Escape Problem Research Articles

Full distribution of first exit times in the narrow escape problem

In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small ‘escape window’ in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container’s boundary. Considerable knowledge is available on the dependence of the mean first-reaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attempts interspersed with bulk excursions. These results add new perspectives and offer a broad comprehension of various features of the by-now classical NEP that are relevant for numerous biological and technological systems.

Locally and globally optimal configurations of N particles on the sphere with applications in the narrow escape and narrow capture problems.

Determination of optimal arrangements of N particles on a sphere is a well-known problem in physics. A famous example of such is the Thomson problem of finding equilibrium configurations of electrical charges on a sphere. More recently, however, similar problems involving other potentials and nonspherical domains have arisen in biophysical systems. Many optimal configurations have previously been computed, especially for the Thomson problem; however, few results exist for potentials that correspond to more applied problems. Here we numerically compute optimal configurations corresponding to the narrow escape and narrow capture problems in biophysics. We provide comprehensive tables of global energy minima for N≤120 and local energy minima for N≤65, and we exclude all saddle points. Local minima up to N=120 are available online.

Narrow escape problem for Brownian particles in a microsphere with internal circulation.

This paper considers the narrow escape problem of a Brownian particle within a two-dimensional domain with two escape windows and an internal circulation modeled by the flow within a Hill's vortex. To account for the spatially inhomogeneous flow within the domain, a Lagrangian study is undertaken using the complete equations of motion for a dense particle which is necessary to distinguish between the various regimes as the strength of the internal circulation is varied. For very low internal circulation the particle undergoes the conventional narrow escape problem, and agreement is good with the asymptotic expression. As the internal circulation is increased, regimes are identified with different scaling for the mean escape time. The potential application of this for drug delivery (were nanoparticles are encased in a microsphere) is discussed.

Formulating the Kramers problem in field theory

The escape problem is defined in the context of quantum field theory. The escape rate is explicitly derived for a scalar field governed by fluctuation-dissipation dynamics, through generalizing the standard Kramers problem. In the presence of thermal fluctuations, there is a nonvanishing probability for a classical background field, initially located at a minimum of its potential in a homogeneous configuration, to escape from the well. The simple and well-known related problem of the escape of a classical point particle due to random forces is first reviewed. We then discuss the difficulties associated with a well-defined formulation of an escape rate for a scalar field and how these can be overcome. A definition of the Kramers problem for a scalar field and a method to obtain the rate are provided. Finally, we discuss some of the potential applications of our results, which can range from condensed matter systems, i.e., nonrelativistic fields, to applications in high-energy physics, like for cosmological phase transitions.

The narrow escape problem in a circular domain with radial piecewise constant diffusivity

The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments. As a first step to understand the consequence of the existence of two compartments with different diffusion constant for stochastic search problems we consider here a Brownian particle in a circular domain with different diffusion constants in the inner and the outer shell. We focus on the narrow escape problem and compute the mean first passage time (MFPT) for Brownian particles starting at some pre-defined position to find a small region on the outer reflecting boundary. For the annulus geometry we find that the MFPT can be minimized for a specific value of the width of the outer shell. In contrast for the two-shell geometry we show that the MFPT depends monotonously on all model parameters, in particular on the outer shell width. Moreover we find that the distance between the starting point and the narrow escape region which maximizes the MFPT depends discontinuously on the ratio between inner and outer diffusivity.

Stability of a gene transcriptional regulatory system under non-Gaussian noise

Abstract Gene transcription regulation plays a very important role in biological processes, which represents a benefit for the recognition of the nature of life. The escape problem of a gene transcriptional regulatory system has been investigated in several papers. However, little research has been performed on the metastability of the system. Based on the stochastic basin of attraction (SBA), this paper is devoted to the analysis of the stability of the metastable low and high concentration states under non-Gaussian noise. Results reveal that unlike Gaussian white noise, the noise intensity and stability index of non-Gaussian noise cause the two concentration states to be unstable, yet exerting a greater influence on higher concentration states. In addition, the dissipation coefficient of non-Gaussian noise can result in the promotion of the transcription process in gene expression.

Escape rate of transiently active Brownian particle in one dimension.

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 barrier. We perform numerical simulations of the escape process in one dimension and find good agreement with the theoretical predictions.

Lévy noise induced escape in the Morris–Lecar model

The phenomenon of an excitable system producing a pulse under external or internal stimulation may be interpreted as a stochastic escape problem. This work addresses this issue by examining the Morris–Lecar neural model driven by symmetric α-stable Lévy motion (non-Gaussian noise) as well as Brownian motion (Gaussian noise). Two deterministic quantities: the first escape probability and the mean first exit time, are adopted to analyze the state transition from the resting state to the excited state and the stability of this stochastic model. Additionally, a recent geometric concept, the stochastic basin of attraction is used to explore the basin stability of the escape region. Our main results include: (i) the larger Lévy motion index with smaller jump magnitude and the relatively small noise intensity are conducive for the Morris–Lecar model to produce pulses; (ii) a smaller noise intensity and a larger Lévy motion index make the mean first exit time longer, which means the stability of the resting state can be enhanced in this case; (iii) the effect of ion channel noise is more pronounced on the stochastic Morris–Lecar model than the current noise. This work provides some numerical simulations about the impact of non-Gaussian, heavy-tailed, burst-like fluctuations on excitable systems such as the Morris–Lecar system.

Non-empirical weighted Langevin mechanics for the potential escape problem: Parallel algorithm and application to the Argon clusters

Recently a non-empirical stochastic walker algorithm has been developed to search for the minimum-energy escape paths (MEP) from the minima of the potential surface (Akashi and Nagornov, 2018). This algorithm is novel in that it tracks the MEP monotonically and does not use the whole Hessian matrix but only gradient and Laplacian of the potential. In this work, we implement an parallelized version of this algorithm in a simple way. We also explore efficient ways to reduce the number of walkers required for the accurate tracking of the MEP and generate initial positions automatically. We apply the whole scheme to the Lennard-Jones argon cluster with 7–38 atoms to demonstrate the successful tracking of the reaction paths. This achievement paves the path to non-empirical simulation of rare reactions without coarse-graining or artificial potential.

Activated carbon-supported catalyst loading of CH4N2O for selective reduction of NO from flue gas at low temperatures

Selective catalytic reduction of nitrogen oxides with loaded CH4N2O (low-temperature urea-SCR) is a novel and promising technology to remove nitrogen oxides from low-temperature oxygen-containing flue gas, which can avoid the problem of NH3 escape. In the present study, a series of industrial-grade biomass-based activated carbon (AC)-supported transition metal oxide catalysts with urea loading were prepared by ultrasound-assisted impregnation, and the physicochemical properties of the catalysts were observed by scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), transmission electron microscopy (TEM), X-ray diffraction (XRD), graphite furnace atomic absorption spectroscopy (GFAAS), X-ray photoelectron spectroscopy (XPS), Brunauer–Emmett–Teller (BET) analysis, Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA). The influences of the AC type, reaction temperature, AC particle size, metal oxide loading, urea load level and loaded active element type on the catalytic activity were studied through experiments. Moreover, the NO adsorption capacities of the AC carrier at different temperatures were also tested and calculated. The results of NO adsorption tests show that the adsorption capacity of AC decreased with increasing temperature. The results of the catalytic performance tests indicate that the copper- and manganese-based catalysts with 6 wt% urea exhibited better activity than the other catalysts. The copper-based catalyst, in particular, yielded better than 93% NO conversion at low temperatures (50–100 °C). Finally, on the basis of the combined characterization results and thermodynamics analysis, a NO removal mechanism of the copper- and manganese-based catalysts was proposed and discussed; the electron transfers of Mn4+ ⇌ Mn2+ and Cu2+ ⇌ Cu0 promoted the low-temperature urea-SCR method.

Graphene Oxide Supported on Amberlite Resin for the Analytical Method Development for Enhanced Column Preconcentration/Sensitive Flame Atomic Absorption Spectrometric Determination of Toxic Metal Ions in Environmental Samples

Graphene oxide (GO)-layered nanosheets with a two-dimensional carbon lattice is linked to styrenic carbon of porous XAD polymeric resin via an azo spacer arm without utilizing any oxygen-containing functionality for the first time. The adopted synthesis approach makes all of the epoxy, hydroxyl, carbonyl, and carboxyl groups on the axial and basal planes of the GO sheet available for coordination with metal ions, and the introduction of hydrophilic character as result the highest preconcentration factor for Pb (500) was observed among the GO composites used as a solid-phase extractant in column operation. The developed analytical methodology using XAD–GO for the preconcentration of Pb, Cd, and Zn ions permits the use of an economically viable less sensitive atomic absorption spectrometry for their trace determination in water samples because of the enhanced quantification limit. The application of polymer-immobilized GO in a column sorts out the problem of escape of toxic GO into the environment, and unde...

Reasons High School Students Use Marijuana: Prevalence and Correlations With Use Across Four Decades

Changes in the legality and prevalence of marijuana raise questions about whether adolescents' reasons for using marijuana and associations between reasons for use and recent marijuana use have changed historically. Using nationally representative data from Monitoring the Future for 1976-2016 (N = 39,964; 47.6% female), we examined changes in self-reported reasons for marijuana use and in the associations between reasons for use and past-30-day marijuana use among 12th graders who used marijuana in the past 12 months. Time-varying effect modeling showed variation in reasons for use among adolescent past-year marijuana users from 1976 to 2016. Social/recreational reasons for marijuana use (i.e., Boredom, Feel Good/Get High, Experiment, Fit In) generally declined in prevalence; the exception was Good Time, which remained quite stable. Prevalence of coping with negative affect reasons (i.e., Anger/Frustration, Escape Problems, Relax, Get Through Day) approximately doubled across 40 years. Over time, social/recreational reasons were consistently associated with greater odds (i.e., Boredom, Feel Good/Get High, Good Time) or lower odds (i.e., Experiment, Fit In) of recent marijuana use. Coping with negative affect reasons, drug effect reasons, and compulsive use were consistently associated with greater odds of recent use. The most common reasons for marijuana use among high school students have shifted markedly in 40 years, with particular increases for coping-related reasons. However, reasons for use remain significant, stable predictors of use. This suggests a move toward riskier (coping-related) use but supports the continued salience of motivation-based approaches for prevention and intervention.

Temporal cooperativity of motor proteins under constant force: insights from Kramers’ escape problem

The microtubule-bound motors kinesin and dynein differ in many respects, a striking difference being that while kinesin is known to function mostly alone, dynein operates in large groups, much like myosinV in actin. Optical tweezer experiments in vitro have shown that the mean detachment time of a bead attached to kinesins under stall conditions is a slowly decreasing function of , while for dyneins, the time increases almost linearly with . This makes dynein a team worker, capable of producing and sustaining a large collective force without detaching. We characterize this phenomenon as ‘temporal cooperativity’ under load. In general, it is unclear which biophysical properties of a single motor determine whether it behaves cooperatively or not in a group. Our theoretical analysis shows that this is determined by two dimensionless parameters: (i) the ratio of single molecule, load-independent detachment and attachment rates and (ii) the ratio of the applied force per motor to the detachment force of a single motor. We show that the attachment-detachment dynamics of a motor assembly may be mapped to the motion of a hypothetical, overdamped Brownian particle in an effective potential, the form of which depends on the load-dependence of binding and unbinding rate of the motor. In this picture, the total number of motors is proportional to the inverse temperature and cooperative behaviour arises from the trapping of the particle in the minima of the potential, when present. In the latter case, application of results from Kramers’ theory predicts that the mean time of escape of the particle, equivalent to the mean detachment time of the bead under stall, increases exponentially with the number of motors, indicating cooperative behaviour. If the potential does not have minima, the detachment time depends only weakly on , which suggests non-cooperative behaviour. In the large limit, the emergence of cooperative behaviour is shown to be similar to a continuous phase transition.

Simulation research of SCR optimal operation

Selective catalytic reduction technology(SCR) has high denitration efficiency. It is the main techniques adopted in our country of flue gas denitrification. Due to lack of effective NH3 spraying methods and means, stock of low efficiency, high rate of ammonia escape problems, secondary pollution is serious in the actual operation of the existing SCR system. In this paper, using computational fluid dynamics (CFD) method, establishing of three dimensional numerical model of SCR system. Flue gas flow and the NH3/NOx distribution characteristics were analyzed by numerical simulation in SCR system. Studying on the effect of different parameters on the ammonia injection of the reactor entrance speed of the first layer of the catalyst entrance section and the distribution of the NH3/NOx molar ratio, then providing optimizational parameters of the ammonia injection.

Neutral atmospheric escape in the Solar and extrasolar planetary systems

AbstractNew data obtained by space missions to various objects in the Solar system and observations of the outer Solar system and exoplanets by space and ground-based telescopes allowed us to conclude that the atmospheric escape plays an important role in the evolution of the terrestrial planets in the Solar system. We present the recent results of application of the kinetic approach to the problem of neutral escape from planetary atmospheres. As an example, the recent measurements by Mars Express and MAVEN spacecraft are compared with the calculations of neutral escape with the aim to understand the atmospheric loss at Mars. Also the recent calculations of the mass-loss rates of the hot Neptune and Jupiter atmospheres are presented.

Minimum Action Path Theory Reveals the Details of Stochastic Transitions Out of Oscillatory States.

Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Transitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible multidimensional paths, with probabilities depending nonlocally on the noise. Here we characterize the escape from an oscillatory biochemical state by minimizing the Freidlin-Wentzell action, deriving from it the stochastic spiral exit path from the limit cycle. We also use the minimized action to infer the escape time probability density function.

Narrow Escape of Interacting Diffusing Particles.

The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain's boundary. Here we develop a formalism which allows us to evaluate the nonescape probability of a gas of diffusing particles that may interact with each other. In some cases the nonescape probability allows us to evaluate the MET of the first particle. The formalism is based on the fluctuating hydrodynamics and the recently developed macroscopic fluctuation theory. We also uncover an unexpected connection between the narrow escape of interacting particles and thermal runaway in chemical reactors.

Spatial Cytoskeleton Organization Supports Targeted Intracellular Transport

The efficiency of intracellular cargo transport from specific sources to target locations is strongly dependent upon molecular motor-assisted motion along the cytoskeleton. Radial transport along microtubules and lateral transport along the filaments of the actin cortex underneath the cell membrane are characteristic for cells with a centrosome. The interplay between the specific cytoskeleton organization and the motor performance results in a spatially inhomogeneous intermittent search strategy. To analyze the efficiency of such intracellular search strategies, we formulate a random velocity model with intermittent arrest states. We evaluate efficiency in terms of mean first passage times for three different, frequently encountered intracellular transport tasks: 1) the narrow escape problem, which emerges during cargo transport to a synapse or other specific region of the cell membrane; 2) the reaction problem, which considers the binding time of two particles within the cell; and 3) the reaction-escape problem, which arises when cargo must be released at a synapse only after pairing with another particle. Our results indicate that cells are able to realize efficient search strategies for various intracellular transport tasks economically through a spatial cytoskeleton organization that involves only a narrow actin cortex rather than a cell body filled with randomly oriented actin filaments.

Efficient potential well escape for bi-stable Duffing oscillators

The problem of escape from a potential well of bi-stable oscillators has attracted attention given the diversity of physical and engineering systems described by this mathematical model. Most previous studies have considered quasi-static dynamics leading to escape. In devising efficient escape strategies for structures, transient conditions have not yet received adequate consideration. In this study, the intra-well nonlinear resonant dynamics of bi-stable systems are studied and exploited, yielding a time-efficient strategy for triggering minimal amplitude escape by employing transient perturbations. The response characteristics of both, the symmetric and asymmetric double-well Duffing oscillators are explored analytically to identify the stable solution branches for any given forcing configuration. Based on the basins of attraction of the stable attractors, a novel actuation methodology employing controlled perturbations in the phase of the forcing for driving the system into a series of high-amplitude limit cycle oscillations and eventual escape to the desired stable solution is proposed. Additionally, accelerated settling to the desired configuration is achieved by implementing state feedback techniques. The proposed algorithm serves as a potential tool for implementing fast shape adaptation in bi-stable structural systems.

Noise-induced phenomena in a versatile class of prototype dynamical system with time delay

This work presents a general class of prototype birhythmic dynamical systems, which can be extensively used to study the generation of complex bifurcation of limit cycles. Using a delay nonlinear Langevin approach, the stationary probability distribution and the escape problem are investigated under the influences of noise and time delay feedback. We discuss a new mechanism for the translocation of the amplitude in which the energy originates from noise. The results indicate that depending on the parameter space the system exhibits a transition from birhythmic to monorhythmic behavior or amplitude death. Besides, results demonstrated that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic bifurcation. Moreover, a novel finding is that the mean first passage time non-monotonically depends on the noise intensity and the dominant frequency of the oscillation. This finding represents the evidence of the noise-enhanced stability and stochastic resonant activation in the prototype dynamical system, whose occurrence is maintained for different values of the delay feedback intensity.