arXiv subjects

Massimo Cencini

Publications and source records attributed to Massimo Cencini.

63 records · Page 4Linked to original sources

arXiv2007

Macroscopic equations for the adiabatic piston

A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on the left and right chambers of the piston are always in equilibrium (that is the molecules are uniformly distributed and their velocities obey the Maxwell-Boltzmann distribution) after any collision with the piston. Then by using kinetic theory we derive the collision statistics from which we obtain a set of ordinary differential equations for the evolution of the macroscopic observables (namely the piston average velocity and position, the velocity variance and the temperatures of the two compartments). The dynamics of these equations is compared with simulations of an ideal gas and a microscopic model of gas settled to verify the assumptions used in the derivation. We show that the equations predict an evolution for the macroscopic variables which catches the basic features of the problem. The results here presented recover those derived, using a different approach, by Gruber, Pache and Lesne in J. Stat. Phys. 108, 669 (2002) and 112, 1177 (2003).

nlin.CD↗

arXiv2006

Synchronization of extended chaotic systems with long-range interactions: an analogy to Levy-flight spreading of epidemics

Spatially extended chaotic systems with power-law decaying interactions are considered. Two coupled replicas of such systems synchronize to a common spatio-temporal chaotic state above a certain coupling strength. The synchronization transition is studied as a nonequilibrium phase transition and its critical properties are analyzed at varying the interaction range. The transition is found to be always continuous, while the critical indexes vary with continuity with the power law exponent characterizing the interaction. Strong numerical evidences indicate that the transition belongs to the {\it anomalous directed percolation} family of universality classes found for L{é}vy-flight spreading of epidemic processes.

nlin.CD↗

arXiv2006

Lyapunov exponents of heavy particles in turbulence

Lyapunov exponents of heavy particles and tracers advected by homogeneous and isotropic turbulent flows are investigated by means of direct numerical simulations. For large values of the Stokes number, the main effect of inertia is to reduce the chaoticity with respect to fluid tracers. Conversely, for small inertia, a counter-intuitive increase of the first Lyapunov exponent is observed. The flow intermittency is found to induce a Reynolds number dependency for the statistics of the finite time Lyapunov exponents of tracers. Such intermittency effects are found to persist at increasing inertia.

nlin.CD↗

arXiv2006

On the effects of vortex trapping on the velocity statistics of tracers and heavy particle in turbulent flows

The Lagrangian statistics of heavy particles and of fluid tracers transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. The Lagrangian velocity structure functions are measured in a time range spanning about three decades, from a tenth of the Kolmogorov timescale up to a few large-scale eddy turnover time. Strong evidence is obtained that fluid tracers statistics are contaminated in the time span 1-10 times the dissipative time scale by a bottleneck effect due to vortex trapping. This effect is found to be significantly reduced for heavy particles which are expelled from vortices by inertia. These findings help in clarifying the results of a recent study by H. Xu et al. Phys. Rev. Lett. 96, 024503 (2006), where differences between experimental and numerical results on scaling properties of fluid tracers were reported.

nlin.CD↗

arXiv2005

Brownian motion and diffusion: from stochastic processes to chaos and beyond

One century after Einstein's work, Brownian Motion still remains both a fundamental open issue and a continous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic approaches proposed in the literature to model the Brownian Motion and more general diffusive behaviours. Then, we focus on the problems concerning the determination of the microscopic nature of diffusion by means of data analysis. Finally, we discuss the general conditions required for the onset of large scale diffusive motion.

nlin.CD↗

arXiv2005

Nonlinearly driven transverse synchronization in coupled chaotic systems

Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When only two maps are considered we always find that the critical coupling $ε_l$ for chaotic synchronization can be predicted within a linear analysis by the vanishing of the transverse Lyapunov exponent $λ_T$. However, major differences between transitions driven by linear or nonlinear mechanisms are revealed by the dynamics of the transient toward the synchronized state. As a representative example of extended systems a one dimensional lattice of chaotic maps with power-law coupling is considered. In this high dimensional model finite amplitude instabilities may have a dramatic effect on the transition. For strong nonlinearities an exponential divergence of the synchronization times with the chain length can be observed above $ε_l$, notwithstanding the transverse dynamics is stable against infinitesimal perturbations at any instant. Therefore, the transition takes place at a coupling $ε_{nl}$ definitely larger than $ε_l$ and its origin is intrinsically nonlinear. The linearly driven transitions are continuous and can be described in terms of mean field results for non-equilibrium phase transitions with long range interactions. While the transitions dominated by nonlinear mechanisms appear to be discontinuous.

nlin.CD↗

arXiv2004

Active and passive fields face to face

The statistical properties of active and passive scalar fields transported by the same turbulent flow are investigated. Four examples of active scalar have been considered: temperature in thermal convection, magnetic potential in two-dimensional magnetohydrodynamics, vorticity in two-dimensional Ekman turbulence and potential temperature in surface flows. In the cases of temperature and vorticity, it is found that the active scalar behavior is akin to that of its co-evolving passive counterpart. The two other cases indicate that this similarity is in fact not generic and differences between passive and active fields can be striking: in two-dimensional magnetohydrodynamics the magnetic potential performs an inverse cascade while the passive scalar cascades toward the small-scales; in surface flows, albeit both perform a direct cascade, the potential temperature and the passive scalar have different scaling laws already at the level of low-order statistical objects. These dramatic differences are rooted in the correlations between the active scalar input and the particle trajectories. The role of such correlations in the issue of universality in active scalar transport and the behavior of dissipative anomalies is addressed.

nlin.CD↗

arXiv2003

Going forth and back in time: a fast and parsimonious algorithm for mixed initial/final-value problems

We present an efficient and parsimonious algorithm to solve mixed initial/final-value problems. The algorithm optimally limits the memory storage and the computational time requirements: with respect to a simple forward integration, the cost factor is only logarithmic in the number of time-steps. As an example, we discuss the solution of the final-value problem for a Fokker-Planck equation whose drift velocity solves a different initial-value problem -- a relevant issue in the context of turbulent scalar transport.

physics.comp-ph↗

arXiv2001

Linear and nonlinear information flow in spatially extended systems

Infinitesimal and finite amplitude error propagation in spatially extended systems are numerically and theoretically investigated. The information transport in these systems can be characterized in terms of the propagation velocity of perturbations $V_p$. A linear stability analysis is sufficient to capture all the relevant aspects associated to propagation of infinitesimal disturbances. In particular, this analysis gives the propagation velocity $V_L$ of infinitesimal errors. If linear mechanisms prevail on the nonlinear ones $V_p = V_L$. On the contrary, if nonlinear effects are predominant finite amplitude disturbances can eventually propagate faster than infinitesimal ones (i.e. $V_p > V_L$). The finite size Lyapunov exponent can be successfully employed to discriminate the linear or nonlinear origin of information flow. A generalization of finite size Lyapunov exponent to a comoving reference frame allows to state a marginal stability criterion able to provide $V_p$ both in the linear and in the nonlinear case. Strong analogies are found between information spreading and propagation of fronts connecting steady states in reaction-diffusion systems. The analysis of the common characteristics of these two phenomena leads to a better understanding of the role played by linear and nonlinear mechanisms for the flow of information in spatially extended systems.

nlin.CD↗