Angelo Vulpiani

The mechanism of stochastic resonance

It is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance (peak in the power spectrum) which is absent when either the forcing or the perturbation is absent.

Correlation functions and relaxation properties in chaotic dynamics and statistical mechanics

Abstract We give a derivation, for chaotic systems, for a general fluctuation-response relation for which the van Kampen critique does not hold. Moreover we discuss the connection between relaxation properties and correlation functions.

Lagrangian Drifter Dispersion in the Southwestern Atlantic Ocean

AbstractIn the framework of Monitoring by Ocean Drifters (MONDO) project, a set of Lagrangian drifters were released in proximity of the Brazil Current, the western branch of the subtropical gyre in the South Atlantic Ocean. The experimental strategy of deploying part of the buoys in clusters offers the opportunity to examine relative dispersion on a wide range of scales. Adopting a dynamical systems approach, the authors focus their attention on scale-dependent indicators, like the finite-scale Lyapunov exponent (FSLE) and the finite-scale (mean square) relative velocity (FSRV) between two drifters as a function of their separation and compare them with classic time-dependent statistical quantities like the mean-square relative displacement between two drifters and the effective diffusivity as functions of the time lag from the release. The authors find that, dependently on the given observable, the quasigeostrophic turbulence scenario is overall compatible with their data analysis, with discrepancies fr...

Evidence for a k−5/3 Spectrum from the EOLE Lagrangian Balloons in the Low Stratosphere

Abstract The EOLE experiment is revisited to study turbulent processes in the lower stratosphere circulation from a Lagrangian viewpoint and to resolve a discrepancy on the slope of the atmospheric energy spectrum between the work of Morel and Larcheveque and recent studies using aircraft data. Relative dispersion of balloon pairs is studied by calculating the finite-scale Lyapunov exponent, an exit-time-based technique that is particularly efficient in cases in which processes with different spatial scales are interfering. The main goal is to reconciliate the EOLE dataset with recent studies supporting a k−5/3 energy spectrum in the 100–1000-km range. The results also show exponential separation at smaller scales, with a characteristic time of order 1 day, and agree with the standard diffusion of about 107 m2 s−1 at large scales. A remaining question is the origin of a k−5/3 spectrum in the mesoscale range between 100 and 1000 km.

Reductionism, Emergence and Levels of Reality

Newton’s third law does not apply to the interaction between philosophers (‘them’) and physicists (‘us’). It has usually been asymmetrical, with ‘us’ influencing ‘them’, without ‘them’ acting on ‘us’. In a way this is natural, because the raw material that philosophers study are the discoveries and theories of science and the interactions between scientists, while the primary preoccupation of physicists is not the study of philosophy or philosophers. I do not deny that there have been eminent scientists (Einstein, Poincare, Bohr...) who have pondered on the philosophical significance of the scientific picture of the world, and much of what they said has been immediately appreciated by practicing scientists. But their wise intellectual interventions have usually been outside the philosophical mainstream.

A GENERAL METHODOLOGY TO PRICE AND HEDGE DERIVATIVES IN INCOMPLETE MARKETS

We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in repeated multiplicative games originally introduced by Kelly. As particular cases we obtain the Cox–Ross–Rubinstein and Black–Scholes in the complete markets case and the Schweizer and Bouchaud–Sornette as a quadratic approximation of our prescription. Technical and numerical aspects for the practical option pricing, as large deviation theory approximation and Monte Carlo computation are discussed in detail.

A Statistical Model for Translocation of Structured Polypeptide Chains through Nanopores

The translocation process of a globular protein (ubiquitin) across a cylindrical nanopore is studied via molecular dynamics simulations. The ubiquitin is described by a native-centric model on a Calpha carbon backbone to investigate the influence of protein-like structural properties on the translocation mechanism. A thermodynamical and kinetic characterization of the process is obtained by studying the statistics of blockage times, the mobility, and the translocation probability as a function of the pulling force F acting in the pore. The transport dynamics occurs when the force exceeds a threshold Fc depending on a free-energy barrier that ubiquitin has to overcome in order to slide along the channel. Such a barrier results from competition of the unfolding energy and the entropy associated with the confinement effects of the pore. We implement appropriate umbrella sampling simulations to compute the free-energy profile as a function of the position of the ubiquitin center of mass inside of the channel (reaction coordinate). This free energy is then used to construct a phenomenological drift-diffusion model in the reaction coordinate which explains and reproduces the behavior of the observables during the translocation.

Scaling law and asymptotic distribution of Lyapunov exponents in conservative dynamical systems with many degrees of freedom

The authors study by numerical means the infinite product of 2N*2N conservative random matrices which mimics the chaotic behaviour of Hamiltonian systems with N+1 degrees of freedom made of weakly nearest-neighbour coupled oscillators. The maximum Lyapunov exponent lambda 1 exhibits a power-law behaviour as a function of the coupling constant epsilon : lambda 1 approximately epsilon beta with either beta =1/2 or beta =2/3, depending on the probability distribution of the matrix elements. These power laws do not depend on N and moreover increasing N, lambda 1 rapidly tends to an asymptotic value lambda *1 which only depends on epsilon and on the kind of probability distribution chosen for building up the matrices. They also compute the spectrum of the Lyapunov exponents and show that is has a thermodynamic limit of large N. This suggests the existence of a Kolmogorov entropy per degree of freedom proportional to lambda *1.

Finite size Lyapunov exponent: review on applications

In dynamical systems, the growth of infinitesimal perturbations is well characterized by the Lyapunov exponents. In many situations of interest, however, important phenomena involve finite amplitude perturbations, which are ruled by nonlinear dynamics out of tangent space, and thus cannot be captured by the standard Lyapunov exponents. We review the application of the finite size Lyapunov exponent (FSLE) for the characterization of non-infinitesimal perturbations in a variety of systems. In particular, we illustrate their usage in the context of predictability of systems with multiple spatio-temporal scales of geophysical relevance, in the characterization of nonlinear instabilities, and in some aspects of transport in fluid flows. We also discuss the application of the FSLE to more general aspects such as chaos-noise detection and coarse-grained descriptions of signals.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’.

Fluctuation-dissipation relation for chaotic non-Hamiltonian systems

In dissipative dynamical systems phase space volumes contract, on average. Therefore, the invariant measure on the attractor is singular with respect to the Lebesgue measure. As noted by Ruelle, a generic perturbation pushes the state out of the attractor, hence the statistical features of the perturbation and, in particular, of the relaxation cannot be understood solely in terms of the unperturbed dynamics on the attractor. This remark seems to seriously limit the applicability of the standard fluctuation-dissipation procedure in the statistical mechanics of nonequilibrium (dissipative) systems. In this letter we show that the singular character of the steady state does not constitute a serious limitation in the case of systems with many degrees of freedom. The reason is that one typically deals with projected dynamics, and these are associated with regular probability distributions in the corresponding lower dimensional spaces.