A generalized spin ladder in a magnetic field

We study the phase diagram of coupled spin-1/2 chains with bilinear and (chiral) three-spin exchange interactions in a magnetic field. The model is soluble on a one-parametric line in the space of coupling constants connecting the limiting cases of a single and two decoupled Heisenberg chains with nearest neighbour exchange only. We give a complete classification of the low-energy properties of the integrable system and introduce a numerical method which allows to study the possible phases of spin ladder systems away from the soluble line in a magnetic field.Comment: Latex2e, 13 pp., 5 figure

An abrasive-corrosive wear evaluation of some aluminium alloys

This investigation evaluates the abrasive-corrosive wear behaviour of aluminium alloys with the aim of establishing a data base of performance and guide lines for material optimisation. Wear test apparatus and standard tests developed by previous research programmes were utilised (Noel and Allen, 1981; Barker, 1988). Further tests were then devised for a more detailed characterisation of wear behaviour. Tests conducted showed that aluminium alloys have approximately a quarter to half the abrasion resistance of mild steel. Poor microfracture properties of Al-Si cast alloys were observed as a result of coarse and brittle silicon rich phases contained in the aluminium matrix. Non heat-treatable wrought alloys exhibit ductile micro-deformation characteristics whilst heat-treatable alloys, having the best abrasion resistance, possess better combinations of strength, hardness and toughness. Tests with combined corrosion and wear showed that most aluminium alloys are subject to pitting corrosion due to localised differences in electrode potentials at constituent sites. Higher series alloys with a large number of constituent particles exhibit higher pitting densities. Due to the high electrode potentials of silicon phases and copper and zinc solid solutions, the alloys LM6+Sr, 2014 and 7075 have poor corrosion resistance and are subject to localised and pitting attack. As a consequence the alloys 2014, 7075 and LM6+Sr show a decrease in wear performance under abrasive-corrosive conditions. In contrast the good corrosion resistance of the alloys 5083, 6261 and 7017 provide a significant improvement in wear performance under conditions of long corrosion periods with light abrasive intervals. This study concludes that the abrasion resistance of wrought alloys may be optimised by designing an alloy with a good combination of tensile strength, fracture toughness and hardness together with an intermediate microstructural size distribution of second phase particles in the aluminium matrix. Ageing of heat treatable alloys improves abrasion resistance significantly, peak hardness and strength conditions resulting in optimum abrasion properties

Importance of fossil fuel emission uncertainties over Europe for CO2 modeling: model intercomparison

Inverse modeling techniques used to quantify surface carbon fluxes commonly assume that the uncertainty of fossil fuel CO2 (FFCO2) emissions is negligible and that intra-annual variations can be neglected. To investigate these assumptions, we analyzed the differences between four fossil fuel emission inventories with spatial and temporal differences over Europe and their impact on the model simulated CO2 concentration. Large temporal flux variations characterize the hourly fields (~40 % and ~80 % for the seasonal and diurnal cycles, peak-to-peak) and annual country totals differ by 10 % on average and up to 40 % for some countries (i.e., the Netherlands). These emissions have been prescribed to seven different transport models, resulting in 28 different FFCO2 concentrations fields. The modeled FFCO2 concentration time series at surface sites using time-varying emissions show larger seasonal cycles (+2 ppm at the Hungarian tall tower (HUN)) and smaller diurnal cycles in summer (-1 ppm at HUN) than when using constant emissions. The concentration range spanned by all simulations varies between stations, and is generally larger in winter (up to ~10 ppm peak-to-peak at HUN) than in summer (~5 ppm). The contribution of transport model differences to the simulated concentration std-dev is 2–3 times larger than the contribution of emission differences only, at typical European sites used in global inversions. These contributions to the hourly (monthly) std-dev's amount to ~1.2 (0.8) ppm and ~0.4 (0.3) ppm for transport and emissions, respectively. First comparisons of the modeled concentrations with 14C-based fossil fuel CO2 observations show that the large transport differences still hamper a quantitative evaluation/validation of the emission inventories. Changes in the estimated monthly biosphere flux (Fbio) over Europe, using two inverse modeling approaches, are relatively small (less that 5 %) while changes in annual Fbio (up to ~0.15 % GtC yr-1) are only slightly smaller than the differences in annual emission totals and around 30 % of the mean European ecosystem carbon sink. These results point to an urgent need to improve not only the transport models but also the assumed spatial and temporal distribution of fossil fuel emission inventories

Global surface-ocean pCO2 and sea–air CO2 flux variability from an observation-driven ocean mixed-layer scheme

A temporally and spatially resolved estimate of the global surface-ocean CO₂ partial pressure field and the sea–air CO₂ flux is presented, obtained by fitting a simple data-driven diagnostic model of ocean mixed-layer biogeochemistry to surface-ocean CO₂ partial pressure data from the SOCAT v1.5 database. Results include seasonal, interannual, and short-term (daily) variations. In most regions, estimated seasonality is well constrained from the data, and compares well to the widely used monthly climatology by Takahashi et al. (2009). Comparison to independent data tentatively supports the slightly higher seasonal variations in our estimates in some areas. We also fitted the diagnostic model to atmospheric CO₂ data. The results of this are less robust, but in those areas where atmospheric signals are not strongly influenced by land flux variability, their seasonality is nevertheless consistent with the results based on surface-ocean data. From a comparison with an independent seasonal climatology of surface-ocean nutrient concentration, the diagnostic model is shown to capture relevant surface-ocean biogeochemical processes reasonably well. Estimated interannual variations will be presented and discussed in a companion paper

How does the terrestrial carbon exchange respond to inter-annual climatic variations? : A quantification based on atmospheric CO2 data

The response of the terrestrial net ecosystem exchange (NEE) of CO2 to climate variations and trends may crucially determine the future climate trajectory. Here we directly quantify this response on inter-annual timescales by building a linear regression of inter-annual NEE anomalies against observed air temperature anomalies into an atmospheric inverse calculation based on long-term atmospheric CO2 observations. This allows us to estimate the sensitivity of NEE to inter-annual variations in temperature (seen as a climate proxy) resolved in space and with season. As this sensitivity comprises both direct temperature effects and the effects of other climate variables co-varying with temperature, we interpret it as "inter-annual climate sensitivity". We find distinct seasonal patterns of this sensitivity in the northern extratropics that are consistent with the expected seasonal responses of photosynthesis, respiration, and fire. Within uncertainties, these sensitivity patterns are consistent with independent inferences from eddy covariance data. On large spatial scales, northern extratropical and tropical interannual NEE variations inferred from the NEE-T regression are very similar to the estimates of an atmospheric inversion with explicit inter-annual degrees of freedom. The results of this study offer a way to benchmark ecosystem process models in more detail than existing effective global climate sensitivities. The results can also be used to gap-fill or extrapolate observational records or to separate inter-annual variations from longer-term trends.Peer reviewe

History of El Nino impacts on the global carbon cycle 1957-2017 : a quantification from atmospheric CO2 data

Interannual variations in the large-scale net ecosystem exchange (NEE) of CO2 between the terrestrial biosphere and the atmosphere were estimated for 1957-2017 from sustained measurements of atmospheric CO2 mixing ratios. As the observations are sparse in the early decades, available records were combined into a 'quasi-homogeneous' dataset based on similarity in their signals, to minimize spurious variations from beginning or ending data records. During El Nino events, CO2 is anomalously released from the tropical band, and a few months later also in the northern extratropical band. This behaviour can approximately be represented by a linear relationship of the NEE anomalies and local air temperature anomalies, with sensitivity coefficients depending on geographical location and season. The apparent climate sensitivity of global total NEE against variations in pan-tropically averaged annual air temperature slowly changed over time during the 1957-2017 period, first increasing (though less strongly than in previous studies) but then decreasing again. However, only part of this change can be attributed to actual changes in local physiological or ecosystem processes, the rest probably arising from shifts in the geographical area of dominating temperature variations. This article is part of a discussion meeting issue 'The impact of the 2015/2016 El Nino on the terrestrial tropical carbon cycle: patterns, mechanisms and implications'.Peer reviewe

Sparse observations induce large biases in estimates of the global ocean CO2 sink: an ocean model subsampling experiment

Estimates of ocean CO2 uptake from global ocean biogeochemistry models and pCO2-based data products differ substantially, especially in high latitudes and in the trend of the CO2 uptake since 2000. Here, we assess the effect of data sparsity on two pCO2-based estimates by subsampling output from a global ocean biogeochemistry model. The estimates of the ocean CO2 uptake are improved from a sampling scheme that mimics present-day sampling to an ideal sampling scheme with 1000 evenly distributed sites. In particular, insufficient sampling has given rise to strong biases in the trend of the ocean carbon sink in the pCO2 products. The overestimation of the CO2 flux trend by 20-35% globally and 50-130% in the Southern Ocean with the present-day sampling is reduced to less than 15% with the ideal sampling scheme. A substantial overestimation of the decadal variability of the Southern Ocean carbon sink occurs in one product and appears related to a skewed data distribution in pCO2 space. With the ideal sampling, the bias in the mean CO2 flux is reduced from 9-12% to 2-9% globally and from 14-26% to 5-17% in the Southern Ocean. On top of that, discrepancies of about 0.4 PgC yr-1 (15%) persist due to uncertainties in the gas-exchange calculation. This article is part of a discussion meeting issue 'Heat and carbon uptake in the Southern Ocean: the state of the art and future priorities'

Integrable models of coupled Heisenberg chains

We show that the solutions of the Yang--Baxter equation invariant under the action of the Yangian $Y(sl_2)$ lead to inhomogenous vertex models. Starting from a four dimensional representation of $Y(sl_2)$ we obtain an integrable family of coupled Heisenberg spin-$1\over2$ chains. Some thermodynamical properties of this model are studied by means of the algebraic Bethe Ansatz.Comment: 10 pages, latex, 5 postscript figure