Plant water uptake modelling : added value of cross-disciplinary approaches

Abstract In recent years, research interest in plant water uptake strategies has significantly grown in many disciplines such as hydrology, plant ecology and ecophysiology. Quantitative modelling approaches to estimate plant water uptake and the spatio-temporal dynamics significantly advanced from different disciplines across scales. Despite this progress, major limitations, i.e. to predict plant water uptake under drought or it?s impact at large-scales remain. These are less attributed to limitations in process understanding, but rather to a lack of implementation of cross-disciplinary insights in plant water uptake model structure. The main goal of this review is to highlight how the 4 dominant model approaches, e.g. Feddes approach, hydrodynamic approach, optimality and statistical approaches, can be and have been used to create interdisciplinary hybrid models enabeling a holistic system understanding that e.g. embeds plant water uptake plasticity into a broader conceptual view of soil-plant feedbacks of water, nutrient and carbon cycling or reflects observed drought responses of plant-soil feedbacks and their dynamics under e.g. drought. Specifically, we provide examples of how integration of Bayesian and hydrodynamic approaches might overcome challenges in interpreting plant water uptake related to e.g. different travel and residence times of different plant water sources or trade-offs between root system optimization to forage for water and nutrients during different seasons and phenological stages.In recent years, research interest in plant water uptake strategies has rapidly increased in many disciplines, such as hydrology, plant ecology and ecophysiology. Quantitative modelling approaches to estimate plant water uptake and spatiotemporal dynamics have significantly advanced through different disciplines across scales. Despite this progress, major limitations, for example, predicting plant water uptake under drought or drought impact at large scales, remain. These are less attributed to limitations in process understanding, but rather to a lack of implementation of cross-disciplinary insights into plant water uptake model structure. The main goal of this review is to highlight how the four dominant model approaches, that is, Feddes approach, hydrodynamic approach, optimality and statistical approaches, can be and have been used to create interdisciplinary hybrid models enabling a holistic system understanding that, among other things, embeds plant water uptake plasticity into a broader conceptual view of soil-plant feedbacks of water, nutrient and carbon cycling, or reflects observed drought responses of plant-soil feedbacks and their dynamics under, that is, drought. Specifically, we provide examples of how integration of Bayesian and hydrodynamic approaches might overcome challenges in interpreting plant water uptake related to different travel and residence times of different plant water sources or trade-offs between root system optimization to forage for water and nutrients during different seasons and phenological stages.Peer reviewe

Angle Dependence of the Transverse Thermal Conductivity in YBa2_2Cu3_3O7_7 single crystals: Doppler Effect vs. Andreev scattering

We have measured the transverse thermal conductivity $\kappa_{xy}$ of twinned and untwinned YBa$_2$Cu$_3$O$_7$ single crystals as a function of angle $\theta$ between the magnetic field applied parallel to the CuO$_2$ planes and the heat current direction, at different magnetic fields and temperatures. For both crystals we observed a clear twofold variation in the field-angle dependence of $\kappa_{xy}(\theta) = - \kappa^0_{xy}(T,B) \sin(2\theta)$. We have found that the oscillation amplitude $\kappa^0_{xy}$ depends on temperature and magnetic field. Our results show that $\kappa^0_{xy} = a B \ln(1/(bB))$ with the temperature- and sample-dependent parameters $a$ and $b$. We discuss our results in terms of Andreev scattering of quasiparticles by vortices and a recently proposed theory based on the Doppler shift in the quasiparticle spectrum.Comment: 5 pages, 4 figure

Evidence for field-induced excitations in low-temperature thermal conductivity of Bi_2Sr_2CaCu_2O_8

The thermal conductivity ,$\kappa$, of Bi_2Sr_2CaCu_2O_8 was studied as a function of magnetic field. Above 5 K, after an initial decrease, $\kappa(H)$ presents a kink followed by a plateau, as recently reported by Krishana et al.. By contrast, below 1K, the thermal conductivity was found to \emph{increase} with increasing field. This behavior is indicative of a finite density of states and is not compatible with the existence of a field-induced fully gapped $d_{x^{2}-y^{2}}+id_{xy}$ state which was recently proposed to describe the plateau regime. Our low-temperature results are in agreement with recent works predicting a field-induced enhancement of thermal conductivity by Doppler shift of quasi-particle spectrum.Comment: 4 pages including 4 eps figures, submitted to Phys. Rev. Let

Transport Properties of d-Wave Superconductors in the Vortex State

We calculate the magnetic field dependence of quasiparticle transport properties in the vortex state of a d-wave superconductor arising solely from the quasiparticle's Doppler shift in the superflow field surrounding the vortex. Qualitative features agree well with experiments on cuprate and heavy fermion superconductors at low fields and temperatures. We derive scaling relations in the variable $T/H^{1/2}$ valid at sufficiently low temperatures $T$ and fields $H$, but show that these relations depend on the scattering phase shift, and are in general fulfilled only approximately even in the clean limit, due to the energy dependence of the quasiparticle relaxation time.Comment: 5 pages, 2 Postscript figure

Theory of vortex lattice effects on STM spectra in d-wave superconductors

Theory of scanning tunneling spectroscopy of low energy quasiparticle (QP) states in vortex lattices of d-wave superconductors is developed taking account of the effects caused by an extremely large extension of QP wavefunctions in the nodal directions and the band structure in the QP spectrum. The oscillatory structures in STM spectra, which correspond to van Hove singularities are analysed. Theoretical calculations carried out for finite temperatures and scattering rates are compared with recent experimental data for high temperature cuprates.Comment: 4 pages, 3 eps figures, M2S-HTSC-VI conference paper, using Elsevier style espcrc2.st

Quasiparticle spectra in the vicinity of a d-wave vortex

We discuss the evolution of the local quasiparticle spectral density and the related tunneling conductance measurable by the scanning tunneling microscope, as a function of distance r and angle \theta from the vortex core in a d_{x^2-y^2} superconductor. We consider the effects of electronic disorder and of a strongly anisotropic tunneling matrix element, and show that in real materials they will likely obscure the ~1/r asymptotic tail in the zero-bias tunneling conductance expected from the straightforward semiclassical analysis. We also give a prediction for the tunneling conductance anisotropy around the vortex core and establish a connection to the structure of the tunneling matrix element.Comment: 9 pages REVTeX + 5 PostScript figures. For related work and info visit http://www.pha.jhu.edu/~fran

Thermal Conductivity Tensor in YBa2_2Cu3_3O7−x_{7-x}: Effects of a Planar Magnetic Field

We have measured the thermal conductivity tensor of a twinned YBa$_2$Cu$_3$O$_{7-x}$ single crystal as a function of angle $\theta$ between the magnetic field applied parallel to the CuO$_2$ planes and the heat current direction, at different magnetic fields and at T=13.8 K. Clear fourfold and twofold variations in the field-angle dependence of $\kappa_{xx}$ and $\kappa_{xy}$ were respectively recorded in accordance with the d-wave pairing symmetry of the order parameter. The oscillation amplitude of the transverse thermal conductivity $\kappa^0_{xy}$ was found to be larger than the longitudinal one $\kappa^0_{xx}$ in the range of magnetic field studied here ($0 T$$\le B \le 9$$T$). From our data we obtain quantities that are free from non-electronic contributions and they allow us a comparison of the experimental results with current models for the quasiparticle transport in the mixed state.Comment: 9 Figures, Phys. Rev. B(in press

Quasiparticle transport in the vortex state of YBa_2Cu_3O_6.9

The effect of vortices on quasiparticle transport in cuprate superconductors was investigated by measuring the low temperature thermal conductivity of YBa_2Cu_3O_6.9 in magnetic fields up to 8 T. The residual linear term (as T \to 0) is found to increase with field, directly reflecting the occupation of extended quasiparticle states. A study for different Zn impurity concentrations reveals a good agreement with recent calculations for a d-wave superconductor, thereby shedding light on the nature of scattering by both impurities and vortices. It also provides a quantitative measure of the gap near the nodes.Comment: 4 pages, 2 included eps figures, significant new analysis wrt other experiments, to appear in Phys Rev Lett 29 March 199

Low temperature superfluid stiffness of d-wave superconductor in a magnetic field

The temperature and field dependence of the superfluid density $\rho_s$ in the vortex state of a d-wave superconductor are calculated using a microscopic model in the quasiclassical approximation. We show that at temperatures below T^{*} \varpropto \sqrt{H}$, the linear T dependence of rho_s crosses over to a T^2 dependence differently from the behavior of the effective penetration depth, lambda_eff^{-2}(T). We point out that the expected dependences could be probed by a mutual-inductance technique experiment.Comment: 4 pages, RevTeX4, 2 EPS figures; minor revisions made and 1 new reference added; final version published in PR

Mixed-state quasiparticle transport in high-T_c cuprates: localization by magnetic field

Theory of quasiparticle transport in the mixed state of a d-wave superconductor is developed under the assumption of disordered vortex array. A novel universal regime is identified at fields above H*= c*H_{c2}(T/T_c)^2, characterized by a field-independent longitudinal thermal conductivity. It is argued that this behavior is responsible for the high-field plateau in the thermal conductivity experimentally observed in cuprates by Krishana, Ong and co-workers.Comment: 4 pages REVTeX + 1 PostScript figure. Final version to appear in PRL. Several changes in response to referee comments. For related work and info visit http://www.pha.jhu.edu/~fran