PT symmetry and large-N models

Recently developed methods for PT-symmetric models can be applied to quantum-mechanical matrix and vector models. In matrix models, the calculation of all singlet wave functions can be reduced to the solution a one-dimensional PT-symmetric model. The large-N limit of a wide class of matrix models exists, and properties of the lowest-lying singlet state can be computed using WKB. For models with cubic and quartic interactions, the ground state energy appears to show rapid convergence to the large-N limit. For the special case of a quartic model, we find explicitly an isospectral Hermitian matrix model. The Hermitian form for a vector model with O(N) symmetry can also be found, and shows many unusual features. The effective potential obtained in the large-N limit of the Hermitian form is shown to be identical to the form obtained from the original PT-symmetric model using familiar constraint field methods. The analogous constraint field prescription in four dimensions suggests that PT-symmetric scalar field theories are asymptotically free.Comment: 15 pages, to be published in J. Phys. A special issue on Pseudo Hermitian Hamiltonians in Quantum Physic

Extinction of metastable stochastic populations

We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling (scenario A) or attracting (scenario B) point of the deterministic rate equation. In scenario A the metastable stochastic population resides in the vicinity of an attracting fixed point next to the repelling point n=0. In scenario B there is an intermediate repelling point n=n_1 between the attracting point n=0 and another attracting point n=n_2 in the vicinity of which the metastable population resides. The crux of the theory is WKB method which assumes that the typical population size in the metastable state is large. Starting from the master equation, we calculate the quasi-stationary probability distribution of the population sizes and the (exponentially long) mean time to extinction for each of the two scenarios. When necessary, the WKB approximation is complemented (i) by a recursive solution of the quasi-stationary master equation at small n and (ii) by the van Kampen system-size expansion, valid near the fixed points of the deterministic rate equation. The theory yields both entropic barriers to extinction and pre-exponential factors, and holds for a general set of multi-step processes when detailed balance is broken. The results simplify considerably for single-step processes and near the characteristic bifurcations of scenarios A and B.Comment: 19 pages, 7 figure

Final Report: Efficient Databases for MPC Microdata

The purpose of this grant was to develop the theory and practice of high-performance databases for massive streamed datasets. Over the last three years, we have developed fast indexing technology, that is, technology for rapidly ingesting data and storing that data so that it can be efficiently queried and analyzed. During this project we developed the technology so that high-bandwidth data streams can be indexed and queried efficiently. Our technology has been proven to work data sets composed of tens of billions of rows when the data streams arrives at over 40,000 rows per second. We achieved these numbers even on a single disk driven by two cores. Our work comprised (1) new write-optimized data structures with better asymptotic complexity than traditional structures, (2) implementation, and (3) benchmarking. We furthermore developed a prototype of TokuFS, a middleware layer that can handle microdata I/O packaged up in an MPI-IO abstraction

Report on water quality data evaluation and program design services for the James and York rivers in conjunction with the 208 planning program for the Tidewater region of Virginia

The study area considered in this report includes the following: The James River from Fort Monroe to the mouth of the Chickahominy River (statute mile 45) including the small tributaries on the north shore but not the Chickahominy; the York River from its mouth to the confluence of the Mattaponi and Pamunkey at West Point (statute mile 33.5) including the small tributaries along the south shore; and the small drainage area adjacent to Chesapeake Bay lying between the York and James basins. The two rivers included in this basin are Poquoson River and Back River

Clustering in mixing flows

We calculate the Lyapunov exponents for particles suspended in a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time. In this limit Lyapunov exponents are obtained as a power series in epsilon, a dimensionless measure of the particle inertia. Although the perturbation generates an asymptotic series, we obtain accurate results from a Pade-Borel summation. Our results prove that particles suspended in an incompressible random mixing flow can show pronounced clustering when the Stokes number is large and we characterise two distinct clustering effects which occur in that limit.Comment: 5 pages, 1 figur

Evaluating Southern Ocean biological production in two ocean biogeochemical models on daily to seasonal timescales using satellite chlorophyll and O2 / Ar observations

© The Author(s), 2015. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Biogeosciences 12 (2015): 681-695, doi:10.5194/bg-12-681-2015.We assess the ability of ocean biogeochemical models to represent seasonal structures in biomass and net community production (NCP) in the Southern Ocean. Two models are compared to observations on daily to seasonal timescales in four different sections of the region. We use daily satellite fields of chlorophyll (Chl) as a proxy for biomass and in situ observations of O2 and Ar supersaturation (ΔO2 / Ar) to estimate NCP. ΔO2 / Ar is converted to the flux of biologically generated O2 from sea to air (O2 bioflux). All data are aggregated to a climatological year with a daily resolution. To account for potential regional differences within the Southern Ocean, we conduct separate analyses of sections south of South Africa, around the Drake Passage, south of Australia, and south of New Zealand. We find that the models simulate the upper range of Chl concentrations well, underestimate spring levels significantly, and show differences in skill between early and late parts of the growing season. While there is a great deal of scatter in the bioflux observations in general, the four sectors each have distinct patterns that the models pick up. Neither model exhibits a significant distinction between the Australian and New Zealand sectors and between the Drake Passage and African sectors. South of 60° S, the models fail to predict the observed extent of biological O2 undersaturation. We suggest that this shortcoming may be due either to problems with the ecosystem dynamics or problems with the vertical transport of oxygen.This work was supported in part by funding from the National Aeronautic and Space Administration (NASA NNX08AF12G) and the National Science Foundation (NSF OPP-0823101)

Atmospheric potential oxygen: New observations and their implications for some atmospheric and oceanic models

Measurements of atmospheric O2/N2 ratios and CO2 concentrations can be combined into a tracer known as atmospheric potential oxygen (APO ≈ O2/N2 + CO2) that is conservative with respect to terrestrial biological activity. Consequently, APO reflects primarily ocean biogeochemistry and atmospheric circulation. Building on the work of Stephens et al. (1998), we present a set of APO observations for the years 1996-2003 with unprecedented spatial coverage. Combining data from the Princeton and Scripps air sampling programs, the data set includes new observations collected from ships in the low-latitude Pacific. The data show a smaller interhemispheric APO gradient than was observed in past studies, and different structure within the hemispheres. These differences appear to be due primarily to real changes in the APO field over time. The data also show a significant maximum in APO near the equator. Following the approach of Gruber et al. (2001), we compare these observations with predictions of APO generated from ocean O2 and CO2 flux fields and forward models of atmospheric transport. Our model predictions differ from those of earlier modeling studies, reflecting primarily the choice of atmospheric transport model (TM3 in this study). The model predictions show generally good agreement with the observations, matching the size of the interhemispheric gradient, the approximate amplitude and extent of the equatorial maximum, and the amplitude and phasing of the seasonal APO cycle at most stations. Room for improvement remains. The agreement in the interhemispheric gradient appears to be coincidental; over the last decade, the true APO gradient has evolved to a value that is consistent with our time-independent model. In addition, the equatorial maximum is somewhat more pronounced in the data than the model. This may be due to overly vigorous model transport, or insufficient spatial resolution in the air-sea fluxes used in our modeling effort. Finally, the seasonal cycles predicted by the model of atmospheric transport show evidence of an excessive seasonal rectifier in the Aleutian Islands and smaller problems elsewhere. Copyright 2006 by the American Geophysical Union

Evaluation of the Southern Ocean O2/Ar-based NCP estimates in a model framework

Author Posting. © American Geophysical Union, 2013. 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: Biogeosciences 118 (2013): 385–399, doi:10.1002/jgrg.20032.The sea-air biological O2 flux assessed from measurements of surface O2 supersaturation in excess of Ar supersaturation (“O2 bioflux”) is increasingly being used to constrain net community production (NCP) in the upper ocean mixed layer. In making these calculations, one generally assumes that NCP is at steady state, mixed layer depth is constant, and there is no O2 exchange across the base of the mixed layer. The object of this paper is to evaluate the magnitude of errors introduced by violations of these assumptions. Therefore, we examine the differences between the sea-air biological O2 flux and NCP in the Southern Ocean mixed layer as calculated using two ocean biogeochemistry general circulation models. In this approach, NCP is considered a known entity in the prognostic model, whereas O2 bioflux is estimated using the model-predicted O2/Ar ratio to compute the mixed layer biological O2 saturation and the gas transfer velocity to calculate flux. We find that the simulated biological O2 flux gives an accurate picture of the regional-scale patterns and trends in model NCP. However, on local scales, violations of the assumptions behind the O2/Ar method lead to significant, non-uniform differences between model NCP and biological O2 flux. These errors arise from two main sources. First, venting of biological O2 to the atmosphere can be misaligned from NCP in both time and space. Second, vertical fluxes of oxygen across the base of the mixed layer complicate the relationship between NCP and the biological O2 flux. Our calculations show that low values of O2 bioflux correctly register that NCP is also low (<10 mmol m−2 day−1), but fractional errors are large when rates are this low. Values between 10 and 40 mmol m−2 day−1 in areas with intermediate mixed layer depths of 30 to 50 m have the smallest absolute and relative errors. Areas with O2 bioflux higher than 30 mmol m−2 day−1 and mixed layers deeper than 40 m tend to underestimate NCP by up to 20 mmol m−2 day−1. Excluding time periods when mixed layer biological O2 is undersaturated, O2 bioflux underestimates time-averaged NCP by 5%–15%. If these time periods are included, O2 bioflux underestimates mixed layer NCP by 20%–35% in the Southern Ocean. The higher error estimate is relevant if one wants to estimate seasonal NCP since a significant amount of biological production takes place when mixed layer biological O2 is undersaturated.This work was supported in part by funding from the National Aeronautic and Space Administration (NASA NNX08AF12G) and National Science Foundation (NSF OPP-0823101)