Quantum curves for Hitchin fibrations and the Eynard-Orantin theory

We generalize the topological recursion of Eynard-Orantin (2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle $T^*C$ of an arbitrary smooth base curve $C$. We then prove that these spectral curves are quantizable, using the new formalism. More precisely, we construct the canonical generators of the formal $\hbar$-deformation family of $D$-modules over an arbitrary projective algebraic curve $C$ of genus greater than $1$, from the geometry of a prescribed family of smooth Hitchin spectral curves associated with the $SL(2,\mathbb{C})$-character variety of the fundamental group $\pi_1(C)$. We show that the semi-classical limit through the WKB approximation of these $\hbar$-deformed $D$-modules recovers the initial family of Hitchin spectral curves.Comment: 34 page

Seasonal patterns and controls on net ecosystem CO2 exchange in a boreal peatland complex

We measured seasonal patterns of net ecosystem exchange (NEE) of CO2 in a diverse peatland complex underlain by discontinuous permafrost in northern Manitoba, Canada, as part of the Boreal Ecosystems Atmosphere Study (BOREAS). Study sites spanned the full range of peatland trophic and moisture gradients found in boreal environments from bog (pH 3.9) to rich fen (pH 7.2). During midseason (July‐August, 1996), highest rates of NEE and respiration followed the trophic sequence of bog (5.4 to −3.9 μmol CO2 m−2 s−1) \u3c poor fen (6.3 to −6.5 μmol CO2 m−2 s−1) \u3c intermediate fen (10.5 to −7.8 μmol CO2 m−2 s−1) \u3c rich fen (14.9 to −8.7 μmol CO2m−2 s−1). The sequence changed during spring (May‐June) and fall (September‐October) when ericaceous shrub (e.g., Chamaedaphne calyculata) bogs and sedge (Carex spp.) communities in poor to intermediate fens had higher maximum CO2 fixation rates than deciduous shrub‐dominated (Salix spp. and Betula spp.) rich fens. Timing of snowmelt and differential rates of peat surface thaw in microtopographic hummocks and hollows controlled the onset of carbon uptake in spring. Maximum photosynthesis and respiration were closely correlated throughout the growing season with a ratio of approximately 1/3 ecosystem respiration to maximum carbon uptake at all sites across the trophic gradient. Soil temperatures above the water table and timing of surface thaw and freeze‐up in the spring and fall were more important to net CO2 exchange than deep soil warming. This close coupling of maximum CO2 uptake and respiration to easily measurable variables, such as trophic status, peat temperature, and water table, will improve models of wetland carbon exchange. Although trophic status, aboveground net primary productivity, and surface temperatures were more important than water level in predicting respiration on a daily basis, the mean position of the water table was a good predictor (r2 = 0.63) of mean respiration rates across the range of plant community and moisture gradients. Q10 values ranged from 3.0 to 4.1 from bog to rich fen, but when normalized by above ground vascular plant biomass, the Q10 for all sites was 3.3

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

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

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

CO₂ transport, variability, and budget over the southern California Air Basin using the high-resolution WRF-VPRM Model during the CalNex 2010 campaign

To study regional-scale carbon dioxide (CO2) transport, temporal variability, and budget over the Southern California Air Basin (SoCAB) during the California Research at the Nexus of Air Quality and Climate Change (CalNex) 2010 campaign period, a model that couples the Weather Research and Forecasting (WRF) Model with the Vegetation Photosynthesis and Respiration Model (VPRM) has been used. Our numerical simulations use anthropogenic CO2 emissions of the Hestia Project 2010 fossil-fuel CO2 emissions data products along with optimized VPRM parameters at ‘‘FLUXNET’’ sites, for biospheric CO2 fluxes over SoCAB. The simulated meteorological conditions have been validated with ground and aircraft observations, as well as with background CO2 concentrations from the coastal Palos Verdes site. The model captures the temporal pattern of CO2 concentrations at the ground site at the California Institute of Technology in Pasadena, but it overestimates the magnitude in early daytime. Analysis ofCO2 by wind directions reveals the overestimate is due to advection from the south and southwest, where downtown Los Angeles is located. The model also captures the vertical profile of CO2 concentrations along with the flight tracks. The optimized VPRM parameters have significantly improved simulated net ecosystem exchange at each vegetation-class site and thus the regional CO2 budget. The total biospheric contribution ranges approximately from 224% to 220% (daytime) of the total anthropogenic CO2 emissions during the study period

Dumber energy at home please: Perceptions of Smart Energy Technologies are dependent on home, workplace, or policy context in the United Kingdom

Smart energy technologies (SETs) are being developed around the world to support using energy more efficiently and to smooth our consumption over time, helping us to meet our carbon reduction targets. Notably, SETs will only be effective with support and engagement from the public. Previous literature has focused on evaluating SETs within a residential context, however, results here may differ from a workplace or policy context. We note that surrogate decision making (SDM [1]) theory indicates we make decisions differently for others than for the self. Study one (N = 213) comprises a survey using a UK population sample that examines public perceptions and support for SETs in different contexts. Study two (N = 12) utilises interviews to explore perceptions in more depth, probing the nature of support using socio-cognitive constructs relating to SDM. We find that people are more likely to support SETs in a workplace or policy context, compared to residential contexts. In addition, we note that support for SETs is related to different socio-cognitive constructs in different contexts, and also that impulsivity of decision making differs across contexts. Decision making within workplace and policy contexts is characterised by higher levels of impulsivity than in a residential context, as well as a sense of shared responsibility. Our results indicate that translational research is needed when considering evidence based on residential studies in making decisions within workplace and policy contexts