Fluid model of the plasma flow in the magnetic tail of a planet

2021 ◽  
Author(s):  
Filippo Pantellini
Keyword(s):  
Rotation Axis ◽  
Fluid Model ◽  
Type Equation ◽  
Radius Of Curvature ◽  
Plasma Velocity ◽  
One Dimensional ◽  
Planetary Rotation ◽  
Transverse Scale ◽  
Magnetohydrodynamic Model ◽  
Field Lines

<p>All planets of the solar system with an active internal dynamo have a their magnetic dipole oriented perpendicularly or nearly perpendicularly to the solar wind during all or part of their orbit  around the Sun. If, in addition, the planetary rotation is slow, or if the angle between dipole and rotation axis is large, planetary field lines crossing the antisolar axis can become stretched to large distances downstream of the planet. Examples where this may occur are Mercury and Uranus at solstice time, respectively. </p><p>Inspired by these examples, we present a tentative one-dimensional magnetohydrodynamic model of the plasma flowing along the antisolar direction. </p><p>Assuming that the radius of curvature R(z) of the planetary field lines is defined locally as R=D/D', where D(z) is a characteristic  transverse scale of the magnetosphere at a distance z downstream of the planet,  we obtain that the plasma velocity u(z) obeys to a Hugoniot type equation  (M<sup>2</sup>-1) u'/u =  D'/D,  where M=u/v<sub>A</sub> is the Alfvén Mach number. </p><p>The solution for a typical profile D(z) will be discussed. </p>

scholarly journals Crystal structure ofcatena-poly[hemi[1,3-bis(2,6-diisopropylphenyl)imidazolium] [[μ3-acetato-κ3O:O:O′-tri-μ2-acetato-κ6O:O′-dicopper(II)(Cu—Cu)]-μ-chlorido] dichloromethane sesquisolvate]

2015 ◽  
Vol 71 (8) ◽  
pp. m148-m149
Author(s):  
Mohammad Iqbal ◽  
James Raftery ◽  
Peter Quayle
Keyword(s):  
Coordination Polymer ◽  
Rotation Axis ◽  
Metal Organic Framework ◽  
Solvent Molecule ◽  
Central Metal ◽  
Imidazolium Cation ◽  
One Dimensional ◽  
Paddle Wheel ◽  
Internuclear Axis ◽  
Solvent Molecules

The title copper(II) complex, {(C27H37N2)[Cu4(CH3COO)8Cl]·3CH2Cl2}n, is a one-dimensional coordination polymer. The asymmetric unit is composed of a copper(II) tetraacetate paddle-wheel complex, a Cl−anion situated on a twofold rotation axis, half a 1,3-bis(2,6-diisopropylphenyl)imidazolium cation (the whole molecule being generated by twofold rotation symmetry) and one and a half of a dichloromethane solvent molecule (one being located about a twofold rotation axis). The central metal-organic framework comprises of a tetranuclear copper(II) acetate `paddle-wheel' complex which arises from the dimerization of the copper(II) tetraacetate core comprising of three μ2-bidentate acetate and one μ3-tridentate acetate ligands per binuclear paddle-wheel complex. Both CuIIatoms of the binuclear component adopt a distorted square-pyramidal coordination geometry (τ = 0.04), with a Cu...Cu separation of 2.6016 (2) Å. The apical coordination site of one CuIIatom is occupied by an O atom of a neighbouring acetate bridge [Cu—O = 2.200 (2) Å], while that of the second CuIIatom is occupied by a bridging chloride ligand [Cu...Cl = 2.4364 (4) Å]. The chloride bridge is slightly bent with respect to the Cu...Cu internuclear axis [Cu—Cl—Cu = 167.06 (6)°] and the tetranuclear units are located about a twofold rotation axis, forming the one-dimensional polymer that propagates along [101]. Charge neutrality is maintained by the inclusion of the 1,3-bis(2,6-diisopropylphenyl)imidazolium cation within the crystal lattice. In the crystal, the cation and dichloromethane solvent molecules are linked to the coordination polymer by various C—H...O and C—H...Cl hydrogen bonds. There are no other significant intermolecular interactions present.

scholarly journals NEW L1-GRADIENT TYPE ESTIMATES OF SOLUTIONS TO ONE-DIMENSIONAL QUASILINEAR PARABOLIC SYSTEMS

2010 ◽  
Vol 12 (01) ◽  
pp. 85-106 ◽  
Author(s):  
S. N. ANTONTSEV ◽  
J. I. DÍAZ
Keyword(s):  
Type Equation ◽  
Parabolic Type ◽  
Parabolic Systems ◽  
Diffusion Term ◽  
One Dimensional ◽  
First Order ◽  
Estimates Of Solutions ◽  
Gradient Type ◽  
Degenerate Type ◽  
Parabolic Type Equation

We consider a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of the degenerate type. We derive some new L1-gradient type estimates for its solutions which are uniform in the sense that they do not depend on the coefficients nor on the size of the spatial domain. We also give some applications of such estimates to gas dynamics, filtration problems, a p-Laplacian parabolic type equation and some first order systems of Hamilton–Jacobi or conservation laws type.

A Physically Based, One-Dimensional Two-Fluid Model for Direct Contact Condensation of Steam Jets Submerged in Subcooled Water

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
David Heinze ◽  
Thomas Schulenberg ◽  
Lars Behnke
Keyword(s):  
Direct Contact ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Interfacial Area ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Two Fluid Model ◽  
Contact Condensation ◽  
Two Fluid

A simulation model for the direct contact condensation of steam in subcooled water is presented that allows determination of major parameters of the process, such as the jet penetration length. Entrainment of water by the steam jet is modeled based on the Kelvin–Helmholtz and Rayleigh–Taylor instability theories. Primary atomization due to acceleration of interfacial waves and secondary atomization due to aerodynamic forces account for the initial size of entrained droplets. The resulting steam-water two-phase flow is simulated based on a one-dimensional two-fluid model. An interfacial area transport equation is used to track changes of the interfacial area density due to droplet entrainment and steam condensation. Interfacial heat and mass transfer rates during condensation are calculated using the two-resistance model. The resulting two-phase flow equations constitute a system of ordinary differential equations, which is solved by means of the explicit Runge–Kutta–Fehlberg algorithm. The simulation results are in good qualitative agreement with published experimental data over a wide range of pool temperatures and mass flow rates.

A Study of a Sharp 90 Degree Curved Flow

1992 ◽  
Author(s):  
R. H. Kim
Keyword(s):  
Turbulence Model ◽  
Ideal Gas ◽  
Radius Of Curvature ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Algebraic Stress Model ◽  
Finite Difference Technique ◽  
Curved Tube ◽  
Kinetic Energy Loss ◽  
The Ideal

Abstract An investigation of air flow along a 90 degree elbow-like tube is conducted to determine the velocity and temperature distributions of the flow. The tube has a sharp 90 degree turn with a radius of curvature of almost zero. The flow is assumed to be a steady two-dimensional turbulent flow satisfying the ideal gas relation. The flow will be analyzed using a finite difference technique with the K-ε turbulence model, and the algebraic stress model (ASM). The FLUENT code was used to determine the parameter distributions in the passage. There are certain conditions for which the K-ε model does not describe the fluid phenomenon properly. For these conditions, an alternative turbulence model, the ASM with or without QUICK was employed. FLUENT has these models among its features. The results are compared with the result computed by using elementary one-dimensional theory including the kinetic energy loss along the passage of the sharp 90 degree curved tube.

scholarly journals Isotypic one-dimensional coordination polymers:catena-poly[[dichloridocadmium]-μ-5,6-bis(pyridin-2-yl)pyrazine-2,3-dicarboxylato-κ2N5:N6] andcatena-poly[[dichloridomercury(II)]-μ-5,6-bis(pyridin-2-yl)pyrazine-2,3-dicarboxylato-κ2N5:N6]

2016 ◽  
Vol 72 (8) ◽  
pp. 1214-1218 ◽  
Author(s):  
Montserrat Alfonso ◽  
Helen Stoeckli-Evans
Keyword(s):  
Hydrogen Bonds ◽  
Metal Ions ◽  
Coordination Polymers ◽  
Rotation Axis ◽  
Dimethyl Ester ◽  
Polymer Chains ◽  
Coordination Geometry ◽  
One Dimensional ◽  
The Difference ◽  
Title One

The isotypic title one-dimensional coordination polymers, [CdCl2(C18H14N4O4)]n, (I), and [HgCl2(C18H14N4O4)]n, (II), are, respectively, the cadmium(II) and mercury(II) complexes of the dimethyl ester of 5,6-bis(pyridin-2-yl)pyrazine-2,3-dicarboxylic acid. In both compounds, the metal ions are located on a twofold rotation axis and a second such axis bisects the Car—Carbonds of the pyrazine ring. The metal ions are bridged by binding to the N atoms of the two pyridine rings and have anMN2Cl2bisphenoidal coordination geometry. The metal–Npyrazinedistances are much longer than the metal–Npyridinedistances; the difference is 0.389 (2) Å for the Cd—N bonds but only 0.286 (5) Å for the Hg—N bond lengths. In the crystals of both compounds, the polymer chains are linkedviapairs of C—H...Cl hydrogen bonds, forming corrugated slabs parallel to theacplane.

Expansion of hot plasma with Kappa distribution in coronal flare sources

2021 ◽  
Author(s):  
Jan Benáček ◽  
Marian Karlický
Keyword(s):  
Langmuir Wave ◽  
Maxwellian Distribution ◽  
Double Layers ◽  
Kappa Distribution ◽  
One Dimensional ◽  
X Ray ◽  
Particle In Cell ◽  
Hot Plasma ◽  
The Difference ◽  
Field Lines

<p>We study how hot plasma that is released during a solar flare can be confined in its source and interact with surrounding colder plasma. The X-ray emission of coronal flare sources is well explained using Kappa velocity distribution. Therefore, we compare the difference in the confinement of plasma with Kappa and Maxwellian distribution. We use a 3D Particle-in-Cell code, which is large along magnetic field lines, effectively one-dimensional, but contains all electromagnetic effects. In the case with Kappa distribution, contrary to Maxwellian distribution, we found formation of several thermal fronts associated with double-layers that suppress particle fluxes. As the Kappa distribution of electrons forms an extended tail, more electrons are not confined by the first front and cause formation of multiple fronts. A beam of electrons from the hot part is formed at each front; it generates return current, Langmuir wave density depressions, and a double layer with a higher potential step than in the Maxwellian case. We compare the Kappa and Maxwellian cases and discuss how these processes could be observed.</p>

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