Vlasov Equation In Magnetic Field

The linearized Vlasov equation for a plasma system in a uniform magnetic field and the corresponding linear Vlasov operator are studied. The spectrum and the corresponding eigenfunctions of the Vlasov operator are found. The spectrum of this operator consists of two parts: one is continuous and real; the other is discrete and complex. Interestingly, the real eigenvalues are infinitely degenerate, which causes difficulty solving this initial value problem by using the conventional eigenfunction expansion method. Finally, the Vlasov equation is solved by the resolvent method.Comment: 15 page

Variational data assimilation for the initial-value dynamo problem

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries

PKS 1830-211: A Possible Compound Gravitational Lens

Measurements of the properties of gravitational lenses have the power to tell us what sort of universe we live in. The brightest known radio Einstein ring/gravitational lens PKS 1830-211 (Jauncey et al., 1991), whilst obscured by our Galaxy at optical wavelengths, has recently been shown to contain absorption at the millimetre waveband at a redshift of 0.89 (Wiklind and Combes, 1996a). We report the detection of a new absorption feature, most likely due to neutral hydrogen in a second redshift system at z = 0.19. Follow-up VLBI observations have spatially resolved the absorption and reveal it to cover the NE compact component and part of the lower surface brightness ring. This new information, together with existing evidence of the unusual VLBI radio structure and difficulties in modeling the lensing system, points to the existence of a second lensing galaxy along our line of sight and implies that PKS 1830-211 may be a compound gravitational lens.Comment: 8 pages, 2 figures, LaTeX (aasms4.sty). Accepted for publication in ApJ Letters. Preprint also available at http://kerr.phys.utas.edu.au/preprints

New Interstellar Dust Models Consistent with Extinction, Emission, and Abundance Constraints

We present new interstellar dust models which have been derived by simultaneously fitting the far-ultraviolet to near-infrared extinction, the diffuse infrared (IR) emission and, unlike previous models, the elemental abundance constraints on the dust for different interstellar medium abundances, including solar, F and G star, and B star abundances. The fitting problem is a typical ill-posed inversion problem, in which the grain size distribution is the unknown, which we solve by using the method of regularization. The dust model contains various components: PAHs, bare silicate, graphite, and amorphous carbon particles, as well as composite particles containing silicate, organic refractory material, water ice, and voids. The optical properties of these components were calculated using physical optical constants. As a special case, we reproduce the Li & Draine (2001) results, however their model requires an excessive amount of silicon, magnesium, and iron to be locked up in dust: about 50 ppm (atoms per million of H atoms), significantly more than the upper limit imposed by solar abundances of these elements, about 34, 35, and 28 ppm, respectively. A major conclusion of this paper is that there is no unique interstellar dust model that simultaneously fits the observed extinction, diffuse IR emission, and abundances constraints.Comment: 70 pages, 23 figures, accepted for publication in the Astrophysical Journal Supplemen

Business cycles, international trade and capital flows: Evidence from Latin America

This paper adopts a flexible framework to assess both short- and long-run business cycle linkages between six Latin American (LA) countries and the four largest economies in the world (namely the US, the Euro area, Japan and China) over the period 1980:I-2011:IV. The result indicate that within the LA region there are considerable differences between countries, success stories coexisting with extremely vulnerable economies. They also show that the LA region as a whole is largely dependent on external developments, especially in the years after the great recession of 2008 and 2009. The trade channel appears to be the most important source of business cycle comovement, whilst capital flows are found to have a limited role, especially in the very short run

Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data

The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The results suggest that atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at http://neon.cchem.berkeley.edu/~dan