Analysis of the vibrational mode spectrum of a linear chain with spatially exponential properties

We deduce the dynamic frequency-domain-lattice Green's function of a linear chain with properties (masses and next-neighbor spring constants) of exponential spatial dependence. We analyze the system as discrete chain as well as the continuous limiting case which represents an elastic I D exponentially graded material. The discrete model yields closed form expressions for the N x N Green's function for an arbitrary number N = 2,...,infinity of particles of the chain. Utilizing this Green's function yields an explicit expression for the vibrational mode density. Despite of its simplicity the model reflects some characteristics of the dynamics of a I D exponentially graded elastic material. As a special case the well-known expressions for the Green's function and oscillator density of the homogeneous linear chain are contained in the model. The width of the frequency band is determined by the grading parameter which characterizes the exponential spatial dependence of the properties. In the limiting case of large grading parameter, the frequency band is localized around a single finite frequency where the band width tends to zero inversely with the grading parameter. In the continuum limit the discrete Green's function recovers the Green's function of the continuous equation of motion which takes in the time domain the form of a Klein-Gordon equation. (C) 2008 Elsevier Ltd. All rights reserved

Managing Forests for Biodiversity Conservation and Climate Change Mitigation

We include biodiversity impacts in forest management decision making by incorporating the countryside species area relationship model into the partial equilibrium model GLOBIOM-Forest. We tested three forest management intensities (low, medium, and high) and limited biodiversity loss via an additional constraint on regional species loss. We analyzed two scenarios for climate change mitigation. RCP1.9, the higher mitigation scenario, has more biodiversity loss than the reference RCP7.0, suggesting a trade-off between climate change mitigation, with increased bioenergy use, and biodiversity conservation in forests. This trade-off can be alleviated with biodiversity-conscious forest management by (1) shifting biomass production destined to bioenergy from forests to energy crops, (2) increasing areas under unmanaged secondary forest, (3) reducing forest management intensity, and (4) reallocating biomass production between and within regions. With these mechanisms, it is possible to reduce potential global biodiversity loss by 10% with minor changes in economic outcomes. The global aggregated reduction in biodiversity impacts does not imply that biodiversity impacts are reduced in each ecoregion. We exemplify how to connect an ecologic and an economic model to identify trade-offs, challenges, and possibilities for improved decisions. We acknowledge the limitations of this approach, especially of measuring and projecting biodiversity loss

Sur une généralisation de l'opérateur fractionnaire

Les matériaux dont la microstructure est invariante par changement d'échelle est peu abordée par la mécanique, faute d'approches réellement satisfaisantes. On propose ici une approche à partir des « fonctions auto-similaires » (Michelitsch, Maugin et al. PRE 80, 011135, 2009) en introduisant la notion de « dérivée généralisée ».On définit la « dérivée généralisée » résultant d'un processus (h vers 0) d'une fonction opérateur A(T(h)-1)/A(h) appliquée à f(x) avec l'opérateur de translation T(h) (T(h)f(x)=f(x+h)). Quelques exemples dynamiques en mécanique des matériaux seront discutés

An approach to generalized one-dimensional self-similar elasticity

International audienceWe employ a self-similar Laplacian in the one-dimensional infinite space and deduce a model for one-dimensional self-similar elasticity. As a consequence of self-similarity this Laplacian assumes the non-local form of a self-adjoint combination of fractional integrals. The linear elastic constitutive law becomes a non-local convolution with the elastic modulus function being a power-law kernel. We outline some principal features of a linear self-similar elasticity theory in one dimension. We find an anomalous behavior of the elastic modulus function reflecting a regime of critically slowly decreasing interparticle interactions in one dimension. The approach can be generalized to the n dimensional physical space (Michelitsch, Maugin, Nowakowski, Nicolleau, & Rahman, to be published)