Participatory monitoring of the impact of watershed interventions in the tropical Andes

This chapter documents the motivations and methods of the Regional Initiative for Hydrological Monitoring of Andean Ecosystems (iMHEA). First, it introduces the context that led to the formation of a diverse consortium of institutions with a joint interest in Andean ecosystems and water. The methodological approach adopted by the monitoring network is then presented in detail. Lastly, this chapter shows preliminary main results, the most relevant milestones and breakthroughs, and the major remaining challenges and perspectives in the scientific, technological and social domains. The objective of the monitoring, as promoted by iMHEA, is to generate standardized data that can be used to increase the knowledge about hydrological ecosystem services in Andean watersheds and the impacts of watershed interventions. The correct use of the generated knowledge, from community level to national governance entities, proves crucial to increase catchment intervention efficiency and improve decision-making on water resources management in data-scarce regions, with potential application to other regions of the world

Massless scalar field in two-dimensional de Sitter universe

We study the massless minimally coupled scalar field on a two--dimensional de Sitter space-time in the setting of axiomatic quantum field theory. We construct the invariant Wightman distribution obtained as the renormalized zero--mass limit of the massive one. Insisting on gauge invariance of the model we construct a vacuum state and a Hilbert space of physical states which are invariant under the action of the whole de Sitter group. We also present the integral expression of the conserved charge which generates the gauge invariance and propose a definition of dual field.Comment: 13 page

QUANTIZATION OF A CLASS OF PIECEWISE AFFINE TRANSFORMATIONS ON THE TORUS

We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the automorphisms, translations and skew translations. We then treat some discontinuous transformations such as the Baker map and the sawtooth-like maps. Our approach extends some ideas from geometric quantization and it is both conceptually and calculationally simple.Comment: no. 28 pages in AMSTE

User-driven design of decision support systems for polycentric environmental resources management

Open and decentralized technologies such as the Internet provide increasing opportunities to create knowledge and deliver computer-based decision support for multiple types of users across scales. However, environmental decision support systems/tools (henceforth EDSS) are often strongly science-driven and assuming single types of decision makers, and hence poorly suited for more decentralized and polycentric decision making contexts. In such contexts, EDSS need to be tailored to meet diverse user requirements to ensure that it provides useful (relevant), usable (intuitive), and exchangeable (institutionally unobstructed) information for decision support for different types of actors. To address these issues, we present a participatory framework for designing EDSS that emphasizes a more complete understanding of the decision making structures and iterative design of the user interface. We illustrate the application of the framework through a case study within the context of water-stressed upstream/downstream communities in Lima, Peru

Equilibration, generalized equipartition, and diffusion in dynamical Lorentz gases

We prove approach to thermal equilibrium for the fully Hamiltonian dynamics of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a $d$-dimensional array of fixed soft scatterers that each possess an internal harmonic or anharmonic degree of freedom to which moving particles locally couple. We establish that the momentum distribution of the moving particles approaches a Maxwell-Boltzmann distribution at a certain temperature $T$, provided that they are initially fast and the scatterers are in a sufficiently energetic but otherwise arbitrary stationary state of their free dynamics--they need not be in a state of thermal equilibrium. The temperature $T$ to which the particles equilibrate obeys a generalized equipartition relation, in which the associated thermal energy $k_{\mathrm B}T$ is equal to an appropriately defined average of the scatterers' kinetic energy. In the equilibrated state, particle motion is diffusive

Magnetic strip waveguides

We analyze the spectrum of the "local" Iwatsuka model, i.e. a two-dimensional charged particle interacting with a magnetic field which is homogeneous outside a finite strip and translationally invariant along it. We derive two new sufficient conditions for absolute continuity of the spectrum. We also show that in most cases the number of open spectral gaps of the model is finite. To illustrate these results we investigate numerically the situation when the field is zero in the strip being screened, e.g. by a superconducting mask.Comment: 22 pages, a LaTeX source file with three eps figure

Classical motion in force fields with short range correlations

We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and mean-squared displacement is shown to exhibit a large degree of universality; it depends only on whether the force is, or is not, a gradient vector field. When it is, p^{2}(t) ~ t^{2/5} independently of the details of the potential and of the space dimension. Motion is then superballistic in one dimension, with q^{2}(t) ~ t^{12/5}, and ballistic in higher dimensions, with q^{2}(t) ~ t^{2}. These predictions are supported by numerical results in one and two dimensions. For force fields not obtained from a potential field, the power laws are different: p^{2}(t) ~ t^{2/3} and q^{2}(t) ~ t^{8/3} in all dimensions d\geq 1

Parabolic maps with spin: Generic spectral statistics with non-mixing classical limit

We investigate quantised maps of the torus whose classical analogues are ergodic but not mixing. Their quantum spectral statistics shows non-generic behaviour, i.e.it does not follow random matrix theory (RMT). By coupling the map to a spin 1/2, which corresponds to changing the quantisation without altering the classical limit of the dynamics on the torus, we numerically observe a transition to RMT statistics. The results are interpreted in terms of semiclassical trace formulae for the maps with and without spin respectively. We thus have constructed quantum systems with non-mixing classical limit which show generic (i.e. RMT) spectral statistics. We also discuss the analogous situation for an almost integrable map, where we compare to Semi-Poissonian statistics.Comment: 29 pages, 20 figure

Weyl's law and quantum ergodicity for maps with divided phase space

For a general class of unitary quantum maps, whose underlying classical phase space is divided into several invariant domains of positive measure, we establish analogues of Weyl's law for the distribution of eigenphases. If the map has one ergodic component, and is periodic on the remaining domains, we prove the Schnirelman-Zelditch-Colin de Verdiere Theorem on the equidistribution of eigenfunctions with respect to the ergodic component of the classical map (quantum ergodicity). We apply our main theorems to quantised linked twist maps on the torus. In the Appendix, S. Zelditch connects these studies to some earlier results on `pimpled spheres' in the setting of Riemannian manifolds. The common feature is a divided phase space with a periodic component.Comment: Colour figures. Black & white figures available at http://www2.maths.bris.ac.uk/~majm. Appendix by Steve Zelditc