Comparison of fractal dimensions based on segmented NDVI fields obtained from different remote sensors.

Satellite image data have become an important source of information for monitoring vegetation and mapping land cover at several scales. Beside this, the distribution and phenology of vegetation is largely associated with climate, terrain characteristics and human activity. Various vegetation indices have been developed for qualitative and quantitative assessment of vegetation using remote spectral measurements. In particular, sensors with spectral bands in the red (RED) and near-infrared (NIR) lend themselves well to vegetation monitoring and based on them [(NIR - RED) / (NIR + RED)] Normalized Difference Vegetation Index (NDVI) has been widespread used. Given that the characteristics of spectral bands in RED and NIR vary distinctly from sensor to sensor, NDVI values based on data from different instruments will not be directly comparable. The spatial resolution also varies significantly between sensors, as well as within a given scene in the case of wide-angle and oblique sensors. As a result, NDVI values will vary according to combinations of the heterogeneity and scale of terrestrial surfaces and pixel footprint sizes. Therefore, the question arises as to the impact of differences in spectral and spatial resolutions on vegetation indices like the NDVI. The aim of this study is to establish a comparison between two different sensors in their NDVI values at different spatial resolutions

Communication: Transition State Theory for dissipative systems without a dividing surface

Transition state theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when the reactive system is coupled to an environment. The calculations made in this way then overestimate the reaction rate and the results depend critically on the choice of the dividing surface. In this Communication, we study the phase space of a stochastically driven system close to an energetic barrier in order to identify the geometric structure unambiguously determining the reactive trajectories, which is then incorporated in a simple rate formula for reactions in condensed phase that is both independent of the dividing surface and exact

A Multi-Fractal approach to soil thin sections in gray levels.

In the environment, as it is complex flows where Reynold number is quite high due to non-linear interactions in flows, several scales are developed. This type of hierarchy is detected in velocities as well as in the structure of scalar fields, as temperatures, tracer concentrations, density, etc. In these cases is interesting to relate in some way the geometrical o topological characteristics observed in flow images with their physical properties and dynamics. In the last decades many scientist has been applying fractal analysis to these types of images extracting several fractal dimensions for different intensity intervals. This type of analysis is what we call Multi-Fracta

Editorial on "Multiplex networks: Structure, dynamics and applications"

There is a wide range of systems in the real world where components cannot function independently, so that these components interact with others through different channels of connectivity and dependencies. Complex Networks theory is, in fact, the formal tool for describing and analyzing fields as disparate as sociology (social networks, acquaintances or collaborations between individuals), biology (metabolic and protein networks, neural networks) or technology (phone call networks, computers in telecommunication networks

Rate calculation in two dimensional barriers with colored noise

The identification of an optimal dividing surface that is free of recrossings is the most important re- quirement for transition state theory to be exact. This task is particularly difficult in the presence of non-Markovian friction, i.e., colored noise forces. In this paper, we report a novel geometric method that circumvents the recross- ing problem and is able to (i) identify reactive trajectories exactly, and (ii) compute reaction rates in a system with two degrees of freedom driven by non-Markovian friction. The extension of our method to higher dimensional systems is also discussed

Network models of soil porous structure

Soils sustain life on Earth. In times of increasing anthropogenic demands on soils [1] there is growing need to seek for novel approaches to understand the relationships between the soil porous structure and specific soil functions. Recently [2-4], soil pore structure was described as a complex network of pores using spatially embedded varying fitness network model [2] or heterogeneous preferential attachment scheme [3-4], both approaches revealing the apparent scale-free topology of soils. Here, we show, using a large set of soil images of structures obtained by X-ray computed tomography that both methods predict topological similar networks of soil pore structures. Furthermore, by analyzing the node-node link correlation properties of the obtained networks we suggest an approach to quantify the complexity of soil pore structur

Community Structure in Soil Porous System

Diffusion controls the gaseous transport process in soils when advective transport is almost null. Knowledge of the soil structure and pore connectivity are critical issues to understand and modelling soil aeration, sequestration or emission of greenhouse gasses, volatilization of volatile organic chemicals among other phenomena. In the last decades these issues increased our attention as scientist have realize that soil is one of the most complex materials on the earth, within which many biological, physical and chemical processes that support life and affect climate change take place. A quantitative and explicit characterization of soil structure is difficult because of the complexity of the pore space. This is the main reason why most theoretical approaches to soil porosity are idealizations to simplify this system. In this work, we proposed a more realistic attempt to capture the complexity of the system developing a model that considers the size and location of pores in order to relate them into a network. In the model we interpret porous soils as heterogeneous networks where pores are represented by nodes, characterized by their size and spatial location, and the links representing flows between them. In this work we perform an analysis of the community structure of porous media of soils represented as networks. For different real soils samples, modelled as heterogeneous complex networks, spatial communities of pores have been detected depending on the values of the parameters of the porous soil model used. These types of models are named as Heterogeneous Preferential Attachment (HPA). Developing an exhaustive analysis of the model, analytical solutions are obtained for the degree densities and degree distribution of the pore networks generated by the model in the thermodynamic limit and shown that the networks exhibit similar properties to those observed in other complex networks. With the aim to study in more detail topological properties of these networks, the presence of soil pore community structures is studied. The detection of communities of pores, as groups densely connected with only sparser connections between groups, could contribute to understand the mechanisms of the diffusion phenomena in soils

Multiscaling of soils as heterogeneous complex networks

In this paper we present a complex network model based on a heterogeneous preferential attachment scheme to quantify the structure of porous soils. Under this perspective pores are represented by nodes and the space for the flow of fluids between them is represented by links. Pore properties such as position and size are described by fixed states in a metric space, while an affinity function is introduced to bias the attachment probabilities of links according to these properties. We perform an analytical study of the degree distributions in the soil model and show that under reasonable conditions all the model variants yield a multiscaling behavior in the connectivity degrees, leaving a empirically testable signature of heterogeneity in the topology of pore networks. We also show that the power-law scaling in the degree distribution is a robust trait of the soil model and analyze the influence of the parameters on the scaling exponents. We perform a numerical analysis of the soil model for a combination of parameters corresponding to empirical samples with different properties, and show that the simulation results exhibit a good agreement with the analytical predictions

Unveiling the chaotic structure in molecular systems using Lagrangian descriptors

The phase space structure of a dynamical system determines, among other issues, its regular and chaotic bahavior, and the several indicators have been developed in order to correctly detect, characterize and analyze it

Unveiling the chaotic structure in molecular systems using Lagrangian descriptors

The phase space structure of a dynamical system determines, among other issues, its regular and chaotic bahavior, and the several indicators have been developed in order to correctly detect, characterize and analyze it