Universal persistence exponents in an extremally driven system

The local persistence R(t), defined as the proportion of the system still in its initial state at time t, is measured for the Bak--Sneppen model. For 1 and 2 dimensions, it is found that the decay of R(t) depends on one of two classes of initial configuration. For a subcritical initial state, R(t)\sim t^{-\theta}, where the persistence exponent \theta can be expressed in terms of a known universal exponent. Hence \theta is universal. Conversely, starting from a supercritical state, R(t) decays by the anomalous form 1-R(t)\sim t^{\tau_{\rm ALL}} until a finite time t_{0}, where \tau_{\rm ALL} is also a known exponent. Finally, for the high dimensional model R(t) decays exponentially with a non--universal decay constant.Comment: 4 pages, 6 figures. To appear in Phys. Rev.

Stripes ordering in self-stratification experiments of binary and ternary granular mixtures

The self-stratification of binary and ternary granular mixtures has been experimentally investigated. Ternary mixtures lead to a particular ordering of the strates which was not accounted for in former explanations. Bouncing grains are found to have an important effect on strate formation. A complementary mechanism for self-stratification of binary and ternary granular mixtures is proposed.Comment: 4 pages, 5 figures. submitted for pubication, guess wher

Rheological Chaos in a Scalar Shear-Thickening Model

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress \sigma is driven at a constant shear rate \dot\gamma and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(\sigma_1) and a linear decay at rate \lambda\sigma_2. Here \sigma_{1,2}(t) = \tau_{1,2}^{-1}\int_0^t\sigma(t')\exp[-(t-t')/\tau_{1,2}] {\rm d}t' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when \tau_2>\tau_1 and 0>R'(\sigma)>-\lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case \tau_1\to 0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.Comment: Reference added; typos corrected. To appear in PRE Rap. Com

Neuroscience and end-of-life decisions. New anthropological challenges for constitutional law: «Is Human Nature the only science of man»?

Nowadays, neuroscience permits the unveiling of interior elements of hu-man beings - the perception of pain, the presence of consciousness and even the will - in the absence of external manifestations. Physicians, indeed, seem capable of measuring the true mental state of individuals and their inner world through an elec-troencephalography or a functional magnetic resonance imaging. This new frontier affects the world of law and places heavy demands for lawyers embroiled in end-of-life matters. The present paper focuses on the use of neuroscientific acquisitions within end-of-life decisions, aiming to highlight two risks embedded in this use: the utmost deference towards science and scientific authority and the maximization of self-determination. The paper will provide, at the beginning, a framework of case law and end-of-life regulatory attempts; it will follow the analysis of the main challenges posed to law by advances in neuroscience. In the latter part of this paper, we will of-fer food for thought on the role of neuroscience and - in a broader perspective - of science in law

A microscopic 2D lattice model of dimer granular compaction with friction

We study by Monte Carlo simulation the compaction dynamics of hard dimers in 2D under the action of gravity, subjected to vertical and horizontal shaking, considering also the case in which a friction force acts for horizontal displacements of the dimers. These forces are modeled by introducing effective probabilities for all kinds of moves of the particles. We analyze the dynamics for different values of the time $\tau$ during which the shaking is applied to the system and for different intensities of the forces. It turns out that the density evolution in time follows a stretched exponential behavior if $\tau$ is not very large, while a power law tail develops for larger values of $\tau$. Moreover, in the absence of friction, a critical value $\tau^*$ exists which signals the crossover between two different regimes: for $\tau < \tau^*$ the asymptotic density scales with a power law of $\tau$, while for $\tau > \tau^*$ it reaches logarithmically a maximal saturation value. Such behavior smears out when a finite friction force is present. In this situation the dynamics is slower and lower asymptotic densities are attained. In particular, for significant friction forces, the final density decreases linearly with the friction coefficient. We also compare the frictionless single tap dynamics to the sequential tapping dynamics, observing in the latter case an inverse logarithmic behavior of the density evolution, as found in the experiments.Comment: 10 pages, 15 figures, to be published in Phys. Rev.

Transverse fluctuations of grafted polymers

We study the statistical mechanics of grafted polymers of arbitrary stiffness in a two-dimensional embedding space with Monte Carlo simulations. The probability distribution function of the free end is found to be highly anisotropic and non-Gaussian for typical semiflexible polymers. The reduced distribution in the transverse direction, a Gaussian in the stiff and flexible limits, shows a double peak structure at intermediate stiffnesses. We also explore the response to a transverse force applied at the polymer free end. We identify F-Actin as an ideal benchmark for the effects discussed.Comment: 10 pages, 4 figures, submitted to Physical Review

Long-range effects in granular avalanching

We introduce a model for granular flow in a one-dimensional rice pile that incorporates rolling effects through a long-range rolling probability for the individual rice grains proportional to $r^{-\rho}$, $r$ being the distance traveled by a grain in a single topling event. The exponent $\rho$ controls the average rolling distance. We have shown that the crossover from power law to stretched exponential behaviors observed experimentally in the granular dynamics of rice piles can be well described as a long-range effect resulting from a change in the transport properties of individual grains. We showed that stretched exponential avalanche distributions can be associated with a long-range regime for $1<\rho<2$ where the average rolling distance grows as a power law with the system size, while power law distributions are associated with a short range regime for $\rho>2$, where the average rolling distance is independent of the system size.Comment: 5 pages, 3 figure

Linear response of vibrated granular systems to sudden changes in the vibration intensity

The short-term memory effects recently observed in vibration-induced compaction of granular materials are studied. It is shown that they can be explained by means of quite plausible hypothesis about the mesoscopic description of the evolution of the system. The existence of a critical time separating regimes of ``anomalous'' and ``normal'' responses is predicted. A simple model fitting into the general framework is analyzed in the detail. The relationship between this work and previous studies is discussed.Comment: 10 pages, 6 figures; fixed errata, updtated reference

Phenomenological glass model for vibratory granular compaction

A model for weakly excited granular media is derived by combining the free volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)]. This is made possible by relating the granular excitation parameter \Gamma, defined as the peak acceleration of the driving pulse scaled by gravity, to a temperature-like parameter \eta(\Gamma). The resulting master equation is formally identical to that of Bouchaud's trap model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are shown to compare favourably with a range of known experimental behaviour. This includes the logarithmic densification and power spectrum of fluctuations under constant \eta, the annealing curve when \eta is varied cyclically in time, and memory effects observed for a discontinuous shift in \eta. Finally, we discuss the physical interpretation of the model parameters and suggest further experiments for this class of systems.Comment: 2 references added; some figure labels tweaked. To appear in PR