Analytic and Fast Numerical Solutions and Approximations for Cross-Association Models within Statistical Association Fluid Theory

1998 ◽  
Vol 37 (12) ◽  
pp. 4889-4892 ◽  
Author(s):  
Thomas Kraska
Keyword(s):  
Numerical Solutions ◽  
Statistical Association ◽  
Association Models ◽  
Fluid Theory ◽  
Statistical Association Fluid Theory

Modeling the Viscosity of Ionic Liquids with the Electrolyte Perturbed-Chain Statistical Association Fluid Theory

2014 ◽  
Vol 53 (52) ◽  
pp. 20258-20268 ◽  
Author(s):  
Gulou Shen ◽  
Christoph Held ◽  
Jyri-Pekka Mikkola ◽  
Xiaohua Lu ◽  
Xiaoyan Ji
Keyword(s):  
Ionic Liquids ◽  
Statistical Association ◽  
Fluid Theory ◽  
Statistical Association Fluid Theory

scholarly journals Modelling of mirror mode structures as propagating slow magnetosonic solitons

2009 ◽  
Vol 27 (12) ◽  
pp. 4379-4389 ◽  
Author(s):  
K. Stasiewicz ◽  
C. Z. Cheng
Keyword(s):  
Numerical Modelling ◽  
Excellent Agreement ◽  
Plasma Flow ◽  
Numerical Solutions ◽  
Small Subset ◽  
Instability Condition ◽  
Magnetic Pulsations ◽  
Fluid Theory ◽  
Mirror Mode ◽  
Two Fluid

Abstract. Cluster measurements in the magnetosheath with spacecraft separations of 2000 km indicate that magnetic pulsations interpreted as mirror mode structures are not frozen in plasma flow, but do propagate with speeds of up to ~50 km/s. Properties of these pulsations are shown to be consistent with propagating slow magnetosonic solitons. By using nonlinear two fluid theory we demonstrate that the well known classical mirror instability condition corresponds to a small subset in a continuum of exponentially varying solutions. With the measured plasma moments we have determined parameters of the polybaric pressure model in the region of occurrence of mirror type structures and applied it to numerical modelling of these structures. In individual cases we obtain excellent agreement between observed mirror mode structures and numerical solutions for magnetosonic solitons.

scholarly journals Disruption of magnetospheric current sheet by quasi-electrostatic field

2009 ◽  
Vol 27 (5) ◽  
pp. 1941-1950 ◽  
Author(s):  
W. W. Liu ◽  
J. Liang
Keyword(s):  
Current Sheet ◽  
Drift Velocity ◽  
Electrostatic Field ◽  
Numerical Solutions ◽  
External Perturbation ◽  
Ion Drift ◽  
Current Disruption ◽  
Local Current ◽  
Fluid Theory ◽  
Two Fluid

Abstract. Recent observational evidence has indicated that local current sheet disruptions are excited by an external perturbation likely associated with the kinetic ballooning (KB) instability initiating at the transition region separating the dipole- and tail-like geometries. Specifically a quasi-electrostatic field pointing to the neutral sheet was identified in the interval between the arrival of KB perturbation and local current disruption. How can such a field drive the local current sheet unstable? This question is considered through a fluid treatment of thin current sheet (TCS) where the generalized Ohm's law replaces the frozen-in-flux condition. A perturbation with the wavevector along the current is applied, and eigenmodes with frequency much below the ion gyrofrequency are sought. We show that the second-order derivative of ion drift velocity along the thickness of the current sheet is a critical stability parameter. In an E-field-free Harris sheet in which the drift velocity is constant, the current sheet is stable against this particular mode. As the electrostatic field grows, however, potential for instability arises. The threshold of instability is identified through an approximate analysis of the theory. For a nominal current sheet half-thickness of 1000 km, the estimated instability threshold is E~4 mV/m. Numerical solutions indicate that the two-fluid theory gives growth rate and wave period consistent with observations.

Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

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