Coupling, Attractiveness and Hydrodynamics for Conservative Particle Systems

Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in simple exclusion. The derived Markovian coupled process $(\xi_t,\zeta_t)_{t\geq 0}$ satisfies: (A) if $\xi_0\leq\zeta_0$ (coordinate-wise), then for all $t\geq 0$, $\xi_t\leq\zeta_t$ a.s. In this paper, we consider generalized misanthrope models which are conservative particle systems on $\Z^d$ such that, in each transition, $k$ particles may jump from a site $x$ to another site $y$, with $k\geq 1$. These models include simple exclusion for which $k=1$, but, beyond that value, the basic coupling construction is not possible and a more refined one is required. We give necessary and sufficient conditions on the rates to insure attractiveness; we construct a Markovian coupled process which both satisfies (A) and makes discrepancies between its two marginals non-increasing. We determine the extremal invariant and translation invariant probability measures under general irreducibility conditions. We apply our results to examples including a two-species asymmetric exclusion process with charge conservation (for which $k\le 2$) which arises from a Solid-on-Solid interface dynamics, and a stick process (for which $k$ is unbounded) in correspondence with a generalized discrete Hammersley-Aldous-Diaconis model. We derive the hydrodynamic limit of these two one-dimensional models

Quadratic Mean Field Games

Mean field games were introduced independently by J-M. Lasry and P-L. Lions, and by M. Huang, R.P. Malham\'e and P. E. Caines, in order to bring a new approach to optimization problems with a large number of interacting agents. The description of such models split in two parts, one describing the evolution of the density of players in some parameter space, the other the value of a cost functional each player tries to minimize for himself, anticipating on the rational behavior of the others. Quadratic Mean Field Games form a particular class among these systems, in which the dynamics of each player is governed by a controlled Langevin equation with an associated cost functional quadratic in the control parameter. In such cases, there exists a deep relationship with the non-linear Schr\"odinger equation in imaginary time, connexion which lead to effective approximation schemes as well as a better understanding of the behavior of Mean Field Games. The aim of this paper is to serve as an introduction to Quadratic Mean Field Games and their connexion with the non-linear Schr\"odinger equation, providing to physicists a good entry point into this new and exciting field.Comment: 62 pages, 4 figure

'Phase diagram' of a mean field game

Mean field games were introduced by J-M.Lasry and P-L. Lions in the mathematical community, and independently by M. Huang and co-workers in the engineering community, to deal with optimization problems when the number of agents becomes very large. In this article we study in detail a particular example called the 'seminar problem' introduced by O.Gu\'eant, J-M Lasry, and P-L. Lions in 2010. This model contains the main ingredients of any mean field game but has the particular feature that all agent are coupled only through a simple random event (the seminar starting time) that they all contribute to form. In the mean field limit, this event becomes deterministic and its value can be fixed through a self consistent procedure. This allows for a rather thorough understanding of the solutions of the problem, through both exact results and a detailed analysis of various limiting regimes. For a sensible class of initial configurations, distinct behaviors can be associated to different domains in the parameter space . For this reason, the 'seminar problem' appears to be an interesting toy model on which both intuition and technical approaches can be tested as a preliminary study toward more complex mean field game models

Landsat 7 Enhanced Thematic Mapper JRC-FAPAR Algorithm Theoretical Basis Document

This Algorithm Theoretical Basis document (ATBd) describes the Joint Research Center (JRC)- procedure used to retrieve information of absorbed photosynthetical radiation by the vegetated terrestrial surfaces from an analysis of the Top Of Atmosphere (TOA) data acquired by the Landsat 7 Enhanced Thematic Mapper (ETM+) instrument. The corresponding data consist of eight spectral bands, with a spatial resolution of 30 meters for bands 1 to 5 and band 7 whereas the resolution for band 6 (thermal infrared) is 60 meters and resolution for band 8 (panchromatic) is 15 meters. Approximate scene size is 170 km north-south by 183 km east-west. The code of the proposed algorithm takes the form of a set of several formulae which transform calibrated spectral directional reflectances into a single numerical value. These formulae are designed to extract the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) in the plant canopy from the measurements. The methodology described in this document has been optimized to assess the presence on the ground of healthy live green vegetation. The optimization procedure has been constrained to provide an estimate of FAPAR in the plant canopy, although the outputs are expected to be used in a wide range of applications. This algorithm delivers, in addition to the FAPAR product, the so-called rectied reflectance values in the red and near-infrared spectral bands (Landsat 7 ETM+ Band 3 and Band 4). These are virtual reflectances largely decontaminated from atmospheric and angular effects. It also provides a categorization of pixel types thanks to a pre-processing identication based on multi-spectral properties.JRC.H.3-Global environement monitorin

Envisat's Medium Resolution Imaging Spectrometer (MERIS) Algorithm Theoretical Basis Document: FAPAR and Rectied Channels over Terrestrial Surfaces

This Algorithm Theoretical Basis document (ATBd) describes the Joint Research Center (JRC) procedure used to retrieve information of absorbed photosynthetical radiation by the vegetated terrestrial surfaces from an analysis of the Top Of Atmosphere (TOA) data acquired by MERIS. The code of the proposed algorithm takes the form of a set of several formulae which transform calibrated spectral directional reflectances into a single numerical value. These formulae are designed to extract the green Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) in the plant canopy from the measurements and the rectified channels in the red and near-infrared bands. The methodology described in this document has been optimized to assess the presence on the ground of healthy live green vegetation. The main optimization procedure has been constrained to provide an estimate of FAPAR in the plant canopy, although the outputs are expected to be used in a wide range of applications. This algorithm delivers, in addition to the FAPAR product, the so-called rectified reflectance values in the red and near-infrared spectral bands. These are virtual reflectances largely decontaminated from atmospheric and angular effects. It also provides a categorization of pixel types thanks to a pre-processing identification based on multi-spectral properties. These two virtual reflectances are also computed over bare soils using specific coefficients. This document identifies the sources of input data, outlines the physical principles and mathematical background justifying this approach, describes the proposed algorithm, and lists the assumptions and limitations of this technique.JRC.DDG.H.3-Global environement monitorin

Land Surface Indicators from Space: Methodology and Preliminary Results

This document overviews the content and the preliminary results of a specific work package entitled Land Surface Indicators from Space of the Land Use and Landscapes from the Joint Research Center (JRC) and the European Environment Agency (EEA) 2006 work plan described in Kennedy and Stanners (2005). The first section summarizes the objectives of the activities in the context of the EEA project Land and Ecosystems Accounts. The main goal is the estimate and the analysis of the Net Primary Productivity (NPP) over terrestrial surfaces from space remote sensing products over various land cover types in Europe. The Knorr and Heimann (1995)'s model is applied to compute the NPP using the current JRC- Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) products as input. This simple generic global biosphere model requires also the downward photosynthetic active radiation (PAR) at the surface level. Sections 3, 4 and 5 outline the model, identify the sources of input data stream, and present preliminary results over European countries, respectively. Concluding remarks and perspectives are then given at the end of the document.JRC.H.3-Global environement monitorin

On The Response Of The European Vegetation Phenology To Hydroclimatic Anomalies

Climate change is expected to alter vegetation and carbon cycle processes, with implications for ecosystems and feedback to regional and global climate. Notably, understanding the sensitivity of vegetation to the anomalies of precipitation and temperature over different land cover classes and the corresponding temporal response is essential for improved climate prediction. In this paper, we analyse vegetation response to hydroclimatic forcings using the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) derived from SeaWiFS (1998-2002) and MERIS (2003-2011) sensors at 1 km resolution. Based on land cover and pixel-wise analysis, we quantify the extent of the dependence between the FAPAR, and ultimately the phenology, and the anomalies of precipitation and temperature over Europe. Statistical tests are performed to establish where this correlation may be regarded as statistically dependent. Further, we assess a statistical link between the climate variables and a set of phenological metrics defined from FAPAR measurement. Variation in the phenological response to the unusual values of precipitation and temperature can be interpreted as the result of balanced opposite effects of water and temperature on vegetation processes. Results suggest very different responses on different land cover classes and timing seasons. The degree of observed coupled behaviour also indicates that European phenology may be quite sensitive to the perturbations in precipitation and temperature regimes such as those induced by the climate change.JRC.H.7-Climate Risk Managemen