(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves

Via the BGG correspondence a simplicial complex Delta on [n] is transformed into a complex of coherent sheaves on P^n-1. We show that this complex reduces to a coherent sheaf F exactly when the Alexander dual Delta^* is Cohen-Macaulay. We then determine when both Delta and Delta^* are Cohen-Macaulay. This corresponds to F being a locally Cohen-Macaulay sheaf. Lastly we conjecture for which range of invariants of such Delta it must be a cone.Comment: 16 pages, some minor change

Gauge invariance in two-particle scattering

It is shown how gauge invariance is obtained for the coupling of a photon to a two-body state described by the solution of the Bethe-Salpeter equation. This is illustrated both for a complex scalar field theory and for interaction kernels derived from chiral effective Lagrangians.Comment: 16 pages, 2 figures, references added and commented o

Three-dimensional compressible turbulent computations for a diffusing S-duct

The purpose of the present study was to evaluate the capability of the computational fluid dynamics computer program PARC3D to model flow in a typical diffusing subsonic S-duct, with strong secondary flows. This evaluation is needed to provide confidence in the analysis of aircraft inlets, which have similar geometries. The performance predictions include total pressure profiles, static pressures, velocity profiles, boundary layer data, and skin friction data. Flow in the S-duct is subsonic, and the boundary layers are assumed to be turbulent. The results for both H and O grid solutions, are compared with existing test data

Three-dimensional compressible turbulent computations for a nondiffusing S-duct

The PARC3D code was used to compute the compressible turbulent flow within a three dimensional, nondiffusing S-duct. A frame of reference is provided for future computational fluid dynamics studies of internal flows with strong secondary flows and provides an understanding of the performance characteristics of a typical S-duct with attached flow. The predicted results, obtained with both H- and O-grids, are compared with the experimental wall pressure, static and total pressure fields, and velocity vectors. Additionally, computed boundary layer thickness, velocity profiles in wall coordinates, and skin friction values are presented

Mitochondria and Metabolism in Right Heart Failure

Heart failure (HF) is a clinically complex and heterogenous disease characterized by an inability of the heart to pump sufficient blood to the periphery. As such, it has historically been thought of and studied as a disease of the left ventricle (LV). While LV failure is the most common form of HF, it is the ability of the right heart to function that predicts survival in many clinical settings. Extrapolation of mechanisms of left HF to the right ventricle (RV) has yet to prove fruitful in identification of therapeutic approaches, in large part due to a lack of basic mechanistic understanding of the RV which is embryologically, anatomically, and physiologically distinct from the LV. The failing LV is characterized by mitochondrial dysfunction and a metabolic switch, both of which contribute to an energetically starved heart with poor contractile ability. These mechanisms, however, are far less described in the failing RV. The purpose of this chapter is to present the current literature examining the role of mitochondria and metabolism in the healthy right heart, treatments to target deficits in the failing RV, and to identify knowledge gaps for future research in this clinically important area