By using the screened Coulomb potential a generalized version of Newton's Shell Theorem is developed and analytical equations are derived to calculate i) the potential of a charged sphere surrounded by electrolyte, ii) the potential of two concentric charged spheres surrounded by electrolyte, and iii) the potential inside the membrane of a charged lipid vesicle surrounded by electrolyte with high ion concentration. By numerical integration the potential of a lipid vesicle is calculated at any electrolyte concentration.
Citation: István P. Sugár. A generalization of the Shell Theorem.Electric potential of charged spheres and charged vesicles surrounded by electrolyte[J]. AIMS Biophysics, 2020, 7(2): 76-89. doi: 10.3934/biophy.2020007
[1] | István P. Sugár . Density of electric field energy around two surface-charged spheres surrounded by electrolyte I. The spheres are separated from each other. AIMS Biophysics, 2022, 9(2): 86-95. doi: 10.3934/biophy.2022008 |
[2] |
István P. Sugár .
A generalization of the Shell Theorem. Electric potential of charged spheres and charged vesicles surrounded by electrolyte. AIMS Biophysics, 2023, 10(1): 23-24. doi: 10.3934/biophy.2023003 |
[3] | István P. Sugár . Density of electric field energy around two surface-charged spheres surrounded by electrolyte II. The smaller sphere is inside the larger one. AIMS Biophysics, 2022, 9(1): 61-71. doi: 10.3934/biophy.2022006 |
[4] | István P. Sugár . Electric energies of a charged sphere surrounded by electrolyte. AIMS Biophysics, 2021, 8(2): 157-164. doi: 10.3934/biophy.2021012 |
[5] | István P. Sugár, Parkson Lee-Gau Chong . Monte Carlo simulations of the distributions of intra- and extra-vesicular ions and membrane associated charges in hybrid liposomes composed of negatively charged tetraether and zwitterionic diester phospholipids. AIMS Biophysics, 2017, 4(2): 316-336. doi: 10.3934/biophy.2017.2.316 |
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By using the screened Coulomb potential a generalized version of Newton's Shell Theorem is developed and analytical equations are derived to calculate i) the potential of a charged sphere surrounded by electrolyte, ii) the potential of two concentric charged spheres surrounded by electrolyte, and iii) the potential inside the membrane of a charged lipid vesicle surrounded by electrolyte with high ion concentration. By numerical integration the potential of a lipid vesicle is calculated at any electrolyte concentration.
Conflict constitutes, at all geographical scales, an essential category for reading the tensions that traverse the world [1]. Landscape, in its transient dimension [2], represents in this sense, at least in the epistemological perspective proper to geography, the most exposed and representative device of the transformative dynamics of complexity [3].
It constitutes a junction that is both concrete and ideal [4] of the relationship between communities and spaces: in the landscape, processes, projects, contrasts, and conflicts find both formal and conceptual outcomes. Augustin Berque [5], noting its mediance value, has, not surprisingly, attributed to the landscape dimension an eminent cognitive perspective. In an era such as ours [6], marked by extreme anthropic pressure on spaces, against the backdrop of an increasingly unavoidable focus on climate equity policies, landscape transformations constitute a necessary horizon [7] for reading them in depth without risking leaving out any tension, whatever the scale of reference [8].
The study of landscape evolution and transformation is relevant not only from a geographical, but also from a geopolitical perspective. This is because, as Yves Lacoste observed [9], geopolitics should be underwritten by regional analysis (i.e., demonstrating an appreciation for local and regional differences) and understanding of the connections between geographical knowledge and political practice [10]. The current redetermination of the global geopolitical chessboard coincides with a period in which conflicts cut across territories and communities in a multi-scalar sense. The world is undergoing an epochal spatial transition [11] whose boundaries are being defined [12]. Ours is a disordered, fluid, and dynamic world in transition from an international to a glocal system (i.e., based on a close correlation between the local and the global spheres) [13].
On a global scale, we are seeing an increase in instability and uncertainty. We have entered the world of G-Zero, a neologism coined by the American political scientist Ian Bremmer. It means that we are moving from G-20 to G-Zero. Many powers will confront each other, but for the first time in the last 70 years, there will be no single power or alliance of power capable of assuming global leadership [14]. The absence of a global geopolitical dominus is driving more and more states into what John Agnew called the territorial trap [15]. Indeed, an increasing number of governments are responding to global threats (from pandemics to climate crises) with national policies that protect political, economic, social, and health interests only within their own territorial borders, ignoring the importance of transnational cooperation.
The concept of space and time is changing not only on the geopolitical chessboard [16], but also in the spaces of everyday life, from homes to offices and from city streets to suburbs. Faced with the network of bits that connects the whole [17], the architecture of the places where we live and work must adapt to new forms of urban planning and new ways of experiencing space. Take, for example, the consequences of the destructive innovation of teleworking [18].
Studying this disordered world [19] characterized by profound changes in the global and local landscape is relevant for understanding conflict dynamics at different scales of analysis.
The congeries of processes and phenomena through which community initiative is articulated, some of which are addressed within the research articles of the special issue "Conflicts and landscapes: toward a new Anthropocene?", activate ever-changing conflict dynamics with differentiated levels of complexity. Think of tourism, the effort to implement more sustainable environmental policies, or the tensions underlying urban and rural areas' dynamics. But think also of food, demographic, and migration crises; the digital and the technological revolution; health threats such as pandemics; or the emergence of new private geopolitical actors eroding the power of nation states. Nothing escapes landscape transformations.
In our call for papers, we stated that "The aim of this special issue is therefore to stimulate a theoretical reflection on the connections between conflict and landscape, but also to host analyses of case studies consistent with the identified theme". Critically reading the contributions received, we can say that the reflection has been started and we need to continue it boldly.
The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.
The authors declare no conflict of interest.
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