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Sego TJ, Comlekoglu T, Peirce SM, Desimone DW, Glazier JA. General, open-source vertex modeling in biological applications using Tissue Forge. Sci Rep 2023; 13:17886. [PMID: 37857673 PMCID: PMC10587242 DOI: 10.1038/s41598-023-45127-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 10/16/2023] [Indexed: 10/21/2023] Open
Abstract
Vertex models are a widespread approach for describing the biophysics and behaviors of multicellular systems, especially of epithelial tissues. Vertex models describe a wide variety of developmental scenarios and behaviors like cell rearrangement and tissue folding. Often, these models are implemented as single-use or closed-source software, which inhibits reproducibility and decreases accessibility for researchers with limited proficiency in software development and numerical methods. We developed a physics-based vertex model methodology in Tissue Forge, an open-source, particle-based modeling and simulation environment. Our methodology describes the properties and processes of vertex model objects on the basis of vertices, which allows integration of vertex modeling with the particle-based formalism of Tissue Forge, enabling an environment for developing mixed-method models of multicellular systems. Our methodology in Tissue Forge inherits all features provided by Tissue Forge, delivering open-source, extensible vertex modeling with interactive simulation, real-time simulation visualization and model sharing in the C, C++ and Python programming languages and a Jupyter Notebook. Demonstrations show a vertex model of cell sorting and a mixed-method model of cell migration combining vertex- and particle-based models. Our methodology provides accessible vertex modeling for a broad range of scientific disciplines, and we welcome community-developed contributions to our open-source software implementation.
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Affiliation(s)
- T J Sego
- Department of Medicine, University of Florida, Gainesville, FL, USA.
| | - Tien Comlekoglu
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
- Department of Cell Biology, University of Virginia, Charlottesville, VA, USA
| | - Shayn M Peirce
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
| | - Douglas W Desimone
- Department of Cell Biology, University of Virginia, Charlottesville, VA, USA
| | - James A Glazier
- Department of Intelligent Engineering and Biocomplexity Institute, Indiana University, Bloomington, IN, USA
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2
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Chieco AT, Durian DJ. Simply solvable model capturing the approach to statistical self-similarity for the diffusive coarsening of bubbles, droplets, and grains. Phys Rev E 2023; 108:034606. [PMID: 37849107 DOI: 10.1103/physreve.108.034606] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2023] [Accepted: 08/31/2023] [Indexed: 10/19/2023]
Abstract
Aqueous foams and a wide range of related systems are believed to coarsen by diffusion between neighboring domains into a statistically self-similar scaling state, after the decay of initial transients, such that dimensionless domain size and shape distributions become time independent and the average grows as a power law. Partial integrodifferential equations for the time evolution of the size distribution for such phase separating systems can be formulated for arbitrary initial conditions, but these are cumbersome for analyzing data on nonscaling state preparations. Here we show that essential features of the approach to the scaling state are captured by an exactly-solvable ordinary differential equation for the evolution of the average bubble size. The key ingredient is to characterize the bubble size distribution approximately, using the average size of all bubbles and the average size of the critical bubbles, which instantaneously neither grow nor shrink. The difference between these two averages serves as a proxy for the width of the size distribution. Solution of our model shows that behavior is controlled by a signed length δ that is proportional to the width of the initial distribution relative to that in the scaling state. In particular, δ is negative if the initial preparation is too monodisperse, and is positive if it is too polydisperse. To test our approach, we compare with data for quasi-two dimensional dry foams created with three different initial amounts of polydispersity. This allows us to readily identify the critical radius from the average area of six-sided bubbles, whose growth rate is zero by the von Neumann law. The growth of the average and critical radii agree quite well with exact solution, though the most monodisperse sample crosses over to the scaling state faster than expected. A simpler approximate solution of our model performs equally well. Our approach is applicable to 3d foams, which we demonstrate by re-analyzing prior data, as well as to froths of dilute droplets and to phase separation kinetics for more general systems such as emulsions, binary mixtures, and alloys.
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Affiliation(s)
- Anthony T Chieco
- Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
| | - Douglas J Durian
- Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
- Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, New York 10010, USA
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Sego T, Comlekoglu T, Peirce SM, Desimone D, Glazier JA. General, Open-Source Vertex Modeling in Biological Applications Using Tissue Forge. RESEARCH SQUARE 2023:rs.3.rs-2886960. [PMID: 37214822 PMCID: PMC10197754 DOI: 10.21203/rs.3.rs-2886960/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Vertex models are a widespread approach for describing the biophysics and behaviors of multicellular systems, especially of epithelial tissues. Vertex models describe a wide variety of developmental scenarios and behaviors like cell rearrangement and tissue folding. Often, these models are implemented as single-use or closed-source software, which inhibits reproducibility and decreases accessibility for researchers with limited proficiency in software development and numerical methods. We developed a physics-based vertex model methodology in Tissue Forge, an open-source, particle-based modeling and simulation environment. Our methodology describes the properties and processes of vertex model objects on the basis of vertices, which allows integration of vertex modeling with the particle-based formalism of Tissue Forge, enabling an environment for developing mixed-method models of multicellular systems. Our methodology in Tissue Forge inherits all features provided by Tissue Forge, delivering opensource, extensible vertex modeling with interactive simulation, real-time simulation visualization and model sharing in the C , C + + and Python programming languages and a Jupyter Notebook. Demonstrations show a vertex model of cell sorting and a mixed-method model of cell migration combining vertex- and particle-based models. Our methodology provides accessible vertex modeling for a broad range of scientific disciplines, and we welcome community-developed contributions to our open-source software implementation.
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Affiliation(s)
- T.J. Sego
- Department of Medicine, University of Florida, Gainesville, FL, USA
| | - Tien Comlekoglu
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
- Department of Cell Biology, University of Virginia, Charlottesville, VA, USA
| | - Shayn M. Peirce
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
| | - Douglas Desimone
- Department of Cell Biology, University of Virginia, Charlottesville, VA, USA
| | - James A. Glazier
- Department of Intelligent Engineering and Biocomplexity Institute, Indiana University,Bloomington, IN, USA
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Koride S, Loza AJ, Sun SX. Epithelial vertex models with active biochemical regulation of contractility can explain organized collective cell motility. APL Bioeng 2018; 2:031906. [PMID: 31069315 PMCID: PMC6324211 DOI: 10.1063/1.5023410] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2018] [Accepted: 06/14/2018] [Indexed: 01/22/2023] Open
Abstract
Collective motions of groups of cells are observed in many biological settings such as embryo development, tissue formation, and cancer metastasis. To effectively model collective cell movement, it is important to incorporate cell specific features such as cell size, cell shape, and cell mechanics, as well as active behavior of cells such as protrusion and force generation, contractile forces, and active biochemical signaling mechanisms that regulate cell behavior. In this paper, we develop a comprehensive model of collective cell migration in confluent epithelia based on the vertex modeling approach. We develop a method to compute cell-cell viscous friction based on the vertex model and incorporate RhoGTPase regulation of cortical myosin contraction. Global features of collective cell migration are examined by computing the spatial velocity correlation function. As active cell force parameters are varied, we found rich dynamical behavior. Furthermore, we find that cells exhibit nonlinear phenomena such as contractile waves and vortex formation. Together our work highlights the importance of active behavior of cells in generating collective cell movement. The vertex modeling approach is an efficient and versatile approach to rigorously examine cell motion in the epithelium.
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Affiliation(s)
- Sarita Koride
- Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Andrew J Loza
- Department of Cell Biology, Washington University School of Medicine, St. Louis, Missouri 63110, USA
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Scianna M, Preziosi L. A node-based version of the cellular Potts model. Comput Biol Med 2016; 76:94-112. [PMID: 27416549 DOI: 10.1016/j.compbiomed.2016.06.027] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2016] [Revised: 06/25/2016] [Accepted: 06/27/2016] [Indexed: 10/21/2022]
Abstract
The cellular Potts model (CPM) is a lattice-based Monte Carlo method that uses an energetic formalism to describe the phenomenological mechanisms underlying the biophysical problem of interest. We here propose a CPM-derived framework that relies on a node-based representation of cell-scale elements. This feature has relevant consequences on the overall simulation environment. First, our model can be implemented on any given domain, provided a proper discretization (which can be regular or irregular, fixed or time evolving). Then, it allowed an explicit representation of cell membranes, whose displacements realistically result in cell movement. Finally, our node-based approach can be easily interfaced with continuous mechanics or fluid dynamics models. The proposed computational environment is here applied to some simple biological phenomena, such as cell sorting and chemotactic migration, also in order to achieve an analysis of the performance of the underlying algorithm. This work is finally equipped with a critical comparison between the advantages and disadvantages of our model with respect to the traditional CPM and to some similar vertex-based approaches.
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Affiliation(s)
- Marco Scianna
- Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
| | - Luigi Preziosi
- Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
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Fletcher AG, Osterfield M, Baker RE, Shvartsman SY. Vertex models of epithelial morphogenesis. Biophys J 2015; 106:2291-304. [PMID: 24896108 DOI: 10.1016/j.bpj.2013.11.4498] [Citation(s) in RCA: 289] [Impact Index Per Article: 32.1] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2012] [Revised: 11/06/2013] [Accepted: 11/08/2013] [Indexed: 01/06/2023] Open
Abstract
The dynamic behavior of epithelial cell sheets plays a central role during numerous developmental processes. Genetic and imaging studies of epithelial morphogenesis in a wide range of organisms have led to increasingly detailed mechanisms of cell sheet dynamics. Computational models offer a useful means by which to investigate and test these mechanisms, and have played a key role in the study of cell-cell interactions. A variety of modeling approaches can be used to simulate the balance of forces within an epithelial sheet. Vertex models are a class of such models that consider cells as individual objects, approximated by two-dimensional polygons representing cellular interfaces, in which each vertex moves in response to forces due to growth, interfacial tension, and pressure within each cell. Vertex models are used to study cellular processes within epithelia, including cell motility, adhesion, mitosis, and delamination. This review summarizes how vertex models have been used to provide insight into developmental processes and highlights current challenges in this area, including progressing these models from two to three dimensions and developing new tools for model validation.
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Affiliation(s)
- Alexander G Fletcher
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom.
| | - Miriam Osterfield
- Lewis-Sigler Institute for Integrative Genomics, Princeton, New Jersey
| | - Ruth E Baker
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom.
| | - Stanislav Y Shvartsman
- Lewis-Sigler Institute for Integrative Genomics, Princeton, New Jersey; Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey.
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Abstract
ABSTRACTThis paper will review the topic of computer simulation of the evolution of grain structure in polycrystalline thin films, with particular attention to the modelling of the grain growth process. If the grain size is small compared to the film thickness, then the grain structure is three-dimensional. As the grains grow to become larger than the film thickness, so that most grains traverse the entire thickness of the film, the microstructure may approach the conditions for a two-dimensional grain structure. Both two- and three-dimensional grain growth have been simulated by various authors.When the grains become large enough for the microstructure to be two-dimensional, the surface energy associated with the two free surfaces of the film becomes comparable to the surface energy of the grain boundaries. In this condition, the free surface may profoundly effect the grain growth. One effect is that grooves may develop along the lines where the grain boundaries meet the free surfaces. This grooving may pin the boundaries against further migration and lead to grain-growth stagnation. Another possible effect is that differences in the free surface energy for grains with different crystallographic orientation may provide a driving force for the migration of the boundaries which is additional to that provided by grain boundary capillarity. Grains with favorable orientations will grow at the expense of grains with unfavorable orientations. The coupling of grain-growth stagnation with an additional driving force can produce abnormal or secondary grain growth in which a few grains grow very large by consuming the normal grains.
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Guttenberg N, Goldenfeld N, Dantzig J. Emergence of foams from the breakdown of the phase field crystal model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:065301. [PMID: 20866468 DOI: 10.1103/physreve.81.065301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2010] [Indexed: 05/29/2023]
Abstract
The phase field crystal (PFC) model captures the elastic and topological properties of crystals with a single scalar field at small undercooling. At large undercooling, new foamlike behavior emerges. We characterize this foam phase of the PFC equation and propose a modified PFC equation that may be used for the simulation of foam dynamics. This minimal model reproduces von Neumann's rule for two-dimensional dry foams and Lifshitz-Slyozov coarsening for wet foams. We also measure the coordination number distribution and find that its second moment is larger than previously reported experimental and theoretical studies of soap froths, a finding that we attribute to the wetness of the foam increasing with time.
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Affiliation(s)
- Nicholas Guttenberg
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
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Trittel T, John T, Stannarius R. Smectic foams. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2010; 26:7899-7904. [PMID: 20180603 DOI: 10.1021/la904779a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Because of their layered structure, thermotropic smectic mesogens can form stable foams. In this study, two-dimensional foams of 8CB are prepared in the smectic A phase. We determine the structures of the foam cells and study the aging dynamics. Three stages of foam evolution are distinguished. The freshly prepared foam consists of multilayers of small cells. After several hours, a 2D foam with predominantly hexagonal cells develops. It takes several days until the foam reaches an asymptotic structure with a characteristic distribution of n-polygons and self-similar scaling behavior of the coarsening. The structural changes are essentially caused by gas exchange between cells; film rupture can be neglected. We confirm predicted distributions and asymptotic scaling laws quantitatively. In the nematic phase, stable foams could not be produced, but smectic foams survive a transition into the nematic state up to several degrees above the phase transition. The reason for that is obviously smectic ordering at the film surfaces. The nematic foams coarsen much faster than smectic foams; film rupture is the dominant contribution to the aging dynamics. With 5CB, which has no smectic phase, we were not able to prepare foams.
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Affiliation(s)
- Torsten Trittel
- Institut für Experimentalphysik, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany.
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10
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Glazier JA, Anderson MP, Grest GS. Coarsening in the two-dimensional soap froth and the large-QPotts model: A detailed comparison. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/13642819008215259] [Citation(s) in RCA: 116] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- James A. Glazier
- a James Franck Institute and Department of Physics , University of Chicago , 5640 S. Ellis Avenue, Chicago , Illinois , 60637 , U.S.A
- c AT&T Bell Laboratories , 600 Mountain Avenue, Murray Hill , New Jersey , 07974 , U.S.A
| | - Michael P. Anderson
- b Corporate Research Science Laboratory , Exxon Research and Engineering Company , Annadale , New Jersey , 08801 , U.S.A
| | - Gary S. Grest
- b Corporate Research Science Laboratory , Exxon Research and Engineering Company , Annadale , New Jersey , 08801 , U.S.A
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11
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Anderson MP, Grest GS, Srolovitz DJ. Computer simulation of normal grain growth in three dimensions. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/13642818908220181] [Citation(s) in RCA: 259] [Impact Index Per Article: 14.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- M. P. Anderson
- a Corporate Research Science Laboratory , Exxon Research and Engineering Company , Annandale , New Jersey , 08801 , U.S.A
| | - G. S. Grest
- a Corporate Research Science Laboratory , Exxon Research and Engineering Company , Annandale , New Jersey , 08801 , U.S.A
| | - D. J. Srolovitz
- b Los Alamos National Laboratory , Los Alamos , New Mexico , 87545 , U.S.A
- c Department of Material Science and Engineering , University of Michigan , Ann Arbor , Michigan , 48109 , U.S.A
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Thomas GL, de Almeida RMC, Graner F. Coarsening of three-dimensional grains in crystals, or bubbles in dry foams, tends towards a universal, statistically scale-invariant regime. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:021407. [PMID: 17025425 DOI: 10.1103/physreve.74.021407] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2006] [Indexed: 05/12/2023]
Abstract
We perform extensive Potts model simulations of three-dimensional dry foam coarsening. Starting with 2.25 million bubbles, we have enough statistics to fulfill the three constraints required for the study of statistical scale invariance: first, enough time for the transient to end and reach the scaling state; then, enough time in the scaling state itself to characterize its properties; and finally, enough bubbles at the end to avoid spurious finite size effects. In the scaling state, we find that the average surface area of the bubbles increases linearly with time. The geometry (bubble shape and size) and topology (number of faces and edges), as well as their correlations, become constant in time. Their distributions agree with the data of the literature. We present an analytical model (universal, up to parameters extracted from the simulations) for a disordered foam minimizing its free energy, which agrees with the simulations. We discuss the limitations of the simulations and of the model.
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Affiliation(s)
- Gilberto L Thomas
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-051 Porto Alegre, RS, Brazil.
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13
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Miri M, Rivier N. Universality in two-dimensional cellular structures evolving by cell division and disappearance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:031101. [PMID: 16605494 DOI: 10.1103/physreve.73.031101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2005] [Indexed: 05/08/2023]
Abstract
The dynamics of two-dimensional cellular networks is written in terms of coupled population equations, which describe how the population of s-sided cells is affected by cell division and disappearance. In these equations the effect of the rest of the foam on the disappearing or dividing cell is treated as a local mean field. Under not too restrictive conditions, the equilibrium distribution P(s) of cells satisfies a linear difference equation of order two or higher. The population equations are asymptotically integrable. The asymptotic integrability implies a "universal" distribution P(s) approximately Cs-kZs for large values of s, which is also the Boltzmann distribution associated with the maximum entropy inference. Asymptotic integrability of the population equations is absent in a global mean-field approximation. The importance of short-range topological information to control the evolution of foams is thus confirmed.
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Affiliation(s)
- MirFaez Miri
- Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159, Iran
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14
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Fernández-Toledano JC, Moncho-Jordá A, Martínez-López F, González AE, Hidalgo-Alvarez R. Short- and long-range topological correlations in two-dimensional aggregation of dense colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:041401. [PMID: 15903665 DOI: 10.1103/physreve.71.041401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2004] [Revised: 01/28/2005] [Indexed: 05/02/2023]
Abstract
We have studied the average properties and the topological correlations of computer-simulated two-dimensional (2D) aggregating systems at different initial surface packing fractions. For this purpose, the centers of mass of the growing clusters have been used to build the Voronoi diagram, where each cell represents a single cluster. The number of sides (n) and the area (A) of the cells are related to the size of the clusters and the number of nearest neighbors, respectively. We have focused our paper in the study of the topological quantities derived from number of sides, n , and we leave for a future work the study of the dependence of these magnitudes on the area of the cells, A . In this work, we go beyond the adjacent cluster correlations and explore the organization of the whole system of clusters by dividing the space in concentric layers around each cluster: the shell structure. This method allows us to analyze the time behavior of the long-range intercluster correlations induced by the aggregation process. We observed that kinetic and topological properties are intimately connected. Particularly, we found a continuous ordering of the shell structure from the earlier stages of the aggregation process, where clusters positions approach a hexagonal distribution in the plane. For long aggregation times, when the dynamic scaling regime is achieved, the short- and long-range topological properties reached a final stationary state. This ordering is stronger for high particle densities. Comparison between simulation and theoretical data points out the fact that 2D colloidal aggregation in the absence of interactions (diffusion-limited cluster aggregation regimen) is only able to produce short-range cluster-cluster correlations. Moreover, we showed that the correlation between adjacent clusters verifies the Aboav-Weaire law, while all the topological properties for nonadjacent clusters are mainly determined by only two parameters: the second central moment of number-of-sides distribution mu(2) = sumP (n) (n-6)(2) and the screening factor a (defined through the Aboav-Weaire equation). We also found that the values of mu(2) and a calculated for two-dimensional aggregating system are related through a single universal common form a proportional to mu2(-0.89), which is independent of the particle concentration.
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Affiliation(s)
- J C Fernández-Toledano
- Departamento de Física Aplicada, Facultad de Ciencias, Campus Fuentenueva S/N, 18071 Granada, Spain
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MATSUMOTO K, YUASA K, NAKAGAWA K. Protection against Localized Corrosion of Stainless Steel below 843K in Molten Lithium-Sodium Carbonate. ELECTROCHEMISTRY 1999. [DOI: 10.5796/electrochemistry.67.253] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Affiliation(s)
| | - Kouichi YUASA
- Ishikawajima-Harima Heavy Industries Co., Ltd. Research Institute
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16
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Almeida RMCD, Iglesias JR. Towards statistical mechanics of a 2D random cellular structure. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/21/16/013] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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17
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Levitan B, Domany E. Topological simulations of dynamical features in coarsening soap froth. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:2766-2772. [PMID: 9965390 DOI: 10.1103/physreve.54.2766] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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18
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Jiang Y, Mombach JC, Glazier JA. Grain growth from homogeneous initial conditions: Anomalous grain growth and special scaling states. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:R3333-R3336. [PMID: 9963953 DOI: 10.1103/physreve.52.r3333] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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19
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Sagui C, Desai RC. Late-stage kinetics of systems with competing interactions quenched into the hexagonal phase. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:2807-2821. [PMID: 9963728 DOI: 10.1103/physreve.52.2807] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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20
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Burnett GD, Chae JJ, Tam WY, Tabor M. Structure and dynamics of breaking foams. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:5788-5796. [PMID: 9963315 DOI: 10.1103/physreve.51.5788] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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21
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Seul M, Morgan NY, Sire C. Domain coarsening in a two-dimensional binary mixture: Growth dynamics and spatial correlations. PHYSICAL REVIEW LETTERS 1994; 73:2284-2287. [PMID: 10057021 DOI: 10.1103/physrevlett.73.2284] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Levitan B, Slepyan E, Krichevsky O, Stavans J, Domany E. Topological distribution of survivors in an evolving cellular structure. PHYSICAL REVIEW LETTERS 1994; 73:756-759. [PMID: 10057529 DOI: 10.1103/physrevlett.73.756] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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23
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Fradkov V, Glicksman M, Palmer M, Rajan K. Topological events in two-dimensional grain growth: Experiments and simulations. ACTA ACUST UNITED AC 1994. [DOI: 10.1016/0956-7151(94)90213-5] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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24
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Sagui C, Desai RC. Kinetics of topological defects in systems with competing interactions. PHYSICAL REVIEW LETTERS 1993; 71:3995-3998. [PMID: 10055127 DOI: 10.1103/physrevlett.71.3995] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Peczak P, Grest GS, Levine D. Monte Carlo studies of grain growth on curved surfaces. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:4470-4482. [PMID: 9961129 DOI: 10.1103/physreve.48.4470] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Flyvbjerg H. Model for coarsening froths and foams. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:4037-4054. [PMID: 9960478 DOI: 10.1103/physreve.47.4037] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Segel D, Mukamel D, Krichevsky O, Stavans J. Selection mechanism and area distribution in two-dimensional cellular structures. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:812-819. [PMID: 9960077 DOI: 10.1103/physreve.47.812] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Andrienko YA, Brilliantov NV, Krapivsky PL. Nucleation and growth in systems with many stable phases. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:2263-2269. [PMID: 9907247 DOI: 10.1103/physreva.45.2263] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Stavans J. Temporal evolution of two-dimensional drained soap froths. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 42:5049-5051. [PMID: 9904626 DOI: 10.1103/physreva.42.5049] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Berge B, Simon AJ, Libchaber A. Dynamics of gas bubbles in monolayers. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:6893-6900. [PMID: 9903105 DOI: 10.1103/physreva.41.6893] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Roland C, Grant M. Monte Carlo renormalization-group study of domain growth in the Potts model on a triangular lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:4663-4668. [PMID: 9994294 DOI: 10.1103/physrevb.41.4663] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Babcock KL, Seshadri R, Westervelt RM. Coarsening of cellular domain patterns in magnetic garnet films. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:1952-1962. [PMID: 9903306 DOI: 10.1103/physreva.41.1952] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Glazier JA, Stavans J. Nonideal effects in the two-dimensional soap froth. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 40:7398-7401. [PMID: 9902164 DOI: 10.1103/physreva.40.7398] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Babcock KL, Westervelt RM. Elements of cellular domain patterns in magnetic garnet films. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 40:2022-2037. [PMID: 9902360 DOI: 10.1103/physreva.40.2022] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Stavans J, Glazier JA. Soap froth revisited: Dynamic scaling in the two-dimensional froth. PHYSICAL REVIEW LETTERS 1989; 62:1318-1321. [PMID: 10039639 DOI: 10.1103/physrevlett.62.1318] [Citation(s) in RCA: 60] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Beenakker CW. Numerical simulation of a coarsening two-dimensional network. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 37:1697-1702. [PMID: 9899847 DOI: 10.1103/physreva.37.1697] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Glazier JA, Gross SP, Stavans J. Dynamics of two-dimensional soap froths. PHYSICAL REVIEW. A, GENERAL PHYSICS 1987; 36:306-312. [PMID: 9898684 DOI: 10.1103/physreva.36.306] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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