A Shape Theorem for Riemannian First-Passage Percolation

Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in $\R^d$. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability one

Quantum dynamics of Bose-polaron in a dd-dimensional Bose Einstein condensate

We study the quantum motion of an impurity atom immersed in a Bose Einstein condensate in arbitrary dimension. The Bogoliubov excitations of the Bose Einstein condensate act as a bosonic bath for the impurity. We present a detailed derivation of the $d$-dimensional Langevin equations that describe the quantum dynamics of the system, and of the associated generalized tensor that describes the spectral density in the full generality. When the impurity is not trapped, we calculate the mean square displacement, showing that the motion is super diffusive. We obtain also explicit expressions for the super diffusive coefficient in the small and large temperature limits. We find that, in the latter case, the maximal value of this coefficient is the same in all dimensions. We study also the behaviour of the average energy and compare the results for various dimensions. In the trapped case, we study squeezing and find that the stronger position squeezing can be obtained in lower dimensions. We quantify the non-Markovianity of the particle's motion, and find that it increases with dimensionality.Comment: 18 pages, 12 figure

Classical Spin Models with Broken Continuous Symmetry: Random Field Induced Order and Persistence of Spontaneous Magnetization

We consider a classical spin model, of two-dimensional spins, with continuous symmetry, and investigate the effect of a symmetry breaking unidirectional quenched disorder on the magnetization of the system. We work in the mean field regime. We show, by numerical simulations and by perturbative calculations in the low as well as in the high temperature limits, that although the continuous symmetry of the magnetization is lost, the system still magnetizes, albeit with a lower value as compared to the case without disorder. The critical temperature at which the system starts magnetizing, also decreases with the introduction of disorder. However, with the introduction of an additional constant magnetic field, the component of magnetization in the direction that is transverse to the disorder field increases with the introduction of the quenched disorder. We discuss the same effects also for three-dimensional spins.Comment: 12 pages, 12 figures, RevTeX

The EarthCARE mission – science and system overview

The Earth Cloud, Aerosol and Radiation Explorer (EarthCARE) is a satellite mission implemented by the European Space Agency (ESA), in cooperation with the Japan Aerospace Exploration Agency (JAXA), to measure global profiles of aerosols, clouds and precipitation properties together with radiative fluxes and derived heating rates. The simultaneous measurements of the vertical structure and horizontal distribution of cloud and aerosol fields, together with outgoing radiation, will be used in particular to evaluate their representation in weather forecasting and climate models and to improve our understanding of cloud and aerosol radiative impact and feedback mechanisms. To achieve the objective, the goal is that a retrieved scene with footprint size of 10 km × 10 km is measured with sufficiently high resolution that the atmospheric vertical profile of short-wave (solar) and long-wave (thermal) flux can be reconstructed with an accuracy of 10 W m−2 at the top of the atmosphere. To optimise the performance of the two active instruments, the platform will fly at a relatively low altitude of 393 km, with an equatorial revisit time of 25 d. The scientific payload consists of four instruments: an atmospheric lidar, a cloud-profiling radar with Doppler capability, a multi-spectral imager and a broadband radiometer. Co-located measurements from these instruments are processed in the ground segment, which produces and distributes a wide range of science data products. As well as the Level 1 (L1) product of each instrument, a large number of multiple-instrument L2 products have been developed, in both Europe and Japan, benefiting from the data synergy. An end-to-end simulator and several test scenes have been developed that simulate EarthCARE observations and provide a development and test environment for L1 and L2 processors. Within this paper the EarthCARE observational requirements are addressed. An overview is given of the space segment with a detailed description of the four science instruments, demonstrating how the observational requirements will be met. Furthermore, the elements of the space segment and ground segment that are relevant for science data users are described and the data products are introduced.</p

Partitioning controls on Amazon forest photosynthesis between environmental and biotic factors at hourly to interannual timescales

Gross ecosystem productivity (GEP) in tropical forests varies both with the environment and with biotic changes in photosynthetic infrastructure, but our understanding of the relative effects of these factors across timescales is limited. Here, we used a statistical model to partition the variability of seven years of eddy covariance-derived GEP in a central Amazon evergreen forest into two main causes: variation in environmental drivers (solar radiation, diffuse light fraction, and vapor pressure deficit) that interact with model parameters that govern photosynthesis and biotic variation in canopy photosynthetic light-use efficiency associated with changes in the parameters themselves. Our fitted model was able to explain most of the variability in GEP at hourly (R2 = 0.77) to interannual (R2 = 0.80) timescales. At hourly timescales, we found that 75% of observed GEP variability could be attributed to environmental variability. When aggregating GEP to the longer timescales (daily, monthly, and yearly), however, environmental variation explained progressively less GEP variability: At monthly timescales, it explained only 3%, much less than biotic variation in canopy photosynthetic light-use efficiency, which accounted for 63%. These results challenge modeling approaches that assume GEP is primarily controlled by the environment at both short and long timescales. Our approach distinguishing biotic from environmental variability can help to resolve debates about environmental limitations to tropical forest photosynthesis. For example, we found that biotically regulated canopy photosynthetic light-use efficiency (associated with leaf phenology) increased with sunlight during dry seasons (consistent with light but not water limitation of canopy development) but that realized GEP was nonetheless lower relative to its potential efficiency during dry than wet seasons (consistent with water limitation of photosynthesis in given assemblages of leaves). This work highlights the importance of accounting for differential regulation of GEP at different timescales and of identifying the underlying feedbacks and adaptive mechanisms

Ergodic properties of a model for turbulent dispersion of inertial particles

We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schroedinger equation in a random delta-correlated potential. The ergodic properties of the dispersion process are investigated by proving that its generator is hypoelliptic and using control theory