Harris sheet solution for magnetized quantum plasmas

We construct an infinite family of one-dimensional equilibrium solutions for purely magnetized quantum plasmas described by the quantum hydrodynamic model. The equilibria depends on the solution of a third-order ordinary differential equation, which is written in terms of two free functions. One of these free functions is associated to the magnetic field configuration, while the other is specified by an equation of state. The case of a Harris sheet type magnetic field, together with an isothermal distribution, is treated in detail. In contrast to the classical Harris sheet solution, the quantum case exhibits an oscillatory pattern for the density.Comment: 2 figure

Variational Method for the Three-Dimensional Many-Electron Dynamics of Semiconductor Quantum Wells

The three-dimensional nonlinear dynamics of an electron gas in a semiconductor quantum well is analyzed in terms of a self-consistent fluid formulation and a variational approach. Assuming a time-dependent localized profile for the fluid density and appropriated spatial dependences of the scalar potential and fluid velocity, a set of ordinary differential equations is derived. In the radially symmetric case, the prominent features of the associated breathing mode are characterized

Towards a “market continuum”? Structural models and interaction between credit and equity markets.

The theory of the firm developed by Merton in the 1970s shows how the two financing instruments used by firms, i.e. equity and debt may be viewed as options on the value of their assets. Thus, a shareholder may be regarded as a holder of a call option on the firm’s assets, while a lender may be seen as a seller of a put option on these same assets. So-called structural models derived from this theory have been developed in recent years. They formalise the relationship between equity and debt, and more specifically, endeavour to assess the credit risk attached to each individual issuer on the basis of accounting data, such as its level of debt, and equity market data, such as volatility and stock prices. This article aims to describe these models and analyse the effect of the use of these models on capital markets from the perspective of financial stability. By fostering interactions between asset classes, their increased use has opened up the different market segments and, ultimately, has contributed to the creation of a market continuum. This type of quantitative analysis is thus likely to improve the way financial asset prices are formed, making relative asset prices more coherent and homogeneous. Developing models based on this approach is nevertheless a complex task and the relevance of this whole approach may be called into question if it gives rise to oversimplification or excessive confidence in the signals produced by such models. Structural models add to the spectrum of instruments for credit risk analysis at market participants’ disposal, but are not intended to replace them.

Connection between the two branches of the quantum two-stream instability across the k space

The stability of two quantum counter-streaming electron beams is investigated within the quantum plasma fluid equations for arbitrarily oriented wave vectors. The analysis reveals that the two quantum two-stream unstable branches are indeed connected by a continuum of unstable modes with oblique wave vectors. Using the longitudinal approximation, the stability domain for any k is analytically explained, together with the growth rate

Comment on "A note on the construction of the Ermakov-Lewis invariant"

We show that the basic results on the paper referred in the title [J. Phys. A: Math. Gen. v. 35 (2002) 5333-5345], concerning the derivation of the Ermakov invariant from Noether symmetry methods, are not new

Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities

The interaction of a plane weak shock wave with a single discrete gaseous inhomogeneity is studied as a model of the mechanisms by which finite-amplitude waves in random media generate turbulence and intensify mixing. The experiments are treated as an example of the shock-induced Rayleigh-Taylor instability. or Richtmyer-Meshkov instability, with large initial distortions of the gas interfaces. The inhomogeneities are made by filling large soap bubbles and cylindrical refraction cells (5 cm diameter) whose walls are thin plastic membranes with gases both lighter and heavier than the ambient air in a square (8.9 cm side shock-tube text section. The wavefront geometry and the deformation of the gas volume are visualized by shadowgraph photography. Wave configurations predicted by geometrical acoustics, including the effects of refraction, reflection and diffraction, are compared to the observations. Departures from the predictions of acoustic theory are discussed in terms of gasdynamic nonlinearity. The pressure field on the axis of symmetry downstream of the inhomogeneity is measured by piezoelectric pressure transducers. In the case of a cylindrical or spherical volume filled with heavy low-sound-speed gas the wave which passes through the interior focuses just behind the cylinder. On the other hand, the wave which passes through the light high-sound-speed volume strongly diverges. Visualization of the wavefronts reflected from and diffracted around the inhomogeneities exhibit many features known in optical and acoustic scattering. Rayleigh-Taylor instability induced by shock acceleration deforms the initially circular cross-section of the volume. In the case of the high-sound-speed sphere, a strong vortex ring forms and separates from the main volume of gas. Measurements of the wave and gas-interface velocities are compared to values calculated for one-dimensional interactions and for a simple model of shock-induced Rayleigh-Taylor instability. The circulation and Reynolds number of the vortical structures are calculated from the measured velocities by modeling a piston vortex generator. The results of the flow visualization are also compared with contemporary numerical simulations