Blowout bifurcation and spatial mode excitation in the bubbling transition to turbulence

The transition to turbulence (spatio-temporal chaos) in a wide class of spatially extended dynamical system is due to the loss of transversal stability of a chaotic attractor lying on a homogeneous manifold (in the Fourier phase space of the system) causing spatial mode excitation Since the latter manifests as intermittent spikes this has been called a bubbling transition We present numerical evidences that this transition occurs due to the so called blowout bifurcation whereby the attractor as a whole loses transversal stability and becomes a chaotic saddle We used a nonlinear three-wave interacting model with spatial diffusion as an example of this transition (C) 2010 Elsevier B V All rights reserved

A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.

Menopausal status: A possible predictive factor for recurrence in women with cancer of the uterine cervix without pelvic lymph node metastasis

Objectives: To evaluate risk factors for recurrence of carcinoma of the uterine cervix among women who had undergone radical hysterectomy without pelvic lymph node metastasis, while taking into consideration not only the classical histopathological factors but also sociodemographic, clinical and treatment-related factors. Study design: This was an exploratory analysis on 233 women with carcinoma of the uterine cervix (stages IB and IIA) who were treated by means of radical hysterectomy and pelvic lymphadenectomy, with free surgical margins and without lymph node metastases on conventional histopathological examination. Women with histologically normal lymph nodes but with micrometastases in the immunohistochemical analysis (AE1/AE3) were excluded. Disease-free survival for sociodemographic, clinical and histopathological variables was calculated using the Kaplan-Meier method. The Cox proportional hazards model was used to identify the independent risk factors for recurrence. Results: Twenty-seven recurrences were recorded (11.6%), of which 18 were pelvic, four were distant, four were pelvic + distant and one was of unknown location. The five-year disease-free survival rate among the study population was 88.4%. The independent risk factors for recurrence in the multivariate analysis were: postmenopausal status (HR 14.1; 95% CI: 3.7-53.6; P < 0.001), absence of or slight inflammatory reaction (HR 7.9; 95% CI: 1.7-36.5; P = 0.008) and invasion of the deepest third of the cervix (FIR 6.1; 95% CI: 1.3-29.1; P = 0.021). Postoperative radiotherapy was identified as a protective factor against recurrence (HR 0.02; 95% CI: 0.001-0.25; P = 0.003). Conclusion: Postmenopausal status is a possible independent risk factor for recurrence even when adjusted for classical prognostic factors (such as tumour size, depth of turnout invasion, capillary embolisation) and treatment-related factors (period of treatment and postoperative radiotherapy status). (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Effects of Crossing Saddle Coil Conductors: Electric Length X Mutual Inductance

In magnetic resonance imaging (MRI), either on human or animal studies, the main requirements for radiofrequency (RF) coils are to produce a homogeneous RF field while used as a transmitter coil and to have the best signal-to-noise ratio (SNR) while used as a receiver. Besides, they need to be easily frequency adjustable and have input impedance matching 50 Omega to several different load conditions. New theoretical and practical concepts are presented here for considerable enhancing of RF coil homogeneity for MRI experiments on small animals. To optimize field homogeneity, we have performed simulations using Blot and Savart law varying the coil`s window angle, achieving the optimum one. However, when the coil`s dimensions are the same order of the wave length and according to transmission line theory, differences in electrical length and effects of mutual inductances between adjacent strip conductors decrease both field homogeneity and SNR. The problematic interactions between strip conductors by means of mutual inductance were eliminated by inserting crossings at half electrical length, avoiding distortion on current density, thus eliminating sources of field inhomogeneity. Experimental results show that measured field maps and simulations are in good agreement. The new coil design, dubbed double-crossed saddle described here have field homogeneity and SNR superior than the linearly driven 8-rung birdcage coil. One of our major findings was that the effects of mutual inductance are more significant than differences in electrical length for this frequency and coil dimensions. In vitro images of a primate Cebus paela brain were acquired, confirming double-crossed saddle superiority. (C) 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 193-201, 2010

Bifurcation analysis of a model for biological control

In this paper we study the Lyapunov stability and Hopf bifurcation in a biological system which models the biological control of parasites of orange plantations. (c) 2007 Elsevier Ltd. All rights reserved.

Stability and Hopf bifurcation in an hexagonal governor system

In this paper we study the Lyapunov stability and the Hopf bifurcation in a system coupling an hexagonal centrifugal governor with a steam engine. Here are given sufficient conditions for the stability of the equilibrium state and of the bifurcating periodic orbit. These conditions are expressed in terms of the physical parameters of the system, and hold for parameters outside a variety of codimension two. (C) 2007 Elsevier Ltd. All rights reserved.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.