arXiv subjects

Umberto Marini Bettolo Marconi

Publications and source records attributed to Umberto Marini Bettolo Marconi.

At least 55 records · Page 3Linked to original sources

arXiv2018

Activity induced delocalization and freezing in self-propelled systems

We study a system of interacting active particles, propelled by colored noises, characterized by an activity time τ, and confined by a single-well anharmonic potential. We assume pair-wise repulsive forces among particles, modelling the steric interactions among microswimmers. This system has been experimentally studied in the case of a dilute suspension of Janus particles confined through acoustic traps. We observe that already in the dilute regime - when inter-particle interactions are negligible - increasing the persistent time pushes the particles away from the potential minimum, until a saturation distance is reached. We compute the phase diagram (activity versus interaction length), showing that the interaction does not suppress this delocalization phenomenon but induces a liquid- or solid-like structure in the densest regions. Interestingly a reentrant behavior is observed: a first increase of τ from small values acts as an effective warming, favouring fluidization; at higher values, when the delocalization occurs, a further increase of τ induces freezing inside the densest regions. An approximate analytical scheme gives fair predictions for the density profiles in the weakly interacting case. The analysis of non-equilibrium heat fluxes reveals that in the region of largest particle concentration equilibrium is restored in several aspects.

cond-mat.stat-mech↗

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

Effective equilibrium picture in $xy-$model with exponentially correlated noise

We study the effect of exponentially correlated noise on $xy-$model in the limit of small correlation time discussing the order-disorder transition in mean-field and the topological transition in two dimensions. We map the steady states of the non-equilibrium dynamics into an effective equilibrium theory. In mean-field, the critical temperature increases with the noise correlation time $τ$ indicating that memory effects promote ordering. This finding is confirmed by numerical simulations. The topological transition temperature in two dimensions remains untouched. However, finite size effects induce a crossover in the vortices proliferation that is confirmed by numerical simulations.

cond-mat.stat-mech↗

arXiv2018

Effective equilibrium states in mixtures of active particles driven by colored noise

We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with exponential correlation functions whose intensities and correlation times vary from species to species. By extending Fox's theory to many components, we derive by functional calculus an approximate Fokker-Planck equation for the configurational distribution function of the system. After illustrating the predicted distribution in the solvable case of two particles interacting via a harmonic potential, we consider systems of particles repelling through inverse power laws potentials. We compare the analytic predictions to computer simulations for such soft-repulsive interactions in one dimension, and show that at linear order in the persistence times the theory is satisfactory. This work provides the toolbox to qualitatively describe many-body phenomena, such as demixing and depletion, by means of effective pair potentials.

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

Effective equilibrium states in the colored-noise model for active matter I. Pairwise forces in the Fox and unified colored noise approximations

The equations of motion of active systems can be modeled in terms of Ornstein-Uhlenbeck processes (OUPs) with appropriate correlators. For further theoretical studies, these should be approximated to yield a Markovian picture for the dynamics and a simplified steady-state condition. We perform a comparative study of the Unified Colored Noise Approximation (UCNA) and the approximation scheme by Fox recently employed within this context. We review the approximations necessary to define effective interaction potentials in the low-density limit and study the conditions for which these represent the behavior observed in two-body simulations for the OUPs model and Active Brownian particles. The demonstrated limitations of the theory for potentials with a negative slope or curvature can be qualitatively corrected by a new empirical modification. In general, we find that in the presence of translational white noise the Fox approach is more accurate. Finally, we examine an alternative way to define a force-balance condition in the limit of small activity.

cond-mat.soft↗

arXiv2017

Effective equilibrium states in the colored-noise model for active matter II. A unified framework for phase equilibria, structure and mechanical properties

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.

cond-mat.soft↗

arXiv2017

Electrokinetic Lattice Boltzmann solver coupled to Molecular Dynamics: application to polymer translocation

We develop a theoretical and computational approach to deal with systems that involve a disparate range of spatio-temporal scales, such as those comprised of colloidal particles or polymers moving in a fluidic molecular environment. Our approach is based on a multiscale modeling that combines the slow dynamics of the large particles with the fast dynamics of the solvent into a unique framework. The former is numerically solved via Molecular Dynamics and the latter via a multi-component Lattice Boltzmann. The two techniques are coupled together to allow for a seamless exchange of information between the descriptions. Being based on a kinetic multi-component description of the fluid species, the scheme is flexible in modeling charge flow within complex geometries and ranging from large to vanishing salt concentration. The details of the scheme are presented and the method is applied to the problem of translocation of a charged polymer through a nanopores. In the end, we discuss the advantages and complexities of the approach.

cond-mat.soft↗

arXiv2017

Heat, temperature and Clausius inequality in a model for active brownian particles

Methods of stochastic thermodynamics and hydrodynamics are applied to the 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 fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.

cond-mat.stat-mech↗

arXiv2017

Pressure in an exactly solvable model of active fluid

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 model (UCNA). 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 an assembly of elastic dumbbells confined to a parabolic well. By employing the UCNA we find that, for this model, the pressure determined by the thermodynamic method coincides with the pressures obtained by the virial and mechanical methods. The three methods when applied to the GCN give a pressure identical to that obtained via the UCNA. Finally, we find that the ABP virial pressure exactly agrees with the UCNA and GCN result.

cond-mat.soft↗

arXiv2017

Clausius relation for active particles: what can we learn from fluctuations?

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 original Clausius relation and can be experimentally verified.

cond-mat.stat-mech↗

arXiv2016

Critical Phenomena in Active Matter

We investigate the effect of self-propulsion on a mean-field order-disorder transition. Starting from a $φ^4$ scalar field theory subject to an exponentially correlated noise, we exploit the Unified Colored Noise Approximation to map the non-equilibrium active dynamics onto an effective equilibrium one. This allows us to follow the evolution of the second-order critical point as a function of the noise parameters: the correlation time $τ$ and the noise strength $D$. Our results suggest that $τ$ is a crucial ingredient that changes the location of the critical point but, remarkably, not the universality class of the model. We also estimate the effect of Gaussian fluctuations on the mean-field approximation finding an Ornstein-Zernike like expression for the static structure factor at long wave lengths. Finally, to assess the validity of our predictions, we compare the mean-field theoretical results with numerical simulations of active Lennard-Jones particles in two and three dimensions, finding a good qualitative agreement at small $τ$ values.

cond-mat.stat-mech↗

arXiv2016

Effective potential method for active particles

We investigate the steady state properties of an active fluid modeled as an assembly of soft repulsive spheres subjected to Gaussian colored noise. Such a noise captures one of the salient aspects of active particles, namely the persistence of their motion and determines a variety of novel features with respect to familiar passive fluids. We show that within the so-called multidimensional unified colored noise approximation, recently introduced in the field of active matter, the model can be treated by methods similar to those employed in the study of standard molecular fluids. The system shows a tendency of the particles to aggregate even in the presence of purely repulsive forces because the combined action of colored noise and interactions enhances the the effective friction between nearby particles. We also discuss whether an effective two-body potential approach, which would allow to employ methods similar to those of density functional theory, is appropriate. The limits of such an approximation are discussed.

cond-mat.soft↗

arXiv2016

Pressure and surface tension of an active simple liquid: a comparison between kinetic, mechanical and free-energy based approaches

We discuss different definitions of pressure for a system of active spherical particles driven by a non-thermal coloured noise. We show that mechanical, kinetic and free-energy based approaches lead to the same result up to first order in the non-equilibrium expansion parameter. The first prescription is based on a generalisation of the kinetic mesoscopic virial equation and expresses the pressure exerted on the walls in terms of the average of the virial of the inter-particle forces. In the second approach, the pressure and the surface tension are identified with the volume and area derivatives, respectively, of the partition function associated with the known stationary non-equilibrium distribution of the model. The third method is a mechanical approach and is related to the work necessary to deform the system. The pressure is obtained by comparing the expression of the work in terms of local stress and strain with the corresponding expression in terms of microscopic distribution. This is determined from the force balance encoded in the Born-Green-Yvon equation. Such a method has the advantage of giving a formula for the local pressure tensor and the surface tension even in inhomogeneous situations. By direct inspection, we show that the three procedures lead to the same values of the pressure, and give support to the idea that the partition function, obtained via the unified coloured noise approximation, is more than a formal property of the system, but determines the stationary non-equilibrium thermodynamics of the model.

cond-mat.stat-mech↗

arXiv2015

Velocity distribution in active particles systems

We derive an analytic expression for the distribution of velocities of multiple interacting active particles which we test by numerical simulations. In clear contrast with equilibrium we find that the velocities are coupled to positions. Our model shows that, even for two particles only, the individual velocities display a variance depending on the interparticle separation and the emergence of correlations between the velocities of the particles. When considering systems composed of many particles we find an analytic expression connecting the overall velocity variance to density, at the mean-field level, and to the pair distribution function valid in the limit of small noise correlation times. Finally we discuss the intriguing analogies and main differences between our effective free energy functional and the theoretical scenario proposed so far for phase-separating active particles.

cond-mat.stat-mech↗

arXiv2015

Towards a statistical mechanical theory of active fluids

We present a stochastic description of a model of N mutually repelling active spheres in the presence of external fields and characterize its steady state behavior. To reproduce the effects of the experimentally observed persistence of the trajectories of the active particles we consider a Gaussian forcing having a non vanishing correlation time $τ$, whose finiteness is a measure of the activity of the system. With these ingredients we show that it is possible to develop a statistical mechanical approach similar to the one employed in the study of equilibrium liquids and to obtain the explicit form of the many-particle distribution function by means of the multidimensional unified colored noise approximation. Such a distribution plays a role analogous to the Gibbs distribution in equilibrium statistical mechanics and provides a complete information about the microscopic state of the system. From here we develop a method to determine the one and two-particle distribution functions in the spirit of the Born-Green-Yvon (BGY) equations of equilibrium statistical mechanics. The resulting equations which contain extra-correlations induced by the activity allow to determine the stationary density profiles in the presence of external fields, the pair correlations and the pressure of active fluids. In the low density regime we obtain the effective pair potential $ϕ(r)$ acting between two isolated particles separated by a distance, $r$, showing the existence an effective attraction between them induced by activity. Based on these results, in the second half of the paper we propose a mean field theory as an approach simpler than the BGY hierarchy and use it to derive a van der Waals expression of the equation of state, which can serve as the basis to understand the phase behavior of active fluids.

cond-mat.soft↗

arXiv2015

Tracer diffusion of hard-sphere binary mixtures under nano-confinement

The physics of diffusion phenomena in nano and micro channels has attracted a lot of attention in recent years, due to its close connection with many technological, medical and industrial applications. In the present paper we employ a kinetic approach to investigate how the confinement in nanostructured geometries affects the diffusive properties of fluid mixtures and leads to the appearance of properties different from those of bulk systems. In particular, we derive an expression for the friction tensor in the case of a bulk fluid mixture confined to a narrow slit having undulated walls. The boundary roughness leads to a new mechanism for transverse diffusion, and can even lead to an effective diffusion along the channel larger than the one corresponding to a planar channel of equivalent section. Finally we discuss a reduction of the previous equation to a one dimensional effective diffusion equation in which an entropic term encapsulates the geometrical information on the channel shape.

cond-mat.soft↗

arXiv2015

Modulation of current through a nanopore induced by a charged globule: implications for DNA-docking

The passage of DNA through a nanopore can be effectively decomposed into two distinct phases, docking and actual translocation. In experiments each phase is characterized by a distinct current signature which allows the discrimination of the two events. However, at low voltages a clear distinction of the two phases is lost. By using numerical simulations we clarify how the current signature associated to the docking events depends on the applied voltage. The simulations show that at small voltage the DNA globule enhances the pore conductance due to an enrichment of charge carriers. At high voltage, the globule drains substantial charge carriers from the pore region, thereby reducing the overall conductance. The results provide a new interpretation to the experimental data on conductance and show how docking interferes with the translocation signal, of potential interest for sequencing applications.

physics.bio-ph↗