Diffusion in the Lorentz Gas

Dettmann, Carl P.

doi:10.1088/0253-6102/62/4/10

Cited by 57 publications

(63 citation statements)

References 233 publications

(397 reference statements)

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“…The resulting relative diffusivities D/D 0 decrease as void fraction y is decreased and confinement parameters z and l are increased, as shown in Fig. 23,24 In this family of models, diffusive-like motion of a single tracer particle arises from its interactions with an array of scatterers. Initially, the decrease in relative diffusivity is nearly linear with y and z, as also reported in our earlier study; 14 particles experiencing the strongest confinements, however, exhibit diffusivities that are somewhat larger than those expected by extrapolating from low-to-moderate confinements.…”

Section: View Article Onlinementioning

confidence: 82%

“…In our earlier study of the diffusion of modestly confined nanoparticles, in media with effective void fractions ranging from 0.76 to 0.99, the diffusive dynamics of the nanoparticles slowed with confinement and the distribution of displacements became increasingly non-Gaussian. 21 Additionally, statistical models such as the Lorentz gas [22][23][24] (a single tracer diffusing in an array of scatterers) can exhibit slowed and/or anomalous diffusion arising from the interplay of dynamics and geometry. 19 The widespread occurrence of Fickian but non-Gaussian diffusion suggests a general physical origin of these dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Diffusive dynamics of nanoparticles in ultra-confined media

Jacob

Retterer

et al. 2015

Soft Matter

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Differential dynamic microscopy (DDM) was used to investigate the diffusive dynamics of nanoparticles of diameter 200-400 nm that were strongly confined in a periodic square array of cylindrical nanoposts. The minimum distance between posts was 1.3-5 times the diameter of the nanoparticles. The image structure functions obtained from the DDM analysis were isotropic and could be fit by a stretched exponential function. The relaxation time scaled diffusively across the range of wave vectors studied, and the corresponding scalar diffusivities decreased monotonically with increased confinement. The decrease in diffusivity could be described by models for hindered diffusion that accounted for steric restrictions and hydrodynamic interactions. The stretching exponent decreased linearly as the nanoparticles were increasingly confined by the posts. Together, these results are consistent with a picture in which strongly confined nanoparticles experience a heterogeneous spatial environment arising from hydrodynamics and volume exclusion on time scales comparable to cage escape, leading to multiple relaxation processes and Fickian but non-Gaussian diffusive dynamics.

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Section: View Article Onlinementioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Diffusive dynamics of nanoparticles in ultra-confined media

Jacob

Retterer

et al. 2015

Soft Matter

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“…(1) are known to occur when the free paths are distributed as in Eq. (17). In a separate publication, we will show that the narrow corridor limit of the infinite-horizon Lorentz gas is a fertile study ground for a class of such walks, where both normal and anomalous diffusion coexist.…”

Section: Discussionmentioning

confidence: 92%

“…4 for ρ = 0.14, differ from Eqs. (17) and (18) by a numerical factor which is O(1 − 2ρ). In the narrow corridor limit, transitions between cells are overwhelmingly dominated by segments of unit lengths; ballistic segments are thus infrequent.…”

Section: B Time Span Of Measurementsmentioning

confidence: 99%

Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards

et al. 2014

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We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of superdiffusion, in the sense that there is a logarithmic correction to the linear growth in time of the mean-squared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time range accessible to numerical simulations. We compare our simulations to analytical results for the variance of the anomalously rescaled limiting normal distributions.

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“…These aspects of the physics of heterogeneous media are also minimally captured by the random variant of the Lorentz gas (RLG), which since its introduction as a model for electron transport in metals has become a staple of statistical mechanics and mathematical physics [4,5]. In the RLG, a spherical particle of radius σ (the tracer) elastically bounces off Poisson-distributed point obstacles (scatterers).…”

Section: Introductionmentioning

confidence: 99%

Dimensional study of the dynamical arrest in a random Lorentz gas

Jin

Charbonneau

2015

Phys. Rev. E

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The random Lorentz gas (RLG) is a minimal model for transport in heterogeneous media. Upon increasing the obstacle density, it exhibits a growing subdiffusive transport regime and then a dynamical arrest. Here, we study the dimensional dependence of the dynamical arrest, which can be mapped onto the void percolation transition for Poisson-distributed point obstacles. We numerically determine the arrest in dimensions d = 2-6. Comparison of the results with standard mode-coupling theory reveals that the dynamical theory prediction grows increasingly worse with d. In an effort to clarify the origin of this discrepancy, we relate the dynamical arrest in the RLG to the dynamic glass transition of the infinite-range Mari-Kurchan-model glass former. Through a mixed static and dynamical analysis, we then extract an improved dimensional scaling form as well as a geometrical upper bound for the arrest. The results suggest that understanding the asymptotic behavior of the random Lorentz gas may be key to surmounting fundamental difficulties with the mode-coupling theory of glasses.

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Diffusion in the Lorentz Gas

Cited by 57 publications

References 233 publications

Diffusive dynamics of nanoparticles in ultra-confined media

Diffusive dynamics of nanoparticles in ultra-confined media

Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards

Dimensional study of the dynamical arrest in a random Lorentz gas

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