Vertex corrections in localized and extended systems

Within many-body perturbation theory we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a DFT-LDA Green's function. The vertex appears in two places -- in the screened Coulomb interaction, W, and in the self-energy, \Sigma -- and we obtain a systematic discrimination of these two effects by turning the vertex in \Sigma on and off. We also make comparisons to standard GW results within the usual random-phase approximation (RPA), which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate only limited improvements over standard GW. For jellium we observe marked improvement in the quasiparticle band width when the vertex is included only in W, whereas turning on the vertex in \Sigma leads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in W is a valid way to improve quasiparticle energy calculations, while the vertex in \Sigma is unphysical, and points the way to development of improved vertices for ab initio electronic structure calculations.Comment: 8 Pages, 6 Figures. Updated with quasiparticle neon results, extended conclusions and references section. Minor changes: Updated references, minor improvement

The Three-Dimensional Structure of Interior Ejecta in Cassiopeia A at High Spectral Resolution

We used the Spitzer Space Telescope's Infrared Spectrograph to create a high resolution spectral map of the central region of the Cassiopeia A supernova remnant, allowing us to make a Doppler reconstruction of its 3D structure. The ejecta responsible for this emission have not yet encountered the remnant's reverse shock or the circumstellar medium, making it an ideal laboratory for exploring the dynamics of the supernova explosion itself. We observe that the O, Si, and S ejecta can form both sheet-like structures as well as filaments. Si and O, which come from different nucleosynthetic layers of the star, are observed to be coincident in velocity space in some regions, and separated by 500 km/s or more in others. Ejecta traveling toward us are, on average, ~900 km/s slower than the material traveling away from us. We compare our observations to recent supernova explosion models and find that no single model can simultaneously reproduce all the observed features. However, models of different supernova explosions can collectively produce the observed geometries and structures of the interior emission. We use the results from the models to address the conditions during the supernova explosion, concentrating on asymmetries in the shock structure. We also predict that the back surface of Cassiopeia A will begin brightening in ~30 years, and the front surface in ~100 years.Comment: 35 pages, 16 figures, accepted to Ap

The Lillie Mae: A Capital Investment Project In Riverboat Restoration

This case involves a proposed capital investment project. It was written for use in an introductory business finance course to present students a capital budgeting scenario involving elements of both an expansion project and a replacement project that is more complex than the usual textbook problems. It also provides students an exercise in the application of standard spreadsheet software to a common analytical problem in corporate finance, namely, a proposed capital expenditure

The Lillie Mae: A Capital Investment Project In Riverboat Restoration

This case involves a proposed capital investment project.  It was written for use in an introductory business finance course to present students a capital budgeting scenario involving elements of both an expansion project and a replacement project that is more complex than the usual textbook problems.  It also provides students an exercise in the application of standard spreadsheet software to a common analytical problem in corporate finance, namely, a proposed capital expenditure

A Paradox Within The Time Value Of Money: A Critical Thinking Exercise For Finance Students

This study presents a paradox within the time value of money (TVM), namely, that the interest-principal sequence embedded in the payment stream of an amortized loan is exactly the opposite of the interest-principal sequence implicit in the present value of a matching annuity.  We examine this inverse sequence, both mathematically and intuitively, and argue that it provides an excellent exercise for finance students to explore, both to enhance their critical thinking skills as well as to strengthen their understanding of TVM concepts.  Additionally, such an exercise will involve them actively in the learning process, as mandated by AACSB International’s Eligibility Procedures and Standards for Business Accreditation

Coherent States Formulation of Polymer Field Theory

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well known auxiliary-field (AF) framework, the CS formulation does not contain an embedded non-linear, non-local functional of the auxiliary fields, and the action of the field theory has a fully explicit, finite-order and semi-local polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.Comment: 14pages 8 figure

Mapping the spectral index of Cassiopeia A : evidence for flattening from radio to infrared

Funding: The work of VD is supported by a grant from the NWO graduate programme/GRAPPA-PhD programme. JVHS acknowledges support from the STFC grant ST/R000824/1.Synchrotron radiation from supernova remnants is caused by electrons accelerated through diffusive shock acceleration (DSA). The standard DSA theory predicts an electron spectral index of p = 2, corresponding to a radio spectral index of α = −0.5. An extension of DSA theory predicts that the accelerated particles change the shock structure, resulting in a spectrum that is steeper than p > 2 (α < −0.5) at low energies and flattens with energy. For Cassiopeia A, a synchrotron spectral flattening was previously reported for a small part of the remnant in the mid-infrared regime. Here, we present new measurements for spectral flattening using archival radio (4.72 GHz) and mid-infrared (3.6 μm) data, and we produce a complete spectral index map to investigate the spatial variations within the remnant. We compare this to measurements of the radio spectral index from L-band (1.285 GHz) and C-band (4.64 GHz) maps. Our result shows overall spectral flattening across the remnant (αR-IR ∼ −0.5 to −0.7), to be compared with the radio spectral index of αR = −0.77. The flattest values coincide with the locations of most recent particle acceleration. In addition to overall flattening, we detect a relatively steeper region in the south-east of the remnant (αR-IR ∼ −0.67). We explore whether these locally steeper spectra could be the result of synchrotron cooling, which provides constraints on the local magnetic field strengths and the age of the plasma, suggesting B ≲ 2 mG for an age of 100 yr, and even B ≲ 1 mG using the age of Cas A, in agreement with other estimates.Publisher PDFPeer reviewe

The Three-Dimensional Structure of Cassiopeia A

We used the Spitzer Space Telescope's Infrared Spectrograph to map nearly the entire extent of Cassiopeia A between 5-40 micron. Using infrared and Chandra X-ray Doppler velocity measurements, along with the locations of optical ejecta beyond the forward shock, we constructed a 3-D model of the remnant. The structure of Cas A can be characterized into a spherical component, a tilted thick disk, and multiple ejecta jets/pistons and optical fast-moving knots all populating the thick disk plane. The Bright Ring in Cas A identifies the intersection between the thick plane/pistons and a roughly spherical reverse shock. The ejecta pistons indicate a radial velocity gradient in the explosion. Some ejecta pistons are bipolar with oppositely-directed flows about the expansion center while some ejecta pistons show no such symmetry. Some ejecta pistons appear to maintain the integrity of the nuclear burning layers while others appear to have punched through the outer layers. The ejecta pistons indicate a radial velocity gradient in the explosion. In 3-D, the Fe jet in the southeast occupies a "hole" in the Si-group emission and does not represent "overturning", as previously thought. Although interaction with the circumstellar medium affects the detailed appearance of the remnant and may affect the visibility of the southeast Fe jet, the bulk of the symmetries and asymmetries in Cas A are intrinsic to the explosion.Comment: Accepted to ApJ. 54 pages, 21 figures. For high resolution figures and associated mpeg movie and 3D PDF files, see http://homepages.spa.umn.edu/~tdelaney/pape