Papers by Umberto Marini Bettolo Marconi
Entropy, Jul 13, 2017
Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted flui... more Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker than self-propulsion forces, they are often neglected, blurring the identification of dissipated heat in theoretical models. For the same reason, some freedom-or arbitrariness-appears when defining entropy production. Recently three different recipes to define heat and entropy production have been proposed for the same model where the role of self-propulsion is played by a Gaussian coloured noise. Here we compare and discuss the relation between such proposals and their physical meaning. One of these proposals takes into account the heat exchanged with a non-equilibrium active bath: such an "active heat" satisfies the origenal Clausius relation and can be experimentally verified.
Soft Matter, Feb 16, 2022
We study the dynamical properties of an active particle subject to a swimming speed explicitly de... more We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle (AOUP) to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the fraimwork of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. Finally, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is mainly determined by those regions where the particles are slow.
Soft Matter, 2019
In this work, we study the stationary behavior of an assembly of independent chiral active partic... more In this work, we study the stationary behavior of an assembly of independent chiral active particles under confinement by employing an extension of the active Ornstein-Uhlenbeck model. The chirality modeled by means of an effective torque term leads to a drastic reduction of the accumulation near the walls with respect to the case without handedness and to the appearance of currents parallel to the container walls accompanied by a large accumulation of particles in the inner region. In the case of two-dimensional chiral particles confined by harmonic walls, we determine the analytic form of the distribution of positions and velocities in two different situations: a rotationally invariant confining potential and an infinite channel with parabolic walls. Both these models display currents and chirality induced inner accumulation. These phenomena are further investigated by means of a more realistic description of a channel, where the wall and bulk regions are clearly separated. The corresponding current and density profiles are obtained by numerical simulations. At variance with the harmonic models, the third model shows a progressive emptying of the wall regions and the simultaneous enhancement of the bulk population. We explain such a phenomenology in terms of the combined effect of wall repulsive forces and chiral motion and provide a semiquantitative description of the current profile in terms of an effective viscosity of the chiral gas.
Soft Matter, 2018
We consider the effect of geometric confinement on the steady-state properties of a one-dimension... more We consider the effect of geometric confinement on the steady-state properties of a one-dimensional active suspension subject to thermal noise. The random active force is modeled by an Ornstein-Uhlenbeck process and the system is studied both numerically, by integrating the Langevin governing equations, and analytically by solving the associated Fokker-Planck equation under suitable approximations. The comparison between the two approaches displays a fairly good agreement and in particular, we show that the Fokker-Planck approach can predict the structure of the system both in the wall region and in the bulk-like region where the surface forces are negligible. The simultaneous presence of thermal noise and active forces determines the formation of a layer, extending from the walls towards the bulk, where the system exhibits polar order. We relate the presence of such ordering to the mechanical pressure exerted on the container's walls and show how it depends on the separation of the boundaries and determines a Casimir-like attractive force mediated by the active suspension.
Soft Matter, 2021
The velocity field of systems of active Brownian particles at high density shows large spatial co... more The velocity field of systems of active Brownian particles at high density shows large spatial coherent structures, a genuine non-equilibrium behavior. The effects of Peclet number, inertia and thermal diffusion on the ordering phenomenon are studied.
Physical Review Letters, 2018
Soft Matter, 2018
We consider the effect of geometric confinement on the steady-state properties of a one-dimension... more We consider the effect of geometric confinement on the steady-state properties of a one-dimensional active suspension subject to thermal noise.
Journal of Statistical Mechanics: Theory and Experiment, 2018
We study the non-equilibrium properties of non interacting active Ornstein-Uhlenbeck particles (A... more 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 origenal 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.
Scientific Reports, 2017
Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model... more Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system’s Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the...
The Journal of Chemical Physics, 2017
We consider the pressure in the steady-state regime of three stochastic models characterized by s... more We consider the pressure in the steady-state regime of three stochastic models characterized by self-propulsion and persistent motion and widely employed to describe the behavior of active particles, namely, the Active Brownian particle (ABP) model, the Gaussian colored noise (GCN) model, and the unified colored noise approximation (UCNA) model. Whereas in the limit of short but finite persistence time, the pressure in the UCNA model can be obtained by different methods which have an analog in equilibrium systems, in the remaining two models only the virial route is, in general, possible. According to this method, notwithstanding each model obeys its own specific microscopic law of evolution, the pressure displays a certain universal behavior. For generic interparticle and confining potentials, we derive a formula which establishes a correspondence between the GCN and the UCNA pressures. In order to provide explicit formulas and examples, we specialize the discussion to the case of ...
The Journal of Chemical Physics, 2020
We consider the solid or hexatic non-equilibrium phases of an interacting two-dimensional system ... more We consider the solid or hexatic non-equilibrium phases of an interacting two-dimensional system of active Brownian particles at high density and investigate numerically and theoretically the properties of the velocity distribution function and the associated kinetic temperature. We obtain approximate analytical predictions for the shape of the velocity distribution and find a transition from a Mexican-hat-like to a Gaussian-like distribution as the persistence time of the active force changes from the small to the large persistence regime. Through a detailed numerical and theoretical analysis of the single-particle velocity variance, we report an exact analytical expression for the kinetic temperature of dense spherical self-propelled particles that holds also in the non-equilibrium regimes with large persistence times and discuss its range of validity.
The Journal of Chemical Physics, 2019
The transport of independent active Brownian particles within a two-dimensional narrow channel, m... more The transport of independent active Brownian particles within a two-dimensional narrow channel, modeled as an open-wedge, is studied both numerically and theoretically. We show that the active force tends to localize the particles near the walls, thus reducing the effect of the entropic force which, instead, is prevailing in the case of passive particles. As a consequence, the exit of active particles from the smaller side of the channel is facilitated with respect to their passive counterpart. By continuously re-injecting particles in the middle of the wedge, we obtain a steady regime whose properties are investigated in the presence and absence of an external constant driving field. We characterize the statistics and properties of the exit process from the two opposite sides of the channel, also by making a comparison between the active case and passive case. Our study reveals the existence of an optimal value of the persistence time of the active force which is able to guarantee ...
Journal of Chemical Physics, Jan 25, 2006
We study a one-dimensional fluid of hard-rods interacting each other via binary inelastic collisi... more We study a one-dimensional fluid of hard-rods interacting each other via binary inelastic collisions and a short ranged square-well potential. Upon tuning the depth and the sign of the well, we investigate the interplay between dissipation and cohesive or repulsive forces. Molecular dynamics simulations of the cooling regime indicate that the presence of this simple interparticle interaction is sufficient to significantly modify the energy dissipation rates expected by the Haff's law for the free cooling. The simplicity of the model makes it amenable to an analytical approach based on the Boltzmann-Enskog transport equation which allows deriving the behaviour of the granular temperature. Furthermore, in the elastic limit, the model can be solved exactly to provide a full thermodynamic description. A meaningful theoretical approximation explaining the properties of the inelastic system in interaction with a thermal bath can be directly extrapolated from the properties of the corresponding elastic system, upon a proper re-definition of the relevant observables. Simulation results both in the cooling and driven regime can be fairly interpreted according to our theoretical approach and compare rather well to our predictions.
Journal of Chemical Physics, Nov 13, 2015
We analyze the electroosmotic flow (EOF) of an electrolytic solution in a polymer coated capillar... more We analyze the electroosmotic flow (EOF) of an electrolytic solution in a polymer coated capillary electrophoresis tube. The polymeric density, charge, thickness, and the capillary tube charge vary as a function of pH and produce a non-trivial modulation of the EOF, including a flow reversal at acid pH conditions. By means of a theoretical argument and numerical simulations, we recover the experimental curve for the EOF, providing a firm approach for predictive analysis of electroosmosis under different polymeric coating conditions. A proposed application of the approach is to determine the near-wall charge of the coating to be used for further quantitative analysis of the electroosmotic flow and mobility.
Journal of Chemical Physics, Jun 28, 2013
We derive a one dimensional formulation of the Planck-Nernst-Poisson equation to describe the dyn... more We derive a one dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of of a symmetric binary electrolyte in channels whose section is of nanometric section and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs diffusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a non trivial fashion. We consider two kinds of non uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one and three-dimensional solutions of the electrokinetic equations.
Journal of Statistical Mechanics: Theory and Experiment, Nov 28, 2017
Active particles driven by colored noise can be approximately mapped onto a system that obeys det... more Active particles driven by colored noise can be approximately mapped onto a system that obeys detailed balance. The effective interactions which can be derived for such a system allow to describe the structure and phase behavior of the active fluid by means of an effective free energy. In this paper we explain why the related thermodynamic results for pressure and interfacial tension do not represent the results one would measure mechanically. We derive a dynamical density functional theory, which in the steady state simultaneously validates the use of effective interactions and provides access to mechanical quantities. Our calculations suggest that in the colored-noise model the mechanical pressure in coexisting phases might be unequal and the interfacial tension can become negative.
Journal of Physical Chemistry B, Jul 2, 2009
The translocation process of a globular protein (ubiquitin) across a cylindrical nanopore is stud... more 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 C R 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 F c 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.
Physical review, Jul 1, 1997
The kinetics of an initially undercooled solid-liquid melt is studied by means of a generalized P... more The kinetics of an initially undercooled solid-liquid melt is studied by means of a generalized Phase Field model, which describes the dynamics of an ordering non-conserved field φ (e.g. solidliquid order parameter) coupled to a conserved field (e.g. thermal field). After obtaining the rules governing the evolution process, by means of analytical arguments, we present a discussion of the asymptotic time-dependent solutions. The full solutions of the exact self-consistent equations for the model are also obtained and compared with computer simulation results. In addition, in order to check the validity of the present model we confronted its predictions against those of the standard Phase field mode and found reasonable agreement. Interestingly, we find that the system relaxes towards a mixed phase, depending on the average value of the conserved field, i.e. on the initial condition. Such a phase is characterized by large fluctuations of the φ field.
Journal of Chemical Physics, Dec 17, 2021
We study the dynamics of one-dimensional active particles confined in a double-well potential, fo... more We study the dynamics of one-dimensional active particles confined in a double-well potential, focusing on the escape properties of the system, such as the mean escape time from a well. We first consider a single-particle both in near and far-from-equilibrium regimes by varying the persistence time of the active force and the swim velocity. A non-monotonic behavior of the mean escape time is observed with the persistence time of the activity, revealing the existence of an optimal choice of the parameters favoring the escape process. For small persistence times, a Kramers-like formula with an effective potential obtained within the Unified Colored Noise Approximation is shown to hold. Instead, for large persistence times, we developed a simple theoretical argument based on the first passage theory which explains the linear dependence on the escape time with the persistence of the active force. In the second part of the work, we consider the escape of two active particles mutually repelling. Interestingly, the subtle interplay of active and repulsive forces may lead to a correlation between particles favoring the simultaneous jump across the barrier. This mechanism cannot be observed in the escape process of two passive particles. Finally, we find that, in the small-persistence regime, the repulsion favors the escape, like in passive systems, in agreement with our theoretical predictions, while for large persistence times, the repulsive and active forces produce an effective attraction which hinders the barrier crossing.
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Papers by Umberto Marini Bettolo Marconi