On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

Non-linear dynamics of a tower orchard sprayer based on an inverted pendulum model

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

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

Non-linear growth models for bullfrog tadpoles

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

Comparison of simulated periodontal bone defect depth measured in digital radiographs in dedicated and non-dedicated software systems

Objectives: To compare simulated periodontal bone defect depth measured in digital radiographs with dedicated and non-dedicated software systems and to compare the depth measurements from each program with the measurements in dry mandibles.Methods: Forty periodontal bone defects were created at the proximal area of the first premolar in dry pig mandibles. Measurements of the defects were performed with a periodontal probe in the dry mandible. Periapical digital radiographs of the defects were recorded using the Schick sensor in a standardized exposure setting. All images were read using a Schick dedicated software system (CDR DICOM for Windows v.3.5), and three commonly available non-dedicated software systems (Vix Win 2000 v.1.2; Adobe Photoshop 7.0 and Image Tool 3.0). The defects were measured three times in each image and a consensus was reached among three examiners using the four software systems. The difference between the radiographic measurements was analysed using analysis of variance (ANOVA) and by comparing the measurements from each software system with the dry mandibles measurements using Student's t-test.Results: the mean values of the bone defects measured in the radiographs were 5.07 rum, 5.06 rum, 5.01 mm and 5.11 mm for CDR Digital Image and Communication in Medicine (DICOM) for Windows, Vix Win, Adobe Photoshop, and Image Tool, respectively, and 6.67 mm for the dry mandible. The means of the measurements performed in the four software systems were not significantly different, ANOVA (P = 0.958). A significant underestimation of defect depth was obtained when we compared the mean depths from each software system with the dry mandible measurements (t-test; P congruent to 0.000).Conclusions: the periodontal bone defect measurements in dedicated and in three non-dedicated software systems were not significantly different, but they all underestimated the measurements when compared with the measurements obtained in the dry mandibles.

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

Structure characterization of molecular complexes for non-linear optical materials. II. 1 : 1 complexes of 4-methyl-morpholine-N-oxide (1) and 3-picoline-N-oxide (2) with 2,4,6-trinitrophenol, studied by X-ray, AM1 and DFT calculations

(1) C6H2N3O7- center dot C5H12NO2+, Mr = 346.26, P2(1)/c, a = 7.2356(6), b = 10.5765(9), c = 19.593(2) angstrom, 3 beta=95.101(6)degrees, V = 1493.5(2) angstrom(3), Z = 4, R-1 = 0.0414; (2) C6H2N3O7- center dot C6H8NO+, Mr = 38.24, P2(1)/n, a = 7.8713(5), b = 6.1979(7), c = 28.697(3) angstrom, beta = 90.028(7)degrees, V = 1400.0(2) angstrom(3), Z = 4, R-1 = 0.0416. The packing units in both compounds consist of hydrogen bonded cation-anion pairs. The (hyper)polarizabilities have been calculated for the crystallographic and optimized molecules, by AM1 and at the DFT/B3LYP(6-31G**) level.

Non-linear boundary element analysis of floor slabs reinforced with rectangular beams

In this work, a numerical model to perform non-linear analysis of building floor structures is proposed. The presented model is derived from the Kirchhoff-s plate bending formulation of the boundary element method (BENI) for zoned domains, in which the plate stiffness is modified by the presence of membrane effects. In this model, no approximation of the generalized forces along the interface is required and the compatibility and equilibrium conditions along interfaces are imposed at the integral equation level. In order to reduce the number of degrees of freedom, the Navier Bernoulli hypothesis is assumed to simplify the strain field for the thin sub-regions (rectangular beams). The non-linear formulation is obtained from the linear formulation by incorporating initial internal force fields, which are approximated by using the well-known cell sub-division. Then, the non-linear solution of algebraic equations is obtained by using the concept of the consistent tangent operator. The Von Mises criterion is adopted to govern the elasto-plastic material behaviour checked at points along the plate thickness and along the rectangular beam element axes. The numerical representations are accurately obtained by either computing analytically the element integrals or performing the numerical integration accurately using an appropriate sub-elementation scheme. (C) 2007 Elsevier Ltd. All rights reserved.

On the limit cycles of a class of piecewise linear differential systems in R-4 with two zones

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

Sufficients conditions for analysis of extrema in the step-response of the linear control systems

This note deals whith the problem of extrema which may occur in the step-response of a stable linear system with real zeros and poles. Some simple sufficients conditions and necessary conditions are presented for analyses when zeros located between the dominant and fastest pole does not cause extrema in the step-response. These conditions require knowledge of the pole-zero configuration of the corresponding transfer-function.

Non-linear analysis of reinforced concrete plates by the boundary element method and continuum damage mechanics

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

On non-linear W-infinity symmetry of generalized Liouville and conformal Toda models

Invariance under non-linear Ŵ∞ algebra is shown for the two-boson Liouville type of model and its algebraic generalizations, the extended conformal Toda models. The realization of the corresponding generators in terms of two boson currents within KP hierarchy is presented.

Giant non-linear absorption in Er3+-doped fluoroindate glass

Non-linear absorption is observed in Er3+-doped fluoroindate glass (in mol% 37InF2:20ZnF2:20SrF2:16BaF2:2GdF2: 2NaF:1GaF3:2ErF3) when the sample is irradiated with a CW laser emitting at 650 nm. An intensity dependence of the optical transmittance is detected. Saturation and sequential absorption of two photons are responsible for the decrease of 50% in the transmittance. The results are explained by simple models which are solved based on rate-equations for the populations of energy levels.