arXiv subjects

Angelo Vulpiani

Publications and source records attributed to Angelo Vulpiani.

At least 55 records · Page 3Linked to original sources

arXiv2018

Active escape dynamics: the effect of persistence on barrier crossing

We study a system of non-interacting active particles, propelled by colored noises, characterized by an activity time $τ$, and confined by a double-well potential. A straightforward application of this system is the problem of barrier crossing of active particles, which has been studied only in the limit of small activity. When $τ$ is sufficiently large, equilibrium-like approximations break down in the barrier crossing region. In the model under investigation, it emerges a sort of "negative temperature" region, and numerical simulations confirm the presence of non-convex local velocity distributions. We propose, in the limit of large $τ$, approximate equations for the typical trajectories which successfully predict many aspects of the numerical results. The local breakdown of detailed balance and its relation with a recent definition of non-equilibrium heat exchange is also discussed.

cond-mat.stat-mech↗

arXiv2018

Law without law or "just" limit theorems?

About 35 years ago Wheeler introduced the motto `law without law' to highlight the possibility that (at least a part of) Physics may be understood only following {\em regularity principles} and few relevant facts, rather than relying on a treatment in terms of fundamental theories. Such a proposal can be seen as part of a more general attempt (including the maximum entropy approach) summarized by the slogan `it from bit', which privileges the information as the basic ingredient. Apparently it seems that it is possible to obtain, without the use of physical laws, some important results in an easy way, for instance, the probability distribution of the canonical ensemble. In this paper we will present a general discussion on those ideas of Wheeler's that originated the motto `law without law'. In particular we will show how the claimed simplicity is only apparent and it is rather easy to produce wrong results. We will show that it is possible to obtain some of the results treated by Wheeler in the realm of the statistical mechanics, using precise assumptions and nontrivial results of probability theory, mainly concerning ergodicity and limit theorems.

cond-mat.stat-mech↗

arXiv2018

The Role of Data in Model Building and Prediction: A Survey Through Examples

The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of quantitative sciences, mean abstract mathematical or algorithmical representations. This short review discusses a few key examples from Physics, taken from dynamical systems theory, biophysics, and statistical mechanics, representing three paradigmatic procedures to build models and predictions from available data. In the case of dynamical systems we show how predictions can be obtained in a virtually model-free framework using the methods of analogues, and we briefly discuss other approaches based on machine learning methods. In cases where the complexity of systems is challenging, like in biophysics, we stress the necessity to include part of the empirical knowledge in the models to gain the minimal amount of realism. Finally, we consider many body systems where many (temporal or spatial) scales are at play and show how to derive from data a dimensional reduction in terms of a Langevin dynamics for their slow components.

cond-mat.stat-mech↗

arXiv2018

Reaction fronts in persistent random walks with demographic stochasticity

Standard Reaction-Diffusion (RD) systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle model in which individuals move following a persistent random walk with finite speed and grow with logistic dynamics. We show that when the number of individuals is very large, the individual-based model is well described by the continuous Reactive Cattaneo Equation (RCE), but for smaller values of the carrying capacity important finite-population effects arise. The effects of fluctuations on the propagation speed are investigated both considering the RCE with a cutoff in the reaction term and by means of numerical simulations of the individual-based model. Finally, a more general Lévy walk process for the transport of individuals is examined and an expression for the front speed of the resulting traveling wave is proposed.

physics.bio-ph↗

arXiv2018

DCA for genome-wide epistasis analysis: the statistical genetics perspective

Direct Coupling Analysis (DCA) is a now widely used method to leverage statistical information from many similar biological systems to draw meaningful conclusions on each system separately. DCA has been applied with great success to sequences of homologous proteins, and also more recently to whole-genome population-wide sequencing data. We here argue that the use of DCA on the genome scale is contingent on fundamental issues of population genetics. DCA can be expected to yield meaningful results when a population is in the Quasi-Linkage Equilibrium (QLE) phase studied by Kimura and others, but not, for instance, in a phase of Clonal Competition. We discuss how the exponential (Potts model) distributions emerge in QLE, and compare couplings to correlations obtained in a study of about 3,000 genomes of the human pathogen Streptococcus pneumoniae.

q-bio.PE↗

arXiv2018

Frequency-control of protein translocation across an oscillating nanopore

The translocation of a Lipid Binding Protein (LBP) is studied using a phenomenological coarse-grained computational model that simplifies both chain and pore geometry. We investigated via molecular dynamics the interplay between transport and unfolding in the presence of a nanopore whose section oscillates periodically in time with a frequency omega, a motion often referred to as radial breathing mode (RBM). We found that the LPB when mechanically pulled into the vibrating nanopore exhibits a translocation dynamics that in some frequency range is accelerated and shows a frequency locking to the pore dynamics. The main effect of pore vibrations is the suppression of stalling events of the translocation dynamics, hence, a proper frequency tuning allows both regularization and control of the overall transport process. Finally, the interpretation of the simulation results is easily achieved by resorting to a first passage theory of elementary driven-diffusion processes.

cond-mat.soft↗

arXiv2018

Linear response and correlation of a self-propelled particle in the presence of external fields

We study the non-equilibrium properties of non interacting active Ornstein-Uhlenbeck particles (AOUP) subject to an external nonuniform field using a Fokker-Planck approach with a focus on the linear response and time-correlation functions. In particular, we compare different methods to compute these functions including the unified colored noise approximation (UCNA). The AOUP model, described by the position of the particle and the active force acting on it, is usually mapped into a Markovian process, describing the motion of a fictitious passive particle in terms of its position and velocity, where the effect of the activity is transferred into a position-dependent friction. We show that the form of the response function of the AOUP depends on whether we put the perturbation on the position and keep unperturbed the active force in the original variables or perturb the position and maintain unperturbed the velocity in the transformed variables. Indeed, as a result of the change of variables the perturbation on the position becomes a perturbation both on the position and on the fictitious velocity. We test these predictions by considering the response for three types of convex potentials: quadratic, quartic and double-well potential. Moreover, by comparing the response of the AOUP model with the corresponding response of the UCNA model we conclude that although the stationary properties are fairly well approximated by the UCNA, the non equilibrium properties are not, an effect which is not negligible when the persistence time is large.

cond-mat.stat-mech↗

arXiv2017

Compressibility, laws of nature, initial conditions and complexity

We critically analyse the point of view for which laws of nature are just a mean to compress data. Discussing some basic notions of dynamical systems and information theory, we show that the idea that the analysis of large amount of data by means of an algorithm of compression is equivalent to the knowledge one can have from scientific laws, is rather naive. In particular we discuss the subtle conceptual topic of the initial conditions of phenomena which are generally incompressible. Starting from this point, we argue that laws of nature represent more than a pure compression of data, and that the availability of large amount of data, in general, is not particularly useful to understand the behaviour of complex phenomena.

cond-mat.stat-mech↗

arXiv2017

Fourier's Law in a Generalized Piston Model

A simplified, but non trivial, mechanical model -- gas of $N$ particles of mass $m$ in a box partitioned by $n$ mobile adiabatic walls of mass $M$ -- interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an approach due to Smoluchowski, from an analysis of the collisions particles/walls, we derive the values of the main thermodynamic quantities for the stationary non-equilibrium states. The results are compared with extensive numerical simulations; in the limit of large $n$, $mN/M\gg 1$ and $m/M \ll 1$, we find a good approximation of Fourier's law.

cond-mat.stat-mech↗

arXiv2017

Forecasting in the light of Big Data

Predicting the future state of a system has always been a natural motivation for science and practical applications. Such a topic, beyond its obvious technical and societal relevance, is also interesting from a conceptual point of view. This owes to the fact that forecasting lends itself to two equally radical, yet opposite methodologies. A reductionist one, based on the first principles, and the naive inductivist one, based only on data. This latter view has recently gained some attention in response to the availability of unprecedented amounts of data and increasingly sophisticated algorithmic analytic techniques. The purpose of this note is to assess critically the role of big data in reshaping the key aspects of forecasting and in particular the claim that bigger data leads to better predictions. Drawing on the representative example of weather forecasts we argue that this is not generally the case. We conclude by suggesting that a clever and context-dependent compromise between modelling and quantitative analysis stands out as the best forecasting strategy, as anticipated nearly a century ago by Richardson and von Neumann.

physics.soc-ph↗

arXiv2017

Chaotic Lagrangian models for turbulent relative dispersion

A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian Chaos. The anomalous "sweeping effect", a known drawback common to kinematic simulations, is removed thanks to the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analysed by computing the Finite-Scale Lyapunov Exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous and isotropic conditions. The mathematics of the model is relatively simple and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer and/or boundary layer turbulence models as well as Lagrangian predictability studies.

physics.flu-dyn↗

arXiv2016

Reaction Spreading in Systems With Anomalous Diffusion

We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider {\it strong anomalous} diffusion characterized by the moment behaviour $\langle x(t)^q \rangle \sim t^{q ν(q)}$, where $ν(q)$ is a non constant function, and we discuss its consequences. Even in the apparently simple case $ν(2)=1/2$, strong anomalous diffusion may correspond to non trivial features, such as non Gaussian probability distribution and peculiar scaling of large order moments. When a reactive term is added to a normal diffusion process, one has a propagating front with a constant velocity. The presence of anomalous diffusion by itself does not guarantee a changing in the front propagation scenario; a key factor to select linear in time or faster front propagation has been identified in the shape of the probability distribution tail in absence of reaction. In addition, we discuss the reaction spreading on graphs, underlying the major role of the connectivity properties of these structures, characterized by the {\em connectivity dimension}

cond-mat.stat-mech↗

arXiv2016

Linear and anomalous front propagation in system with non Gaussian diffusion: the importance of tails

We investigate front propagation in systems with diffusive and sub-diffusive behavior. The scaling behavior of moments of the diffusive problem, both in the standard and in the anomalous cases, is not enough to determine the features of the reactive front. In fact, the shape of the bulk of the probability distribution of the transport process, which determines the diffusive properties, is important just for pre-asymptotic behavior of front propagation, while the precise shape of the tails of the probability distribution determines asymptotic behavior of front propagation.

cond-mat.stat-mech↗

arXiv2016

Chaos and Stochastic Models in Physics: Ontic and Epistemic Aspects

There is a persistent confusion about determinism and predictability. In spite of the opinions of some eminent philosophers (e.g., Popper), it is possible to understand that the two concepts are completely unrelated. In few words we can say that determinism is ontic and has to do with how Nature behaves, while predictability is epistemic and is related to what the human beings are able to compute. An analysis of the Lyapunov exponents and the Kolmogorov-Sinai entropy shows how deterministic chaos, although with an epistemic character, is non subjective at all. This should clarify the role and content of stochastic models in the description of the physical world.

nlin.CD↗

arXiv2016

Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations

We investigate a kinetic heat engine model constituted by particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period $τ$ : their relative excursions, $δ$ and $ε$ respectively, constitute the thermodynamic forces dragging the system out-of-equilibrium. The analysis of the entropy production of the system allows to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. In the limit of small $δ$ and $ε$ the fluxes are linear in the forces through a $τ$-dependent Onsager matrix whose off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which - in the linear regime - yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon-Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e. outside of the linear regime. In all our analysis the adiabatic limit $τ\to \infty$ and the the small force limit $δ,ε\to 0$ are not directly related.

cond-mat.stat-mech↗

arXiv2015

About the maximum entropy principle in non equilibrium statistical mechanics

The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make predictions in physics and other disciplines, which constitutes an alternative and more general method than the traditional ones of statistical mechanics. Actually, careful inspection shows that such a success is due to a series of fortunate facts that characterize the physics of equilibrium systems, but which are absent in situations not described by Hamiltonian dynamics, or generically in nonequilibrium phenomena. Here we discuss several important examples in non equilibrium statistical mechanics, in which the MEP leads to incorrect predictions, proving that it does not have a predictive nature. We conclude that, in these paradigmatic examples, the "traditional" methods based on a detailed analysis of the relevant dynamics cannot be avoided.

cond-mat.stat-mech↗

arXiv2015

Consistent description of fluctuations requires negative temperatures

We review two definitions of temperature in statistical mechanics, $T_B$ and $T_G$, corresponding to two possible definitions of entropy, $S_B$ and $S_G$, known as surface and volume entropy respectively. We restrict our attention to a class of systems with bounded energy and such that the second derivative of $S_B$ with respect to energy is always negative: the second request is quite natural and holds in systems of obvious relevance, i.e. with a number $N$ of degrees of freedom sufficiently large (examples are shown where $N \sim 100$ is sufficient) and without long-range interactions. We first discuss the basic role of $T_B$, even when negative, as the parameter describing fluctuations of observables in a sub-system. Then, we focus on how $T_B$ can be measured dynamically, i.e. averaging over a single long experimental trajectory. On the contrary, the same approach cannot be used in a generic system for $T_G$, since the equipartition theorem may be spoiled by boundary effects due to the limited energy. These general results are substantiated by the numerical study of a Hamiltonian model of interacting rotators with bounded kinetic energy. The numerical results confirm that the kind of configurational order realized in the regions at small $S_B$, or equivalently at small $|T_B|$, depends on the sign of $T_B$.

cond-mat.stat-mech↗

arXiv2015

The role of the number of degrees of freedom and chaos in macroscopic irreversibility

This article aims at revisiting, with the aid of simple and neat numerical examples, some of the basic features of macroscopic irreversibility, and, thus, of the mechanical foundation of the second principle of thermodynamics as drawn by Boltzmann. Emphasis will be put on the fact that, in systems characterized by a very large number of degrees of freedom, irreversibility is already manifest at a single-trajectory level for the vast majority of the far-from-equilibrium initial conditions - a property often referred to as typicality. We also discuss the importance of the interaction among the microscopic constituents of the system and the irrelevance of chaos to irreversibility, showing that the same irreversible behaviours can be observed both in chaotic and non-chaotic systems.

cond-mat.stat-mech↗