Fractal analysis of weld defect patterns obtained by radiographic tests

This paper presents a fractal analysis of radiographic patterns obtained from specimens with three types of inserted welding defects: lack of fusion, lack of penetration, and porosity. The study focused on patterns of carbon steel beads from radiographs of the International Institute of Welding (IIW). The radiographs were scanned using a greyscale with 256 levels, and the fractal features of the surfaces constructed from the radiographic images were characterized by means of Hurst, detrended-fluctuation, and minimal-cover analyses. A Karhunen-Loeve transformation was then used to classify the curves obtained from the fractal analyses of the various images, and a study of the classification errors was performed. The obtained results indicate that fractal analyses can be an effective additional tool for pattern recognition of weld defects in radiographic tests.Comment: 7 pages, 2 figures. To appear AIP Conference Proceedings - QNDE 200

Neural networks with dynamical synapses: from mixed-mode oscillations and spindles to chaos

Understanding of short-term synaptic depression (STSD) and other forms of synaptic plasticity is a topical problem in neuroscience. Here we study the role of STSD in the formation of complex patterns of brain rhythms. We use a cortical circuit model of neural networks composed of irregular spiking excitatory and inhibitory neurons having type 1 and 2 excitability and stochastic dynamics. In the model, neurons form a sparsely connected network and their spontaneous activity is driven by random spikes representing synaptic noise. Using simulations and analytical calculations, we found that if the STSD is absent, the neural network shows either asynchronous behavior or regular network oscillations depending on the noise level. In networks with STSD, changing parameters of synaptic plasticity and the noise level, we observed transitions to complex patters of collective activity: mixed-mode and spindle oscillations, bursts of collective activity, and chaotic behaviour. Interestingly, these patterns are stable in a certain range of the parameters and separated by critical boundaries. Thus, the parameters of synaptic plasticity can play a role of control parameters or switchers between different network states. However, changes of the parameters caused by a disease may lead to dramatic impairment of ongoing neural activity. We analyze the chaotic neural activity by use of the 0-1 test for chaos (Gottwald, G. & Melbourne, I., 2004) and show that it has a collective nature.Comment: 7 pages, Proceedings of 12th Granada Seminar, September 17-21, 201

Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows

We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN], on the vanishing viscosity limit of circularly symmetric viscous flow in a disk with rotating boundary, shown there to converge to the inviscid limit in $L^2$-norm as long as the prescribed angular velocity $\alpha(t)$ of the boundary has bounded total variation. Here we establish convergence in stronger $L^2$ and $L^p$-Sobolev spaces, allow for more singular angular velocities $\alpha$, and address the issue of analyzing the behavior of the boundary layer. This includes an analysis of concentration of vorticity in the vanishing viscosity limit. We also consider such flows on an annulus, whose two boundary components rotate independently. [LMN] Lopes Filho, M. C., Mazzucato, A. L. and Nussenzveig Lopes, H. J., Vanishing viscosity limit for incompressible flow inside a rotating circle, preprint 2006

Critical and resonance phenomena in neural networks

Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural networks with stochastic neurons in the presence of noise, we show that spontaneous appearance of network oscillations occurs as a dynamical (non-equilibrium) phase transition at a critical point determined by the noise level, network structure, the balance between excitatory and inhibitory neurons, and other parameters. We find that the relaxation time of neural activity to a steady state, response to periodic stimuli at the frequency of the oscillations, amplitude of damped oscillations, and stochastic fluctuations of neural activity are dramatically increased when approaching the critical point of the transition.Comment: 8 pages, Proceedings of 12th Granada Seminar, September 17-21, 201