Self-Affinity for the Growing Interface of Bacterial Colonies

Wakita, Jun–ichi; Itoh, Hiroto; Matsuyama, Tohey; Matsushita, Mitsugu

doi:10.1143/jpsj.66.67

Cited by 97 publications

(118 citation statements)

References 33 publications

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“…Their observations caught the imagination of many and the paper deserves the full credit of having triggered a large number of investigations. Examples of physical phenomena modeled by the KPZ class include turbulent liquid crystals [159], crystal growth on a thin film [171], facet boundaries [52], bacteria colony growth [172,122], paper wetting [109], crack formation [67], and burning fronts [118,116,119].…”

Section: Kardar Parisi Andmentioning

confidence: 99%

The Kardar–parisi–zhang Equation and Universality Class

Corwin

2012

Random Matrices: Theory Appl.

719

824

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Abstract. Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its universality class. Over the past twenty five years a new universality class has emerged to describe a host of important physical and probabilistic models (including one dimensional interface growth processes, interacting particle systems and polymers in random environments) which display characteristic, though unusual, scalings and new statistics. This class is called the Kardar-Parisi-Zhang (KPZ) universality class and underlying it is, again, a continuum object -a non-linear stochastic partial differential equation -known as the KPZ equation.The purpose of this survey is to explain the context for, as well as the content of a number of mathematical breakthroughs which have culminated in the derivation of the exact formula for the distribution function of the KPZ equation started with narrow wedge initial data. In particular we emphasize three topics: (1) The approximation of the KPZ equation through the weakly asymmetric simple exclusion process; (2) The derivation of the exact one-point distribution of the solution to the KPZ equation with narrow wedge initial data; (3) Connections with directed polymers in random media.As the purpose of this article is to survey and review, we make precise statements but provide only heuristic arguments with indications of the technical complexities necessary to make such arguments mathematically rigorous.

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Section: Kardar Parisi Andmentioning

confidence: 99%

The Kardar–parisi–zhang Equation and Universality Class

Corwin

2012

Random Matrices: Theory Appl.

719

824

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“…Examples of surface and interfacial growth phenomena are diverse, ranging from the production of uniform coatings by vapor deposition of atoms onto a substrate [1], to burning paper wherein the combustion front roughens as it spreads [2,3], to bacterial colonies whose boundaries expand and fluctuate as bacteria replicate [4]. The morphology of the resulting interfaces is a property that affects the macroscopic responses of such systems, and it is therefore desirable to relate interface morphology to the microscopic rules that govern growth [1,5,6].…”

mentioning

confidence: 99%

“…The KPZ class presents a rare opportunity for connecting exact theoretical predictions about nonequilibrium growth phenomena with experiment. However, to date only a few members of the KPZ class have been experimentally identified [2][3][4]17]. This paucity of KPZ examples is due, in part, to the presence of quenched disorder and long-range interactions in experiment, as well as to limited statistics, which make growth process differences difficult to discern.…”

mentioning

confidence: 99%

Effects of Particle Shape on Growth Dynamics at Edges of Evaporating Drops of Colloidal Suspensions

et al. 2013

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We study the influence of particle shape on growth processes at the edges of evaporating drops. Aqueous suspensions of colloidal particles evaporate on glass slides, and convective flows during evaporation carry particles from drop center to drop edge, where they accumulate. The resulting particle deposits grow inhomogeneously from the edge in two-dimensions, and the deposition front, or growth line, varies spatio-temporally. Measurements of the fluctuations of the deposition front during evaporation enable us to identify distinct growth processes that depend strongly on particle shape. Sphere deposition exhibits a classic Poisson like growth process; deposition of slightly anisotropic particles, however, belongs to the Kardar-Parisi-Zhang (KPZ) universality class, and deposition of highly anisotropic ellipsoids appears to belong to a third universality class, characterized by KPZ fluctuations in the presence of quenched disorder.

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“…Such a multiple-fission process without cell separation is commonly observed in the early stage of the growth process even if the agar concentration is changed, while the structure and motion of an entangled filament of cells in the later stage depend on environmental conditions [18,21,3,17,27]. Takeuchi et al reported a study on filamentous cells of E.coli [28].…”

Section: Discussionmentioning

confidence: 99%

“…As illustrated by [3] in Fig. 4, a part of the elongating twofold segments becomes a fourfold segment.…”

Section: Systems Of Differential Equations and Their Solutionsmentioning

confidence: 98%

Self-Elongation with Sequential Folding of a Filament of Bacterial Cells

2015

Self Cite

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Under hard-agar and nutrient-rich conditions, a cell of Bacillus subtilis grows as a single filament owing to the failure of cell separation after each growth and division cycle. The self-elongating filament of cells shows sequential folding processes, and multifold structures extend over an agar plate. We report that the growth process from the exponential phase to the stationary phase is well described by the time evolution of fractal dimensions of the filament configuration. We propose a method of characterizing filament configurations using a set of lengths of multifold parts of a filament. Systems of differential equations are introduced to describe the folding processes that create multifold structures in the early stage of the growth process. We show that the fitting of experimental data to the solutions of equations is excellent, and the parameters involved in our model systems are determined.

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Self-Affinity for the Growing Interface of Bacterial Colonies

Cited by 97 publications

References 33 publications

The Kardar–parisi–zhang Equation and Universality Class

The Kardar–parisi–zhang Equation and Universality Class

Effects of Particle Shape on Growth Dynamics at Edges of Evaporating Drops of Colloidal Suspensions

Self-Elongation with Sequential Folding of a Filament of Bacterial Cells

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