98 research outputs found
Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model
We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of
neuronal action potentials, in parameter regimes characterised by mixed-mode
oscillations. The interspike time interval is related to the random number of
small-amplitude oscillations separating consecutive spikes. We prove that this
number has an asymptotically geometric distribution, whose parameter is related
to the principal eigenvalue of a substochastic Markov chain. We provide
rigorous bounds on this eigenvalue in the small-noise regime, and derive an
approximation of its dependence on the system's parameters for a large range of
noise intensities. This yields a precise description of the probability
distribution of observed mixed-mode patterns and interspike intervals.Comment: 36 page
Convergence to equilibrium for many particle systems
The goal of this paper is to give a short review of recent results of the
authors concerning classical Hamiltonian many particle systems. We hope that
these results support the new possible formulation of Boltzmann's ergodicity
hypothesis which sounds as follows. For almost all potentials, the minimal
contact with external world, through only one particle of , is sufficient
for ergodicity. But only if this contact has no memory. Also new results for
quantum case are presented
Corrosion Grade on Anchor Rods of Guyed Transmission Towers Applying Machine Committee / Grau de Corrosão em Hastes de Âncora de Torres de Transmissão Guiadas Comitê de Aplicação de Máquinas
The use of guyed structures in electric power transmission lines is a growing practice because of their cost efficiency. However, the anchor systems are subject to corrosion, which can lead to their rupture and loss of tower support. Monitoring the evolution of the corrosion of the anchor rods by visual inspection is a destructive and costly method; therefore, there is considerable interest in developing methods and tools that are capable of generating a maintenance diagnosis of the system. This work aimed to propose a classification tool for guyed towers in terms of the corrosion degree by a machine committee with neural networks and applied it to the Paraiso-Açu line located in Rio Grande do Norte in Brazil. Thirty-eight samples were collected and 33 variables related to the soil corrosion along the line were analyzed. The targets for training the networks were obtained from the inspection of anchor rods taken from the field. A simplification of the problem's dimension was proposed by principal component analysis, describing the phenomenon with 6 variables instead of 33, simplifying the practical application by massively reducing the requirements for data sampling in the field. Several network typologies were trained and the best ones in terms of their generalist and specialist capacities were combined in a machine committee for the final proposal of this work. The classification obtained by the application of the committee for 10 towers was compared with the classification from non-destructive impulse reflectometry tests and showed an 80% correlation
Richardson's pair diffusion and the stagnation point structure of turbulence
DNS and laboratory experiments show that the spatial distribution of
straining stagnation points in homogeneous isotropic 3D turbulence has a
fractal structure with dimension D_s = 2. In Kinematic Simulations the time
exponent gamma in Richardson's law and the fractal dimension D_s are related by
gamma = 6/D_s. The Richardson constant is found to be an increasing function of
the number of straining stagnation points in agreement with pair duffusion
occuring in bursts when pairs meet such points in the flow.Comment: 4 pages; Submitted to Phys. Rev. Let
Large deviation principle for Benedicks-Carleson quadratic maps
Since the pioneering works of Jakobson and Benedicks & Carleson and others,
it has been known that a positive measure set of quadratic maps admit invariant
probability measures absolutely continuous with respect to Lebesgue. These
measures allow one to statistically predict the asymptotic fate of Lebesgue
almost every initial condition. Estimating fluctuations of empirical
distributions before they settle to equilibrium requires a fairly good control
over large parts of the phase space. We use the sub-exponential slow recurrence
condition of Benedicks & Carleson to build induced Markov maps of arbitrarily
small scale and associated towers, to which the absolutely continuous measures
can be lifted. These various lifts together enable us to obtain a control of
recurrence that is sufficient to establish a level 2 large deviation principle,
for the absolutely continuous measures. This result encompasses dynamics far
from equilibrium, and thus significantly extends presently known local large
deviations results for quadratic maps.Comment: 23 pages, no figure, former title: Full large deviation principle for
Benedicks-Carleson quadratic map
Quais Elementos Caracterizam uma Atividade de Modelagem Matemática na Perspectiva SociocrĂtica?
Boundaries from Inhomogeneous Bernoulli Trials
The boundary problem is considered for inhomogeneous increasing random walks on the square lattice \mathbbZ2+Z2+ with weighted edges. Explicit solutions are given for some instances related to the classical and generalized number triangles
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