Numerical shadow and geometry of quantum states

The totality of normalised density matrices of order N forms a convex set Q_N in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt distance we consider images of orthogonal projections of Q_N onto a two-plane and show that they are similar to the numerical ranges of matrices of order N. For a matrix A of a order N one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold CP^(N-1). We define generalized, mixed-states shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.Comment: 19 pages, 5 figure

Lewis Phenotype in Women With Preterm Labor and Premature Rupture of the Membranes

Objective: The purpose of this study was to evaluate the possible association between Lewis phenotype status in pregnant women and preterm labor (PTL) or preterm rupture of the membranes (PROM)

Coordinates for a High Performance 4:1 Pressure Ratio Centrifugal Compressor

The objective of this program was to define the aerodynamic design and manufacturing coordinates for an advanced 4:1 pressure ratio, single stage centrifugal compressor at a 10 lbm/sec flow size. The approach taken was to perform an exact scale of an existing DDA compressor originally designed at a flow size of 3.655 lbm/sec

Numerical shadows: measures and densities on the numerical range

For any operator $M$ acting on an $N$-dimensional Hilbert space $H_N$ we introduce its numerical shadow, which is a probability measure on the complex plane supported by the numerical range of $M$. The shadow of $M$ at point $z$ is defined as the probability that the inner product $(Mu,u)$ is equal to $z$, where $u$ stands for a random complex vector from $H_N$, satisfying $||u||=1$. In the case of N=2 the numerical shadow of a non-normal operator can be interpreted as a shadow of a hollow sphere projected on a plane. A similar interpretation is provided also for higher dimensions. For a hermitian $M$ its numerical shadow forms a probability distribution on the real axis which is shown to be a one dimensional $B$-spline. In the case of a normal $M$ the numerical shadow corresponds to a shadow of a transparent solid simplex in $R^{N-1}$ onto the complex plane. Numerical shadow is found explicitly for Jordan matrices $J_N$, direct sums of matrices and in all cases where the shadow is rotation invariant. Results concerning the moments of shadow measures play an important role. A general technique to study numerical shadow via the Cartesian decomposition is described, and a link of the numerical shadow of an operator to its higher-rank numerical range is emphasized.Comment: 37 pages, 8 figure

Seismic estimates of turbulent diffusivity and evidence of nonlinear internal wave forcing by geometric resonance in the South China Sea

Author Posting. © American Geophysical Union, 2017. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 122 (2017): 8063–8078, doi:10.1002/2017JC012690.The Luzon Passage generates some of the largest amplitude internal waves in the global ocean as the result of coupling between strong tides, strong stratification, and topography. These internal waves propagate into the South China Sea (SCS) and develop into soliton-like internal wave pulses that are observed by moored instruments and satellite backscatter data. Despite the observation of these waves, little is known of the mechanisms related to their evolution into nonlinear wave pulses. Using seismic data, we find evidence that the geometry of bathymetric conditions between the Heng-Chun and Lan-Yu ridges drive nonlinear internal wave pulse generation. We produce three seismic images and associated maps of turbulent diffusivity to investigate structure around the two ridges and into the SCS. We do not observe large amplitude soliton-like internal waves between the ridges, but do observe one outside the ridges, a finding in accord with the interpretation that wave pulses form due to geometrical resonance. Additionally, we find no evidence for lee wave activity above the ridges in either the seismic images or associated turbulence maps, suggesting an unlikelihood of hydraulic jump driven generation around the ridges. Our results show increased levels of turbulent diffusivity (1) in deep water below 1000 m, (2) associated with internal tide pulses, and (3) near the steep slopes of the Heng-Chun and Lan-Yu ridges as explored in this paper.NSF Grant Number: 0648620; ONR/DEPSCoR Grant Grant Number: DODONR400272018-04-2

Mapping turbulent diffusivity associated with oceanic internal lee waves offshore Costa Rica

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Ocean Science 12 (2016): 601-612, doi:10.5194/os-12-601-2016.Breaking internal waves play a primary role in maintaining the meridional overturning circulation. Oceanic lee waves are known to be a significant contributor to diapycnal mixing associated with internal wave dissipation, but direct measurement is difficult with standard oceanographic sampling methods due to the limited spatial extent of standing lee waves. Here, we present an analysis of oceanic internal lee waves observed offshore eastern Costa Rica using seismic imaging and estimate the turbulent diffusivity via a new seismic slope spectrum method that extracts diffusivities directly from seismic images, using tracked reflections only to scale diffusivity values. The result provides estimates of turbulent diffusivities throughout the water column at scales of a few hundred meters laterally and 10 m vertically. Synthetic tests demonstrate the method's ability to resolve turbulent structures and reproduce accurate diffusivities. A turbulence map of our seismic section in the western Caribbean shows elevated turbulent diffusivities near rough seafloor topography as well as in the mid-water column where observed lee wave propagation terminates. Mid-water column hotspots of turbulent diffusivity show levels 5 times higher than surrounding waters and 50 times greater than typical open-ocean diffusivities. This site has steady currents that make it an exceptionally accessible laboratory for the study of lee-wave generation, propagation, and decay.This work was funded by NSF Grants 0405654 and 0648620, and ONR/DEPSCoR Grant DODONR4002

Ebola Virus Localization in the Macaque Reproductive Tract during Acute Ebola Virus Disease.

Sexual transmission of Ebola virus (EBOV) has been demonstrated more than a year after recovery from the acute phase of Ebola virus disease (EVD). The mechanisms underlying EBOV persistence and sexual transmission are not currently understood. Using the acute macaque model of EVD, we hypothesized EBOV would infect the reproductive tissues and sought to localize the infection in these tissues using immunohistochemistry and transmission electron microscopy. In four female and eight male macaques that succumbed to EVD between 6 and 9 days after EBOV challenge, we demonstrate widespread EBOV infection of the interstitial tissues and endothelium in the ovary, uterus, testis, seminal vesicle, epididymis, and prostate gland, with minimal associated tissue immune response or organ pathology. Given the widespread involvement of EBOV in the reproductive tracts of both male and female macaques, it is reasonable to surmise that our understanding of the mechanisms underlying sexual transmission of EVD and persistence of EBOV in immune-privileged sites would be facilitated by the development of a nonhuman primate model in which the macaques survived past the acute stage into convalescence