Bifurcation analysis of an aeroelastic system with concentrated nonlinearities

Analytical and numerical analyses of the nonlinear response of a three-degree-of-freedom nonlinear aeroelastic system are performed. Particularly, the effects of concentrated structural nonlinearities on the different motions are determined. The concentrated nonlinearities are introduced in the pitch, plunge, and flap springs by adding cubic stiffness in each of them. Quasi-steady approximation and the Duhamel formulation are used to model the aerodynamic loads. Using the quasi-steady approach, we derive the normal form of the Hopf bifurcation associated with the system's instability. Using the nonlinear form, three configurations including supercritical and subcritical aeroelastic systems are defined and analyzed numerically. The characteristics of these different configurations in terms of stability and motions are evaluated. The usefulness of the two aerodynamic formulations in the prediction of the different motions beyond the bifurcation is discussed.

Modeling the emergence of HIV-1 drug resistance resulting from antiretroviral therapy: Insights from theoretical and numerical studies

The use of antiretroviral therapy has proven to be remarkably effective in controlling the progression of human immunodeficiency virus (HIV) infection and prolonging patient's survival. Therapy however may fail and therefore these benefits can be compromised by the emergence of HIV strains that are resistant to the therapy. In view of these facts, the question of finding the reason for which drug-resistant strains emerge during therapy has become a worldwide problem of great interest. This paper presents a deterministic HIV-1 model to examine the mechanisms underlying the emergence of drug-resistance during therapy. The aim of this study is to determine whether, and how fast, antiretroviral therapy may determine the emergence of drug resistance by calculating the basic reproductive numbers. The existence, feasibility and local stability of the equilibriums are also analyzed. By performing numerical simulations we show that Hopf bifurcation may occur. The model suggests that the individuals with drug-resistant infection may play an important role in the epidemic of HIV. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Modeling and identification of freeplay nonlinearity

A nonlinear analysis is performed for the purpose of identification of the pitch freeplay nonlinearity and its effect on the type of bifurcation of a two degree-of-freedom aeroelastic system. The databases for the identification are generated from experimental investigations of a pitch-plunge rigid airfoil supported by a nonlinear torsional spring. Experimental data and linear analysis are performed to validate the parameters of the linearized equations. Based on the periodic responses of the experimental data which included the flutter frequency and its third harmonics, the freeplay nonlinearity is approximated by a polynomial expansion up to the third order. This representation allows us to use the normal form of the Hopf bifurcation to characterize the type of instability. Based on numerical integrations, the coefficients of the polynomial expansion representing the freeplay nonlinearity are identified. Published by Elsevier Ltd.

Linear parameter varying control design for rotating systems supported by journal bearings

Linear parameter varying (LPV) control is a model-based control technique that takes into account time-varying parameters of the plant. In the case of rotating systems supported by lubricated bearings, the dynamic characteristics of the bearings change in time as a function of the rotating speed. Hence, LPV control can tackle the problem of run-up and run-down operational conditions when dynamic characteristics of the rotating system change significantly in time due to the bearings and high vibration levels occur. In this work, the LPV control design for a flexible shaft supported by plain journal bearings is presented. The model used in the LPV control design is updated from unbalance response experimental results and dynamic coefficients for the entire range of rotating speeds are obtained by numerical optimization. Experimental implementation of the designed LPV control resulted in strong reduction of vibration amplitudes when crossing the critical speed, without affecting system behavior in sub- or supercritical speeds. (C) 2012 Elsevier Ltd. All rights reserved.

Buccal Bone Plate Remodeling After Immediate Implant Placement With and Without Synthetic Bone Grafting and Flapless Surgery: Radiographic Study in Dogs

Recent studies in animals have shown pronounced resorption of the buccal bone plate after immediate implantation. The use of flapless surgical procedures prior to the installation of immediate implants, as well as the use of synthetic bone graft in the gaps represent viable alternatives to minimize buccal bone resorption and to favor osseointegration. The aim of this study was to evaluate the healing of the buccal bone plate following immediate implantation using the flapless approach, and to compare this process with sites in which a synthetic bone graft was or was not inserted into the gap between the implant and the buccal bone plate. Lower bicuspids from 8 dogs were bilaterally extracted without the use of flaps, and 4 implants were installed in the alveoli in each side of the mandible and were positioned 2.0 mm from the buccal bone plate (gap). Four groups were devised: 2.0-mm subcrestal implants (3.3 x 8 mm) using bone grafts (SCTG), 2.0-mm subcrestal implants without bone grafts (SCCG), equicrestal implants (3.3 x 10 mm) with bone grafts (EGG), and equicrestal implants without bone grafts (ECCG). One week following the surgical procedures, metallic prostheses were installed, and within 12 weeks the dogs were sacrificed. The blocks containing the individual implants were turned sideways, and radiographic imaging was obtained to analyze the remodeling of the buccal bone plate. In the analysis of the resulting distance between the implant shoulder and the bone crest, statistically significant differences were found in the SCTG when compared to the ECTG (P = .02) and ECCG (P = .03). For mean value comparison of the resulting linear distance between the implant surface and the buccal plate, no statistically significant difference was found among all groups (P > .05). The same result was observed in the parameter for presence or absence of tissue formation between the implant surface and buccal plate. Equicrestally placed implants, in this methodology, presented little or no loss of the buccal bone. The subcrestally positioned implants presented loss of buccal bone, even though synthetic bone graft was used. The buccal bone, however, was always coronal to the implant shoulder.

Hero's journey in bifurcation diagram

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films. (C) 2011 Elsevier B.V. All rights reserved.