Nonautonomous difference equations with applications

This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.

Short-term temporal changes of soil carbon losses after tillage described by a first-order decay model

Tillage stimulates soil carbon (C) losses by increasing aeration, changing temperature and moisture conditions, and thus favoring microbial decomposition. In addition, soil aggregate disruption by tillage exposes once protected organic matter to decomposition. We propose a model to explain carbon dioxide (CO2) emission after tillage as a function of the no-till emission plus a correction due to the tillage disturbance. The model assumes that C in the readily decomposable organic matter follows a first-order reaction kinetics equation as: dC(sail)(t)/dt = -kC(soil)(t) and that soil C-CO2 emission is proportional to the C decay rate in soil, where C-soil(t) is the available labile soil C (g m(-2)) at any time (t). Emissions are modeled in terms soil C available to decomposition in the tilled and non-tilled plots, and a relationship is derived between no-till (F-NT) and tilled (F-Gamma) fluxes, which is: F-T = a1F(NT)e(-a2t), where t is time after tillage. Predicted and observed fluxes showed good agreement based on determination coefficient (R-2), index of agreement and model efficiency, with R-2 as high as 0.97. The two parameters included in the model are related to the difference between the decay constant (k factor) of tilled and no-till plots (a(2)) and also to the amount of labile carbon added to the readily decomposable soil organic matter due to tillage (a,). These two parameters were estimated in the model ranging from 1.27 and 2.60 (a(1)) and - 1.52 x 10(-2) and 2.2 x 10(-2) day(-1) (a(2)). The advantage is that temporal variability of tillage-induced emissions can be described by only one analytical function that includes the no-till emission plus an exponential term modulated by tillage and environmentally dependent parameters. (C) 2008 Elsevier B.V. All rights reserved.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom-Pom model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GPS Satellite Kinematic Relative Positioning: Analyzing and Improving the Functional Mathematical Model Using Wavelets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A model to predict R134a refrigerant leakage through the radial clearance of rolling piston compressors

In this paper a non-isothermal two-phase model for oil-R134a refrigerant mixture flow is presented to predict the R134a leakage through the radial clearance of rolling piston compressors. The flow is divided in a liquid single-phase region and in a two-phase region, in which the homogeneous model is used to simulate the flow. The refrigerant leakage is determined using the mixture mass flow rate and the refrigerant mass fraction variation along the flow. The results are obtained for inlet pressures varying from 200 to 700 kPa, inlet temperatures ranging from 40 to 60 degrees C, and minimal clearances between 10 and 60 mu m. The results are firstly compared to existing isothermal model data, showing that there is a significant difference between the leakage flow rates predicted by isothermal and non-isothermal models. Finally, a useful general equation for compressor designers is proposed to calculate the refrigerant leakage for a large range of operation conditions. (C) 2012 Elsevier Ltd and IIR. All rights reserved.

Experimental model of bladder instability in rabbits

OBJECTIVE: Propose a new experimental model of bladder instability in rabbits after partial bladder obstruction. MATERIALS and METHODS: Thirty North Folk male rabbits, weighting 1,700 to 2,820 g (mean: 2,162 g) were studied. The animals were distributed in 2 experimental groups, formed by 15 rabbits each: Group 1 - clinical control. In this group there was no surgical intervention; Group 2 - bladder outlet obstruction. In this group, after anesthetizing the animal, urethral cannulation with Foley catheter 10F was performed and then an adjustable plastic bracelet was passed around the bladder neck. It was then adjusted in order to not constrict the urethra. The following parameters were studied in M1 - pre-operative period; M2 - 4 weeks post-operatively moments: 1)- urine culture; 2)- cystometric study; 3)- serum creatinine and BUN. RESULTS: Bladder weight was 2.5 times larger in the group with obstruction than in the control group. Cystometric evaluation showed a significant increase in maximal vesical volume in the final moment at Group G2. However, there was no statistically significant difference among the groups studied. There was no statistically significant difference between maximal detrusor pressure and vesical compliance in the different moments or in the studied groups. There was an absence of uninhibited detrusor contractions in all the animals in group 1, and involuntary contractions were detected in 93% of group 2 animals. There was no significant variation in BUN and serum creatinine either among the groups or in the same group. CONCLUSIONS: We observed in the group with obstruction a bladder weight 2.5 higher than normal bladders. We detected involuntary contractions in 93% of the animals in group 2, establishing this experimental model as appropriate to secondary bladder instability and partial bladder outlet obstruction.

Growth hormone 1 gene (GH1) polymorphisms as possible markers of the production potential of beef cattle using the Brazilian Canchim breed as a model

The growth hormone 1 gene (GH1) is a candidate gene for body weight and weight gain in cattle since it plays a fundamental role in growth regulation. We investigated the GH1 gene AluI and DdeI restriction enzyme polymorphisms, located 149 bp apart in the cattle genome, as possible markers of the production potential of Canchim crossbreed cattle, a 5/8 Charolais (Bos taurus) and 3/8 Nelore (Bos indicus) breed developed in Brazil, by evaluating the birth weight, weaning weight, yearling weight and plasma insulin-like growth factor-1 (IGF-1) concentration of 7 month to 10 months old Canchim calves (n = 204) of known genealogy and which had been genotyped for the AluI and DdeI markers. Our results showed significant effect (p < 0.05) between the homozygous DdeI+/DdeI+ polymorphism and the estimated breeding value for weaning weight (ESB-WW), while the AluI leucine homozygous (L/L) and leucine/valine (L/V) heterozygous polymorphisms showed no significant effect on the traits studied. The restriction sites of the two enzymes led to the formation of haplotypes which also exerted a significant effect (p < 0.05) on the ESB-WW, with the largest difference being 8.5 kg in favor of the homozygous L plus DdeI+/L plus DdeI+ genotype over the heterozygous L plus DdeI-/V plus DdeI+ genotype.

Susceptibility of Candida albicans to photodynamic therapy in a murine model of oral candidosis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Vector and axial-vector correlators in a non-local chiral quark model

The behavior of the non-perturbative parts of the isovector-vector and isovector and isosinglet axial-vector correlators at Euclidean momenta is studied in the framework of a covariant chiral quark model with non-local quark-quark interactions. The gauge covariance is ensured with the help of the P-exponents, with the corresponding modification of the quark-current interaction vertices taken into account. The low- and high-momentum behavior of the correlators is compared with the chiral perturbation theory and with the QCD operator product expansion, respectively. The V-A combination of the correlators obtained in the model reproduces quantitatively the ALEPH and OPAL data on hadronic tau decays, transformed into the Euclidean domain via dispersion relations. The predictions for the electromagnetic pi(+/-) - pi(0) mass difference and for the pion electric polarizability are also in agreement with the experimental values. The topological susceptibility of the vacuum is evaluated as a function of the momentum, and its first moment is predicted to be chi'(0) approximate to (50 MeV)(2). In addition, the fulfillment of the Crewther theorem is demonstrated.

IMPROVED STATISTICAL QCD MODEL FOR THE QUARK CONTENT of THE NUCLEON

The neutron-to-proton ratio of the structure functions, F(2)(n)/F(2)(p), as well as the corresponding difference F(2)(p)-F(2)(n) are obtained within a statistical quark model for the nucleon, where the quark energy levels are given by a central linear confining potential.

THE HIGGS PORTAL and AN UNIFIED MODEL FOR DARK ENERGY and DARK MATTER

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Direct measurement of the mass difference between top and antitop quarks

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Genetic trends in the expected progeny difference of the asymptotic weight of Nelore females

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Difference variance dispersion graphs for comparing response surface designs with applications in food technology

Variance dispersion graphs have become a popular tool in aiding the choice of a response surface design. Often differences in response from some particular point, such as the expected position of the optimum or standard operating conditions, are more important than the response itself. We describe two examples from food technology. In the first, an experiment was conducted to find the levels of three factors which optimized the yield of valuable products enzymatically synthesized from sugars and to discover how the yield changed as the levels of the factors were changed from the optimum. In the second example, an experiment was conducted on a mixing process for pastry dough to discover how three factors affected a number of properties of the pastry, with a view to using these factors to control the process. We introduce the difference variance dispersion graph (DVDG) to help in the choice of a design in these circumstances. The DVDG for blocked designs is developed and the examples are used to show how the DVDG can be used in practice. In both examples a design was chosen by using the DVDG, as well as other properties, and the experiments were conducted and produced results that were useful to the experimenters. In both cases the conclusions were drawn partly by comparing responses at different points on the response surface.