, in the estimated aqueous volume of the guard-cell wall. The conclusion is that mannitol, a xenobiotic with structural similarity to sucrose, can move throughout the apoplast of a transpiring leaflet and accumulate in an osmotically significant concentration in the guard-cell wall. These data therefore provide support for a new role for sucrose as a signal metabolite that integrates essential functions of the whole leaf. In addition, the results raise questions about the physiological or experimental accumulation of other guard-cell-targeted apoplastic solutes such as plant growth regulators, particularly abscisic acid, and ions.

Cost functions formulated in four-dimensional variational data assimilation (4DVAR) are nonsmooth in the presence of discontinuous physical processes (i.e., the presence of ''on-off'' switches in NWP models). The adjoint model integration produces values of subgradients, instead of gradients, of these cost functions with respect to the model's control variables at discontinuous points. Minimization of these cost functions using conventional differentiable optimization algorithms may encounter difficulties. In this paper an idealized discontinuous model and an actual shallow convection parameterization are used, both including on-off switches, to illustrate the performances of differentiable and nondifferentiable optimization algorithms. It was found that (i) the differentiable optimization, such as the limited memory quasi-Newton (L-BFGS) algorithm, may still work well for minimizing a nondifferentiable cost function, especially when the changes made in the forecast model at switching points to the model state are not too large; (ii) for a differentiable optimization algorithm to find the true minimum of a nonsmooth cost function, introducing a local smoothing that removes discontinuities may lead to more problems than solutions due to the insertion of artificial stationary points; and (iii) a nondifferentiable optimization algorithm is found to be able to find the true minima in cases where the differentiable minimization failed. For the case of strong smoothing, differentiable minimization performance is much improved, as compared to the weak smoothing cases.

The microscopic mechanism for electron pairing in heavy-fermion superconductors remains a major challenge in quantum materials. Some form of magnetic mediation is widely accepted with spin fluctuations as a prime candidate. A novel mechanism, "composite pairing" based on the cooperative two-channel Kondo effect directly involving the f-electron moments has also been proposed for some heavy fermion compounds including CeCoIn 5 . The origin of the spin resonance peak observed in neutron scattering measurements on CeCoIn 5 is still controversial and the corresponding hump-dip structure in the tunneling conductance is missing. This is in contrast to the cuprate and Fe-based high-temperature superconductors, where both characteristic signatures are observed, indicating spin fluctuations are likely involved in the pairing process. Here, we report results from planar tunneling spectroscopy along three major crystallographic orientations of CeCoIn 5 over wide ranges of temperature and magnetic field. The pairing gap opens at T p ~ 5 K, well above the bulk T c = 2.3 K, and its directional dependence is consistent with d x2-y2 symmetry. With increasing magnetic field, this pairing gap is suppressed as expected but, intriguingly, a gaplike structure emerges smoothly, increasing linearly up to the highest field applied. This field-induced gaplike feature is only observed below T p . The concomitant appearance of the pairing gap and the fieldinduced gaplike feature, along with its linear increase with field, indicates that the f-electron local moments are directly involved in the pairing process in CeCoIn 5 .

Results are reported for the f -electron intermetallic CeAuAl4Ge2, where the atomic arrangement of the cerium ions creates the conditions for geometric frustration. Despite this, magnetic susceptibility measurements reveal that the low temperature magnetic exchange interaction is weak, resulting in marginally frustrated behavior and ordering near TM ≈ 1.4 K. This occurs within a metallic Kondo lattice, where electrical resistivity and heat capacity measurements show that the Kondo-driven electronic correlations are negligible. Quantum oscillations are detected in acmagnetic susceptibility measurements and uncover small charge carrier effective masses. Electronic structure calculations reveal that when the experimentally observed antiferromagnetic exchange interaction and the on-f -site Coulomb repulsion (Hubbard) U are considered, the f -electron bands move away from the Fermi level, resulting in electronic behavior that is dominated by the s-, p-, and d-bands, which are all characterized by light electron masses. Thus, CeAuAl4Ge2 provides a starting point for investigating geometric magnetic frustration in a cerium lattice without strong Kondo hybridization, where calculations provide useful guidance.