67 research outputs found
Non-Gaussian Resistance Noise near Electrical Breakdown in Granular Materials
The distribution of resistance fluctuations of conducting thin films with
granular structure near electrical breakdown is studied by numerical
simulations. The film is modeled as a resistor network in a steady state
determined by the competition between two biased processes, breaking and
recovery. Systems of different sizes and with different levels of internal
disorder are considered. Sharp deviations from a Gaussian distribution are
found near breakdown and the effect increases with the degree of internal
disorder. However, we show that in general this non-Gaussianity is related to
the finite size of the system and vanishes in the large size limit.
Nevertheless, near the critical point of the conductor-insulator transition,
deviations from Gaussianity persist when the size is increased and the
distribution of resistance fluctuations is well fitted by the universal
Bramwell-Holdsworth-Pinton distribution.Comment: 8 pages, 6 figures; accepted for publication on Physica
Gain in Stochastic Resonance: Precise Numerics versus Linear Response Theory beyond the Two-Mode Approximation
In the context of the phenomenon of Stochastic Resonance (SR) we study the
correlation function, the signal-to-noise ratio (SNR) and the ratio of output
over input SNR, i.e. the gain, which is associated to the nonlinear response of
a bistable system driven by time-periodic forces and white Gaussian noise.
These quantifiers for SR are evaluated using the techniques of Linear Response
Theory (LRT) beyond the usually employed two-mode approximation scheme. We
analytically demonstrate within such an extended LRT description that the gain
can indeed not exceed unity. We implement an efficient algorithm, based on work
by Greenside and Helfand (detailed in the Appendix), to integrate the driven
Langevin equation over a wide range of parameter values. The predictions of LRT
are carefully tested against the results obtained from numerical solutions of
the corresponding Langevin equation over a wide range of parameter values. We
further present an accurate procedure to evaluate the distinct contributions of
the coherent and incoherent parts of the correlation function to the SNR and
the gain. As a main result we show for subthreshold driving that both, the
correlation function and the SNR can deviate substantially from the predictions
of LRT and yet, the gain can be either larger or smaller than unity. In
particular, we find that the gain can exceed unity in the strongly nonlinear
regime which is characterized by weak noise and very slow multifrequency
subthreshold input signals with a small duty cycle. This latter result is in
agreement with recent analogue simulation results by Gingl et al. in Refs. [18,
19].Comment: 22 pages, 5 eps figures, submitted to PR
Tuning the Correlation Decay in the Resistance Fluctuations of Multi-Species Networks
A new network model is proposed to describe the resistance noise
in disordered materials for a wide range of values ().
More precisely, we have considered the resistance fluctuations of a thin
resistor with granular structure in different stationary states: from nearly
equilibrium up to far from equilibrium conditions. This system has been
modelled as a network made by different species of resistors, distinguished by
their resistances, temperature coefficients and by the energies associated with
thermally activated processes of breaking and recovery. The correlation
behavior of the resistance fluctuations is analyzed as a function of the
temperature and applied current, in both the frequency and time domains. For
the noise frequency exponent, the model provides at low
currents, in the Ohmic regime, with decreasing inversely with the
temperature, and at high currents, in the non-Ohmic regime.
Since the threshold current associated with the onset of nonlinearity also
depends on the temperature, the proposed model qualitatively accounts for the
complicate behavior of versus temperature and current observed in many
experiments. Correspondingly, in the time domain, the auto-correlation function
of the resistance fluctuations displays a variety of behaviors which are tuned
by the external conditions.Comment: 26 pages, 16 figures, Submitted to JSTAT - Special issue SigmaPhi200
Respiratory impedance in healthy unsedated South African infants: Effects of maternal smoking
Background and objective: Non-invasive techniques for measuring lung mechanics in infants are needed for a better understanding of lung growth and function, and to study the effects of prenatal factors on subsequent lung growth in healthy infants. The forced oscillation technique requires minimal cooperation from the individual but has rarely been used in infants. The study aims to assess the use of the forced oscillation technique to measure the influence of antenatal exposures on respiratory mechanics in unsedated infants enrolled in a birth cohort study in Cape Town, South Africa. Methods: Healthy term infants were studied at 6–10 weeks of age using the forced oscillation technique. Respiratory impedance was measured in the frequency range 8–48 Hz via a face mask during natural sleep. Respiratory system resistance, compliance and inertance were calculated from the impedance spectra. Results: Of 177 infants tested, successful measurements were obtained in 164 (93%). Median (25–75%) values for resistance, compliance and inertance were 50.2 (39.5–60.6) cmH2O.s.L−1, 0.78 (0.61–0.99) mL.cmH2O−1 and 0.062 (0.050–0.086) cmH2O.s2.L−1, respectively. As a group, male infants had 16% higher resistance (P = 0.006) and 18% lower compliance (P = 0.02) than females. Infants whose mothers smoked during pregnancy had a 19% lower compliance than infants not exposed to tobacco smoke during pregnancy (P = 0.005). Neither maternal HIV infection nor ethnicity had a significant effect on respiratory mechanics. Conclusions: The forced oscillation technique is sensitive enough to demonstrate the effects of tobacco smoke exposure and sex in respiratory mechanics in healthy infants. This technique will facilitate assessing perinatal influences of lung function in infancy
Exact solutions to chaotic and stochastic systems
We investigate functions that are exact solutions to chaotic dynamical
systems. A generalization of these functions can produce truly random numbers.
For the first time, we present solutions to random maps. This allows us to
check, analytically, some recent results about the complexity of random
dynamical systems. We confirm the result that a negative Lyapunov exponent does
not imply predictability in random systems. We test the effectiveness of
forecasting methods in distinguishing between chaotic and random time-series.
Using the explicit random functions, we can give explicit analytical formulas
for the output signal in some systems with stochastic resonance. We study the
influence of chaos on the stochastic resonance. We show, theoretically, the
existence of a new type of solitonic stochastic resonance, where the shape of
the kink is crucial. Using our models we can predict specific patterns in the
output signal of stochastic resonance systems.Comment: 31 pages, 18 figures (.eps). To appear in Chaos, March 200
Stochastic Resonance in a Dipole
We show that the dipole, a system usually proposed to model relaxation
phenomena, exhibits a maximum in the signal-to-noise ratio at a non-zero noise
level, thus indicating the appearance of stochastic resonance. The phenomenon
occurs in two different situations, i.e. when the minimum of the potential of
the dipole remains fixed in time and when it switches periodically between two
equilibrium points. We have also found that the signal-to-noise ratio has a
maximum for a certain value of the amplitude of the oscillating field.Comment: 4 pages, RevTex, 6 PostScript figures available upon request; to
appear in Phys. Rev.
Stochastic Resonance in Noisy Non-Dynamical Systems
We have analyzed the effects of the addition of external noise to
non-dynamical systems displaying intrinsic noise, and established general
conditions under which stochastic resonance appears. The criterion we have
found may be applied to a wide class of non-dynamical systems, covering
situations of different nature. Some particular examples are discussed in
detail.Comment: 4 pages, RevTex, 3 PostScript figures available upon reques
Nonstationary Stochastic Resonance in a Single Neuron-Like System
Stochastic resonance holds much promise for the detection of weak signals in
the presence of relatively loud noise. Following the discovery of nondynamical
and of aperiodic stochastic resonance, it was recently shown that the
phenomenon can manifest itself even in the presence of nonstationary signals.
This was found in a composite system of differentiated trigger mechanisms
mounted in parallel, which suggests that it could be realized in some
elementary neural networks or nonlinear electronic circuits. Here, we find that
even an individual trigger system may be able to detect weak nonstationary
signals using stochastic resonance. The very simple modification to the trigger
mechanism that makes this possible is reminiscent of some aspects of actual
neuron physics. Stochastic resonance may thus become relevant to more types of
biological or electronic systems injected with an ever broader class of
realistic signals.Comment: Plain Latex, 7 figure
Noise and Periodic Modulations in Neural Excitable Media
We have analyzed the interplay between noise and periodic modulations in a
mean field model of a neural excitable medium. To this purpose, we have
considered two types of modulations; namely, variations of the resistance and
oscillations of the threshold. In both cases, stochastic resonance is present,
irrespective of if the system is monostable or bistable.Comment: 13 pages, RevTex, 5 PostScript figure
Markov analysis of stochastic resonance in a periodically driven integrate-fire neuron
We model the dynamics of the leaky integrate-fire neuron under periodic
stimulation as a Markov process with respect to the stimulus phase. This avoids
the unrealistic assumption of a stimulus reset after each spike made in earlier
work and thus solves the long-standing reset problem. The neuron exhibits
stochastic resonance, both with respect to input noise intensity and stimulus
frequency. The latter resonance arises by matching the stimulus frequency to
the refractory time of the neuron. The Markov approach can be generalized to
other periodically driven stochastic processes containing a reset mechanism.Comment: 23 pages, 10 figure
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