103 research outputs found
High resolution stopwatch for cents
A very low-cost, easy-to-make stopwatch is presented to support various
experiments in mechanics. The high-resolution stopwatch is based on two
photodetectors connected directly to the microphone input of the sound card. A
dedicated free open-source software has been developed and made available to
download. The efficiency is demonstrated by a free fall experiment
Spectra for the product of Gaussian noises
Products of Gaussian noises often emerge as the result of non-linear
detection techniques or as a parasitic effect, and their proper handling is
important in many practical applications, including in fluctuation-enhanced
sensing, indoor air or environmental quality monitoring, etc. We use Rice's
random phase oscillator formalism to calculate the power density spectra
variance for the product of two Gaussian band-limited white noises with
zero-mean and the same bandwidth W. The ensuing noise spectrum is found to
decrease linearly from zero frequency to 2W, and it is zero for frequencies
greater than 2W. Analogous calculations performed for the square of a single
Gaussian noise confirm earlier results. The spectrum at non-zero frequencies,
and the variance of the square of a noise, is amplified by a factor two as a
consequence of correlation effects between frequency products. Our analytic
results is corroborated by computer simulations.Comment: submitted for publicatio
Two-state theory of nonlinear Stochastic Resonance
An amenable, analytical two-state description of the nonlinear population
dynamics of a noisy bistable system driven by a rectangular subthreshold signal
is put forward. Explicit expressions for the driven population dynamics, the
correlation function (its coherent and incoherent part), the signal-to-noise
ratio (SNR) and the Stochastic Resonance (SR) gain are obtained. Within a
suitably chosen range of parameter values this reduced description yields
anomalous SR-gains exceeding unity and, simultaneously, gives rise to a
non-monotonic behavior of the SNR vs. the noise strength. The analytical
results agree well with those obtained from numerical solutions of the Langevin
equation.Comment: 4 pages, 1 figur
Stochastic Resonance in Nonpotential Systems
We propose a method to analytically show the possibility for the appearance
of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our
results to the FitzHugh-Nagumo model under a periodic external forcing, showing
that the model exhibits stochastic resonance. The procedure that we follow is
based on the reduction to a one-dimensional dynamics in the adiabatic limit,
and in the topology of the phase space of the systems under study. Its
application to other nonpotential systems is also discussed.Comment: Submitted to Phys. Rev.
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
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
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.
Noise suppression by noise
We have analyzed the interplay between an externally added noise and the
intrinsic noise of systems that relax fast towards a stationary state, and
found that increasing the intensity of the external noise can reduce the total
noise of the system. We have established a general criterion for the appearance
of this phenomenon and discussed two examples in detail.Comment: 4 pages, 4 figure
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
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