Consistent Relationship between Field-Measured Stomatal Conductance and Theoretical Maximum Stomatal Conductance in C₃ Woody Angiosperms in Four Major Biomes

Premise of research. Understanding the relationship between field-measured operating stomatal conductance (gop) and theoretical maximum stomatal conductance (gmax), calculated from stomatal density and geometry, provides an important framework that can be used to infer leaf-level gas exchange of historical, herbarium, and fossil plants. To date, however, investigation of the nature of the relationship between gop and theoretical gmax remains limited to a small number of experiments on relatively few taxa and is virtually undefined for plants in natural ecosystems. Methodology. We used the gop measurements of 74 species and 35 families across four biomes from a published contemporary data set of field-measured leaf-level stomatal conductance in woody angiosperms and calculated the theoretical gmax from the same leaves to investigate the relationship between gop and gmax across multiple species and biomes and determine whether such relationships are widely conserved. Pivotal results. We observed significant relationships between gop and gmax, with consistency in the gop ∶ gmax ratio across biomes, growth habits (shrubs and trees), and habitats (open canopy and understory subcanopy). An overall mean gop ∶ gmax ratio of 0.26 ± 0.11 (mean ± SD) was observed. The consistently observed gop ∶ gmax ratio in this study strongly agrees with previous hypotheses that an ideal gop ∶ gmax ratio exists. Conclusions. These results build substantially on previous studies by presenting a new reference for a consistent gop ∶ gmax ratio across many levels and offer great potential to enhance paleoclimate proxies and vegetation-climate models alike

Using modern plant trait relationships between observed and theoretical maximum stomatal conductance and vein density to examine patterns of plant macroevolution

Understanding the drivers of geological-scale patterns in plant macroevolution is limited by a hesitancy to use measurable traits of fossils to infer palaeoecophysiological function. Here, scaling relationships between morphological traits including maximum theoretical stomatal conductance (gmax) and leaf vein density (Dv) and physiological measurements including operational stomatal conductance (gop), saturated (Asat) and maximum (Amax) assimilation rates were investigated for 18 extant taxa in order to improve understanding of angiosperm diversification in the Cretaceous. Our study demonstrated significant relationships between gop, gmax and Dv that together can be used to estimate gas exchange and the photosynthetic capacities of fossils. We showed that acquisition of high gmax in angiosperms conferred a competitive advantage over gymnosperms by increasing the dynamic range (plasticity) of their gas exchange and expanding their ecophysiological niche space. We suggest that species with a high gmax (> 1400 mmol m-2 s-1) would have been capable of maintaining a high Amax as the atmospheric CO2 declined through the Cretaceous, whereas gymnosperms with a low gmax would experience severe photosynthetic penalty. Expansion of the ecophysiological niche space in angiosperms, afforded by coordinated evolution of high gmax, Dv and increased plasticity in gop, adds further functional insights into the mechanisms driving angiosperm speciation

A Multivariate Adaptive Regression Spline Approach for Prediction of Maximum Shear Modulus and Minimum Damping Ratio

This study uses multivariate adaptive regression spline (MARS) for determination of maximum shear modulus (Gmax) and minimum damping ratio (ξmin) of synthetic reinforced soil. MARS employs confining pressure (σ, psi), rubber (r, %) and sand (s, %) as input variables. The outputs of the MARS are Gmax and ξmin. The developed MARS gives equations for determination of Gmax and ξmin. The results of MARS have been compared with the adaptive neuro-fuzzy inference system (ANFIS), multi-layer perception (MLP) and multiple regression analysis method (MRM). A sensitivity analysis has been also carried out to determine the effect of each input variable on Gmax and ξmin. This study shows that the developed MARS is a robust model for prediction of Gmax and ξmin

Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

A 2D linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of Reduced MHD. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al, Phys. Plasmas {\bf 14}, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids (k_{\rm max}\Lsheet \sim S^{3/8}, where $k_{\rm max}$ is the wave-number of fastest growing mode, S=\Lsheet V_A/\eta is the Lundquist number, \Lsheet is the length of the sheet, $V_A$ is the Alfv\'en speed and $\eta$ is the plasma resistivity), which grows super-Alfv\'enically fast (\gmax\tau_A\sim S^{1/4}, where \gmax is the maximum growth rate, and \tau_A=\Lsheet/V_A). For typical background profiles, the growth rate and the wave-number are found to {\it increase} in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfv\'en speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability, \gmax \tau_A \sim k_{\rm max} \Lsheet\sim S^{1/2}. The effect of viscosity ($\nu$) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers, $Pm=\nu/\eta$, it is found that \gmax\sim S^{1/4}Pm^{-5/8} and k_{\rm max} \Lsheet\sim S^{3/8}Pm^{-3/16}, leading to the prediction that the critical Lundquist number for plasmoid instability in the $Pm\gg1$ regime is \Scrit\sim 10^4Pm^{1/2}. These results are verified via direct numerical simulation of the linearized equations, using a new, analytical 2D SP equilibrium solution.Comment: 21 pages, 9 figures, submitted to Phys. Rev.

Approaching the ground states of the random maximum two-satisfiability problem by a greedy single-spin flipping process

In this brief report we explore the energy landscapes of two spin glass models using a greedy single-spin flipping process, {\tt Gmax}. The ground-state energy density of the random maximum two-satisfiability problem is efficiently approached by {\tt Gmax}. The achieved energy density $e(t)$ decreases with the evolution time $t$ as $e(t)-e(\infty)=h (\log_{10} t)^{-z}$ with a small prefactor $h$ and a scaling coefficient $z > 1$, indicating an energy landscape with deep and rugged funnel-shape regions. For the $\pm J$ Viana-Bray spin glass model, however, the greedy single-spin dynamics quickly gets trapped to a local minimal region of the energy landscape.Comment: 5 pages with 4 figures included. Accepted for publication in Physical Review E as a brief repor

Experimental study on dynamic properties of sand-rubber mixtures in a small range of shearing strain amplitudes

Sand-rubber mixtures has characteristics of light weight, cheap and environmental-friendly, thereby it has a great potential to be used in geotechnical engineering for sustainable development. Dynamic properties (i.e. shear modulus and damping ratio) of sand-rubber mixtures in a small range of shearing strain amplitudes (i.e. 10-6-10-4) were investigated in this study through a series of resonant column tests. The effects of shearing strain amplitude, confining pressure and rubber content on dynamic shear modulus (G), maximum dynamic shear modulus (Gmax), damping ratio (D) and dynamic shear modulus ratio G/Gmax of the mixtures were also discussed. Based on the analyses of the relationship among confining pressure, rubber content and Gmax, an empirical formula for predicting Gmax considering the effects of confining pressure and rubber content was also proposed. The model prediction agreed with the experimental results very well

Maximising the number of induced cycles in a graph

We determine the maximum number of induced cycles that can be contained in a graph on $n\ge n_0$ vertices, and show that there is a unique graph that achieves this maximum. This answers a question of Tuza. We also determine the maximum number of odd or even cycles that can be contained in a graph on $n\ge n_0$ vertices and characterise the extremal graphs. This resolves a conjecture of Chv\'atal and Tuza from 1988.Comment: 36 page