The effect of an external force on the kinetics of diffusion-assisted escaping of Brownian particles from a potential well is analyzed in detail. The analysis is made within the two-state model of the process which is known to be valid in the deep well limit in the absence of external force. The generalized variant of this model, taking into account the effect of the force, is shown to be quite accurate as well for some shapes of the well. Within the generalized two-state model simple expressions for the well depopulation kinetics and, in particular, the for the escape rate are obtained. These expressions show that the effect of the force ($F$) manifests itself in the escape rate dependence on the only parameter $φ= Fa/(2k_b T)$, where $a$ is the Onzager radius of the attractive part of the well $U(r)$, defined by the relation $|U(a)| = k_b T$. The limiting behavior of this dependence in the cases of weak and strong force is analyzed in detail. Possible applications as well as the relation of the results of the analysis to those obtained earlier are briefly discussed.
We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a nonmonotonic dependence on the noise intensity. We relate this behavior to the fact that the active particle escapes from a limit cycle rather than from a fixed point and that a certain amount of noise can stabilize the sojourn of the particle on this limit cycle.
Thermally activated escape of a Brownian particle over a potential barrier is well understood within Kramers theory. When subjected to an external magnetic field, the Lorentz force slows down the escape dynamics via a rescaling of the diffusion coefficient without affecting the exponential dependence on the barrier height. Here, we study the escape dynamics of a charged Brownian particle from a two-dimensional truncated harmonic potential under the influence of Lorentz force due to an external magnetic field. The particle is driven anisotropically by subjecting it to noises with different stre…
Brownian escape is key to a wealth of physico-chemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynami…
The probability per unit time for a thermally activated Brownian particle to escape over a potential well is in general well-described by Kramers theory. Kramers showed that the escape time decreases exponentially with increasing barrier height. The dynamics slow down when the particle is charged and subjected to a Lorentz force due to an external magnetic field. This is evident via a rescaling of the diffusion coefficient entering as a prefactor in the Kramers escape rate without any impact on the barrier-height-dependent exponent. Here we show that the barrier height can be effectively chang…
Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape rate of the particle. In this paper we study the escape problem for a Brownian particle that is transiently active; the activity decreases rapidly during the escape process. Using the effective equilibrium approach we analytically calculate the escape rate, under the assumption that the particle is either completely passive or fully active when crossing the b…
A system reservoir model, where the associated reservoir is modulated by an external colored random force, is proposed to study the transport of an overdamped Brownian particle in a periodic potential. We then derive the analytical expression for the average velocity, mobility, and diffusion rate. The bistable kinetics and escape rate from a metastable state in the overdamped region are studied consequently. By numerical simulation we then demonstrate that our analytical escape rate is in good agreement with that of numerical result.
The escape rate of a Brownian particle over a potential barrier is accurately described by the Kramers theory. A quantitative theory explicitly taking the activity of Brownian particles into account has been lacking due to the inherently out-of-equilibrium nature of these particles. Using an effective equilibrium approach [Farage et al., Phys. Rev. E 91, 042310 (2015)] we study the escape rate of active particles over a potential barrier and compare our analytical results with data from direct numerical simulation of the colored noise Langevin equation. The effective equilibrium approach gener…
Cells have evolved efficient strategies to probe their surroundings and navigate through complex environments. From metastatic spread in the body to swimming cells in porous materials, escape through narrow constrictions - a key component of any structured environment connecting isolated micro-domains - is one ubiquitous and crucial aspect of cell exploration. Here, using the model microalgae Chlamydomonas reinhardtii, we combine experiments and simulations to achieve a tractable realization of the classical Brownian narrow escape problem in the context of active confined matter. Our results d…
The kinetics of two (2D) and three (3D) dimensional diffusion-assisted escaping of Brownian particles from a potential well in the presence of an external force is analyzed in detail. The kinetics is studied within the two-state model (TSM) proposed for processes in the absence of external force. The generalized variant of this model, taking into account the force effect, is proposed which is shown to be quite accurate for some shapes of the well both for 2D and 3D processes. Within the generalized TSM simple expressions for the well depopulation kinetics and, in particular, for the escape rat…
We study the noise-driven escape of active Brownian particles (ABPs) and run-and-tumble particles (RTPs) from confining potentials. In the small noise limit, we provide an exact expression for the escape rate in term of a variational problem in any dimension. For RTPs in one dimension, we obtain an explicit solution, including the first sub-leading correction. In two dimensions we solve the escape from a quadratic well for both RTPs and ABPs. In contrast to the equilibrium problem we find that the escape rate depends explicitly on the full shape of the potential barrier, and not only on its he…
Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time averaged mean squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular we study the degree of weak ergodicity breaking and scatter between different single trajecto…
The dynamics of active particles is of interest at many levels and is the focus of theoretical and experimental research. There have been many attempts to describe the dynamics of particles affected by random active forces in terms of an effective temperature. This kind of description is tempting due to the similarities (or lack thereof) with systems in or near thermal equilibrium. However, the generality and validity of the effective temperature is not yet fully understood. Here, we studied the dynamics of trapped particles subjected to both thermal and active forces. The particles were not o…
We investigate the escape rate of an overdamped, self-propelled spherical Brownian particle on a surface from a metastable potential well. Within a modeling in terms of a 1D constant speed of the particle's active dynamics we consider the associated rate using both numerical and analytical approaches. Regarding the properties of the stationary state in the potential well, two major timescales exist, each governing the translational and the rotational dynamics of the particle, respectively. The particle radius is identified to present the essential quantity in charge of regulating the ratio bet…
The paper addresses Brownian motion in the logarithmic potential with time-dependent strength, $U(x,t) = g(t) \log(x)$, subject to the absorbing boundary at the origin of coordinates. Such model can represent kinetics of diffusion-controlled reactions of charged molecules or escape of Brownian particles over a time-dependent entropic barrier at the end of a biological pore. We present a simple asymptotic theory which yields the long-time behavior of both the survival probability (first-passage properties) and the moments of the particle position (dynamics). The asymptotic survival probability,…
The motion of a Brownian particle in the presence of Coulomb friction and an asymmetric spatial potential was evaluated in this study. The system exhibits a ratchet effect, i.e., an average directed motion even in the absence of an external force, induced by the coupling of non-equilibrium conditions with the spatial asymmetry. Both the average motion and the fluctuations of the Brownian particle were analysed. The stationary velocity shows a non-monotonic behaviour as a function of both the temperature and the viscosity of the bath. The diffusion properties of the particle, which show several…
A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian particle on a one-dimensional half-line. The motion of a Brownian particle is decomposed into a component that is affected by hard-body interactions and into components that are unaffected. The hard-body interactions are incorporated by replacing the affected component of motion by the evolution on a half-line. It is discussed under which circumstances this a…
The escape process from the native valley for proteins subjected to a constant stretching force is examined using a model for a Beta-barrel. For a wide range of forces, the unfolding dynamics can be treated as one-dimensional diffusion, parametrized in terms of the end-to-end distance. In particular, the escape times can be evaluated as first passage times for a Brownian particle moving on the protein free-energy landscape, using the Smoluchowski equation. At strong forces, the unfolding process can be viewed as a diffusive drift away from the native state, while at weak forces thermal activat…
We study the dynamics of a Brownian circle swimmer with a time-dependent self-propulsion velocity in an external temporally varying harmonic potential. For several situations, the noise-free swimming paths, the noise-averaged mean trajectories, and the mean square displacements are calculated analytically or by computer simulation. Based on our results, we discuss optimal swimming strategies in order to explore a maximum spatial range around the trap center. In particular, we find a resonance situation for the maximum escape distance as a function of the various frequencies in the system. More…
We study escape dynamics of a double-stranded DNA (dsDNA) through an idealized double nanopore (DNP) geometry subject to two equal and opposite forces (tug-of-war) using Brownian dynamics (BD) simulation. In addition to the geometrical restrictions imposed on the cocaptured dsDNA segment in between the pores, the presence of tug-of-war forces at each pore results in a variation of the local chain stiffness for the segment of the chain in between the pores which increases the overall stiffness of the chain. We use BD simulation results to understand how the intrinsic chain stiffness and the TOW…
A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs es…
It is often desirable to know the controlling mechanism of survival probability of nano - or microscale particles in small cavities such as, e.g., confined submicron particles in fiber beds of high-efficiency filter media or ions/small molecules in confined cellular structures. Here we address this issue based on numerical study of the escape kinetics of inertial Brownian colloidal particles from various types of cavities with single and multiple pores. We consider both the situations of strong and weak viscous damping. Our simulation results show that as long as the thermal length is larger t…
Recently, it has been discovered that systems of Active Brownian particles (APB) at high density organise their velocities into coherent domains showing large spatial structures in the velocity field. Such a collective behavior occurs spontaneously, i.e. is not caused by any specific interparticle force favoring the alignment of the velocities. This phenomenon was investigated in the absence of thermal noise and in the overdamped regime where inertial forces could be neglected. In this work, we demonstrate through numerical simulations and theoretical analysis that the velocity alignment is a …
Using dynamical density functional theory (DDFT), we theoretically study Brownian self-diffusion and structural relaxation of hard disks and compare to experimental results on quasi two-dimensional colloidal hard spheres. To this end, we calculate the self and distinct van Hove correlation functions by extending a recently proposed DDFT-approach for three-dimensional systems to two dimensions. We find that the theoretical results for both self- and distinct part of the van Hove function are in very good quantitative agreement with the experiments up to relatively high fluid packing fractions o…
