Brownian Motor Research Articles

Noise-induced transport in a periodic square-well potential

We investigate a thermal ratchet based on a Brownian particle in a spatially periodic square-well potential driven by a time-dependent square-wave signal. In this model, we rock the Brownian particle between two square-well potentials tilted in opposite directions to induce a net current. Employing the Stratonovich formula and an independent approach using suitable boundary conditions and a normalization condition, we obtain an exact expression for the current in the adiabatic limit, and we observe that there are optimal values of various parameters at which the current can be maximized. In several parameter regimes, our simple non-linear model displays a behavior distinct from some other models of a rocked ratchet. For example, a reversal in the current direction is observed as the square-wave signal’s amplitude or the thermal bath’s temperature is varied. However, under similar conditions, no such current reversal was seen in the case of a periodically rocked Brownian motor in a sawtooth or a smooth potential. Furthermore, unlike the latter type of rocked Brownian motors, the square-well model yields zero current in the deterministic limit, as thermal energy is indispensable for the functioning of the motor.

In Ukrainian

Brownian motors belong to the class of nanoscale devices that use the thermal noise of the environment as one of the necessary components in the mechanism of their operation. Today, there are a lot of practical implementations of such nanomachines, both inorganic, fairly simple mechanisms produced artificially, and more complex ones created from separate biological components available at the cellular level. One of the options for implementing the mechanism of straightening the chaotic thermal noise of the environment into unidirectional motion is the presence of a motor particle in the field of action of an asymmetric periodic stationary potential, which undergoes certain small disturbances (fluctuations) periodically over time. To describe such asymmetric one-dimensional structures (for example, dipole chains or fibers of the cytoskeleton) in the theory of Brownian motors, two model potentials are most often used: piecewise linear sawtooth and double sinusoidal. In this work, within the framework of the approximation of small fluctuations, a model of a pulsating Brownian motor with a stationary double sinusoidal potential and a disturbing small harmonic signal is considered. A new method of parametrization of such a problem is proposed, which allows to separate the contributions from various factors affecting the operation of the ratchet, and the numerical procedure for calculating the average speed of the directional movement of nanoparticles for the selected type of model potentials is specified. A number of numerical dependences of the average speed on the main parameters of the system were obtained. Peculiarities of the behavior of the motor as dependent on the parameter responsible for asymmetry and the number of potential wells on the spatial period of the stationary potential have been investigated. It is shown that the direction of the generated flux of nanoparticles depends not only on the phase shift between the stationary and fluctuating components of the potential, but also on the temperature of the system and the frequency of fluctuations, i.e., a possibility of temperature-frequency control of the direction of movement in the considered model has been found. Diagrams have been constructed that allow you to choose the ratio between the parameters of the nanomotor to create a flux of particles in the desired direction.

Quantum particle in a V-shaped well of arbitrary asymmetry. Brownian motors

Quantum particle in a V-shaped well of arbitrary asymmetry. Brownian motors

Quantum particle in a V-shaped well of arbitrary asymmetry. Brownian motors

Quantum particle in a V-shaped well of arbitrary asymmetry. Brownian motors

Microscopic model for a Brownian translator

A microscopic model for a translational Brownian motor, dubbed a Brownian translator, is introduced. It is inspired by the Brownian gyrator described by Filliger and Reimann (2007 Phys. Rev. Lett. 99 230602). The Brownian translator consists of a spatially asymmetric object moving freely along a line due to perpetual collisions with a surrounding ideal gas. When this gas has an anisotropic temperature, both spatial and temporal symmetries are broken and the object acquires a nonzero drift. Onsager reciprocity implies the opposite phenomenon, that is dragging a spatially asymmetric object into an (initially at) equilibrium gas induces an energy flow that results in anisotropic gas temperatures. Expressions for the dynamical and energetic properties are derived as a series expansion in the mass ratio (of gas particle vs. object). These results are in excellent agreement with molecular dynamics simulations.

From Brownian to Deterministic Motor Movement in a DNA-Based Molecular Rotor.

Molecular devices that have an anisotropic periodic potential landscape can be operated as Brownian motors. When the potential landscape is cyclically switched with an external force, such devices can harness random Brownian fluctuations to generate a directed motion. Recently, directed Brownian motor-like rotatory movement was demonstrated with an electrically switched DNA origami rotor with designed ratchet-like obstacles. Here, we demonstrate that the intrinsic anisotropy of DNA origami rotors is also sufficient to result in motor movement. We show that for low amplitudes of an external switching field, such devices operate as Brownian motors, while at higher amplitudes, they behave deterministically as overdamped electrical motors. We characterize the amplitude and frequency dependence of the movements, showing that after an initial steep rise, the angular speed peaks and drops for excessive driving amplitudes and frequencies. The rotor movement can be well described by a simple stochastic model of the system.

Maximum power and the corresponding efficiency for a Carnot-like thermoelectric cycle based on fluctuation theorem.

Here, we investigate the maximum power and efficiency of thermoelectric generators through devising a set of protocols for the isothermal and adiabatic processes of thermoelectricity to build a Carnot-like thermoelectric cycle, with the analysis based on fluctuation theorem. The Carnot efficiency can be readily obtained for the quasistatic thermoelectric cycle with vanishing power. The maximum power-efficiency pair of the finite-time thermoelectric cycle is derived, which is found to have the identical form to that of Brownian motors characterized by the stochastic thermodynamics. However, it is of significant discrepancy compared to the linear-irreversible and endoreversible-thermodynamics based formulations. The distinction with the linear-irreversible-thermodynamics case could result from the difference in the definitions of Peltier and Seebeck coefficients in the thermoelectric cycle. As for the endoreversible thermodynamics, we argue the applicability of endoreversibility could be questionable for analyzing the Carnot-like thermoelectric cycle, due to the incompatibility of the endoreversible hypothesis that attributes the irreversibility to finite heat transfer with thermal reservoirs, though the distinction in the mathematical expressions can vanish with the assumption that the ratio of thermoelectric power factors at the high and low temperatures (γ) is equal to the square root of the temperature ratio, γ=sqrt[T_{L}/T_{H}] (this condition could significantly deviate from the practical case). Last, utilizing our models as a concise tool to evaluate the maximum power-efficiency pairs of realistic thermoelectric material, we present a case study on the n-type silicon.

Brownian motors powered by nonreciprocal interactions.

Traditional models for molecular (Brownian) motors predominantly depend on nonequilibrium driving, while particle interactions rigorously adhere to Newton's third law. However, numerous living and natural systems at various scales seem to defy this well-established law. In this study, we investigated the transport of mixed Brownian particles in a two-dimensional ratchet potential with nonreciprocal interactions. Our findings reveal that these nonreciprocal interactions can introduce a zero-mean nonequilibrium driving force. This force is capable of disrupting the thermodynamic equilibrium and inducing directed motion. The direction of this motion is determined by the asymmetry of the potential. Interestingly, the average velocity is a peaked function of the degree of nonreciprocity, while the effective diffusion consistently increases with the increase of nonreciprocity. There exists an optimal temperature or packing fraction at which the average velocity reaches its maximum value. We share a mechanism for particle rectification, devoid of particle-autonomous nonequilibrium drive, with potential usage in systems characterized by nonreciprocal interactions.

Nanoscale feedback control of six degrees of freedom of a near-sphere

Manipulating the rotational as well as the translational degrees of freedom of rigid bodies has been a crucial ingredient in diverse areas, from optically controlled micro-robots, navigation, and precision measurements at macroscale to artificial and biological Brownian motors at nanoscale. Here, we demonstrate feedback cooling of all the angular motions of a near-spherical neutral nanoparticle with all the translational motions feedback-cooled to near the ground state. The occupation numbers of the three translational motions are 6 ± 1, 6 ± 1, and 0.69 ± 0.18. A tight, anisotropic optical confinement allows us to clearly observe three angular oscillations and to identify the ratio of two radii to the longest radius with a precision of 0.08 %. We develop a thermometry for three angular oscillations and realize feedback cooling of them to temperatures of lower than 0.03 K by electrically controlling the electric dipole moment of the nanoparticle.

Symmetric Brownian motor subjected to Lévy noise

In the past few years, attention has mainly been focused on the symmetric Brownian motor (BM) with Gaussian noises, whose current and energy conversion efficiency are very low. Here, we investigate the operating performance of the symmetric BM subjected to Lévy noise. Through numerical simulations, it is found that the operating performance of the motor can be greatly improved in asymmetric Lévy noise. Without any load, the Lévy noises with smaller stable indexes can let the motor give rise to a much greater current. With a load, the energy conversion efficiency of the motor can be enhanced by adjusting the stable indexes of the Lévy noises with symmetry breaking. The results of this research are of great significance for opening up BM’s intrinsic physical mechanism and promoting the development of nanotechnology.

Brownian motor inspired monodirectional continuous spinning triboelectric nanogenerators for extracting energy from irregular gentle water waves

A TENG intrinsically adaptive to chaotic agitations like the Brownian motors is designed based on dual symmetry breakings.

A dynamical model for Brownian molecular motors driven by inelastic electron tunneling

In recent years, several artificial molecular motors driven and controlled by electric currents have been proposed. Similar to Brownian machines, these systems work by turning random inelastic tunneling events into a directional rotation of the molecule. Despite their importance as the ultimate component of future molecular machines, their modeling has not been sufficiently studied. Here, we develop a dynamical model to describe these systems. We illustrate the validity and usefulness of our model by applying it to a well-known molecular motor, showing that the obtained results are consistent with the available experimental data. Moreover, we demonstrate how to use our model to extract some difficult-to-access microscopic parameters. Finally, we include an analysis of the expected effects of current-induced forces (CIFs). Our analysis suggests that, although nonconservative contributions of the CIFs can be important in some scenarios, they do not seem important in the analyzed case. Despite this, the conservative contributions of CIFs could be strong enough to significantly alter the system's dynamics.

In Ukrainian

The ratchet effect is a directed nanoparticle flux phenomenon induced by nonequilibrium fluctuations in a system with spatial and (or) temporal asymmetry. One is used as the way to create a controlled nanotransport and is the basis of the theory of Brownian motors. Fluctuation motion simulation is a promising way to calculate the main characteristics of Brownian motors, it avoids complex calculations and quickly obtains predictions about the appearance or absence of generated directional motion in a specific model. Nonequilibrium fluctuations are usually introduced into the system by a dichotomous process that switches two periodic asymmetric potential profiles at certain fixed intervals (deterministic process), or randomly with average potential lifetimes (stochastic process). We investigate the modeling of the process of the ratchet effect in the framework of the Brownian motor jump-like model by the method of Parrondo’s paradoxical game for the stochastic dichotomous process and compare results with a similar deterministic process. A calculus method for the main characteristics obtaining of the motor with stochastic dichotomous process is proposed, it is shown correspondence to the analytical description of this model in extreme cases. It is shown that the stochasticity of the process directly affects the characteristics of the ratchet effect: the trajectories of the average displacements of nanoparticles fundamentally differs in the deterministic description, and a gradual difference in these processes is observed at low values. The study of asymmetric dichotomous processes for different temperature modes of motor operation is carried out. The model allows one to analyze the peculiarities of the directional motion starting at the level of single jumps, as well as to formulate recommendations for possible improvement of motor efficiency for different temperatures. For high-temperature mode, it is advisable to reduce the lifetime of the state with the active potential, and for low-temperature mode, arbitrary, it should be increased.

Controllable transport and size segregation of tiny particles harnessing noise in 2D Brownian motor system

Controllable transport and size segregation of tiny particles following the Brownian motor mechanism are investigated with pseudo-particle modeling (PPM), a simplified molecular simulation approach, in which the liquid surrounding the Brownian particle is discretized into many pseudo particles and naturally introduces thermal noise by hard-sphere interaction between the pseudo particles. An asymmetric periodic potential is applied to the Brownian particles acting as a flashing ratchet model. The macroscopic directional motion of a single Brownian particle in external non-equilibrium fluctuation is reproduced well by the method. Illustratively, the PPM method is successfully employed to conduct the simulations of Brownian motor and testify the adaptability of the method. The segregation of different-sized particles is also studied by varying the size ratio and operation conditions, such as temperature. The simulations will help a quantitative design of Brownian motors and their application in particle transport, separation, and segregation.

Placement of Biological Membrane Patches in a Nanofluidic Gap With Control Over Position and Orientation

AbstractPurple membranes from the archaeon Halobacterium salinarum consist of 2D crystals of the light‐driven proton pump bacteriorhodopsin, which convert photons into a proton gradient across the cell membrane. This functional feature and the structural rigidity make them appealing candidates for integration into biomimetic devices. To this end, and in order to carry out their function, purple membranes must be positioned in the correct orientation at the position of interest. Precise placement and control over the orientation of nanoscale objects still constitutes a formidable challenge. Here, it is shown that isolated purple membrane patches can be transported and positioned at predefined locations in nanofluidic confinement, with control over their orientation at the target sites. The transport is achieved through a rocking Brownian motor scheme, while the controlled deposition of the membranes is realized by engineering the surface potential of a fluid‐filled nanofluidic slit. This controlled manipulation of purple membrane patches outlines a new pathway toward the integration of biological or other delicate supramolecular structures into top–down‐fabricated patterns, for the assembly of nanoscale hybrid devices that serve as a light‐driven source of (chemical) energy.

Exact time-dependent analytical solutions for entropy production rate in a system operating in a heat bath in which temperature varies linearly in space.

The nonequilibrium thermodynamics feature of a Brownian motor is investigated by obtaining exact time-dependent solutions. This in turn enables us to investigate not only the long time property (steady state) but also the short time the behavior of the system. The general expressions for the free energy, entropy production e[over ̇]_{p}(t) as well as entropy extraction h[over ̇]_{d}(t) rates are derived for a system that is genuinely driven out of equilibrium by time-independent force as well as by spatially varying thermal background. We show that for a system that operates between hot and cold reservoirs, most of the thermodynamics quantities approach a nonequilibrium steady state in the long time limit. The change in free energy becomes minimal at a steady state. However, for a system that operates in a heat bath where its temperature varies linearly in space, the entropy production and extraction rates approach a nonequilibrium steady state while the change in free energy varies linearly in space. This reveals that unlike systems at equilibrium, when systems are driven out of equilibrium, their free energy may not be minimized. The thermodynamic properties of a system that operates between the hot and cold baths are further compared and contrasted with a system that operates in a heat bath where its temperature varies linearly in space along with the reaction coordinate. We show that the entropy, entropy production, and extraction rates are considerably larger for the linearly varying temperature case than a system that operates between the hot and cold baths revealing such systems are inherently irreversible. For both cases, in the presence of load or when a distinct temperature difference is retained, the entropy S(t) monotonously increases with time and saturates to a constant value as t further steps up. The entropy production rate e[over ̇]_{p} decreases in time and at steady state, e[over ̇]_{p}=h[over ̇]_{d}>0, which agrees with the results shown in M. Asfaw's [Phys. Rev. E 89, 012143 (2014)1539-375510.1103/PhysRevE.89.012143; Phys. Rev. E 92, 032126 (2015)10.1103/PhysRevE.92.032126]. Moreover, the velocity, as well as the efficiency of the system that operates between the hot and cold baths, are also collated and contrasted with a system that operates in a heat bath where its temperature varies linearly in space along with the reaction coordinate. A system that operates between the hot and cold baths has significantly lower velocity but a higher efficiency in comparison with a linearly varying temperature case.

Modeling the Jump-like Diffusion Motion of a Brownian Motor by a Game- Theory Approach: Deterministic and Stochastic Models

Methods of paradoxical games are used to construct a stochastic hopping model of Brownian ratchets which extends the well-known analogous deterministic model. The dependencies of the average displacements of a Brownian particle in a stochastic ratchet system on a discrete time parameter are calculated, as well as the dependencies of the average ratchet velocity on the average lifetimes of the states of the governing dichotomous process. The results obtained are compared with both the results of modeling a similar deterministic model and the results of a known analytic description. While for the hopping analogue of the deterministic on-off ratchet, the time dependence of the displacement contains periodically repeated hopping changes when the potential is switched on and plateau of the diffusion stage of the motion when it is switched off, the stochastic dependencies, that are of an averaged character, are monotonous and do not contain jumps. It is shown that, with other things being equal, the difference in the results for the hopping ratchet model driven by the stochastic and deterministic dichotomous process of switching the potential profiles (game selection) is more pronounced at short lifetimes of the dichotomous states and vanishes with their increase.

Exact Time-Dependent Solutions and Information Geometry of a Rocking Ratchet

The noise-induced transport due to spatial symmetry-breaking is a key mechanism for the generation of a uni-directional motion by a Brownian motor. By utilising an asymmetric sawtooth periodic potential and three different types of periodic forcing G(t) (sinusoidal, square and sawtooth waves) with period T and amplitude A, we investigate the performance (energetics, mean current, Stokes efficiency) of a rocking ratchet in light of thermodynamic quantities (entropy production) and the path-dependent information geometric measures. For each G(t), we calculate exact time-dependent probability density functions under different conditions by varying T, A and the strength of the stochastic noise D in an unprecedentedly wide range. Overall similar behaviours are found for different cases of G(t). In particular, in all cases, the current, Stokes efficiency and the information rate normalised by A and D exhibit one or multiple local maxima and minima as A increases. However, the dependence of the current and Stokes efficiency on A can be quite different, while the behaviour of the information rate normalised by A and D tends to resemble that of the Stokes efficiency. In comparison, the irreversibility measured by a normalised entropy production is independent of A. The results indicate the utility of the information geometry as a proxy of a motor efficiency.

Effect of Binding-Affinity and ATPase Activity on the Velocities of Kinesins Using Ratchet Models.

We use two-state ratchet models containing single and coupled Brownian motors to understand the role of motor-microtubule binding, ATPase reaction rate and dimerisation on the translational velocities of Kinesin motors. We use model parameters derived from the experimental measurements on KIF1A, KIF13A, KIF13B, and KIF16B motors to compute velocities in μm/s. We observe that both the models show the same trend in velocities (KIF1A > KIF13A > KIF13B > KIF16B) as the experimental results. However, the models significantly underpredict the velocities when compared with the experiments. The predictions of the coupled-motor model are closer to the experiments than those of the single-motor model. Our results indicate that the variation of ATPase reaction rate governs the trend in velocities for the above four motors. The variation of motor-microtubule binding affinity and the coupling strength between the motor domains may only have a secondary effect. More rigorous models that incorporate the power-stroke mechanism are necessary for better quantitative compliance with the experiments.

A generalized irreversible thermal Brownian motor cycle and its optimal performance

A generalized irreversible thermal Brownian motor cycle and its optimal performance