1
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Ledesma-Durán A, Juárez-Valencia LH. Diffusion coefficients and MSD measurements on curved membranes and porous media. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:70. [PMID: 37578670 DOI: 10.1140/epje/s10189-023-00329-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 07/28/2023] [Indexed: 08/15/2023]
Abstract
We study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different approaches to surface diffusion based on the Laplace-Beltrami operator adapted to predict concentration along entire membranes, confined subdomains along surfaces, or within porous media. Our goal is to summarize, firstly, how diffusion in these systems results in different types of diffusion coefficients and mean square displacement measurements, and secondly, how these two factors are affected by the concavity of the surface, the shape of the possible barriers or obstacles that form the available domains, the sinuosity, tortuosity, and constrictions of the trajectories and even how the observation plane affects the measurements of the diffusion. In addition to presenting a critical and organized comparison between different notions of MSD, in this review, we test the correspondence between theoretical predictions and numerical simulations by performing finite element simulations and illustrate some situations where diffusion theory can be applied. We briefly reviewed computational schemes for understanding surface diffusion and finally, discussed how this work contributes to understanding the role of surface diffusion transport properties in porous media and their relationship to other transport processes.
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Affiliation(s)
- Aldo Ledesma-Durán
- Departmento de Matemáticas, Universidad Autónoma Metropolitana, CDMX, Mexico
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2
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Ballow A, Linton P, Priour DJ. Percolation through voids around toroidal inclusions. Phys Rev E 2023; 107:014902. [PMID: 36797924 DOI: 10.1103/physreve.107.014902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Accepted: 01/04/2023] [Indexed: 01/28/2023]
Abstract
In the case of media comprised of impermeable particles, fluid flows through voids around impenetrable grains. For sufficiently low concentrations of the latter, spaces around grains join to allow transport on macroscopic scales, whereas greater impenetrable inclusion densities disrupt void networks and block macroscopic fluid flow. A critical grain concentration ρ_{c} marks the percolation transition or phase boundary separating these two regimes. With a dynamical infiltration technique in which virtual tracer particles explore void spaces, we calculate critical grain concentrations for randomly placed interpenetrating impermeable toroidal inclusions; the latter consist of surfaces of revolution with circular and square cross sections. In this manner, we study continuum percolation transitions involving nonconvex grains. As the radius of revolution increases relative to the length scale of the torus cross section, the tori develop a central hole, a topological transition accompanied by a cusp in the critical porosity fraction for percolation. With a further increase in the radius of revolution, as constituent grains become more ringlike in appearance, we find that the critical porosity fraction converges to that of high-aspect-ratio cylindrical counterparts only for randomly oriented grains.
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Affiliation(s)
- A Ballow
- Department of Physics and Astronomy, Youngstown State University, Youngstown, Ohio 44555, USA
| | - P Linton
- Department of Physics and Astronomy, Youngstown State University, Youngstown, Ohio 44555, USA
| | - D J Priour
- Department of Physics and Astronomy, Youngstown State University, Youngstown, Ohio 44555, USA
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3
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Relaxation, temporal diffusion, and polarity of aromatic hydrocarbons in ionic liquid. APPLIED NANOSCIENCE 2022. [DOI: 10.1007/s13204-022-02696-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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4
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Torquato S. Diffusion spreadability as a probe of the microstructure of complex media across length scales. Phys Rev E 2021; 104:054102. [PMID: 34942710 DOI: 10.1103/physreve.104.054102] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2021] [Accepted: 10/15/2021] [Indexed: 11/07/2022]
Abstract
Understanding time-dependent diffusion processes in multiphase media is of great importance in physics, chemistry, materials science, petroleum engineering, and biology. Consider the time-dependent problem of mass transfer of a solute between two phases and assume that the solute is initially distributed in one phase (phase 2) and absent from the other (phase 1). We desire the fraction of total solute present in phase 1 as a function of time, S(t), which we call the spreadability, since it is a measure of the spreadability of diffusion information as a function of time. We derive exact direct-space formulas for S(t) in any Euclidean space dimension d in terms of the autocovariance function as well as corresponding Fourier representations of S(t) in terms of the spectral density, which are especially useful when scattering information is available experimentally or theoretically. These are singular results because they are rare examples of mass transport problems where exact solutions are possible. We derive closed-form general formulas for the short- and long-time behaviors of the spreadability in terms of crucial small- and large-scale microstructural information, respectively. The long-time behavior of S(t) enables one to distinguish the entire spectrum of microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the "excess" spreadability, S(∞)-S(t), decays to its long-time behavior exponentially faster than that of any nonhyperuniform two-phase medium, the "slowest" being antihyperuniform media. The stealthy hyperuniform class is characterized by an excess spreadability with the fastest decay rate among all translationally invariant microstructures. We obtain exact results for S(t) for a variety of specific ordered and disordered model microstructures across dimensions that span from hyperuniform to antihyperuniform media. Moreover, we establish a remarkable connection between the spreadability and an outstanding problem in discrete geometry, namely, microstructures with "fast" spreadabilities are also those that can be derived from efficient "coverings" of space. We also identify heretofore unnoticed, to our best knowledge, remarkable links between the spreadability S(t) and NMR pulsed field gradient spin-echo amplitude as well as diffusion MRI measurements. This investigation reveals that the time-dependent spreadability is a powerful, dynamic-based figure of merit to probe and classify the spectrum of possible microstructures of two-phase media across length scales.
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Affiliation(s)
- Salvatore Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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5
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Atamas N, Gavryushenko D, Yablochkova K, Lazarenko M, Taranyik G. Temperature and temporal heterogeneities of water dynamics in the physiological temperature range. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.117201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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6
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Charbonneau B, Charbonneau P, Hu Y, Yang Z. High-dimensional percolation criticality and hints of mean-field-like caging of the random Lorentz gas. Phys Rev E 2021; 104:024137. [PMID: 34525662 DOI: 10.1103/physreve.104.024137] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 06/22/2021] [Indexed: 11/07/2022]
Abstract
The random Lorentz gas (RLG) is a minimal model for transport in disordered media. Despite the broad relevance of the model, theoretical grasp over its properties remains weak. For instance, the scaling with dimension d of its localization transition at the void percolation threshold is not well controlled analytically nor computationally. A recent study [Biroli et al., Phys. Rev. E 103, L030104 (2021)2470-004510.1103/PhysRevE.103.L030104] of the caging behavior of the RLG motivated by the mean-field theory of glasses has uncovered physical inconsistencies in that scaling that heighten the need for guidance. Here we first extend analytical expectations for asymptotic high-d bounds on the void percolation threshold and then computationally evaluate both the threshold and its criticality in various d. In high-d systems, we observe that the standard percolation physics is complemented by a dynamical slowdown of the tracer dynamics reminiscent of mean-field caging. A simple modification of the RLG is found to bring the interplay between percolation and mean-field-like caging down to d=3.
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Affiliation(s)
- Benoit Charbonneau
- Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G3, Canada.,Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G3, Canada
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.,Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Yi Hu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Zhen Yang
- Department of Physics, Duke University, Durham, North Carolina 27708, USA.,Kuang Yaming Honors School, Nanjing University, Nanjing 210023, China
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7
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Klatt MA, Ziff RM, Torquato S. Critical pore radius and transport properties of disordered hard- and overlapping-sphere models. Phys Rev E 2021; 104:014127. [PMID: 34412300 DOI: 10.1103/physreve.104.014127] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Accepted: 06/29/2021] [Indexed: 02/01/2023]
Abstract
Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δ_{c}. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δ_{c} is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)10.1016/j.advwatres.2020.103565] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ^{2}〉, which is easier to determine than δ_{c}. Here, we compare δ_{c} to the second moment of the pore size 〈δ^{2}〉, and indeed confirm that, for all porosities and all models considered, δ_{c}^{2} is to a good approximation proportional to 〈δ^{2}〉. However, unlike 〈δ^{2}〉, the permeability estimate based on δ_{c}^{2} does not predict the correct ranking of k for our models. Thus, we confirm 〈δ^{2}〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.
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Affiliation(s)
- Michael A Klatt
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.,Institut für Theoretische Physik, FAU Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
| | - Robert M Ziff
- Center for the Study of Complex Systems and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Salvatore Torquato
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.,Department of Chemistry, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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8
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Biroli G, Charbonneau P, Hu Y, Ikeda H, Szamel G, Zamponi F. Mean-Field Caging in a Random Lorentz Gas. J Phys Chem B 2021; 125:6244-6254. [PMID: 34096720 DOI: 10.1021/acs.jpcb.1c02067] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, d → ∞ limit: the localization transition is then expected to be continuous for the former and discontinuous for the latter. As a putative resolution, we have recently suggested that, as d increases, the behavior of the RLG converges to the glassy description and that percolation physics is recovered thanks to finite-d perturbative and nonperturbative (instantonic) corrections [Biroli et al. Phys. Rev. E 2021, 103, L030104]. Here, we expand on the d → ∞ physics by considering a simpler static solution as well as the dynamical solution of the RLG. Comparing the 1/d correction of this solution with numerical results reveals that even perturbative corrections fall out of reach of existing theoretical descriptions. Comparing the dynamical solution with the mode-coupling theory (MCT) results further reveals that, although key quantitative features of MCT are far off the mark, it does properly capture the discontinuous nature of the d → ∞ RLG. These insights help chart a path toward a complete description of finite-dimensional glasses.
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Affiliation(s)
- Giulio Biroli
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States.,Department of Physics, Duke University, Durham, North Carolina 27708, United States
| | - Yi Hu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Harukuni Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, United States
| | - Francesco Zamponi
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
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9
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Atamas N, Yablochkova K, Lazarenko M. Microscopic dynamics and the dynamic heterogeneity of motion of polar molecules in ionic liquids. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.115900] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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10
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Zimmermann U, Löwen H, Kreuter C, Erbe A, Leiderer P, Smallenburg F. Negative resistance for colloids driven over two barriers in a microchannel. SOFT MATTER 2021; 17:516-522. [PMID: 33226041 DOI: 10.1039/d0sm01700k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
When considering the flow of currents through obstacles, one core expectation is that the total resistance of sequential single resistors is additive. While this rule is most commonly applied to electronic circuits, it also applies to other transport phenomena such as the flow of colloids or nanoparticles through channels containing multiple obstacles, as long as these obstacles are sufficiently far apart. Here we explore the breakdown of this additivity for fluids of repulsive colloids driven over two energetic barriers in a microchannel, using real-space microscopy experiments, particle-resolved simulations, and dynamical density functional theory. If the barrier separation is comparable to the particle correlation length, the resistance is highly non-additive, such that the resistance added by the second barrier can be significantly higher or lower than that of the first. Surprisingly, in some cases the second barrier can even add a negative resistance, such that two identical barriers are easier to cross than a single one. We explain this counterintuitive observation in terms of the structuring of particles trapped between the barriers.
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Affiliation(s)
- Urs Zimmermann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | | | - Artur Erbe
- Institut für Ionenstrahlphysik und Materialforschung, Helmholtz-Zentrum Dresden-Rossendorf, D-01328 Dresden, Germany
| | - Paul Leiderer
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
| | - Frank Smallenburg
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany and Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France.
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11
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Atamas NA, Lazarenko MM, Yablochkova KS, Taranyik G. Strongly diluted dimethyl-imidazolium chloride–alcohol solutions: solvents are structurally different but dynamic heterogeneities are similar. RSC Adv 2021; 11:37307-37316. [PMID: 35496433 PMCID: PMC9043748 DOI: 10.1039/d1ra05633f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 11/05/2021] [Indexed: 11/21/2022] Open
Abstract
Based on the analysis of dynamic properties of ionic liquid solutions, the descriptions of diffusion mechanisms are built for dimethylimidazolium chloride (dmim+/Cl−)–alcohol solute systems and the influence of the monohydric alcohols' molecular structure on their diffusion mechanisms in dmim+/Cl−–alcohol at T = 400 K by molecular dynamics simulations are studied. From the analysis of radial distribution functions, MSDs, velocity autocorrelation function, and autocorrelation functions of dispersion we found that the motion of all components in IL dmim+/Cl−–alcohol (ethanol, propanol) systems at T = 400 K occurs in the sub-diffuse regime and that the dynamics of the dmim+/Cl−–alcohol (ethanol, propanol) systems is heterogeneous. The increase of the alkyl chain length of the alcohol molecule does not affect the motion of the ionic liquid components; instead, it increases the characteristic times describing the model representation of alcohol molecule diffusion at short and medium times, without affecting diffusion mechanisms. The increase of the alkyl chain length of the alcohol molecule does not affect the motion of the ionic liquid components.![]()
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Affiliation(s)
- N. A. Atamas
- Taras Shevchenko National University of Kyiv, 64, Volodymyrska Street, Kyiv, UA 01601, Ukraine
| | - M. M. Lazarenko
- Taras Shevchenko National University of Kyiv, 64, Volodymyrska Street, Kyiv, UA 01601, Ukraine
| | - K. S. Yablochkova
- Taras Shevchenko National University of Kyiv, 64, Volodymyrska Street, Kyiv, UA 01601, Ukraine
| | - G. Taranyik
- International European University, 42V, Akademika Hlushkova Ave, Kyiv, Ukraine
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12
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Ebrahimi Viand R, Höfling F, Klein R, Delle Site L. Theory and simulation of open systems out of equilibrium. J Chem Phys 2020; 153:101102. [PMID: 32933284 DOI: 10.1063/5.0014065] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution simulation molecular dynamics technique. We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with the results obtained from the simulation of a larger locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations.
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Affiliation(s)
- R Ebrahimi Viand
- Freie Universität Berlin, Institute of Mathematics, Arnimallee 6, 14195 Berlin, Germany
| | - F Höfling
- Freie Universität Berlin, Institute of Mathematics, Arnimallee 6, 14195 Berlin, Germany
| | - R Klein
- Freie Universität Berlin, Institute of Mathematics, Arnimallee 6, 14195 Berlin, Germany
| | - L Delle Site
- Freie Universität Berlin, Institute of Mathematics, Arnimallee 6, 14195 Berlin, Germany
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13
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Abstract
To know how liquid matter moves through a crowded medium due to the action of a force constitutes currently a problem of great practical importance, present in cases as diverse as the transport of particles through a cell membrane and through a particulate porous medium. To calculate the mass flow through the system, we present an approach that emulates the texture of the medium by using entropic barriers that the particles must overcome in order to move. The model reproduces the scaling behavior of the velocity with the force found in many systems in order to show how the scaling exponent depends on the micro-structure of the medium. Our model offers a new perspective that is able to characterize the flow of matter through the medium and may be useful in studies of nano-fluids, oil recovery, soil drainage, tissue engineering, and drug delivery.
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Affiliation(s)
- A Arango-Restrepo
- Departament de Física de la Matéria Condensada, Facultat de Física, Universitat de Barcelona, Barcelona, Spain
| | - J M Rubi
- Departament de Física de la Matéria Condensada, Facultat de Física, Universitat de Barcelona, Barcelona, Spain
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14
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Voigtmann T, Siebenbürger M, Amann CP, Egelhaaf SU, Fritschi S, Krüger M, Laurati M, Mutch KJ, Samwer KH. Rheology of colloidal and metallic glass formers. Colloid Polym Sci 2020. [DOI: 10.1007/s00396-020-04654-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
AbstractColloidal hard-sphere suspensions are convenient experimental models to understand soft matter, and also by analogy the structural-relaxation behavior of atomic or small-molecular fluids. We discuss this analogy for the flow and deformation behavior close to the glass transition. Based on a mapping of temperature to effective hard-sphere packing, the stress–strain curves of typical bulk metallic glass formers can be quantitatively compared with those of hard-sphere suspensions. Experiments on colloids give access to the microscopic structure under deformation on a single-particle level, providing insight into the yielding mechanisms that are likely also relevant for metallic glasses. We discuss the influence of higher-order angular signals in connection with non-affine particle rearrangements close to yielding. The results are qualitatively explained on the basis of the mode-coupling theory. We further illustrate the analogy of pre-strain dependence of the linear-elastic moduli using data on PS-PNiPAM suspensions.
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15
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Dibak M, Fröhner C, Noé F, Höfling F. Diffusion-influenced reaction rates in the presence of pair interactions. J Chem Phys 2019; 151:164105. [PMID: 31675872 DOI: 10.1063/1.5124728] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi's volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction-diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction-diffusion equation in the steady state and derive semi-analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion-limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions.
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Affiliation(s)
- Manuel Dibak
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
| | - Christoph Fröhner
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
| | - Felix Höfling
- Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany
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16
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Petersen CF, Franosch T. Anomalous transport in the soft-sphere Lorentz model. SOFT MATTER 2019; 15:3906-3913. [PMID: 30998231 DOI: 10.1039/c9sm00442d] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The sensitivity of anomalous transport in crowded media to the form of the inter-particle interactions is investigated through computer simulations. We extend the highly simplified Lorentz model towards realistic natural systems by modeling the interactions between the tracer and the obstacles with a smooth potential. We find that the anomalous transport at the critical point happens to be governed by the same universal exponent as for hard exclusion interactions, although the mechanism of how narrow channels are probed is rather different. The scaling behavior of simulations close to the critical point confirm this exponent. Our result indicates that the simple Lorentz model may be applicable to describing the fundamental properties of long-range transport in real crowded environments.
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Affiliation(s)
- Charlotte F Petersen
- Institut für Theoretische Physik, Leopold-Franzens-Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria.
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17
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Poling-Skutvik R, Roberts RC, Slim AH, Narayanan S, Krishnamoorti R, Palmer JC, Conrad JC. Structure Dominates Localization of Tracers within Aging Nanoparticle Glasses. J Phys Chem Lett 2019; 10:1784-1789. [PMID: 30916569 DOI: 10.1021/acs.jpclett.9b00309] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We investigate the transport and localization of tracer probes in a glassy matrix as a function of relative size using dynamic X-ray scattering experiments and molecular dynamics simulations. The quiescent relaxations of tracer particles evolve with increasing waiting time, tw. The corresponding relaxation times increase exponentially at small tw and then transition to a power-law behavior at longer tw. As tracer size decreases, the aging behavior weakens and the particles become less localized within the matrix until they delocalize at a critical size ratio δ0 ≈ 0.38. Localization does not vary with sample age even as the relaxations slow by approximately an order of magnitude, suggesting that matrix structure controls tracer localization.
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Affiliation(s)
- Ryan Poling-Skutvik
- Department of Chemical and Biomolecular Engineering , University of Houston , Houston , Texas 77204-4004 , United States
| | - Ryan C Roberts
- Department of Chemical and Biomolecular Engineering , University of Houston , Houston , Texas 77204-4004 , United States
| | - Ali H Slim
- Department of Chemical and Biomolecular Engineering , University of Houston , Houston , Texas 77204-4004 , United States
| | - Suresh Narayanan
- Advanced Photon Source , Argonne National Laboratory , Argonne , Illinois 60439 , United States
| | - Ramanan Krishnamoorti
- Department of Chemical and Biomolecular Engineering , University of Houston , Houston , Texas 77204-4004 , United States
| | - Jeremy C Palmer
- Department of Chemical and Biomolecular Engineering , University of Houston , Houston , Texas 77204-4004 , United States
| | - Jacinta C Conrad
- Department of Chemical and Biomolecular Engineering , University of Houston , Houston , Texas 77204-4004 , United States
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18
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Gniewek P, Hallatschek O. Fluid flow through packings of elastic shells. Phys Rev E 2019; 99:023103. [PMID: 30934257 PMCID: PMC6542697 DOI: 10.1103/physreve.99.023103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2018] [Indexed: 11/07/2022]
Abstract
Fluid transport in porous materials is commonly studied in geological samples (soil, sediments, etc.) or idealized systems, but the fluid flow through compacted granular materials, consisting of substantially strained granules, remains relatively unexplored. As a step toward filling this gap, we study a model of liquid transport in packings of deformable elastic shells using finite-element and lattice-Boltzmann methods. We find that the fluid flow abruptly vanishes as the porosity of the material falls below a critical value, and the flow obstruction exhibits features of a percolation transition. We further show that the fluid flow can be captured by a simplified permeability model in which the complex porous material is replaced by a collection of disordered capillaries, which are distributed and shaped by the percolation transition. To that end, we numerically explore the divergence of hydraulic tortuosity τ_{H} and the decrease of a hydraulic radius R_{h} as the percolation threshold is approached. We interpret our results in terms of scaling predictions derived from the percolation theory applied to random packings of spheres.
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Affiliation(s)
- Pawel Gniewek
- Biophysics Graduate Group, University of California, Berkeley, USA
| | - Oskar Hallatschek
- Departments of Physics and Integrative Biology, University of California, Berkeley, USA
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19
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Non-universality of the dynamic exponent in two-dimensional random media. Sci Rep 2019; 9:251. [PMID: 30670711 PMCID: PMC6342955 DOI: 10.1038/s41598-018-36236-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2018] [Accepted: 11/12/2018] [Indexed: 11/09/2022] Open
Abstract
The diffusion of solutes in two-dimensional random media is important in diverse physical situations including the dynamics of proteins in crowded cell membranes and the adsorption on nano-structured substrates. It has generally been thought that the diffusion constant, D, should display universal behavior near the percolation threshold, i.e., D ~ (ϕ − ϕc)μ, where ϕ is the area fraction of the matrix, ϕc is the value of ϕ at the percolation threshold, and μ is the dynamic exponent. The universality of μ is important because it implies that very different processes, such as protein diffusion in membranes and the electrical conductivity in two-dimensional networks, obey similar underlying physical principles. In this work we demonstrate, using computer simulations on a model system, that the exponent μ is not universal, but depends on the microscopic nature of the dynamics. We consider a hard disc that moves via random walk in a matrix of fixed hard discs and show that μ depends on the maximum possible displacement Δ of the mobile hard disc, ranging from 1.31 at Δ ≤ 0.1 to 2.06 for relatively large values of Δ. We also show that this behavior arises from a power-law singularity in the distribution of transition rates due to a failure of the local equilibrium approximation. The non-universal value of μ obeys the prediction of the renormalization group theory. Our simulations do not, however, exclude the possibility that the non-universal values of μ might be a crossover between two different limiting values at very large and small values of Δ. The results allow one to rationalize experiments on diffusion in two-dimensional systems.
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20
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Chepizhko O, Franosch T. Ideal circle microswimmers in crowded media. SOFT MATTER 2019; 15:452-461. [PMID: 30574653 PMCID: PMC6336149 DOI: 10.1039/c8sm02030b] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2018] [Accepted: 12/08/2018] [Indexed: 05/26/2023]
Abstract
Microswimmers are exposed in nature to crowded environments and their transport properties depend in a subtle way on the interaction with obstacles. Here, we investigate a model for a single ideal circle swimmer exploring a two-dimensional disordered array of impenetrable obstacles. The microswimmer moves on circular orbits in the freely accessible space and follows the surface of an obstacle for a certain time upon collision. Depending on the obstacle density and the radius of the circular orbits, the microswimmer displays either long-range transport or is localized in a finite region. We show that there are transitions from two localized states to a diffusive state each driven by an underlying static percolation transition. We determine the non-equilibrium state diagram and calculate the mean-square displacements and diffusivities by computer simulations. Close to the transition lines transport becomes subdiffusive which is rationalized as a dynamic critical phenomenon.
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Affiliation(s)
- Oleksandr Chepizhko
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria.
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria.
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21
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Priour DJ, McGuigan NJ. Percolation through Voids around Randomly Oriented Polyhedra and Axially Symmetric Grains. PHYSICAL REVIEW LETTERS 2018; 121:225701. [PMID: 30547614 DOI: 10.1103/physrevlett.121.225701] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2018] [Revised: 07/10/2018] [Indexed: 06/09/2023]
Abstract
Porous materials made up of impermeable grains constrain fluid flow to voids around the impenetrable inclusions. A percolation transition marks the boundary between densities of grains permitting bulk transport and concentrations blocking traversal on macroscopic scales. With dynamical infiltration of void spaces using virtual tracer particles, we treat inclusion geometries exactly. We calculate the critical number density per volume ρ_{c} for a variety of axially symmetric shapes and faceted solids with the former including cylinders, ellipsoids, cones, and tablet shaped grains from highly oblate (platelike) to highly prolate (needlelike) extremes. For the latter, results suggest a common asymptotic value identical to the counterpart for aligned cylindrical grains. We find percolation thresholds for each of the five platonic solids (i.e., tetrahedra, cubes, octahedra, dodecahedra, and icosahedra) as well as truncated icosahedra. For each polyhedron type, we consider aligned and randomly oriented grains, finding distinct percolation thresholds for the former versus the latter only for cubes. The anomalous diffusion exponents we find differ from those of the universality class for discrete models on 3D lattices.
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Affiliation(s)
- D J Priour
- Department of Physics & Astronomy, Youngstown State University, Youngstown, Ohio 44555, USA
| | - N J McGuigan
- Department of Physics & Astronomy, Youngstown State University, Youngstown, Ohio 44555, USA
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22
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Mandal S, Franosch T, Voigtmann T. Glassy relaxation slows down by increasing mobility. SOFT MATTER 2018; 14:9153-9158. [PMID: 30421769 DOI: 10.1039/c8sm01581c] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We find a striking trend reversal in the relaxation dynamics of mixtures with strong dynamical asymmetry. Simulations by both Brownian and Newtonian dynamics reveal that in mixtures of fast and slow hard spheres, above a critical density, the dynamics becomes slower upon increasing the mobility of the fast particles. Below that density, the same increase in mobility speeds up the dynamics. The critical density itself can be identified with the glass transition of the mode-coupling theory that does not depend on the dynamical asymmetry. The asymptotic dynamics close to the critical density is universal, but strong pre-asymptotic effects prevail in particular when the dynamical asymmetry also involves size asymmetry. Our observations reconcile earlier findings, where a strong dependence on kinetic parameters was found for the glassy dynamics, with the paradigm that the glass transition is determined by the properties of configuration space alone.
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Affiliation(s)
- Suvendu Mandal
- Institut für Theoretische Physik, Universität Innsbruck, Austria
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23
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Grebenkov DS, Tupikina L. Heterogeneous continuous-time random walks. Phys Rev E 2018; 97:012148. [PMID: 29448342 DOI: 10.1103/physreve.97.012148] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2017] [Indexed: 11/07/2022]
Abstract
We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.
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Affiliation(s)
- Denis S Grebenkov
- Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, 91128 Palaiseau, France.,Interdisciplinary Scientific Center Poncelet (ISCP), (UMI 2615 CNRS/IUM/IITP RAS/Steklov MI RAS/Skoltech/HSE), Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia
| | - Liubov Tupikina
- Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, 91128 Palaiseau, France
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24
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Zarfaty L, Peletskyi A, Fouxon I, Denisov S, Barkai E. Dispersion of particles in an infinite-horizon Lorentz gas. Phys Rev E 2018; 98:010101. [PMID: 30110737 DOI: 10.1103/physreve.98.010101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2017] [Indexed: 06/08/2023]
Abstract
We consider a two-dimensional Lorentz gas with infinite horizon. This paradigmatic model consists of pointlike particles undergoing elastic collisions with fixed scatterers arranged on a periodic lattice. It was rigorously shown that when t→∞, the distribution of particles is Gaussian. However, the convergence to this limit is ultraslow, hence it is practically unattainable. Here, we obtain an analytical solution for the Lorentz gas' kinetics on physically relevant timescales, and find that the density in its far tails decays as a universal power law of exponent -3. We also show that the arrangement of scatterers is imprinted in the shape of the distribution.
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Affiliation(s)
- Lior Zarfaty
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Alexander Peletskyi
- Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg Germany
- Sumy State University, Rimsky-Korsakov Street 2, 40007 Sumy, Ukraine
| | - Itzhak Fouxon
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Sergey Denisov
- Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg Germany
- Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Gagarina Avenue 23, Nizhny Novgorod 603950, Russia
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
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25
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Schilling T, Voigtmann T. Clearing out a maze: A model of chemotactic motion in porous media. J Chem Phys 2018; 147:214905. [PMID: 29221379 DOI: 10.1063/1.4999485] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
We study the anomalous dynamics of a biased "hungry" (or "greedy") random walk on a percolating cluster. The model mimics chemotaxis in a porous medium: In close resemblance to the 1980s arcade game PAC-MAN®, the hungry random walker consumes food, which is initially distributed in the maze, and biases its movement towards food-filled sites. We observe that the mean-squared displacement of the process follows a power law with an exponent that is different from previously known exponents describing passive or active microswimmer dynamics. The change in dynamics is well described by a dynamical exponent that depends continuously on the propensity to move towards food. It results in slower differential growth when compared to the unbiased random walk.
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Affiliation(s)
- Tanja Schilling
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, 79104 Freiburg, Germany
| | - Thomas Voigtmann
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany
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26
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Zierenberg J, Fricke N, Marenz M, Spitzner FP, Blavatska V, Janke W. Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects. Phys Rev E 2018; 96:062125. [PMID: 29347311 DOI: 10.1103/physreve.96.062125] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2017] [Indexed: 11/07/2022]
Abstract
We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to such system details. By contrast, we verify that the fractal dimension d_{f} is a universal quantity and unaffected by the choice of metric. We also show that for weak correlations, its value coincides with that for the uncorrelated system. In two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength, approaching d_{f}→2. The onset of this change does not seem to be determined by the extended Harris criterion.
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Affiliation(s)
- Johannes Zierenberg
- Institut für Theoretische Physik, Universität Leipzig Postfach 100 920, 04009 Leipzig, Germany.,Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L^{4}), Postfach 100 920, 04009 Leipzig, Germany.,Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany.,Bernstein Center for Computational Neuroscience, Am Fassberg 17, 37077 Göttingen, Germany
| | - Niklas Fricke
- Institut für Theoretische Physik, Universität Leipzig Postfach 100 920, 04009 Leipzig, Germany.,Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L^{4}), Postfach 100 920, 04009 Leipzig, Germany
| | - Martin Marenz
- Institut für Theoretische Physik, Universität Leipzig Postfach 100 920, 04009 Leipzig, Germany.,Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L^{4}), Postfach 100 920, 04009 Leipzig, Germany
| | - F P Spitzner
- Institut für Theoretische Physik, Universität Leipzig Postfach 100 920, 04009 Leipzig, Germany
| | - Viktoria Blavatska
- Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L^{4}), Postfach 100 920, 04009 Leipzig, Germany.,Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig Postfach 100 920, 04009 Leipzig, Germany.,Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L^{4}), Postfach 100 920, 04009 Leipzig, Germany
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27
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Leitmann S, Höfling F, Franosch T. Dynamically crowded solutions of infinitely thin Brownian needles. Phys Rev E 2018; 96:012118. [PMID: 29347251 DOI: 10.1103/physreve.96.012118] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Indexed: 11/07/2022]
Abstract
We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is essentially restricted to a one-dimensional sliding in a confining tube composed of neighboring needles. From the density-dependent behavior of the orientational and translational diffusion, we extract the long-time transport coefficients and the geometry of the confining tube. The sliding motion within the tube becomes visible in the non-Gaussian parameter of the translational motion as an extended plateau at intermediate times and in the intermediate scattering function as an algebraic decay. This transient dynamic arrest is also corroborated by the local exponent of the mean-square displacements perpendicular to the needle axis. Moreover, the probability distribution of the displacements perpendicular to the needle becomes strongly non-Gaussian; rather, it displays an exponential distribution for large displacements. On the other hand, based on the analysis of higher-order correlations of the orientation we find that the rotational motion becomes diffusive again for strong confinement. At coarse-grained time and length scales, the spatiotemporal dynamics of the needle for the high entanglement is captured by a single freely diffusing phantom needle with long-time transport coefficients obtained from the needle in solution. The time-dependent dynamics of the phantom needle is also assessed analytically in terms of spheroidal wave functions. The dynamic behavior of the needle in solution is found to be identical to needle Lorentz systems, where a tracer needle explores a quenched disordered array of other needles.
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Affiliation(s)
- Sebastian Leitmann
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Felix Höfling
- Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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28
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Konincks T, Krakoviack V. Dynamics of fluids in quenched-random potential energy landscapes: a mode-coupling theory approach. SOFT MATTER 2017; 13:5283-5297. [PMID: 28677713 DOI: 10.1039/c7sm00984d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Motivated by a number of recent experimental and computational studies of the dynamics of fluids plunged in quenched-disordered external fields, we report on a theoretical investigation of this topic within the framework of the mode-coupling theory, based on the simple model of the hard-sphere fluid in a Gaussian random field. The possible dynamical arrest scenarios driven by an increase of the disorder strength and/or of the fluid density are mapped, and the corresponding evolutions of time-dependent quantities typically used for the characterization of anomalous self-diffusion are illustrated with detailed computations. Overall, a fairly reasonable picture of the dynamics of the system at hand is outlined, which in particular involves a non-monotonicity of the self-diffusion coefficient with fluid density at fixed disorder strength, in agreement with experiments. The disorder correlation length is shown to have a strong influence on the latter feature.
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Affiliation(s)
- Thomas Konincks
- Univ Lyon, ENS de Lyon, CNRS UMR 5182, Université Claude Bernard Lyon 1, Laboratoire de Chimie, F-69342, Lyon, France.
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29
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Zeitz M, Wolff K, Stark H. Active Brownian particles moving in a random Lorentz gas. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:23. [PMID: 28236113 DOI: 10.1140/epje/i2017-11510-0] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2016] [Accepted: 02/02/2017] [Indexed: 06/06/2023]
Abstract
Biological microswimmers often inhabit a porous or crowded environment such as soil. In order to understand how such a complex environment influences their spreading, we numerically study non-interacting active Brownian particles (ABPs) in a two-dimensional random Lorentz gas. Close to the percolation transition in the Lorentz gas, they perform the same subdiffusive motion as ballistic and diffusive particles. However, due to their persistent motion they reach their long-time dynamics faster than passive particles and also show superdiffusive motion at intermediate times. While above the critical obstacle density [Formula: see text] the ABPs are trapped, their long-time diffusion below [Formula: see text] is strongly influenced by the propulsion speed v0. With increasing v0, ABPs are stuck at the obstacles for longer times. Thus, for large propulsion speed, the long-time diffusion constant decreases more strongly in a denser obstacle environment than for passive particles. This agrees with the behavior of an effective swimming velocity and persistence time, which we extract from the velocity autocorrelation function.
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Affiliation(s)
- Maria Zeitz
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany.
| | - Katrin Wolff
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany
| | - Holger Stark
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany
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