Recent developments on the Kardar–Parisi–Zhang surface-growth equation

Wio, Horacio S.; Escudero, Carlos; Revelli, Jorge A.; Deza, Roberto R.; Lama, M. S. de la

doi:10.1098/rsta.2010.0259

Cited by 24 publications

(21 citation statements)

References 49 publications

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“…(iii) A stochastic term that should principally involve the cell proliferation dynamics at the 2D cell layer. Improved versions of the KPZ 1D and 2D equations have recently been proposed [62,63], including the KPZ formality to 2D cell colony spreading on a tessellation-structured lattice [31]. The analysis of the internal structure of the system under propagation as well as distinct lattice scale events were also considered to infer the universality of the processes as an alternative to the roughness dynamic scaling analysis [64][65][66].…”

Section: Front Roughness Scaling and Individual Cell Trajectoriesmentioning

confidence: 99%

Influence of individual cell motility on the 2D front roughness dynamics of tumour cell colonies

et al. 2014

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The dynamics of in situ 2D HeLa cell quasi-linear and quasi-radial colony fronts in a standard culture medium is investigated. For quasi-radial colonies, as the cell population increased, a kinetic transition from an exponential to a constant front average velocity regime was observed. Special attention was paid to individual cell motility evolution under constant average colony front velocity looking for its impact on the dynamics of the 2D colony front roughness. From the directionalities and velocity components of cell trajectories in colonies with different cell populations, the influence of both local cell density and cell crowding effects on individual cell motility was determined. The average dynamic behaviour of individual cells in the colony and its dependence on both local spatio-temporal heterogeneities and growth geometry suggested that cell motion undergoes under a concerted cell migration mechanism, in which both a limiting random walk-like and a limiting ballistic-like contribution were involved. These results were interesting to infer how biased cell trajectories influenced both the 2D colony spreading dynamics and the front roughness characteristics by local biased contributions to individual cell motion. These data are consistent with previous experimental and theoretical cell colony spreading data and provide additional evidence of the validity of the Kardar-Parisi-Zhang equation, within a certain range of time and colony front size, for describing the dynamics of 2D colony front roughness.

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Section: Front Roughness Scaling and Individual Cell Trajectoriesmentioning

confidence: 99%

Influence of individual cell motility on the 2D front roughness dynamics of tumour cell colonies

et al. 2014

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“…It is remarkable that this does not seem to affect the large-distance physics. Such a robustness of Galilean invariance was pointed out in [124][125][126] (see [127] for an overview). From an RG point of view, this suggests that Galilean invariance is emergent like the time-reversal symmetry.…”

Section: Comparison Between the Np-frg Predictions And Previous Numermentioning

confidence: 85%

Kardar-Parisi-Zhang equation with short-range correlated noise: Emergent symmetries and nonuniversal observables

et al. 2017

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We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the Kardar-Parisi-Zhang (KPZ) dynamics with a noise featuring smooth spatial correlations of characteristic range ξ. We employ nonperturbative functional renormalization group methods to resolve the properties of the system at all scales. We show that the physics of the standard (uncorrelated) KPZ equation emerges on large scales independently of ξ. Moreover, the renormalization group flow is followed from the initial condition to the fixed point, that is, from the microscopic dynamics to the large-distance properties. This provides access to the small-scale features (and their dependence on the details of the noise correlations) as well as to the universal large-scale physics. In particular, we compute the kinetic energy spectrum of the stationary state as well as its nonuniversal amplitude. The latter is experimentally accessible by measurements at large scales and retains a signature of the microscopic noise correlations. Our results are compared to previous analytical and numerical results from independent approaches. They are in agreement with direct numerical simulations for the kinetic energy spectrum as well as with the prediction, obtained with the replica trick by Gaussian variational method, of a crossover in ξ of the nonuniversal amplitude of this spectrum.

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“…Economic and sociological spatiotemporal patterns belong to the class of phenomena far from thermodynamic equilibrium, among other ubiquitous natural processes like turbulence in fluids, interface and growth problems, chemical reactions, and biological systems [118]. Economic and sociological spatiotemporal patterns belong to the class of phenomena far from thermodynamic equilibrium, among other ubiquitous natural processes like turbulence in fluids, interface and growth problems, chemical reactions, and biological systems [118].…”

Section: Social Topological Patternsmentioning

confidence: 99%

Boundaries of a Complex World

Ludu

2016

Springer Series in Synergetics

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Complexity is an interdisciplinary program publishing the best research and academic-level teaching on both fundamental and applied aspects of complex systemscutting across all traditional disciplines of the natural and life sciences, engineering, economics, medicine, neuroscience, social and computer science.Complex Systems are systems that comprise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous formation of distinctive temporal, spatial or functional structures. Models of such systems can be successfully mapped onto quite diverse "real-life" situations like the climate, the coherent emission of light from lasers, chemical reaction-diffusion systems, biological cellular networks, the dynamics of stock markets and of the internet, earthquake statistics and prediction, freeway traffic, the human brain, or the formation of opinions in social systems, to name just some of the popular applications.Although their scope and methodologies overlap somewhat, one can distinguish the following main concepts and tools: self-organization, nonlinear dynamics, synergetics, turbulence, dynamical systems, catastrophes, instabilities, stochastic processes, chaos, graphs and networks, cellular automata, adaptive systems, genetic algorithms and computational intelligence.The three major book publication platforms of the Springer Complexity program are the monograph series "Understanding Complex Systems" focusing on the various applications of complexity, the "Springer Series in Synergetics", which is devoted to the quantitative theoretical and methodological foundations, and the "SpringerBriefs in Complexity" which are concise and topical working reports, case-studies, surveys, essays and lecture notes of relevance to the field. In addition to the books in these two core series, the program also incorporates individual titles ranging from textbooks to major reference works.The Springer Series in Synergetics was founded by Herman Haken in 1977. Since then, the series has evolved into a substantial reference library for the quantitative, theoretical and methodological foundations of the science of complex systems.Through many enduring classic texts, such as Haken's Synergetics and Information and Self-Organization, Gardiner's Handbook of Stochastic Methods, Risken's The Fokker Planck-Equation or Haake's Quantum Signatures of Chaos, the series has made, and continues to make, important contributions to shaping the foundations of the field.The series publishes monographs and graduate-level textbooks of broad and general interest, with a pronounced emphasis on the physico-mathematical approach.More information about this series at

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Recent developments on the Kardar–Parisi–Zhang surface-growth equation

Cited by 24 publications

References 49 publications

Influence of individual cell motility on the 2D front roughness dynamics of tumour cell colonies

Influence of individual cell motility on the 2D front roughness dynamics of tumour cell colonies

Kardar-Parisi-Zhang equation with short-range correlated noise: Emergent symmetries and nonuniversal observables

Boundaries of a Complex World

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