Direct 3D Tomographic Reconstruction and Phase-Retrieval of Far-Field Coherent Diffraction Patterns

We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm. We demonstrate the performance of our proposed method with simulation studies

Multi-Kˉ\bar{K} nuclei and kaon condensation

We extend previous relativistic mean-field (RMF) calculations of multi-$\bar K$ nuclei, using vector boson fields with SU(3) PPV coupling constants and scalar boson fields constrained phenomenologically. For a given core nucleus, the resulting $\bar K$ separation energy $B_{\bar K}$, as well as the associated nuclear and $\bar K$-meson densities, saturate with the number $\kappa$ of $\bar K$ mesons for $\kappa > \kappa_{\rm sat} \sim 10$. Saturation appears robust against a wide range of variations, including the RMF nuclear model used and the type of boson fields mediating the strong interactions. Because $B_{\bar K}$ generally does not exceed 200 MeV, it is argued that multi-$\bar K$ nuclei do not compete with multihyperonic nuclei in providing the ground state of strange hadronic configurations and that kaon condensation is unlikely to occur in strong-interaction self-bound strange hadronic matter. Last, we explore possibly self-bound strange systems made of neutrons and ${\bar K}^0$ mesons, or protons and $K^-$ mesons, and study their properties.Comment: 21 pages, 8 figures, revised text and reference

The treatment of zero eigenvalues of the matrix governing the equations of motion in many-body Green's function theory

The spectral theorem of many-body Green's function theory relates thermodynamic correlations to Green's functions. More often than not, the matrix governing the equations of motion has zero eigenvalues. In this case, the standard text-book approach requires both commutator and anti-commutator Green's functions to obtain equations for that part of the correlation which does not lie in the null space of the matrix. In this paper, we show that this procedure fails if the projector onto the null space is dependent on the momentum vector. We propose an alternative formulation of the theory in terms of the non-null space alone and we show that a solution is possible if one can find a momentum-independent projector onto some subspace of the non-null space. To do this, we enlist the aid of the singular value decomposition (SVD) of the equation of motion matrix in order to project out the null space, thus reducing the size of the matrix and eliminating the need for the anti-commutator Green's function. We extend our previous work, dealing with a ferromagnetic Heisenberg monolayer and a momentum-independent projector onto the null space, where both multilayer films and a momentum-dependent projector are considered. We develop the numerical methods capable of handling these cases and offer a computational algorithmus that should be applicable to any similar problem arising in Green's function theory.Comment: 16 pages, 7 figure

Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics, with zero cosmological constant

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras-McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras-McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we are able to obtain complete agreement with the results obtained in intrinsic coordinates. In particular, we have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.Comment: Extended version of GRG publication, with some typos etc correcte

VISIR-VLT high resolution study of the extended emission of four obscured post-AGB candidates

The onset of the asymmetry of planetary nebulae (PNe) is expected to occur during the late Asymptotic Giant Branch (AGB) and early post-AGB phases of low- and intermediate-mass stars. Among all post-AGB objects, the most heavily obscured ones might have escaped the selection criteria of previous studies detecting extreme axysimmetric structures in young PNe. Since the most heavily obscured post-AGB sources can be expected to descend from the most massive PN progenitors, these should exhibit clear asymmetric morphologies. We have obtained VISIR-VLT mid-IR images of four heavily obscured post-AGB objects barely resolved in previous Spitzer IRAC observations to analyze their morphology and physical conditions across the mid-IR. The VISIR-VLT images have been deconvolved, flux calibrated, and used to construct RGB composite pictures as well as color and optical depth maps that allow us to study the morphology and physical properties of the extended emission of these sources. We have detected extended emission from the four objects in our sample and resolved it into several structural components that are greatly enhanced in the temperature and optical depth maps. They reveal the presence of asymmetry in three young PNe (IRAS 15534-5422, IRAS 17009-4154, and IRAS 18454+0001), where the asymmetries can be associated with dusty torii and slightly bipolar outflows. The fourth source (IRAS 18229-1127), a possible post-AGB star, is better described as a rhomboidal detached shell. The heavily obscured sources in our sample do not show extreme axisymmetric morphologies. This is at odds with the expectation of highly asymmetrical morphologies in post-AGB sources descending from massive PN progenitors. The sources presented in this paper may be sampling critical early phases in the evolution of massive PN progenitors, before extreme asymmetries develop.Comment: 9 pages, 4 figure

Equilibrium onions?

We demonstrate the possibility of a stable equilibrium multi-lamellar ("onion") phase in pure lamellar systems (no excess solvent) due to a sufficiently negative Gaussian curvature modulus. The onion phase is stabilized by non-linear elastic moduli coupled to a polydisperse size distribution (Apollonian packing) to allow space-filling without appreciable elastic distortion. This model is compared to experiments on copolymer-decorated lamellar surfactant systems, with reasonable qualitative agreement

The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry

The relation of the recently proposed E(5) critical point symmetry with the interacting boson model is investigated. The large-N limit of the interacting boson model at the critical point in the transition from U(5) to O(6) is obtained by solving the Richardson equations. It is shown explicitly that this algebraic calculation leads to the same results as the solution of the Bohr differential equation with a $\beta^4$ potential.Comment: Accepted in PR