@article{GodecMetzler2017,
  author    = {Godec, Aljaž and Metzler, Ralf},
  title     = {First passage time statistics for two-channel diffusion},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {50},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {8},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/aa5204},
  pages     = {17},
  year      = {2017},
  abstract  = {We present rigorous results for the mean first passage time and first passage time statistics for two-channel Markov additive diffusion in a 3-dimensional spherical domain. Inspired by biophysical examples we assume that the particle can only recognise the target in one of the modes, which is shown to effect a non-trivial first passage behaviour. We also address the scenario of intermittent immobilisation. In both cases we prove that despite the perfectly non-recurrent motion of two-channel Markov additive diffusion in 3 dimensions the first passage statistics at long times do not display Poisson-like behaviour if none of the phases has a vanishing diffusion coefficient. This stands in stark contrast to the standard (one-channel) Markov diffusion counterpart. We also discuss the relevance of our results in the context of cellular signalling.},
  language  = {en}
}
@article{GodecMetzler2013,
  author    = {Godec, Aljaz and Metzler, Ralf},
  title     = {Finite-Time effects and ultraweak ergodicity breaking in superdiffusive dynamics},
  series = {Physical review letters},
  volume    = {110},
  journal   = {Physical review letters},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.110.020603},
  pages     = {5},
  year      = {2013},
  abstract  = {We study the ergodic properties of superdiffusive, spatiotemporally coupled Levy walk processes. For trajectories of finite duration, we reveal a distinct scatter of the scaling exponents of the time averaged mean squared displacement (delta x(2)) over bar around the ensemble value 3 - alpha (1 < alpha < 2) ranging from ballistic motion to subdiffusion, in strong contrast to the behavior of subdiffusive processes. In addition we find a significant dependence of the average of (delta x(2)) over bar over an ensemble of trajectories as a function of the finite measurement time. This so-called finite-time amplitude depression and the scatter of the scaling exponent is vital in the quantitative evaluation of superdiffusive processes. Comparing the long time average of the second moment with the ensemble mean squared displacement, these only differ by a constant factor, an ultraweak ergodicity breaking.},
  language  = {en}
}
@article{GodecSmithMerzel2013,
  author    = {Godec, Aljaz and Smith, Jeremy C. and Merzel, Franci},
  title     = {Soft Collective Fluctuations Governing Hydrophobic Association},
  series = {PHYSICAL REVIEW LETTERS},
  volume    = {111},
  journal   = {PHYSICAL REVIEW LETTERS},
  number    = {12},
  publisher = {AMER PHYSICAL SOC},
  address   = {COLLEGE PK},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.111.127801},
  pages     = {5},
  year      = {2013},
  abstract  = {The interaction between two associating hydrophobic particles has traditionally been explained in terms of the release of entropically frustrated hydration shell water molecules. However, this picture cannot account for the kinetics of hydrophobic association and is therefore not capable of providing a microscopic description of the hydrophobic interaction (HI). Here, Monte Carlo simulations of a pair of molecular-scale apolar solutes in aqueous solution reveal the critical role of collective fluctuations in the hydrogen bond (HB) network for the microscopic picture of the HI. The main contribution to the HI is the relaxation of solute-water translational correlations. The existence of a heat capacity maximum at the desolvation barrier is shown to arise from softening of non-HB water fluctuations and the relaxation of many-body correlations in the labile HB network. The microscopic event governing the kinetics of hydrophobic association has turned out to be a relatively large critical collective fluctuation in hydration water displacing a substantial fraction of HB clusters from the inner to the outer region of the first hydration shell.},
  language  = {en}
}
@article{GodecBauerMetzler2014,
  author    = {Godec, Aljaz and Bauer, Maximilian and Metzler, Ralf},
  title     = {Collective dynamics effect transient subdiffusion of inert tracers in flexible gel networks},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {16},
  journal   = {New journal of physics : the open-access journal for physics},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/16/9/092002},
  pages     = {13},
  year      = {2014},
  abstract  = {Based on extensive Brownian dynamics simulations we study the thermal motion of a tracer bead in a cross-linked, flexible gel in the limit when the tracer particle size is comparable to or even larger than the equilibrium mesh size of the gel. The analysis of long individual trajectories of the tracer demonstrates the existence of pronounced transient anomalous diffusion. From the time averaged mean squared displacement and the time averaged van Hove correlation functions we elucidate the many-body origin of the non-Brownian tracer bead dynamics. Our results shed new light onto the ongoing debate over the physical origin of steric tracer interactions with structured environments.},
  language  = {en}
}
@article{BauerGodecMetzler2014,
  author    = {Bauer, Maximilian and Godec, Aljaz and Metzler, Ralf},
  title     = {Diffusion of finite-size particles in two-dimensional channels with random wall configurations},
  series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  volume    = {16},
  journal   = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  number    = {13},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c3cp55160a},
  pages     = {6118 -- 6128},
  year      = {2014},
  abstract  = {Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda},
  language  = {en}
}
@article{GodecMetzler2015,
  author    = {Godec, Aljaz and Metzler, Ralf},
  title     = {Optimization and universality of Brownian search in a basic model of quenched heterogeneous media},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {91},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {5},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.91.052134},
  pages     = {17},
  year      = {2015},
  abstract  = {The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time ( MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.},
  language  = {en}
}
@article{KruesemannGodecMetzler2015,
  author    = {Kr{\"u}semann, Henning and Godec, Aljaz and Metzler, Ralf},
  title     = {Ageing first passage time density in continuous time random walks and quenched energy landscapes},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {48},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {28},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8113/48/28/285001},
  pages     = {20},
  year      = {2015},
  abstract  = {We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function Psi (t) similar or equal to t(-1-alpha) (0 <= alpha <= 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time t(a), the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs with 0 < alpha < 1 describe systems such as charge carriers in amorphous semiconducters, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1 < alpha < 2, for sufficiently long ta. We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the ageing CTRW results. With small bias or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape.},
  language  = {en}
}
@article{GodecChechkinBarkaietal.2014,
  author    = {Godec, Aljaz and Chechkin, Aleksei V. and Barkai, Eli and Kantz, Holger and Metzler, Ralf},
  title     = {Localisation and universal fluctuations in ultraslow diffusion processes},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {47},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {49},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8113/47/49/492002},
  pages     = {10},
  year      = {2014},
  abstract  = {We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) < x(2)(t)> similar or equal to log(gamma)t. Comparison of annealed (renewal) continuous time random walks (CTRWs) with logarithmic waiting time distribution psi(tau) similar or equal to 1/(tau log(1+gamma)tau) and Sinai diffusion in quenched random landscapes reveals striking similarities, despite the great differences in their physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time-averaged and ensemble-averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal, with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble-averaged MSD and time-averaged MSD.},
  language  = {en}
}
@article{KruesemannGodecMetzler2014,
  author    = {Kr{\"u}semann, Henning and Godec, Aljaz and Metzler, Ralf},
  title     = {First-passage statistics for aging diffusion in systems with annealed and quenched disorder},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {89},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {4},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.89.040101},
  pages     = {5},
  year      = {2014},
  abstract  = {Aging, the dependence of the dynamics of a physical process on the time t(a) since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of quantum dots to the tracer dispersion in living biological cells. Here we study the effects of aging on one of the most fundamental properties of a stochastic process, the first-passage dynamics. We find that for an aging continuous time random walk process, the scaling exponent of the density of first-passage times changes twice as the aging progresses and reveals an intermediate scaling regime. The first-passage dynamics depends on t(a) differently for intermediate and strong aging. Similar crossovers are obtained for the first-passage dynamics for a confined and driven particle. Comparison to the motion of an aged particle in the quenched trap model with a bias shows excellent agreement with our analytical findings. Our results demonstrate how first-passage measurements can be used to unravel the age t(a) of a physical system.},
  language  = {en}
}
@article{GodecMetzler2016,
  author    = {Godec, Aljaz and Metzler, Ralf},
  title     = {First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time},
  series = {Scientific reports},
  volume    = {6},
  journal   = {Scientific reports},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/srep20349},
  pages     = {11},
  year      = {2016},
  abstract  = {The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening series of new results focusing mostly on the so-called mean and global first passage time (MFPT and GFPT, respectively) of such processes. Here we push the understanding of first passage processes one step further. For a simple heterogeneous system we derive rigorously the complete distribution of first passage times (FPTs). Our results demonstrate that the typical FPT significantly differs from the MFPT, which corresponds to the long time behaviour of the FPT distribution. Conversely, the short time behaviour is shown to correspond to trajectories connecting directly from the initial value to the target. Remarkably, we reveal a previously overlooked third characteristic time scale of the first passage dynamics mirroring brief excursion away from the target.},
  language  = {en}
}
@article{SchwarzlGodecOshaninetal.2016,
  author    = {Schwarzl, Maria and Godec, Aljaz and Oshanin, Gleb and Metzler, Ralf},
  title     = {A single predator charging a herd of prey: effects of self volume and predator-prey decision-making},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {49},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8113/49/22/225601},
  pages     = {19},
  year      = {2016},
  abstract  = {We study the degree of success of a single predator hunting a herd of prey on a two-dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into directed escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornstein-Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by an effective Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant.},
  language  = {en}
}
@article{GodecMetzler2016,
  author    = {Godec, Aljaz and Metzler, Ralf},
  title     = {Universal Proximity Effect in Target Search Kinetics in the Few-Encounter Limit},
  series = {Physical review : X, Expanding access},
  volume    = {6},
  journal   = {Physical review : X, Expanding access},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2160-3308},
  doi       = {10.1103/PhysRevX.6.041037},
  pages     = {11},
  year      = {2016},
  abstract  = {When does a diffusing particle reach its target for the first time? This first-passage time (FPT) problem is central to the kinetics of molecular reactions in chemistry and molecular biology. Here, we explain the behavior of smooth FPT densities, for which all moments are finite, and demonstrate universal yet generally non-Poissonian long-time asymptotics for a broad variety of transport processes. While Poisson-like asymptotics arise generically in the presence of an effective repulsion in the immediate vicinity of the target, a time-scale separation between direct and reflected indirect trajectories gives rise to a universal proximity effect: Direct paths, heading more or less straight from the point of release to the target, become typical and focused, with a narrow spread of the corresponding first-passage times. Conversely, statistically dominant indirect paths exploring the entire system tend to be massively dissimilar. The initial distance to the target particularly impacts gene regulatory or competitive stochastic processes, for which few binding events often determine the regulatory outcome. The proximity effect is independent of details of the transport, highlighting the robust character of the FPT features uncovered here.},
  language  = {en}
}
@article{GodecMetzler2016,
  author    = {Godec, Aljaz and Metzler, Ralf},
  title     = {Active transport improves the precision of linear long distance molecular signalling},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {49},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8113/49/36/364001},
  pages     = {11},
  year      = {2016},
  abstract  = {Molecular signalling in living cells occurs at low copy numbers and is thereby inherently limited by the noise imposed by thermal diffusion. The precision at which biochemical receptors can count signalling molecules is intimately related to the noise correlation time. In addition to passive thermal diffusion, messenger RNA and vesicle-engulfed signalling molecules can transiently bind to molecular motors and are actively transported across biological cells. Active transport is most beneficial when trafficking occurs over large distances, for instance up to the order of 1 metre in neurons. Here we explain how intermittent active transport allows for faster equilibration upon a change in concentration triggered by biochemical stimuli. Moreover, we show how intermittent active excursions induce qualitative changes in the noise in effectively one-dimensional systems such as dendrites. Thereby they allow for significantly improved signalling precision in the sense of a smaller relative deviation in the concentration read-out by the receptor. On the basis of linear response theory we derive the exact mean field precision limit for counting actively transported molecules. We explain how intermittent active excursions disrupt the recurrence in the molecular motion, thereby facilitating improved signalling accuracy. Our results provide a deeper understanding of how recurrence affects molecular signalling precision in biological cells and novel medical-diagnostic devices.},
  language  = {en}
}
@article{SchwarzlGodecMetzler2017,
  author    = {Schwarzl, Maria and Godec, Aljaž and Metzler, Ralf},
  title     = {Quantifying non-ergodicity of anomalous diffusion with higher order moments},
  series = {Scientific reports},
  volume    = {7},
  journal   = {Scientific reports},
  publisher = {Macmillan Publishers Limited},
  address   = {London},
  doi       = {10.1038/s41598-017-03712-x},
  pages     = {18},
  year      = {2017},
  abstract  = {Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.},
  language  = {en}
}
@misc{SchwarzlGodecMetzler2017,
  author    = {Schwarzl, Maria and Godec, Aljaž and Metzler, Ralf},
  title     = {Quantifying non-ergodicity of anomalous diffusion with higher order moments},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-402109},
  pages     = {18},
  year      = {2017},
  abstract  = {Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.},
  language  = {en}
}
@article{SchwarzlGodecMetzler2017,
  author    = {Schwarzl, Maria and Godec, Aljaz and Metzler, Ralf},
  title     = {Quantifying non-ergodicity of anomalous diffusion with higher order moments},
  series = {Scientific reports},
  volume    = {7},
  journal   = {Scientific reports},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/s41598-017-03712-x},
  pages     = {18},
  year      = {2017},
  abstract  = {Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.},
  language  = {en}
}
@article{BauerGodecMetzler2014,
  author    = {Bauer, Maximilian and Godec, Aljaž and Metzler, Ralf},
  title     = {Diffusion of finite-size particles in two-dimensional channels with random wall configurations},
  series = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies},
  volume    = {16},
  journal   = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies},
  number    = {13},
  publisher = {RSC Publications},
  address   = {Cambridge},
  issn      = {1463-9084},
  doi       = {10.1039/C3CP55160A},
  pages     = {6118 -- 6128},
  year      = {2014},
  abstract  = {Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].},
  language  = {en}
}
@misc{BauerGodecMetzler2014,
  author    = {Bauer, Maximilian and Godec, Aljaž and Metzler, Ralf},
  title     = {Diffusion of finite-size particles in two-dimensional channels with random wall configurations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76199},
  year      = {2014},
  abstract  = {Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].},
  language  = {en}
}