Behavioural Analysis of a Nonlinear Mechanical System Using Transient Trajectories

This work aims at a better comprehension of the features of the solution surface of a dynamical system presenting a numerical procedure based on transient trajectories. For a given set of initial conditions an analysis is made, similar to that of a return map, looking for the new configuration of this set in the first Poincaré sections. The mentioned set of I.C. will result in a curve that can be fitted by a polynomial, i.e. an analytical expression that will be called initial function in the undamped case and transient function in the damped situation. Thus, it is possible to identify using analytical methods the main stable regions of the phase portrait without a long computational time, making easier a global comprehension of the nonlinear dynamics and the corresponding stability analysis of its solutions. This strategy allows foreseeing the dynamic behavior of the system close to the region of fundamental resonance, providing a better visualization of the structure of its phase portrait. The application chosen to present this methodology is a mechanical pendulum driven through a crankshaft that moves horizontally its suspension point.

Reversible Hamiltonian Liapunov center theorem

We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.

Nonlinear absorption spectrum in perylene derivatives

Knowledge about nonlinear absorption spectra of materials used in photonic devices is of paramount importance in determining their optimum operation wavelengths. In this work, we have investigated the two-photon absorption (2PA) degenerate cross-section spectrum for perylene derivatives using the Z-scan technique with femtosecond laser pulses. All perylene derivatives studied present large 2PA cross-sections, only comparable to the best ones reported in the literature. The results achieved in the present investigation indicate perylene derivatives as promising materials for two-photon applications. ©2005 Optical Society of America.

Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.

Aspirado traqueal de cavalos clinicamente sadios da raça quarto de milha após prova de três tambores

The aim of the present study was to evaluate through endoscopy the tracheal aspiration cytology in twenty seven Quarter Horses from Curitiba and surroundings, following the Three Barrel Competittion. Upper respiratory tract secretion was obtained by tracheal aspiration using a polyethylene catheter introduced through the endoscopic fiberoptic working channel, at the level of tracheal bifurcation. Cytologic slides were prepared by smear and stained by diff-quick technique and the differential was performed in 500 cells counting by 1,000X optic microscopy. None of the horses presented abnormality, including epixtasis, at the clinical examination. However, hemosiderophages were detected at cytology in three animals, suggesting that some may be suffering of subclinical pulmonary hemorrhage. Differential cell counting of tracheal aspiration results were, in average: 44.09 ± 35.68% of epithelial cells; 1.10 ± 2.18% of Globet cells; 23.10 ± 35.93% of neutrophils; 0.13 ± 0.37% of lymphocytes; 0.91 ± 2.81% of eosinophils; 30.57 ± 23.62% of macrophages and 0.13 + 0.93% of hemosiderophages. In conclusion, based in the present study, the evaluation of cellular populations with the tracheal aspiration may offer important additional information to the clinician, particularly about the inflammatory processes of lower respiratory tract and pulmonary bleeding.

Dynamics of a piecewise-linear oscillator with limited power supply

We discuss dynamics of a vibro-impact system consisting of a cart with an piecewise-linear restoring force, which vibrates under driving by a source with limited power supply. From the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In our analyzes, we use bifurcation diagrams, basins of attractions, identifying several non-linear phenomena, such as chaotic regimes, crises, intermittent mechanisms, and coexistence of attractors with complex basins of attraction. © 2009 by ASME.

Chiral symmetry breaking with a confining propagator and dynamically massive gluons

Chiral symmetry breaking in QCD is studied introducing a confining effective propagator, as proposed recently by Cornwall, and considering the effect of dynamically massive gluons. The effective confining propagator has the form 1/(k2 +m2)2 and we study the bifurcation equation finding limits on the parameter m below which a satisfactory fermion mass solution is generated. Since the coupling constant and gluon propagator are damped in the infrared, due to the presence of a dynamical gluon mass, the major part of the chiral breaking is only due to the confining propagator and related to the low momentum region of the gap equation. We study the asymptotic behavior of the gap equation containing this confinement effect and massive gluon exchange, and find that the symmetry breaking can be approximated by an effective four-fermion interaction generated by the confining propagator. We compute some QCD chiral parameters as a function of m, finding values compatible with the experimental data. We find a simple approximate relation between the fermion condensate and dynamical mass for a given representation as a function of the parameters appearing in the effective confining propagator. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

On a control design to an AFM microcantilever beam, operating in a tapping-mode, with irregular behavior

In last decades, control of nonlinear dynamic systems became an important and interesting problem studied by many authors, what results the appearance of lots of works about this subject in the scientific literature. In this paper, an Atomic Force Microscope micro cantilever operating in tapping mode was modeled, and its behavior was studied using bifurcation diagrams, phase portraits, time history, Poincare maps and Lyapunov exponents. Chaos was detected in an interval of time; those phenomena undermine the achievement of accurate images by the sample surface. In the mathematical model, periodic and chaotic motion was obtained by changing parameters. To control the chaotic behavior of the system were implemented two control techniques. The SDRE control (State Dependent Riccati Equation) and Time-delayed feedback control. Simulation results show the feasibility of the bothmethods, for chaos control of an AFM system. Copyright © 2011 by ASME.

Nonlinear dynamics of a flexible portal frame under support excitation

This paper presents a nonlinear dynamic analysis of a flexible portal frame subjected to support excitation, which is provided by an electro-dynamical shaker. The problem is reduced to a mathematical model of four degrees of freedom and the equations of motion are derived via Lagrangian formulation. The main goal of this study is to investigate the dynamic interactions between a flexible portal frame and a non-ideal support excitation. The numerical analysis shows a complex behavior of the system, which can be observed by phase spaces, Poincaŕ sections and bifurcation diagrams. © 2012 American Institute of Physics.

Compartimentação geomorfológica e processos deposicionais no megaleque fluvial do rio São Lourenço, Pantanal mato-grossense

The Pantanal wetland is an extensive depositional tract characterized by the presence of fluvial megafans, from which that of the Taquari River is the most extensive and well known. Located on the northern border of the Pantanal, the São Lourenço megafan is a large distributary fluvial system with an area of 16,000 km2, but poorly known regarding its geomorphological and geological features. The Sao Lourenço and the Taquari are coalescent megafans, having the Piquiri interfan meander river in between them. Based on the interpretation of satellite images and field validation, it was possible to identify channel patterns, to interpret depositional and erosional processes, to recognize the phenomena of river avulsion and to map depositional lobes. Three geomorphological zones were recognized on the São Lourenço megafan: 1) abandoned depositional lobes located in the upper/intermediate fan, composed of Pleistocene fluvial deposits and exhibiting distributary paleochannels on their surfaces, which are currently being dissected by tributary channels; 2) an active Holocene confined meander belt formed by fluvial aggradation in a N65E incised-valley; 3) active depositional lobes placed on the distal part of the system, which are the main site of sedimentation and are characterized by frequent avulsion events, channel bifurcation, distributary drainage pattern and the presence of depositional lobated landforms. The active depositional lobes were formed due to an important event of river avulsion that caused the lower portion of the meander belt to be abandoned.

On the periodic solutions of a class of duffing differential equations

In this work we study the periodic solutions, their stability and bifurcation for the class of Duffing differential equation mathematical equation represented where C > 0, ε > 0 and Λ are real parameter, A(t), b(t) and h(t) are continuous T periodic functions and ε is sufficiently small. Our results are proved using the averaging method of first order.

Chromosome painting of Z and W sex chromosomes in Characidium (Characiformes, Crenuchidae)

Some species of the genus Characidium have heteromorphic ZZ/ZW sex chromosomes with a totally heterochromatic W chromosome. Methods for chromosome microdissection associated with chromosome painting have become important tools for cytogenetic studies in Neotropical fish. In Characidium cf. fasciatum, the Z chromosome contains a pericentromeric heterochromatin block, whereas the W chromosome is completely heterochromatic. Therefore, a probe was produced from the W chromosome through microdissection and degenerate oligonucleotide-primed polymerase chain reaction amplification. FISH was performed using the W probe on the chromosomes of specimens of this species. This revealed expressive marks in the pericentromeric region of the Z chromosome as well as a completely painted W chromosome. When applying the same probe on chromosome preparations of C. cf. gomesi and Characidium sp., a pattern similar to C. cf. fasciatum was found, while C. cf. zebra, C. cf. lagosantense and Crenuchus spilurus species showed no hybridization signals. Structural changes in the chromosomes of an ancestral sexual system in the group that includes the species C. cf. gomesi, C. cf. fasciatum and Characidium sp., could have contributed to the process of speciation and could represent a causal mechanism of chromosomal diversification in this group. The heterochromatinization process possibly began in homomorphic and homologous chromosomes of an ancestral form, and this process could have given rise to the current patterns found in the species with sex chromosome heteromorphism. © 2013 Springer Science+Business Media Dordrecht.

Local attractors, degeneracy and analyticity: Symmetry effects on the locally coupled Kuramoto model

In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart from the existence of local attractors, some unexpected features resulting from the symmetry properties, such as intermittent and chaotic period phase slips, degeneracy of stable solutions and double bifurcation composition. As a result of our analysis, we show that stable fixed points in the synchronized region may be obtained with just a small amount of the existent solutions, and for a class of natural frequencies configuration we show analytical expressions for the critical synchronization coupling as a function of the number of oscillators, both exact and asymptotic. © 2013 Elsevier Ltd. All rights reserved.

Mesh cancer: long-term mesh infection leading to squamous-cell carcinoma of the abdominal wall

Purpose: It is recognized that chronic inflammation can cause cancer. Even though most of the available synthetic meshes are considered non-carcinogenic, the inflammatory response to an infected mesh plays a constant aggression to the skin. Chronic mesh infection is frequently the result of misuse of mesh, and due to the challenging nature of this condition, patients usually suffer for years until the infected mesh is removed by surgical excision. Methods: We report two cases of squamous-cell carcinoma (SCC) of the abdominal wall, arising in patients with long-term mesh infection. Results: In both patients, the degeneration of mesh infection into SCC was presumably caused by the long-term inflammation secondary to infection. Patients presented with advanced SCC behaving just like the Marjolin's ulcers of burns. Radical surgical excision was the treatment of choice. The involvement of the bowel played an additional challenge in case 1, but it was possible to resect the tumor and the involved bowel and reconstruct the abdominal wall using polypropylene mesh as onlay reinforcement, in a single stage operation. He is now under adjuvant chemotherapy. The big gap in the midline after tumor resection in case 2 required mesh bridging to close the defect. The poor prognosis of case 2 who died months after the operation, and the involvement of the armpit, groin and mesenteric nodes in case 1 shows how aggressive this disease can be. Conclusion: Infected mesh must be treated early, by complete excision of the mesh. Long-standing mesh infection can degenerate into aggressive squamous-cell carcinoma of the skin. © 2013 Springer-Verlag France.