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

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.

Tuning the Correlation Decay in the Resistance Fluctuations of Multi-Species Networks

A new network model is proposed to describe the $1/f^\alpha$ resistance noise in disordered materials for a wide range of $\alpha$ values ($0< \alpha < 2$). 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 $0< \alpha < 1$ at low currents, in the Ohmic regime, with $\alpha$ decreasing inversely with the temperature, and $1< \alpha <2$ 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 $\alpha$ 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

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

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

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

Resistance and Resistance Fluctuations in Random Resistor Networks Under Biased Percolation

We consider a two-dimensional random resistor network (RRN) in the presence of two competing biased percolations consisting of the breaking and recovering of elementary resistors. These two processes are driven by the joint effects of an electrical bias and of the heat exchange with a thermal bath. The electrical bias is set up by applying a constant voltage or, alternatively, a constant current. Monte Carlo simulations are performed to analyze the network evolution in the full range of bias values. Depending on the bias strength, electrical failure or steady state are achieved. Here we investigate the steady-state of the RRN focusing on the properties of the non-Ohmic regime. In constant voltage conditions, a scaling relation is found between $/_0$ and $V/V_0$, where $$ is the average network resistance, $_0$ the linear regime resistance and $V_0$ the threshold value for the onset of nonlinearity. A similar relation is found in constant current conditions. The relative variance of resistance fluctuations also exhibits a strong nonlinearity whose properties are investigated. The power spectral density of resistance fluctuations presents a Lorentzian spectrum and the amplitude of fluctuations shows a significant non-Gaussian behavior in the pre-breakdown region. These results compare well with electrical breakdown measurements in thin films of composites and of other conducting materials.Comment: 15 figures, 23 page