Fergal Dalton

Brownian ratchet in a thermal bath driven by Coulomb friction.

The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical nonequilibrium conditions. Here we propose a new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts. Numerical simulations and analytical calculations demonstrate a net drift induced by friction. If the thermal bath is replaced by a granular gas, the well-known granular ratchet effect also intervenes, becoming dominant at high collision rates. For our chosen wheel shape the granular effect acts in the opposite direction with respect to the friction-induced torque, resulting in the inversion of the ratchet direction as the collision rate increases. We have realized a new granular ratchet experiment where both these ratchet effects are observed, as well as the predicted inversion at their crossover. Our discovery paves the way to the realization of micro and submicrometer Brownian motors in an equilibrium fluid, based purely upon nanofriction.

Brownian Forces in Sheared Granular Matter

We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting in the system performs a Brownian motion. The same assumption has been utilized, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.

Stochastic dynamics of a sheared granular medium

We experimentally investigate the response of a sheared granular medium in a Couette geometry. The apparatus exhibits the expected stick-slip motion and we probe it in the very intermittent regime resulting from low driving. Statistical analysis of the dynamic fluctuations reveals notable regularities. We observe a possible stability property for the torque distribution, reminiscent of the stability of Gaussian independent variables. In this case, however, the variables are correlated and the distribution is skewed. Moreover, the whole dynamical intermittent regime can be described with a simple stochastic model, finding good quantitative agreement with the experimental data. Interestingly, a similar model has been previously introduced in the study of magnetic domain wall motion, a source of Barkhausen noise. Our study suggests interesting connections between different complex phenomena and reveals some unexpected features that remain to be explained.

Shear stress fluctuations in the granular liquid and solid phases.

We report on experimentally observed shear stress fluctuations in both granular solid and fluid states, showing that they are non-Gaussian at low shear rates, reflecting the predominance of correlated structures (force chains) in the solidlike phase, which also exhibit finite rigidity to shear. Peaks in the rigidity and the stress distributions skewness indicate that a change to the force-bearing mechanism occurs at the transition to fluid behavior, which, it is shown, can be predicted from the behavior of the stress at lower shear rates. In the fluid state stress is Gaussian distributed, suggesting that the central limit theorem holds. The fiber bundle model with random load sharing effectively reproduces the stress distribution at the yield point and also exhibits the exponential stress distribution anticipated from extant work on stress propagation in granular materials.

Analysis of metal cutting acoustic emissions by time series models.

We analyse some acoustic emission time series obtained from a lathe machining process. Considering the dynamic evolution of the process, we apply two classes of well known stationary stochastic time series models. We apply a preliminary root mean square (RMS) transformation followed by an auto regressive moving average analysis; results thereof are mainly related to the description of the continuous part (plastic deformation) of the signal. An analysis of acoustic emission, as some previous works show, may also be performed with the scope of understanding the evolution of the ageing process that causes the degradation of the working tools. Once the importance of the discrete part of the acoustic emission signals (i.e. isolated amplitude bursts) in the ageing process is understood, we apply a stochastic analysis based on point processes’ waiting times between bursts and to identify a parameter with which to characterise the wear level of the working tool. A Weibull distribution seems to adequately describe the waiting times distribution.

The Role of Interstitial Impurities in the Frictional Instability of Seismic Fault Models

The presence of impurities between two surfaces may greatly affect their frictional properties. In this article, we investigate the role of the impurities by studying experimental and numerical models of geophysical interest. Both model and experiments are considered to be representative of the dynamics of an earthquake fault and both systems reliably produce salient traits of earthquake dynamics such as stick-slip intermittent dynamics and power-law event distributions. The impurities are granular particles enclosed in the fault, known as fault gouge. We consider the role of the granular particles in the statistics of the slip events, and in the production of acoustic emissions.

Granular Shearing and Barkhausen Noise

We report the result of new experiments on a granular medium sheared in a Couette geometry. We investigate in particular the dependence of the resulting stick-slip patterns on the imposed shear rate. A model equation based on a stochastic description of the internal forces of the granular medium allows us to recover the experimental results and unveils similarities between the stick slip motion and the Barkhausen noise emitted by a ferromagnet during a hysteresis cycle. We show that, because of the stochastic nature of forces in the granular medium, there is indeed a correspondence in the statistical properties between shear rate fluctuations in granular media and displacement of magnetic domain walls under a varying external field. The main difference between the two systems consists of a characteristic behavior on the part of the granular medium, but which is not exhibited by the Barkhausen effect. The stochastic model proposed allows us to ascribe this behavior to the moment of inertia of the plate and, on the basis of available data from the statistical properties of friction in solid-on-solid systems and in polymer mono-layers, suggests the possibility of describing a larger class of driven instabilities in terms of similar general mechanisms.

The electoral system for the Italian Senate: an analogy with deterministic chaos?

The electoral system adopted for the allocation of seats in the Italian Senate utilizes a complex mechanism of awards at a regional level with the aim of strengthening, when necessary, the winning coalition and so improve overall government stability. The results presented here demonstrate that in a significant number of cases, the effect of the mechanism is opposite to that desired, to wit, weakening the resultant government by awarding more seats to the minority coalition. Indeed the award to the minority can even be such that the minority coalition becomes the majority and wins the election. The application of the award mechanism is strongly unpredictable as it depends crucially on the precise number of seats independently obtained in each region, and that each adjustment thereof can be positive, zero or negative; a characteristic that closely resembles the behaviour of a chaotic dynamical system whose trajectory, although purely deterministic, depends on infinitely precise details and is therefore unpredictable. To perform the systematic numerical analysis of the award effectiveness, we introduce characteristic polynomials, one for each electoral district, which carry information about all possible outcomes and award applications. Their product yields a polynomial containing the dependence of the result at national level on each of the regional awards.

Stick‐slip dynamics of a granular medium

Under certain limits, granular materials share many features with fluids and solids. Most of the time, however, they exhibit peculiar features which originate in the non‐equilibrium and dissipative character of the grain dynamics. We have investigated the dynamics of a granular medium in a channel, when subject to continuous shear stress from a plate connected to a motor by an elastic spring. We have shown [1] that the statistical features of granular stick‐slip dynamics are not simply Gaussian and that [2] can be described in a quantitative way by a simple stochastic equation. Extant work, such as the statistical properties of friction in solid‐on‐solid systems, further suggests that a large class of driven instabilities can be described in terms of similar general mechanisms. The intensity of the acoustic signals emitted by the granular medium during the slip events displays a non trivial correlation with the plate velocity. [1] F. Dalton et al., Phys. Rev. Lett. 95, 138001 (2005) [2] A. Baldassarri et ...

Component Analysis of Granular Friction

We perform an analysis of the stick-slip properties of a granular bed. The granulate is confined to a circular channel and sheared by an overhead top plate with a stick-slip motion. We attempt to decompose the frictional torque F f subtended by the medium into its independent components by graphical and phenomenological analyses. We find clear functional dependence on the position, velocity and acceleration of the plate and the residual torque signal shows some dependence on the properties of the stick events. This article is related to that of Baldassarri et al. in these proceedings.