Uniform infinite planar triangulation and related time-reversed critical branching process

We establish a connection between the uniform infinite planar triangulation and some critical time-reversed branching process. This allows to find a scaling limit for the principal boundary component of a ball of radius R for large R (i.e. for a boundary component separating the ball from infinity). We show also that outside of R-ball a contour exists that has length linear in R.Comment: 27 pages, 5 figures, LaTe

Predicting the effects of climate change on water yield and forest production in the northeastern United States

Rapid and simultaneous changes in temperature, precipitation and the atmospheric concentration of CO2 are predicted to occur over the next century. Simple, well-validated models of ecosystem function are required to predict the effects of these changes. This paper describes an improved version of a forest carbon and water balance model (PnET-II) and the application of the model to predict stand- and regional-level effects of changes in temperature, precipitation and atmospheric CO2 concentration. PnET-II is a simple, generalized, monthly time-step model of water and carbon balances (gross and net) driven by nitrogen availability as expressed through foliar N concentration. Improvements from the original model include a complete carbon balance and improvements in the prediction of canopy phenology, as well as in the computation of canopy structure and photosynthesis. The model was parameterized and run for 4 forest/site combinations and validated against available data for water yield, gross and net carbon exchange and biomass production. The validation exercise suggests that the determination of actual water availability to stands and the occurrence or non-occurrence of soil-based water stress are critical to accurate modeling of forest net primary production (NPP) and net ecosystem production (NEP). The model was then run for the entire NewEngland/New York (USA) region using a 1 km resolution geographic information system. Predicted long-term NEP ranged from -85 to +275 g C m-2 yr-1 for the 4 forest/site combinations, and from -150 to 350 g C m-2 yr-1 for the region, with a regional average of 76 g C m-2 yr-1. A combination of increased temperature (+6*C), decreased precipitation (-15%) and increased water use efficiency (2x, due to doubling of CO2) resulted generally in increases in NPP and decreases in water yield over the region

Exact Solution of a Drop-push Model for Percolation

Motivated by a computer science algorithm known as `linear probing with hashing' we study a new type of percolation model whose basic features include a sequential `dropping' of particles on a substrate followed by their transport via a `pushing' mechanism. Our exact solution in one dimension shows that, unlike the ordinary random percolation model, the drop-push model has nontrivial spatial correlations generated by the dynamics itself. The critical exponents in the drop-push model are also different from that of the ordinary percolation. The relevance of our results to computer science is pointed out.Comment: 4 pages revtex, 2 eps figure

Boreal forest CO2 exchange and evapotranspiration predicted by nine ecosystem process models: Intermodel comparisons and relationships to field measurements

Nine ecosystem process models were used to predict CO2 and water vapor exchanges by a 150-year-old black spruce forest in central Canada during 1994–1996 to evaluate and improve the models. Three models had hourly time steps, five had daily time steps, and one had monthly time steps. Model input included site ecosystem characteristics and meteorology. Model predictions were compared to eddy covariance (EC) measurements of whole-ecosystem CO2exchange and evapotranspiration, to chamber measurements of nighttime moss-surface CO2release, and to ground-based estimates of annual gross primary production, net primary production, net ecosystem production (NEP), plant respiration, and decomposition. Model-model differences were apparent for all variables. Model-measurement agreement was good in some cases but poor in others. Modeled annual NEP ranged from −11 g C m−2 (weak CO2source) to 85 g C m−2 (moderate CO2 sink). The models generally predicted greater annual CO2sink activity than measured by EC, a discrepancy consistent with the fact that model parameterizations represented the more productive fraction of the EC tower “footprint.” At hourly to monthly timescales, predictions bracketed EC measurements so median predictions were similar to measurements, but there were quantitatively important model-measurement discrepancies found for all models at subannual timescales. For these models and input data, hourly time steps (and greater complexity) compared to daily time steps tended to improve model-measurement agreement for daily scale CO2 exchange and evapotranspiration (as judged by root-mean-squared error). Model time step and complexity played only small roles in monthly to annual predictions

ABCD of Beta Ensembles and Topological Strings

We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.Comment: 33 pages, 1 figur

Ecosystem carbon 7 dioxide fluxes after disturbance in forests of North America

Disturbances are important for renewal of North American forests. Here we summarize more than 180 site years of eddy covariance measurements of carbon dioxide flux made at forest chronosequences in North America. The disturbances included stand-replacing fire (Alaska, Arizona, Manitoba, and Saskatchewan) and harvest (British Columbia, Florida, New Brunswick, Oregon, Quebec, Saskatchewan, and Wisconsin) events, insect infestations (gypsy moth, forest tent caterpillar, and mountain pine beetle), Hurricane Wilma, and silvicultural thinning (Arizona, California, and New Brunswick). Net ecosystem production (NEP) showed a carbon loss from all ecosystems following a stand-replacing disturbance, becoming a carbon sink by 20 years for all ecosystems and by 10 years for most. Maximum carbon losses following disturbance (g C m−2y−1) ranged from 1270 in Florida to 200 in boreal ecosystems. Similarly, for forests less than 100 years old, maximum uptake (g C m−2y−1) was 1180 in Florida mangroves and 210 in boreal ecosystems. More temperate forests had intermediate fluxes. Boreal ecosystems were relatively time invariant after 20 years, whereas western ecosystems tended to increase in carbon gain over time. This was driven mostly by gross photosynthetic production (GPP) because total ecosystem respiration (ER) and heterotrophic respiration were relatively invariant with age. GPP/ER was as low as 0.2 immediately following stand-replacing disturbance reaching a constant value of 1.2 after 20 years. NEP following insect defoliations and silvicultural thinning showed lesser changes than stand-replacing events, with decreases in the year of disturbance followed by rapid recovery. NEP decreased in a mangrove ecosystem following Hurricane Wilma because of a decrease in GPP and an increase in ER

The Bivariate Rogers-Szeg\"{o} Polynomials

We present an operator approach to deriving Mehler's formula and the Rogers formula for the bivariate Rogers-Szeg\"{o} polynomials $h_n(x,y|q)$. The proof of Mehler's formula can be considered as a new approach to the nonsymmetric Poisson kernel formula for the continuous big $q$-Hermite polynomials $H_n(x;a|q)$ due to Askey, Rahman and Suslov. Mehler's formula for $h_n(x,y|q)$ involves a ${}_3\phi_2$ sum and the Rogers formula involves a ${}_2\phi_1$ sum. The proofs of these results are based on parameter augmentation with respect to the $q$-exponential operator and the homogeneous $q$-shift operator in two variables. By extending recent results on the Rogers-Szeg\"{o} polynomials $h_n(x|q)$ due to Hou, Lascoux and Mu, we obtain another Rogers-type formula for $h_n(x,y|q)$. Finally, we give a change of base formula for $H_n(x;a|q)$ which can be used to evaluate some integrals by using the Askey-Wilson integral.Comment: 16 pages, revised version, to appear in J. Phys. A: Math. Theo