Spatiotemporal complexity of a ratio-dependent predator-prey system

In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten-type functional response and reaction-diffusion. We derive the conditions for Hopf, Turing and Wave bifurcation on a spatial domain. Furthermore, we present a theoretical analysis of evolutionary processes that involves organisms distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripelike or spotted or coexistence of both. Our study shows that the spatially extended model has not only more complex dynamic patterns in the space, but also chaos and spiral waves. It may help us better understand the dynamics of an aquatic community in a real marine environment.Comment: 6pages, revtex

An atmospheric perspective on North American carbon dioxide exchange: CarbonTracker

We present an estimate of net CO2 exchange between the terrestrial biosphere and the atmosphere across North America for every week in the period 2000 through 2005. This estimate is derived from a set of 28,000 CO2 mole fraction observations in the global atmosphere that are fed into a state-of-the-art data assimilation system for CO2 called CarbonTracker. By design, the surface fluxes produced in CarbonTracker are consistent with the recent history of CO2 in the atmosphere and provide constraints on the net carbon flux independent from national inventories derived from accounting efforts. We find the North American terrestrial biosphere to have absorbed –0.65 PgC/yr (1 petagram = 10^15 g; negative signs are used for carbon sinks) averaged over the period studied, partly offsetting the estimated 1.85 PgC/yr release by fossil fuel burning and cement manufacturing. Uncertainty on this estimate is derived from a set of sensitivity experiments and places the sink within a range of –0.4 to –1.0 PgC/yr. The estimated sink is located mainly in the deciduous forests along the East Coast (32%) and the boreal coniferous forests (22%). Terrestrial uptake fell to –0.32 PgC/yr during the large-scale drought of 2002, suggesting sensitivity of the contemporary carbon sinks to climate extremes. CarbonTracker results are in excellent agreement with a wide collection of carbon inventories that form the basis of the first North American State of the Carbon Cycle Report (SOCCR), to be released in 2007. All CarbonTracker results are freely available at http://carbontracker.noaa.gov

Emissions and topographic effects on column CO_2 (XCO_2) variations, with a focus on the Southern California Megacity

Within the California South Coast Air Basin (SoCAB), X_(CO)_2 varies significantly due to atmospheric dynamics and the nonuniform distribution of sources. X_(CO)_2 measurements within the basin have seasonal variation compared to the “background” due primarily to dynamics, or the origins of air masses coming into the basin. We observe basin-background differences that are in close agreement for three observing systems: Total Carbon Column Observing Network (TCCON) 2.3 ± 1.2 ppm, Orbiting Carbon Observatory-2 (OCO-2) 2.4 ± 1.5 ppm, and Greenhouse gases Observing Satellite 2.4 ± 1.6 ppm (errors are 1σ). We further observe persistent significant differences (∼0.9 ppm) in X_(CO)_2 between two TCCON sites located only 9 km apart within the SoCAB. We estimate that 20% (±1σ confidence interval (CI): 0%, 58%) of the variance is explained by a difference in elevation using a full physics and emissions model and 36% (±1σ CI: 10%, 101%) using a simple, fixed mixed layer model. This effect arises in the presence of a sharp gradient in any species (here we focus on CO_2) between the mixed layer (ML) and free troposphere. Column differences between nearby locations arise when the change in elevation is greater than the change in ML height. This affects the fraction of atmosphere that is in the ML above each site. We show that such topographic effects produce significant variation in X_(CO)_2 across the SoCAB as well

Emissions and topographic effects on column CO2 (XCO2) variations, with a focus on the Southern California Megacity

Within the California South Coast Air Basin (SoCAB), XCO2 varies significantly due to atmospheric dynamics and the nonuniform distribution of sources. XCO2 measurements within the basin have seasonal variation compared to the “background” due primarily to dynamics, or the origins of air masses coming into the basin. We observe basin‐background differences that are in close agreement for three observing systems: Total Carbon Column Observing Network (TCCON) 2.3 ± 1.2 ppm, Orbiting Carbon Observatory‐2 (OCO‐2) 2.4 ± 1.5 ppm, and Greenhouse gases Observing Satellite 2.4 ± 1.6 ppm (errors are 1σ). We further observe persistent significant differences (∼0.9 ppm) in XCO2 between two TCCON sites located only 9 km apart within the SoCAB. We estimate that 20% (±1σ confidence interval (CI): 0%, 58%) of the variance is explained by a difference in elevation using a full physics and emissions model and 36% (±1σ CI: 10%, 101%) using a simple, fixed mixed layer model. This effect arises in the presence of a sharp gradient in any species (here we focus on CO2) between the mixed layer (ML) and free troposphere. Column differences between nearby locations arise when the change in elevation is greater than the change in ML height. This affects the fraction of atmosphere that is in the ML above each site. We show that such topographic effects produce significant variation in XCO2 across the SoCAB as well.Plain Language SummaryCities persistently have elevated carbon dioxide (CO2) levels as compared to surrounding regions. Within a city CO2 levels can also vary significantly at different locations for reasons such as more CO2 being emitted in some parts than others. Elevated column CO2 levels in the South Coast Air Basin (SoCAB) are in agreement for three observation systems (two satellite and one ground‐based) systems and vary with regional wind patterns throughout the year. In Pasadena, California, within the SoCAB, a significant fraction (about 25%) of variation in the column‐averaged CO2 can be explained by differences in surface altitude. This is important to understand so that all variations in column CO2 within an urban region are not mistakenly interpreted as being from CO2 surface fluxes.Key PointsIn the SoCAB, 20–36% of spatial variance in XCO2 is explained by topography on scales ≲10 kmIn Pasadena, XCO2 is enhanced by 2.3 ± 1.2 (1σ) ppm above background levels, at 1300 (UTC 8) with seasonal variationThe SoCAB XCO2 enhancement is in agreement for 3 different observation sets (TCCON, GOSAT, and OCO‐2)Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137737/1/jgrd53887.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137737/2/jgrd53887_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137737/3/jgrd53887-sup-0001-supinfo.pd

Resonance expansions in quantum mechanics

The goal of this contribution is to discuss various resonance expansions that have been proposed in the literature.Comment: 10 pages and 1 figure; presented at the Istanbul workshop on pseudo-Hermitian Hamiltonian

Quantum tunneling across spin domains in a Bose-Einstein condensate

Quantum tunneling was observed in the decay of metastable spin domains in gaseous Bose-Einstein condensates. A mean-field description of the tunneling was developed and compared with measurement. The tunneling rates are a sensitive probe of the boundary between spin domains, and indicate a spin structure in the boundary between spin domains which is prohibited in the bulk fluid. These experiments were performed with optically trapped F=1 spinor Bose-Einstein condensates of sodium.Comment: 5 pages, 4 figure

Repeatability of IVIM biomarkers from diffusion-weighted MRI in head and neck:Bayesian probability versus neural network

Purpose: The intravoxel incoherent motion (IVIM) model for DWI might provide useful biomarkers for disease management in head and neck cancer. This study compared the repeatability of three IVIM fitting methods to the conventional nonlinear least-squares regression: Bayesian probability estimation, a recently introduced neural network approach, IVIM-NET, and a version of the neural network modified to increase consistency, IVIM-NETmod. Methods: Ten healthy volunteers underwent two imaging sessions of the neck, two weeks apart, with two DWI acquisitions per session. Model parameters (ADC, diffusion coefficient (Formula presented.), perfusion fraction (Formula presented.), and pseudo-diffusion coefficient (Formula presented.)) from each fit method were determined in the tonsils and in the pterygoid muscles. Within-subject coefficients of variation (wCV) were calculated to assess repeatability. Training of the neural network was repeated 100 times with random initialization to investigate consistency, quantified by the coefficient of variance. Results: The Bayesian and neural network approaches outperformed nonlinear regression in terms of wCV. Intersession wCV of (Formula presented.) in the tonsils was 23.4% for nonlinear regression, 9.7% for Bayesian estimation, 9.4% for IVIM-NET, and 11.2% for IVIM-NETmod. However, results from repeated training of the neural network on the same data set showed differences in parameter estimates: The coefficient of variances over the 100 repetitions for IVIM-NET were 15% for both (Formula presented.) and (Formula presented.), and 94% for (Formula presented.); for IVIM-NETmod, these values improved to 5%, 9%, and 62%, respectively. Conclusion: Repeatabilities from the Bayesian and neural network approaches are superior to that of nonlinear regression for estimating IVIM parameters in the head and neck

A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker-Planck equation for the stochastic fluctuations. The McKendrick--von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation and the McKendrick--von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.Comment: 27 pages, 4 figures. Final version as published. Only minor change

Network 'small-world-ness': a quantitative method for determining canonical network equivalence

Background: Many technological, biological, social, and information networks fall into the broad class of 'small-world' networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction ('small/not-small') rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a network's small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model-the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified. Methodology/Principal Findings: We defined a precise measure of 'small-world-ness' S based on the trade off between high local clustering and short path length. A network is now deemed a 'small-world' if S. 1-an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process. Conclusions/Significance: We have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing

Centrality dependence of the expansion dynamics in Pb-Pb collisions at 158 A GeV/c

Two-particle correlation functions of negatively charged hadrons from Pb-Pb collisions at 158 GeV/c per nucleon have been measured by the WA97 experiment at the CERN SPS. A Coulomb correction procedure that assumes an expanding source has been implemented. Within the framework of an expanding thermalized source model the size and dynamical state of the collision fireball at freeze-out have been reconstructed as a function of the centrality of the collision. Less central collisions exhibit a different dynamics than central ones: both transverse and longitudinal expansion velocities are slower, the expansion duration is shorter and the system freezes out showing smaller dimensions and higher temperature.Comment: 22 pages, 11 figures, Te