni+1/2+σni+1/2Φ(rmi+1/2), | (3.13) |
where ˜αni+1/2 is given by (3.11), and Φi+1/2=Φ(ri+1/2) is a function that limits the slope. While for
ri+1/2=Wi+1−q−Wi−qWi+1−Wi,q=sgn[F′(Xn+1,Wni+1/2)] |
and
σni+1/2=ΔtΔxSni+1/2−Sni+1/2sni+1/2. |
One may use any slope limiter function, including minmod, superbee, and Van leer [28] and [29]. At the end, the G. Rusanov scheme for Eq (2.3) can be written as follows
{Wni+12=12(Wni+Wni+1)−αni+122Snj+12[F(Wni+1)−F(Wni)]+αni+122Snj+12Qni+12,Wn+1i=Wni−rn[F(Wni+12)−F(Wni−12)]+ΔtnQin. | (3.14) |
With a definition of the C-property [30], the source term in (2.1) is discretized in the G. Rusanov method in a way that is well-balanced with the discretization of the flux gradients. According to [30,31], if the following formulas hold, a numerical scheme is said to achieve the C-property for the system (3.1).
(hp11)n= constant,hn+B= constantandvn1=vn2=0. | (4.1) |
When we set v1=v2=0 in the stationary flow at rest, we get system (3.1), which can be expressed as follows.
∂∂t(h0012hp1112hp1212hp22)+∂∂x(0hp11+12gh2hp12000)=(0−gh∂B∂x0000)=Q(x,t). | (4.2) |
We can express the predictor stage (3.14) as follows after applying the G. Rusanov scheme to the previous system
Wni+12=(12(hni+hni+1)−αni+124Sni+12(hni+hni+1)[(hni+1+Bi+1)−(hni+Bi)]−αni+122Sni+12((hp11)ni+1−(hp11)ni−αni+122Sni+12((hp12)ni+1−(hp12)ni)14((hp11)ni+1+(hp11)ni)14((hp12)ni+1+(hp12)ni)14((hp22)ni+1+(hp22)ni)). | (4.3) |
Also, we can write the previous equations as follows
Wni+12=(hni+120−αni+122Sni+12((hp12)ni+1−(hp12)ni)12(hp11)ni+1212(hp12)ni+1212(hp22)ni+12), | (4.4) |
and the stage of the corrector updates the solution to take on the desired form.
((h)n+1i(hv1)n+1i(hv2)n+1i(E11)n+1i(E12)n+1i(E22)n+1i)=((h)ni(hv1)ni(hv2)ni(E11)ni(E12)ni(E22)ni)−ΔtnΔx(0g2((hni+12)2−(hni−12)2)(hp12)ni+12−(hp12)ni−12000) | (4.5) |
+(0ΔtnQni0000). |
The solution is stationary when Wn+1i=Wni and this leads us to rewrite the previous system (4.5) as follows
Δtn2Δxg((hni+12)2−(hni−12)2)−ΔtnQni. |
This lead to the following
Qni=−g8Δx(hni+1+2hni+hni−1)(Bi+1−Bi−1). | (4.6) |
Afterward, when the source term in the corrector stage is discretized in the earlier equations, this leads to the G. Rusanov satisfying the C-property.
In order to simulate the SSW system numerically, we provide five test cases without a source term using the G. Rusanov, Rusanov, and Lax-Friedrichs schemes to illustrate the effectiveness and precision of the suggested G. Rusanov scheme. The computational domain for all cases is L=[0,1] divided into 300 gridpoints, and the final time is t=0.5s, except for test case 2, where the final time is t=10s. We evaluate the three schemes with the reference solution on the extremely fine mesh of 30000 cells that was produced by the traditional Rusanov scheme. Also, we provide one test case with a source term using the G. Rusanov scheme in the domain [0,1] divided into 200 gridpoints and final time t=0.5. We select the stability condition [19] in the following sense
Δt=CFLΔxmaxi(|αni+12Sni+12|), | (5.1) |
where a constant CFL=0.5.
This test case was studied in [24] and [32], and the initial condition is given by
(h,v1,v2,p11,p22,p12)={(0.01,0.1,0.2,0.04,0.04,1×10−8)ifx≤L2,(0.02,0.1,−0.2,0.04,0.04,1×10−8)ifx>L2. | (5.2) |
The solution include five waves, which are represented by 1− shock and 6− rarefaction. We compare the numerical results with the reference solution, which is calculated with the Rusanov scheme with very fine mesh of 30000 cells. Figures 1–3 show the numerical results and variation of parameter of control. We note that all waves are captured by this scheme and the numerical solution agrees with the reference solution. Table 1 shows the CPU time of computation for the three schemes by using a Dell i5 laptop, CPU 2.5 GHZ.
Scheme | G. Rusanov | Rusanov | Lax-Friedrichs |
CPU time | 0.068005 | 0.056805 | 0.0496803 |
This test case (the shear waves problem) was studied in [24] and [32], and the initial condition is given by
(h,v1,v2,p11,p22,p12)={(0.01,0,0.2,1×10−4,1×10−4,0)ifx≤L2,(0.01,0,−0.2,1×10−4,1×10−4,0)ifx>L2. | (5.3) |
The solution is represented by two shear waves with only transverse velocity discontinuities, the p12 and p22 elements of a stress tensor. We compare the numerical results by G. Rusanov, Rusanov, and Lax-Friedrichs with the reference solution, which is calculated with the Rusanov scheme with very fine mesh of 30000 cells and a final time t=10s, see Figures 4 and 5. We observe that Figure 5 displays a spurious rise in the central of the domain of computation, which has also been seen in the literature using different methods, see [24,32].
This test case was studied in [24] with the following initial condition
(h,v1,v2,p11,p22,p12)={(0.02,0,0,4×10−2,4×10−2,0)ifx≤L2,(0.01,0,0,4×10−2,4×10−2,0)ifx>L2. | (5.4) |
The solution for h, v1, and p11 consists of two shear rarefaction waves, one moving to the right and the other moving to the left, and a shock wave to the right. See Figures 6 and 7 which show the behavior of the height of the water, velocity, pressure, and variation of the parameter of control.
We take the same example, but with another variant of the modified test case, where p12=1×10−8 is set to a small non-zero value. We notice that the behavior of h, v1, and p11 is the same, but there is a change in the behavior of p12 such that it displays all of the five waves (four rarefaction and one shock) of the shear shallow water model, see Figures 8 and 9.
This test case was studied in [24] with the following initial condition
(h,v1,v2,p11,p22,p12)={(0.02,0,0,1×10−4,1×10−4,0)ifx≤L2,(0.03,−0.221698,0.0166167,1×10−4,1×10−4,0)ifx>L2. | (5.5) |
The solution for this test case consists of a single shock wave. We compare the numerical results with the reference solution, which is calculated with the Rusanov scheme with very fine mesh of 30000 cells and a final time t=0.5s. Figures 10 and 11 show the numerical results, and we note that all waves are captured by this scheme and the numerical solution agrees with the reference solution, but the solution of p11 does not agree with the exact solution [24]. There is an oscillation with Lax-Friedrichs scheme in the water height h and the pressure p11.
This test case (the shear waves problem) was studied in [24] and [32] with the following initial condition
(h,v1,v2,p11,p22,p12)={(0.02,0,0,1×10−4,1×10−4,0)ifx≤L2,(0.01,0,0,1×10−4,1×10−4,0)ifx>L2. | (5.6) |
The solution of this test case has a single shock wave and a single rarefaction wave, separated by a contact discontinuity. We compare the numerical results with the reference solution, which is calculated with the Rusanov scheme with very fine mesh of 30000 cells and a final time t=0.5s. Figures 12 and 13 show the numerical results, and we note that all waves are captured by this scheme and the numerical solution agrees with the reference solution, but the solution of p11 does not agree with the reference solution [24].
In this test case, we take the previous test case 3 and we added the discontinuous fond topography with the following initial condition
(h,v1,v2,p11,p22,p12,B)={(0.02,0,0,4×10−2,4×10−2,1×10−8,0)ifx≤L2,(0.01,0,0,4×10−2,4×10−2,1×10−8,0.01)ifx>L2. | (5.7) |
We simulate this test case with the G. Rusanov scheme with 200 gridpoints on the domain L=[0,1] at the final time t=0.5s, and we note that the behavior of the solution for h consists of one shear rarefaction wave moving to the left, a contact discontinuity after that two shear rarefaction waves, one moving to the right and the other moving to the left (see the left side of Figure 14. The right side of the Figure 14 shows the behavior of the velocity v1, which it consists of a rarefaction wave, a contact discontinuity after that, and two shear rarefactions. The left side of Figure 14 displays the behavior of the velocity v1. It is composed of two shear rarefactions followed by a contact discontinuity and three rarefaction waves moving to the right. The the right side of Figure 14 displays the behavior of the velocity v2. It is composed of two shear rarefactions moving to the left followed by a contact discontinuity after that, and two rarefaction waves moving to the right.
In summary, we have reported five numerical examples to solve the SSW model. Namely, we implemented the G. Rusanov, Rusanov, and Lax-Friedrichs schemes. We also compared the numerical solutions with the reference solution obtained by the classical Rusanov scheme on the very fine mesh of 30000 gridpoints. The three schemes were capable of capturing shock waves and rarefaction. Also, we have given the last numerical test with a source term. Finally, we discovered that the G. Rusanov scheme was more precise than the Rusanov and Lax-Friedrichs schemes.
The current study is concerned with the SSW model, which is a higher order variant of the traditional shallow water model since it adds vertical shear effects. The model features a non-conservative structure, which makes numerical solutions problematic. The 1D SSW model was solved using the G. Rusanov technique. We clarify that this scheme satisfied the C-property. Several numerical examples were given to solve the SSW model using the G. Rusanov, Rusanov, Lax-Friedrichs, and reference solution techniques. The simulations given verified the G. Rusanov technique's high resolution and validated its capabilities and efficacy in dealing with such models. This approach may be expanded in a two-dimensional space.
H. S. Alayachi: Conceptualization, Data curation, Formal analysis, Writing - original draft; Mahmoud A. E. Abdelrahman: Conceptualization, Data curation, Formal analysis, Writing - original draft; K. Mohamed: Conceptualization, Software, Formal analysis, Writing - original draft.
The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.
The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number 445-9-753.
The authors declare that they have no competing interests.
[1] |
Duggan C, Peeren E (2020) Making up the British countryside: a posthuman critique of Country Life's narratives of rural resilience and conservation. J Rural Stud 80: 350-359. https://doi.org/10.1016/j.jrurstud.2020.10.011 doi: 10.1016/j.jrurstud.2020.10.011
![]() |
[2] | Ronningen K (2016) Environment and resources. New and old questions for rural landscapes. In: Shucksmith M, Brown DL (eds.), Routledge International Handbook of Rural Studies. Routledge, London, 265-271. https://doi.org/10.4324/9781315753041-70 |
[3] |
Bridge G, Bouzarovski S, Bradshaw M, et al. (2013) Geographies of energy transition: Space, place and the low-carbon economy. Energy Policy 53: 331-340. https://doi.org/10.1016/j.enpol.2012.10.066 doi: 10.1016/j.enpol.2012.10.066
![]() |
[4] | Murdoch J (2006) Post-structuralist geography. SAGE, London. http://dx.doi.org/10.4135/9781446221426 |
[5] | Woods M (2016) Confronting globalisation? Rural protest, resistance and social movements. In: Shucksmith M, Brown DL (eds.), Routledge International Handbook of Rural Studies. Routledge, London, 626-637. https://doi.org/10.4324/9781315753041-70 |
[6] |
Warren CR, Birnie RV (2009) Re-powering Scotland: wind farms and the 'energy or envionrment?' Debate. Scott Geogr J 125: 97-126. https://doi.org/10.1080/14702540802712502 doi: 10.1080/14702540802712502
![]() |
[7] |
Goodwin M (2013) Regions, territories and relationality: exploring the regional dimensions of political practice. Reg Stud 47: 1181-1190. https://doi.org/10.1080/00343404.2012.697138 doi: 10.1080/00343404.2012.697138
![]() |
[8] |
Scott M (2008) Managing rural change and competing rationalities: insights from conflicting rural storylines and local policy making in Ireland. Plan Theory Pract 9: 9-32. https://doi.org/10.1080/14649350701843689 doi: 10.1080/14649350701843689
![]() |
[9] |
Robinson GM, Carson DA (2016) Resilient communities: transitions, pathways and resourcefulness. Geogr J 182: 114-122. https://doi.org/10.1111/geoj.12144 doi: 10.1111/geoj.12144
![]() |
[10] |
Welsh M (2014) Resilience and responsibility: governing uncertainty in a complex world. Geogr J 180: 15-26. https://doi.org/10.1111/geoj.12012 doi: 10.1111/geoj.12012
![]() |
[11] | Paniagua A (2021) Climate change and depopulated rural areas in the Global North: Geographical Sociopolitical processes and resistances. In: Leal Filho W, Luetz JM, Ayal D (Eds), Handbook of Climate Change Management. Springer, Cham. https://doi.org/10.1007/978-3-030-22759-3_4-1 |
[12] |
Paniagua A (2015) Geographical trajectories, biographical determinants and (new) place political elites in selected remote rural areas of north-central Spain. Geogr J 181: 401-412. https://doi.org/10.1111/geoj.12110 doi: 10.1111/geoj.12110
![]() |
[13] |
Hicks J, Ison N (2011) Community-owned renewable energy (CRE): Opportunities for rural Australia. Rural Soc 20: 244-255. https://doi.org/10.5172/rsj.20.3.244 doi: 10.5172/rsj.20.3.244
![]() |
[14] |
Walker G, Cass N (2007) Carbon reduction, the public and renewable energy: engaging with socio-technical configurations. Area 39: 458-469. https://doi.org/10.1111/j.1475-4762.2007.00772.x doi: 10.1111/j.1475-4762.2007.00772.x
![]() |
[15] |
Ulrich-Schad JD, Duncan CM (2018) People and places left behind: work, culture and politics in the rural United States. J Peasant Stud 45: 59-79. https://doi.org/10.1080/03066150.2017.1410702 doi: 10.1080/03066150.2017.1410702
![]() |
[16] |
Kousis M (1993) Collective resistance and sustainable development in rural Greece: the case of geothermal energy on the island of Milos. Sociol Rural 33: 3-24. https://doi.org/10.1111/j.1467-9523.1993.tb00944.x doi: 10.1111/j.1467-9523.1993.tb00944.x
![]() |
[17] |
Phillips M, Dickie J (2014) Narratives of transition/non-transition towards low carbon futures within English rural communities. J Rural Stud 34: 79-95. https://doi.org/10.1016/j.jrurstud.2014.01.002 doi: 10.1016/j.jrurstud.2014.01.002
![]() |
[18] | Horton H (2003) Green distinctions. The performance of identity among environmental activists. In: Szerszynski B, Wallace HS, Waterton C (eds.) Nature performed. Environment, culture and performance. London, Blackwell, 63-77. https: //doi.org/10.1111/j.1467-954X.2004.00451.x |
[19] |
Dmochowska-Dudek K, Bednarek-Szczepanska M (2018) A profile of the Polish rural NIMBYist. J Rural Stud 58: 52-66. https://doi.org/10.1016/j.jrurstud.2017.12.025 doi: 10.1016/j.jrurstud.2017.12.025
![]() |
[20] |
Mkutu K, Mkutu T, Marani M, et al. (2019) New oil developments in a remote area: environmental justice and participation in Turkana, Kenya. J Environ Dev 28: 223-252. https://doi.org/10.1177/1070496519857776 doi: 10.1177/1070496519857776
![]() |
[21] | Brown DL, Schafft KA (2011) Rural people & communities in the 21st Century. Resilience & transformation. Polity, Cambridge. |
[22] |
Bristow G, Cowell C, Munday M (2012) Windfalls for whom? The evolving notion of 'community' in community benefit provisions from wind farms. Geoforum 43: 1108-1120. https://doi.org/10.1016/j.geoforum.2012.06.015 doi: 10.1016/j.geoforum.2012.06.015
![]() |
[23] |
Calvert K (2016) From 'energy geography' to 'energy geographies': perspectives on a fertile academic borderland. Prog Hum Geogr 40: 105-125. https://doi.org/10.1177/0309132514566343 doi: 10.1177/0309132514566343
![]() |
[24] |
Beetz S, Huning S, Plieninger T (2008) Landscapes of peripherization in north-eastern germany's countryside: new challenges for planning theory and practice. Int Plan Stud 13: 295-310. https://doi.org/10.1080/13563470802518909 doi: 10.1080/13563470802518909
![]() |
[25] |
Hoggart K, Paniagua A (2001) What rural restructuring? J Rural Stud 17: 41-62. https://doi.org/10.1016/S0743-0167(00)00036-X doi: 10.1016/S0743-0167(00)00036-X
![]() |
[26] |
Arnold G, Farrer B, Holahan R (2018) Measuring environmental and economic opinions about hydraulic fracturing: a survey of landowners in active or planned drilling units. Rev Policy Res 35: 258-279. https://doi.org/10.1111/ropr.12276 doi: 10.1111/ropr.12276
![]() |
[27] |
Murphy T, Brannstrom C, Fry M (2017) Ownership and spatial distribution of eagle ford mineral wealth in live Oak County, Texas. Prof Geogr 69: 616-628. https://doi.org/10.1080/00330124.2017.1298451 doi: 10.1080/00330124.2017.1298451
![]() |
[28] |
Haggerty J, McBride K (2016) Does local monitoring empower fracking host communities? A case study from the gas fields of Wyoming. J Rural Stud 43: 235-247. https://doi.org/10.1016/j.jrurstud.2015.11.005 doi: 10.1016/j.jrurstud.2015.11.005
![]() |
[29] |
Köhne M, Rasch ED (2018) Belonging to and in the Shale gas fields. A case-study of the Noordoostpolder, the Netherlands. Sociol Rural 58: 604-624. https://doi.org/10.1111/soru.12184 doi: 10.1111/soru.12184
![]() |
[30] |
Rohse M, Day R, Llewellyn D (2020) Towards an emotional energy geography: attending to emotions and affects in a former coal mining community in South Wales, UK. Geoforum 110: 136-146. https://doi.org/10.1016/j.geoforum.2020.02.006 doi: 10.1016/j.geoforum.2020.02.006
![]() |
[31] |
Bailey MS, Osborne N (2020) Extractive resources and emotional geographies: the battle for treasured places in the Gloucester Valley. Geoforum 116: 153-162. https://doi.org/10.1016/j.geoforum.2020.07.006 doi: 10.1016/j.geoforum.2020.07.006
![]() |
[32] |
Evensen D, Stedman R (2018) 'Fracking': promoter and destroyer of 'the good life'. J Rural Stud 59: 142-152. https://doi.org/10.1016/j.jrurstud.2017.02.020 doi: 10.1016/j.jrurstud.2017.02.020
![]() |
[33] |
Aldred TL, Alderfer-Mumma C, de Leeuw S, et al. (2021) Mining sick: creatively unsettling normative narratives about industry, environment, extraction, and the health geographies of rural, remote, northern, and indigenous communities in British Columbia. Can Geogr 65: 82-96. https://doi.org/10.1111/cag.12660 doi: 10.1111/cag.12660
![]() |
[34] |
Mincyte D, Bartkiene A (2019) The anti-fracking movement and the politics of rural marginalization in Lithuania: intersectionality in environmental justice. Environ Sociol 5: 177-187. https://doi.org/10.1080/23251042.2018.1544834 doi: 10.1080/23251042.2018.1544834
![]() |
[35] |
Mayer A, Olson-Hazboun S, Malin S (2018) Fracking fortunes: economic well-being and oil and gas development along the urban-rural continuum. Rural Sociol 83: 532-567. https://doi.org/10.1111/ruso.12198 doi: 10.1111/ruso.12198
![]() |
[36] |
Short D, Szoluha A (2019) Fracking Lancashire: the planning process, social harm and collective trauma. Geoforum 98: 264-276. https://doi.org/10.1016/j.geoforum.2017.03.001 doi: 10.1016/j.geoforum.2017.03.001
![]() |
[37] | Castelli M (2015) Fracking and the rural poor: negative externalities, failing remedies, and federal legislation. Indiana J Law Soc Equal 3: 281-304. |
[38] | Kelly MG, Schafft KA (2020) Fracking 'boom' does not deliver funds for rural Penn. Schools. Daily younder. Available from: https://dailyyounder.com/research-fracking-boom-does-not-delive. |
[39] |
Schafft KA, Glenna LL, Green B, et al. (2014) Local impacts of unconventional gas development within Pennsyvania's Marcellus Shale Region: gaugning boomtown development through the perspectives of educational administrators. Soc Nat Resour 27: 389-404. https://doi.org/10.1080/08941920.2013.861561 doi: 10.1080/08941920.2013.861561
![]() |
[40] | Powell DE (2018) Landscapes of power: politics of energy in the Navajo Nation. Duke University Press, Durham. https://doi.org/10.1215/9780822372295 |
[41] |
Woods M (2003) Conflicting environmental visions of the rural: wind farm development in Mid Wales. Sociol Rural 43: 271-288. https://doi.org/10.1111/1467-9523.00245 doi: 10.1111/1467-9523.00245
![]() |
[42] |
Fast S (2015) Qualified, absolute, idealistic, impatient: dimensions of host community responses to wind energy projects. Environ Plan A 47: 1399-1592. https://doi.org/10.1177/0308518X15595887 doi: 10.1177/0308518X15595887
![]() |
[43] |
Lennon M, Scott M (2017) Opportunity or threat: dissecting tensions in a post-carbon rural transition. Sociol Rural 57: 87-109. https://doi.org/10.1111/soru.12106 doi: 10.1111/soru.12106
![]() |
[44] |
Wheler R (2017) Reconciling windfarms with rural place identity: exploring residents' attitudes to existing sites. Sociol Rural 57: 110-132. https://doi.org/10.1111/soru.12121 doi: 10.1111/soru.12121
![]() |
[45] |
Zoografos C, Martínez-Alier J (2009) The politics of landscape value: a case study of wind farm conflict in rural Catalonia. Environ Plan A 41: 1726-1744. https://doi.org/10.1068/a41208 doi: 10.1068/a41208
![]() |
[46] |
Ogilvie M, Rootes C (2015) The impact of local campaigns against wind energy developments. Environ Polit 24: 874-893. https://doi.org/10.1080/09644016.2015.1063301 doi: 10.1080/09644016.2015.1063301
![]() |
[47] |
Mordue T, Moss O, Johnston L (2020) The impacts of onshore-wind farms on a UK rural tourism landscape: objective evidence, local opposition, and national politics. J Sustain Tour 28: 1882-1904. https://doi.org/10.1080/09669582.2020.1769110 doi: 10.1080/09669582.2020.1769110
![]() |
[48] |
Morris W, Bowen R (2020) Renewable energy diversification: considerations for farm business resilience. J Rural Stud 80: 380-390. https://doi.org/10.1016/j.jrurstud.2020.10.014 doi: 10.1016/j.jrurstud.2020.10.014
![]() |
[49] | Smith D (2013) Reclaiming the 'public' lands: community conflict and rural gentrification. J Rural Community Dev 8: 215-227. |
[50] |
Chezel E, Labussière O (2018) Energy landscape as a polity. Wind power practice in Northern Friesland (Germany). Landscape Res 43: 503-516. https://doi.org/10.1080/01426397.2017.1336516 doi: 10.1080/01426397.2017.1336516
![]() |
[51] |
Dunlap A, Correa-Arce M (2021) 'Murderous energy' in Oazaca, Mexico: wind factories, territorial struggle and social warfare. J Peasant Stud 2021: 1-26. https://doi.org/10.1080/03066150.2020.1862090 doi: 10.1080/03066150.2020.1862090
![]() |
[52] | Fernández M (2021) Los nuevos terratenientes de España. Available from: https://elpais-com.cdn.amproject.org/v/s/elpais.com/economia/2021-03-21/los nuevos terratenientes. |
[53] |
Ward N, Brown DL (2009) Placing the rural in regional development. Reg Stud 43: 1237-1244. https://doi.org/10.1080/00343400903234696 doi: 10.1080/00343400903234696
![]() |
[54] |
Naumann M, Rudolph D (2020) Conceptualizing rural energy transitions: energizing rural studies, ruralizing energy research. J Rural Stud 73: 97-104. https://doi.org/10.1016/j.jrurstud.2019.12.011 doi: 10.1016/j.jrurstud.2019.12.011
![]() |
1. | Georges Chamoun, Finite Volume Analysis of the Two Competing-species Chemotaxis Models with General Diffusive Functions, 2025, 22, 2224-2902, 232, 10.37394/23208.2025.22.24 |
Scheme | G. Rusanov | Rusanov | Lax-Friedrichs |
CPU time | 0.068005 | 0.056805 | 0.0496803 |