Transverse electrical conductivity of a quantum collisional plasma in the Mermin approach

We derive formulas for the transverse electrical conductivity and the permittivity in a quantum collisional plasma using the kinetic equation for the density matrix in the relaxation approximation in the momentum space. We show that the derived formula becomes the classical formula when the Planck constant tends to zero and that when the electron collision rate tends to zero (i.e., the plasma becomes collisionless), the derived formulas become the previously obtained Lindhard formulas. We also show that when the wave number tends to zero, the quantum conductivity becomes classical. We compare the obtained conductivity with the conductivity obtained by Lindhard and with the classical conductivity     

Global well-posedness of the two-dimensional incompressible magnetohydrodynamics system with variable density and electrical conductivity

Studied in this paper is the Cauchy problem of the two-dimensional magnetohydrodynamics system with inhomogeneous density and electrical conductivity. It is shown that the 2-D incompressible inhomogeneous magnetohydrodynamics system with a constant viscosity is globally well-posed for a generic family of the variations of the initial data and an inhomogeneous electrical conductivity. Moreover, it is established that the system is globally well-posed in the critical spaces if the electrical conductivity is homogeneous.     

On measurement of electrical conductivity

A complete uniform asymptotic expansion is found for the integral ?_S ?² udxdy, where u is the solution of the Neumann problem with a delta-function-like derivative on the boundary. A physical application of the result is discussed.     

An analysis of two-dimensional aligned-field magnetogasdynamic flows

Zusammenfassung Eine zähigkeitslose Flüssigkeit endlicher Leitfähigkeit wird in einem Zustand stationärer zweidimensionaler Bewegung betrachtet, d.h. der Geschwindigkeitsvektor besitzt eine Nullkomponente in einer bestimmten Richtung. Eine Analyse der Strömung wird vorgenommen, wenn die Magnet- und Geschwindigkeitsfelder überall parallel sind. Zwei mögliche Gruppen von Gebietsströmungen sind festzustellen: a) wo das Magnetfeld drallfrei ist, b) wo die Ladungsdichte überall null ist. Durch Anwendung komplexer Variabeln werden die allgemeinen Gleichungen in beiden Fällen beträchtlich vereinfacht; dadurch lassen sich die notwendigen parametrischen Formen der betreffenden physikalischen Grössen bestimmen. Dieses Verfahren lässt sich auch auf andere Arten von Strömungsfeldern anwenden.     

On subsonic compressible flows in a two-dimensional duct

This paper concerns subsonic flows passing a two-dimensional duct for the steady compressible Euler system. If the Bernoulli constant is uniform in the flow field, the density at the entry and both the pressures at the entrance and the exit are given, we show that the problem is generally ill-posed; but if we give the pressure at the exit with a constant difference, then under the same other conditions as above we establish the existence of subsonic flows.     

The electrical conductivity of silica sols

Proceedings - Mathematical Sciences - In the case of silica sols prepared by peptizing silica gel with ammonia, ammonium silicate is the stabilizing electrolyte. When the sols are allowed to age,...     

Langmuir oscillations in two-dimensional plasma

Translated from Matematicheskie Modeli i Optimizatsiya Vychislitel'nykh Algoritmov, pp. 199–206, 1993.     

Blast waves in magneto-gas-dynamics with finite electrical conductivity

Zusammenfassung Die Arbeit befasst sich mit dem Einfluss endlicher elektrischer Leitfähigkeit auf eine Stosswelle in der Magneto-Gasdynamik. Andere dissipative Mechanismen werden vernachlässigt. Die zur Stossfront tangentiale Komponente des Magnetfeldes beeinflusst die änderung des Wirbels und den Strom durch die Welle. Für den Fall einer Punktquelle werden Potenzgesetze erhalten, die denjenigen in Ähnlichkeitslösungen verwandt sind.

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This work was done at the Iowa State University, Ames, Iowa, towards partial fulfilment of the requirements for the degree of Ph. D. of the first author.     

Homogenization of random transport along periodic two-dimensional flows

We present a model for random transport along periodic two-dimensional flows and use the concept of rotation numbers from dynamical systems to prove a functional central limit theorem for this model. The limiting law turns out to be a stable Lévy process.     

Subsonic irrotational flows in a two-dimensional finitely long curved nozzle

This is a continuation of our previous paper Du et al. (http://www.ims.cuhk.edu.hk/publications/reports/2012-06.pdf), where we have characterized a set of physical boundary conditions that ensures the existence and uniqueness of subsonic irrotational flow in a flat nozzle. In this paper, we will investigate the influence of the incoming flow angle and the geometry structure of the nozzle walls on subsonic flows in a finitely long curved nozzle. It turns out to be interesting that the incoming flow angle and the angle of inclination of nozzle walls play the same role as the end pressure for the stabilization of subsonic flows. In other words, the L ² and L ^∞ bounds of the derivative of these two quantities cannot be too large, similar as we have indicated in Du et al. (http://www.ims.cuhk.edu.hk/publications/reports/2012-06.pdf) for the end pressure. The curvatures of the nozzle walls will also play an important role in the stability of the subsonic flow.     

Well-posedness of transonic characteristic discontinuities in two-dimensional steady compressible Euler flows

In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total variation of the incoming supersonic flow over a solid right wedge. It is a free boundary problem in Eulerian coordinates and, across the free boundary (characteristic discontinuity), the Euler equations are of elliptic–hyperbolic composite-mixed type. In this paper, we further prove that such a transonic characteristic discontinuity solution is unique and L ¹–stable with respect to the small perturbation of the incoming supersonic flow in Lagrangian coordinates.     

Crisis induced intermittency in the electrical conductivity of TlInTe2

The electrical conductivity of the ternary semiconductor TlInTe₂ exhibits irregular behaviour in a broad range of its S-shaped I–V characteristics. Just above the critical current value intermittent jumping between two or more levels of conductivity is observed. Statistical examinations of the jump heights and of the time intervals between jumps (the laminar lengths of the system) show power law distributions. Furthermore these laminar lengths also exhibit a power law dependence on I–I_c. These observations indicate that the system is governed by a form of crisis induced intermittency, which is caused by the merging of two or more attractors corresponding to different conductivity levels. The analysis of the dynamic behaviour using the Grassberger and Procaccia algorithm shows that these attractors are high dimensional.     

A vortex method for computing two-dimensional inviscid incompressible flows

A vortex method is suggested for computing two-dimensional inviscid incompressible flows in a closed domain with a possible flow through it. An algorithm for searching for stable steady vortex configurations is described. The method developed is used to study the dynamics of the Chaplygin-Lamb dipole in a rectangular channel in various flow regimes.     

Exact topological classification of Hamiltonian flows on smooth two-dimensional surfaces

The present paper contains an exact topological classification of all nondegenerate Hamiltonian systems on smooth closed two-dimensional surfaces. Bibliography: 8 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 235, 1900, pp. 22–53.     

Global subsonic compressible flows through a two-dimensional periodic duct

We deal with two-dimensional compressible potential subsonic flows in an infinitely long duct with periodic walls. It is shown that there exists a critical value of mass flux: If the incoming mass flux is less than the critical value, then the flow is also periodic. Existence, uniqueness and regularity of the periodic solution are obtained by techniques of elliptic equations.