1
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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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2
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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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3
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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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4
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Biroli G, Charbonneau P, Corwin EI, Hu Y, Ikeda H, Szamel G, Zamponi F. Interplay between percolation and glassiness in the random Lorentz gas. Phys Rev E 2021; 103:L030104. [PMID: 33862778 DOI: 10.1103/physreve.103.l030104] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Accepted: 02/23/2021] [Indexed: 11/07/2022]
Abstract
The random Lorentz gas (RLG) is a minimal model of transport in heterogeneous media that exhibits a continuous localization transition controlled by void space percolation. The RLG also provides a toy model of particle caging, which is known to be relevant for describing the discontinuous dynamical transition of glasses. In order to clarify the interplay between the seemingly incompatible percolation and caging descriptions of the RLG, we consider its exact mean-field solution in the infinite-dimensional d→∞ limit and perform numerics in d=2...20. We find that for sufficiently high d the mean-field caging transition precedes and prevents the percolation transition, which only happens on timescales diverging with d. We further show that activated processes related to rare cage escapes destroy the glass transition in finite dimensions, leading to a rich interplay between glassiness and percolation physics. This advance suggests that the RLG can be used as a toy model to develop a first-principle description of particle hopping in structural 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, USA.,Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Eric I Corwin
- Department of Physics and Material Science Institute, University of Oregon, Eugene, Oregon 97403, USA
| | - Yi Hu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - 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, USA
| | - 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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5
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He B, Ye A, Chi S, Mi P, Ran Y, Zhang L, Zou X, Pu B, Zhao Q, Zou Z, Wang D, Zhang W, Zhao J, Avdeev M, Shi S. CAVD, towards better characterization of void space for ionic transport analysis. Sci Data 2020; 7:153. [PMID: 32444597 PMCID: PMC7244509 DOI: 10.1038/s41597-020-0491-x] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2020] [Accepted: 04/15/2020] [Indexed: 12/03/2022] Open
Abstract
Geometric crystal structure analysis using three-dimensional Voronoi tessellation provides intuitive insights into the ionic transport behavior of metal-ion electrode materials or solid electrolytes by mapping the void space in a framework onto a network. The existing tools typically consider only the local voids by mapping them with Voronoi polyhedra vertices and then define the mobile ions pathways using the Voronoi edges connecting these vertices. We show that in some structures mobile ions are located on Voronoi polyhedra faces and thus cannot be located by a standard approach. To address this deficiency, we extend the method to include Voronoi faces in the constructed network. This method has been implemented in the CAVD python package. Its effectiveness is demonstrated by 99% recovery rate for the lattice sites of mobile ions in 6,955 Li-, Na-, Mg- and Al-containing ionic compounds extracted from the Inorganic Crystal Structure Database. In addition, various quantitative descriptors of the network can be used to identify and rank the materials and further used in materials databases for machine learning.
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Affiliation(s)
- Bing He
- School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China
| | - Anjiang Ye
- School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China
| | - Shuting Chi
- School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China
| | - Penghui Mi
- School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China
| | - Yunbing Ran
- State Key Laboratory of Advanced Special Steel, School of Materials Science and Engineering, Shanghai University, Shanghai, 200444, China
| | - Liwen Zhang
- State Key Laboratory of Advanced Special Steel, School of Materials Science and Engineering, Shanghai University, Shanghai, 200444, China
| | - Xinxin Zou
- School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China
| | - Bowei Pu
- State Key Laboratory of Advanced Special Steel, School of Materials Science and Engineering, Shanghai University, Shanghai, 200444, China
| | - Qian Zhao
- Materials Genome Institute, Shanghai University, Shanghai, 200444, China
| | - Zheyi Zou
- State Key Laboratory of Advanced Special Steel, School of Materials Science and Engineering, Shanghai University, Shanghai, 200444, China
| | - Da Wang
- State Key Laboratory of Advanced Special Steel, School of Materials Science and Engineering, Shanghai University, Shanghai, 200444, China
| | - Wenqing Zhang
- Department of Physics and Shenzhen Institute for Quantum Science & Technology, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Jingtai Zhao
- School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin, 541004, China
| | - Maxim Avdeev
- Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC, NSW, 2232, Australia
- School of Chemistry, The University of Sydney, Sydney, 2006, Australia
| | - Siqi Shi
- State Key Laboratory of Advanced Special Steel, School of Materials Science and Engineering, Shanghai University, Shanghai, 200444, China.
- Materials Genome Institute, Shanghai University, Shanghai, 200444, China.
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6
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Ramirez LS, Centres PM, Ramirez-Pastor AJ. Percolation phase transition by removal of k^{2}-mers from fully occupied lattices. Phys Rev E 2019; 100:032105. [PMID: 31640014 DOI: 10.1103/physreve.100.032105] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2019] [Indexed: 11/07/2022]
Abstract
Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse site percolation by the removal of k×k square tiles (k^{2}-mers) from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by occupied sites. Then the system is diluted by removing k^{2}-mers of occupied sites from the lattice following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be removed due to the absence of occupied sites clusters of appropriate size and shape. The central idea of this paper is based on finding the maximum concentration of occupied sites, p_{c,k}, for which the connectivity disappears. This particular value of the concentration is called the inverse percolation threshold and determines a well-defined geometrical phase transition in the system. The results obtained for p_{c,k} show that the inverse percolation threshold is a decreasing function of k in the range 1≤k≤4. For k≥5, all jammed configurations are percolating states, and consequently, there is no nonpercolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed sites is reached. The jamming exponent ν_{j} was measured, being ν_{j}=1 regardless of the size k considered. In addition, the accurate determination of the critical exponents ν, β, and γ reveals that the percolation phase transition involved in the system, which occurs for k varying between one and four, has the same universality class as the standard percolation problem.
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Affiliation(s)
- L S Ramirez
- Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW, San Luis, Argentina
| | - P M Centres
- Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW, San Luis, Argentina
| | - A J Ramirez-Pastor
- Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, D5700HHW, San Luis, Argentina
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7
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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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8
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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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9
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Treado JD, Mei Z, Regan L, O’Hern CS. Void distributions reveal structural link between jammed packings and protein cores. Phys Rev E 2019; 99:022416. [PMID: 30934238 PMCID: PMC6902428 DOI: 10.1103/physreve.99.022416] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2018] [Indexed: 11/07/2022]
Abstract
Dense packing of hydrophobic residues in the cores of globular proteins determines their stability. Recently, we have shown that protein cores possess packing fraction ϕ≈0.56, which is the same as dense, random packing of amino-acid-shaped particles. In this article, we compare the structural properties of protein cores and jammed packings of amino-acid-shaped particles in much greater depth by measuring their local and connected void regions. We find that the distributions of surface Voronoi cell volumes and local porosities obey similar statistics in both systems. We also measure the probability that accessible, connected void regions percolate as a function of the size of a spherical probe particle and show that both systems possess the same critical probe size. We measure the critical exponent τ that characterizes the size distribution of connected void clusters at the onset of percolation. We find that the cluster size statistics are similar for void percolation in packings of amino-acid-shaped particles and randomly placed spheres, but different from that for void percolation in jammed sphere packings. We propose that the connected void regions are a defining structural feature of proteins and can be used to differentiate experimentally observed proteins from decoy structures that are generated using computational protein design software. This work emphasizes that jammed packings of amino-acid-shaped particles can serve as structural and mechanical analogs of protein cores, and could therefore be useful in modeling the response of protein cores to cavity-expanding and -reducing mutations.
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Affiliation(s)
- John D. Treado
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Integrated Graduate Program in Physical & Engineering Biology, Yale University, New Haven, Connecticut 06520, USA
| | - Zhe Mei
- Integrated Graduate Program in Physical & Engineering Biology, Yale University, New Haven, Connecticut 06520, USA
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, USA
| | - Lynne Regan
- Integrated Graduate Program in Physical & Engineering Biology, Yale University, New Haven, Connecticut 06520, USA
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, USA
- Department of Molecular Biophysics & Biochemistry, Yale University, New Haven, Connecticut 06520, USA
| | - Corey S. O’Hern
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Integrated Graduate Program in Physical & Engineering Biology, Yale University, New Haven, Connecticut 06520, USA
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06520, USA
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10
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Popović P, Cael BB, Silber M, Abbot DS. Simple Rules Govern the Patterns of Arctic Sea Ice Melt Ponds. PHYSICAL REVIEW LETTERS 2018; 120:148701. [PMID: 29694130 DOI: 10.1103/physrevlett.120.148701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Indexed: 06/08/2023]
Abstract
Climate change, amplified in the far north, has led to rapid sea ice decline in recent years. In the summer, melt ponds form on the surface of Arctic sea ice, significantly lowering the ice reflectivity (albedo) and thereby accelerating ice melt. Pond geometry controls the details of this crucial feedback; however, a reliable model of pond geometry does not currently exist. Here we show that a simple model of voids surrounding randomly sized and placed overlapping circles reproduces the essential features of pond patterns. The only two model parameters, characteristic circle radius and coverage fraction, are chosen by comparing, between the model and the aerial photographs of the ponds, two correlation functions which determine the typical pond size and their connectedness. Using these parameters, the void model robustly reproduces the ponds' area-perimeter and area-abundance relationships over more than 6 orders of magnitude. By analyzing the correlation functions of ponds on several dates, we also find that the pond scale and the connectedness are surprisingly constant across different years and ice types. Moreover, we find that ponds resemble percolation clusters near the percolation threshold. These results demonstrate that the geometry and abundance of Arctic melt ponds can be simply described, which can be exploited in future models of Arctic melt ponds that would improve predictions of the response of sea ice to Arctic warming.
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Affiliation(s)
- Predrag Popović
- Department of the Geophysical Sciences, The University of Chicago, Chicago, Illinois 60637, USA
| | - B B Cael
- Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mary Silber
- Department of Statistics and Committee on Computational and Applied Mathematics, The University of Chicago, Chicago, Illinois 60637, USA
| | - Dorian S Abbot
- Department of the Geophysical Sciences, The University of Chicago, Chicago, Illinois 60637, USA
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11
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Bakhshian S, Sahimi M. Computer simulation of the effect of deformation on the morphology and flow properties of porous media. Phys Rev E 2016; 94:042903. [PMID: 27841555 DOI: 10.1103/physreve.94.042903] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2016] [Indexed: 06/06/2023]
Abstract
We report on the results of extensive computer simulation of the effect of deformation on the morphology of a porous medium and its fluid flow properties. The porous medium is represented by packings of spherical particles. Both random and regular as well as dense and nondense packings are used. A quasistatic model based on Hertz's contact theory is used to model the mechanical deformation of the packings, while the evolution of the permeability with the deformation is computed by the lattice-Boltzmann approach. The evolution of the pore-size and pore-length distributions, the porosity, the particles' contacts, the permeability, and the distribution of the stresses that the fluid exerts in the pore space are all studied in detail. The distribution of the pores' lengths, the porosity, and the particles' connectivity change strongly with the application of an external strain to the porous media, whereas the pore-size distribution is not affected as strongly. The permeability of the porous media strongly reduces even when the applied strain is small. When the permeabilities and porosities of the random packings are normalized with respect to their predeformation values, they all collapse onto a single curve, independent of the particle-size distribution. The porosity reduces as a power law with the external strain. The fluid stresses in the pore space follow roughly a log-normal distribution, both before and after deformation.
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Affiliation(s)
- Sahar Bakhshian
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
| | - Muhammad Sahimi
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
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12
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Spanner M, Höfling F, Kapfer SC, Mecke KR, Schröder-Turk GE, Franosch T. Splitting of the Universality Class of Anomalous Transport in Crowded Media. PHYSICAL REVIEW LETTERS 2016; 116:060601. [PMID: 26918973 DOI: 10.1103/physrevlett.116.060601] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2015] [Indexed: 06/05/2023]
Abstract
We investigate the emergence of subdiffusive transport by obstruction in continuum models for molecular crowding. While the underlying percolation transition for the accessible space displays universal behavior, the dynamic properties depend in a subtle nonuniversal way on the transport through narrow channels. At the same time, the different universality classes are robust with respect to introducing correlations in the obstacle matrix as we demonstrate for quenched hard-sphere liquids as underlying structures. Our results confirm that the microscopic dynamics can dominate the relaxational behavior even at long times, in striking contrast to glassy dynamics.
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Affiliation(s)
- Markus Spanner
- Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
| | - Felix Höfling
- Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany, and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Sebastian C Kapfer
- Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
| | - Klaus R Mecke
- Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
| | - Gerd E Schröder-Turk
- Murdoch University, School of Engineering and IT, Mathematics and Statistics, Murdoch, Western Australia 6150, Australia
| | - Thomas Franosch
- Institut für Theoretische Physik, Leopold-Franzens-Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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13
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Jin Y, Charbonneau P. Dimensional study of the dynamical arrest in a random Lorentz gas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042313. [PMID: 25974497 DOI: 10.1103/physreve.91.042313] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2014] [Indexed: 06/04/2023]
Abstract
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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Affiliation(s)
- Yuliang Jin
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Dipartimento di Fisica, Sapienza Università di Roma and INFN, Sezione di Roma I, IPFC-CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
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14
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Schnyder SK, Spanner M, Höfling F, Franosch T, Horbach J. Rounding of the localization transition in model porous media. SOFT MATTER 2015; 11:701-711. [PMID: 25467065 DOI: 10.1039/c4sm02334j] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The generic mechanisms of anomalous transport in porous media are investigated by computer simulations of two-dimensional model systems. In order to bridge the gap between the strongly idealized Lorentz model and realistic models of porous media, two models of increasing complexity are considered: a cherry-pit model with hard-core correlations as well as a soft-potential model. An ideal gas of tracer particles inserted into these structures is found to exhibit anomalous transport which extends up to several decades in time. Also, the self-diffusion of the tracers becomes suppressed upon increasing the density of the systems. These phenomena are attributed to an underlying percolation transition. In the soft potential model the transition is rounded, since each tracer encounters its own critical density according to its energy. Therefore, the rounding of the transition is a generic occurrence in realistic, soft systems.
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Affiliation(s)
- Simon K Schnyder
- Institut für Theoretische Physik II: Weiche Materie, Heinrich Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany.
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15
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Priour DJ. Percolation through voids around overlapping spheres: a dynamically based finite-size scaling analysis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012148. [PMID: 24580213 DOI: 10.1103/physreve.89.012148] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2012] [Indexed: 06/03/2023]
Abstract
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is calculated. With large-scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the impenetrable spheres and the spaces between them. To properly exploit finite-size scaling, we examine multiple systems of differing sizes, with suitable averaging over disorder, and extrapolate to the thermodynamic limit. An order parameter based on the statistical sampling of stochastically driven dynamical excursions and amenable to finite-size scaling analysis is defined, calculated for various system sizes, and used to determine the critical volume fraction ϕc=0.0317±0.0004 and the correlation length exponent ν=0.92±0.05.
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Affiliation(s)
- D J Priour
- Department of Science, Kansas City Kansas Community College, Kansas City, Kansas 66112, USA and Department of Physics and Astronomy, Youngstown State University, Youngstown, Ohio 44555, USA
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16
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Höfling F, Franosch T. Anomalous transport in the crowded world of biological cells. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:046602. [PMID: 23481518 DOI: 10.1088/0034-4885/76/4/046602] [Citation(s) in RCA: 584] [Impact Index Per Article: 53.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.
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Affiliation(s)
- Felix Höfling
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, and Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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17
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Pinheiro M, Martin RL, Rycroft CH, Haranczyk M. High accuracy geometric analysis of crystalline porous materials. CrystEngComm 2013. [DOI: 10.1039/c3ce41057a] [Citation(s) in RCA: 60] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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18
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Maiti M, Lakshminarayanan A, Sastry S. Characterization of void space in polydisperse sphere packings: Applications to hard-sphere packings and to protein structure analysis. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2013; 36:5. [PMID: 23355091 DOI: 10.1140/epje/i2013-13005-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2012] [Revised: 10/27/2012] [Accepted: 12/19/2012] [Indexed: 06/01/2023]
Abstract
The implementation of a method for the exact evaluation of the volume and surface area of cavities and free volumes in polydisperse sphere packings is described. The generalization of an algorithm for Voronoi tessellation by Tanemura et al. is presented, employing the radical plane construction, as a part of the method. We employ this method to calculate the equation of state for monodisperse and polydisperse hard-sphere fluids, crystals, and for the metastable amorphous branch up to random close packing or jamming densities. We compute the distribution of free volumes, and compare with previous results employing a heuristic definition of free volume. We show the efficacy of the method for analyzing protein structure, by computing various quantities such as the distribution of sizes of buried cavities and pockets, the scaling of solvent accessible area to the corresponding occupied volume, the composition of residues lining cavities, etc.
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Affiliation(s)
- Moumita Maiti
- Theoretical Sciences Unit, JNCASR, 560065, Jakkur, Banglore, India
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19
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Kurzidim J, Kahl G. Accessible volume in quenched-annealed mixtures of hard spheres: a geometric decomposition. Mol Phys 2011. [DOI: 10.1080/00268976.2011.556579] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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20
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Two-dimensional continuum percolation threshold for diffusing particles of nonzero radius. Biophys J 2010; 99:1490-9. [PMID: 20816061 DOI: 10.1016/j.bpj.2010.06.033] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2010] [Revised: 06/14/2010] [Accepted: 06/16/2010] [Indexed: 11/20/2022] Open
Abstract
Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing obstructed diffusion is the percolation threshold. The thresholds are well known for point tracers, but for tracers of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. Here thresholds are obtained for circular obstacles on the continuum. Random obstacle configurations are generated by Brownian dynamics or Monte Carlo methods, the obstacles are immobilized, and the percolation threshold is obtained by solving a bond percolation problem on the Voronoi diagram of the obstacles. The percolation threshold is expressed as the diameter of the largest tracer that can cross a set of immobile obstacles at a prescribed number density. For random overlapping obstacles, the results agree with the known analytical solution quantitatively. When the obstacles are soft disks with a 1/r(12) repulsion, the percolating diameter is approximately 20% lower than for overlapping obstacles. A percolation model predicts that the threshold is highly sensitive to the tracer radius. To our knowledge, such a strong dependence has so far not been reported for the plasma membrane, suggesting that percolation is not the factor controlling lateral diffusion. A definitive experiment is proposed.
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21
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Sung BJ, Yethiraj A. Structure of void space in polymer solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:031801. [PMID: 20365759 DOI: 10.1103/physreve.81.031801] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2009] [Revised: 12/21/2009] [Indexed: 05/29/2023]
Abstract
The structure of void space in two- and three-dimensional (3D) polymer solutions is studied using Voronoi tessellation and percolation theory. The polymer molecules are modeled as freely jointed chains of N tangent hard disks (two dimensions) or spheres (three dimensions). Polymer chains are equilibrated via Monte Carlo simulations and the pore space in configurations of equilibrated chains is mapped using Voronoi tessellation. In d dimensions a Voronoi vertex is the center of the sphere tangent to the d+1 nearest monomers. An edge of the Voronoi diagram is the shortest route between two neighboring vertices. The edge is considered connected if a monomer can pass through and disconnected otherwise. The Voronoi construction is used to calculate the percolation threshold of the void space. The most interesting result is that the polymer area fraction at the percolation threshold is a nonmonotonic function of N in two dimensions but monotonically reaches a constant value in three dimensions. The crossover behavior of the percolation threshold is also observed in pseudo-3D. The pore size distribution decreases monotonically with increasing pore size. This is markedly different from that in configurations of hard disks (monomeric fluid) where the pore size distribution is peaked at finite size.
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Affiliation(s)
- Bong June Sung
- Department of Chemistry, Sogang University, Seoul 121-742, Republic of Korea
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22
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SASTRY SRIKANTH, TRUSKETT THOMASM, DEBENEDETTI PABLOG, TORQUATO SALVATORE, STILLINGER FRANKH. Free volume in the hard sphere liquid. Mol Phys 2009. [DOI: 10.1080/00268979809483161] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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23
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Höfling F, Munk T, Frey E, Franosch T. Critical dynamics of ballistic and Brownian particles in a heterogeneous environment. J Chem Phys 2008; 128:164517. [PMID: 18447469 DOI: 10.1063/1.2901170] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed large-scale computer simulations, demonstrating that universality holds at long times in the immediate vicinity of the transition. The scaling function describing the crossover from anomalous transport to diffusive motion is found to vary extremely slowly and spans at least five decades in time. To extract the scaling function, one has to allow for the leading universal corrections to scaling. Our findings suggest that apparent power laws with varying exponents generically occur and dominate experimentally accessible time windows as soon as the heterogeneities cover a decade in length scale. We extract the divergent length scales, quantify the spatial heterogeneities in terms of the non-Gaussian parameter, and corroborate our results by a thorough finite-size analysis.
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Affiliation(s)
- Felix Höfling
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience, Fakultät für Physik, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany.
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24
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Sung BJ, Yethiraj A. The effect of matrix structure on the diffusion of fluids in porous media. J Chem Phys 2008; 128:054702. [PMID: 18266457 DOI: 10.1063/1.2823735] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The effect of matrix structure on the transport properties of adsorbed fluids is studied using computer simulations and percolation theory. The model system consists of a fluid of hard spheres diffusing in a matrix of hard spheres fixed in space. Three different arrangements of the fixed spheres, random, templated, and polymeric, are investigated. For a given matrix volume fraction the diffusion coefficient of the fluid, D, is sensitive to the manner in which the matrix is constructed, with large differences between the three types of matrices. The matrix is mapped onto an effective lattice composed of vertices and bonds using a Voronoi tessellation method where the connectivity of bonds is determined using a geometric criterion, i.e., a bond is connected if a fluid particle can pass directly between the two pores the bond connects, and disconnected otherwise. The percolation threshold is then determined from the connectivity of the bonds. D displays universal scaling behavior in the reduced volume fraction, i.e., D approximately (1-phi(m)phi(c))(gamma), where phi(m) is the matrix volume fraction and phi(c) is the matrix volume fraction at the percolation threshold. We find that gamma approximately 2.2, independent of matrix type, which is different from the result gamma approximately 1.53 for diffusion in lattice models, but similar to that for conduction in Swiss cheese models. Lattice simulations with biased hopping probabilities are consistent with the continuous-space simulations, and this shows that the universal behavior of diffusion is sensitive to details of local dynamics.
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Affiliation(s)
- Bong June Sung
- Department of Chemistry, Sogang University, Seoul 121-742, Republic of Korea
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25
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Yi YB. Void percolation and conduction of overlapping ellipsoids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031112. [PMID: 17025599 DOI: 10.1103/physreve.74.031112] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2006] [Revised: 07/17/2006] [Indexed: 05/12/2023]
Abstract
The void percolation and conduction problems for equisized overlapping ellipsoids of revolution are investigated using the discretization method. The method is validated by comparing the estimated percolation threshold of spheres with the precise result found in literature. The technique is then extended to determine the threshold of void percolation as a function of the geometric aspect ratio of ellipsoidal particles. The finite element method is also applied to evaluate the equivalent conductivity of the void phase in the system. The results confirm that there are no universalities for void percolation threshold and conductivity in particulate systems, and these properties are clearly dependent on the geometrical shape of particles. As a consequence, void percolation and conduction associated with ellipsoidal particles of large aspect ratio should be treated differently from spheres.
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Affiliation(s)
- Y B Yi
- Department of Engineering, University of Denver, Denver, Colorodo 80208, USA
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26
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Sung BJ, Yethiraj A. Lateral diffusion and percolation in membranes. PHYSICAL REVIEW LETTERS 2006; 96:228103. [PMID: 16803348 DOI: 10.1103/physrevlett.96.228103] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2006] [Indexed: 05/10/2023]
Abstract
An algorithm based on Voronoi tessellation and percolation theory is presented to study the diffusion of model membrane components (solutes) in the plasma membrane. The membrane is modeled as a two-dimensional space with integral membrane proteins as static obstacles. The Voronoi diagram consists of vertices, which are equidistant from three matrix obstacles, joined by edges. An edge between two vertices is said to be connected if solute particles can pass directly between the two regions. The percolation threshold, pc, determined using this passage criterion is pc approximately equal to 0.53. This is smaller than if the connectivity of edges were assigned randomly, in which case the percolation threshold pr=2/3, where p is the fraction of connected edges. Molecular dynamics simulations show that diffusion is determined by percolation of clusters of edges.
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Affiliation(s)
- Bong June Sung
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, USA
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27
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Höfling F, Franosch T, Frey E. Localization transition of the three-dimensional lorentz model and continuum percolation. PHYSICAL REVIEW LETTERS 2006; 96:165901. [PMID: 16712247 DOI: 10.1103/physrevlett.96.165901] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2005] [Indexed: 05/09/2023]
Abstract
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation theory and obtain an excellent matching of the critical density and exponents. Within a dynamic scaling ansatz incorporating two divergent length scales we achieve data collapse for the mean-square displacements and identify the leading corrections to scaling. We provide evidence for a divergent non-Gaussian parameter close to the transition.
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Affiliation(s)
- Felix Höfling
- Hahn-Meitner-Institut Berlin, Abteilung Theorie, Germany
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28
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Ripoll M, Ernst MH. Model system for classical fluids out of equilibrium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:041104. [PMID: 15903654 DOI: 10.1103/physreve.71.041104] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2004] [Revised: 09/20/2004] [Indexed: 05/02/2023]
Abstract
A model system for classical fluids out of equilibrium, referred to as a dissipative particles dynamics (DPD) solid, is studied by analytical and simulation methods. The time evolution of a DPD particle is described by a fluctuating heat equation. This DPD solid with transport based on collisional transfer (high-density mechanism) is complementary to the Lorentz gas with only kinetic transport (low-density mechanism). Combination of both models covers the qualitative behavior of transport properties of classical fluids over the full-density range. The heat diffusivity is calculated using a mean-field theory, leading to a linear-density dependence of this transport coefficient, which is exact at high densities. Subleading density corrections are obtained as well. At lower densities the model has a conductivity threshold below which heat conduction is absent. The observed threshold is explained in terms of percolation diffusion on a random proximity network. The geometrical structure of this network is the same as in continuum percolation of completely overlapping spheres, but the dynamics on this network differs from continuum percolation diffusion. Furthermore, the kinetic theory for DPD is extended to the generalized hydrodynamic regime, where the wave-number-dependent decay rates of the Fourier modes of the energy and temperature fields are calculated.
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Affiliation(s)
- M Ripoll
- Institut für Festkörperforschung, Forschungszentrum Jülich - 52425 Jülich, Germany
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29
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Pore network model of deactivation of immobilized glucose isomerase in packed-bed reactors. Part III: Multiscale modelling. Chem Eng Sci 2003. [DOI: 10.1016/j.ces.2003.07.006] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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30
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Rintoul MD. Precise determination of the void percolation threshold for two distributions of overlapping spheres. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:68-72. [PMID: 11088435 DOI: 10.1103/physreve.62.68] [Citation(s) in RCA: 55] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2000] [Indexed: 11/06/2022]
Abstract
The void percolation threshold is calculated for a distribution of overlapping spheres with equal radii, and for a binary-sized distribution of overlapping spheres, where half of the spheres have radii twice as large as the other half. Using systems much larger than previous work, we determine a much more precise value for the percolation thresholds and correlation length exponent. The value of the percolation threshold for the monodisperse case is shown to be 0. 0301+/-0.0003, whereas the value for the bidisperse case is shown to be p(c)=0.0287+/-0.0005. The fact that these are significantly different is in contrast with previous, less precise works that speculated that the threshold might be universal with respect to sphere size distribution.
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Affiliation(s)
- MD Rintoul
- MS 1111, Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185-1111, USA
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31
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Voloshin VP, Medvedev NN, Fenelonov VB, Parmon VN. Pore structure study by computer simulation of dense and loose packings of spherical particles. J STRUCT CHEM+ 1999. [DOI: 10.1007/bf02700718] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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32
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Luchnikov VA, Medvedev NN, Oger L, Troadec JP. Voronoi-Delaunay analysis of voids in systems of nonspherical particles. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 59:7205-12. [PMID: 11969711 DOI: 10.1103/physreve.59.7205] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/1998] [Revised: 02/17/1999] [Indexed: 04/18/2023]
Abstract
The Voronoi network is known to be a useful tool for the structural description of voids in the packings of spheres produced by computer simulations. In this article we extend the Voronoi-Delaunay analysis to packings of nonspherical convex objects. Main properties of the Voronoi network, which are known for systems of spheres, are valid for systems of any convex objects. A general numerical algorithm for calculation of the Voronoi network in three dimensions is proposed. It is based on the calculation of the trajectory of the imaginary empty sphere of variable size, moving inside a system (the Delaunay empty sphere method). Analysis of voids is presented for an ensemble of random straight lines and for a molecular dynamics model of liquid crystal. The spatial distribution of voids and a simple percolation analysis are obtained. The distributions of the bottleneck radii and the radii of spheres inscribed in the voids are calculated.
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Affiliation(s)
- V A Luchnikov
- Institute of Chemical Kinetics and Combustion, 630090 Novosibirsk, Russia.
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33
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Network Approach to Void Percolation in a Pack of Unequal Spheres. PHYSICAL REVIEW LETTERS 1996; 77:1785-1788. [PMID: 10063171 DOI: 10.1103/physrevlett.77.1785] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
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34
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Sahimi M. Fractal and superdiffusive transport and hydrodynamic dispersion in heterogeneous porous media. Transp Porous Media 1993. [DOI: 10.1007/bf00613269] [Citation(s) in RCA: 79] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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35
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Simon SH, Dobrosavljević V, Stratt RM. The mobility of electrons in simple insulating fluids as a percolation problem. J Chem Phys 1991. [DOI: 10.1063/1.460168] [Citation(s) in RCA: 31] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Feng S, Halperin BI, Sen PN. Transport properties of continuum systems near the percolation threshold. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 35:197-214. [PMID: 9940585 DOI: 10.1103/physrevb.35.197] [Citation(s) in RCA: 265] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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38
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Machta J, Moore SM. Diffusion and long-time tails in the overlapping Lorentz gas. PHYSICAL REVIEW. A, GENERAL PHYSICS 1985; 32:3164-3167. [PMID: 9896481 DOI: 10.1103/physreva.32.3164] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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39
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Roberts JN, Schwartz LM. Grain consolidation and electrical conductivity in porous media. PHYSICAL REVIEW. B, CONDENSED MATTER 1985; 31:5990-5997. [PMID: 9936596 DOI: 10.1103/physrevb.31.5990] [Citation(s) in RCA: 169] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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