scholarly journals Weak-Strong Uniqueness for Compressible Magnetohydrodynamic Equations with Coulomb Force

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Lianhua He ◽  
Yonghui Zhou
Keyword(s):  
Relative Entropy ◽  
Coulomb Force ◽  
Two Dimensional ◽  
Strong Uniqueness ◽  
Magnetohydrodynamic Equations ◽  
Uniqueness Property ◽  
Magnetohydrodynamic System

In this paper, we consider the two-dimensional compressible magnetohydrodynamic system with Coulomb force. We apply the method of relative entropy to establish the weak-strong uniqueness property of this system.

scholarly journals The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

2016 ◽  
Vol 34 (4) ◽  
pp. 421-425
Author(s):  
Christian Nabert ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Necessary Conditions ◽  
The Other ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Alfven Velocity

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

scholarly journals Weak–strong uniqueness property for models of compressible viscous fluids near vacuum*

Nonlinearity ◽  
2021 ◽  
Vol 34 (9) ◽  
pp. 6627-6650
Author(s):  
Eduard Feireisl ◽  
Antonín Novotný
Keyword(s):  
Viscous Fluids ◽  
Strong Uniqueness ◽  
Uniqueness Property

scholarly journals Nonlocal Means Two Dimensional Histogram-Based Image Segmentation via Minimizing Relative Entropy

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 827 ◽  
Author(s):  
Chundi Jiang ◽  
Wei Yang ◽  
Yu Guo ◽  
Fei Wu ◽  
Yinggan Tang
Keyword(s):  
Image Segmentation ◽  
Relative Entropy ◽  
Spatial Information ◽  
Two Dimensional ◽  
Nonlocal Means ◽  
Mean Filter ◽  
Filter Process ◽  
Local Mean ◽  
Non Local ◽  
Correlation Information

Spatial correlation information between pixels is considered to be very important in thresholding methods. However, it is often ignored and thus unsatisfied segmentation results maybe obtained. To overcome this shortcoming, we propose a new image segmentation approach by taking not only pixels’ spatial information but also pixels’s gray level into account. First, a non-local mean filter is imposed on the image. Then the filtered image and the original image together are adopted to build a two dimensional histogram, it is called non-local mean two dimensional histogram. Finally, a minimum relative entropy criteria is used to select the ideal thresholding vector. Since the non-local mean filter process is performed in a neighborhood of current pixel, it carries out the spatial information of current pixel. Segmentation results on several images illustrate the effectiveness of the proposed thresholding method, whose segmentation accuracy are greatly improved compared to most existing thresholding methods.

Excitation and damping of disturbances in cylindrical coronal loops

2005 ◽  
Vol 364 (1839) ◽  
pp. 547-550 ◽  
Author(s):  
Jaume Terradas ◽  
Ramón Oliver ◽  
José Luis Ballester
Keyword(s):  
Boundary Layer ◽  
Coronal Loop ◽  
Normal Mode Analysis ◽  
Resonant Absorption ◽  
Time Dependent ◽  
Mode Analysis ◽  
Coronal Loops ◽  
Two Dimensional ◽  
Magnetohydrodynamic Equations ◽  
Kink Mode

The excitation and damping of transversal coronal loop oscillations is studied using one-and two-dimensional models of line-tied cylindrical loops. By solving the time-dependent magnetohydrodynamic equations it is shown how an initial disturbance generated in the solar corona induces kink mode oscillations. We investigate the effect of the disturbance on a loop with a non-uniform boundary layer. In particular, a strong damping of transversal oscillations due to resonant absorption is found, such as predicted by previous works based on normal mode analysis.

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