In this work we experimentally study the behavior of a freely-rotating asymmetric probe immersed in a vibrated granular medium. For a wide variety of vibration conditions the probe exhibits a steady rotation whose direction is constant with respect to the asymmetry. By changing the vibration amplitude and by filtering the noise in different frequency bands we show that the velocity of rotation does not depend only on the RMS acceleration $Γ$, but also on the amount of energy provided to two separate frequency bands which are revealed to be important for the dynamics of the granular medium: the first band governs the transfer of energy from the grains to the probe, and the second affects the dynamics by altering the viscosity of the vibro-fluidized material.
A model of an autonomous isothermal Brownian motor with an internal propulsion mechanism is considered. The motor is a Brownian particle which is semi-transparent for molecules of surrounding ideal gas. Molecular passage through the particle is controlled by a potential similar to that in the transition rate theory, i.e. characterized by two stationary states with a finite energy difference separated by a potential barrier. The internal potential drop maintains the diode-like asymmetry of molecular fluxes through the particle, which results in the particle's stationary drift.
A Brownian Motor is a nanoscale or molecular device that combines the effects of thermal noise, spatial or temporal asymmetry, and directionless input energy to drive directed motion. Because of the input energy, Brownian motors function away from thermodynamic equilibrium and concepts such as linear response theory, fluctuation dissipation relations, and detailed balance do not apply. The {\em generalized} fluctuation-dissipation relation, however, states that even under strongly thermodynamically non-equilibrium conditions the ratio of the probability of a transition to the probability of th…
With this work we investigate an often neglected aspect of Brownian motor transport: The rôle of fluctuations of the noise-induced current and its consequences for the efficiency of rectifying noise. In doing so, we consider a Brownian inertial motor that is driven by an unbiased monochromatic, time-periodic force and thermal noise. Typically, we find that the asymptotic, time- and noise-averaged transport velocities are small, possessing rather broad velocity fluctuations. This implies a corresponding poor performance for the rectification power. However, for tailored profiles of the ratchet …
The noise-assisted, directed transport in a one-dimensional dissipative, inertial Brownian motor of the rocking type that is exposed to an external bias is investigated. We demonstrate that the velocity-load characteristics is distinctly non-monotonic, possessing regimes with a {\em negative differential mobility}. In addition, we evaluate several possible efficiency quantifiers which are compared among each other. These quantifiers characterize the mutual interplay between the viscous drag and the external load differently, weighing the inherent rectification features from different physical …
Based on recent work [L. Machura, M. Kostur, P. Talkner, J. Luczka, and P. Hanggi, Phys. Rev. Lett. 98, 040601 (2007)], we extend the study of inertial Brownian motors to the case of an asymmetric potential. It is found that some transport phenomena appear in the presence of an asymmetric potential. Within tailored parameter regimes, there exists two optimal values of the load at which the mean velocity takes its maximum, which means that a load can facilitate the transport in the two parameter regimes. In addition, the phenomenon of multiple current reversals can be observed when the load is …
We report the study of a new experimental granular Brownian motor, inspired to the one published in [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating pawl whose surfaces break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main novelty of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for th…
A reversal of the particle current in rocking Brownian motors was predicted more than 20 years ago; however, an experimental verification and a deeper insight into the underlying mechanisms remained elusive. Here, we investigate the high frequency behaviour of a rocking Brownian motor for charged nanoparticles based on electrostatic interactions in a 3D shaped nanofluidic slit and electro-osmotic forcing of the particles. A sub ms temporal and $\approx\,10\,$nm spatial resolution of the 60 nm gold spheres allows us to measure the time-resolved and frequency dependent evolution of the particle …
We extend the Langevin dynamics so that particles can be exchanged with a particle reservoir. We show that grand canonical ensembles are realized at equilibrium and derive the relations of thermodynamics for processes between equilibrium states. As an application of the proposed evolution rule, we devise a simple model of Brownian motors driven by particle exchange. KEYWORDS: Langevin Dynamics, Thermodynamics, Open Systems
Active gels perform key mechanical roles inside the cell, such as cell division, motion and force sensing. The unique mechanical properties required to perform such functions arise from the interactions between molecular motors and semi-flexible polymeric filaments. Molecular motors can convert the energy released in the hydrolysis of ATP into forces of up to pico-Newton magnitudes. Moreover, the polymeric filaments that form active gels are flexible enough to respond to Brownian forces, but also stiff enough to support the large tensions induced by the motor-generated forces. Brownian forces …
Brownian motion in a granular gas in a homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principle model for the impact-velocity dependent restitution coefficient, as it follows for the model of viscoelastic spheres. We reveal that for a wide range of initial conditions the ratio of granular temperatures of Brownian and bath particles demonstrates complicated non-monotonous behavior, which results in transition between different regimes of Brownian dynamics: It starts from the ballistic motion, switches later to superballistic one …
We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting in the system performs a Brownian motion. The same assumption has been utilised, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.
This article reports on an experimental study of the fluctuations of energy flux between a granular gas and a small driven harmonic oscillator. The DC-motor driving this system is used simultaneously as actuator and probe. The statistics of work fluctuations at controlled forcing, between the motor and the gas are examined from the viewpoint of the Fluctuation Theorem. A characteristic energy $E_c$ of the granular gas, is obtained from this relation between the probabilities of an event and its reversal.
A ratchet model for coupled Brownian motors, inspired by the motion of individual two-headed molecular motors on cytoskeletal filaments, is proposed. Such motors are modeled as two elastically coupled Brownian particles, each of which moves in a flashing ratchet potential. The ratchet potentials felt by the individual particles are anti-correlated, modeling the successive binding and unbinding of the two motor heads to the filament. We obtain, via Langevin simulations, steady-state currents as functions of noise strength, the equilibrium separation of the particles and the rate of switching be…
A quantum Smoluchowski equation is put forward that consistently describes thermal quantum states. In particular, it notably does not induce a violation of the second law of thermodynamics. This so modified kinetic equation is applied to study {\it analytically} directed quantum transport at strong friction in arbitrarily shaped ratchet potentials that are driven by nonthermal two-state noise. Depending on the mutual interplay of quantum tunneling and quantum reflection these quantum corrections can induce both, either a sizable enhancement or a suppression of transport. Moreover, the threshol…
Control and transport of nanoscale objects in fluids is challenging because of the unfavorable scaling of most interaction mechanisms to small length scales. We design energy landscapes for nanoparticles by accurately shaping the geometry of a nanofluidic slit and exploiting the electrostatic interaction between like charged particles and walls. Directed transport is performed by combining asymmetric potentials with an oscillating electric field to achieve a rocking Brownian motor. Using 60\,nm diameter gold spheres, we investigate the physics of the motors with high spatio-temporal resolution…
The interplay between Coulomb friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently fluidized by a vertical shaker, acting as a 'heat bath' for the Brownian-like motion of the probe. Two ball bearings supporting the probe exert nonlinear Coulomb friction upon it. The experimental velocity distribution of the probe, autocorrelation function, and power spectra are compared with the predictions of a linear Boltzmann equation with friction, which is known to simplify in two opposite l…
We calculate the systematic average speed of the adiabatic piston and a thermal Brownian motor, introduced in [Van den Broeck, Kawai and Meurs, \emph{Microscopic analysis of a thermal Brownian motor}, to appear in Phys. Rev. Lett.], by an expansion of the Boltzmann equation and compare with the exact numerical solution.
We show by numerical simulations that a non rotationally symmetric body, whose orientation is fixed and whose center of mass can only slide along a rectilinear guide, under the effect of inelastic collisions with a surrounding gas of particles, displays directed motion. We present a theory which explains how the lack of time reversal induced by the inelasticity of collisions can be exploited to generate a steady average drift. In the limit of an heavy ratchet, we derive an effective Langevin equation whose parameters depend on the microscopic properties of the system and obtain a fairly good q…
The Kinesin family of motor proteins are involved in a variety of cellular processes that transport materials and generate force. With recent advances in experimental techniques, such as optical tweezers which can probe individual molecules, there has been an increasing interest in understanding the mechanisms by which motor proteins convert chemical energy into mechanical work. Here we present a mathematical model for the chemistry and three dimensional mechanics of the Kinesin motor protein which captures many of the force dependent features of the motor. For the elasticity of the tether tha…
We study the avalanche dynamics of a pile of micrometer-sized silica grains in water-filled microfluidic drums. Contrary to what is expected for classical granular materials, avalanches do not stop at a finite angle of repose. After a first rapid phase during which the angle of the pile relaxes to an angle $θ\_c$, a creep regime is observed where the pile slowly flows until the free surface reaches the horizontal. This relaxation is logarithmic in time and strongly depends on the ratio between the weight of the grains and the thermal agitation (gravitational Péclet number). We propose a simple…
We study the avalanche dynamics of a pile of micron-sized silica grains in miniaturized rotating drums filled with water. Contrary to what is expected for classical granular materials, the avalanches do not stop at a finite angle of repose. Below an angle $θ$\_c, we observe a creep regime where the piles slowly flow until they become flat. In this regime, the relaxation is logarithmic in time and is slower when the ratio between the weight of the grains and the thermal agitation is increased. We propose a simple 1D model based on Kramer's escape rate to describe this flow.
Efficient navigation and precise localization of Brownian micro/nano self-propelled motor particles within complex landscapes could enable future high-tech applications involving for example drug delivery, precision surgery, oil recovery, and environmental remediation. Here we employ a model-free deep reinforcement learning algorithm based on bio-inspired neural networks to enable different types of micro/nano motors to be continuously controlled to carry out complex navigation and localization tasks. Micro/nano motors with either tunable self-propelling speeds or orientations or both, are fou…
A 1 cm coin vibrational motor fixed to the center of a 4 cm square foam platform moves rapidly across granular media (poppy seeds, millet, corn meal) at a speed of up to 30 cm/s, or about 5 body lengths/s. Fast speeds are achieved with dimensionless acceleration number, similar to a Froude number, up to 50, allowing the light-weight 1.4 g mechanism to remain above the substrate, levitated and propelled by its kicks off the surface. The mechanism is low cost and moves without any external moving parts. With 2 s exposures we photograph the trajectory of the mechanism using an LED blocked except …
The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical non-equilibrium conditions. Here we propose a new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts. Numerical simulations and analytical calculations demonstrate a net drift induced by friction. If the thermal bath is replaced by a granular gas, the well known granular ratchet effect also intervenes, becoming dominant at high collision rates. For our chosen wheel s…
The directed transport of an overdamped Brownian motor moving in a spatially periodic potential that lacks reflection symmetry (i.e. a ratchet potential) is studied when driven by thermal and dichotomic nonequilibrium noise in the presence of an external, constant load force. We consider both, the classical and the quantum tunneling assisted regimes. The current-load characteristics are investigated as a function of the system parameters like the load force, the temperature and the amplitude strength of the applied two-state noise.
We use large scale computer simulations and finite size scaling analysis to study the shear rheology of dense three-dimensional suspensions of frictionless non-Brownian particles in the vicinity of the jamming transition. We perform simulations of soft repulsive particles at constant shear rate, constant pressure, and finite system size, and study carefully the asymptotic limits of large system sizes and infinitely hard particle repulsion. Extending earlier analysis by about two orders of magnitude, we first study the asymptotic behavior of the shear viscosity in the hard particle limit. We co…
We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e. a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force which takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum and finally it mono…
A novel equality relating the rate of energy dissipation to a degree of violation of the fluctuation-response relation (FRR) in nonequilibrium Langevin systems is described. The FRR is a relation between the correlation function of the fluctuations and the response function of macroscopic variables. Although it has been established that the FRR holds in equilibrium, physical significance of violation of the FRR in nonequilibrium systems has been under debate. Recently, the authors have found that an extent of the FRR violation is related in a simple equality to the rate of energy dissipation i…
We study the Brownian motion of ellipsoidal particles lying on an agitated granular bath composed of magnetic particles. We quantify the mobility of different floating ellipsoidal particles using the mean square displacement and the mean square angular displacement, and relate the diffusion coefficients to the bath particle motion. In terms of the particle major radius $R$, we find the translational diffusion coefficient scales roughly as $1/R^2$ and the rotational diffusion coefficient scales as roughly $1/R^4$; this is consistent with the assumption that diffusion arises from random kicks of…
Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for aerial granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we introduce a theoretical framework that proposes a tentative, but potentially complete scaling description of stationary flows. Our analysis, which focuses on frictionless particles, applies {\it both} to suspensions and inertial flows of hard particles. We compare our prediction…
We study a general model of granular Brownian ratchet consisting of an asymmetric object moving on a line and surrounded by a two-dimensional granular gas, which in turn is coupled to an external random driving force. We discuss the two resulting Boltzmann equations describing the gas and the object in the dilute limit and obtain a closed system for the first few moments of the system velocity distributions. Predictions for the net ratchet drift, the variance of its velocity fluctuations and the transition rates in the Markovian limit, are compared to numerical simulations and a fair agreement…
The rheology of dense Brownian suspensions of hard spheres is investigated numerically beyond the low shear rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time-scale, both rela…
In a single molecule assay, the motion of a molecular motor is often inferred from measuring the stochastic trajectory of a large probe particle attached to it. We discuss a simple model for this generic set-up taking into account explicitly the elastic coupling between probe and motor. The combined dynamics consists of discrete steps of the motor and continuous Brownian motion of the probe. Motivated by recent experiments on the F1-ATPase, we investigate three types of efficiencies both in simulations and a Gaussian approximation. Overall, we obtain good quantitative agreement with the experi…
A massive intruder in a homogeneously driven granular fluid, in dilute configurations, performs a memory-less Brownian motion with drag and temperature simply related to the average density and temperature of the fluid. At volume fraction $\sim 10-50%$ the intruder's velocity correlates with the local fluid velocity field: such situation is approximately described by a system of coupled linear Langevin equations equivalent to a generalized Brownian motion with memory. Here one may verify the breakdown of the Fluctuation-Dissipation relation and the presence of a net entropy flux - from the flu…
We present a theoretical treatment of energy transfer in a molecular motor described in terms of overdamped Brownian motion on a multidimensional tilted periodic potential. The tilt acts as a thermodynamic force driving the system out of equilibrium and, for non-separable potentials, energy transfer occurs between degrees of freedom. For deep potential wells, the continuous theory transforms to a discrete master equation that is tractable analytically. We use this master equation to derive formal expressions for the hopping rates, drift, diffusion, efficiency and rate of energy transfer in ter…
We study the injection of air in a granular suspension. We use a linear Hele-Saw cell filled with a suspension which is displaced by air, leading to a Saffman-Taylor (fingering) instability. For the suspension, we use an iso-dense mixture where the fluid and the particles have the same density. The volume fraction of particles can thus be adjusted over a wide range. We discuss the question of an effective rheology inside the cell as well as the pattern formation as a function of the granular compacity. We finally report results on the finger width for stable fingers and the thresholds for thei…
Eukaryotic flagella are active structures with a complex architecture of microtubules, motor proteins and elastic links. They are capable of whiplike motions driven by motors sliding along filaments that are themselves constrained at an end. Here, we show that active, self-propelled particles that are connected together to form a single chain that is anchored at one end can produce the graceful beating motions of flagella. We use a combination of numerical simulations, scaling analysis and mean field continuum elastic theory to demarcate the phase diagram for this type of oscillatory motion as…
We show that the correlated stochastic fluctuation of the friction coefficient can give rise to long-range directional motion of a particle undergoing Brownian random walk in a constant periodic energy potential landscape. The occurrence of this motion requires the presence of two additional independent bodies interacting with the particle via friction and via the energy potential, respectively, which can move relative to each other. Such three-body system generalizes the classical Brownian ratchet mechanism, which requires only two interacting bodies. In particular, we describe a simple two-l…
We experimentally investigate the fluidization of a granular material subject to mechanical vibrations by monitoring the angular velocity of a vane suspended in the medium and driven by an external motor. On increasing the frequency we observe a re-entrant transition, as a jammed system first enters a fluidized state, where the vane rotates with high constant velocity, and then returns to a frictional state, where the vane velocity is much lower. While the fluidization frequency is material independent, the viscosity recovery frequency shows a clear dependence on the material, that we rational…
We analyze the performance of a Brownian ratchet in the presence of geometrical constraints. A two-state model that describes the kinetics of molecular motors is used to characterize the energetic cost when the motor proceeds under confinement, in the presence of an external force. We show that the presence of geometrical constraints has a strong effect on the performance of the motor. In particular, we show that it is possible to enhance the ratchet performance by a proper tuning of the parameters characterizing the environment. These results open the possibility of engineering entropically-o…
Brownian rotors play an important role in biological systems and in future nano-technological applications. However the mechanisms determining their dynamics, efficiency and performance remain to be characterized. Here the F0 portion of the F-ATP synthase is considered as a paradigm of a Brownian rotor. In a generic analytical model we analyze the stochastic rotation of F0-like motors as a function of the driving free energy difference and of the free energy profile the rotor is subjected to. The latter is composed of the rotor interaction with its surroundings, of the free energy of chemical …
We examine the spreading of a suspension of non-Brownian spheres suspended in a Newtonian liquid on a solid substrate. We show that the spreading dynamics is well described by the classical Cox-Voinov law provided the value of the fluid viscosity that arises in the capillary number of the problem is adjusted to a value that depends on particle size and volume fraction in a non-trivial way. We demonstrate that this behavior is a signature of the ability of the particles to approach the contact line close enough to affect dissipation.
