EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments

We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and reconstruction, efficient solution of the forward problem and present and future reconstruction algorithms. We also suggest common pitfalls or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of EIT, Manchester, UK, 200

Turbulent Convection in Stellar Interiors. II. The Velocity Field

We analyze stellar convection with the aid of 3D hydrodynamic simulations, introducing the turbulent cascade into our theoretical analysis. We devise closures of the Reynolds-decomposed mean field equations by simple physical modeling of the simulations (we relate temperature and density fluctuations via coefficients); the procedure (CABS, Convection Algorithms Based on Simulations) is terrestrially testable and is amenable to systematic improvement. We develop a turbulent kinetic energy equation which contains both nonlocal and time dependent terms, and is appropriate if the convective transit time is shorter than the evolutionary time scale. The interpretation of mixing-length theory (MLT) as generally used in astrophysics is incorrect; MLT forces the mixing length to be an imposed constant. Direct tests show that the damping associated with the flow is that suggested by Kolmogorov. The eddy size is approximately the depth of the convection zone, and this dissipation length corresponds to the "mixing length". New terms involving local heating by turbulent dissipation should appear in the stellar evolution equations. The enthalpy flux ("convective luminosity") is directly connected to the buoyant acceleration, and hence the velocity scale. MLT tends to systematically underestimate this velocity scale. Quantitative comparison with a variety of 3D simulations reveals a previously recognized consistency. Examples of application to stellar evolution will be presented in subsequent papers in this series.Comment: 47 pages, 7 figures, accepted by Ap

Scattering in Multilayered Structures: Diffraction from a Nanohole

The spectral expansion of the Green's tensor for a planar multilayered structure allows us to semi analytically obtain the angular spectrum representation of the field scattered by an arbitrary dielectric perturbation present in the structure. In this paper we present a method to find the expansion coefficients of the scattered field, given that the electric field inside the perturbation is available. The method uses a complete set of orthogonal vector wave functions to solve the structure's vector wave equation. In the two semi-infinite bottom and top media, those vector wave functions coincide with the plane-wave basis vectors, including both propagating and evanescent components. The technique is used to obtain the complete angular spectrum of the field scattered by a nanohole in a metallic film under Gaussian illumination. We also show how the obtained formalism can easily be extended to spherically and cylindrically multilayered media. In those cases, the expansion coefficients would multiply the spherical and cylindrical vector wave functions.Comment: 9 pages, 5 figure

The SWELLS survey. IV. Precision measurements of the stellar and dark matter distributions in a spiral lens galaxy

We construct a fully self-consistent mass model for the lens galaxy J2141 at z=0.14, and use it to improve on previous studies by modelling its gravitational lensing effect, gas rotation curve and stellar kinematics simultaneously. We adopt a very flexible axisymmetric mass model constituted by a generalized NFW dark matter halo and a stellar mass distribution obtained by deprojecting the MGE fit to the high-resolution K'-band LGSAO imaging data of the galaxy, with the (spatially constant) M/L ratio as a free parameter. We model the stellar kinematics by solving the anisotropic Jeans equations. We find that the inner logarithmic slope of the dark halo is weakly constrained (gamma = 0.82^{+0.65}_{-0.54}), and consistent with an unmodified NFW profile. We infer the galaxy to have (i) a dark matter fraction within 2.2 disk radii of 0.28^{+0.15}_{-0.10}, independent of the galaxy stellar population, implying a maximal disk for J2141; (ii) an apparently uncontracted dark matter halo, with concentration c_{-2} = 7.7_{-2.5}^{+4.2} and virial velocity v_{vir} = 242_{-39}^{+44} km/s, consistent with LCDM predictions; (iii) a slightly oblate halo (q_h = 0.75^{+0.27}_{-0.16}), consistent with predictions from baryon-affected models. Comparing the stellar mass inferred from the combined analysis (log_{10} Mstar/Msun = 11.12_{-0.09}^{+0.05}) with that inferred from SPS modelling of the galaxies colours, and accounting for a cold gas fraction of 20+/-10%, we determine a preference for a Chabrier IMF over Salpeter IMF by a Bayes factor of 5.7 (substantial evidence). We infer a value beta_{z} = 1 - sigma^2_{z}/sigma^2_{R} = 0.43_{-0.11}^{+0.08} for the orbital anisotropy parameter in the meridional plane, in agreement with most studies of local disk galaxies, and ruling out at 99% CL that the dynamics of this system can be described by a two-integral distribution function. [Abridged]Comment: Accepted for publication in MNRAS. 17 pages, 9 figure