A two-scale Stefan problem arising in a model for tree sap exudation

The study of tree sap exudation, in which a (leafless) tree generates elevated stem pressure in response to repeated daily freeze-thaw cycles, gives rise to an interesting multi-scale problem involving heat and multiphase liquid/gas transport. The pressure generation mechanism is a cellular-level process that is governed by differential equations for sap transport through porous cell membranes, phase change, heat transport, and generation of osmotic pressure. By assuming a periodic cellular structure based on an appropriate reference cell, we derive an homogenized heat equation governing the global temperature on the scale of the tree stem, with all the remaining physics relegated to equations defined on the reference cell. We derive a corresponding strong formulation of the limit problem and use it to design an efficient numerical solution algorithm. Numerical simulations are then performed to validate the results and draw conclusions regarding the phenomenon of sap exudation, which is of great importance in trees such as sugar maple and a few other related species. The particular form of our homogenized temperature equation is obtained using periodic homogenization techniques with two-scale convergence, which we investigate theoretically in the context of a simpler two-phase Stefan-type problem corresponding to a periodic array of melting cylindrical ice bars with a constant thermal diffusion coefficient. For this reduced model, we prove results on existence, uniqueness and convergence of the two-scale limit solution in the weak form, clearly identifying the missing pieces required to extend the proofs to the fully nonlinear sap exudation model. Numerical simulations of the reduced equations are then compared with results from the complete sap exudation model.Comment: 35 pages, 8 figures. arXiv admin note: text overlap with arXiv:1411.303

Maintaining Quantum Coherence in the Presence of Noise through State Monitoring

Unsharp POVM measurements allow the estimation and tracking of quantum wavefunctions in real-time with minimal disruption of the dynamics. Here we demonstrate that high fidelity state monitoring, and hence quantum control, is possible even in the presence of classical dephasing and amplitude noise, by simulating such measurements on a two-level system undergoing Rabi oscillations. Finite estimation fidelity is found to persist indefinitely long after the decoherence times set by the noise fields in the absence of measurement.Comment: 5 pages, 4 figure

Exploiting entanglement in communication channels with correlated noise

We develop a model for a noisy communication channel in which the noise affecting consecutive transmissions is correlated. This model is motivated by fluctuating birefringence of fiber optic links. We analyze the role of entanglement of the input states in optimizing the classical capacity of such a channel. Assuming a general form of an ensemble for two consecutive transmissions, we derive tight bounds on the classical channel capacity depending on whether the input states used for communication are separable or entangled across different temporal slots. This result demonstrates that by an appropriate choice, the channel capacity may be notably enhanced by exploiting entanglement.Comment: 9 pages, 5 figure

Conduction Channels of One-Atom Zinc Contacts

We have determined the transmission coefficients of atomic-sized Zn contacts using a new type of breakjunction which contains a whisker as a central bridge. We find that in the last conductance plateau the transport is unexpectedly dominated by a well-transmitting single conduction channel. We explain the experimental findings with the help of a tight-binding model which shows that in an one-atom Zn contact the current proceeds through the 4s and 4p orbitals of the central atom.Comment: revtex4, 5 pages, 5 figure

Experimental demonstration of entanglement-enhanced classical communication over a quantum channel with correlated noise

We present an experiment demonstrating entanglement-enhanced classical communication capacity of a quantum channel with correlated noise. The channel is modelled by a fiber optic link exhibiting random birefringence that fluctuates on a time scale much longer than the temporal separation between consecutive uses of the channel. In this setting, introducing entanglement between two photons travelling down the fiber allows one to encode reliably up to one bit of information into their joint polarization degree of freedom. When no quantum correlations between two separate uses of the channel are allowed, this capacity is reduced by a factor of more than three. We demonstrated this effect using a fiber-coupled source of entagled photon pairs based on spontaneous parametric down-conversion, and a linear-optics Bell state measurement.Comment: 4 pages, 2 figures, REVTe

Altimetry, gravimetry, GPS and viscoelastic modeling data for the joint inversion for glacial isostatic adjustment in Antarctica (ESA STSE Project REGINA)

The poorly known correction for the ongoing deformation of the solid Earth caused by glacial isostatic adjustment (GIA) is a major uncertainty in determining the mass balance of the Antarctic ice sheet from measurements of satellite gravimetry and to a lesser extent satellite altimetry. In the past decade, much progress has been made in consistently modeling ice sheet and solid Earth interactions; however, forward-modeling solutions of GIA in Antarctica remain uncertain due to the sparsity of constraints on the ice sheet evolution, as well as the Earth's rheological properties. An alternative approach towards estimating GIA is the joint inversion of multiple satellite data – namely, satellite gravimetry, satellite altimetry and GPS, which reflect, with different sensitivities, trends in recent glacial changes and GIA. Crucial to the success of this approach is the accuracy of the space-geodetic data sets. Here, we present reprocessed rates of surface-ice elevation change (Envisat/Ice, Cloud,and land Elevation Satellite, ICESat; 2003–2009), gravity field change (Gravity Recovery and Climate Experiment, GRACE; 2003–2009) and bedrock uplift (GPS; 1995–2013). The data analysis is complemented by the forward modeling of viscoelastic response functions to disc load forcing, allowing us to relate GIA-induced surface displacements with gravity changes for different rheological parameters of the solid Earth. The data and modeling results presented here are available in the PANGAEA database (https://doi.org/10.1594/PANGAEA.875745). The data sets are the input streams for the joint inversion estimate of present-day ice-mass change and GIA, focusing on Antarctica. However, the methods, code and data provided in this paper can be used to solve other problems, such as volume balances of the Antarctic ice sheet, or can be applied to other geographical regions in the case of the viscoelastic response functions. This paper presents the first of two contributions summarizing the work carried out within a European Space Agency funded study: Regional glacial isostatic adjustment and CryoSat elevation rate corrections in Antarctica (REGINA)

Sea ice - atmosphere interaction: Application of multispectral satellite data in polar surface energy flux estimates

In the past six months, work has continued on energy flux sensitivity studies, ice surface temperature retrievals, corrections to Advanced Very High Resolution Radiometer (AVHRR) thermal infrared data, modelling of cloud fraction retrievals, and radiation climatologies. We tentatively conclude that the SSM/I may not provide accurate enough estimates of ice concentration and type to improve our shorter term energy flux estimates. SSM/I derived parameters may still be applicable in longer term climatological flux characterizations. We hold promise for a system coupling observation to a ice deformation model. Such a model may provide information on ice distribution which can be used in energy flux calculations. Considerable variation was found in modelled energy flux estimates when bulk transfer coefficients are modulated by lead fetch. It is still unclear what the optimum formulation is and this will be the subject of further work. Data sets for ice surface temperature retrievals were assembled and preliminary data analysis was started. Finally, construction of a conceptual framework for further modelling of the Arctic radiation flux climatology was started

Maximum Matching in Turnstile Streams

We consider the unweighted bipartite maximum matching problem in the one-pass turnstile streaming model where the input stream consists of edge insertions and deletions. In the insertion-only model, a one-pass $2$-approximation streaming algorithm can be easily obtained with space $O(n \log n)$, where $n$ denotes the number of vertices of the input graph. We show that no such result is possible if edge deletions are allowed, even if space $O(n^{3/2-\delta})$ is granted, for every $\delta > 0$. Specifically, for every $0 \le \epsilon \le 1$, we show that in the one-pass turnstile streaming model, in order to compute a $O(n^{\epsilon})$-approximation, space $\Omega(n^{3/2 - 4\epsilon})$ is required for constant error randomized algorithms, and, up to logarithmic factors, space $O( n^{2-2\epsilon} )$ is sufficient. Our lower bound result is proved in the simultaneous message model of communication and may be of independent interest