scholarly journals Allowing Nonlinear Stability Margins in Interconnection of iISS Dissipation Inequalities**The work was supported in part by JSPS KAKENHI Grant Number 26420422.

2016 ◽  
Vol 49 (18) ◽  
pp. 921-926
Author(s):  
Hiroshi Ito
Keyword(s):  
Nonlinear Stability ◽  
Stability Margins ◽  
Dissipation Inequalities

scholarly journals Nonlinear stability of two-layer shallow water flows with a free surface

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190594
Author(s):  
Francisco de Melo Viríssimo ◽  
Paul A. Milewski
Keyword(s):  
Free Surface ◽  
Initial Data ◽  
Nonlinear Stability ◽  
Mathematical Proof ◽  
Passive Layer ◽  
Physical Parameters ◽  
Immiscible Fluid ◽  
Dimensional System ◽  
The Cauchy Problem ◽  
The Difference

The problem of two layers of immiscible fluid, bordered above by an unbounded layer of passive fluid and below by a flat bed, is formulated and discussed. The resulting equations are given by a first-order, four-dimensional system of PDEs of mixed-type. The relevant physical parameters in the problem are presented and used to write the equations in a non-dimensional form. The conservation laws for the problem, which are known to be only six, are explicitly written and discussed in both non-Boussinesq and Boussinesq cases. Both dynamics and nonlinear stability of the Cauchy problem are discussed, with focus on the case where the upper unbounded passive layer has zero density, also called the free surface case. We prove that the stability of a solution depends only on two ‘baroclinic’ parameters (the shear and the difference of layer thickness, the former being the most important one) and give a precise criterion for the system to be well-posed. It is also numerically shown that the system is nonlinearly unstable, as hyperbolic initial data evolves into the elliptic region before the formation of shocks. We also discuss the use of simple waves as a tool to bound solutions and preventing a hyperbolic initial data to become elliptic and use this idea to give a mathematical proof for the nonlinear instability.

scholarly journals Electric Vehicles in Jordan: Challenges and Limitations

2021 ◽  
Vol 13 (6) ◽  
pp. 3199
Author(s):  
Laith Shalalfeh ◽  
Ashraf AlShalalfeh ◽  
Khaled Alkaradsheh ◽  
Mahmoud Alhamarneh ◽  
Ahmad Bashaireh
Keyword(s):  
Electric Vehicles ◽  
Distribution System ◽  
Distribution Systems ◽  
Environmental Benefits ◽  
System Stability ◽  
Loading Conditions ◽  
Stability Margins ◽  
High Penetration ◽  
Node Distribution ◽  
The Impact

An increasing number of electric vehicles (EVs) are replacing gasoline vehicles in the automobile market due to the economic and environmental benefits. The high penetration of EVs is one of the main challenges in the future smart grid. As a result of EV charging, an excessive overloading is expected in different elements of the power system, especially at the distribution level. In this paper, we evaluate the impact of EVs on the distribution system under three loading conditions (light, intermediate, and full). For each case, we estimate the maximum number of EVs that can be charged simultaneously before reaching different system limitations, including the undervoltage, overcurrent, and transformer capacity limit. Finally, we use the 19-node distribution system to study these limitations under different loading conditions. The 19-node system is one of the typical distribution systems in Jordan. Our work estimates the upper limit of the possible EV penetration before reaching the system stability margins.

scholarly journals Optimal Stability Thresholds in Rotating Fully Anisotropic Porous Medium with LTNE

2021 ◽  
Author(s):  
Florinda Capone ◽  
Maurizio Gentile ◽  
Jacopo A. Gianfrani
Keyword(s):  
Porous Layer ◽  
Nonlinear Stability ◽  
Steady Motion ◽  
Vertical Axis ◽  
Linear Instability ◽  
List Type ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Anisotropic Porous Medium ◽  
Necessary And Sufficient

Abstract The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved. Article Highlights A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained. It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly. Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction.

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