scholarly journals Numerical stability of a plasma sheath

2018 ◽  
Vol 64 ◽  
pp. 17-36 ◽  
Author(s):  
Mehdi Badsi ◽  
Michel Mehrenberger ◽  
Laurent Navoret
Keyword(s):  
Boundary Conditions ◽  
Numerical Stability ◽  
Specific Treatment ◽  
Stationary Solutions ◽  
Plasma Sheath ◽  
Time Dependent ◽  
Main Question ◽  
Know How ◽  
Metallic Wall ◽  
Long Time

We are interested in developing a numerical method for capturing stationary sheaths, that a plasma forms in contact with a metallic wall. This work is based on a bi-species (ion/electron) Vlasov-Ampère model proposed in [3]. The main question addressed in this work is to know how accurately classical time-dependent Vlasov-Ampère numerical schemes preserve in long time these non-homogeneous stationary solutions with emission/absorption boundary conditions. In the context of high-order semi-Lagrangian methods, due to their large stencil, interpolation near the boundary of the domain requires also a specific treatment.

Making it abstract, making it contestable: Gender/sex as a politicized concept

2020 ◽  
Author(s):  
Claudia Mazzuca ◽  
Matteo Santarelli
Keyword(s):  
Social Sciences ◽  
Main Question ◽  
Abstract Concepts ◽  
Biological Feature ◽  
Dynamic Approach ◽  
Cognitive Sciences ◽  
Long Time ◽  
Cultural Construct ◽  
Science Framework ◽  
The One

The concept of gender has been the battleground of scientific and political speculations for a long time. On the one hand, some accounts contended that gender is a biological feature, while on the other hand some scholars maintained that gender is a socio-cultural construct (e.g., Butler, 1990; Risman, 2004). Some of the questions that animated the debate on gender over history are: how many genders are there? Is gender rooted in our biological asset? Are gender and sex the same thing? All of these questions entwine one more crucial, and often overlooked interrogative. How is it possible for a concept to be the purview of so many disagreements and conceptual redefinitions? The question that this paper addresses is therefore not which specific account of gender is preferable. Rather, the main question we will address is how and why is even possible to disagree on how gender should be considered. To provide partial answers to these questions, we suggest that gender/sex (van Anders, 2015; Fausto-Sterling, 2019) is an illustrative example of politicized concepts. We show that no concepts are political in themselves; instead, some concepts are subjected to a process involving a progressive detachment from their supposed concrete referent (i.e., abstractness), a tension to generalizability (i.e., abstraction), a partial indeterminacy (i.e., vagueness), and the possibility of being contested (i.e., contestability). All of these features differentially contribute to what we call the politicization of a concept. In short, we will claim that in order to politicize a concept, a possible strategy is to evidence its more abstract facets, without denying its more embodied and perceptual components (Borghi et al., 2019). So, we will first outline how gender has been treated in psychological and philosophical discussions, to evidence its essentially contestable character thereby showing how it became a politicized concept. Then we will review some of the most influential accounts of political concepts, arguing that currently they need to be integrated with more sophisticated distinctions (e.g., Koselleck, 2004). The notions gained from the analyses of some of the most important accounts of political concepts in social sciences and philosophy will allow us to implement a more dynamic approach to political concepts. Specifically, when translated into the cognitive science framework, these reflections will help us clarifying some crucial aspects of the nature of politicized concepts. Bridging together social and cognitive sciences, we will show how politicized concepts are abstract concepts, or better abstract conceptualizations.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

scholarly journals Geometries with mismatched branes

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Andreas Karch ◽  
Lisa Randall
Keyword(s):  
Boundary Conditions ◽  
Effective Action ◽  
Cosmological Models ◽  
Time Dependent ◽  
De Sitter ◽  
Stabilization Mechanism ◽  
New Class ◽  
Vacuum Solutions ◽  
Single Coordinate

Abstract We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time- dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism.

EXPECTED AND UNEXPECTED SOLUTIONS TO THE STATIONARY ONE-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1663-1667
Author(s):  
LINCOLN D. CARR ◽  
CHARLES W. CLARK ◽  
WILLIAM P. REINHARDT
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stationary Solutions ◽  
Einstein Condensate ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Bose Einstein Condensate ◽  
Dilute Gas

We present all stationary solutions to the nonlinear Schrödinger equation in one dimension for box and periodic boundary conditions. For both repulsive and attractive nonlinearity we find expected and unexpected solutions. Expected solutions are those that are in direct analogy with those of the linear Schödinger equation under the same boundary conditions. Unexpected solutions are those that have no such analogy. We give a physical interpretation for the unexpected solutions. We discuss the properties of all solution types and briefly relate them to experiments on the dilute-gas Bose-Einstein condensate.

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