Lyapunov Stability of First and Second Order GeCo and gBBKS Schemes

In this paper we investigate the stability properties of fixed points of the so-called gBBKS and GeCo methods, which belong to the class of non-standard schemes and preserve the positivity as well as all linear invariants of the underlying system of ordinary differential equations for any step size. The schemes are applied to general linear test equations and proven to be generated by $\mathcal C^1$-maps with locally Lipschitz continuous first derivatives. As a result, a recently developed stability theorem can be applied to investigate the Lyapunov stability of non-hyperbolic fixed points of the numerical method by analyzing the spectrum of the corresponding Jacobian of the generating map. In addition, if a fixed point is proven to be stable, the theorem guarantees the local convergence of the iterates towards it. In the case of first and second order gBBKS schemes the stability domain coincides with that of the underlying Runge--Kutta method. Furthermore, while the first order GeCo scheme converts steady states to stable fixed points for all step sizes and all linear test problems of finite size, the second order GeCo scheme has a bounded stability region for the considered test problems. Finally, all theoretical predictions from the stability analysis are validated numerically.Comment: 31 pages, 7 figure

Evaluation of oscillator strength in colloidal CdSe/CdS dots‐in‐rods

The oscillator strength in CdSe/CdS colloidal dot-in-rods is evaluated and assessed to be of ∼1.5. On the basis of this finding, the possibility to reach the strong coupling regime with photonic crystals nanocavities is discussed. In spite that carefully choosing the cavity parameters the strong coupling regime could be analytically achieved at room temperature, theoretical considerations show that the typical Rabi doublet cannot be resolved. The work draws also a viable strategy toward the observation of the strong coupling at cryogenic temperatures. (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Polarized single photon emission for quantum cryptography based on colloidal nanocrystals

In this paper, the evidence of a polarized and room temperature single photon emission from wet-chemically synthesized colloidal dot-in-a-rod is reported. The time and polarization resolved measurements clearly indicate a high degree of linear polarization and a lifetime of ∼11 ns. We report also about a viable strategy to develop single photon sources with polarization control for quantum cryptography

Room temperature-dipolelike single photon source with a colloidal dot-in-rod

We propose colloidal CdSe/CdS dots in rods as nonclassical sources for quantum information technology. Such nanoemitters show specific properties such as strongly polarized emission of on-demand single photons at room temperature, dipolelike behavior and mono-exponential recombination rates, making us envision their suitability as sources of single photons with well defined quantum states in quantum cryptography based devices

The Seascape of Demersal Fish Nursery Areas in the North Mediterranean Sea, a First Step Towards the Implementation of Spatial Planning for Trawl Fisheries

The identification of nursery grounds and other essential fish habitats of exploited stocks is a key requirement for the development of spatial conservation planning aimed at reducing the adverse impact of fishing on the exploited populations and ecosystems. The reduction in juvenile mortality is particularly relevant in the Mediterranean and is considered as one of the main prerequisites for the future sustainability of trawl fisheries. The distribution of nursery areas of 11 important commercial species of demersal fish and shellfish was analysed in the European Union Mediterranean waters using time series of bottom trawl survey data with the aim of identifying the most persistent recruitment areas. A high interspecific spatial overlap between nursery areas was mainly found along the shelf break of many different sectors of the Northern Mediterranean indicating a high potential for the implementation of conservation measures. Overlap of the nursery grounds with existing spatial fisheries management measures and trawl fisheries restricted areas was also investigated. Spatial analyses revealed considerable variation depending on species and associated habitat/depth preferences with increased protection seen in coastal nurseries and minimal protection seen for deeper nurseries (e.g. Parapenaeus longirostris 6%). This is partly attributed to existing environmental policy instruments (e.g. Habitats Directive and Mediterranean Regulation EC 1967/2006) aiming at minimising impacts on coastal priority habitats such as seagrass, coralligenous and maerl beds. The new knowledge on the distribution and persistence of demersal nurseries provided in this study can support the application of spatial conservation measures, such as the designation of no-take Marine Protected Areas in EU Mediterranean waters and their inclusion in a conservation network. The establishment of no-take zones will be consistent with the objectives of the Common Fisheries Policy applying the ecosystem approach to fisheries management and with the requirements of the Marine Strategy Framework Directive to maintain or achieve seafloor integrity and good environmental status.Versión del editor4,411

Non-Standard Discrete RothC Models for Soil Carbon Dynamics

Soil Organic Carbon (SOC) is one of the key indicators of land degradation. SOC positively affects soil functions with regard to habitats, biological diversity and soil fertility; therefore, a reduction in the SOC stock of soil results in degradation, and it may also have potential negative effects on soil-derived ecosystem services. Dynamical models, such as the Rothamsted Carbon (RothC) model, may predict the long-term behaviour of soil carbon content and may suggest optimal land use patterns suitable for the achievement of land degradation neutrality as measured in terms of the SOC indicator. In this paper, we compared continuous and discrete versions of the RothC model, especially to achieve long-term solutions. The original discrete formulation of the RothC model was then compared with a novel non-standard integrator that represents an alternative to the exponential Rosenbrock–Euler approach in the literature

On the dynamics of first and second order {GeCo} and {gBBKS} schemes

In this paper we investigate the stability properties of the so-called gBBKS and GeCo methods, which belong to the class of nonstandard schemes and preserve the positivity as well as all linear invariants of the underlying system of ordinary differential equations for any step size. A stability investigation for these methods, which are outside the class of general linear methods, is challenging since the iterates are always generated by a nonlinear map even for linear problems. Recently, a stability theorem was derived presenting criteria for understanding such schemes. For the analysis, the schemes are applied to general linear equations and proven to be generated by C1-maps with locally Lipschitz continuous first derivatives. As a result, the above mentioned stability theorem can be applied to investigate the Lyapunov stability of non-hyperbolic fixed points of the numerical method by analyzing the spectrum of the corresponding Jacobian of the generating map. In addition, if a fixed point is proven to be stable, the theorem guarantees the local convergence of the iterates towards it. In the case of first and second order gBBKS schemes the stability domain coincides with that of the underlying Runge-Kutta method. Furthermore, while the first order GeCo scheme converts steady states to stable fixed points for all step sizes and all linear test problems of finite size, the second order GeCo scheme has a bounded stability region for the considered test problems. Finally, all theoretical predictions from the stability analysis are validated numerically

Optimal spatiotemporal effort allocation for invasive species removal incorporating a removal handling time and budget

Improving strategies for the control and eradication of invasive species is an important aspect of nature conservation, an aspect where mathematical modeling and optimization play an important role. In this paper, we introduce a reaction-diffusion partial differential equation to model the spatiotemporal dynamics of an invasive species, and we use optimal control theory to solve for optimal management, while implementing a budget constraint. We perform an analytical study of the model properties, including the well-posedness of the problem. We apply this to two hypothetical but realistic problems involving plant and animal invasive species. This allows us to determine the optimal space and time allocation of the efforts, as well as the final length of the removal program so as to reach the local extinction of the species

Mathematical Tools for Controlling Invasive Species in Protected Areas

A challenging task in the management of Protected Areas is to control the spread of invasive species, either floristic or faunistic, and the preservation of indigenous endangered species, typically competing for the use of resources in a fragmented habitat. In this paper, we present some mathematical tools that have been recently applied to contain the worrying diffusion of wolf-wild boars in a Southern Italy Protected Area belonging to the Natura 2000 network. They aim to solve the problem according to three different and in some sense complementary approaches: (i) the qualitative one, based on the use of dynamical systems and bifurcation theory; (ii) the Z-control, an error-based neural dynamic approach; (iii) the optimal control theory. In the case of the wild-boars, the obtained results are illustrated and discussed. To refine the optimal control strategies, a further development is to take into account the spatio-temporal features of the invasive species over large and irregular environments. This approach can be successfully applied, with an optimal allocation of resources, to control an invasive alien species infesting the Alta Murgia National Park: Ailanthus altissima. This species is one of the most invasive species in Europe and its eradication and control is the object of research projects and biodiversity conservation actions in both protected and urban areas. We lastly present, as a further example, the effects of the introduction of the brook trout, an alien salmonid from North America, in naturally fishless lakes of the Gran Paradiso National Park, study site of an on-going H2020 project (ECOPOTENTIAL)