Resonant activation over a fluctuating barrier

Polymer translocation: effects of periodically driven confinement

We study the influence of confinement on the dynamics of translocation of a linear polymer chain in a good solvent through a cone-shaped pore. Using the Langevin dynamics simulations, we calculate both the first attempt time and translocation time as a function of the position of the back wall and apex angle α. As the in vivo confining environment is inherently dynamic, we extended the present study to explore the consequences of a periodically driven back wall and apex angles on the translocation dynamics. Our findings reveal that the translocation time initially decreases as the driving frequency increases, but increases after a certain frequency. The frequency at which the translocation time is found to be minimum is referred to as the resonance activation. Analyzing the distribution of translocation times around this frequency renders interesting information about the translocation process. We further explore the translocation dynamics by calculating the residence time of individual monomers, shedding light on the microscopic aspects of the process.

Polymer translocation driven by longitudinal and transversal time-dependent end-pulling forces

In this article, we simulate the translocation of a semiflexible homopolymer through an extended pore, driven by both a constant and a time-dependent end-pulled force, employing a model introduced in previous studies. The time dependence is simplistically modeled as a cosine function, and we distinguish between two scenarios for the driving--longitudinal force and transversal force-depending on the relative orientation of the force, parallel or perpendicular, respectively, with respect to the pore axis. Besides some key differences between the two drivings, the mean translocation times present a large minimum region as a function of the frequency of the force that is typical of the resonant activation effect. The presence of the minimum is independent on the elastic characteristics of the polymeric chains and reveals a linear relation between the optimum mean translocation time and the corresponding period of the driving. The mean translocation times show different scaling exponents with the polymer length for different flexibilities. Lastly, we derive an analytical expression of the mean translocation time for low driving frequency, which clearly agrees with the simulations.

Run-and-tumble motion in a linear ratchet potential: Analytic solution, power extraction, and first-passage properties

We explore the properties of run-and-tumble particles moving in a piecewise-linear "ratchet" potential by deriving analytic results for the system's steady-state probability density, current, entropy production rate, extractable power, and thermodynamic efficiency. The ratchet's broken spatial symmetry rectifies the particles' self-propelled motion, resulting in a positive current that peaks at finite values of the diffusion strength, ratchet height, and particle self-propulsion speed. Similar nonmonotonic behavior is also observed for the extractable power and efficiency. We find the optimal apex position for generating maximum current varies with diffusion and that entropy production can have nonmonotonic dependence on diffusion. In particular, for vanishing diffusion, entropy production remains finite when particle self-propulsion is weaker than the ratchet force. Furthermore, power extraction with near-perfect efficiency is achievable in certain parameter regimes due to the simplifications afforded by modeling "dry" active particles. In the final part, we derive mean first-passage times and splitting probabilities for different boundary and initial conditions. This work connects the study of work extraction from active matter with exactly solvable active particle models and will therefore facilitate the design of active engines through these analytic results.

Stochastic kinetics under combined action of two noise sources

We are exploring two archetypal noise-induced escape scenarios: Escape from a finite interval and from the positive half-line under the action of the mixture of Lévy and Gaussian white noises in the overdamped regime, for the random acceleration process and higher-order processes. In the case of escape from finite intervals, the mixture of noises can result in the change of value of the mean first passage time in comparison to the action of each noise separately. At the same time, for the random acceleration process on the (positive) half-line, over the wide range of parameters, the exponent characterizing the power-law decay of the survival probability is equal to the one characterizing the decay of the survival probability under action of the (pure) Lévy noise. There is a transient region, the width of which increases with stability index α, when the exponent decreases from the one for Lévy noise to the one corresponding to the Gaussian white noise driving.

Interplay of noise induced stability and stochastic resetting

Stochastic resetting and noise-enhanced stability are two phenomena that can affect the lifetime and relaxation of nonequilibrium states. They can be considered measures of controlling the efficiency of the completion process when a stochastic system has to reach the desired state. Here, we study the interaction of random (Poissonian) resetting and stochastic dynamics in unstable potentials. Unlike noise-induced stability that increases the relaxation time, the stochastic resetting may eliminate winding trajectories contributing to the lifetime and accelerate the escape kinetics from unstable states. In this paper, we present a framework to analyze compromises between the two contrasting phenomena in noise-driven kinetics subject to random restarts.

First detection of threshold crossing events under intermittent sensing

The time taken by a random variable to cross a threshold for the first time, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the notional "sensor" monitoring the threshold crossing event is always active. In many realistic scenarios, the sensor monitoring the stochastic process works intermittently. Then, the relevant quantity of interest is the first detection time, which denotes the time when the sensor detects the random variable to be above the threshold for the first time. In this Letter, a birth-death process monitored by a random intermittent sensor is studied for which the first detection time distribution is obtained. In general, it is shown that the first detection time is related to and is obtainable from the first passage time distribution. Our analytical results display an excellent agreement with simulations. Furthermore, this framework is demonstrated in several applications-the susceptible infected susceptible compartmental and logistic models and birth-death processes with resetting. Finally, we solve the practically relevant problem of inferring the first passage time distribution from the first detection time.

Escape kinetics of self-propelled particles from a circular cavity

We numerically investigate the mean exit time of an inertial active Brownian particle from a circular cavity with single or multiple exit windows. Our simulation results witness distinct escape mechanisms depending on the relative amplitudes of the thermal length and self-propulsion length compared to the cavity and pore sizes. For exceedingly large self-propulsion lengths, overdamped active particles diffuse on the cavity surface, and rotational dynamics solely governs the exit process. On the other hand, the escape kinetics of a very weakly damped active particle is largely dictated by bouncing effects on the cavity walls irrespective of the amplitude of self-propulsion persistence lengths. We show that the exit rate can be maximized for an optimal self-propulsion persistence length, which depends on the damping strength, self-propulsion velocity, and cavity size. However, the optimal persistence length is insensitive to the opening windows' size, number, and arrangement. Numerical results have been interpreted analytically based on qualitative arguments. The present analysis aims at understanding the transport controlling mechanism of active matter in confined structures.

Active binary switching of soft colloids: stability and structural properties

We employ reactive dynamical density functional theory (R-DDFT) and reactive Brownian dynamics (R-BD) simulations to study the non-equilibrium structure and phase behavior of an active dispersion of soft Gaussian colloids with binary interaction switching, i.e., we consider a one-component colloidal system in which every particle can individually switch stochastically between two interaction states (here, sizes 'big' and 'small') at predefined rates. We consider the influence of switching activity on the inhomogeneous density profiles of the colloids confined by various external potentials, as well as on their pair structure and phase behavior in bulk solutions. For the latter, we extend the R-DDFT method to incorporate the Percus test-particle route. Our results demonstrate that switching activity strongly modifies the steady-state density profiles and structural (pair) correlations. In particular, the switching rate interpolates from a near-equilibrium binary colloidal mixture of two states at very low rates to a non-equilibrium, 'one-state liquid' at very high rates characterized by one, average interaction size. The latter limit can be described by an equivalent effective one-component (EOC) equilibrium system, for which the exact analytical expression for the effective pair potential is a diffusion-weighted superposition of the active systems' pair potentials. This leads to the interesting fact that under certain conditions an interacting switching system can behave like a non-interacting (ideal) gas in the limit of high switching rates. Moreover, for colloids that are unstable (i.e., demix) near equilibrium, we demonstrate that phase separation and micro-clustering in both confinement and bulk can be dynamically controlled by the switching rate, and vanish for high rates. All R-DDFT results are in excellent agreement with our R-BD simulations.

Subharmonics and superharmonics of the weak field in a driven two-level quantum system: Vibrational resonance enhancement

We consider a quantum two-level system in bichromatic classical time-periodic fields, the frequency of one of which far exceeds that of the other. Based on systematic separation of timescales and averaging over the fast motion a reduced quantum dynamics in the form of a nonlinear forced Mathieu equation is derived to identify the stable oscillatory resonance zones intercepted by unstable zones in the frequency-amplitude plot. We show how this forcing of the dressed two-level system may generate the subharmonics and superharmonics of the weak field in the stable region, which can be amplified by optimization of the strength of the high frequency field. We have carried out detailed numerical simulations of the driven quantum dynamics to corroborate the theoretical analysis.

Inertial Lévy flights in bounded domains

The escape from a given domain is one of the fundamental problems in statistical physics and the theory of stochastic processes. Here, we explore properties of the escape of an inertial particle driven by Lévy noise from a bounded domain, restricted by two absorbing boundaries. The presence of two absorbing boundaries assures that the escape process can be characterized by the finite mean first passage time. The detailed analysis of escape kinetics shows that properties of the mean first passage time for the integrated Ornstein-Uhlenbeck process driven by Lévy noise are closely related to properties of the integrated Lévy motions, which, in turn, are close to properties of the integrated Wiener process. The extensive studies of the mean first passage time were complemented by examination of the escape velocity and energy along with their sensitivity to initial conditions.

Physics of free climbing

The theory of stochastic processes provides theoretical tools which can be efficiently used to explore the properties of noise-induced escape kinetics. Since noise-facilitated escape over the potential barrier resembles free climbing, one can use the first-passage time theory in an analysis of rock climbing. We perform the analysis of the mean first-passage time in order to answer the question regarding the optimal, i.e., resulting in the fastest climbing, rope length. It is demonstrated that there is a discrete set of favorable rope lengths assuring the shortest climbing times, as they correspond to local minima of mean first-passage time. Within the set of favorable rope lengths there is the optimal rope giving rise to the shortest climbing time. In particular, more experienced climbers can decrease their climbing time by using longer ropes.

Dichotomous flow with thermal diffusion and stochastic resetting

We consider properties of one-dimensional diffusive dichotomous flow and discuss effects of stochastic resonant activation (SRA) in the presence of a statistically independent random resetting mechanism. Resonant activation and stochastic resetting are two similar effects, as both of them can optimize the noise-induced escape. Our studies show completely different origins of optimization in adapted setups. Efficiency of stochastic resetting relies on elimination of suboptimal trajectories, while SRA is associated with matching of time scales in the dynamic environment. Consequently, both effects can be easily tracked by studying their asymptotic properties. Finally, we show that stochastic resetting cannot be easily used to further optimize the SRA in symmetric setups.

Vibrational resonance in a driven two-level quantum system, linear and nonlinear response

We consider a two-level quantum system interacting with two classical time-periodic electromagnetic fields. The frequency of one of the fields far exceeds that of the other. The effect of the high-frequency field can be averaged out of the dynamics to realize an effective transition frequency of the field-dressed two-level system. We examine the linear response, second harmonic response and Stokes and anti-Stokes Raman response of the dressed two-level system, to the weak frequency field. The vibrational resonance enhancement in each case is demonstrated for optimal strength of the high-frequency field. Our theoretical scheme is corroborated by full numerical simulation of the two-level, two-field dynamics governed by loss-free Bloch equations. We suggest that quantum optics can offer an interesting arena for the study of the vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Dynamics and decay rates of a time-dependent two-saddle system

The framework of transition state theory (TST) provides a powerful way for analyzing the dynamics of physical and chemical reactions. While TST has already been successfully used to obtain reaction rates for systems with a single time-dependent saddle point, multiple driven saddles have proven challenging because of their fractal-like phase space structure. This paper presents the construction of an approximately recrossing-free dividing surface based on the normally hyperbolic invariant manifold in a time-dependent two-saddle model system. Based on this, multiple methods for obtaining instantaneous (time-resolved) decay rates of the underlying activated complex are presented and their results discussed.

Lévy noise-driven escape from arctangent potential wells

The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, Lévy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Lévy noise-driven escape from an almost rectangular, arctangent potential well restricted by two absorbing boundaries, mostly under the action of the Cauchy noise. We unveil analogies of the observed transient dynamics to the general properties of stationary states of Lévy processes in single-well potentials. The first-escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness, and height of the arctangent potential. Finally, we explore in detail the behavior of the probability densities of the first-escape time and the last-hitting point.

Underdamped, anomalous kinetics in double-well potentials

The noise-driven motion in a bistable potential acts as the archetypal model of various physical phenomena. Here, we contrast properties of the overdamped escape dynamics with the full (underdamped) dynamics. In the weak noise limit, for the overdamped particle driven by nonequilibrium, α-stable noise the ratio of forward to backward transition rates depends only on the width of a potential barrier separating both minima. Using analytical and numerical methods, we show that in the regime of full dynamics, contrary to the overdamped case, the ratio of transition rates depends on both the widths and the heights of the potential barrier separating minima of the double-well potential. The derived analytical formula for the ratio of transition rates is corroborated by extensive numerical simulations. Results of numerical simulations follow especially well the analytical predictions in the weak noise limit when the most probable escape scenario is via a single, strong, noise kick, which is sufficient to induce a quasideterministic transition over the potential barrier. Such an escape trajectory can be analyzed in terms of the instantaneous velocity, which is fully characterized by its density function, which is of the same type as the probability density underlying the noise distribution.

Dephasing-Assisted Macrospin Transport

Transport phenomena are ubiquitous in physics, and it is generally understood that the environmental disorder and noise deteriorates the transfer of excitations. There are, however, cases in which transport can be enhanced by fluctuations. In the present work, we show, by means of micromagnetics simulations, that transport efficiency in a chain of classical macrospins can be greatly increased by an optimal level of dephasing noise. We also demonstrate the same effect in a simplified model, the dissipative Discrete Nonlinear Schrödinger equation, subject to phase noise. Our results point towards the realization of a large class of magnonics and spintronics devices, where disorder and noise can be used to enhance spin-dependent transport efficiency.

Stochastic fluctuations in apoptotic threshold of tumour cells can enhance apoptosis and combat fractional killing

Fractional killing, which is a significant impediment to successful chemotherapy, is observed even in a population of genetically identical cancer cells exposed to apoptosis-inducing agents. This phenomenon arises not from genetic mutation but from cell-to-cell variation in the activation timing and level of the proteins that regulates apoptosis. To understand the mechanism behind the phenomenon, we formulate complex fractional killing processes as a first-passage time (FPT) problem with a stochastically fluctuating boundary. Analytical calculations are performed for the FPT distribution in a toy model of stochastic p53 gene expression, where the cancer cell is killed only when the p53 expression level crosses an active apoptotic threshold. Counterintuitively, we find that threshold fluctuations can effectively enhance cellular killing by significantly decreasing the mean time that the p53 protein reaches the threshold level for the first time. Moreover, faster fluctuations lead to the killing of more cells. These qualitative results imply that fluctuations in threshold are a non-negligible stochastic source, and can be taken as a strategy for combating fractional killing of cancer cells.

Stochastic neural fields as gradient dynamical systems

Continuous attractor neural networks are used extensively to model a variety of experimentally observed coherent brain states, ranging from cortical waves of activity to stationary activity bumps. The latter are thought to play an important role in various forms of neural information processing, including population coding in primary visual cortex (V1) and working memory in prefrontal cortex. However, one limitation of continuous attractor networks is that the location of the peak of an activity bump (or wave) can diffuse due to intrinsic network noise. This reflects marginal stability of bump solutions with respect to the action of an underlying continuous symmetry group. Previous studies have used perturbation theory to derive an approximate stochastic differential equation for the location of the peak (phase) of the bump. Although this method captures the diffusive wandering of a bump solution, it ignores fluctuations in the amplitude of the bump. In this paper, we show how amplitude fluctuations can be analyzed by reducing the underlying stochastic neural field equation to a finite-dimensional stochastic gradient dynamical system that tracks the stochastic motion of both the amplitude and phase of bump solutions. This allows us to derive exact expressions for the steady-state probability density and its moments, which are then used to investigate two major issues: (i) the input-dependent suppression of neural variability and (ii) noise-induced transitions to bump extinction. We develop the theory by considering the particular example of a ring attractor network with SO(2) symmetry, which is the most common architecture used in attractor models of working memory and population tuning in V1. However, we also extend the analysis to a higher-dimensional spherical attractor network with SO(3) symmetry which has previously been proposed as a model of orientation and spatial frequency tuning in V1. We thus establish how a combination of stochastic analysis and group theoretic methods provides a powerful tool for investigating the effects of noise in continuous attractor networks.

Stationary states for underdamped anharmonic oscillators driven by Cauchy noise

Using numerical methods, we have studied stationary states in the underdamped anharmonic stochastic oscillators driven by Cauchy noise. The shape of stationary states depends on both the potential type and the damping. If the damping is strong enough, for potential wells which in the overdamped regime produce multimodal stationary states, stationary states in the underdamped regime can be multimodal with the same number of modes like in the overdamped regime. For the parabolic potential, the stationary density is always unimodal, and it is given by the two dimensional α-stable density. For the mixture of quartic and parabolic single-well potentials, the stationary density can be bimodal. Nevertheless, the parabolic addition, which is strong enough, can destroy the bimodality of the stationary state.

Variational implicit-solvent predictions of the dry-wet transition pathways for ligand-receptor binding and unbinding kinetics

Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multimethod approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obtain the minimum energy paths and transition states between the various metastable ("dry" and "wet") hydration states. The resulting dry-wet transition rates are then used in a spatially dependent multistate continuous-time Markov chain Brownian dynamics simulation and the related Fokker-Planck equation calculations of the ligand stochastic motion, providing the mean first-passage times for binding and unbinding. We find the hydration transitions to significantly slow down the binding process, in semiquantitative agreement with existing explicit-water simulations, but significantly accelerate the unbinding process. Moreover, our methods allow the characterization of nonequilibrium hydration states of pocket and ligand during the ligand movement, for which we find substantial memory and hysteresis effects for binding vs. unbinding. Our study thus provides a significant step forward toward efficient, physics-based interpretation and predictions of the complex kinetics in realistic ligand-receptor systems.

Vibrational antiresonance in nonlinear coupled systems

We examine the response of a system of coupled nonlinear oscillators driven by a rapidly varying field, to a low frequency weak periodic excitation of one of the oscillators. The response amplitude of the weak field-driven oscillator at an optimal strength of the rapidly varying field exhibits a strong suppression accompanied by a large negative shift in its oscillation phase. The minimum can be identified as vibrational antiresonance in between the two maxima corresponding to vibrational resonance. This vibrational antiresonance can be observed only in nonlinear coupled systems and not in linearly coupled systems or in a single nonlinear oscillator, under similar physical condition. We discuss the underlying dynamical mechanism, the role of nonlinearity and high frequency in characterizing this counter-resonance effect. Our theoretical analysis is corroborated by detailed numerical simulations.

Energetics of single-well undamped stochastic oscillators

This paper discusses analytical and numerical results for nonharmonic, undamped, single-well, stochastic oscillators driven by additive noises. It focuses on average kinetic, potential, and total energies together with the corresponding distributions under random drivings, involving Gaussian white, Ornstein-Uhlenbeck, and Markovian dichotomous noises. It demonstrates that insensitivity of the average total energy to the single-well potential type, V(x)∝x^{2n}, under Gaussian white noise does not extend to other noise types. Nevertheless, in the long-time limit (t→∞), the average energies grow as power law with exponents dependent on the steepness of the potential n. Another special limit corresponds to n→∞, i.e., to the infinite rectangular potential well, when the average total energy grows as a power law with the same exponent for all considered noise types.

Geometric Effects of a Quarter of Corrugated Torus

In the spirit of the thin-layer quantization scheme, we give the effective Shrödinger equation for a particle confined to a corrugated torus, in which the geometric potential is substantially changed by corrugation. We find the attractive wells reconstructed by the corrugation not being at identical depths, which is strikingly different from that of a corrugated nanotube, especially in the inner side of the torus. By numerically calculating the transmission probability, we find that the resonant tunneling peaks and the transmission gaps are merged and broadened by the corrugation of the inner side of torus. These results show that the quarter corrugated torus can be used not only to connect two tubes with different radiuses in different directions, but also to filter the particles with particular incident energies.

Autonomous stochastic resonance driven by colored noise

A one-dimensional linear autonomous system coupled to a generic stationary nonequilibrium fluctuating bath can exhibit resonant response when its damped oscillation period matches some characteristic bath's relaxation time. This condition justifies invoking the stochastic resonance paradigm, even if it can be achieved more easily by tuning the system to the bath and not vice versa, as is usually the case. The simple nature of the mechanism numerically investigated here suggests a number of interesting applications for instance in the context of (1) energy harvesting from random ambient vibrations, (2) activated barrier crossing through a saddle point, or (3) an unstable limit cycle.

Diffusion crossing over a barrier in a random rough metastable potential

We carry out a detailed study of escape dynamics of a particle driven by a white noise over a metastable potential corrugated by spatial disorder in the form of zero-mean random correlated potential. The approach of double-averaging over test particles and statistic ensemble is proposed to calculate the escape rate in a finite-size random rough metastable potential, moreover, the interference mechanism of test particles multi-passing over the saddle point is considered. Through analyzing the dependence of the steady escape rate on various modelled potentials and parameters, we demonstrate that the obstruction induced by roughness leads to a decrease in the steady escape rate with the increase of rough intensity. We also add the random correlated potential into the vicinity of the saddle-point of metastable potentials of three kinds and show an enhancement phenomenon of escape rate similar to the previous study of a surmounting fluctuating sharp barrier.

Enhancing Metastability by Dissipation and Driving in an Asymmetric Bistable Quantum System

The stabilizing effect of quantum fluctuations on the escape process and the relaxation dynamics from a quantum metastable state are investigated. Specifically, the quantum dynamics of a multilevel bistable system coupled to a bosonic Ohmic thermal bath in strong dissipation regime is analyzed. The study is performed by a non-perturbative method based on the real-time path integral approach of the Feynman-Vernon influence functional. We consider a strongly asymmetric double well potential with and without a monochromatic external driving, and with an out-of-equilibrium initial condition. In the absence of driving we observe a nonmonotonic behavior of the escape time from the metastable region, as a function both of the system-bath coupling coefficient and the temperature. This indicates a stabilizing effect of the quantum fluctuations. In the presence of driving our findings indicate that, as the coupling coefficient γ increases, the escape time, initially controlled by the external driving, shows resonant peaks and dips, becoming frequency-independent for higher γ values. Moreover, the escape time from the metastable state displays a nonmonotonic behavior as a function of the temperature, the frequency of the driving, and the thermal-bath coupling, which indicates the presence of a quantum noise enhanced stability phenomenon. Finally, we investigate the role of different spectral densities, both in sub-Ohmic and super-Ohmic dissipation regime and for different cutoff frequencies, on the relaxation dynamics from the quantum metastable state. The results obtained indicate that, in the crossover dynamical regime characterized by damped intrawell oscillations and incoherent tunneling, the spectral properties of the thermal bath influence non-trivially the short time behavior and the time scales of the relaxation dynamics from the metastable state.

Asymmetric noise-induced large fluctuations in coupled systems

Networks of interacting, communicating subsystems are common in many fields, from ecology, biology, and epidemiology to engineering and robotics. In the presence of noise and uncertainty, interactions between the individual components can lead to unexpected complex system-wide behaviors. In this paper, we consider a generic model of two weakly coupled dynamical systems, and we show how noise in one part of the system is transmitted through the coupling interface. Working synergistically with the coupling, the noise on one system drives a large fluctuation in the other, even when there is no noise in the second system. Moreover, the large fluctuation happens while the first system exhibits only small random oscillations. Uncertainty effects are quantified by showing how characteristic time scales of noise-induced switching scale as a function of the coupling between the two coupled parts of the experiment. In addition, our results show that the probability of switching in the noise-free system scales inversely as the square of reduced noise intensity amplitude, rendering the virtual probability of switching an extremely rare event. Our results showing the interplay between transmitted noise and coupling are also confirmed through simulations, which agree quite well with analytic theory.

Activated barrier crossing dynamics of a Janus particle carrying cargo

We numerically study the escape kinetics of a self-propelled Janus particle, carrying a cargo, from a meta-stable state.

Particle transport across a channel via an oscillating potential

Membrane protein transporters alternate their substrate-binding sites between the extracellular and cytosolic side of the membrane according to the alternating access mechanism. Inspired by this intriguing mechanism devised by nature, we study particle transport through a channel coupled with an energy well that oscillates its position between the two entrances of the channel. We optimize particle transport across the channel by adjusting the oscillation frequency. At the optimal oscillation frequency, the translocation rate through the channel is a hundred times higher with respect to free diffusion across the channel. Our findings reveal the effect of time-dependent potentials on particle transport across a channel and will be relevant for membrane transport and microfluidics application.

Resonant activation of population extinctions

Understanding the mechanisms governing population extinctions is of key importance to many problems in ecology and evolution. Stochastic factors are known to play a central role in extinction, but the interactions between a population's demographic stochasticity and environmental noise remain poorly understood. Here we model environmental forcing as a stochastic fluctuation between two states, one with a higher death rate than the other. We find that, in general, there exists a rate of fluctuations that minimizes the mean time to extinction, a phenomenon previously dubbed "resonant activation." We develop a heuristic description of the phenomenon, together with a criterion for the existence of resonant activation. Specifically, the minimum extinction time arises as a result of the system approaching a scenario wherein the severity of rare events is balanced by the time interval between them. We discuss our findings within the context of more general forms of environmental noise and suggest potential applications to evolutionary models.

Escape of coupled Brownian particles across a fluctuating barrier

The escape of two harmonically coupled Brownian particles across the fluctuating barrier of a bistable potential is investigated with correlated additive and multiplicative fluctuations. Positive correlations enhance the rate of escape across the barrier when the coupling is effective, whereas for weakly coupled particles, escape becomes difficult. It is found that the system exhibits the phenomenon of resonant activation when the rate of barrier fluctuations is comparable to the relaxation time in the bistable potential. Using a decoupling ansatz, we derive the Markovian limit of the problem in the steady state, under the constraint that the barriers fluctuate on a time scale faster than the relative oscillation of the two particles. Adiabatic elimination of the fast variable of the dynamical system is discussed in appropriate limits.

Effect of stochastic gating on channel-facilitated transport of non-interacting and strongly repelling solutes

Ligand- or voltage-driven stochastic gating-the structural rearrangements by which the channel switches between its open and closed states-is a fundamental property of biological membrane channels. Gating underlies the channel's ability to respond to different stimuli and, therefore, to be functionally regulated by the changing environment. The accepted understanding of the gating effect on the solute flux through the channel is that the mean flux is the product of the flux through the open channel and the probability of finding the channel in the open state. Here, using a diffusion model of channel-facilitated transport, we show that this is true only when the gating is much slower than the dynamics of solute translocation through the channel. If this condition breaks, the mean flux could differ from this simple estimate by orders of magnitude.

Quantum resonant activation

Quantum resonant activation is investigated for the archetype setup of an externally driven two-state (spin-boson) system subjected to strong dissipation by means of both analytical and extensive numerical calculations. The phenomenon of resonant activation emerges in the presence of either randomly fluctuating or deterministic periodically varying driving fields. Addressing the incoherent regime, a characteristic minimum emerges in the mean first passage time to reach an absorbing neighboring state whenever the intrinsic time scale of the modulation matches the characteristic time scale of the system dynamics. For the case of deterministic periodic driving, the first passage time probability density function (pdf) displays a complex, multipeaked behavior, which depends crucially on the details of initial phase, frequency, and strength of the driving. As an interesting feature we find that the mean first passage time enters the resonant activation regime at a critical frequency ν^{*} which depends very weakly on the strength of the driving. Moreover, we provide the relation between the first passage time pdf and the statistics of residence times.

Noisy-flow-induced instability in a reaction-diffusion system

We consider a generic reaction-diffusion-advection system where the flow velocity of the advection term is subjected to dichotomous noise with zero mean and Ornstein-Zernike correlation. A general condition for noisy-flow-induced instability is derived in the flow velocity-correlation rate parameter plane. Full numerical simulations on Gierer-Meinhardt model with activator-inhibitor kinetics have been performed to show how noisy differential flow can lead to symmetry breaking of a homogeneous stable state in the presence of noise resulting in traveling waves.

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.

Stochastic resonance during a polymer translocation process

We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

Superexponential fluctuation relation for dichotomous work reservoir systems

This paper introduces an analytical description of the probability density function of the dissipated and injected powers p(j_{dis}) and p(j_{inj}), respectively, in a paradigmatic nonequilibrium damped system in contact with a work reservoir that is analytically represented by telegraph noise and to which one can assign an effective temperature. This approach is able to overcome the well-known impossibility of obtaining closed solutions to steady-state distributions of this system and allows determining a superexponential fluctuation relation of the injected power, which is not even asymptotically exponential as for (shot-noise) Poissonian reservoirs. In the white-noise limit, that relation converges to the exponential formula that is standard in thermal systems; however, the distribution of the injected power remains quite different from that of the latter instance. Surprisingly, it is actually shown that a Gaussian distribution, which is archetypal of thermal systems, for the injected power can be achievable only for athermal reservoirs of this kind.

Thermostatistics of a damped bimodal particle

We study the thermostatistics of a damped bimodal particle, i.e., a particle of mass m subject to a work reservoir that is analytically represented by the telegraph noise. Because of the colored nature of the noise, it does not fit the Lévy-Itô class of stochastic processes, making this system an instance of a nonequilibrium system in contact with a non-Gaussian external reservoir. We obtain the statistical description of the position and velocity, namely in the stationary state, as well as the (time-dependent) statistics of the energy fluxes in the system considering no constraints on the telegraph noise features. With that result we are able to give an account of the statistical properties of the large deviations of the injected and dissipated power that can change from sub-Gaussianity to super-Gaussianity depending on the color of the noise. By properly defining an effective temperature for this system, T, we are capable of obtaining an equivalent entropy production-exchange rate equal to the ratio between the dissipation of the medium, γ, and the mass of the particle, m, a relation that concurs with the case of a standard thermal reservoir at temperature, T=T.

Thermal and inertial resonances in DNA unzipping

Single-molecule experiments combined with alternate forces are able to provide useful information not present in standard constant-force and -velocity pulling protocols. Here, we study the effects of such forces in the DNA mechanical unzipping by using an extension of the Peyrard-Bishop-Dauxois model. By changing the damping regime in the dynamical equations, we obtained two resonant mechanisms in both the mean time and the mean force of unzipping. One is thermally assisted and it is characterized by a matching between the period of the external force and the mean unzipping time of the DNA chain, while the other depends on the inertial properties of the system. Both mechanisms are studied systematically under different opening protocols and different parameters of the system. The main results here presented contribute in characterizing and finding optimized conditions in DNA unzipping experiments.

Effect of interference between two colored noises on the stationary states of a Brownian particle

In this paper we present properties of an external colored cross-correlated noise-driven Brownian system which is coupled to a thermal bath. Multiplicative cross-correlated noises can stabilize the transition state. Thus by monitoring the interference between the noises one can understand the mechanism of a chemical reaction. At the same time, we have investigated how the interference affects the barrier-crossing dynamics. In its presence breakdown of the Arrhenius result occurs. The breakdown becomes prominent if the multiplicative noises become additive in nature. We have also investigated how the power law behavior of the rate constant as a function of damping strength is affected by the properties of external colored noises. Furthermore, we have observed that multiplicative colored cross-correlated noises can induce the resonant activation phenomenon.

Active polymer translocation in the three-dimensional domain

In this work we study the translocation process of a polymer through a nanochannel where a time dependent force is acting. Two conceptually different types of driving are used: a deterministic sinusoidal one and a random telegraph noise force. The mean translocation time presents interesting resonant minima as a function of the frequency of the external driving. For the computed sizes, the translocation time scales with the polymer length according to a power law with the same exponent for almost all the frequencies of the two driving forces. The dependence of the translocation time with the polymer rigidity, which accounts for the persistence length of the molecule, shows a different low frequency dependence for the two drivings.

Stationary states in two-dimensional systems driven by bivariate Lévy noises

Systems driven by α-stable noises could be very different from their Gaussian counterparts. Stationary states in single-well potentials can be multimodal. Moreover, a potential well needs to be steep enough in order to produce stationary states. Here it is demonstrated that two-dimensional (2D) systems driven by bivariate α-stable noises are even more surprising than their 1D analogs. In 2D systems, intriguing properties of stationary states originate not only due to heavy tails of noise pulses, which are distributed according to α-stable densities, but also because of properties of spectral measures. Consequently, 2D systems are described by a whole family of Langevin and fractional diffusion equations. Solutions of these equations bear some common properties, but also can be very different. It is demonstrated that also for 2D systems potential wells need to be steep enough in order to produce bounded states. Moreover, stationary states can have local minima at the origin. The shape of stationary states reflects symmetries of the underlying noise, i.e., its spectral measure. Finally, marginal densities in power-law potentials also have power-law asymptotics.