arXiv subjects

Angelo Vulpiani

Publications and source records attributed to Angelo Vulpiani.

102 records · Page 6Linked to original sources

arXiv2003

The origin of diffusion: the case of non chaotic systems

We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1-$d$ map models whose slope is everywhere 1 (therefore the Lyapunov exponent is zero) but with random quenched discontinuities and quasi-periodic forcing. The models are constructed as non-chaotic approximations of chaotic maps showing deterministic diffusion, and represent one-dimensional versions of a Lorentz gas with polygonal obstacles (e.g., the Ehrenfest wind tree model). In particular, a simple construction shows that these maps define non-chaotic billiards in space-time. The models exhibit, in a wide range of the parameters, the same diffusive behavior of the corresponding chaotic versions. We present evidence of two sufficient ingredients for diffusive behavior in one-dimensional, non-chaotic systems: i) a finite-size, algebraic instability mechanism, and ii) a mechanism that suppresses periodic orbits.

nlin.CD↗

arXiv2003

Noise activated granular dynamics

We study the behavior of two particles moving in a bistable potential, colliding inelastically with each other and driven by a stochastic heat bath. The system has the tendency to clusterize, placing the particles in the same well at low drivings, and to fill all of the available space at high temperatures. We show that the hopping over the potential barrier occurs following the Arrhenius rate, where the heat bath temperature is replaced by the granular temperature. Moreover, within the clusterized ``phase'' one encounters two different scenarios: for moderate inelasticity, the jumps from one well to the other involve one particle at a time, whereas for strong inelasticity the two particles hop simultaneously.

cond-mat.stat-mech↗

arXiv2002

Diffusive transport and self-consistent dynamics in coupled maps

The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps. Self-consistency, i.e. the back-influence of the transported quantity on the velocity field of the driving flow, despite of its critical importance, is usually overlooked in the description of realistic systems, for example in plasma physics. We propose a class of self-consistent models consisting of an ensemble of maps globally coupled through a mean field. Depending on the kind of coupling, two different general types of self-consistent maps are considered: maps coupled to the field only through the phase, and fully coupled maps, i.e. through the phase and the amplitude of the external field. The analogies and differences of the diffusion properties of these two kinds of maps are discussed in detail.

nlin.CD↗

arXiv2002

Superfast front propagation in reactive systems with anomalous diffusion

We study a reaction diffusion system where we consider a non-gaussian process instead of a standard diffusion. If the process increments follow a probability distribution with tails approaching to zero faster than a power law, the usual qualitative behaviours of the standard reaction diffusion system, i.e., exponential tails for the reacting field and a constant front speed, are recovered. On the contrary if the process has power law tails, also the reacting field shows power law tail and the front speed increases exponentially with time. The comparison with other reaction-transport systems which exhibit anomalous diffusion shows that, not only the presence of anomalous diffusion, but also the detailed mechanism, is relevant for the front propagation.

nlin.CG↗

arXiv2002

Efficiency of a stirred chemical reaction in a closed vessel

We perform a numerical study of the reaction efficiency in a closed vessel. Starting with a little spot of product, we compute the time needed to complete the reaction in the container following an advection-reaction-diffusion process. Inside the vessel it is present a cellular velocity field that transports the reactants. If the size of the container is not very large compared with the typical length of the velocity field one has a plateau of the reaction time as a function of the strength of the velocity field, $U$. This plateau appears both in the stationary and in the time-dependent flow. A comparison of the results for the finite system with the infinite case (for which the front speed, $v_f$, gives a simple estimate of the reacting time) shows the dramatic effect of the finite size.

nlin.CD↗

arXiv2001

Markov-chain approach to a process with long-time memory

We show that long-term memory effects, present in the chaotic dispersion process generated by a meandering jet model, can be nonetheless taken into account by a first order Markov process, provided that the states of the phase space partition, chosen to describe the system, be appropriately defined.

nlin.CD↗

arXiv2001

Front Propagation in Chaotic and Noisy Reaction-Diffusion Systems: a Discrete-Time Map Approach

We study the front propagation in Reaction-Diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on the wandering of the front around its average position. Assuming that the reaction term acts periodically in an impulsive way, the dynamical evolution of the system can be written as the convolution between a spatial propagator and a discrete-time map acting locally. This approach allows us to perform accurate numerical analysis. They reveal that in the pulled regime the front speed is basically determined by the shape of the map around the unstable fixed point, while its chaotic or noisy features play a marginal role. In contrast, in the pushed regime the presence of chaos or noise is more relevant. In particular the front speed decreases when the degree of chaoticity is increased, but it is not straightforward to derive a direct connection between the chaotic properties (e.g. the Lyapunov exponent) and the behaviour of the front. As for the fluctuations of the front position, we observe for the noisy maps that the associated mean square displacement grows in time as $t^{1/2}$ in the pushed case and as $t^{1/4}$ in the pulled one, in agreement with recent findings obtained for continuous models with multiplicative noise. Moreover we show that the same quantity saturates when a chaotic deterministic dynamics is considered for both pushed and pulled regimes.

cond-mat.stat-mech↗

arXiv2000

Drifters dispersion in the Adriatic Sea: Lagrangian data and chaotic model

We analyze characteristics of drifter trajectories from the Adriatic Sea with recently introduced nonlinear dynamics techniques. We discuss how in quasi-enclosed basins, relative dispersion as function of time, a standard analysis tool in this context, may give a distorted picture of the dynamics. We further show that useful information may be obtained by using two related non-asymptotic indicators, the Finite-Scale Lyapunov Exponent (FSLE) and the Lagrangian Structure Function (LSF), which both describe intrinsic physical properties at a given scale. We introduce a simple chaotic model for drifter motion in this system, and show by comparison with the model that Lagrangian dispersion is mainly driven by advection at sub-basin scales until saturation sets in.

chao-dyn↗

arXiv2000

Population dynamics advected by chaotic flows: a discrete-time map approach

A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map possibly yielding Lagrangian chaos. Each {\it fluid particle} carries concentrations of active substances which evolve according to its own reaction dynamics. This evolution is also modeled in terms of maps. Motivated by the question, of relevance in marine ecology, of how a localized distribution of nutrients or preys affects the spatial structure of predators transported by a fluid flow, we study a specific model in which the population dynamics is given by a logistic map with space-dependent coefficient, and advection is given by the standard map. Fractal and random patterns in the Eulerian spatial concentration of predators are obtained under different conditions. Exploiting the analogies of this coupled-map (advection plus reaction) system with a random map, some features of these patterns are discussed.

nlin.CD↗

arXiv1999

Growth Optimal Investment and Pricing of Derivatives

We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant to the problem of pricing derivatives. We compare our result with other alternative pricing procedures in the literature, and discuss the limits of validity of the lognormal approximation. We also generalize the pricing method to a market with correlated stocks. The expected estimation error of the optimal investment fraction is derived in a closed form, and its validity is checked with a small-scale empirical test.

cond-mat.stat-mech↗

arXiv1999

Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?

We study the time evolution of Solar Flares activity by looking at the statistics of quiescent times $τ_{L}$ between successive bursts. The analysis of 20 years of data reveals a power law distribution with exponent $α\simeq 2.4$ which is an indication of complex dynamics with long correlation times. The observed scaling behavior is in contradiction with the Self-Organized Criticality models of Solar Flares which predict Poisson-like statistics. Chaotic models, including the destabilization of the laminar phases and subsequent restabilization due to nonlinear dynamics, are able to reproduce the power law for the quiescent times. In the case of the more realistic Shell Model of MHD turbulence we are able to reproduce all the observed distributions.

chao-dyn↗

arXiv1995

Strong Chaos without Butterfly Effect in Dynamical Systems with Feedback

We discuss the predictability of a conservative system that drives a chaotic system with positive maximum Lyapunov exponent $λ_0$, such as the erratic motion of an asteroid in the gravitational field of two bodies of much larger mass. We consider the case where in absence of feedback (restricted model), the driving system is regular and completely predictable. A small feedback of strength $ε$ still allows a good forecasting in the driving system up to a very long time $T_p \sim ε^{-α}$, where $α$ depends on the details of the system. The most interesting situation happens when the Lyapunov exponent of the total system is strongly chaotic with $λ_{tot} \approx λ_0$ , practically independent of $ε$. Therefore an exponential amplification of a small incertitude on the initial conditions in the driving system for any $ε\neq 0$ coexists with very long predictability times. The paradox stems from saturation effects in the evolution for the growth of the incertitude as illustrated in a simple model of coupled maps and in a system of three point vortices in a disk.

chao-dyn↗