Unifying Dynamical and Structural Stability of Equilibriums

We exhibit a fundamental relationship between measures of dynamical and structural stability of equilibriums, arising from real dynamical systems. We show that dynamical stability, quantified via systems local response to external perturbations, coincides with the minimal internal perturbation able to destabilize the equilibrium. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a system's local response to white-noise perturbations directly reflects the intensity of internal white noise that it can accommodate before asymptotic mean-square stability of the equilibrium is lost.Comment: 13 pages, 2 figure

Resilience, reactivity and variability : A mathematical comparison of ecological stability measures

In theoretical studies, the most commonly used measure of ecological stability is resilience: ecosystems asymptotic rate of return to equilibrium after a pulse-perturbation $-$or shock. A complementary notion of growing popularity is reactivity: the strongest initial response to shocks. On the other hand, empirical stability is often quantified as the inverse of temporal variability, directly estimated on data, and reflecting ecosystems response to persistent and erratic environmental disturbances. It is unclear whether and how this empirical measure is related to resilience and reactivity. Here, we establish a connection by introducing two variability-based stability measures belonging to the theoretical realm of resilience and reactivity. We call them intrinsic, stochastic and deterministic invariability; respectively defined as the inverse of the strongest stationary response to white-noise and to single-frequency perturbations. We prove that they predict ecosystems worst response to broad classes of disturbances, including realistic models of environmental fluctuations. We show that they are intermediate measures between resilience and reactivity and that, although defined with respect to persistent perturbations, they can be related to the whole transient regime following a shock, making them more integrative notions than reactivity and resilience. We argue that invariability measures constitute a stepping stone, and discuss the challenges ahead to further unify theoretical and empirical approaches to stability.Comment: 35 pages, 7 figures, 2 table

Adsorption and absorption of Boron, Nitrogen, Aluminium and Phosphorus on Silicene: stability, electronic and phonon properties

Ab initio calculations within the density-functional theory formalism are performed to investigate the chemical functionalization of a graphene-like monolayer of silicon - silicene - with B, N, Al or P atoms. The structural, electronic, magnetic and vibrational properties are reported. The most preferable adsorption sites are found to be valley, bridge, valley and hill site for B, N, Al and P adatoms, respectively. All the relaxed systems with adsorbed/substituted atoms exhibit metallic behaviour with strongly bonded B, N, Al, and P atoms accompanied by an appreciable electron transfer from silicene to the B, N and P adatom/substituent. The Al atoms exhibit opposite charge transfer, with n-type doping of silicene and weaker bonding. The adatoms/substituents induce characteristic branches in the phonon spectrum of silicene, which can be probed by Raman measurements. Using molecular dynamics we found that the systems under study are stable up to at least T = 500 K. Our results demonstrate that silicene has a very reactive and functionalizable surface.Comment: 9 pages, 5 figure

Coherent supercontinuum generation in a silicon photonic wire in the telecommunication wavelength range

We demonstrate a fully coherent supercontinuum spectrum spanning 500 nm from a silicon-on-insulator photonic wire waveguide pumped at 1575 nm wavelength. An excellent agreement with numerical simulations is reported. The simulations also show that a high level of two-photon absorption can essentially enforce the coherence of the spectral broadening process irrespective of the pump pulse duration.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Measurement and tuning of the chromatic dispersion of a silicon photonic wire around the half band gap spectral region

We demonstrate the measurement and tuning of second-to-fourth order dispersion of a silicon wire waveguide in a spectral region of low nonlinear losses. Using white light interferometry we extract the chromatic dispersion of our waveguide from 1950 to 2300 nm. Moreover we demonstrate tuning of the zero dispersion wavelength over more than 100 nm, pushing it to longer wavelength by partially underetching the waveguide. © 2014 Optical Society of America.info:eu-repo/semantics/publishe

Observation of an optical event horizon in a silicon-on-insulator photonic wire waveguide

We report on the first experimental observation of an optical analogue of an event horizon in integrated nanophotonic waveguides, through the reflection of a continuous wave on an intense pulse. The experiment is performed in a dispersion-engineered silicon-on-insulator waveguide. In this medium, solitons do not suffer from Raman induced self-frequency shift as in silica fibers, a feature that is interesting for potential applications of optical event horizons. As shown by simulations, this also allows the observation of multiple reflections at the same time on fundamental solitons ejected by soliton fission.SCOPUS: ar.jhttp://www.opticsexpress.org/abstract.cfm?URIinfo:eu-repo/semantics/publishe

Freight Transportation Planning on the European Multimodal Network: the case of the Walloon Region

This paper presents a methodology that can be used for long-term planning of freight transportation on multimodal networks. It is illustrated by research carried out for the Belgian Walloon Ministry of Transport between 1997 and 1999. Its aim was to provide a tool for measuring the impacts of different kinds of policies and/or new infrastructures on freight transport flows in and through Wallonia. The work started with the setting up of a calibrated multimodal and multi-products reference scenario for the year 1995. This reference scenario was then used as a basis to create a projection for the year 2010: in order to make this projection as realistic as possible, all the decided new infrastructures in Belgium and in the border countries that will be effective in 2010 were introduced in the model. Moreover, expected changes in the O-D matrixes were also introduced at a very detailed level. Then, a set of scenarios was build: one for each transportation mode in which specific changes for that mode were introduced, and one in which the external costs of transport were taken into account. On the basis of the obtained results, a ætransportation planÆ was built, in which the most promising changes in the different networks and policies were chosen. A sensitivity analysis (low and high economic activity) was finally performed