On the index system of well-rounded lattices

Let \Lb be a lattice in an $n$-dimensional Euclidean space $E$ and let \Lb' be a Minkowskian sublattice of \Lb, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of \Lb. We consider the set of possible quotients \Lb/\Lb' which may exists in a given dimension or among not too large values of the index [\Lb:\Lb'], indeed [\Lb:\Lb']\le 4, or dimension $n\le 8$.Comment: 17 page

Finite size effects and equilibration in Bose-Hubbard chains with central well dephasing

We investigate Bose-Hubbard chains in a central depleted well configuration, with dephasing in the middle well. We look at equilibration of populations, pseudo-entropy, and entanglement measures. Using stochastic integration in the truncated Wigner representation, we find that the initial quantum states of the occupied wells has an influence on the subsequent dynamics, and that with more than three wells, the chains do not reach a full equilibrium, with edge effects becoming important, and the time to reach the steady state becoming longer. The evolutions with and without phase diffusion are qualitatively different. We find no convincing evidence of entanglement in the final states with phase diffusion. Although at least one accepted measure indicates the presence of mode entanglement, we are easily able to show that it can give ambiguous predictions.Comment: 20 pages, 12 figures, theor

Agricultural land-use and biological conservation

Land use change is a main driver of biodiversity erosion, especially in agricultural landscapes. Incentive-based land-use policies aim at influence land-use pattern, and are usually evaluated with habitat suitability scores, without accounting explicitly for the ecology of the studied population. In this paper, we propose a methodology to define and evaluate agricultural land-use policies with respect to their ecological outcomes directly. We use an ecological-economic model to link the regional abundance of a bird species to the economic context. Policies based on such ecological economics approaches appear to be more efficient than that based on landscape evaluation, from both economic and ecological viewpoints.Ecological-economic model, agriculture, land-use, landscape, conservation

An Environmental-Economic Measure of Sustainable Development

A central issue in the study of sustainable development is the interplay of growth and sacrifice in a dynamic economy. This paper investigates the relationship among current consumption, growth, and sustained consumption in two canonical, stylized economies and in a more general context. It is found that the maximin value measures what is sustainable and provides the limit to growth. Maximin value is interpreted as an environmental-economic carrying capacity and current consumption or utility as an environmental-economic footprint. The time derivative of maximin value is interpreted as net investment in sustainability improvement. It is called durable savings to distinguish it from genuine savings, usually computed with discounted utilitarian prices.sustained development, growth, maximin, sustainability indicator

Embedding smooth and formal diffeomorphisms through the Jordan-Chevalley decomposition

In [Xiang Zhang, The embedding flows of $C^{\infty}$ hyperbolic diffeomorphisms, J. Differential Equations 250 (2011), no. 5, 2283-2298] Zhang proved that any local smooth hyperbolic diffeomorphism whose eigenvalues are weakly nonresonant is embedded in the flow of a smooth vector field. We present a new, simpler and more conceptual proof of such result using the Jordan-Chevalley decomposition in algebraic groups and the properties of the exponential operator. We characterize the hyperbolic smooth (resp. formal) diffeomorphisms that are embedded in a smooth (resp. formal) flow. We introduce a criterium showing that the presence of weak resonances for a diffeomorphism plus two natural conditions imply that it is not embeddable. This solves a conjecture of Zhang. The criterium is optimal, we provide a method to construct embeddable diffeomorphisms with weak resonances if we remove any of the conditions.Comment: 25 page

The simulation of piano string vibration: {F}rom physical models to finite difference schemes and digital waveguides

A model of transverse piano string vibration, second order in time, which models frequency-dependent loss and dispersion effects is presented here. This model has many desirable properties, in particular that it can be written as a well-posed initial-boundary value problem (permitting stable finite difference schemes) and that it may be directly related to a digital waveguide model, a digital filter-based algorithm which can be used for musical sound synthesis. Techniques for the extraction of model parameters from experimental data over the full range of the grand piano are discussed, as is the link between the model parameters and the filter responses in a digital waveguide. Simulations are performed. Finally, the waveguide model is extended to the case of several coupled strings