Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.

Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

Surgical correction of scoliosis: Numerical analysis and optimization of the procedure

A previously developed model is used to numerically simulate real clinical cases of the surgical correction of scoliosis. This model consists of one-dimensional finite elements with spatial deformation in which (i) the column is represented by its axis; (ii) the vertebrae are assumed to be rigid; and (iii) the deformability of the column is concentrated in springs that connect the successive rigid elements. The metallic rods used for the surgical correction are modeled by beam elements with linear elastic behavior. To obtain the forces at the connections between the metallic rods and the vertebrae geometrically, non-linear finite element analyses are performed. The tightening sequence determines the magnitude of the forces applied to the patient column, and it is desirable to keep those forces as small as possible. In this study, a Genetic Algorithm optimization is applied to this model in order to determine the sequence that minimizes the corrective forces applied during the surgery. This amounts to find the optimal permutation of integers 1, ... , n, n being the number of vertebrae involved. As such, we are faced with a combinatorial optimization problem isomorph to the Traveling Salesman Problem. The fitness evaluation requires one computing intensive Finite Element Analysis per candidate solution and, thus, a parallel implementation of the Genetic Algorithm is developed.

Wetting response of KrF laser ablated polyimide surfaces

The wettability of polyimide surfaces microstructured using KrF laser radiation at fluences above the material ablation threshold was studied by static contact angle measurements. The laser-treated surfaces present a morphology consisting of conical features whose dimensions and areal density depend on the fluence. The effect of these parameters on the surface apparent contact angle depends on the wetting regime. When wetting occurs in the homogeneous regime, the apparent contact angle of the treated surfaces increases with the radiation fluence because the cone dimensions increase. In contrast, when wetting occurs in the heterogeneous regime, the apparent contact angle increases with the radiation fluence because the average distance between cones increases. The apparent water contact angle of the laser-treated surfaces can reach values as high as 162 degrees, as compared to 75 degrees for virgin polyimide.

Structural and optical studies of Au doped titanium oxide films

Thin films of TiO2 were doped with Au by ion implantation and in situ during the deposition. The films were grown by reactive magnetron sputtering and deposited in silicon and glass substrates at a temperature around 150 degrees C. The undoped films were implanted with Au fiuences in the range of 5 x 10(15) Au/cm(2)-1 x 10(17) Au/cm(2) with a energy of 150 keV. At a fluence of 5 x 10(16) Au/cm(2) the formation of Au nanoclusters in the films is observed during the implantation at room temperature. The clustering process starts to occur during the implantation where XRD estimates the presence of 3-5 nm precipitates. After annealing in a reducing atmosphere, the small precipitates coalesce into larger ones following an Ostwald ripening mechanism. In situ XRD studies reveal that Au atoms start to coalesce at 350 degrees C, reaching the precipitates dimensions larger than 40 nm at 600 degrees C. Annealing above 700 degrees C promotes drastic changes in the Au profile of in situ doped films with the formation of two Au rich regions at the interface and surface respectively. The optical properties reveal the presence of a broad band centered at 550 nm related to the plasmon resonance of gold particles visible in AFM maps. (C) 2011 Elsevier B.V. All rights reserved.

Mass spectrometry improvement on an high current ion implanter

The development of accurate mass spectrometry, enabling the identification of all the ions extracted from the ion source in a high current implanter is described. The spectrometry system uses two signals (x-y graphic), one proportional to the magnetic field (x-axes), taken from the high-voltage potential with an optic fiber system, and the other proportional to the beam current intensity (y-axes), taken from a beam-stop. The ion beam mass register in a mass spectrum of all the elements magnetically analyzed with the same radius and defined by a pair of analyzing slits as a function of their beam intensity is presented. The developed system uses a PC to control the displaying of the extracted beam mass spectrum, and also recording of all data acquired for posterior analysis. The operator uses a LabView code that enables the interfacing between an I/O board and the ion implanter. The experimental results from an ion implantation experiment are shown. (C) 2011 Elsevier B.V. All rights reserved.

Sobrevivência: jogo interactivo para estudo de arquitecturas de agentes autónomos

Trabalho de projeto para obtenção do grau de Mestre em Engenharia Informática e de Computadores

Gamma radiation effects on microbial inactivation of two medicinal plants

The consumption of natural products has become a public health problem, since these medicinal teas are prepared using natural plants without an effective hygienic and sanitary control. The aim of this study was to assess the effects of gamma radiation, on the microbial burden of two medicinal plants: Melissa officinalis and Lippia citriodora. Dried samples of the two plants were irradiated at a Co-60 experimental equipment. The applied gamma radiation doses were 1, 3, and 5 kGy at a dose rate of 1.34 kGy/h. Non-irradiated samples followed all the experiments. Bacterial and fungal counts were assessed before and after irradiation by membrane filtration method. Challenging tests with Escherichia coli were performed in order to evaluate the disinfection efficiency of gamma radiation treatment. Characterization of M. officinalis and L. citriadora microbiota indicated an average bioburden value of 102CFU/g. The inactivation studies of the bacterial mesophilic population of both dried plants pointed out to a one log reduction of microbial load after irradiation at 5 kGy. Regarding the fungal population, the initial load of 30 CFU/g was only reduced by 0.5 log by an irradiation dose of 5 kGy. The dynamics with radiation doses of plants microbial population’s phenotypes indicated the prevalence of gram-positive rods for M. officinalis before and after irradiation, and the increase of the frequency of gram-negative rods with irradiation for L. citriadora. Among fungal population of both plants, Mucor, Neoscytalidium, Aspergillus and Alternaria were the most isolated genera. The results obtained in the challenging tests with E. coli on plants pointed out to an inactivation efficiency of 99.5% and 99.9% to a dose of 2 kGy, for M.officinalis and L. citriadora, respectively. The gamma radiation treatment can be a significant tool for the microbial control in medicinal plants.

Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.

Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.