Generalized models from Beta(p,2) densities with strong allee effect: dynamical approach

A dynamical approach to study the behaviour of generalized populational growth models from Bets(p, 2) densities, with strong Allee effect, is presented. The dynamical analysis of the respective unimodal maps is performed using symbolic dynamics techniques. The complexity of the correspondent discrete dynamical systems is measured in terms of topological entropy. Different populational dynamics regimes are obtained when the intrinsic growth rates are modified: extinction, bistability, chaotic semistability and essential extinction.

A combined statistical and dynamical approach for downscaling large-scale footprints of European windstorms

The occurrence of mid-latitude windstorms is related to strong socio-economic effects. For detailed and reliable regional impact studies, large datasets of high-resolution wind fields are required. In this study, a statistical downscaling approach in combination with dynamical downscaling is introduced to derive storm related gust speeds on a high-resolution grid over Europe. Multiple linear regression models are trained using reanalysis data and wind gusts from regional climate model simulations for a sample of 100 top ranking windstorm events. The method is computationally inexpensive and reproduces individual windstorm footprints adequately. Compared to observations, the results for Germany are at least as good as pure dynamical downscaling. This new tool can be easily applied to large ensembles of general circulation model simulations and thus contribute to a better understanding of the regional impact of windstorms based on decadal and climate change projections.

Sphere of influence and gravitational capture radius: a dynamical approach

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamical Approach for Real-Time Monitoring of Agricultural Crops

In this paper, a novel approach for exploiting multitemporal remote sensing data focused on real-time monitoring of agricultural crops is presented. The methodology is defined in a dynamical system context using state-space techniques, which enables the possibility of merging past temporal information with an update for each new acquisition. The dynamic system context allows us to exploit classical tools in this domain to perform the estimation of relevant variables. A general methodology is proposed, and a particular instance is defined in this study based on polarimetric radar data to track the phenological stages of a set of crops. A model generation from empirical data through principal component analysis is presented, and an extended Kalman filter is adapted to perform phenological stage estimation. Results employing quad-pol Radarsat-2 data over three different cereals are analyzed. The potential of this methodology to retrieve vegetation variables in real time is shown.

Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Synchronization in Von Bertalanffy’s models

Many data have been useful to describe the growth of marine mammals, invertebrates and reptiles, seabirds, sea turtles and fishes, using the logistic, the Gom-pertz and von Bertalanffy's growth models. A generalized family of von Bertalanffy's maps, which is proportional to the right hand side of von Bertalanffy's growth equation, is studied and its dynamical approach is proposed. The system complexity is measured using Lyapunov exponents, which depend on two biological parameters: von Bertalanffy's growth rate constant and the asymptotic weight. Applications of synchronization in real world is of current interest. The behavior of birds ocks, schools of fish and other animals is an important phenomenon characterized by synchronized motion of individuals. In this work, we consider networks having in each node a von Bertalanffy's model and we study the synchronization interval of these networks, as a function of those two biological parameters. Numerical simulation are also presented to support our approaches.

Caos e termalização na teoria de Yang-Mills com quebra espontânea de simetria

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamic Studies of Shell and Spatial Structures

For the past 20 years, dynamic analysis of shells has been one of the most fascinating fields for research. Using the new light materials the building engineer soon discovered that the subsequent reduction of gravity forces produced not only the desired shape freedom but the appearance of ecologic loads as the first factor of design; loads which present strong random properties and marked dynamic influence. On the other hand, the technological advance in the aeronautical and astronautical field placed the engineers in front of shell structures of nonconventional shape and able to sustain substantialy dynamic loads. The response to the increasingly challenger problems of the last two decades has been very bright; new forms, new materials and new methods of analysis have arosen in the design of off-shore platforms, nuclear vessels, space crafts, etc. Thanks to the intensity of the lived years we have at our disposition a coherent and homogeneous amount of knowledge which enable us to face problems of inconceivable complexity when IASS was founded. The open minded approach to classical problems and the impact of the computer are, probably, important factors in the Renaissance we have enjoyed these years, and a good proof of this are the papers presented to the previous IASS meetings as well as that we are going to consider in this one. Particularly striking is the great number of papers based on a mathematical modeling in front of the meagerness of those treating laboratory experiments on physical models. The universal entering of the computer into almost every phase of our lifes, and the cost of physical models, are –may be- reasons for this lack of experimental methods. Nevertheless they continue offering useful results as are those obtained with the shaking-table in which the computer plays an essential role in the application of loads as well as in the instantaneous treatment of control data. Plates 1 and 2 record the papers presented under dynamic heading, 40% of them are from Japan in good correlation with the relevance that Japanese research has traditionally showed in this area. Also interesting is to find old friends as profesors Tanaka, Nishimura and Kostem who presented valuable papers in previous IASS conferences. As we see there are papers representative of all tendencies, even purely analytical! Better than discuss them in detail, which can be done after the authors presentation, I think we can comment in the general pattern of the dynamical approach are summarized in plate 3.

Microcanonical temperature for a classical field: Application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a uv cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behavior of the specific heat.

Calculation of the microcanonical temperature for the classical Bose field

The ergodic hypothesis asserts that a classical mechanical system will in time visit every available configuration in phase space. Thus, for an ergodic system, an ensemble average of a thermodynamic quantity can equally well be calculated by a time average over a sufficiently long period of dynamical evolution. In this paper, we describe in detail how to calculate the temperature and chemical potential from the dynamics of a microcanonical classical field, using the particular example of the classical modes of a Bose-condensed gas. The accurate determination of these thermodynamics quantities is essential in measuring the shift of the critical temperature of a Bose gas due to nonperturbative many-body effects.

Transport properties of strongly correlated metals: A dynamical mean-field approach

The temperature dependence of the transport properties of the metallic phase of a frustrated Hubbard model on the hypercubic lattice at half-filling is calculated. Dynamical mean-held theory, which maps the Hubbard model onto a single impurity,Anderson model that is solved self-consistently, and becomes exact in the limit of large dimensionality, is used. As the temperature increases there is a smooth crossover from coherent Fermi liquid excitations at low temperatures to incoherent excitations at high temperatures. This crossover leads to a nonmonotonic temperature dependence for the resistance, thermopower, and Hall coefficient, unlike in conventional metals. The resistance smoothly increases from a quadratic temperature dependence at low temperatures to large values which can exceed the Mott-Ioffe-Regel value ha/e(2) (where a is a lattice constant) associated with mean free paths less than a lattice constant. Further signatures of the thermal destruction of quasiparticle excitations are a peak in the thermopower and the absence of a Drude peak in the optical conductivity. The results presented here are relevant to a wide range of strongly correlated metals, including transition metal oxides, strontium ruthenates, and organic metals.