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Angelo Vulpiani

Publications and source records attributed to Angelo Vulpiani.

At least 73 records · Page 4Linked to original sources
arXiv2015

Extinction dynamics of a discrete population in an oasis

Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 50's with the KiSS (after Kierstead, Slobodkin and Skellam) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size $L$ surrounded by a deadly environment with infinite mortality -- i.e. an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence. Here, we introduce an individual-based analogue of the KiSS model to investigate the effects of discreteness and demographic stochasticity. In particular, we study the average time to extinction both above and below the critical patch size of the continuous model and investigate the quasi-stationary distribution of the number of individuals for patch sizes above the critical threshold.

q-bio.PE↗
arXiv2015

Cages and anomalous diffusion in vibrated dense granular media

A vertically shaken granular medium hosts a blade rotating around a fixed vertical axis, which acts as a mesorheological probe. At high densities, independently from the shaking intensity, the blade's dynamics show strong caging effects, marked by transient sub-diffusion and a maximum in the velocity power density spectrum (vpds), at a resonant frequency $\sim 10$ Hz. Interpreting the data through a diffusing harmonic cage model allows us to retrieve the elastic constant of the granular medium and its collective diffusion coefficient. For high frequencies $f$, a tail $\sim 1/f$ in the vpds reveals non-trivial correlations in the intra-cage micro-dynamics. At very long times (larger than $10$ s), a super-diffusive behavior emerges, ballistic in the most extreme cases. Consistently, the distribution of slow velocity inversion times $τ$ displays a power-law decay, likely due to persistent collective fluctuations of the host medium.

cond-mat.soft↗
arXiv2015

A kinetic model for the finite-time thermodynamics of small heat engines

We study a molecular engine constituted by a gas of $N \sim 10^2$ molecules enclosed between a massive piston and a thermostat. The force acting on the piston and the temperature of the thermostat are cyclically changed with a finite period $τ$. In the adiabatic limit $τ\to \infty$, even for finite size $N$, the average work and heats reproduce the thermodynamic values, recovering the Carnot result for the efficiency. The system exhibits a stall time $τ^*$ where net work is zero: for $τ<τ^*$ it consumes work instead of producing it, acting as a refrigerator or as a heat sink. At $τ>τ^*$ the efficiency at maximum power is close to the Curzorn-Ahlborn limit. The fluctuations of work and heat display approximatively a Gaussian behavior. Based upon kinetic theory, we develop a three-variables Langevin model where the piston's position and velocity are linearly coupled together with the internal energy of the gas. The model reproduces many of the system's features, such as the inversion of the work's sign, the efficiency at maximum power and the approximate shape of fluctuations. A further simplification in the model allows to compute analytically the average work, explaining its non-trivial dependence on $τ$.

cond-mat.stat-mech↗
arXiv2014

Transport and fluctuation-dissipation relations in asymptotic and pre-asymptotic diffusion across channels with variable section

We study the asymptotic and pre-asymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient $D_{\mathrm{eff}}$ is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the pre-asymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and pre-asymptotic regimes.

cond-mat.stat-mech↗
arXiv2014

On the foundations of statistical mechanics: ergodicity, many degrees of freedom and inference

The present paper is meant to give a simple introduction to the problem of the connection between microscopic dynamics and statistical laws. For sake of simplicity, we mostly refer to non-dissipative dynamics, since dissipation adds technical difficulties to the conceptual issues, although part of our discussion extends beyond this limit. In particular, the relevance of chaos and ergodicity is here confronted with that of the large number of degrees of freedom. In Section 2, we review the microscopic connection, along the lines of Boltzmann's approach, and of its further developments. In Section 3, we discuss the falsifiability of statistical mechanics and its role as statistical inference. In particular we argue that the Maximum entropy priciple is in general not a predictive tool.

cond-mat.stat-mech↗
arXiv2014

Non-anomalous diffusion is not always Gaussian

Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its diffusion properties can be not trivial. In particular, we show that the following scenarios are consistent with a linear increase of MSD with time: i) the high-order moments, $\langle [x(t)]^q \rangle$ for $q>2$ and the probability density of the process exhibit multiscaling; ii) the random walk on certain fractal graphs, with non integer spectral dimension, can display a fully standard diffusion; iii) positive order moments satisfying standard scaling do not imply an exact scaling property of the probability density.

cond-mat.stat-mech↗
arXiv2014

Nonequilibrium Brownian motion beyond the effective temperature

The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own "effective" temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT) applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein's relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased.

cond-mat.stat-mech↗
arXiv2013

Anomalous diffusion and response in branched systems: a simple analysis

We revisit the diffusion properties and the mean drift induced by an external field of a random walk process in a class of branched structures, as the comb lattice and the linear chains of plaquettes. A simple treatment based on scaling arguments is able to predict the correct anomalous regime for different topologies. In addition, we show that even in the presence of anomalous diffusion, Einstein's relation still holds, implying a proportionality between the mean square displacement of the unperturbed systems and the drift induced by an external forcing.

cond-mat.stat-mech↗
arXiv2013

Reaction spreading on percolating clusters

Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction spreading, numerical data and analytical estimates show a power-law behavior of the reaction product as M(t) \sim t^dl, where dl is the connectivity dimension. In a percolating channel, a statistically stationary traveling wave develops. The speed and the width of the traveling wave are numerically computed. While the front speed is a low-fluctuating quantity and its behavior can be understood using a simple theoretical argument, the front width is a high-fluctuating quantity showing a power-law behavior as a function of the size of the channel

cond-mat.stat-mech↗
arXiv2013

About an H-theorem for systems with non-conservative interactions

We exhibit some arguments in favour of an H-theorem for a generalization of the Boltzmann equation including non-conservative interactions and a linear Fokker-Planck-like thermostatting term. Such a non-linear equation describing the evolution of the single particle probability $P_i(t)$ of being in state $i$ at time $t$, is a suitable model for granular gases and is indicated here as Boltzmann-Fokker-Planck (BFP) equation. The conjectured H-functional, which appears to be non-increasing, is $H_C(t)=\sum_i P_i(t) \ln P_i(t)/Π_i$ with $Π_i = \lim_{t \to \infty} P_i(t)$, in analogy with the H-functional of Markov processes. The extension to continuous states is straightforward. A simple proof can be given for the elastic BFP equation. A semi-analytical proof is also offered for the BFP equation for so-called inelastic Maxwell molecules. Other evidence is obtained by solving particular BFP cases through numerical integration or through "particle schemes" such as the Direct Simulation Monte Carlo.

cond-mat.stat-mech↗
arXiv2013

Front speed in reactive compressible stirred media

We investigated a nonlinear advection-diffusion-reaction equation for a passive scalar field. The purpose is to understand how the compressibility can affect the front dynamics and the bulk burning rate. We study two classes of flows: periodic shear flow and cellular flow both in the case of fast advection regime, analysing the system at varying the extent of compressibility and the reaction rate. We find that the bulk burning rate in a shear flow increases with compressibility intensity. Furthermore, the faster the reaction the more important the difference with respect to the laminar case. The effect has been quantitatively measured and it turns out to be generally little. For the cellular flow, the two extreme cases have been investigated, with the whole perturbation situated either in the centre of the vortex or in the periphery. The dependence in this case does not show a monotonic scaling with different behaviour in the two cases. The enhancing remains modest and always less than 20%

physics.bio-ph↗
arXiv2012

Einstein relation in superdiffusive systems

We study the Einstein relation between diffusion and response to an external field in systems showing superdiffusion. In particular, we investigate a continuous time Levy walk where the velocity remains constant for a time τ, with distribution P(τ) τ^{-g}. At varying g the diffusion can be standard or anomalous; in spite of this, if in the unperturbed system a current is absent, the Einstein relation holds. In the case where a current is present the scenario is more complicated and the usual Einstein relation fails. This suggests that the main ingredient for the breaking of the Einstein relation is not the anomalous diffusion but the presence of a mean drift (current).

cond-mat.stat-mech↗
arXiv2012

Out-of-equilibrium generalized fluctuation-dissipation relations

We discuss fluctuation-dissipation relations valid under general conditions even out of equilibrium. The response function is expressed in terms of unperperturbed correlation functions, where contributions peculiar to non-equilibrium can appear. Such extra terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with two examples: driven granular systems and anomalous diffusion on comb structures.

cond-mat.stat-mech↗
arXiv2012

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 paper 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.

cond-mat.stat-mech↗
arXiv2011

Nonlinear superposition of direct and inverse cascades in two-dimensional turbulence forced at large and small scales

We inquire about the properties of 2d Navier-Stokes turbulence simultaneously forced at small and large scales. The background motivation comes by observational results on atmospheric turbulence. We show that the velocity field is amenable to the sum of two auxiliary velocity fields forced at large and small scale and exhibiting a direct-enstrophy and an inverse-energy cascade, respectively. Remarkably, the two auxiliary fields reconcile universal properties of fluxes with positive statistical correlation in the inertial range.

physics.flu-dyn↗
arXiv2011

Lagrangian drifter dispersion in the southwestern Atlantic Ocean

In 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, we focus our 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 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. We find that, dependently on the given observable, the quasigeostrophic turbulence scenario is overall compatible with our data analysis, with discrepancies from the expected behavior of 2D turbulent trajectories likely to be ascribed to the non stationary and non homogeneous characteristics of the flow, as well as to possible ageostrophic effects. Submesoscale features of O(1) km are considered to play a role, to some extent, in determining the properties of relative dispersion as well as the shape of the energy spectrum. We present, also, numerical simulations of an OGCM of the South Atlantic, and discuss the comparison between experimental and model data about mesoscale dispersion.

nlin.CD↗
arXiv2008

Coarse graining of master equations with fast and slow states

We propose a general method for simplifying master equations by eliminating from the description rapidly evolving states. The physical recipe we impose is the suppression of these states and a renormalization of the rates of all the surviving states. In some cases, this decimation procedure can be analytically carried out and is consistent with other analytical approaches, like in the problem of the random walk in a double-well potential. We discuss the application of our method to nontrivial examples: diffusion in a lattice with defects and a model of an enzymatic reaction outside the steady state regime.

cond-mat.soft↗